diff options
170 files changed, 21129 insertions, 2450 deletions
diff --git a/CMakeLists.txt b/CMakeLists.txt index abae3b23c..b4d28125a 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -1,4 +1,4 @@ -project(Eigen) +project(Eigen3) cmake_minimum_required(VERSION 2.8.5) diff --git a/Eigen/Cholesky b/Eigen/Cholesky index 705a04cc4..369d1f5ec 100644 --- a/Eigen/Cholesky +++ b/Eigen/Cholesky @@ -31,7 +31,8 @@ #include "src/Cholesky/LLT.h" #include "src/Cholesky/LDLT.h" #ifdef EIGEN_USE_LAPACKE -#include "src/Cholesky/LLT_MKL.h" +#include "src/misc/lapacke.h" +#include "src/Cholesky/LLT_LAPACKE.h" #endif #include "src/Core/util/ReenableStupidWarnings.h" diff --git a/Eigen/Core b/Eigen/Core index 1f3a6504e..946ed0677 100644 --- a/Eigen/Core +++ b/Eigen/Core @@ -328,7 +328,6 @@ using std::ptrdiff_t; #include "src/Core/NumTraits.h" #include "src/Core/MathFunctions.h" -#include "src/Core/SpecialFunctions.h" #include "src/Core/GenericPacketMath.h" #if defined EIGEN_VECTORIZE_AVX diff --git a/Eigen/Eigenvalues b/Eigen/Eigenvalues index 216a6d51d..009e529e1 100644 --- a/Eigen/Eigenvalues +++ b/Eigen/Eigenvalues @@ -45,9 +45,10 @@ #include "src/Eigenvalues/GeneralizedEigenSolver.h" #include "src/Eigenvalues/MatrixBaseEigenvalues.h" #ifdef EIGEN_USE_LAPACKE -#include "src/Eigenvalues/RealSchur_MKL.h" -#include "src/Eigenvalues/ComplexSchur_MKL.h" -#include "src/Eigenvalues/SelfAdjointEigenSolver_MKL.h" +#include "src/misc/lapacke.h" +#include "src/Eigenvalues/RealSchur_LAPACKE.h" +#include "src/Eigenvalues/ComplexSchur_LAPACKE.h" +#include "src/Eigenvalues/SelfAdjointEigenSolver_LAPACKE.h" #endif #include "src/Core/util/ReenableStupidWarnings.h" @@ -28,7 +28,8 @@ #include "src/LU/FullPivLU.h" #include "src/LU/PartialPivLU.h" #ifdef EIGEN_USE_LAPACKE -#include "src/LU/PartialPivLU_MKL.h" +#include "src/misc/lapacke.h" +#include "src/LU/PartialPivLU_LAPACKE.h" #endif #include "src/LU/Determinant.h" #include "src/LU/InverseImpl.h" @@ -36,8 +36,9 @@ #include "src/QR/ColPivHouseholderQR.h" #include "src/QR/CompleteOrthogonalDecomposition.h" #ifdef EIGEN_USE_LAPACKE -#include "src/QR/HouseholderQR_MKL.h" -#include "src/QR/ColPivHouseholderQR_MKL.h" +#include "src/misc/lapacke.h" +#include "src/QR/HouseholderQR_LAPACKE.h" +#include "src/QR/ColPivHouseholderQR_LAPACKE.h" #endif #include "src/Core/util/ReenableStupidWarnings.h" @@ -37,7 +37,8 @@ #include "src/SVD/JacobiSVD.h" #include "src/SVD/BDCSVD.h" #if defined(EIGEN_USE_LAPACKE) && !defined(EIGEN_USE_LAPACKE_STRICT) -#include "src/SVD/JacobiSVD_MKL.h" +#include "src/misc/lapacke.h" +#include "src/SVD/JacobiSVD_LAPACKE.h" #endif #include "src/Core/util/ReenableStupidWarnings.h" diff --git a/Eigen/SuperLUSupport b/Eigen/SuperLUSupport index 113f58ee5..59312a82d 100644 --- a/Eigen/SuperLUSupport +++ b/Eigen/SuperLUSupport @@ -43,7 +43,7 @@ namespace Eigen { struct SluMatrix; } * - class SuperLU: a supernodal sequential LU factorization. * - class SuperILU: a supernodal sequential incomplete LU factorization (to be used as a preconditioner for iterative methods). * - * \warning This wrapper is only for the 4.x versions of SuperLU. The 3.x and 5.x versions are not supported. + * \warning This wrapper requires at least versions 4.0 of SuperLU. The 3.x versions are not supported. * * \warning When including this module, you have to use SUPERLU_EMPTY instead of EMPTY which is no longer defined because it is too polluting. * diff --git a/Eigen/src/Cholesky/LDLT.h b/Eigen/src/Cholesky/LDLT.h index 538aff956..69e176110 100644 --- a/Eigen/src/Cholesky/LDLT.h +++ b/Eigen/src/Cholesky/LDLT.h @@ -43,6 +43,8 @@ namespace internal { * Remember that Cholesky decompositions are not rank-revealing. Also, do not use a Cholesky * decomposition to determine whether a system of equations has a solution. * + * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism. + * * \sa MatrixBase::ldlt(), SelfAdjointView::ldlt(), class LLT */ template<typename _MatrixType, int _UpLo> class LDLT @@ -52,7 +54,6 @@ template<typename _MatrixType, int _UpLo> class LDLT enum { RowsAtCompileTime = MatrixType::RowsAtCompileTime, ColsAtCompileTime = MatrixType::ColsAtCompileTime, - Options = MatrixType::Options & ~RowMajorBit, // these are the options for the TmpMatrixType, we need a ColMajor matrix here! MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime, UpLo = _UpLo @@ -61,7 +62,7 @@ template<typename _MatrixType, int _UpLo> class LDLT typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar; typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3 typedef typename MatrixType::StorageIndex StorageIndex; - typedef Matrix<Scalar, RowsAtCompileTime, 1, Options, MaxRowsAtCompileTime, 1> TmpMatrixType; + typedef Matrix<Scalar, RowsAtCompileTime, 1, 0, MaxRowsAtCompileTime, 1> TmpMatrixType; typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> TranspositionType; typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationType; @@ -97,6 +98,7 @@ template<typename _MatrixType, int _UpLo> class LDLT /** \brief Constructor with decomposition * * This calculates the decomposition for the input \a matrix. + * * \sa LDLT(Index size) */ template<typename InputType> @@ -110,6 +112,23 @@ template<typename _MatrixType, int _UpLo> class LDLT compute(matrix.derived()); } + /** \brief Constructs a LDLT factorization from a given matrix + * + * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when \c MatrixType is a Eigen::Ref. + * + * \sa LDLT(const EigenBase&) + */ + template<typename InputType> + explicit LDLT(EigenBase<InputType>& matrix) + : m_matrix(matrix.derived()), + m_transpositions(matrix.rows()), + m_temporary(matrix.rows()), + m_sign(internal::ZeroSign), + m_isInitialized(false) + { + compute(matrix.derived()); + } + /** Clear any existing decomposition * \sa rankUpdate(w,sigma) */ diff --git a/Eigen/src/Cholesky/LLT.h b/Eigen/src/Cholesky/LLT.h index 19578b216..bd966656d 100644 --- a/Eigen/src/Cholesky/LLT.h +++ b/Eigen/src/Cholesky/LLT.h @@ -41,6 +41,8 @@ template<typename MatrixType, int UpLo> struct LLT_Traits; * Example: \include LLT_example.cpp * Output: \verbinclude LLT_example.out * + * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism. + * * \sa MatrixBase::llt(), SelfAdjointView::llt(), class LDLT */ /* HEY THIS DOX IS DISABLED BECAUSE THERE's A BUG EITHER HERE OR IN LDLT ABOUT THAT (OR BOTH) @@ -54,7 +56,6 @@ template<typename _MatrixType, int _UpLo> class LLT enum { RowsAtCompileTime = MatrixType::RowsAtCompileTime, ColsAtCompileTime = MatrixType::ColsAtCompileTime, - Options = MatrixType::Options, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime }; typedef typename MatrixType::Scalar Scalar; @@ -95,6 +96,21 @@ template<typename _MatrixType, int _UpLo> class LLT compute(matrix.derived()); } + /** \brief Constructs a LDLT factorization from a given matrix + * + * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when + * \c MatrixType is a Eigen::Ref. + * + * \sa LLT(const EigenBase&) + */ + template<typename InputType> + explicit LLT(EigenBase<InputType>& matrix) + : m_matrix(matrix.derived()), + m_isInitialized(false) + { + compute(matrix.derived()); + } + /** \returns a view of the upper triangular matrix U */ inline typename Traits::MatrixU matrixU() const { diff --git a/Eigen/src/Cholesky/LLT_MKL.h b/Eigen/src/Cholesky/LLT_LAPACKE.h index f5be3b240..bc6489e69 100644 --- a/Eigen/src/Cholesky/LLT_MKL.h +++ b/Eigen/src/Cholesky/LLT_LAPACKE.h @@ -25,25 +25,22 @@ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ******************************************************************************** - * Content : Eigen bindings to Intel(R) MKL + * Content : Eigen bindings to LAPACKe * LLt decomposition based on LAPACKE_?potrf function. ******************************************************************************** */ -#ifndef EIGEN_LLT_MKL_H -#define EIGEN_LLT_MKL_H - -#include "Eigen/src/Core/util/MKL_support.h" -#include <iostream> +#ifndef EIGEN_LLT_LAPACKE_H +#define EIGEN_LLT_LAPACKE_H namespace Eigen { namespace internal { -template<typename Scalar> struct mkl_llt; +template<typename Scalar> struct lapacke_llt; -#define EIGEN_MKL_LLT(EIGTYPE, MKLTYPE, MKLPREFIX) \ -template<> struct mkl_llt<EIGTYPE> \ +#define EIGEN_LAPACKE_LLT(EIGTYPE, BLASTYPE, LAPACKE_PREFIX) \ +template<> struct lapacke_llt<EIGTYPE> \ { \ template<typename MatrixType> \ static inline Index potrf(MatrixType& m, char uplo) \ @@ -59,7 +56,7 @@ template<> struct mkl_llt<EIGTYPE> \ a = &(m.coeffRef(0,0)); \ lda = convert_index<lapack_int>(m.outerStride()); \ \ - info = LAPACKE_##MKLPREFIX##potrf( matrix_order, uplo, size, (MKLTYPE*)a, lda ); \ + info = LAPACKE_##LAPACKE_PREFIX##potrf( matrix_order, uplo, size, (BLASTYPE*)a, lda ); \ info = (info==0) ? -1 : info>0 ? info-1 : size; \ return info; \ } \ @@ -69,7 +66,7 @@ template<> struct llt_inplace<EIGTYPE, Lower> \ template<typename MatrixType> \ static Index blocked(MatrixType& m) \ { \ - return mkl_llt<EIGTYPE>::potrf(m, 'L'); \ + return lapacke_llt<EIGTYPE>::potrf(m, 'L'); \ } \ template<typename MatrixType, typename VectorType> \ static Index rankUpdate(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma) \ @@ -80,7 +77,7 @@ template<> struct llt_inplace<EIGTYPE, Upper> \ template<typename MatrixType> \ static Index blocked(MatrixType& m) \ { \ - return mkl_llt<EIGTYPE>::potrf(m, 'U'); \ + return lapacke_llt<EIGTYPE>::potrf(m, 'U'); \ } \ template<typename MatrixType, typename VectorType> \ static Index rankUpdate(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma) \ @@ -90,13 +87,13 @@ template<> struct llt_inplace<EIGTYPE, Upper> \ } \ }; -EIGEN_MKL_LLT(double, double, d) -EIGEN_MKL_LLT(float, float, s) -EIGEN_MKL_LLT(dcomplex, MKL_Complex16, z) -EIGEN_MKL_LLT(scomplex, MKL_Complex8, c) +EIGEN_LAPACKE_LLT(double, double, d) +EIGEN_LAPACKE_LLT(float, float, s) +EIGEN_LAPACKE_LLT(dcomplex, lapack_complex_double, z) +EIGEN_LAPACKE_LLT(scomplex, lapack_complex_float, c) } // end namespace internal } // end namespace Eigen -#endif // EIGEN_LLT_MKL_H +#endif // EIGEN_LLT_LAPACKE_H diff --git a/Eigen/src/Core/AssignEvaluator.h b/Eigen/src/Core/AssignEvaluator.h index 1df717bac..b7cc7c0e9 100644 --- a/Eigen/src/Core/AssignEvaluator.h +++ b/Eigen/src/Core/AssignEvaluator.h @@ -88,10 +88,11 @@ private: /* If the destination isn't aligned, we have to do runtime checks and we don't unroll, so it's only good for large enough sizes. */ MaySliceVectorize = bool(MightVectorize) && bool(DstHasDirectAccess) - && (int(InnerMaxSize)==Dynamic || int(InnerMaxSize)>=3*InnerPacketSize) + && (int(InnerMaxSize)==Dynamic || int(InnerMaxSize)>=(EIGEN_UNALIGNED_VECTORIZE?InnerPacketSize:(3*InnerPacketSize))) /* slice vectorization can be slow, so we only want it if the slices are big, which is indicated by InnerMaxSize rather than InnerSize, think of the case of a dynamic block - in a fixed-size matrix */ + in a fixed-size matrix + However, with EIGEN_UNALIGNED_VECTORIZE and unrolling, slice vectorization is still worth it */ }; public: @@ -136,6 +137,11 @@ public: : int(Traversal) == int(LinearTraversal) ? ( bool(MayUnrollCompletely) ? int(CompleteUnrolling) : int(NoUnrolling) ) +#if EIGEN_UNALIGNED_VECTORIZE + : int(Traversal) == int(SliceVectorizedTraversal) + ? ( bool(MayUnrollInner) ? int(InnerUnrolling) + : int(NoUnrolling) ) +#endif : int(NoUnrolling) }; @@ -165,6 +171,7 @@ public: EIGEN_DEBUG_VAR(MayLinearVectorize) EIGEN_DEBUG_VAR(MaySliceVectorize) std::cerr << "Traversal" << " = " << Traversal << " (" << demangle_traversal(Traversal) << ")" << std::endl; + EIGEN_DEBUG_VAR(SrcEvaluator::CoeffReadCost) EIGEN_DEBUG_VAR(UnrollingLimit) EIGEN_DEBUG_VAR(MayUnrollCompletely) EIGEN_DEBUG_VAR(MayUnrollInner) @@ -276,24 +283,20 @@ struct copy_using_evaluator_innervec_CompleteUnrolling<Kernel, Stop, Stop> EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel&) { } }; -template<typename Kernel, int Index_, int Stop> +template<typename Kernel, int Index_, int Stop, int SrcAlignment, int DstAlignment> struct copy_using_evaluator_innervec_InnerUnrolling { typedef typename Kernel::PacketType PacketType; - enum { - SrcAlignment = Kernel::AssignmentTraits::SrcAlignment, - DstAlignment = Kernel::AssignmentTraits::DstAlignment - }; EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel, Index outer) { kernel.template assignPacketByOuterInner<DstAlignment, SrcAlignment, PacketType>(outer, Index_); enum { NextIndex = Index_ + unpacket_traits<PacketType>::size }; - copy_using_evaluator_innervec_InnerUnrolling<Kernel, NextIndex, Stop>::run(kernel, outer); + copy_using_evaluator_innervec_InnerUnrolling<Kernel, NextIndex, Stop, SrcAlignment, DstAlignment>::run(kernel, outer); } }; -template<typename Kernel, int Stop> -struct copy_using_evaluator_innervec_InnerUnrolling<Kernel, Stop, Stop> +template<typename Kernel, int Stop, int SrcAlignment, int DstAlignment> +struct copy_using_evaluator_innervec_InnerUnrolling<Kernel, Stop, Stop, SrcAlignment, DstAlignment> { EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &, Index) { } }; @@ -422,9 +425,10 @@ struct dense_assignment_loop<Kernel, LinearVectorizedTraversal, CompleteUnrollin EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel) { typedef typename Kernel::DstEvaluatorType::XprType DstXprType; + typedef typename Kernel::PacketType PacketType; enum { size = DstXprType::SizeAtCompileTime, - packetSize = packet_traits<typename Kernel::Scalar>::size, + packetSize =unpacket_traits<PacketType>::size, alignedSize = (size/packetSize)*packetSize }; copy_using_evaluator_innervec_CompleteUnrolling<Kernel, 0, alignedSize>::run(kernel); @@ -471,9 +475,11 @@ struct dense_assignment_loop<Kernel, InnerVectorizedTraversal, InnerUnrolling> EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel) { typedef typename Kernel::DstEvaluatorType::XprType DstXprType; + typedef typename Kernel::AssignmentTraits Traits; const Index outerSize = kernel.outerSize(); for(Index outer = 0; outer < outerSize; ++outer) - copy_using_evaluator_innervec_InnerUnrolling<Kernel, 0, DstXprType::InnerSizeAtCompileTime>::run(kernel, outer); + copy_using_evaluator_innervec_InnerUnrolling<Kernel, 0, DstXprType::InnerSizeAtCompileTime, + Traits::SrcAlignment, Traits::DstAlignment>::run(kernel, outer); } }; @@ -553,6 +559,29 @@ struct dense_assignment_loop<Kernel, SliceVectorizedTraversal, NoUnrolling> } }; +#if EIGEN_UNALIGNED_VECTORIZE +template<typename Kernel> +struct dense_assignment_loop<Kernel, SliceVectorizedTraversal, InnerUnrolling> +{ + EIGEN_DEVICE_FUNC static inline void run(Kernel &kernel) + { + typedef typename Kernel::DstEvaluatorType::XprType DstXprType; + typedef typename Kernel::PacketType PacketType; + + enum { size = DstXprType::InnerSizeAtCompileTime, + packetSize =unpacket_traits<PacketType>::size, + vectorizableSize = (size/packetSize)*packetSize }; + + for(Index outer = 0; outer < kernel.outerSize(); ++outer) + { + copy_using_evaluator_innervec_InnerUnrolling<Kernel, 0, vectorizableSize, 0, 0>::run(kernel, outer); + copy_using_evaluator_DefaultTraversal_InnerUnrolling<Kernel, vectorizableSize, size>::run(kernel, outer); + } + } +}; +#endif + + /*************************************************************************** * Part 4 : Generic dense assignment kernel ***************************************************************************/ @@ -680,7 +709,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void call_dense_assignment_loop(const DstX typedef generic_dense_assignment_kernel<DstEvaluatorType,SrcEvaluatorType,Functor> Kernel; Kernel kernel(dstEvaluator, srcEvaluator, func, dst.const_cast_derived()); - + dense_assignment_loop<Kernel>::run(kernel); } @@ -709,7 +738,7 @@ template<> struct AssignmentKind<DenseShape,DenseShape> { typedef Dense2Dense Ki // This is the main assignment class template< typename DstXprType, typename SrcXprType, typename Functor, typename Kind = typename AssignmentKind< typename evaluator_traits<DstXprType>::Shape , typename evaluator_traits<SrcXprType>::Shape >::Kind, - typename Scalar = typename DstXprType::Scalar> + typename EnableIf = void> struct Assignment; @@ -816,8 +845,10 @@ void call_assignment_no_alias_no_transpose(Dst& dst, const Src& src) template<typename Dst, typename Src> void check_for_aliasing(const Dst &dst, const Src &src); // Generic Dense to Dense assignment -template< typename DstXprType, typename SrcXprType, typename Functor, typename Scalar> -struct Assignment<DstXprType, SrcXprType, Functor, Dense2Dense, Scalar> +// Note that the last template argument "Weak" is needed to make it possible to perform +// both partial specialization+SFINAE without ambiguous specialization +template< typename DstXprType, typename SrcXprType, typename Functor, typename Weak> +struct Assignment<DstXprType, SrcXprType, Functor, Dense2Dense, Weak> { EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src, const Functor &func) @@ -834,8 +865,10 @@ struct Assignment<DstXprType, SrcXprType, Functor, Dense2Dense, Scalar> // Generic assignment through evalTo. // TODO: not sure we have to keep that one, but it helps porting current code to new evaluator mechanism. -template< typename DstXprType, typename SrcXprType, typename Functor, typename Scalar> -struct Assignment<DstXprType, SrcXprType, Functor, EigenBase2EigenBase, Scalar> +// Note that the last template argument "Weak" is needed to make it possible to perform +// both partial specialization+SFINAE without ambiguous specialization +template< typename DstXprType, typename SrcXprType, typename Functor, typename Weak> +struct Assignment<DstXprType, SrcXprType, Functor, EigenBase2EigenBase, Weak> { EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/) diff --git a/Eigen/src/Core/Assign_MKL.h b/Eigen/src/Core/Assign_MKL.h index 897187a30..6c2ab9264 100644..100755 --- a/Eigen/src/Core/Assign_MKL.h +++ b/Eigen/src/Core/Assign_MKL.h @@ -81,10 +81,10 @@ class vml_assign_traits #define EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, VMLOP, EIGENTYPE, VMLTYPE, VMLMODE) \ template< typename DstXprType, typename SrcXprNested> \ - struct Assignment<DstXprType, CwiseUnaryOp<scalar_##EIGENOP##_op<EIGENTYPE>, SrcXprNested>, assign_op<EIGENTYPE>, \ - Dense2Dense, typename enable_if<vml_assign_traits<DstXprType,SrcXprNested>::EnableVml,EIGENTYPE>::type> { \ + struct Assignment<DstXprType, CwiseUnaryOp<scalar_##EIGENOP##_op<EIGENTYPE>, SrcXprNested>, assign_op<EIGENTYPE,EIGENTYPE>, \ + Dense2Dense, typename enable_if<vml_assign_traits<DstXprType,SrcXprNested>::EnableVml>::type> { \ typedef CwiseUnaryOp<scalar_##EIGENOP##_op<EIGENTYPE>, SrcXprNested> SrcXprType; \ - static void run(DstXprType &dst, const SrcXprType &src, const assign_op<EIGENTYPE> &/*func*/) { \ + static void run(DstXprType &dst, const SrcXprType &src, const assign_op<EIGENTYPE,EIGENTYPE> &/*func*/) { \ eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols()); \ if(vml_assign_traits<DstXprType,SrcXprNested>::Traversal==LinearTraversal) { \ VMLOP(dst.size(), (const VMLTYPE*)src.nestedExpression().data(), \ @@ -138,22 +138,24 @@ EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(floor, Floor, _) EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(ceil, Ceil, _) #define EIGEN_MKL_VML_DECLARE_POW_CALL(EIGENOP, VMLOP, EIGENTYPE, VMLTYPE, VMLMODE) \ - template< typename DstXprType, typename SrcXprNested> \ - struct Assignment<DstXprType, CwiseUnaryOp<scalar_##EIGENOP##_op<EIGENTYPE>, SrcXprNested>, assign_op<EIGENTYPE>, \ - Dense2Dense, typename enable_if<vml_assign_traits<DstXprType,SrcXprNested>::EnableVml,EIGENTYPE>::type> { \ - typedef CwiseUnaryOp<scalar_##EIGENOP##_op<EIGENTYPE>, SrcXprNested> SrcXprType; \ - static void run(DstXprType &dst, const SrcXprType &src, const assign_op<EIGENTYPE> &/*func*/) { \ + template< typename DstXprType, typename SrcXprNested, typename Plain> \ + struct Assignment<DstXprType, CwiseBinaryOp<scalar_##EIGENOP##_op<EIGENTYPE,EIGENTYPE>, SrcXprNested, \ + const CwiseNullaryOp<internal::scalar_constant_op<EIGENTYPE>,Plain> >, assign_op<EIGENTYPE,EIGENTYPE>, \ + Dense2Dense, typename enable_if<vml_assign_traits<DstXprType,SrcXprNested>::EnableVml>::type> { \ + typedef CwiseBinaryOp<scalar_##EIGENOP##_op<EIGENTYPE,EIGENTYPE>, SrcXprNested, \ + const CwiseNullaryOp<internal::scalar_constant_op<EIGENTYPE>,Plain> > SrcXprType; \ + static void run(DstXprType &dst, const SrcXprType &src, const assign_op<EIGENTYPE,EIGENTYPE> &/*func*/) { \ eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols()); \ - VMLTYPE exponent = reinterpret_cast<const VMLTYPE&>(src.functor().m_exponent); \ + VMLTYPE exponent = reinterpret_cast<const VMLTYPE&>(src.rhs().functor().m_other); \ if(vml_assign_traits<DstXprType,SrcXprNested>::Traversal==LinearTraversal) \ { \ - VMLOP( dst.size(), (const VMLTYPE*)src.nestedExpression().data(), exponent, \ + VMLOP( dst.size(), (const VMLTYPE*)src.lhs().data(), exponent, \ (VMLTYPE*)dst.data() EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_##VMLMODE) ); \ } else { \ const Index outerSize = dst.outerSize(); \ for(Index outer = 0; outer < outerSize; ++outer) { \ - const EIGENTYPE *src_ptr = src.IsRowMajor ? &(src.nestedExpression().coeffRef(outer,0)) : \ - &(src.nestedExpression().coeffRef(0, outer)); \ + const EIGENTYPE *src_ptr = src.IsRowMajor ? &(src.lhs().coeffRef(outer,0)) : \ + &(src.lhs().coeffRef(0, outer)); \ EIGENTYPE *dst_ptr = dst.IsRowMajor ? &(dst.coeffRef(outer,0)) : &(dst.coeffRef(0, outer)); \ VMLOP( dst.innerSize(), (const VMLTYPE*)src_ptr, exponent, \ (VMLTYPE*)dst_ptr EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_##VMLMODE)); \ diff --git a/Eigen/src/Core/ConditionEstimator.h b/Eigen/src/Core/ConditionEstimator.h index 2147f2cb1..aa7efdc76 100644 --- a/Eigen/src/Core/ConditionEstimator.h +++ b/Eigen/src/Core/ConditionEstimator.h @@ -132,7 +132,8 @@ typename Decomposition::RealScalar rcond_invmatrix_L1_norm_estimate(const Decomp // Hager's algorithm to vastly underestimate ||matrix||_1. Scalar alternating_sign(RealScalar(1)); for (Index i = 0; i < n; ++i) { - v[i] = alternating_sign * (RealScalar(1) + (RealScalar(i) / (RealScalar(n - 1)))); + // The static_cast is needed when Scalar is a complex and RealScalar implements expression templates + v[i] = alternating_sign * static_cast<RealScalar>(RealScalar(1) + (RealScalar(i) / (RealScalar(n - 1)))); alternating_sign = -alternating_sign; } v = dec.solve(v); diff --git a/Eigen/src/Core/DiagonalMatrix.h b/Eigen/src/Core/DiagonalMatrix.h index d6f89bced..92b2eee71 100644 --- a/Eigen/src/Core/DiagonalMatrix.h +++ b/Eigen/src/Core/DiagonalMatrix.h @@ -316,8 +316,8 @@ struct Diagonal2Dense {}; template<> struct AssignmentKind<DenseShape,DiagonalShape> { typedef Diagonal2Dense Kind; }; // Diagonal matrix to Dense assignment -template< typename DstXprType, typename SrcXprType, typename Functor, typename Scalar> -struct Assignment<DstXprType, SrcXprType, Functor, Diagonal2Dense, Scalar> +template< typename DstXprType, typename SrcXprType, typename Functor> +struct Assignment<DstXprType, SrcXprType, Functor, Diagonal2Dense> { static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/) { diff --git a/Eigen/src/Core/GenericPacketMath.h b/Eigen/src/Core/GenericPacketMath.h index 76a75dee1..2d17f9ad1 100644 --- a/Eigen/src/Core/GenericPacketMath.h +++ b/Eigen/src/Core/GenericPacketMath.h @@ -306,7 +306,7 @@ template<typename Scalar> EIGEN_DEVICE_FUNC inline void prefetch(const Scalar* a // 32-bit pointer operand constraint for inlined asm asm(" prefetch.L1 [ %1 ];" : "=r"(addr) : "r"(addr)); #endif -#elif !EIGEN_COMP_MSVC +#elif (!EIGEN_COMP_MSVC) && (EIGEN_COMP_GNUC || EIGEN_COMP_CLANG || EIGEN_COMP_ICC) __builtin_prefetch(addr); #endif } @@ -435,42 +435,6 @@ Packet pfloor(const Packet& a) { using numext::floor; return floor(a); } template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet pceil(const Packet& a) { using numext::ceil; return ceil(a); } -/** \internal \returns the ln(|gamma(\a a)|) (coeff-wise) */ -template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS -Packet plgamma(const Packet& a) { using numext::lgamma; return lgamma(a); } - -/** \internal \returns the derivative of lgamma, psi(\a a) (coeff-wise) */ -template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS -Packet pdigamma(const Packet& a) { using numext::digamma; return digamma(a); } - -/** \internal \returns the zeta function of two arguments (coeff-wise) */ -template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS -Packet pzeta(const Packet& x, const Packet& q) { using numext::zeta; return zeta(x, q); } - -/** \internal \returns the polygamma function (coeff-wise) */ -template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS -Packet ppolygamma(const Packet& n, const Packet& x) { using numext::polygamma; return polygamma(n, x); } - -/** \internal \returns the erf(\a a) (coeff-wise) */ -template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS -Packet perf(const Packet& a) { using numext::erf; return erf(a); } - -/** \internal \returns the erfc(\a a) (coeff-wise) */ -template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS -Packet perfc(const Packet& a) { using numext::erfc; return erfc(a); } - -/** \internal \returns the incomplete gamma function igamma(\a a, \a x) */ -template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE -Packet pigamma(const Packet& a, const Packet& x) { using numext::igamma; return igamma(a, x); } - -/** \internal \returns the complementary incomplete gamma function igammac(\a a, \a x) */ -template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE -Packet pigammac(const Packet& a, const Packet& x) { using numext::igammac; return igammac(a, x); } - -/** \internal \returns the complementary incomplete gamma function betainc(\a a, \a b, \a x) */ -template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE -Packet pbetainc(const Packet& a, const Packet& b,const Packet& x) { using numext::betainc; return betainc(a, b, x); } - /*************************************************************************** * The following functions might not have to be overwritten for vectorized types ***************************************************************************/ diff --git a/Eigen/src/Core/GlobalFunctions.h b/Eigen/src/Core/GlobalFunctions.h index b9c3ec25b..769dc255c 100644 --- a/Eigen/src/Core/GlobalFunctions.h +++ b/Eigen/src/Core/GlobalFunctions.h @@ -78,6 +78,7 @@ namespace Eigen EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs2,scalar_abs2_op,squared absolute value,\sa ArrayBase::abs2 DOXCOMMA MatrixBase::cwiseAbs2) EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(arg,scalar_arg_op,complex argument,\sa ArrayBase::arg) EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sqrt,scalar_sqrt_op,square root,\sa ArrayBase::sqrt DOXCOMMA MatrixBase::cwiseSqrt) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(rsqrt,scalar_rsqrt_op,reciprocal square root,\sa ArrayBase::rsqrt) EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(square,scalar_square_op,square (power 2),\sa Eigen::abs2 DOXCOMMA Eigen::pow DOXCOMMA ArrayBase::square) EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cube,scalar_cube_op,cube (power 3),\sa Eigen::pow DOXCOMMA ArrayBase::cube) EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(round,scalar_round_op,nearest integer,\sa Eigen::floor DOXCOMMA Eigen::ceil DOXCOMMA ArrayBase::round) @@ -102,8 +103,7 @@ namespace Eigen pow(const Eigen::ArrayBase<Derived>& x, const ScalarExponent& exponent); #else template<typename Derived,typename ScalarExponent> - inline typename internal::enable_if< !(internal::is_same<typename Derived::Scalar,ScalarExponent>::value) - && ScalarBinaryOpTraits<typename Derived::Scalar,ScalarExponent,internal::scalar_pow_op<typename Derived::Scalar,ScalarExponent> >::Defined, + inline typename internal::enable_if< !(internal::is_same<typename Derived::Scalar,ScalarExponent>::value) && EIGEN_SCALAR_BINARY_SUPPORTED(pow,typename Derived::Scalar,ScalarExponent), const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,ScalarExponent,pow) >::type pow(const Eigen::ArrayBase<Derived>& x, const ScalarExponent& exponent) { return x.derived().pow(exponent); @@ -156,8 +156,7 @@ namespace Eigen pow(const Scalar& x,const Eigen::ArrayBase<Derived>& x); #else template<typename Scalar, typename Derived> - inline typename internal::enable_if< !(internal::is_same<typename Derived::Scalar,Scalar>::value) - && ScalarBinaryOpTraits<Scalar,typename Derived::Scalar,internal::scalar_pow_op<Scalar,typename Derived::Scalar> >::Defined, + inline typename internal::enable_if< !(internal::is_same<typename Derived::Scalar,Scalar>::value) && EIGEN_SCALAR_BINARY_SUPPORTED(pow,Scalar,typename Derived::Scalar), const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,Derived,pow) >::type pow(const Scalar& x, const Eigen::ArrayBase<Derived>& exponents) { @@ -174,111 +173,6 @@ namespace Eigen } #endif - /** \cpp11 \returns an expression of the coefficient-wise igamma(\a a, \a x) to the given arrays. - * - * This function computes the coefficient-wise incomplete gamma function. - * - * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types, - * or float/double in non c++11 mode, the user has to provide implementations of igammac(T,T) for any scalar - * type T to be supported. - * - * \sa Eigen::igammac(), Eigen::lgamma() - */ - template<typename Derived,typename ExponentDerived> - inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived, const ExponentDerived> - igamma(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x) - { - return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived, const ExponentDerived>( - a.derived(), - x.derived() - ); - } - - /** \cpp11 \returns an expression of the coefficient-wise igammac(\a a, \a x) to the given arrays. - * - * This function computes the coefficient-wise complementary incomplete gamma function. - * - * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types, - * or float/double in non c++11 mode, the user has to provide implementations of igammac(T,T) for any scalar - * type T to be supported. - * - * \sa Eigen::igamma(), Eigen::lgamma() - */ - template<typename Derived,typename ExponentDerived> - inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived, const ExponentDerived> - igammac(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x) - { - return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived, const ExponentDerived>( - a.derived(), - x.derived() - ); - } - - /** \cpp11 \returns an expression of the coefficient-wise polygamma(\a n, \a x) to the given arrays. - * - * It returns the \a n -th derivative of the digamma(psi) evaluated at \c x. - * - * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types, - * or float/double in non c++11 mode, the user has to provide implementations of polygamma(T,T) for any scalar - * type T to be supported. - * - * \sa Eigen::digamma() - */ - // * \warning Be careful with the order of the parameters: x.polygamma(n) is equivalent to polygamma(n,x) - // * \sa ArrayBase::polygamma() - template<typename DerivedN,typename DerivedX> - inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_polygamma_op<typename DerivedX::Scalar>, const DerivedN, const DerivedX> - polygamma(const Eigen::ArrayBase<DerivedN>& n, const Eigen::ArrayBase<DerivedX>& x) - { - return Eigen::CwiseBinaryOp<Eigen::internal::scalar_polygamma_op<typename DerivedX::Scalar>, const DerivedN, const DerivedX>( - n.derived(), - x.derived() - ); - } - - /** \cpp11 \returns an expression of the coefficient-wise betainc(\a x, \a a, \a b) to the given arrays. - * - * This function computes the regularized incomplete beta function (integral). - * - * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types, - * or float/double in non c++11 mode, the user has to provide implementations of betainc(T,T,T) for any scalar - * type T to be supported. - * - * \sa Eigen::betainc(), Eigen::lgamma() - */ - template<typename ArgADerived, typename ArgBDerived, typename ArgXDerived> - inline const Eigen::CwiseTernaryOp<Eigen::internal::scalar_betainc_op<typename ArgXDerived::Scalar>, const ArgADerived, const ArgBDerived, const ArgXDerived> - betainc(const Eigen::ArrayBase<ArgADerived>& a, const Eigen::ArrayBase<ArgBDerived>& b, const Eigen::ArrayBase<ArgXDerived>& x) - { - return Eigen::CwiseTernaryOp<Eigen::internal::scalar_betainc_op<typename ArgXDerived::Scalar>, const ArgADerived, const ArgBDerived, const ArgXDerived>( - a.derived(), - b.derived(), - x.derived() - ); - } - - - /** \returns an expression of the coefficient-wise zeta(\a x, \a q) to the given arrays. - * - * It returns the Riemann zeta function of two arguments \a x and \a q: - * - * \param x is the exposent, it must be > 1 - * \param q is the shift, it must be > 0 - * - * \note This function supports only float and double scalar types. To support other scalar types, the user has - * to provide implementations of zeta(T,T) for any scalar type T to be supported. - * - * \sa ArrayBase::zeta() - */ - template<typename DerivedX,typename DerivedQ> - inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_zeta_op<typename DerivedX::Scalar>, const DerivedX, const DerivedQ> - zeta(const Eigen::ArrayBase<DerivedX>& x, const Eigen::ArrayBase<DerivedQ>& q) - { - return Eigen::CwiseBinaryOp<Eigen::internal::scalar_zeta_op<typename DerivedX::Scalar>, const DerivedX, const DerivedQ>( - x.derived(), - q.derived() - ); - } namespace internal { diff --git a/Eigen/src/Core/IO.h b/Eigen/src/Core/IO.h index 2198f5668..94e00f58b 100644 --- a/Eigen/src/Core/IO.h +++ b/Eigen/src/Core/IO.h @@ -125,30 +125,18 @@ DenseBase<Derived>::format(const IOFormat& fmt) const namespace internal { -template<typename Scalar, bool IsInteger> -struct significant_decimals_default_impl -{ - typedef typename NumTraits<Scalar>::Real RealScalar; - static inline int run() - { - return cast<RealScalar,int>(numext::ceil(-numext::log(NumTraits<RealScalar>::epsilon())/numext::log(RealScalar(10)))); - } -}; - +// NOTE: This helper is kept for backward compatibility with previous code specializing +// this internal::significant_decimals_impl structure. In the future we should directly +// call digits10() which has been introduced in July 2016 in 3.3. template<typename Scalar> -struct significant_decimals_default_impl<Scalar, true> +struct significant_decimals_impl { static inline int run() { - return 0; + return NumTraits<Scalar>::digits10(); } }; -template<typename Scalar> -struct significant_decimals_impl - : significant_decimals_default_impl<Scalar, NumTraits<Scalar>::IsInteger> -{}; - /** \internal * print the matrix \a _m to the output stream \a s using the output format \a fmt */ template<typename Derived> diff --git a/Eigen/src/Core/NumTraits.h b/Eigen/src/Core/NumTraits.h index 03f64a8e9..42cffbd3b 100644 --- a/Eigen/src/Core/NumTraits.h +++ b/Eigen/src/Core/NumTraits.h @@ -12,6 +12,37 @@ namespace Eigen { +namespace internal { + +// default implementation of digits10(), based on numeric_limits if specialized, +// 0 for integer types, and log10(epsilon()) otherwise. +template< typename T, + bool use_numeric_limits = std::numeric_limits<T>::is_specialized, + bool is_integer = NumTraits<T>::IsInteger> +struct default_digits10_impl +{ + static int run() { return std::numeric_limits<T>::digits10; } +}; + +template<typename T> +struct default_digits10_impl<T,false,false> // Floating point +{ + static int run() { + using std::log10; + using std::ceil; + typedef typename NumTraits<T>::Real Real; + return int(ceil(-log10(NumTraits<Real>::epsilon()))); + } +}; + +template<typename T> +struct default_digits10_impl<T,false,true> // Integer +{ + static int run() { return 0; } +}; + +} // end namespace internal + /** \class NumTraits * \ingroup Core_Module * @@ -44,10 +75,14 @@ namespace Eigen { * \li An enum value \a IsSigned. It is equal to \c 1 if \a T is a signed type and to 0 if \a T is unsigned. * \li An enum value \a RequireInitialization. It is equal to \c 1 if the constructor of the numeric type \a T must * be called, and to 0 if it is safe not to call it. Default is 0 if \a T is an arithmetic type, and 1 otherwise. - * \li An epsilon() function which, unlike std::numeric_limits::epsilon(), returns a \a Real instead of a \a T. + * \li An epsilon() function which, unlike <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/epsilon">std::numeric_limits::epsilon()</a>, + * it returns a \a Real instead of a \a T. * \li A dummy_precision() function returning a weak epsilon value. It is mainly used as a default * value by the fuzzy comparison operators. * \li highest() and lowest() functions returning the highest and lowest possible values respectively. + * \li digits10() function returning the number of decimal digits that can be represented without change. This is + * the analogue of <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/digits10">std::numeric_limits<T>::digits10</a> + * which is used as the default implementation if specialized. */ template<typename T> struct GenericNumTraits @@ -93,6 +128,13 @@ template<typename T> struct GenericNumTraits { return numext::numeric_limits<T>::epsilon(); } + + EIGEN_DEVICE_FUNC + static inline int digits10() + { + return internal::default_digits10_impl<T>::run(); + } + EIGEN_DEVICE_FUNC static inline Real dummy_precision() { @@ -161,6 +203,8 @@ template<typename _Real> struct NumTraits<std::complex<_Real> > static inline Real epsilon() { return NumTraits<Real>::epsilon(); } EIGEN_DEVICE_FUNC static inline Real dummy_precision() { return NumTraits<Real>::dummy_precision(); } + EIGEN_DEVICE_FUNC + static inline int digits10() { return NumTraits<Real>::digits10(); } }; template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols> @@ -190,6 +234,27 @@ struct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> > static inline RealScalar dummy_precision() { return NumTraits<RealScalar>::dummy_precision(); } }; +template<> struct NumTraits<std::string> + : GenericNumTraits<std::string> +{ + enum { + RequireInitialization = 1, + ReadCost = HugeCost, + AddCost = HugeCost, + MulCost = HugeCost + }; + + static inline int digits10() { return 0; } + +private: + static inline std::string epsilon(); + static inline std::string dummy_precision(); + static inline std::string lowest(); + static inline std::string highest(); + static inline std::string infinity(); + static inline std::string quiet_NaN(); +}; + } // end namespace Eigen #endif // EIGEN_NUMTRAITS_H diff --git a/Eigen/src/Core/ProductEvaluators.h b/Eigen/src/Core/ProductEvaluators.h index 77549e709..955668bef 100644 --- a/Eigen/src/Core/ProductEvaluators.h +++ b/Eigen/src/Core/ProductEvaluators.h @@ -134,7 +134,7 @@ protected: // Dense = Product template< typename DstXprType, typename Lhs, typename Rhs, int Options, typename Scalar> struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::assign_op<Scalar,Scalar>, Dense2Dense, - typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct),Scalar>::type> + typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct)>::type> { typedef Product<Lhs,Rhs,Options> SrcXprType; static EIGEN_STRONG_INLINE @@ -148,7 +148,7 @@ struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::assign_op<Scal // Dense += Product template< typename DstXprType, typename Lhs, typename Rhs, int Options, typename Scalar> struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::add_assign_op<Scalar,Scalar>, Dense2Dense, - typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct),Scalar>::type> + typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct)>::type> { typedef Product<Lhs,Rhs,Options> SrcXprType; static EIGEN_STRONG_INLINE @@ -162,7 +162,7 @@ struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::add_assign_op< // Dense -= Product template< typename DstXprType, typename Lhs, typename Rhs, int Options, typename Scalar> struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::sub_assign_op<Scalar,Scalar>, Dense2Dense, - typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct),Scalar>::type> + typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct)>::type> { typedef Product<Lhs,Rhs,Options> SrcXprType; static EIGEN_STRONG_INLINE @@ -179,7 +179,7 @@ struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::sub_assign_op< // for instance, this is not good for inner products template< typename DstXprType, typename Lhs, typename Rhs, typename AssignFunc, typename Scalar, typename ScalarBis, typename Plain> struct Assignment<DstXprType, CwiseBinaryOp<internal::scalar_product_op<ScalarBis,Scalar>, const CwiseNullaryOp<internal::scalar_constant_op<ScalarBis>,Plain>, - const Product<Lhs,Rhs,DefaultProduct> >, AssignFunc, Dense2Dense, Scalar> + const Product<Lhs,Rhs,DefaultProduct> >, AssignFunc, Dense2Dense> { typedef CwiseBinaryOp<internal::scalar_product_op<ScalarBis,Scalar>, const CwiseNullaryOp<internal::scalar_constant_op<ScalarBis>,Plain>, @@ -259,7 +259,7 @@ struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,InnerProduct> // Column major result template<typename Dst, typename Lhs, typename Rhs, typename Func> -EIGEN_DONT_INLINE void outer_product_selector_run(Dst& dst, const Lhs &lhs, const Rhs &rhs, const Func& func, const false_type&) +void outer_product_selector_run(Dst& dst, const Lhs &lhs, const Rhs &rhs, const Func& func, const false_type&) { evaluator<Rhs> rhsEval(rhs); typename nested_eval<Lhs,Rhs::SizeAtCompileTime>::type actual_lhs(lhs); @@ -272,7 +272,7 @@ EIGEN_DONT_INLINE void outer_product_selector_run(Dst& dst, const Lhs &lhs, cons // Row major result template<typename Dst, typename Lhs, typename Rhs, typename Func> -EIGEN_DONT_INLINE void outer_product_selector_run(Dst& dst, const Lhs &lhs, const Rhs &rhs, const Func& func, const true_type&) +void outer_product_selector_run(Dst& dst, const Lhs &lhs, const Rhs &rhs, const Func& func, const true_type&) { evaluator<Lhs> lhsEval(lhs); typename nested_eval<Rhs,Lhs::SizeAtCompileTime>::type actual_rhs(rhs); @@ -489,11 +489,8 @@ struct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, DenseShape, SameType = is_same<typename LhsNestedCleaned::Scalar,typename RhsNestedCleaned::Scalar>::value, - CanVectorizeRhs = bool(RhsRowMajor) && (RhsFlags & PacketAccessBit) - && (ColsAtCompileTime == Dynamic || ((ColsAtCompileTime % RhsVecPacketSize) == 0) ), - - CanVectorizeLhs = (!LhsRowMajor) && (LhsFlags & PacketAccessBit) - && (RowsAtCompileTime == Dynamic || ((RowsAtCompileTime % LhsVecPacketSize) == 0) ), + CanVectorizeRhs = bool(RhsRowMajor) && (RhsFlags & PacketAccessBit) && (ColsAtCompileTime!=1), + CanVectorizeLhs = (!LhsRowMajor) && (LhsFlags & PacketAccessBit) && (RowsAtCompileTime!=1), EvalToRowMajor = (MaxRowsAtCompileTime==1&&MaxColsAtCompileTime!=1) ? 1 : (MaxColsAtCompileTime==1&&MaxRowsAtCompileTime!=1) ? 0 diff --git a/Eigen/src/Core/Solve.h b/Eigen/src/Core/Solve.h index 038ad5b11..8fc69c4b8 100644 --- a/Eigen/src/Core/Solve.h +++ b/Eigen/src/Core/Solve.h @@ -134,7 +134,7 @@ protected: // Specialization for "dst = dec.solve(rhs)" // NOTE we need to specialize it for Dense2Dense to avoid ambiguous specialization error and a Sparse2Sparse specialization must exist somewhere template<typename DstXprType, typename DecType, typename RhsType, typename Scalar> -struct Assignment<DstXprType, Solve<DecType,RhsType>, internal::assign_op<Scalar,Scalar>, Dense2Dense, Scalar> +struct Assignment<DstXprType, Solve<DecType,RhsType>, internal::assign_op<Scalar,Scalar>, Dense2Dense> { typedef Solve<DecType,RhsType> SrcXprType; static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &) @@ -146,7 +146,7 @@ struct Assignment<DstXprType, Solve<DecType,RhsType>, internal::assign_op<Scalar // Specialization for "dst = dec.transpose().solve(rhs)" template<typename DstXprType, typename DecType, typename RhsType, typename Scalar> -struct Assignment<DstXprType, Solve<Transpose<const DecType>,RhsType>, internal::assign_op<Scalar,Scalar>, Dense2Dense, Scalar> +struct Assignment<DstXprType, Solve<Transpose<const DecType>,RhsType>, internal::assign_op<Scalar,Scalar>, Dense2Dense> { typedef Solve<Transpose<const DecType>,RhsType> SrcXprType; static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &) @@ -158,7 +158,7 @@ struct Assignment<DstXprType, Solve<Transpose<const DecType>,RhsType>, internal: // Specialization for "dst = dec.adjoint().solve(rhs)" template<typename DstXprType, typename DecType, typename RhsType, typename Scalar> struct Assignment<DstXprType, Solve<CwiseUnaryOp<internal::scalar_conjugate_op<typename DecType::Scalar>, const Transpose<const DecType> >,RhsType>, - internal::assign_op<Scalar,Scalar>, Dense2Dense, Scalar> + internal::assign_op<Scalar,Scalar>, Dense2Dense> { typedef Solve<CwiseUnaryOp<internal::scalar_conjugate_op<typename DecType::Scalar>, const Transpose<const DecType> >,RhsType> SrcXprType; static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &) diff --git a/Eigen/src/Core/TriangularMatrix.h b/Eigen/src/Core/TriangularMatrix.h index c599e0b32..e9606ec33 100644 --- a/Eigen/src/Core/TriangularMatrix.h +++ b/Eigen/src/Core/TriangularMatrix.h @@ -812,8 +812,8 @@ template<> struct AssignmentKind<DenseShape,TriangularShape> { typedef Tria template<> struct AssignmentKind<TriangularShape,DenseShape> { typedef Dense2Triangular Kind; }; -template< typename DstXprType, typename SrcXprType, typename Functor, typename Scalar> -struct Assignment<DstXprType, SrcXprType, Functor, Triangular2Triangular, Scalar> +template< typename DstXprType, typename SrcXprType, typename Functor> +struct Assignment<DstXprType, SrcXprType, Functor, Triangular2Triangular> { EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const Functor &func) { @@ -823,8 +823,8 @@ struct Assignment<DstXprType, SrcXprType, Functor, Triangular2Triangular, Scalar } }; -template< typename DstXprType, typename SrcXprType, typename Functor, typename Scalar> -struct Assignment<DstXprType, SrcXprType, Functor, Triangular2Dense, Scalar> +template< typename DstXprType, typename SrcXprType, typename Functor> +struct Assignment<DstXprType, SrcXprType, Functor, Triangular2Dense> { EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const Functor &func) { @@ -832,8 +832,8 @@ struct Assignment<DstXprType, SrcXprType, Functor, Triangular2Dense, Scalar> } }; -template< typename DstXprType, typename SrcXprType, typename Functor, typename Scalar> -struct Assignment<DstXprType, SrcXprType, Functor, Dense2Triangular, Scalar> +template< typename DstXprType, typename SrcXprType, typename Functor> +struct Assignment<DstXprType, SrcXprType, Functor, Dense2Triangular> { EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const Functor &func) { @@ -933,7 +933,7 @@ namespace internal { // Triangular = Product template< typename DstXprType, typename Lhs, typename Rhs, typename Scalar> -struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::assign_op<Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, Dense2Triangular, Scalar> +struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::assign_op<Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, Dense2Triangular> { typedef Product<Lhs,Rhs,DefaultProduct> SrcXprType; static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename SrcXprType::Scalar> &) @@ -945,7 +945,7 @@ struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::assign_ // Triangular += Product template< typename DstXprType, typename Lhs, typename Rhs, typename Scalar> -struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::add_assign_op<Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, Dense2Triangular, Scalar> +struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::add_assign_op<Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, Dense2Triangular> { typedef Product<Lhs,Rhs,DefaultProduct> SrcXprType; static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<Scalar,typename SrcXprType::Scalar> &) @@ -956,7 +956,7 @@ struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::add_ass // Triangular -= Product template< typename DstXprType, typename Lhs, typename Rhs, typename Scalar> -struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::sub_assign_op<Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, Dense2Triangular, Scalar> +struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::sub_assign_op<Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, Dense2Triangular> { typedef Product<Lhs,Rhs,DefaultProduct> SrcXprType; static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<Scalar,typename SrcXprType::Scalar> &) diff --git a/Eigen/src/Core/VectorwiseOp.h b/Eigen/src/Core/VectorwiseOp.h index 00a4a8c39..dd382e990 100644 --- a/Eigen/src/Core/VectorwiseOp.h +++ b/Eigen/src/Core/VectorwiseOp.h @@ -284,6 +284,7 @@ template<typename ExpressionType, int Direction> class VectorwiseOp typedef typename ReturnType<internal::member_any>::Type AnyReturnType; typedef PartialReduxExpr<ExpressionType, internal::member_count<Index>, Direction> CountReturnType; typedef typename ReturnType<internal::member_prod>::Type ProdReturnType; + typedef Reverse<const ExpressionType, Direction> ConstReverseReturnType; typedef Reverse<ExpressionType, Direction> ReverseReturnType; template<int p> struct LpNormReturnType { @@ -456,7 +457,15 @@ template<typename ExpressionType, int Direction> class VectorwiseOp * * \sa DenseBase::reverse() */ EIGEN_DEVICE_FUNC - const ReverseReturnType reverse() const + const ConstReverseReturnType reverse() const + { return ConstReverseReturnType( _expression() ); } + + /** \returns a writable matrix expression + * where each column (or row) are reversed. + * + * \sa reverse() const */ + EIGEN_DEVICE_FUNC + ReverseReturnType reverse() { return ReverseReturnType( _expression() ); } typedef Replicate<ExpressionType,(isVertical?Dynamic:1),(isHorizontal?Dynamic:1)> ReplicateReturnType; diff --git a/Eigen/src/Core/arch/AltiVec/Complex.h b/Eigen/src/Core/arch/AltiVec/Complex.h index 58c296171..45213f791 100644 --- a/Eigen/src/Core/arch/AltiVec/Complex.h +++ b/Eigen/src/Core/arch/AltiVec/Complex.h @@ -2,6 +2,7 @@ // for linear algebra. // // Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr> +// Copyright (C) 2010-2016 Konstantinos Margaritis <markos@freevec.org> // // This Source Code Form is subject to the terms of the Mozilla // Public License v. 2.0. If a copy of the MPL was not distributed @@ -15,18 +16,20 @@ namespace Eigen { namespace internal { static Packet4ui p4ui_CONJ_XOR = vec_mergeh((Packet4ui)p4i_ZERO, (Packet4ui)p4f_ZERO_);//{ 0x00000000, 0x80000000, 0x00000000, 0x80000000 }; -#ifdef _BIG_ENDIAN +#ifdef __VSX__ +#if defined(_BIG_ENDIAN) static Packet2ul p2ul_CONJ_XOR1 = (Packet2ul) vec_sld((Packet4ui) p2d_ZERO_, (Packet4ui) p2l_ZERO, 8);//{ 0x8000000000000000, 0x0000000000000000 }; static Packet2ul p2ul_CONJ_XOR2 = (Packet2ul) vec_sld((Packet4ui) p2l_ZERO, (Packet4ui) p2d_ZERO_, 8);//{ 0x8000000000000000, 0x0000000000000000 }; #else static Packet2ul p2ul_CONJ_XOR1 = (Packet2ul) vec_sld((Packet4ui) p2l_ZERO, (Packet4ui) p2d_ZERO_, 8);//{ 0x8000000000000000, 0x0000000000000000 }; static Packet2ul p2ul_CONJ_XOR2 = (Packet2ul) vec_sld((Packet4ui) p2d_ZERO_, (Packet4ui) p2l_ZERO, 8);//{ 0x8000000000000000, 0x0000000000000000 }; #endif +#endif //---------- float ---------- struct Packet2cf { - EIGEN_STRONG_INLINE Packet2cf() {} + EIGEN_STRONG_INLINE explicit Packet2cf() : v(p4f_ZERO) {} EIGEN_STRONG_INLINE explicit Packet2cf(const Packet4f& a) : v(a) {} Packet4f v; }; @@ -39,6 +42,7 @@ template<> struct packet_traits<std::complex<float> > : default_packet_traits Vectorizable = 1, AlignedOnScalar = 1, size = 2, + HasHalfPacket = 0, HasAdd = 1, HasSub = 1, @@ -49,6 +53,9 @@ template<> struct packet_traits<std::complex<float> > : default_packet_traits HasAbs2 = 0, HasMin = 0, HasMax = 0, +#ifdef __VSX__ + HasBlend = 1, +#endif HasSetLinear = 0 }; }; @@ -58,7 +65,6 @@ template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type; template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>& from) { Packet2cf res; - /* On AltiVec we cannot load 64-bit registers, so wa have to take care of alignment */ if((ptrdiff_t(&from) % 16) == 0) res.v = pload<Packet4f>((const float *)&from); else @@ -67,26 +73,32 @@ template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<flo return res; } +template<> EIGEN_STRONG_INLINE Packet2cf pload<Packet2cf>(const std::complex<float>* from) { return Packet2cf(pload<Packet4f>((const float *) from)); } +template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) { return Packet2cf(ploadu<Packet4f>((const float*) from)); } +template<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>* from) { return pset1<Packet2cf>(*from); } + +template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> * to, const Packet2cf& from) { pstore((float*)to, from.v); } +template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> * to, const Packet2cf& from) { pstoreu((float*)to, from.v); } + template<> EIGEN_DEVICE_FUNC inline Packet2cf pgather<std::complex<float>, Packet2cf>(const std::complex<float>* from, Index stride) { std::complex<float> EIGEN_ALIGN16 af[2]; af[0] = from[0*stride]; af[1] = from[1*stride]; - return Packet2cf(vec_ld(0, (const float*)af)); + return pload<Packet2cf>(af); } template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet2cf>(std::complex<float>* to, const Packet2cf& from, Index stride) { std::complex<float> EIGEN_ALIGN16 af[2]; - vec_st(from.v, 0, (float*)af); + pstore<std::complex<float> >((std::complex<float> *) af, from); to[0*stride] = af[0]; to[1*stride] = af[1]; } - -template<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_add(a.v,b.v)); } -template<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_sub(a.v,b.v)); } +template<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(a.v + b.v); } +template<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(a.v - b.v); } template<> EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a) { return Packet2cf(pnegate(a.v)); } -template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a) { return Packet2cf((Packet4f)vec_xor((Packet4ui)a.v, p4ui_CONJ_XOR)); } +template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a) { return Packet2cf(pxor<Packet4f>(a.v, reinterpret_cast<Packet4f>(p4ui_CONJ_XOR))); } template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { @@ -100,30 +112,19 @@ template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, con v1 = vec_madd(v1, b.v, p4f_ZERO); // multiply a_im * b and get the conjugate result v2 = vec_madd(v2, b.v, p4f_ZERO); - v2 = (Packet4f) vec_xor((Packet4ui)v2, p4ui_CONJ_XOR); + v2 = reinterpret_cast<Packet4f>(pxor(v2, reinterpret_cast<Packet4f>(p4ui_CONJ_XOR))); // permute back to a proper order v2 = vec_perm(v2, v2, p16uc_COMPLEX32_REV); - return Packet2cf(vec_add(v1, v2)); + return Packet2cf(padd<Packet4f>(v1, v2)); } -template<> EIGEN_STRONG_INLINE Packet2cf pand <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_and(a.v,b.v)); } -template<> EIGEN_STRONG_INLINE Packet2cf por <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_or(a.v,b.v)); } -template<> EIGEN_STRONG_INLINE Packet2cf pxor <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_xor(a.v,b.v)); } -template<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_and(a.v, vec_nor(b.v,b.v))); } +template<> EIGEN_STRONG_INLINE Packet2cf pand <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pand<Packet4f>(a.v, b.v)); } +template<> EIGEN_STRONG_INLINE Packet2cf por <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(por<Packet4f>(a.v, b.v)); } +template<> EIGEN_STRONG_INLINE Packet2cf pxor <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pxor<Packet4f>(a.v, b.v)); } +template<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pandnot<Packet4f>(a.v, b.v)); } -template<> EIGEN_STRONG_INLINE Packet2cf pload <Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>((const float*)from)); } -template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>((const float*)from)); } - -template<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>* from) -{ - return pset1<Packet2cf>(*from); -} - -template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> * to, const Packet2cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((float*)to, from.v); } -template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> * to, const Packet2cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((float*)to, from.v); } - -template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> * addr) { vec_dstt((float *)addr, DST_CTRL(2,2,32), DST_CHAN); } +template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> * addr) { EIGEN_PPC_PREFETCH(addr); } template<> EIGEN_STRONG_INLINE std::complex<float> pfirst<Packet2cf>(const Packet2cf& a) { @@ -143,23 +144,23 @@ template<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a) template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a) { Packet4f b; - b = (Packet4f) vec_sld(a.v, a.v, 8); - b = padd(a.v, b); - return pfirst(Packet2cf(b)); + b = vec_sld(a.v, a.v, 8); + b = padd<Packet4f>(a.v, b); + return pfirst<Packet2cf>(Packet2cf(b)); } template<> EIGEN_STRONG_INLINE Packet2cf preduxp<Packet2cf>(const Packet2cf* vecs) { Packet4f b1, b2; #ifdef _BIG_ENDIAN - b1 = (Packet4f) vec_sld(vecs[0].v, vecs[1].v, 8); - b2 = (Packet4f) vec_sld(vecs[1].v, vecs[0].v, 8); + b1 = vec_sld(vecs[0].v, vecs[1].v, 8); + b2 = vec_sld(vecs[1].v, vecs[0].v, 8); #else - b1 = (Packet4f) vec_sld(vecs[1].v, vecs[0].v, 8); - b2 = (Packet4f) vec_sld(vecs[0].v, vecs[1].v, 8); + b1 = vec_sld(vecs[1].v, vecs[0].v, 8); + b2 = vec_sld(vecs[0].v, vecs[1].v, 8); #endif - b2 = (Packet4f) vec_sld(b2, b2, 8); - b2 = padd(b1, b2); + b2 = vec_sld(b2, b2, 8); + b2 = padd<Packet4f>(b1, b2); return Packet2cf(b2); } @@ -168,10 +169,10 @@ template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const P { Packet4f b; Packet2cf prod; - b = (Packet4f) vec_sld(a.v, a.v, 8); - prod = pmul(a, Packet2cf(b)); + b = vec_sld(a.v, a.v, 8); + prod = pmul<Packet2cf>(a, Packet2cf(b)); - return pfirst(prod); + return pfirst<Packet2cf>(prod); } template<int Offset> @@ -223,12 +224,30 @@ template<> struct conj_helper<Packet2cf, Packet2cf, true,true> } }; +template<> struct conj_helper<Packet4f, Packet2cf, false,false> +{ + EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet4f& x, const Packet2cf& y, const Packet2cf& c) const + { return padd(c, pmul(x,y)); } + + EIGEN_STRONG_INLINE Packet2cf pmul(const Packet4f& x, const Packet2cf& y) const + { return Packet2cf(internal::pmul<Packet4f>(x, y.v)); } +}; + +template<> struct conj_helper<Packet2cf, Packet4f, false,false> +{ + EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet4f& y, const Packet2cf& c) const + { return padd(c, pmul(x,y)); } + + EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& x, const Packet4f& y) const + { return Packet2cf(internal::pmul<Packet4f>(x.v, y)); } +}; + template<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { // TODO optimize it for AltiVec - Packet2cf res = conj_helper<Packet2cf,Packet2cf,false,true>().pmul(a,b); - Packet4f s = vec_madd(b.v, b.v, p4f_ZERO); - return Packet2cf(pdiv(res.v, vec_add(s,vec_perm(s, s, p16uc_COMPLEX32_REV)))); + Packet2cf res = conj_helper<Packet2cf,Packet2cf,false,true>().pmul(a, b); + Packet4f s = pmul<Packet4f>(b.v, b.v); + return Packet2cf(pdiv(res.v, padd<Packet4f>(s, vec_perm(s, s, p16uc_COMPLEX32_REV)))); } template<> EIGEN_STRONG_INLINE Packet2cf pcplxflip<Packet2cf>(const Packet2cf& x) @@ -243,6 +262,14 @@ EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2cf,2>& kernel) kernel.packet[0].v = tmp; } +#ifdef __VSX__ +template<> EIGEN_STRONG_INLINE Packet2cf pblend(const Selector<2>& ifPacket, const Packet2cf& thenPacket, const Packet2cf& elsePacket) { + Packet2cf result; + result.v = reinterpret_cast<Packet4f>(pblend<Packet2d>(ifPacket, reinterpret_cast<Packet2d>(thenPacket.v), reinterpret_cast<Packet2d>(elsePacket.v))); + return result; +} +#endif + //---------- double ---------- #ifdef __VSX__ struct Packet1cd @@ -277,10 +304,10 @@ template<> struct packet_traits<std::complex<double> > : default_packet_traits template<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1, alignment=Aligned16}; typedef Packet1cd half; }; -template<> EIGEN_STRONG_INLINE Packet1cd pload <Packet1cd>(const std::complex<double>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet1cd(pload<Packet2d>((const double*)from)); } -template<> EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet1cd(ploadu<Packet2d>((const double*)from)); } -template<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> * to, const Packet1cd& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((double*)to, from.v); } -template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> * to, const Packet1cd& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((double*)to, from.v); } +template<> EIGEN_STRONG_INLINE Packet1cd pload <Packet1cd>(const std::complex<double>* from) { return Packet1cd(pload<Packet2d>((const double*)from)); } +template<> EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from) { return Packet1cd(ploadu<Packet2d>((const double*)from)); } +template<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> * to, const Packet1cd& from) { pstore((double*)to, from.v); } +template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> * to, const Packet1cd& from) { pstoreu((double*)to, from.v); } template<> EIGEN_STRONG_INLINE Packet1cd pset1<Packet1cd>(const std::complex<double>& from) { /* here we really have to use unaligned loads :( */ return ploadu<Packet1cd>(&from); } @@ -300,10 +327,10 @@ template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<double>, Packet1c to[1*stride] = af[1]; } -template<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_add(a.v,b.v)); } -template<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_sub(a.v,b.v)); } +template<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v + b.v); } +template<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v - b.v); } template<> EIGEN_STRONG_INLINE Packet1cd pnegate(const Packet1cd& a) { return Packet1cd(pnegate(Packet2d(a.v))); } -template<> EIGEN_STRONG_INLINE Packet1cd pconj(const Packet1cd& a) { return Packet1cd((Packet2d)vec_xor((Packet2d)a.v, (Packet2d)p2ul_CONJ_XOR2)); } +template<> EIGEN_STRONG_INLINE Packet1cd pconj(const Packet1cd& a) { return Packet1cd(pxor(a.v, reinterpret_cast<Packet2d>(p2ul_CONJ_XOR2))); } template<> EIGEN_STRONG_INLINE Packet1cd pmul<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { @@ -317,23 +344,20 @@ template<> EIGEN_STRONG_INLINE Packet1cd pmul<Packet1cd>(const Packet1cd& a, con v1 = vec_madd(a_re, b.v, p2d_ZERO); // multiply a_im * b and get the conjugate result v2 = vec_madd(a_im, b.v, p2d_ZERO); - v2 = (Packet2d) vec_sld((Packet4ui)v2, (Packet4ui)v2, 8); - v2 = (Packet2d) vec_xor((Packet2d)v2, (Packet2d) p2ul_CONJ_XOR1); + v2 = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(v2), reinterpret_cast<Packet4ui>(v2), 8)); + v2 = pxor(v2, reinterpret_cast<Packet2d>(p2ul_CONJ_XOR1)); - return Packet1cd(vec_add(v1, v2)); + return Packet1cd(padd<Packet2d>(v1, v2)); } -template<> EIGEN_STRONG_INLINE Packet1cd pand <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_and(a.v,b.v)); } -template<> EIGEN_STRONG_INLINE Packet1cd por <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_or(a.v,b.v)); } -template<> EIGEN_STRONG_INLINE Packet1cd pxor <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_xor(a.v,b.v)); } -template<> EIGEN_STRONG_INLINE Packet1cd pandnot<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_and(a.v, vec_nor(b.v,b.v))); } +template<> EIGEN_STRONG_INLINE Packet1cd pand <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(pand(a.v,b.v)); } +template<> EIGEN_STRONG_INLINE Packet1cd por <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(por(a.v,b.v)); } +template<> EIGEN_STRONG_INLINE Packet1cd pxor <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(pxor(a.v,b.v)); } +template<> EIGEN_STRONG_INLINE Packet1cd pandnot<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(pandnot(a.v, b.v)); } -template<> EIGEN_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<double>* from) -{ - return pset1<Packet1cd>(*from); -} +template<> EIGEN_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<double>* from) { return pset1<Packet1cd>(*from); } -template<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> * addr) { vec_dstt((long *)addr, DST_CTRL(2,2,32), DST_CHAN); } +template<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> * addr) { EIGEN_PPC_PREFETCH(addr); } template<> EIGEN_STRONG_INLINE std::complex<double> pfirst<Packet1cd>(const Packet1cd& a) { @@ -345,20 +369,10 @@ template<> EIGEN_STRONG_INLINE std::complex<double> pfirst<Packet1cd>(const Pac template<> EIGEN_STRONG_INLINE Packet1cd preverse(const Packet1cd& a) { return a; } -template<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet1cd>(const Packet1cd& a) -{ - return pfirst(a); -} +template<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet1cd>(const Packet1cd& a) { return pfirst(a); } +template<> EIGEN_STRONG_INLINE Packet1cd preduxp<Packet1cd>(const Packet1cd* vecs) { return vecs[0]; } -template<> EIGEN_STRONG_INLINE Packet1cd preduxp<Packet1cd>(const Packet1cd* vecs) -{ - return vecs[0]; -} - -template<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet1cd>(const Packet1cd& a) -{ - return pfirst(a); -} +template<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet1cd>(const Packet1cd& a) { return pfirst(a); } template<int Offset> struct palign_impl<Offset,Packet1cd> @@ -402,13 +416,30 @@ template<> struct conj_helper<Packet1cd, Packet1cd, true,true> return pconj(internal::pmul(a, b)); } }; +template<> struct conj_helper<Packet2d, Packet1cd, false,false> +{ + EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet2d& x, const Packet1cd& y, const Packet1cd& c) const + { return padd(c, pmul(x,y)); } + + EIGEN_STRONG_INLINE Packet1cd pmul(const Packet2d& x, const Packet1cd& y) const + { return Packet1cd(internal::pmul<Packet2d>(x, y.v)); } +}; + +template<> struct conj_helper<Packet1cd, Packet2d, false,false> +{ + EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet2d& y, const Packet1cd& c) const + { return padd(c, pmul(x,y)); } + + EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& x, const Packet2d& y) const + { return Packet1cd(internal::pmul<Packet2d>(x.v, y)); } +}; template<> EIGEN_STRONG_INLINE Packet1cd pdiv<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { // TODO optimize it for AltiVec Packet1cd res = conj_helper<Packet1cd,Packet1cd,false,true>().pmul(a,b); - Packet2d s = vec_madd(b.v, b.v, p2d_ZERO_); - return Packet1cd(pdiv(res.v, vec_add(s,vec_perm(s, s, p16uc_REVERSE64)))); + Packet2d s = pmul<Packet2d>(b.v, b.v); + return Packet1cd(pdiv(res.v, padd<Packet2d>(s, vec_perm(s, s, p16uc_REVERSE64)))); } EIGEN_STRONG_INLINE Packet1cd pcplxflip/*<Packet1cd>*/(const Packet1cd& x) diff --git a/Eigen/src/Core/arch/AltiVec/MathFunctions.h b/Eigen/src/Core/arch/AltiVec/MathFunctions.h index 9e37e93f8..5511245dd 100644 --- a/Eigen/src/Core/arch/AltiVec/MathFunctions.h +++ b/Eigen/src/Core/arch/AltiVec/MathFunctions.h @@ -3,6 +3,7 @@ // // Copyright (C) 2007 Julien Pommier // Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr> +// Copyright (C) 2016 Konstantinos Margaritis <markos@freevec.org> // // This Source Code Form is subject to the terms of the Mozilla // Public License v. 2.0. If a copy of the MPL was not distributed @@ -19,38 +20,79 @@ namespace Eigen { namespace internal { -template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED -Packet4f plog<Packet4f>(const Packet4f& _x) -{ - Packet4f x = _x; - _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f); - _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f); - _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f); - _EIGEN_DECLARE_CONST_Packet4i(23, 23); +static _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f); +static _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f); +static _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f); +static _EIGEN_DECLARE_CONST_Packet4i(23, 23); - _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000); +static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000); - /* the smallest non denormalized float number */ - _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000); - _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf, 0xff800000); // -1.f/0.f - _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_nan, 0xffffffff); +/* the smallest non denormalized float number */ +static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000); +static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf, 0xff800000); // -1.f/0.f +static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_nan, 0xffffffff); - /* natural logarithm computed for 4 simultaneous float - return NaN for x <= 0 - */ - _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f); - _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f); - _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f); - _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f); - _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f); - _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f); - _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f); - _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f); - _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f); - _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f); - _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f); - _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f); +/* natural logarithm computed for 4 simultaneous float + return NaN for x <= 0 +*/ +static _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f); +static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f); +static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f); +static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f); +static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f); +static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f); +static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f); +static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f); +static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f); +static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f); +static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f); +static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f); + +static _EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647950f); +static _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f); + +static _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f); +static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f); +static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f); + +static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f); +static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f); +static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f); +static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f); +static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f); +static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f); + +#ifdef __VSX__ +static _EIGEN_DECLARE_CONST_Packet2d(1 , 1.0); +static _EIGEN_DECLARE_CONST_Packet2d(2 , 2.0); +static _EIGEN_DECLARE_CONST_Packet2d(half, 0.5); +static _EIGEN_DECLARE_CONST_Packet2d(exp_hi, 709.437); +static _EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303); + +static _EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599); + +static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4); +static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2); +static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1); + +static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6); +static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3); +static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1); +static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0); + +static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125); +static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6); + +static Packet2l p2l_1023 = { 1023, 1023 }; +static Packet2ul p2ul_52 = { 52, 52 }; + +#endif + +template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED +Packet4f plog<Packet4f>(const Packet4f& _x) +{ + Packet4f x = _x; Packet4i emm0; @@ -112,36 +154,17 @@ template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f pexp<Packet4f>(const Packet4f& _x) { Packet4f x = _x; - _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f); - _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f); - _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f); - _EIGEN_DECLARE_CONST_Packet4i(23, 23); - - - _EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647950f); - _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f); - - _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f); - _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f); - _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f); - - _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f); - _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f); - _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f); - _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f); - _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f); - _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f); Packet4f tmp, fx; Packet4i emm0; // clamp x - x = vec_max(vec_min(x, p4f_exp_hi), p4f_exp_lo); + x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo); - /* express exp(x) as exp(g + n*log(2)) */ + // express exp(x) as exp(g + n*log(2)) fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half); - fx = vec_floor(fx); + fx = pfloor(fx); tmp = pmul(fx, p4f_cephes_exp_C1); Packet4f z = pmul(fx, p4f_cephes_exp_C2); @@ -171,14 +194,44 @@ Packet4f pexp<Packet4f>(const Packet4f& _x) isnumber_mask); } +#ifndef EIGEN_COMP_CLANG +template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED +Packet4f prsqrt<Packet4f>(const Packet4f& x) +{ + return vec_rsqrt(x); +} +#endif + #ifdef __VSX__ +#ifndef EIGEN_COMP_CLANG +template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED +Packet2d prsqrt<Packet2d>(const Packet2d& x) +{ + return vec_rsqrt(x); +} +#endif + +template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED +Packet4f psqrt<Packet4f>(const Packet4f& x) +{ + return vec_sqrt(x); +} + +template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED +Packet2d psqrt<Packet2d>(const Packet2d& x) +{ + return vec_sqrt(x); +} + // VSX support varies between different compilers and even different // versions of the same compiler. For gcc version >= 4.9.3, we can use // vec_cts to efficiently convert Packet2d to Packet2l. Otherwise, use // a slow version that works with older compilers. +// Update: apparently vec_cts/vec_ctf intrinsics for 64-bit doubles +// are buggy, https://gcc.gnu.org/bugzilla/show_bug.cgi?id=70963 static inline Packet2l ConvertToPacket2l(const Packet2d& x) { -#if EIGEN_GNUC_AT_LEAST(5, 0) || \ - (EIGEN_GNUC_AT(4, 9) && __GNUC_PATCHLEVEL__ >= 3) +#if EIGEN_GNUC_AT_LEAST(5, 4) || \ + (EIGEN_GNUC_AT(6, 1) && __GNUC_PATCHLEVEL__ >= 1) return vec_cts(x, 0); // TODO: check clang version. #else double tmp[2]; @@ -194,36 +247,16 @@ Packet2d pexp<Packet2d>(const Packet2d& _x) { Packet2d x = _x; - _EIGEN_DECLARE_CONST_Packet2d(1 , 1.0); - _EIGEN_DECLARE_CONST_Packet2d(2 , 2.0); - _EIGEN_DECLARE_CONST_Packet2d(half, 0.5); - - _EIGEN_DECLARE_CONST_Packet2d(exp_hi, 709.437); - _EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303); - - _EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599); - - _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4); - _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2); - _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1); - - _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6); - _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3); - _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1); - _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0); - - _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125); - _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6); - Packet2d tmp, fx; Packet2l emm0; // clamp x x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo); + /* express exp(x) as exp(g + n*log(2)) */ - fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half); + fx = pmadd(x, p2d_cephes_LOG2EF, p2d_half); - fx = vec_floor(fx); + fx = pfloor(fx); tmp = pmul(fx, p2d_cephes_exp_C1); Packet2d z = pmul(fx, p2d_cephes_exp_C2); @@ -249,9 +282,6 @@ Packet2d pexp<Packet2d>(const Packet2d& _x) emm0 = ConvertToPacket2l(fx); #ifdef __POWER8_VECTOR__ - static const Packet2l p2l_1023 = { 1023, 1023 }; - static const Packet2ul p2ul_52 = { 52, 52 }; - emm0 = vec_add(emm0, p2l_1023); emm0 = vec_sl(emm0, p2ul_52); #else diff --git a/Eigen/src/Core/arch/AltiVec/PacketMath.h b/Eigen/src/Core/arch/AltiVec/PacketMath.h index 0dbbc2e42..cbfef3503 100755 --- a/Eigen/src/Core/arch/AltiVec/PacketMath.h +++ b/Eigen/src/Core/arch/AltiVec/PacketMath.h @@ -1,7 +1,7 @@ // This file is part of Eigen, a lightweight C++ template library // for linear algebra. // -// Copyright (C) 2008-2014 Konstantinos Margaritis <markos@freevec.org> +// Copyright (C) 2008-2016 Konstantinos Margaritis <markos@freevec.org> // // This Source Code Form is subject to the terms of the Mozilla // Public License v. 2.0. If a copy of the MPL was not distributed @@ -42,7 +42,7 @@ typedef __vector unsigned char Packet16uc; // and it doesn't really work to declare them global, so we define macros instead #define _EIGEN_DECLARE_CONST_FAST_Packet4f(NAME,X) \ - Packet4f p4f_##NAME = (Packet4f) vec_splat_s32(X) + Packet4f p4f_##NAME = reinterpret_cast<Packet4f>(vec_splat_s32(X)) #define _EIGEN_DECLARE_CONST_FAST_Packet4i(NAME,X) \ Packet4i p4i_##NAME = vec_splat_s32(X) @@ -69,13 +69,13 @@ typedef __vector unsigned char Packet16uc; // These constants are endian-agnostic static _EIGEN_DECLARE_CONST_FAST_Packet4f(ZERO, 0); //{ 0.0, 0.0, 0.0, 0.0} static _EIGEN_DECLARE_CONST_FAST_Packet4i(ZERO, 0); //{ 0, 0, 0, 0,} -#ifndef __VSX__ static _EIGEN_DECLARE_CONST_FAST_Packet4i(ONE,1); //{ 1, 1, 1, 1} -static Packet4f p4f_ONE = vec_ctf(p4i_ONE, 0); //{ 1.0, 1.0, 1.0, 1.0} -#endif static _EIGEN_DECLARE_CONST_FAST_Packet4i(MINUS16,-16); //{ -16, -16, -16, -16} static _EIGEN_DECLARE_CONST_FAST_Packet4i(MINUS1,-1); //{ -1, -1, -1, -1} static Packet4f p4f_ZERO_ = (Packet4f) vec_sl((Packet4ui)p4i_MINUS1, (Packet4ui)p4i_MINUS1); //{ 0x80000000, 0x80000000, 0x80000000, 0x80000000} +#ifndef __VSX__ +static Packet4f p4f_ONE = vec_ctf(p4i_ONE, 0); //{ 1.0, 1.0, 1.0, 1.0} +#endif static Packet4f p4f_COUNTDOWN = { 0.0, 1.0, 2.0, 3.0 }; static Packet4i p4i_COUNTDOWN = { 0, 1, 2, 3 }; @@ -95,8 +95,10 @@ static Packet16uc p16uc_DUPLICATE32_HI = { 0,1,2,3, 0,1,2,3, 4,5,6,7, 4,5,6,7 }; // Handle endianness properly while loading constants // Define global static constants: #ifdef _BIG_ENDIAN -static Packet16uc p16uc_FORWARD = vec_lvsl(0, (float*)0); +static Packet16uc p16uc_FORWARD = vec_lvsl(0, (float*)0); +#ifdef __VSX__ static Packet16uc p16uc_REVERSE64 = { 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 }; +#endif static Packet16uc p16uc_PSET32_WODD = vec_sld((Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 0), (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 2), 8);//{ 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 }; static Packet16uc p16uc_PSET32_WEVEN = vec_sld(p16uc_DUPLICATE32_HI, (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 3), 8);//{ 4,5,6,7, 4,5,6,7, 12,13,14,15, 12,13,14,15 }; static Packet16uc p16uc_HALF64_0_16 = vec_sld((Packet16uc)p4i_ZERO, vec_splat((Packet16uc) vec_abs(p4i_MINUS16), 3), 8); //{ 0,0,0,0, 0,0,0,0, 16,16,16,16, 16,16,16,16}; @@ -110,8 +112,8 @@ static Packet16uc p16uc_HALF64_0_16 = vec_sld(vec_splat((Packet16uc) vec_abs(p4i static Packet16uc p16uc_PSET64_HI = (Packet16uc) vec_mergeh((Packet4ui)p16uc_PSET32_WODD, (Packet4ui)p16uc_PSET32_WEVEN); //{ 0,1,2,3, 4,5,6,7, 0,1,2,3, 4,5,6,7 }; static Packet16uc p16uc_PSET64_LO = (Packet16uc) vec_mergel((Packet4ui)p16uc_PSET32_WODD, (Packet4ui)p16uc_PSET32_WEVEN); //{ 8,9,10,11, 12,13,14,15, 8,9,10,11, 12,13,14,15 }; -static Packet16uc p16uc_TRANSPOSE64_HI = vec_add(p16uc_PSET64_HI, p16uc_HALF64_0_16); //{ 0,1,2,3, 4,5,6,7, 16,17,18,19, 20,21,22,23}; -static Packet16uc p16uc_TRANSPOSE64_LO = vec_add(p16uc_PSET64_LO, p16uc_HALF64_0_16); //{ 8,9,10,11, 12,13,14,15, 24,25,26,27, 28,29,30,31}; +static Packet16uc p16uc_TRANSPOSE64_HI = p16uc_PSET64_HI + p16uc_HALF64_0_16; //{ 0,1,2,3, 4,5,6,7, 16,17,18,19, 20,21,22,23}; +static Packet16uc p16uc_TRANSPOSE64_LO = p16uc_PSET64_LO + p16uc_HALF64_0_16; //{ 8,9,10,11, 12,13,14,15, 24,25,26,27, 28,29,30,31}; static Packet16uc p16uc_COMPLEX32_REV = vec_sld(p16uc_REVERSE32, p16uc_REVERSE32, 8); //{ 4,5,6,7, 0,1,2,3, 12,13,14,15, 8,9,10,11 }; @@ -121,6 +123,12 @@ static Packet16uc p16uc_COMPLEX32_REV2 = vec_sld(p16uc_FORWARD, p16uc_FORWARD, 8 static Packet16uc p16uc_COMPLEX32_REV2 = vec_sld(p16uc_PSET64_HI, p16uc_PSET64_LO, 8); //{ 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 }; #endif // _BIG_ENDIAN +#if EIGEN_HAS_BUILTIN(__builtin_prefetch) || EIGEN_COMP_GNUC + #define EIGEN_PPC_PREFETCH(ADDR) __builtin_prefetch(ADDR); +#else + #define EIGEN_PPC_PREFETCH(ADDR) asm( " dcbt [%[addr]]\n" :: [addr] "r" (ADDR) : "cc" ); +#endif + template<> struct packet_traits<float> : default_packet_traits { typedef Packet4f type; @@ -129,15 +137,35 @@ template<> struct packet_traits<float> : default_packet_traits Vectorizable = 1, AlignedOnScalar = 1, size=4, - HasHalfPacket=0, + HasHalfPacket = 1, - // FIXME check the Has* + HasAdd = 1, + HasSub = 1, + HasMul = 1, HasDiv = 1, + HasMin = 1, + HasMax = 1, + HasAbs = 1, HasSin = 0, HasCos = 0, - HasLog = 1, + HasLog = 0, HasExp = 1, - HasSqrt = 0 +#ifdef __VSX__ + HasSqrt = 1, +#if !EIGEN_COMP_CLANG + HasRsqrt = 1, +#else + HasRsqrt = 0, +#endif +#else + HasSqrt = 0, + HasRsqrt = 0, +#endif + HasRound = 1, + HasFloor = 1, + HasCeil = 1, + HasNegate = 1, + HasBlend = 1 }; }; template<> struct packet_traits<int> : default_packet_traits @@ -145,10 +173,16 @@ template<> struct packet_traits<int> : default_packet_traits typedef Packet4i type; typedef Packet4i half; enum { - // FIXME check the Has* Vectorizable = 1, AlignedOnScalar = 1, - size=4 + size = 4, + HasHalfPacket = 0, + + HasAdd = 1, + HasSub = 1, + HasMul = 1, + HasDiv = 0, + HasBlend = 1 }; }; @@ -200,41 +234,56 @@ inline std::ostream & operator <<(std::ostream & s, const Packet4ui & v) s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3]; return s; } -/* -inline std::ostream & operator <<(std::ostream & s, const Packetbi & v) + +// Need to define them first or we get specialization after instantiation errors +template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from) { - union { - Packet4bi v; - unsigned int n[4]; - } vt; - vt.v = v; - s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3]; - return s; -}*/ + EIGEN_DEBUG_ALIGNED_LOAD +#ifdef __VSX__ + return vec_vsx_ld(0, from); +#else + return vec_ld(0, from); +#endif +} +template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int* from) +{ + EIGEN_DEBUG_ALIGNED_LOAD +#ifdef __VSX__ + return vec_vsx_ld(0, from); +#else + return vec_ld(0, from); +#endif +} -// Need to define them first or we get specialization after instantiation errors -template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from) { EIGEN_DEBUG_ALIGNED_LOAD return vec_ld(0, from); } -template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int* from) { EIGEN_DEBUG_ALIGNED_LOAD return vec_ld(0, from); } +template<> EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet4f& from) +{ + EIGEN_DEBUG_ALIGNED_STORE +#ifdef __VSX__ + vec_vsx_st(from, 0, to); +#else + vec_st(from, 0, to); +#endif +} -template<> EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet4f& from) { EIGEN_DEBUG_ALIGNED_STORE vec_st(from, 0, to); } -template<> EIGEN_STRONG_INLINE void pstore<int>(int* to, const Packet4i& from) { EIGEN_DEBUG_ALIGNED_STORE vec_st(from, 0, to); } +template<> EIGEN_STRONG_INLINE void pstore<int>(int* to, const Packet4i& from) +{ + EIGEN_DEBUG_ALIGNED_STORE +#ifdef __VSX__ + vec_vsx_st(from, 0, to); +#else + vec_st(from, 0, to); +#endif +} template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float& from) { - // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html - float EIGEN_ALIGN16 af[4]; - af[0] = from; - Packet4f vc = pload<Packet4f>(af); - vc = vec_splat(vc, 0); - return vc; + Packet4f v = {from, from, from, from}; + return v; } template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int& from) { - int EIGEN_ALIGN16 ai[4]; - ai[0] = from; - Packet4i vc = pload<Packet4i>(ai); - vc = vec_splat(vc, 0); - return vc; + Packet4i v = {from, from, from, from}; + return v; } template<> EIGEN_STRONG_INLINE void pbroadcast4<Packet4f>(const float *a, @@ -294,58 +343,24 @@ template<> EIGEN_DEVICE_FUNC inline void pscatter<int, Packet4i>(int* to, const to[3*stride] = ai[3]; } -template<> EIGEN_STRONG_INLINE Packet4f plset<Packet4f>(const float& a) { return vec_add(pset1<Packet4f>(a), p4f_COUNTDOWN); } -template<> EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int& a) { return vec_add(pset1<Packet4i>(a), p4i_COUNTDOWN); } +template<> EIGEN_STRONG_INLINE Packet4f plset<Packet4f>(const float& a) { return pset1<Packet4f>(a) + p4f_COUNTDOWN; } +template<> EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int& a) { return pset1<Packet4i>(a) + p4i_COUNTDOWN; } -template<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_add(a,b); } -template<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_add(a,b); } +template<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return a + b; } +template<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return a + b; } -template<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_sub(a,b); } -template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_sub(a,b); } +template<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return a - b; } +template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return a - b; } -template<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a) { return psub<Packet4f>(p4f_ZERO, a); } -template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) { return psub<Packet4i>(p4i_ZERO, a); } +template<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a) { return p4f_ZERO - a; } +template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) { return p4i_ZERO - a; } template<> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; } template<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; } -template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_madd(a,b,p4f_ZERO); } -/* Commented out: it's actually slower than processing it scalar - * -template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b) -{ - // Detailed in: http://freevec.org/content/32bit_signed_integer_multiplication_altivec - //Set up constants, variables - Packet4i a1, b1, bswap, low_prod, high_prod, prod, prod_, v1sel; - - // Get the absolute values - a1 = vec_abs(a); - b1 = vec_abs(b); - - // Get the signs using xor - Packet4bi sgn = (Packet4bi) vec_cmplt(vec_xor(a, b), p4i_ZERO); - - // Do the multiplication for the asbolute values. - bswap = (Packet4i) vec_rl((Packet4ui) b1, (Packet4ui) p4i_MINUS16 ); - low_prod = vec_mulo((Packet8i) a1, (Packet8i)b1); - high_prod = vec_msum((Packet8i) a1, (Packet8i) bswap, p4i_ZERO); - high_prod = (Packet4i) vec_sl((Packet4ui) high_prod, (Packet4ui) p4i_MINUS16); - prod = vec_add( low_prod, high_prod ); +template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_madd(a,b, p4f_ZERO); } +template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b) { return a * b; } - // NOR the product and select only the negative elements according to the sign mask - prod_ = vec_nor(prod, prod); - prod_ = vec_sel(p4i_ZERO, prod_, sgn); - - // Add 1 to the result to get the negative numbers - v1sel = vec_sel(p4i_ZERO, p4i_ONE, sgn); - prod_ = vec_add(prod_, v1sel); - - // Merge the results back to the final vector. - prod = vec_sel(prod, prod_, sgn); - - return prod; -} -*/ template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b) { #ifndef __VSX__ // VSX actually provides a div instruction @@ -370,8 +385,8 @@ template<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, co } // for some weird raisons, it has to be overloaded for packet of integers -template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vec_madd(a, b, c); } -template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return padd(pmul(a,b), c); } +template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vec_madd(a,b,c); } +template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return a*b + c; } template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_min(a, b); } template<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_min(a, b); } @@ -391,6 +406,10 @@ template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_and(a, vec_nor(b, b)); } template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_and(a, vec_nor(b, b)); } +template<> EIGEN_STRONG_INLINE Packet4f pround<Packet4f>(const Packet4f& a) { return vec_round(a); } +template<> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const Packet4f& a) { return vec_ceil(a); } +template<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a) { return vec_floor(a); } + #ifdef _BIG_ENDIAN template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from) { @@ -418,12 +437,12 @@ template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from) // We also need ot redefine little endian loading of Packet4i/Packet4f using VSX template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from) { - EIGEN_DEBUG_ALIGNED_LOAD + EIGEN_DEBUG_UNALIGNED_LOAD return (Packet4i) vec_vsx_ld((long)from & 15, (const int*) _EIGEN_ALIGNED_PTR(from)); } template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from) { - EIGEN_DEBUG_ALIGNED_LOAD + EIGEN_DEBUG_UNALIGNED_LOAD return (Packet4f) vec_vsx_ld((long)from & 15, (const float*) _EIGEN_ALIGNED_PTR(from)); } #endif @@ -494,16 +513,19 @@ template<> EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet4f& } #endif -#ifndef __VSX__ -template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { vec_dstt(addr, DST_CTRL(2,2,32), DST_CHAN); } -template<> EIGEN_STRONG_INLINE void prefetch<int>(const int* addr) { vec_dstt(addr, DST_CTRL(2,2,32), DST_CHAN); } -#endif +template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { EIGEN_PPC_PREFETCH(addr); } +template<> EIGEN_STRONG_INLINE void prefetch<int>(const int* addr) { EIGEN_PPC_PREFETCH(addr); } -template<> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) { float EIGEN_ALIGN16 x[4]; vec_st(a, 0, x); return x[0]; } -template<> EIGEN_STRONG_INLINE int pfirst<Packet4i>(const Packet4i& a) { int EIGEN_ALIGN16 x[4]; vec_st(a, 0, x); return x[0]; } +template<> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) { float EIGEN_ALIGN16 x; vec_ste(a, 0, &x); return x; } +template<> EIGEN_STRONG_INLINE int pfirst<Packet4i>(const Packet4i& a) { int EIGEN_ALIGN16 x; vec_ste(a, 0, &x); return x; } -template<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a) { return (Packet4f)vec_perm((Packet16uc)a,(Packet16uc)a, p16uc_REVERSE32); } -template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a) { return (Packet4i)vec_perm((Packet16uc)a,(Packet16uc)a, p16uc_REVERSE32); } +template<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a) +{ + return reinterpret_cast<Packet4f>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE32)); +} +template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a) +{ + return reinterpret_cast<Packet4i>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE32)); } template<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a) { return vec_abs(a); } template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) { return vec_abs(a); } @@ -511,10 +533,10 @@ template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) { return vec_abs template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a) { Packet4f b, sum; - b = (Packet4f) vec_sld(a, a, 8); - sum = vec_add(a, b); - b = (Packet4f) vec_sld(sum, sum, 4); - sum = vec_add(sum, b); + b = vec_sld(a, a, 8); + sum = a + b; + b = vec_sld(sum, sum, 4); + sum += b; return pfirst(sum); } @@ -537,11 +559,11 @@ template<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs) // Now do the summation: // Lines 0+1 - sum[0] = vec_add(sum[0], sum[1]); + sum[0] = sum[0] + sum[1]; // Lines 2+3 - sum[1] = vec_add(sum[2], sum[3]); + sum[1] = sum[2] + sum[3]; // Add the results - sum[0] = vec_add(sum[0], sum[1]); + sum[0] = sum[0] + sum[1]; return sum[0]; } @@ -577,11 +599,11 @@ template<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs) // Now do the summation: // Lines 0+1 - sum[0] = vec_add(sum[0], sum[1]); + sum[0] = sum[0] + sum[1]; // Lines 2+3 - sum[1] = vec_add(sum[2], sum[3]); + sum[1] = sum[2] + sum[3]; // Add the results - sum[0] = vec_add(sum[0], sum[1]); + sum[0] = sum[0] + sum[1]; return sum[0]; } @@ -591,8 +613,8 @@ template<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs) template<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a) { Packet4f prod; - prod = pmul(a, (Packet4f)vec_sld(a, a, 8)); - return pfirst(pmul(prod, (Packet4f)vec_sld(prod, prod, 4))); + prod = pmul(a, vec_sld(a, a, 8)); + return pfirst(pmul(prod, vec_sld(prod, prod, 4))); } template<> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a) @@ -716,33 +738,52 @@ ptranspose(PacketBlock<Packet4i,4>& kernel) { kernel.packet[3] = vec_mergel(t1, t3); } +template<> EIGEN_STRONG_INLINE Packet4i pblend(const Selector<4>& ifPacket, const Packet4i& thenPacket, const Packet4i& elsePacket) { + Packet4ui select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3] }; + Packet4ui mask = reinterpret_cast<Packet4ui>(vec_cmpeq(reinterpret_cast<Packet4ui>(select), reinterpret_cast<Packet4ui>(p4i_ONE))); + return vec_sel(elsePacket, thenPacket, mask); +} + +template<> EIGEN_STRONG_INLINE Packet4f pblend(const Selector<4>& ifPacket, const Packet4f& thenPacket, const Packet4f& elsePacket) { + Packet4ui select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3] }; + Packet4ui mask = reinterpret_cast<Packet4ui>(vec_cmpeq(reinterpret_cast<Packet4ui>(select), reinterpret_cast<Packet4ui>(p4i_ONE))); + return vec_sel(elsePacket, thenPacket, mask); +} + //---------- double ---------- #ifdef __VSX__ typedef __vector double Packet2d; typedef __vector unsigned long long Packet2ul; typedef __vector long long Packet2l; +#if EIGEN_COMP_CLANG +typedef Packet2ul Packet2bl; +#else +typedef __vector __bool long Packet2bl; +#endif -static Packet2l p2l_ZERO = (Packet2l) p4i_ZERO; -static Packet2d p2d_ONE = { 1.0, 1.0 }; -static Packet2d p2d_ZERO = (Packet2d) p4f_ZERO; -static Packet2d p2d_ZERO_ = { -0.0, -0.0 }; +static Packet2l p2l_ONE = { 1, 1 }; +static Packet2l p2l_ZERO = reinterpret_cast<Packet2l>(p4i_ZERO); +static Packet2d p2d_ONE = { 1.0, 1.0 }; +static Packet2d p2d_ZERO = reinterpret_cast<Packet2d>(p4f_ZERO); +static Packet2d p2d_ZERO_ = { -0.0, -0.0 }; #ifdef _BIG_ENDIAN -static Packet2d p2d_COUNTDOWN = (Packet2d) vec_sld((Packet16uc) p2d_ZERO, (Packet16uc) p2d_ONE, 8); +static Packet2d p2d_COUNTDOWN = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(p2d_ZERO), reinterpret_cast<Packet4f>(p2d_ONE), 8)); #else -static Packet2d p2d_COUNTDOWN = (Packet2d) vec_sld((Packet16uc) p2d_ONE, (Packet16uc) p2d_ZERO, 8); +static Packet2d p2d_COUNTDOWN = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(p2d_ONE), reinterpret_cast<Packet4f>(p2d_ZERO), 8)); #endif -static EIGEN_STRONG_INLINE Packet2d vec_splat_dbl(Packet2d& a, int index) +template<int index> Packet2d vec_splat_dbl(Packet2d& a); + +template<> EIGEN_STRONG_INLINE Packet2d vec_splat_dbl<0>(Packet2d& a) { - switch (index) { - case 0: - return (Packet2d) vec_perm(a, a, p16uc_PSET64_HI); - case 1: - return (Packet2d) vec_perm(a, a, p16uc_PSET64_LO); - } - return a; + return reinterpret_cast<Packet2d>(vec_perm(a, a, p16uc_PSET64_HI)); +} + +template<> EIGEN_STRONG_INLINE Packet2d vec_splat_dbl<1>(Packet2d& a) +{ + return reinterpret_cast<Packet2d>(vec_perm(a, a, p16uc_PSET64_LO)); } template<> struct packet_traits<double> : default_packet_traits @@ -753,16 +794,41 @@ template<> struct packet_traits<double> : default_packet_traits Vectorizable = 1, AlignedOnScalar = 1, size=2, - HasHalfPacket = 0, + HasHalfPacket = 1, + HasAdd = 1, + HasSub = 1, + HasMul = 1, HasDiv = 1, + HasMin = 1, + HasMax = 1, + HasAbs = 1, + HasSin = 0, + HasCos = 0, + HasLog = 0, HasExp = 1, - HasSqrt = 0 + HasSqrt = 1, + HasRsqrt = 1, + HasRound = 1, + HasFloor = 1, + HasCeil = 1, + HasNegate = 1, + HasBlend = 1 }; }; template<> struct unpacket_traits<Packet2d> { typedef double type; enum {size=2, alignment=Aligned16}; typedef Packet2d half; }; +inline std::ostream & operator <<(std::ostream & s, const Packet2l & v) +{ + union { + Packet2l v; + int64_t n[2]; + } vt; + vt.v = v; + s << vt.n[0] << ", " << vt.n[1]; + return s; +} inline std::ostream & operator <<(std::ostream & s, const Packet2d & v) { @@ -776,28 +842,43 @@ inline std::ostream & operator <<(std::ostream & s, const Packet2d & v) } // Need to define them first or we get specialization after instantiation errors -template<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from) { EIGEN_DEBUG_ALIGNED_LOAD return (Packet2d) vec_ld(0, (const float *) from); } //FIXME +template<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from) +{ + EIGEN_DEBUG_ALIGNED_LOAD +#ifdef __VSX__ + return vec_vsx_ld(0, from); +#else + return vec_ld(0, from); +#endif +} -template<> EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet2d& from) { EIGEN_DEBUG_ALIGNED_STORE vec_st((Packet4f)from, 0, (float *)to); } +template<> EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet2d& from) +{ + EIGEN_DEBUG_ALIGNED_STORE +#ifdef __VSX__ + vec_vsx_st(from, 0, to); +#else + vec_st(from, 0, to); +#endif +} template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) { - double EIGEN_ALIGN16 af[2]; - af[0] = from; - Packet2d vc = pload<Packet2d>(af); - vc = vec_splat_dbl(vc, 0); - return vc; + Packet2d v = {from, from}; + return v; } + template<> EIGEN_STRONG_INLINE void pbroadcast4<Packet2d>(const double *a, Packet2d& a0, Packet2d& a1, Packet2d& a2, Packet2d& a3) { a1 = pload<Packet2d>(a); - a0 = vec_splat_dbl(a1, 0); - a1 = vec_splat_dbl(a1, 1); + a0 = vec_splat_dbl<0>(a1); + a1 = vec_splat_dbl<1>(a1); a3 = pload<Packet2d>(a+2); - a2 = vec_splat_dbl(a3, 0); - a3 = vec_splat_dbl(a3, 1); + a2 = vec_splat_dbl<0>(a3); + a3 = vec_splat_dbl<1>(a3); } + template<> EIGEN_DEVICE_FUNC inline Packet2d pgather<double, Packet2d>(const double* from, Index stride) { double EIGEN_ALIGN16 af[2]; @@ -812,13 +893,14 @@ template<> EIGEN_DEVICE_FUNC inline void pscatter<double, Packet2d>(double* to, to[0*stride] = af[0]; to[1*stride] = af[1]; } -template<> EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a) { return vec_add(pset1<Packet2d>(a), p2d_COUNTDOWN); } -template<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_add(a,b); } +template<> EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a) { return pset1<Packet2d>(a) + p2d_COUNTDOWN; } + +template<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return a + b; } -template<> EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_sub(a,b); } +template<> EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return a - b; } -template<> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a) { return psub<Packet2d>(p2d_ZERO, a); } +template<> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a) { return p2d_ZERO - a; } template<> EIGEN_STRONG_INLINE Packet2d pconj(const Packet2d& a) { return a; } @@ -840,17 +922,22 @@ template<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const template<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_and(a, vec_nor(b, b)); } +template<> EIGEN_STRONG_INLINE Packet2d pround<Packet2d>(const Packet2d& a) { return vec_round(a); } +template<> EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const Packet2d& a) { return vec_ceil(a); } +template<> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a) { return vec_floor(a); } + template<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from) { EIGEN_DEBUG_ALIGNED_LOAD - return (Packet2d) vec_vsx_ld((long)from & 15, (const float*) _EIGEN_ALIGNED_PTR(from)); + return (Packet2d) vec_vsx_ld((long)from & 15, (const double*) _EIGEN_ALIGNED_PTR(from)); } + template<> EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double* from) { Packet2d p; if((ptrdiff_t(from) % 16) == 0) p = pload<Packet2d>(from); else p = ploadu<Packet2d>(from); - return vec_perm(p, p, p16uc_PSET64_HI); + return vec_splat_dbl<0>(p); } template<> EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet2d& from) @@ -859,32 +946,34 @@ template<> EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet2d& vec_vsx_st((Packet4f)from, (long)to & 15, (float*) _EIGEN_ALIGNED_PTR(to)); } -template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { vec_dstt((const float *) addr, DST_CTRL(2,2,32), DST_CHAN); } +template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { EIGEN_PPC_PREFETCH(addr); } -template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { double EIGEN_ALIGN16 x[2]; pstore(x, a); return x[0]; } - -template<> EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a) { return (Packet2d)vec_perm((Packet16uc)a,(Packet16uc)a, p16uc_REVERSE64); } +template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { double EIGEN_ALIGN16 x[2]; pstore<double>(x, a); return x[0]; } +template<> EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a) +{ + return reinterpret_cast<Packet2d>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE64)); +} template<> EIGEN_STRONG_INLINE Packet2d pabs(const Packet2d& a) { return vec_abs(a); } template<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a) { Packet2d b, sum; - b = (Packet2d) vec_sld((Packet4ui) a, (Packet4ui)a, 8); - sum = vec_add(a, b); - return pfirst(sum); + b = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(a), reinterpret_cast<Packet4f>(a), 8)); + sum = a + b; + return pfirst<Packet2d>(sum); } template<> EIGEN_STRONG_INLINE Packet2d preduxp<Packet2d>(const Packet2d* vecs) { Packet2d v[2], sum; - v[0] = vec_add(vecs[0], (Packet2d) vec_sld((Packet4ui) vecs[0], (Packet4ui) vecs[0], 8)); - v[1] = vec_add(vecs[1], (Packet2d) vec_sld((Packet4ui) vecs[1], (Packet4ui) vecs[1], 8)); + v[0] = vecs[0] + reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(vecs[0]), reinterpret_cast<Packet4f>(vecs[0]), 8)); + v[1] = vecs[1] + reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(vecs[1]), reinterpret_cast<Packet4f>(vecs[1]), 8)); #ifdef _BIG_ENDIAN - sum = (Packet2d) vec_sld((Packet4ui) v[0], (Packet4ui) v[1], 8); + sum = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(v[0]), reinterpret_cast<Packet4f>(v[1]), 8)); #else - sum = (Packet2d) vec_sld((Packet4ui) v[1], (Packet4ui) v[0], 8); + sum = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(v[1]), reinterpret_cast<Packet4f>(v[0]), 8)); #endif return sum; @@ -893,19 +982,19 @@ template<> EIGEN_STRONG_INLINE Packet2d preduxp<Packet2d>(const Packet2d* vecs) // mul template<> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a) { - return pfirst(pmul(a, (Packet2d)vec_sld((Packet4ui) a, (Packet4ui) a, 8))); + return pfirst(pmul(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(a), reinterpret_cast<Packet4ui>(a), 8)))); } // min template<> EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a) { - return pfirst(vec_min(a, (Packet2d) vec_sld((Packet4ui) a, (Packet4ui) a, 8))); + return pfirst(pmin(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(a), reinterpret_cast<Packet4ui>(a), 8)))); } // max template<> EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a) { - return pfirst(vec_max(a, (Packet2d) vec_sld((Packet4ui) a, (Packet4ui) a, 8))); + return pfirst(pmax(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(a), reinterpret_cast<Packet4ui>(a), 8)))); } template<int Offset> @@ -915,9 +1004,9 @@ struct palign_impl<Offset,Packet2d> { if (Offset == 1) #ifdef _BIG_ENDIAN - first = (Packet2d) vec_sld((Packet4ui) first, (Packet4ui) second, 8); + first = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(first), reinterpret_cast<Packet4ui>(second), 8)); #else - first = (Packet2d) vec_sld((Packet4ui) second, (Packet4ui) first, 8); + first = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(second), reinterpret_cast<Packet4ui>(first), 8)); #endif } }; @@ -931,6 +1020,11 @@ ptranspose(PacketBlock<Packet2d,2>& kernel) { kernel.packet[1] = t1; } +template<> EIGEN_STRONG_INLINE Packet2d pblend(const Selector<2>& ifPacket, const Packet2d& thenPacket, const Packet2d& elsePacket) { + Packet2l select = { ifPacket.select[0], ifPacket.select[1] }; + Packet2bl mask = vec_cmpeq(reinterpret_cast<Packet2d>(select), reinterpret_cast<Packet2d>(p2l_ONE)); + return vec_sel(elsePacket, thenPacket, mask); +} #endif // __VSX__ } // end namespace internal diff --git a/Eigen/src/Core/arch/CUDA/Half.h b/Eigen/src/Core/arch/CUDA/Half.h index 87bdbfd1e..9df7c2f69 100644 --- a/Eigen/src/Core/arch/CUDA/Half.h +++ b/Eigen/src/Core/arch/CUDA/Half.h @@ -1,11 +1,3 @@ -// Standard 16-bit float type, mostly useful for GPUs. Defines a new -// class Eigen::half (inheriting from CUDA's __half struct) with -// operator overloads such that it behaves basically as an arithmetic -// type. It will be quite slow on CPUs (so it is recommended to stay -// in fp32 for CPUs, except for simple parameter conversions, I/O -// to disk and the likes), but fast on GPUs. -// -// // This file is part of Eigen, a lightweight C++ template library // for linear algebra. // @@ -32,6 +24,15 @@ // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +// Standard 16-bit float type, mostly useful for GPUs. Defines a new +// type Eigen::half (inheriting from CUDA's __half struct) with +// operator overloads such that it behaves basically as an arithmetic +// type. It will be quite slow on CPUs (so it is recommended to stay +// in fp32 for CPUs, except for simple parameter conversions, I/O +// to disk and the likes), but fast on GPUs. + + #ifndef EIGEN_HALF_CUDA_H #define EIGEN_HALF_CUDA_H @@ -42,6 +43,10 @@ #endif +namespace Eigen { + +namespace half_impl { + #if !defined(EIGEN_HAS_CUDA_FP16) // Make our own __half definition that is similar to CUDA's. @@ -53,16 +58,10 @@ struct __half { #endif -namespace Eigen { - -namespace internal { - EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half raw_uint16_to_half(unsigned short x); EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half float_to_half_rtne(float ff); EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC float half_to_float(__half h); -} // end namespace internal - // Class definition. struct half : public __half { EIGEN_DEVICE_FUNC half() {} @@ -71,52 +70,52 @@ struct half : public __half { EIGEN_DEVICE_FUNC half(const half& h) : __half(h) {} explicit EIGEN_DEVICE_FUNC half(bool b) - : __half(internal::raw_uint16_to_half(b ? 0x3c00 : 0)) {} + : __half(raw_uint16_to_half(b ? 0x3c00 : 0)) {} template<class T> explicit EIGEN_DEVICE_FUNC half(const T& val) - : __half(internal::float_to_half_rtne(static_cast<float>(val))) {} + : __half(float_to_half_rtne(static_cast<float>(val))) {} explicit EIGEN_DEVICE_FUNC half(float f) - : __half(internal::float_to_half_rtne(f)) {} + : __half(float_to_half_rtne(f)) {} EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(bool) const { // +0.0 and -0.0 become false, everything else becomes true. return (x & 0x7fff) != 0; } EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(signed char) const { - return static_cast<signed char>(internal::half_to_float(*this)); + return static_cast<signed char>(half_to_float(*this)); } EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(unsigned char) const { - return static_cast<unsigned char>(internal::half_to_float(*this)); + return static_cast<unsigned char>(half_to_float(*this)); } EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(short) const { - return static_cast<short>(internal::half_to_float(*this)); + return static_cast<short>(half_to_float(*this)); } EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(unsigned short) const { - return static_cast<unsigned short>(internal::half_to_float(*this)); + return static_cast<unsigned short>(half_to_float(*this)); } EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(int) const { - return static_cast<int>(internal::half_to_float(*this)); + return static_cast<int>(half_to_float(*this)); } EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(unsigned int) const { - return static_cast<unsigned int>(internal::half_to_float(*this)); + return static_cast<unsigned int>(half_to_float(*this)); } EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(long) const { - return static_cast<long>(internal::half_to_float(*this)); + return static_cast<long>(half_to_float(*this)); } EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(unsigned long) const { - return static_cast<unsigned long>(internal::half_to_float(*this)); + return static_cast<unsigned long>(half_to_float(*this)); } EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(long long) const { - return static_cast<long long>(internal::half_to_float(*this)); + return static_cast<long long>(half_to_float(*this)); } EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(unsigned long long) const { - return static_cast<unsigned long long>(internal::half_to_float(*this)); + return static_cast<unsigned long long>(half_to_float(*this)); } EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(float) const { - return internal::half_to_float(*this); + return half_to_float(*this); } EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(double) const { - return static_cast<double>(internal::half_to_float(*this)); + return static_cast<double>(half_to_float(*this)); } EIGEN_DEVICE_FUNC half& operator=(const half& other) { @@ -246,7 +245,7 @@ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator >= (const half& a, const hal // Division by an index. Do it in full float precision to avoid accuracy // issues in converting the denominator to half. EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator / (const half& a, Index b) { - return Eigen::half(static_cast<float>(a) / static_cast<float>(b)); + return half(static_cast<float>(a) / static_cast<float>(b)); } // Conversion routines, including fallbacks for the host or older CUDA. @@ -254,8 +253,6 @@ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator / (const half& a, Index b) { // these in hardware. If we need more performance on older/other CPUs, they are // also possible to vectorize directly. -namespace internal { - EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half raw_uint16_to_half(unsigned short x) { __half h; h.x = x; @@ -351,92 +348,62 @@ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC float half_to_float(__half h) { #endif } -} // end namespace internal - -// Traits. - -namespace internal { - -template<> struct is_arithmetic<half> { enum { value = true }; }; - -} // end namespace internal +// --- standard functions --- -template<> struct NumTraits<Eigen::half> - : GenericNumTraits<Eigen::half> -{ - EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half epsilon() { - return internal::raw_uint16_to_half(0x0800); - } - EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half dummy_precision() { return half(1e-2f); } - EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half highest() { - return internal::raw_uint16_to_half(0x7bff); - } - EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half lowest() { - return internal::raw_uint16_to_half(0xfbff); - } - EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half infinity() { - return internal::raw_uint16_to_half(0x7c00); - } - EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half quiet_NaN() { - return internal::raw_uint16_to_half(0x7c01); - } -}; - -// Infinity/NaN checks. - -namespace numext { - -EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isinf)(const Eigen::half& a) { +EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isinf)(const half& a) { return (a.x & 0x7fff) == 0x7c00; } -EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isnan)(const Eigen::half& a) { +EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isnan)(const half& a) { #if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 530 return __hisnan(a); #else return (a.x & 0x7fff) > 0x7c00; #endif } -EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isfinite)(const Eigen::half& a) { - return !(Eigen::numext::isinf)(a) && !(Eigen::numext::isnan)(a); +EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isfinite)(const half& a) { + return !(isinf EIGEN_NOT_A_MACRO (a)) && !(isnan EIGEN_NOT_A_MACRO (a)); } -template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half abs(const Eigen::half& a) { - Eigen::half result; +EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half abs(const half& a) { + half result; result.x = a.x & 0x7FFF; return result; } -template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half exp(const Eigen::half& a) { - return Eigen::half(::expf(float(a))); +EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half exp(const half& a) { + return half(::expf(float(a))); } -template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half log(const Eigen::half& a) { - return Eigen::half(::logf(float(a))); +EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log(const half& a) { + return half(::logf(float(a))); } -template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half sqrt(const Eigen::half& a) { - return Eigen::half(::sqrtf(float(a))); +EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log10(const half& a) { + return half(::log10f(float(a))); } -template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half pow(const Eigen::half& a, const Eigen::half& b) { - return Eigen::half(::powf(float(a), float(b))); +EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half sqrt(const half& a) { + return half(::sqrtf(float(a))); } -template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half sin(const Eigen::half& a) { - return Eigen::half(::sinf(float(a))); +EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half pow(const half& a, const half& b) { + return half(::powf(float(a), float(b))); } -template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half cos(const Eigen::half& a) { - return Eigen::half(::cosf(float(a))); +EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half sin(const half& a) { + return half(::sinf(float(a))); } -template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half tan(const Eigen::half& a) { - return Eigen::half(::tanf(float(a))); +EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half cos(const half& a) { + return half(::cosf(float(a))); } -template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half tanh(const Eigen::half& a) { - return Eigen::half(::tanhf(float(a))); +EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half tan(const half& a) { + return half(::tanf(float(a))); } -template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half floor(const Eigen::half& a) { - return Eigen::half(::floorf(float(a))); +EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half tanh(const half& a) { + return half(::tanhf(float(a))); } -template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half ceil(const Eigen::half& a) { - return Eigen::half(::ceilf(float(a))); +EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half floor(const half& a) { + return half(::floorf(float(a))); +} +EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half ceil(const half& a) { + return half(::ceilf(float(a))); } -template <> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half mini(const Eigen::half& a, const Eigen::half& b) { +EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half (min)(const half& a, const half& b) { #if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 530 return __hlt(b, a) ? b : a; #else @@ -445,7 +412,7 @@ template <> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half mini(const Eigen:: return f2 < f1 ? b : a; #endif } -template <> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half maxi(const Eigen::half& a, const Eigen::half& b) { +EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half (max)(const half& a, const half& b) { #if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 530 return __hlt(a, b) ? b : a; #else @@ -455,40 +422,59 @@ template <> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half maxi(const Eigen:: #endif } -#if EIGEN_HAS_C99_MATH -template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half lgamma(const Eigen::half& a) { - return Eigen::half(Eigen::numext::lgamma(static_cast<float>(a))); -} -template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half digamma(const Eigen::half& a) { - return Eigen::half(Eigen::numext::digamma(static_cast<float>(a))); -} -template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half zeta(const Eigen::half& x, const Eigen::half& q) { - return Eigen::half(Eigen::numext::zeta(static_cast<float>(x), static_cast<float>(q))); -} -template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half polygamma(const Eigen::half& n, const Eigen::half& x) { - return Eigen::half(Eigen::numext::polygamma(static_cast<float>(n), static_cast<float>(x))); -} -template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half erf(const Eigen::half& a) { - return Eigen::half(Eigen::numext::erf(static_cast<float>(a))); -} -template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half erfc(const Eigen::half& a) { - return Eigen::half(Eigen::numext::erfc(static_cast<float>(a))); -} -template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half igamma(const Eigen::half& a, const Eigen::half& x) { - return Eigen::half(Eigen::numext::igamma(static_cast<float>(a), static_cast<float>(x))); -} -template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half igammac(const Eigen::half& a, const Eigen::half& x) { - return Eigen::half(Eigen::numext::igammac(static_cast<float>(a), static_cast<float>(x))); -} -template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half betainc(const Eigen::half& a, const Eigen::half& b, const Eigen::half& x) { - return Eigen::half(Eigen::numext::betainc(static_cast<float>(a), static_cast<float>(b), static_cast<float>(x))); +EIGEN_ALWAYS_INLINE std::ostream& operator << (std::ostream& os, const half& v) { + os << static_cast<float>(v); + return os; } -#endif -} // end namespace numext + +} // end namespace half_impl + +// import Eigen::half_impl::half into Eigen namespace +using half_impl::half; + +namespace internal { + +template<> +struct random_default_impl<half_impl::half, false, false> +{ + static inline half run(const half& x, const half& y) + { + return x + (y-x) * half(float(std::rand()) / float(RAND_MAX)); + } + static inline half run() + { + return run(half(-1.f), half(1.f)); + } +}; + +template<> struct is_arithmetic<half_impl::half> { enum { value = true }; }; + +} // end namespace internal + +template<> struct NumTraits<Eigen::half_impl::half> + : GenericNumTraits<Eigen::half_impl::half> +{ + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half_impl::half epsilon() { + return half_impl::raw_uint16_to_half(0x0800); + } + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half_impl::half dummy_precision() { return half_impl::half(1e-2f); } + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half_impl::half highest() { + return half_impl::raw_uint16_to_half(0x7bff); + } + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half_impl::half lowest() { + return half_impl::raw_uint16_to_half(0xfbff); + } + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half_impl::half infinity() { + return half_impl::raw_uint16_to_half(0x7c00); + } + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half_impl::half quiet_NaN() { + return half_impl::raw_uint16_to_half(0x7c01); + } +}; } // end namespace Eigen -// Standard mathematical functions and trancendentals. +// C-like standard mathematical functions and trancendentals. EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half fabsh(const Eigen::half& a) { Eigen::half result; result.x = a.x & 0x7FFF; @@ -512,24 +498,9 @@ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half floorh(const Eigen::half& a) { EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half ceilh(const Eigen::half& a) { return Eigen::half(::ceilf(float(a))); } -EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC int (isnan)(const Eigen::half& a) { - return (Eigen::numext::isnan)(a); -} -EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC int (isinf)(const Eigen::half& a) { - return (Eigen::numext::isinf)(a); -} -EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC int (isfinite)(const Eigen::half& a) { - return !(Eigen::numext::isinf)(a) && !(Eigen::numext::isnan)(a); -} - namespace std { -EIGEN_ALWAYS_INLINE ostream& operator << (ostream& os, const Eigen::half& v) { - os << static_cast<float>(v); - return os; -} - #if __cplusplus > 199711L template <> struct hash<Eigen::half> { @@ -552,10 +523,9 @@ __device__ EIGEN_STRONG_INLINE Eigen::half __shfl_xor(Eigen::half var, int laneM // ldg() has an overload for __half, but we also need one for Eigen::half. #if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 350 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half __ldg(const Eigen::half* ptr) { - return Eigen::internal::raw_uint16_to_half( + return Eigen::half_impl::raw_uint16_to_half( __ldg(reinterpret_cast<const unsigned short*>(ptr))); } #endif - #endif // EIGEN_HALF_CUDA_H diff --git a/Eigen/src/Core/arch/CUDA/MathFunctions.h b/Eigen/src/Core/arch/CUDA/MathFunctions.h index 8b5e8204f..5b5bf4c94 100644 --- a/Eigen/src/Core/arch/CUDA/MathFunctions.h +++ b/Eigen/src/Core/arch/CUDA/MathFunctions.h @@ -27,6 +27,7 @@ float4 plog<float4>(const float4& a) template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 plog<double2>(const double2& a) { + using ::log; return make_double2(log(a.x), log(a.y)); } @@ -39,6 +40,7 @@ float4 pexp<float4>(const float4& a) template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pexp<double2>(const double2& a) { + using ::exp; return make_double2(exp(a.x), exp(a.y)); } @@ -51,6 +53,7 @@ float4 psqrt<float4>(const float4& a) template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 psqrt<double2>(const double2& a) { + using ::sqrt; return make_double2(sqrt(a.x), sqrt(a.y)); } @@ -66,138 +69,6 @@ double2 prsqrt<double2>(const double2& a) return make_double2(rsqrt(a.x), rsqrt(a.y)); } -template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE -float4 plgamma<float4>(const float4& a) -{ - return make_float4(lgammaf(a.x), lgammaf(a.y), lgammaf(a.z), lgammaf(a.w)); -} - -template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE -double2 plgamma<double2>(const double2& a) -{ - return make_double2(lgamma(a.x), lgamma(a.y)); -} - -template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE -float4 pdigamma<float4>(const float4& a) -{ - using numext::digamma; - return make_float4(digamma(a.x), digamma(a.y), digamma(a.z), digamma(a.w)); -} - -template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE -double2 pdigamma<double2>(const double2& a) -{ - using numext::digamma; - return make_double2(digamma(a.x), digamma(a.y)); -} - -template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE -float4 pzeta<float4>(const float4& x, const float4& q) -{ - using numext::zeta; - return make_float4(zeta(x.x, q.x), zeta(x.y, q.y), zeta(x.z, q.z), zeta(x.w, q.w)); -} - -template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE -double2 pzeta<double2>(const double2& x, const double2& q) -{ - using numext::zeta; - return make_double2(zeta(x.x, q.x), zeta(x.y, q.y)); -} - -template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE -float4 ppolygamma<float4>(const float4& n, const float4& x) -{ - using numext::polygamma; - return make_float4(polygamma(n.x, x.x), polygamma(n.y, x.y), polygamma(n.z, x.z), polygamma(n.w, x.w)); -} - -template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE -double2 ppolygamma<double2>(const double2& n, const double2& x) -{ - using numext::polygamma; - return make_double2(polygamma(n.x, x.x), polygamma(n.y, x.y)); -} - -template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE -float4 perf<float4>(const float4& a) -{ - return make_float4(erff(a.x), erff(a.y), erff(a.z), erff(a.w)); -} - -template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE -double2 perf<double2>(const double2& a) -{ - return make_double2(erf(a.x), erf(a.y)); -} - -template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE -float4 perfc<float4>(const float4& a) -{ - return make_float4(erfcf(a.x), erfcf(a.y), erfcf(a.z), erfcf(a.w)); -} - -template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE -double2 perfc<double2>(const double2& a) -{ - return make_double2(erfc(a.x), erfc(a.y)); -} - - -template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE -float4 pigamma<float4>(const float4& a, const float4& x) -{ - using numext::igamma; - return make_float4( - igamma(a.x, x.x), - igamma(a.y, x.y), - igamma(a.z, x.z), - igamma(a.w, x.w)); -} - -template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE -double2 pigamma<double2>(const double2& a, const double2& x) -{ - using numext::igamma; - return make_double2(igamma(a.x, x.x), igamma(a.y, x.y)); -} - -template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE -float4 pigammac<float4>(const float4& a, const float4& x) -{ - using numext::igammac; - return make_float4( - igammac(a.x, x.x), - igammac(a.y, x.y), - igammac(a.z, x.z), - igammac(a.w, x.w)); -} - -template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE -double2 pigammac<double2>(const double2& a, const double2& x) -{ - using numext::igammac; - return make_double2(igammac(a.x, x.x), igammac(a.y, x.y)); -} - -template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE -float4 pbetainc<float4>(const float4& a, const float4& b, const float4& x) -{ - using numext::betainc; - return make_float4( - betainc(a.x, b.x, x.x), - betainc(a.y, b.y, x.y), - betainc(a.z, b.z, x.z), - betainc(a.w, b.w, x.w)); -} - -template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE -double2 pbetainc<double2>(const double2& a, const double2& b, const double2& x) -{ - using numext::betainc; - return make_double2(betainc(a.x, b.x, x.x), betainc(a.y, b.y, x.y)); -} #endif diff --git a/Eigen/src/Core/arch/CUDA/PacketMathHalf.h b/Eigen/src/Core/arch/CUDA/PacketMathHalf.h index 959dff886..0bf891d24 100644 --- a/Eigen/src/Core/arch/CUDA/PacketMathHalf.h +++ b/Eigen/src/Core/arch/CUDA/PacketMathHalf.h @@ -228,7 +228,7 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux<half2>(const #else float a1 = __low2float(a); float a2 = __high2float(a); - return Eigen::half(internal::raw_uint16_to_half(__float2half_rn(a1 + a2))); + return Eigen::half(half_impl::raw_uint16_to_half(__float2half_rn(a1 + a2))); #endif } @@ -262,7 +262,7 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_mul<half2>(c #else float a1 = __low2float(a); float a2 = __high2float(a); - return Eigen::half(internal::raw_uint16_to_half(__float2half_rn(a1 * a2))); + return Eigen::half(half_impl::raw_uint16_to_half(__float2half_rn(a1 * a2))); #endif } @@ -372,7 +372,7 @@ template<> EIGEN_STRONG_INLINE Packet8h pset1<Packet8h>(const Eigen::half& from) } template<> EIGEN_STRONG_INLINE Eigen::half pfirst<Packet8h>(const Packet8h& from) { - return raw_uint16_to_half(static_cast<unsigned short>(_mm_extract_epi16(from.x, 0))); + return half_impl::raw_uint16_to_half(static_cast<unsigned short>(_mm_extract_epi16(from.x, 0))); } template<> EIGEN_STRONG_INLINE Packet8h pload<Packet8h>(const Eigen::half* from) { @@ -607,7 +607,7 @@ template<> EIGEN_STRONG_INLINE Packet4h pset1<Packet4h>(const Eigen::half& from) } template<> EIGEN_STRONG_INLINE Eigen::half pfirst<Packet4h>(const Packet4h& from) { - return raw_uint16_to_half(static_cast<unsigned short>(_mm_cvtsi64_si32(from.x))); + return half_impl::raw_uint16_to_half(static_cast<unsigned short>(_mm_cvtsi64_si32(from.x))); } template<> EIGEN_STRONG_INLINE Packet4h pconj(const Packet4h& a) { return a; } @@ -618,17 +618,17 @@ template<> EIGEN_STRONG_INLINE Packet4h padd<Packet4h>(const Packet4h& a, const Eigen::half h[4]; - Eigen::half ha = raw_uint16_to_half(static_cast<unsigned short>(a64)); - Eigen::half hb = raw_uint16_to_half(static_cast<unsigned short>(b64)); + Eigen::half ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64)); + Eigen::half hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64)); h[0] = ha + hb; - ha = raw_uint16_to_half(static_cast<unsigned short>(a64 >> 16)); - hb = raw_uint16_to_half(static_cast<unsigned short>(b64 >> 16)); + ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 16)); + hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 16)); h[1] = ha + hb; - ha = raw_uint16_to_half(static_cast<unsigned short>(a64 >> 32)); - hb = raw_uint16_to_half(static_cast<unsigned short>(b64 >> 32)); + ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 32)); + hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 32)); h[2] = ha + hb; - ha = raw_uint16_to_half(static_cast<unsigned short>(a64 >> 48)); - hb = raw_uint16_to_half(static_cast<unsigned short>(b64 >> 48)); + ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 48)); + hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 48)); h[3] = ha + hb; Packet4h result; result.x = _mm_set_pi16(h[3].x, h[2].x, h[1].x, h[0].x); @@ -641,17 +641,17 @@ template<> EIGEN_STRONG_INLINE Packet4h pmul<Packet4h>(const Packet4h& a, const Eigen::half h[4]; - Eigen::half ha = raw_uint16_to_half(static_cast<unsigned short>(a64)); - Eigen::half hb = raw_uint16_to_half(static_cast<unsigned short>(b64)); + Eigen::half ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64)); + Eigen::half hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64)); h[0] = ha * hb; - ha = raw_uint16_to_half(static_cast<unsigned short>(a64 >> 16)); - hb = raw_uint16_to_half(static_cast<unsigned short>(b64 >> 16)); + ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 16)); + hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 16)); h[1] = ha * hb; - ha = raw_uint16_to_half(static_cast<unsigned short>(a64 >> 32)); - hb = raw_uint16_to_half(static_cast<unsigned short>(b64 >> 32)); + ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 32)); + hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 32)); h[2] = ha * hb; - ha = raw_uint16_to_half(static_cast<unsigned short>(a64 >> 48)); - hb = raw_uint16_to_half(static_cast<unsigned short>(b64 >> 48)); + ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 48)); + hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 48)); h[3] = ha * hb; Packet4h result; result.x = _mm_set_pi16(h[3].x, h[2].x, h[1].x, h[0].x); diff --git a/Eigen/src/Core/arch/NEON/Complex.h b/Eigen/src/Core/arch/NEON/Complex.h index aa9797885..3e121dce5 100644 --- a/Eigen/src/Core/arch/NEON/Complex.h +++ b/Eigen/src/Core/arch/NEON/Complex.h @@ -2,6 +2,7 @@ // for linear algebra. // // Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr> +// Copyright (C) 2010 Konstantinos Margaritis <markos@freevec.org> // // This Source Code Form is subject to the terms of the Mozilla // Public License v. 2.0. If a copy of the MPL was not distributed diff --git a/Eigen/src/Core/arch/NEON/PacketMath.h b/Eigen/src/Core/arch/NEON/PacketMath.h index e1247696d..2a8f58d74 100644 --- a/Eigen/src/Core/arch/NEON/PacketMath.h +++ b/Eigen/src/Core/arch/NEON/PacketMath.h @@ -2,7 +2,7 @@ // for linear algebra. // // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr> -// Copyright (C) 2010 Konstantinos Margaritis <markos@codex.gr> +// Copyright (C) 2010 Konstantinos Margaritis <markos@freevec.org> // Heavily based on Gael's SSE version. // // This Source Code Form is subject to the terms of the Mozilla diff --git a/Eigen/src/Core/arch/ZVector/Complex.h b/Eigen/src/Core/arch/ZVector/Complex.h index 9a8735ac1..e9d83eca6 100644 --- a/Eigen/src/Core/arch/ZVector/Complex.h +++ b/Eigen/src/Core/arch/ZVector/Complex.h @@ -57,21 +57,6 @@ template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex< template<> EIGEN_STRONG_INLINE Packet1cd pset1<Packet1cd>(const std::complex<double>& from) { /* here we really have to use unaligned loads :( */ return ploadu<Packet1cd>(&from); } -template<> EIGEN_DEVICE_FUNC inline Packet1cd pgather<std::complex<double>, Packet1cd>(const std::complex<double>* from, Index stride) -{ - std::complex<double> EIGEN_ALIGN16 af[2]; - af[0] = from[0*stride]; - af[1] = from[1*stride]; - return pload<Packet1cd>(af); -} -template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<double>, Packet1cd>(std::complex<double>* to, const Packet1cd& from, Index stride) -{ - std::complex<double> EIGEN_ALIGN16 af[2]; - pstore<std::complex<double> >(af, from); - to[0*stride] = af[0]; - to[1*stride] = af[1]; -} - template<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v + b.v); } template<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v - b.v); } template<> EIGEN_STRONG_INLINE Packet1cd pnegate(const Packet1cd& a) { return Packet1cd(pnegate(Packet2d(a.v))); } diff --git a/Eigen/src/Core/functors/BinaryFunctors.h b/Eigen/src/Core/functors/BinaryFunctors.h index 2c1331208..dc3690444 100644 --- a/Eigen/src/Core/functors/BinaryFunctors.h +++ b/Eigen/src/Core/functors/BinaryFunctors.h @@ -429,57 +429,6 @@ template<> struct functor_traits<scalar_boolean_xor_op> { }; }; -/** \internal - * \brief Template functor to compute the incomplete gamma function igamma(a, x) - * - * \sa class CwiseBinaryOp, Cwise::igamma - */ -template<typename Scalar> struct scalar_igamma_op : binary_op_base<Scalar,Scalar> -{ - EIGEN_EMPTY_STRUCT_CTOR(scalar_igamma_op) - EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& x) const { - using numext::igamma; return igamma(a, x); - } - template<typename Packet> - EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const { - return internal::pigamma(a, x); - } -}; -template<typename Scalar> -struct functor_traits<scalar_igamma_op<Scalar> > { - enum { - // Guesstimate - Cost = 20 * NumTraits<Scalar>::MulCost + 10 * NumTraits<Scalar>::AddCost, - PacketAccess = packet_traits<Scalar>::HasIGamma - }; -}; - - -/** \internal - * \brief Template functor to compute the complementary incomplete gamma function igammac(a, x) - * - * \sa class CwiseBinaryOp, Cwise::igammac - */ -template<typename Scalar> struct scalar_igammac_op : binary_op_base<Scalar,Scalar> -{ - EIGEN_EMPTY_STRUCT_CTOR(scalar_igammac_op) - EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& x) const { - using numext::igammac; return igammac(a, x); - } - template<typename Packet> - EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const - { - return internal::pigammac(a, x); - } -}; -template<typename Scalar> -struct functor_traits<scalar_igammac_op<Scalar> > { - enum { - // Guesstimate - Cost = 20 * NumTraits<Scalar>::MulCost + 10 * NumTraits<Scalar>::AddCost, - PacketAccess = packet_traits<Scalar>::HasIGammac - }; -}; //---------- binary functors bound to a constant, thus appearing as a unary functor ---------- diff --git a/Eigen/src/Core/functors/TernaryFunctors.h b/Eigen/src/Core/functors/TernaryFunctors.h index 8b9e53062..b254e96c6 100644 --- a/Eigen/src/Core/functors/TernaryFunctors.h +++ b/Eigen/src/Core/functors/TernaryFunctors.h @@ -16,29 +16,7 @@ namespace internal { //---------- associative ternary functors ---------- -/** \internal - * \brief Template functor to compute the incomplete beta integral betainc(a, b, x) - * - */ -template<typename Scalar> struct scalar_betainc_op { - EIGEN_EMPTY_STRUCT_CTOR(scalar_betainc_op) - EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& x, const Scalar& a, const Scalar& b) const { - using numext::betainc; return betainc(x, a, b); - } - template<typename Packet> - EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& x, const Packet& a, const Packet& b) const - { - return internal::pbetainc(x, a, b); - } -}; -template<typename Scalar> -struct functor_traits<scalar_betainc_op<Scalar> > { - enum { - // Guesstimate - Cost = 400 * NumTraits<Scalar>::MulCost + 400 * NumTraits<Scalar>::AddCost, - PacketAccess = packet_traits<Scalar>::HasBetaInc - }; -}; + } // end namespace internal diff --git a/Eigen/src/Core/functors/UnaryFunctors.h b/Eigen/src/Core/functors/UnaryFunctors.h index a7d8c3b52..04208c9fe 100644 --- a/Eigen/src/Core/functors/UnaryFunctors.h +++ b/Eigen/src/Core/functors/UnaryFunctors.h @@ -473,142 +473,6 @@ struct functor_traits<scalar_asin_op<Scalar> > /** \internal - * \brief Template functor to compute the natural log of the absolute - * value of Gamma of a scalar - * \sa class CwiseUnaryOp, Cwise::lgamma() - */ -template<typename Scalar> struct scalar_lgamma_op { - EIGEN_EMPTY_STRUCT_CTOR(scalar_lgamma_op) - EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { - using numext::lgamma; return lgamma(a); - } - typedef typename packet_traits<Scalar>::type Packet; - EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::plgamma(a); } -}; -template<typename Scalar> -struct functor_traits<scalar_lgamma_op<Scalar> > -{ - enum { - // Guesstimate - Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost, - PacketAccess = packet_traits<Scalar>::HasLGamma - }; -}; - -/** \internal - * \brief Template functor to compute psi, the derivative of lgamma of a scalar. - * \sa class CwiseUnaryOp, Cwise::digamma() - */ -template<typename Scalar> struct scalar_digamma_op { - EIGEN_EMPTY_STRUCT_CTOR(scalar_digamma_op) - EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { - using numext::digamma; return digamma(a); - } - typedef typename packet_traits<Scalar>::type Packet; - EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pdigamma(a); } -}; -template<typename Scalar> -struct functor_traits<scalar_digamma_op<Scalar> > -{ - enum { - // Guesstimate - Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost, - PacketAccess = packet_traits<Scalar>::HasDiGamma - }; -}; - -/** \internal - * \brief Template functor to compute the Riemann Zeta function of two arguments. - * \sa class CwiseUnaryOp, Cwise::zeta() - */ -template<typename Scalar> struct scalar_zeta_op { - EIGEN_EMPTY_STRUCT_CTOR(scalar_zeta_op) - EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& x, const Scalar& q) const { - using numext::zeta; return zeta(x, q); - } - typedef typename packet_traits<Scalar>::type Packet; - EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& x, const Packet& q) const { return internal::pzeta(x, q); } -}; -template<typename Scalar> -struct functor_traits<scalar_zeta_op<Scalar> > -{ - enum { - // Guesstimate - Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost, - PacketAccess = packet_traits<Scalar>::HasZeta - }; -}; - -/** \internal - * \brief Template functor to compute the polygamma function. - * \sa class CwiseUnaryOp, Cwise::polygamma() - */ -template<typename Scalar> struct scalar_polygamma_op { - EIGEN_EMPTY_STRUCT_CTOR(scalar_polygamma_op) - EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& n, const Scalar& x) const { - using numext::polygamma; return polygamma(n, x); - } - typedef typename packet_traits<Scalar>::type Packet; - EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& n, const Packet& x) const { return internal::ppolygamma(n, x); } -}; -template<typename Scalar> -struct functor_traits<scalar_polygamma_op<Scalar> > -{ - enum { - // Guesstimate - Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost, - PacketAccess = packet_traits<Scalar>::HasPolygamma - }; -}; - -/** \internal - * \brief Template functor to compute the Gauss error function of a - * scalar - * \sa class CwiseUnaryOp, Cwise::erf() - */ -template<typename Scalar> struct scalar_erf_op { - EIGEN_EMPTY_STRUCT_CTOR(scalar_erf_op) - EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { - using numext::erf; return erf(a); - } - typedef typename packet_traits<Scalar>::type Packet; - EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::perf(a); } -}; -template<typename Scalar> -struct functor_traits<scalar_erf_op<Scalar> > -{ - enum { - // Guesstimate - Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost, - PacketAccess = packet_traits<Scalar>::HasErf - }; -}; - -/** \internal - * \brief Template functor to compute the Complementary Error Function - * of a scalar - * \sa class CwiseUnaryOp, Cwise::erfc() - */ -template<typename Scalar> struct scalar_erfc_op { - EIGEN_EMPTY_STRUCT_CTOR(scalar_erfc_op) - EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { - using numext::erfc; return erfc(a); - } - typedef typename packet_traits<Scalar>::type Packet; - EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::perfc(a); } -}; -template<typename Scalar> -struct functor_traits<scalar_erfc_op<Scalar> > -{ - enum { - // Guesstimate - Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost, - PacketAccess = packet_traits<Scalar>::HasErfc - }; -}; - - -/** \internal * \brief Template functor to compute the atan of a scalar * \sa class CwiseUnaryOp, ArrayBase::atan() */ diff --git a/Eigen/src/Core/products/GeneralBlockPanelKernel.h b/Eigen/src/Core/products/GeneralBlockPanelKernel.h index 63a9fc462..c66882012 100644 --- a/Eigen/src/Core/products/GeneralBlockPanelKernel.h +++ b/Eigen/src/Core/products/GeneralBlockPanelKernel.h @@ -299,16 +299,6 @@ void computeProductBlockingSizes(Index& k, Index& m, Index& n, Index num_threads if (!useSpecificBlockingSizes(k, m, n)) { evaluateProductBlockingSizesHeuristic<LhsScalar, RhsScalar, KcFactor, Index>(k, m, n, num_threads); } - - typedef gebp_traits<LhsScalar,RhsScalar> Traits; - enum { - kr = 8, - mr = Traits::mr, - nr = Traits::nr - }; - if (k > kr) k -= k % kr; - if (m > mr) m -= m % mr; - if (n > nr) n -= n % nr; } template<typename LhsScalar, typename RhsScalar, typename Index> @@ -1536,12 +1526,12 @@ void gebp_kernel<LhsScalar,RhsScalar,Index,DataMapper,mr,nr,ConjugateLhs,Conjuga const RhsScalar* blB = &blockB[j2*strideB+offsetB*nr]; // The following piece of code wont work for 512 bit registers - // Moreover it assumes that there is a half packet of the same size + // Moreover, if LhsProgress==8 it assumes that there is a half packet of the same size // as nr (which is currently 4) for the return type. typedef typename unpacket_traits<SResPacket>::half SResPacketHalf; if ((SwappedTraits::LhsProgress % 4) == 0 && (SwappedTraits::LhsProgress <= 8) && - unpacket_traits<SResPacketHalf>::size==4) + (SwappedTraits::LhsProgress!=8 || unpacket_traits<SResPacketHalf>::size==nr)) { SAccPacket C0, C1, C2, C3; straits.initAcc(C0); diff --git a/Eigen/src/Core/util/BlasUtil.h b/Eigen/src/Core/util/BlasUtil.h index a85ad558f..8b3b44a58 100755 --- a/Eigen/src/Core/util/BlasUtil.h +++ b/Eigen/src/Core/util/BlasUtil.h @@ -111,7 +111,7 @@ template<typename RealScalar,bool Conj> struct conj_helper<RealScalar, std::comp }; template<typename From,typename To> struct get_factor { - EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE To run(const From& x) { return x; } + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE To run(const From& x) { return To(x); } }; template<typename Scalar> struct get_factor<Scalar,typename NumTraits<Scalar>::Real> { diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h index 1c90c0e2b..ea107393a 100644 --- a/Eigen/src/Core/util/ForwardDeclarations.h +++ b/Eigen/src/Core/util/ForwardDeclarations.h @@ -203,15 +203,21 @@ template<typename Scalar> struct scalar_random_op; template<typename Scalar> struct scalar_constant_op; template<typename Scalar> struct scalar_identity_op; template<typename Scalar,bool iscpx> struct scalar_sign_op; -template<typename Scalar> struct scalar_igamma_op; -template<typename Scalar> struct scalar_igammac_op; -template<typename Scalar> struct scalar_betainc_op; - template<typename Scalar,typename ScalarExponent> struct scalar_pow_op; template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_hypot_op; template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_product_op; template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_quotient_op; +// SpecialFunctions module +template<typename Scalar> struct scalar_lgamma_op; +template<typename Scalar> struct scalar_digamma_op; +template<typename Scalar> struct scalar_erf_op; +template<typename Scalar> struct scalar_erfc_op; +template<typename Scalar> struct scalar_igamma_op; +template<typename Scalar> struct scalar_igammac_op; +template<typename Scalar> struct scalar_zeta_op; +template<typename Scalar> struct scalar_betainc_op; + } // end namespace internal struct IOFormat; diff --git a/Eigen/src/Core/util/MKL_support.h b/Eigen/src/Core/util/MKL_support.h index 8c9239b1d..26b59669e 100644..100755 --- a/Eigen/src/Core/util/MKL_support.h +++ b/Eigen/src/Core/util/MKL_support.h @@ -49,7 +49,7 @@ #define EIGEN_USE_LAPACKE #endif -#if defined(EIGEN_USE_LAPACKE) || defined(EIGEN_USE_MKL_VML) +#if defined(EIGEN_USE_MKL_VML) #define EIGEN_USE_MKL #endif @@ -72,7 +72,7 @@ #endif #if defined EIGEN_USE_MKL -#include <mkl_lapacke.h> + #define EIGEN_MKL_VML_THRESHOLD 128 /* MKL_DOMAIN_BLAS, etc are defined only in 10.3 update 7 */ diff --git a/Eigen/src/Core/util/Macros.h b/Eigen/src/Core/util/Macros.h index 6de21d2bb..a7c4ec9a6 100644 --- a/Eigen/src/Core/util/Macros.h +++ b/Eigen/src/Core/util/Macros.h @@ -13,7 +13,7 @@ #define EIGEN_WORLD_VERSION 3 #define EIGEN_MAJOR_VERSION 2 -#define EIGEN_MINOR_VERSION 92 +#define EIGEN_MINOR_VERSION 93 #define EIGEN_VERSION_AT_LEAST(x,y,z) (EIGEN_WORLD_VERSION>x || (EIGEN_WORLD_VERSION>=x && \ (EIGEN_MAJOR_VERSION>y || (EIGEN_MAJOR_VERSION>=y && \ @@ -71,6 +71,15 @@ #define EIGEN_COMP_MSVC 0 #endif +// For the record, here is a table summarizing the possible values for EIGEN_COMP_MSVC: +// name ver MSC_VER +// 2008 9 1500 +// 2010 10 1600 +// 2012 11 1700 +// 2013 12 1800 +// 2015 14 1900 +// "15" 15 1900 + /// \internal EIGEN_COMP_MSVC_STRICT set to 1 if the compiler is really Microsoft Visual C++ and not ,e.g., ICC #if EIGEN_COMP_MSVC && !(EIGEN_COMP_ICC) #define EIGEN_COMP_MSVC_STRICT _MSC_VER @@ -897,6 +906,9 @@ namespace Eigen { return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,OPNAME)(derived(), other.derived()); \ } +#define EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,TYPEA,TYPEB) \ + (Eigen::internal::has_ReturnType<Eigen::ScalarBinaryOpTraits<TYPEA,TYPEB,EIGEN_CAT(EIGEN_CAT(Eigen::internal::scalar_,OPNAME),_op)<TYPEA,TYPEB> > >::value) + #define EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(EXPR,SCALAR,OPNAME) \ CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<typename internal::traits<EXPR>::Scalar,SCALAR>, const EXPR, \ const typename internal::plain_constant_type<EXPR,SCALAR>::type> @@ -905,20 +917,27 @@ namespace Eigen { CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<SCALAR,typename internal::traits<EXPR>::Scalar>, \ const typename internal::plain_constant_type<EXPR,SCALAR>::type, const EXPR> +// Workaround for MSVC 2010 (see ML thread "patch with compile for for MSVC 2010") +#if EIGEN_COMP_MSVC_STRICT<=1600 +#define EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(X) typename internal::enable_if<true,X>::type +#else +#define EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(X) X +#endif + #define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(METHOD,OPNAME) \ template <typename T> EIGEN_DEVICE_FUNC inline \ - const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,typename internal::promote_scalar_arg<Scalar EIGEN_COMMA T EIGEN_COMMA ScalarBinaryOpTraits<Scalar EIGEN_COMMA T EIGEN_COMMA EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<Scalar EIGEN_COMMA T> >::Defined>::type,OPNAME) \ + EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,typename internal::promote_scalar_arg<Scalar EIGEN_COMMA T EIGEN_COMMA EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,Scalar,T)>::type,OPNAME))\ (METHOD)(const T& scalar) const { \ - typedef typename internal::promote_scalar_arg<Scalar,T,ScalarBinaryOpTraits<Scalar,T,EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<Scalar,T> >::Defined>::type PromotedT; \ + typedef typename internal::promote_scalar_arg<Scalar,T,EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,Scalar,T)>::type PromotedT; \ return EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,PromotedT,OPNAME)(derived(), \ typename internal::plain_constant_type<Derived,PromotedT>::type(derived().rows(), derived().cols(), internal::scalar_constant_op<PromotedT>(scalar))); \ } #define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(METHOD,OPNAME) \ template <typename T> EIGEN_DEVICE_FUNC inline friend \ - const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename internal::promote_scalar_arg<Scalar EIGEN_COMMA T EIGEN_COMMA ScalarBinaryOpTraits<T EIGEN_COMMA Scalar EIGEN_COMMA EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<T EIGEN_COMMA Scalar> >::Defined>::type,Derived,OPNAME) \ + EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename internal::promote_scalar_arg<Scalar EIGEN_COMMA T EIGEN_COMMA EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,T,Scalar)>::type,Derived,OPNAME)) \ (METHOD)(const T& scalar, const StorageBaseType& matrix) { \ - typedef typename internal::promote_scalar_arg<Scalar,T,ScalarBinaryOpTraits<T,Scalar,EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<T,Scalar> >::Defined>::type PromotedT; \ + typedef typename internal::promote_scalar_arg<Scalar,T,EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,T,Scalar)>::type PromotedT; \ return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(PromotedT,Derived,OPNAME)( \ typename internal::plain_constant_type<Derived,PromotedT>::type(matrix.derived().rows(), matrix.derived().cols(), internal::scalar_constant_op<PromotedT>(scalar)), matrix.derived()); \ } diff --git a/Eigen/src/Core/util/Meta.h b/Eigen/src/Core/util/Meta.h index 02b3d961a..4b35761e0 100644..100755 --- a/Eigen/src/Core/util/Meta.h +++ b/Eigen/src/Core/util/Meta.h @@ -16,6 +16,10 @@ #include <math_constants.h> #endif +#if EIGEN_COMP_ICC>=1600 && __cplusplus >= 201103L +#include <cstdint> +#endif + namespace Eigen { namespace internal { @@ -29,7 +33,7 @@ namespace internal { // Only recent versions of ICC complain about using ptrdiff_t to hold pointers, // and older versions do not provide *intptr_t types. -#if EIGEN_COMP_ICC>=1600 +#if EIGEN_COMP_ICC>=1600 && __cplusplus >= 201103L typedef std::intptr_t IntPtr; typedef std::uintptr_t UIntPtr; #else @@ -145,7 +149,7 @@ struct is_convertible /** \internal Allows to enable/disable an overload * according to a compile time condition. */ -template<bool Condition, typename T> struct enable_if; +template<bool Condition, typename T=void> struct enable_if; template<typename T> struct enable_if<true,T> { typedef T type; }; @@ -354,6 +358,19 @@ struct result_of<Func(ArgType0,ArgType1,ArgType2)> { }; #endif +// Check whether T::ReturnType does exist +template <typename T> +struct has_ReturnType +{ + typedef char yes[1]; + typedef char no[2]; + + template <typename C> static yes& testFunctor(C const *, typename C::ReturnType const * = 0); + static no& testFunctor(...); + + static const bool value = sizeof(testFunctor(static_cast<T*>(0))) == sizeof(yes); +}; + /** \internal In short, it computes int(sqrt(\a Y)) with \a Y an integer. * Usage example: \code meta_sqrt<1023>::ret \endcode */ @@ -431,67 +448,6 @@ T div_ceil(const T &a, const T &b) } // end namespace numext - -/** \class ScalarBinaryOpTraits - * \ingroup Core_Module - * - * \brief Determines whether the given binary operation of two numeric types is allowed and what the scalar return type is. - * - * \sa CwiseBinaryOp - */ -template<typename ScalarA, typename ScalarB, typename BinaryOp=void> -struct ScalarBinaryOpTraits -#ifndef EIGEN_PARSED_BY_DOXYGEN - // for backward compatibility, use the hints given by the (deprecated) internal::scalar_product_traits class. - : internal::scalar_product_traits<ScalarA,ScalarB> -#endif // EIGEN_PARSED_BY_DOXYGEN -{}; - -template<typename T, typename BinaryOp> -struct ScalarBinaryOpTraits<T,T,BinaryOp> -{ - enum { Defined = 1 }; - typedef T ReturnType; -}; - -// For Matrix * Permutation -template<typename T, typename BinaryOp> -struct ScalarBinaryOpTraits<T,void,BinaryOp> -{ - enum { Defined = 1 }; - typedef T ReturnType; -}; - -// For Permutation * Matrix -template<typename T, typename BinaryOp> -struct ScalarBinaryOpTraits<void,T,BinaryOp> -{ - enum { Defined = 1 }; - typedef T ReturnType; -}; - -// for Permutation*Permutation -template<typename BinaryOp> -struct ScalarBinaryOpTraits<void,void,BinaryOp> -{ - enum { Defined = 1 }; - typedef void ReturnType; -}; - -template<typename T, typename BinaryOp> -struct ScalarBinaryOpTraits<T,std::complex<T>,BinaryOp> -{ - enum { Defined = 1 }; - typedef std::complex<T> ReturnType; -}; - -template<typename T, typename BinaryOp> -struct ScalarBinaryOpTraits<std::complex<T>, T,BinaryOp> -{ - enum { Defined = 1 }; - typedef std::complex<T> ReturnType; -}; - } // end namespace Eigen #endif // EIGEN_META_H diff --git a/Eigen/src/Core/util/XprHelper.h b/Eigen/src/Core/util/XprHelper.h index 2f06c36aa..a98ba6e86 100644 --- a/Eigen/src/Core/util/XprHelper.h +++ b/Eigen/src/Core/util/XprHelper.h @@ -48,7 +48,7 @@ inline IndexDest convert_index(const IndexSrc& idx) { // promote_scalar_arg is an helper used in operation between an expression and a scalar, like: // expression * scalar // Its role is to determine how the type T of the scalar operand should be promoted given the scalar type ExprScalar of the given expression. -// The IsSupported template parameter must be provided by the caller as: ScalarBinaryOpTraits<ExprScalar,T,op>::Defined using the proper order for ExprScalar and T. +// The IsSupported template parameter must be provided by the caller as: internal::has_ReturnType<ScalarBinaryOpTraits<ExprScalar,T,op> >::value using the proper order for ExprScalar and T. // Then the logic is as follows: // - if the operation is natively supported as defined by IsSupported, then the scalar type is not promoted, and T is returned. // - otherwise, NumTraits<ExprScalar>::Literal is returned if T is implicitly convertible to NumTraits<ExprScalar>::Literal AND that this does not imply a float to integer conversion. @@ -708,12 +708,88 @@ std::string demangle_flags(int f) } // end namespace internal + +/** \class ScalarBinaryOpTraits + * \ingroup Core_Module + * + * \brief Determines whether the given binary operation of two numeric types is allowed and what the scalar return type is. + * + * This class permits to control the scalar return type of any binary operation performed on two different scalar types through (partial) template specializations. + * + * For instance, let \c U1, \c U2 and \c U3 be three user defined scalar types for which most operations between instances of \c U1 and \c U2 returns an \c U3. + * You can let Eigen knows that by defining: + \code + template<typename BinaryOp> + struct ScalarBinaryOpTraits<U1,U2,BinaryOp> { typedef U3 ReturnType; }; + template<typename BinaryOp> + struct ScalarBinaryOpTraits<U2,U1,BinaryOp> { typedef U3 ReturnType; }; + \endcode + * You can then explicitly disable some particular operations to get more explicit error messages: + \code + template<> + struct ScalarBinaryOpTraits<U1,U2,internal::scalar_max_op<U1,U2> > {}; + \endcode + * Or customize the return type for individual operation: + \code + template<> + struct ScalarBinaryOpTraits<U1,U2,internal::scalar_sum_op<U1,U2> > { typedef U1 ReturnType; }; + \endcode + * + * \sa CwiseBinaryOp + */ +template<typename ScalarA, typename ScalarB, typename BinaryOp=internal::scalar_product_op<ScalarA,ScalarB> > +struct ScalarBinaryOpTraits +#ifndef EIGEN_PARSED_BY_DOXYGEN + // for backward compatibility, use the hints given by the (deprecated) internal::scalar_product_traits class. + : internal::scalar_product_traits<ScalarA,ScalarB> +#endif // EIGEN_PARSED_BY_DOXYGEN +{}; + +template<typename T, typename BinaryOp> +struct ScalarBinaryOpTraits<T,T,BinaryOp> +{ + typedef T ReturnType; +}; + +// For Matrix * Permutation +template<typename T, typename BinaryOp> +struct ScalarBinaryOpTraits<T,void,BinaryOp> +{ + typedef T ReturnType; +}; + +// For Permutation * Matrix +template<typename T, typename BinaryOp> +struct ScalarBinaryOpTraits<void,T,BinaryOp> +{ + typedef T ReturnType; +}; + +// for Permutation*Permutation +template<typename BinaryOp> +struct ScalarBinaryOpTraits<void,void,BinaryOp> +{ + typedef void ReturnType; +}; + +template<typename T, typename BinaryOp> +struct ScalarBinaryOpTraits<T,std::complex<T>,BinaryOp> +{ + typedef std::complex<T> ReturnType; +}; + +template<typename T, typename BinaryOp> +struct ScalarBinaryOpTraits<std::complex<T>, T,BinaryOp> +{ + typedef std::complex<T> ReturnType; +}; + // We require Lhs and Rhs to have "compatible" scalar types. // It is tempting to always allow mixing different types but remember that this is often impossible in the vectorized paths. // So allowing mixing different types gives very unexpected errors when enabling vectorization, when the user tries to // add together a float matrix and a double matrix. #define EIGEN_CHECK_BINARY_COMPATIBILIY(BINOP,LHS,RHS) \ - EIGEN_STATIC_ASSERT(int(ScalarBinaryOpTraits<LHS, RHS,BINOP>::Defined), \ + EIGEN_STATIC_ASSERT((Eigen::internal::has_ReturnType<ScalarBinaryOpTraits<LHS, RHS,BINOP> >::value), \ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY) } // end namespace Eigen diff --git a/Eigen/src/Eigenvalues/ComplexSchur_MKL.h b/Eigen/src/Eigenvalues/ComplexSchur_LAPACKE.h index a689f768e..4980a3ede 100644 --- a/Eigen/src/Eigenvalues/ComplexSchur_MKL.h +++ b/Eigen/src/Eigenvalues/ComplexSchur_LAPACKE.h @@ -25,21 +25,19 @@ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ******************************************************************************** - * Content : Eigen bindings to Intel(R) MKL + * Content : Eigen bindings to LAPACKe * Complex Schur needed to complex unsymmetrical eigenvalues/eigenvectors. ******************************************************************************** */ -#ifndef EIGEN_COMPLEX_SCHUR_MKL_H -#define EIGEN_COMPLEX_SCHUR_MKL_H - -#include "Eigen/src/Core/util/MKL_support.h" +#ifndef EIGEN_COMPLEX_SCHUR_LAPACKE_H +#define EIGEN_COMPLEX_SCHUR_LAPACKE_H namespace Eigen { -/** \internal Specialization for the data types supported by MKL */ +/** \internal Specialization for the data types supported by LAPACKe */ -#define EIGEN_MKL_SCHUR_COMPLEX(EIGTYPE, MKLTYPE, MKLPREFIX, MKLPREFIX_U, EIGCOLROW, MKLCOLROW) \ +#define EIGEN_LAPACKE_SCHUR_COMPLEX(EIGTYPE, LAPACKE_TYPE, LAPACKE_PREFIX, LAPACKE_PREFIX_U, EIGCOLROW, LAPACKE_COLROW) \ template<> template<typename InputType> inline \ ComplexSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >& \ ComplexSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(const EigenBase<InputType>& matrix, bool computeU) \ @@ -61,9 +59,9 @@ ComplexSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(const Eigen return *this; \ } \ lapack_int n = internal::convert_index<lapack_int>(matrix.cols()), sdim, info; \ - lapack_int matrix_order = MKLCOLROW; \ + lapack_int matrix_order = LAPACKE_COLROW; \ char jobvs, sort='N'; \ - LAPACK_##MKLPREFIX_U##_SELECT1 select = 0; \ + LAPACK_##LAPACKE_PREFIX_U##_SELECT1 select = 0; \ jobvs = (computeU) ? 'V' : 'N'; \ m_matU.resize(n, n); \ lapack_int ldvs = internal::convert_index<lapack_int>(m_matU.outerStride()); \ @@ -71,7 +69,7 @@ ComplexSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(const Eigen lapack_int lda = internal::convert_index<lapack_int>(m_matT.outerStride()); \ Matrix<EIGTYPE, Dynamic, Dynamic> w; \ w.resize(n, 1);\ - info = LAPACKE_##MKLPREFIX##gees( matrix_order, jobvs, sort, select, n, (MKLTYPE*)m_matT.data(), lda, &sdim, (MKLTYPE*)w.data(), (MKLTYPE*)m_matU.data(), ldvs ); \ + info = LAPACKE_##LAPACKE_PREFIX##gees( matrix_order, jobvs, sort, select, n, (LAPACKE_TYPE*)m_matT.data(), lda, &sdim, (LAPACKE_TYPE*)w.data(), (LAPACKE_TYPE*)m_matU.data(), ldvs ); \ if(info == 0) \ m_info = Success; \ else \ @@ -83,11 +81,11 @@ ComplexSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(const Eigen \ } -EIGEN_MKL_SCHUR_COMPLEX(dcomplex, MKL_Complex16, z, Z, ColMajor, LAPACK_COL_MAJOR) -EIGEN_MKL_SCHUR_COMPLEX(scomplex, MKL_Complex8, c, C, ColMajor, LAPACK_COL_MAJOR) -EIGEN_MKL_SCHUR_COMPLEX(dcomplex, MKL_Complex16, z, Z, RowMajor, LAPACK_ROW_MAJOR) -EIGEN_MKL_SCHUR_COMPLEX(scomplex, MKL_Complex8, c, C, RowMajor, LAPACK_ROW_MAJOR) +EIGEN_LAPACKE_SCHUR_COMPLEX(dcomplex, lapack_complex_double, z, Z, ColMajor, LAPACK_COL_MAJOR) +EIGEN_LAPACKE_SCHUR_COMPLEX(scomplex, lapack_complex_float, c, C, ColMajor, LAPACK_COL_MAJOR) +EIGEN_LAPACKE_SCHUR_COMPLEX(dcomplex, lapack_complex_double, z, Z, RowMajor, LAPACK_ROW_MAJOR) +EIGEN_LAPACKE_SCHUR_COMPLEX(scomplex, lapack_complex_float, c, C, RowMajor, LAPACK_ROW_MAJOR) } // end namespace Eigen -#endif // EIGEN_COMPLEX_SCHUR_MKL_H +#endif // EIGEN_COMPLEX_SCHUR_LAPACKE_H diff --git a/Eigen/src/Eigenvalues/EigenSolver.h b/Eigen/src/Eigenvalues/EigenSolver.h index 233e72353..f205b185d 100644 --- a/Eigen/src/Eigenvalues/EigenSolver.h +++ b/Eigen/src/Eigenvalues/EigenSolver.h @@ -324,11 +324,12 @@ template<typename MatrixType> MatrixType EigenSolver<MatrixType>::pseudoEigenvalueMatrix() const { eigen_assert(m_isInitialized && "EigenSolver is not initialized."); + const RealScalar precision = RealScalar(2)*NumTraits<RealScalar>::epsilon(); Index n = m_eivalues.rows(); MatrixType matD = MatrixType::Zero(n,n); for (Index i=0; i<n; ++i) { - if (internal::isMuchSmallerThan(numext::imag(m_eivalues.coeff(i)), numext::real(m_eivalues.coeff(i)))) + if (internal::isMuchSmallerThan(numext::imag(m_eivalues.coeff(i)), numext::real(m_eivalues.coeff(i)), precision)) matD.coeffRef(i,i) = numext::real(m_eivalues.coeff(i)); else { @@ -345,11 +346,12 @@ typename EigenSolver<MatrixType>::EigenvectorsType EigenSolver<MatrixType>::eige { eigen_assert(m_isInitialized && "EigenSolver is not initialized."); eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues."); + const RealScalar precision = RealScalar(2)*NumTraits<RealScalar>::epsilon(); Index n = m_eivec.cols(); EigenvectorsType matV(n,n); for (Index j=0; j<n; ++j) { - if (internal::isMuchSmallerThan(numext::imag(m_eivalues.coeff(j)), numext::real(m_eivalues.coeff(j))) || j+1==n) + if (internal::isMuchSmallerThan(numext::imag(m_eivalues.coeff(j)), numext::real(m_eivalues.coeff(j)), precision) || j+1==n) { // we have a real eigen value matV.col(j) = m_eivec.col(j).template cast<ComplexScalar>(); @@ -451,26 +453,6 @@ EigenSolver<MatrixType>::compute(const EigenBase<InputType>& matrix, bool comput return *this; } -// Complex scalar division. -template<typename Scalar> -std::complex<Scalar> cdiv(const Scalar& xr, const Scalar& xi, const Scalar& yr, const Scalar& yi) -{ - using std::abs; - Scalar r,d; - if (abs(yr) > abs(yi)) - { - r = yi/yr; - d = yr + r*yi; - return std::complex<Scalar>((xr + r*xi)/d, (xi - r*xr)/d); - } - else - { - r = yr/yi; - d = yi + r*yr; - return std::complex<Scalar>((r*xr + xi)/d, (r*xi - xr)/d); - } -} - template<typename MatrixType> void EigenSolver<MatrixType>::doComputeEigenvectors() @@ -557,7 +539,7 @@ void EigenSolver<MatrixType>::doComputeEigenvectors() } else { - std::complex<Scalar> cc = cdiv<Scalar>(Scalar(0),-m_matT.coeff(n-1,n),m_matT.coeff(n-1,n-1)-p,q); + ComplexScalar cc = ComplexScalar(Scalar(0),-m_matT.coeff(n-1,n)) / ComplexScalar(m_matT.coeff(n-1,n-1)-p,q); m_matT.coeffRef(n-1,n-1) = numext::real(cc); m_matT.coeffRef(n-1,n) = numext::imag(cc); } @@ -580,7 +562,7 @@ void EigenSolver<MatrixType>::doComputeEigenvectors() l = i; if (m_eivalues.coeff(i).imag() == RealScalar(0)) { - std::complex<Scalar> cc = cdiv(-ra,-sa,w,q); + ComplexScalar cc = ComplexScalar(-ra,-sa) / ComplexScalar(w,q); m_matT.coeffRef(i,n-1) = numext::real(cc); m_matT.coeffRef(i,n) = numext::imag(cc); } @@ -594,7 +576,7 @@ void EigenSolver<MatrixType>::doComputeEigenvectors() if ((vr == Scalar(0)) && (vi == Scalar(0))) vr = eps * norm * (abs(w) + abs(q) + abs(x) + abs(y) + abs(lastw)); - std::complex<Scalar> cc = cdiv(x*lastra-lastw*ra+q*sa,x*lastsa-lastw*sa-q*ra,vr,vi); + ComplexScalar cc = ComplexScalar(x*lastra-lastw*ra+q*sa,x*lastsa-lastw*sa-q*ra) / ComplexScalar(vr,vi); m_matT.coeffRef(i,n-1) = numext::real(cc); m_matT.coeffRef(i,n) = numext::imag(cc); if (abs(x) > (abs(lastw) + abs(q))) @@ -604,7 +586,7 @@ void EigenSolver<MatrixType>::doComputeEigenvectors() } else { - cc = cdiv(-lastra-y*m_matT.coeff(i,n-1),-lastsa-y*m_matT.coeff(i,n),lastw,q); + cc = ComplexScalar(-lastra-y*m_matT.coeff(i,n-1),-lastsa-y*m_matT.coeff(i,n)) / ComplexScalar(lastw,q); m_matT.coeffRef(i+1,n-1) = numext::real(cc); m_matT.coeffRef(i+1,n) = numext::imag(cc); } diff --git a/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h b/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h index 650617ca7..6eeeb174e 100644 --- a/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h +++ b/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h @@ -310,6 +310,7 @@ GeneralizedEigenSolver<MatrixType>::compute(const MatrixType& A, const MatrixTyp if (m_realQZ.info() == Success) { m_matS = m_realQZ.matrixS(); + const MatrixType &matT = m_realQZ.matrixT(); if (computeEigenvectors) m_eivec = m_realQZ.matrixZ().transpose(); @@ -322,7 +323,7 @@ GeneralizedEigenSolver<MatrixType>::compute(const MatrixType& A, const MatrixTyp if (i == A.cols() - 1 || m_matS.coeff(i+1, i) == Scalar(0)) { m_alphas.coeffRef(i) = m_matS.coeff(i, i); - m_betas.coeffRef(i) = m_realQZ.matrixT().coeff(i,i); + m_betas.coeffRef(i) = matT.coeff(i,i); ++i; } else @@ -332,7 +333,9 @@ GeneralizedEigenSolver<MatrixType>::compute(const MatrixType& A, const MatrixTyp // T = [a 0] // [0 b] - RealScalar a = m_realQZ.matrixT().coeff(i, i), b = m_realQZ.matrixT().coeff(i+1, i+1); + RealScalar a = matT.diagonal().coeff(i), + b = matT.diagonal().coeff(i+1); + // ^^ NOTE: using diagonal()(i) instead of coeff(i,i) workarounds a MSVC bug. Matrix<RealScalar,2,2> S2 = m_matS.template block<2,2>(i,i) * Matrix<Scalar,2,1>(b,a).asDiagonal(); Scalar p = Scalar(0.5) * (S2.coeff(0,0) - S2.coeff(1,1)); diff --git a/Eigen/src/Eigenvalues/RealSchur.h b/Eigen/src/Eigenvalues/RealSchur.h index f4ded69b6..9d9063004 100644 --- a/Eigen/src/Eigenvalues/RealSchur.h +++ b/Eigen/src/Eigenvalues/RealSchur.h @@ -236,7 +236,7 @@ template<typename _MatrixType> class RealSchur typedef Matrix<Scalar,3,1> Vector3s; Scalar computeNormOfT(); - Index findSmallSubdiagEntry(Index iu); + Index findSmallSubdiagEntry(Index iu, const Scalar& maxDiagEntry); void splitOffTwoRows(Index iu, bool computeU, const Scalar& exshift); void computeShift(Index iu, Index iter, Scalar& exshift, Vector3s& shiftInfo); void initFrancisQRStep(Index il, Index iu, const Vector3s& shiftInfo, Index& im, Vector3s& firstHouseholderVector); @@ -253,19 +253,25 @@ RealSchur<MatrixType>& RealSchur<MatrixType>::compute(const EigenBase<InputType> if (maxIters == -1) maxIters = m_maxIterationsPerRow * matrix.rows(); + Scalar scale = matrix.derived().cwiseAbs().maxCoeff(); + // Step 1. Reduce to Hessenberg form - m_hess.compute(matrix.derived()); + m_hess.compute(matrix.derived()/scale); // Step 2. Reduce to real Schur form computeFromHessenberg(m_hess.matrixH(), m_hess.matrixQ(), computeU); + + m_matT *= scale; return *this; } template<typename MatrixType> template<typename HessMatrixType, typename OrthMatrixType> RealSchur<MatrixType>& RealSchur<MatrixType>::computeFromHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ, bool computeU) -{ - m_matT = matrixH; +{ + using std::abs; + + m_matT = matrixH; if(computeU) m_matU = matrixQ; @@ -287,14 +293,18 @@ RealSchur<MatrixType>& RealSchur<MatrixType>::computeFromHessenberg(const HessMa if(norm!=0) { + Scalar maxDiagEntry = m_matT.cwiseAbs().diagonal().maxCoeff(); + while (iu >= 0) { - Index il = findSmallSubdiagEntry(iu); + Index il = findSmallSubdiagEntry(iu,maxDiagEntry); // Check for convergence if (il == iu) // One root found { m_matT.coeffRef(iu,iu) = m_matT.coeff(iu,iu) + exshift; + // keep track of the largest diagonal coefficient + maxDiagEntry = numext::maxi<Scalar>(maxDiagEntry,abs(m_matT.coeffRef(iu,iu))); if (iu > 0) m_matT.coeffRef(iu, iu-1) = Scalar(0); iu--; @@ -303,6 +313,8 @@ RealSchur<MatrixType>& RealSchur<MatrixType>::computeFromHessenberg(const HessMa else if (il == iu-1) // Two roots found { splitOffTwoRows(iu, computeU, exshift); + // keep track of the largest diagonal coefficient + maxDiagEntry = numext::maxi<Scalar>(maxDiagEntry,numext::maxi(abs(m_matT.coeff(iu,iu)), abs(m_matT.coeff(iu-1,iu-1)))); iu -= 2; iter = 0; } @@ -317,6 +329,8 @@ RealSchur<MatrixType>& RealSchur<MatrixType>::computeFromHessenberg(const HessMa Index im; initFrancisQRStep(il, iu, shiftInfo, im, firstHouseholderVector); performFrancisQRStep(il, im, iu, computeU, firstHouseholderVector, workspace); + // keep track of the largest diagonal coefficient + maxDiagEntry = numext::maxi(maxDiagEntry,m_matT.cwiseAbs().diagonal().segment(im,iu-im).maxCoeff()); } } } @@ -346,14 +360,13 @@ inline typename MatrixType::Scalar RealSchur<MatrixType>::computeNormOfT() /** \internal Look for single small sub-diagonal element and returns its index */ template<typename MatrixType> -inline Index RealSchur<MatrixType>::findSmallSubdiagEntry(Index iu) +inline Index RealSchur<MatrixType>::findSmallSubdiagEntry(Index iu, const Scalar& maxDiagEntry) { using std::abs; Index res = iu; while (res > 0) { - Scalar s = abs(m_matT.coeff(res-1,res-1)) + abs(m_matT.coeff(res,res)); - if (abs(m_matT.coeff(res,res-1)) <= NumTraits<Scalar>::epsilon() * s) + if (abs(m_matT.coeff(res,res-1)) <= NumTraits<Scalar>::epsilon() * maxDiagEntry) break; res--; } diff --git a/Eigen/src/Eigenvalues/RealSchur_MKL.h b/Eigen/src/Eigenvalues/RealSchur_LAPACKE.h index 1ca30cc16..2c2251715 100644 --- a/Eigen/src/Eigenvalues/RealSchur_MKL.h +++ b/Eigen/src/Eigenvalues/RealSchur_LAPACKE.h @@ -25,21 +25,19 @@ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ******************************************************************************** - * Content : Eigen bindings to Intel(R) MKL + * Content : Eigen bindings to LAPACKe * Real Schur needed to real unsymmetrical eigenvalues/eigenvectors. ******************************************************************************** */ -#ifndef EIGEN_REAL_SCHUR_MKL_H -#define EIGEN_REAL_SCHUR_MKL_H - -#include "Eigen/src/Core/util/MKL_support.h" +#ifndef EIGEN_REAL_SCHUR_LAPACKE_H +#define EIGEN_REAL_SCHUR_LAPACKE_H namespace Eigen { -/** \internal Specialization for the data types supported by MKL */ +/** \internal Specialization for the data types supported by LAPACKe */ -#define EIGEN_MKL_SCHUR_REAL(EIGTYPE, MKLTYPE, MKLPREFIX, MKLPREFIX_U, EIGCOLROW, MKLCOLROW) \ +#define EIGEN_LAPACKE_SCHUR_REAL(EIGTYPE, LAPACKE_TYPE, LAPACKE_PREFIX, LAPACKE_PREFIX_U, EIGCOLROW, LAPACKE_COLROW) \ template<> template<typename InputType> inline \ RealSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >& \ RealSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(const EigenBase<InputType>& matrix, bool computeU) \ @@ -47,9 +45,9 @@ RealSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(const EigenBas eigen_assert(matrix.cols() == matrix.rows()); \ \ lapack_int n = internal::convert_index<lapack_int>(matrix.cols()), sdim, info; \ - lapack_int matrix_order = MKLCOLROW; \ + lapack_int matrix_order = LAPACKE_COLROW; \ char jobvs, sort='N'; \ - LAPACK_##MKLPREFIX_U##_SELECT2 select = 0; \ + LAPACK_##LAPACKE_PREFIX_U##_SELECT2 select = 0; \ jobvs = (computeU) ? 'V' : 'N'; \ m_matU.resize(n, n); \ lapack_int ldvs = internal::convert_index<lapack_int>(m_matU.outerStride()); \ @@ -57,7 +55,7 @@ RealSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(const EigenBas lapack_int lda = internal::convert_index<lapack_int>(m_matT.outerStride()); \ Matrix<EIGTYPE, Dynamic, Dynamic> wr, wi; \ wr.resize(n, 1); wi.resize(n, 1); \ - info = LAPACKE_##MKLPREFIX##gees( matrix_order, jobvs, sort, select, n, (MKLTYPE*)m_matT.data(), lda, &sdim, (MKLTYPE*)wr.data(), (MKLTYPE*)wi.data(), (MKLTYPE*)m_matU.data(), ldvs ); \ + info = LAPACKE_##LAPACKE_PREFIX##gees( matrix_order, jobvs, sort, select, n, (LAPACKE_TYPE*)m_matT.data(), lda, &sdim, (LAPACKE_TYPE*)wr.data(), (LAPACKE_TYPE*)wi.data(), (LAPACKE_TYPE*)m_matU.data(), ldvs ); \ if(info == 0) \ m_info = Success; \ else \ @@ -69,11 +67,11 @@ RealSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(const EigenBas \ } -EIGEN_MKL_SCHUR_REAL(double, double, d, D, ColMajor, LAPACK_COL_MAJOR) -EIGEN_MKL_SCHUR_REAL(float, float, s, S, ColMajor, LAPACK_COL_MAJOR) -EIGEN_MKL_SCHUR_REAL(double, double, d, D, RowMajor, LAPACK_ROW_MAJOR) -EIGEN_MKL_SCHUR_REAL(float, float, s, S, RowMajor, LAPACK_ROW_MAJOR) +EIGEN_LAPACKE_SCHUR_REAL(double, double, d, D, ColMajor, LAPACK_COL_MAJOR) +EIGEN_LAPACKE_SCHUR_REAL(float, float, s, S, ColMajor, LAPACK_COL_MAJOR) +EIGEN_LAPACKE_SCHUR_REAL(double, double, d, D, RowMajor, LAPACK_ROW_MAJOR) +EIGEN_LAPACKE_SCHUR_REAL(float, float, s, S, RowMajor, LAPACK_ROW_MAJOR) } // end namespace Eigen -#endif // EIGEN_REAL_SCHUR_MKL_H +#endif // EIGEN_REAL_SCHUR_LAPACKE_H diff --git a/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h index f96fe698e..8258fadbf 100644 --- a/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h +++ b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h @@ -492,11 +492,12 @@ ComputationInfo computeFromTridiagonal_impl(DiagType& diag, SubDiagType& subdiag typedef typename DiagType::RealScalar RealScalar; const RealScalar considerAsZero = (std::numeric_limits<RealScalar>::min)(); + const RealScalar precision = RealScalar(2)*NumTraits<RealScalar>::epsilon(); while (end>0) { for (Index i = start; i<end; ++i) - if (internal::isMuchSmallerThan(abs(subdiag[i]),(abs(diag[i])+abs(diag[i+1]))) || abs(subdiag[i]) <= considerAsZero) + if (internal::isMuchSmallerThan(abs(subdiag[i]),(abs(diag[i])+abs(diag[i+1])),precision) || abs(subdiag[i]) <= considerAsZero) subdiag[i] = 0; // find the largest unreduced block @@ -739,14 +740,18 @@ struct direct_selfadjoint_eigenvalues<SolverType,2,false> EigenvectorsType& eivecs = solver.m_eivec; VectorType& eivals = solver.m_eivalues; - // map the matrix coefficients to [-1:1] to avoid over- and underflow. - Scalar scale = mat.cwiseAbs().maxCoeff(); - scale = numext::maxi(scale,Scalar(1)); - MatrixType scaledMat = mat / scale; - + // Shift the matrix to the mean eigenvalue and map the matrix coefficients to [-1:1] to avoid over- and underflow. + Scalar shift = mat.trace() / Scalar(2); + MatrixType scaledMat = mat; + scaledMat.coeffRef(0,1) = mat.coeff(1,0); + scaledMat.diagonal().array() -= shift; + Scalar scale = scaledMat.cwiseAbs().maxCoeff(); + if(scale > Scalar(0)) + scaledMat /= scale; + // Compute the eigenvalues computeRoots(scaledMat,eivals); - + // compute the eigen vectors if(computeEigenvectors) { @@ -774,10 +779,11 @@ struct direct_selfadjoint_eigenvalues<SolverType,2,false> eivecs.col(0) << eivecs.col(1).unitOrthogonal(); } } - + // Rescale back to the original size. eivals *= scale; - + eivals.array() += shift; + solver.m_info = Success; solver.m_isInitialized = true; solver.m_eigenvectorsOk = computeEigenvectors; diff --git a/Eigen/src/Eigenvalues/SelfAdjointEigenSolver_MKL.h b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver_LAPACKE.h index b75de1734..3891cf883 100644 --- a/Eigen/src/Eigenvalues/SelfAdjointEigenSolver_MKL.h +++ b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver_LAPACKE.h @@ -25,21 +25,19 @@ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ******************************************************************************** - * Content : Eigen bindings to Intel(R) MKL + * Content : Eigen bindings to LAPACKe * Self-adjoint eigenvalues/eigenvectors. ******************************************************************************** */ -#ifndef EIGEN_SAEIGENSOLVER_MKL_H -#define EIGEN_SAEIGENSOLVER_MKL_H - -#include "Eigen/src/Core/util/MKL_support.h" +#ifndef EIGEN_SAEIGENSOLVER_LAPACKE_H +#define EIGEN_SAEIGENSOLVER_LAPACKE_H namespace Eigen { -/** \internal Specialization for the data types supported by MKL */ +/** \internal Specialization for the data types supported by LAPACKe */ -#define EIGEN_MKL_EIG_SELFADJ(EIGTYPE, MKLTYPE, MKLRTYPE, MKLNAME, EIGCOLROW, MKLCOLROW ) \ +#define EIGEN_LAPACKE_EIG_SELFADJ(EIGTYPE, LAPACKE_TYPE, LAPACKE_RTYPE, LAPACKE_NAME, EIGCOLROW, LAPACKE_COLROW ) \ template<> template<typename InputType> inline \ SelfAdjointEigenSolver<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >& \ SelfAdjointEigenSolver<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(const EigenBase<InputType>& matrix, int options) \ @@ -65,11 +63,11 @@ SelfAdjointEigenSolver<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(c } \ \ lda = internal::convert_index<lapack_int>(m_eivec.outerStride()); \ - matrix_order=MKLCOLROW; \ + matrix_order=LAPACKE_COLROW; \ char jobz, uplo='L'/*, range='A'*/; \ jobz = computeEigenvectors ? 'V' : 'N'; \ \ - info = LAPACKE_##MKLNAME( matrix_order, jobz, uplo, n, (MKLTYPE*)m_eivec.data(), lda, (MKLRTYPE*)m_eivalues.data() ); \ + info = LAPACKE_##LAPACKE_NAME( matrix_order, jobz, uplo, n, (LAPACKE_TYPE*)m_eivec.data(), lda, (LAPACKE_RTYPE*)m_eivalues.data() ); \ m_info = (info==0) ? Success : NoConvergence; \ m_isInitialized = true; \ m_eigenvectorsOk = computeEigenvectors; \ @@ -77,15 +75,15 @@ SelfAdjointEigenSolver<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(c } -EIGEN_MKL_EIG_SELFADJ(double, double, double, dsyev, ColMajor, LAPACK_COL_MAJOR) -EIGEN_MKL_EIG_SELFADJ(float, float, float, ssyev, ColMajor, LAPACK_COL_MAJOR) -EIGEN_MKL_EIG_SELFADJ(dcomplex, MKL_Complex16, double, zheev, ColMajor, LAPACK_COL_MAJOR) -EIGEN_MKL_EIG_SELFADJ(scomplex, MKL_Complex8, float, cheev, ColMajor, LAPACK_COL_MAJOR) +EIGEN_LAPACKE_EIG_SELFADJ(double, double, double, dsyev, ColMajor, LAPACK_COL_MAJOR) +EIGEN_LAPACKE_EIG_SELFADJ(float, float, float, ssyev, ColMajor, LAPACK_COL_MAJOR) +EIGEN_LAPACKE_EIG_SELFADJ(dcomplex, lapack_complex_double, double, zheev, ColMajor, LAPACK_COL_MAJOR) +EIGEN_LAPACKE_EIG_SELFADJ(scomplex, lapack_complex_float, float, cheev, ColMajor, LAPACK_COL_MAJOR) -EIGEN_MKL_EIG_SELFADJ(double, double, double, dsyev, RowMajor, LAPACK_ROW_MAJOR) -EIGEN_MKL_EIG_SELFADJ(float, float, float, ssyev, RowMajor, LAPACK_ROW_MAJOR) -EIGEN_MKL_EIG_SELFADJ(dcomplex, MKL_Complex16, double, zheev, RowMajor, LAPACK_ROW_MAJOR) -EIGEN_MKL_EIG_SELFADJ(scomplex, MKL_Complex8, float, cheev, RowMajor, LAPACK_ROW_MAJOR) +EIGEN_LAPACKE_EIG_SELFADJ(double, double, double, dsyev, RowMajor, LAPACK_ROW_MAJOR) +EIGEN_LAPACKE_EIG_SELFADJ(float, float, float, ssyev, RowMajor, LAPACK_ROW_MAJOR) +EIGEN_LAPACKE_EIG_SELFADJ(dcomplex, lapack_complex_double, double, zheev, RowMajor, LAPACK_ROW_MAJOR) +EIGEN_LAPACKE_EIG_SELFADJ(scomplex, lapack_complex_float, float, cheev, RowMajor, LAPACK_ROW_MAJOR) } // end namespace Eigen diff --git a/Eigen/src/Geometry/Homogeneous.h b/Eigen/src/Geometry/Homogeneous.h index 1c35ca486..4e2213b33 100644 --- a/Eigen/src/Geometry/Homogeneous.h +++ b/Eigen/src/Geometry/Homogeneous.h @@ -329,7 +329,7 @@ protected: // dense = homogeneous template< typename DstXprType, typename ArgType, typename Scalar> -struct Assignment<DstXprType, Homogeneous<ArgType,Vertical>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense, Scalar> +struct Assignment<DstXprType, Homogeneous<ArgType,Vertical>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense> { typedef Homogeneous<ArgType,Vertical> SrcXprType; static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename ArgType::Scalar> &) @@ -341,7 +341,7 @@ struct Assignment<DstXprType, Homogeneous<ArgType,Vertical>, internal::assign_op // dense = homogeneous template< typename DstXprType, typename ArgType, typename Scalar> -struct Assignment<DstXprType, Homogeneous<ArgType,Horizontal>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense, Scalar> +struct Assignment<DstXprType, Homogeneous<ArgType,Horizontal>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense> { typedef Homogeneous<ArgType,Horizontal> SrcXprType; static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename ArgType::Scalar> &) diff --git a/Eigen/src/Geometry/Quaternion.h b/Eigen/src/Geometry/Quaternion.h index fc5175f01..c4a0eabb5 100644 --- a/Eigen/src/Geometry/Quaternion.h +++ b/Eigen/src/Geometry/Quaternion.h @@ -726,7 +726,7 @@ QuaternionBase<Derived>::slerp(const Scalar& t, const QuaternionBase<OtherDerive using std::acos; using std::sin; using std::abs; - static const Scalar one = Scalar(1) - NumTraits<Scalar>::epsilon(); + const Scalar one = Scalar(1) - NumTraits<Scalar>::epsilon(); Scalar d = this->dot(other); Scalar absD = abs(d); diff --git a/Eigen/src/IterativeLinearSolvers/SolveWithGuess.h b/Eigen/src/IterativeLinearSolvers/SolveWithGuess.h index 7d67d3ce2..0498db396 100644 --- a/Eigen/src/IterativeLinearSolvers/SolveWithGuess.h +++ b/Eigen/src/IterativeLinearSolvers/SolveWithGuess.h @@ -44,6 +44,7 @@ public: typedef typename internal::traits<SolveWithGuess>::Scalar Scalar; typedef typename internal::traits<SolveWithGuess>::PlainObject PlainObject; typedef typename internal::generic_xpr_base<SolveWithGuess<Decomposition,RhsType,GuessType>, MatrixXpr, typename internal::traits<RhsType>::StorageKind>::type Base; + typedef typename internal::ref_selector<SolveWithGuess>::type Nested; SolveWithGuess(const Decomposition &dec, const RhsType &rhs, const GuessType &guess) : m_dec(dec), m_rhs(rhs), m_guess(guess) @@ -81,7 +82,8 @@ struct evaluator<SolveWithGuess<Decomposition,RhsType, GuessType> > : m_result(solve.rows(), solve.cols()) { ::new (static_cast<Base*>(this)) Base(m_result); - solve.dec()._solve_with_guess_impl(solve.rhs(), m_result, solve().guess()); + m_result = solve.guess(); + solve.dec()._solve_with_guess_impl(solve.rhs(), m_result); } protected: @@ -91,7 +93,7 @@ protected: // Specialization for "dst = dec.solveWithGuess(rhs)" // NOTE we need to specialize it for Dense2Dense to avoid ambiguous specialization error and a Sparse2Sparse specialization must exist somewhere template<typename DstXprType, typename DecType, typename RhsType, typename GuessType, typename Scalar> -struct Assignment<DstXprType, SolveWithGuess<DecType,RhsType,GuessType>, internal::assign_op<Scalar,Scalar>, Dense2Dense, Scalar> +struct Assignment<DstXprType, SolveWithGuess<DecType,RhsType,GuessType>, internal::assign_op<Scalar,Scalar>, Dense2Dense> { typedef SolveWithGuess<DecType,RhsType,GuessType> SrcXprType; static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &) diff --git a/Eigen/src/Jacobi/Jacobi.h b/Eigen/src/Jacobi/Jacobi.h index 55de15e87..d25af8e90 100644 --- a/Eigen/src/Jacobi/Jacobi.h +++ b/Eigen/src/Jacobi/Jacobi.h @@ -85,7 +85,8 @@ bool JacobiRotation<Scalar>::makeJacobi(const RealScalar& x, const Scalar& y, co using std::sqrt; using std::abs; typedef typename NumTraits<Scalar>::Real RealScalar; - if(y == Scalar(0)) + RealScalar deno = RealScalar(2)*abs(y); + if(deno < (std::numeric_limits<RealScalar>::min)()) { m_c = Scalar(1); m_s = Scalar(0); @@ -93,7 +94,7 @@ bool JacobiRotation<Scalar>::makeJacobi(const RealScalar& x, const Scalar& y, co } else { - RealScalar tau = (x-z)/(RealScalar(2)*abs(y)); + RealScalar tau = (x-z)/deno; RealScalar w = sqrt(numext::abs2(tau) + RealScalar(1)); RealScalar t; if(tau>RealScalar(0)) diff --git a/Eigen/src/LU/FullPivLU.h b/Eigen/src/LU/FullPivLU.h index 2d01b18c6..1632d3ac3 100644 --- a/Eigen/src/LU/FullPivLU.h +++ b/Eigen/src/LU/FullPivLU.h @@ -52,6 +52,8 @@ template<typename _MatrixType> struct traits<FullPivLU<_MatrixType> > * \include class_FullPivLU.cpp * Output: \verbinclude class_FullPivLU.out * + * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism. + * * \sa MatrixBase::fullPivLu(), MatrixBase::determinant(), MatrixBase::inverse() */ template<typename _MatrixType> class FullPivLU @@ -97,6 +99,15 @@ template<typename _MatrixType> class FullPivLU template<typename InputType> explicit FullPivLU(const EigenBase<InputType>& matrix); + /** \brief Constructs a LU factorization from a given matrix + * + * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when \c MatrixType is a Eigen::Ref. + * + * \sa FullPivLU(const EigenBase&) + */ + template<typename InputType> + explicit FullPivLU(EigenBase<InputType>& matrix); + /** Computes the LU decomposition of the given matrix. * * \param matrix the matrix of which to compute the LU decomposition. @@ -105,7 +116,11 @@ template<typename _MatrixType> class FullPivLU * \returns a reference to *this */ template<typename InputType> - FullPivLU& compute(const EigenBase<InputType>& matrix); + FullPivLU& compute(const EigenBase<InputType>& matrix) { + m_lu = matrix.derived(); + computeInPlace(); + return *this; + } /** \returns the LU decomposition matrix: the upper-triangular part is U, the * unit-lower-triangular part is L (at least for square matrices; in the non-square @@ -459,25 +474,28 @@ FullPivLU<MatrixType>::FullPivLU(const EigenBase<InputType>& matrix) template<typename MatrixType> template<typename InputType> -FullPivLU<MatrixType>& FullPivLU<MatrixType>::compute(const EigenBase<InputType>& matrix) +FullPivLU<MatrixType>::FullPivLU(EigenBase<InputType>& matrix) + : m_lu(matrix.derived()), + m_p(matrix.rows()), + m_q(matrix.cols()), + m_rowsTranspositions(matrix.rows()), + m_colsTranspositions(matrix.cols()), + m_isInitialized(false), + m_usePrescribedThreshold(false) { - check_template_parameters(); - - // the permutations are stored as int indices, so just to be sure: - eigen_assert(matrix.rows()<=NumTraits<int>::highest() && matrix.cols()<=NumTraits<int>::highest()); - - m_lu = matrix.derived(); - m_l1_norm = m_lu.cwiseAbs().colwise().sum().maxCoeff(); - computeInPlace(); - - m_isInitialized = true; - return *this; } template<typename MatrixType> void FullPivLU<MatrixType>::computeInPlace() { + check_template_parameters(); + + // the permutations are stored as int indices, so just to be sure: + eigen_assert(m_lu.rows()<=NumTraits<int>::highest() && m_lu.cols()<=NumTraits<int>::highest()); + + m_l1_norm = m_lu.cwiseAbs().colwise().sum().maxCoeff(); + const Index size = m_lu.diagonalSize(); const Index rows = m_lu.rows(); const Index cols = m_lu.cols(); @@ -557,6 +575,8 @@ void FullPivLU<MatrixType>::computeInPlace() m_q.applyTranspositionOnTheRight(k, m_colsTranspositions.coeff(k)); m_det_pq = (number_of_transpositions%2) ? -1 : 1; + + m_isInitialized = true; } template<typename MatrixType> diff --git a/Eigen/src/LU/PartialPivLU.h b/Eigen/src/LU/PartialPivLU.h index ac2902261..87ac6a281 100644 --- a/Eigen/src/LU/PartialPivLU.h +++ b/Eigen/src/LU/PartialPivLU.h @@ -26,6 +26,17 @@ template<typename _MatrixType> struct traits<PartialPivLU<_MatrixType> > }; }; +template<typename T,typename Derived> +struct enable_if_ref; +// { +// typedef Derived type; +// }; + +template<typename T,typename Derived> +struct enable_if_ref<Ref<T>,Derived> { + typedef Derived type; +}; + } // end namespace internal /** \ingroup LU_Module @@ -57,6 +68,8 @@ template<typename _MatrixType> struct traits<PartialPivLU<_MatrixType> > * * The data of the LU decomposition can be directly accessed through the methods matrixLU(), permutationP(). * + * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism. + * * \sa MatrixBase::partialPivLu(), MatrixBase::determinant(), MatrixBase::inverse(), MatrixBase::computeInverse(), class FullPivLU */ template<typename _MatrixType> class PartialPivLU @@ -102,8 +115,22 @@ template<typename _MatrixType> class PartialPivLU template<typename InputType> explicit PartialPivLU(const EigenBase<InputType>& matrix); + /** Constructor for \link InplaceDecomposition inplace decomposition \endlink + * + * \param matrix the matrix of which to compute the LU decomposition. + * + * \warning The matrix should have full rank (e.g. if it's square, it should be invertible). + * If you need to deal with non-full rank, use class FullPivLU instead. + */ + template<typename InputType> + explicit PartialPivLU(EigenBase<InputType>& matrix); + template<typename InputType> - PartialPivLU& compute(const EigenBase<InputType>& matrix); + PartialPivLU& compute(const EigenBase<InputType>& matrix) { + m_lu = matrix.derived(); + compute(); + return *this; + } /** \returns the LU decomposition matrix: the upper-triangular part is U, the * unit-lower-triangular part is L (at least for square matrices; in the non-square @@ -251,6 +278,8 @@ template<typename _MatrixType> class PartialPivLU EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar); } + void compute(); + MatrixType m_lu; PermutationType m_p; TranspositionType m_rowsTranspositions; @@ -284,7 +313,7 @@ PartialPivLU<MatrixType>::PartialPivLU(Index size) template<typename MatrixType> template<typename InputType> PartialPivLU<MatrixType>::PartialPivLU(const EigenBase<InputType>& matrix) - : m_lu(matrix.rows(), matrix.rows()), + : m_lu(matrix.rows(),matrix.cols()), m_p(matrix.rows()), m_rowsTranspositions(matrix.rows()), m_l1_norm(0), @@ -294,6 +323,19 @@ PartialPivLU<MatrixType>::PartialPivLU(const EigenBase<InputType>& matrix) compute(matrix.derived()); } +template<typename MatrixType> +template<typename InputType> +PartialPivLU<MatrixType>::PartialPivLU(EigenBase<InputType>& matrix) + : m_lu(matrix.derived()), + m_p(matrix.rows()), + m_rowsTranspositions(matrix.rows()), + m_l1_norm(0), + m_det_p(0), + m_isInitialized(false) +{ + compute(); +} + namespace internal { /** \internal This is the blocked version of fullpivlu_unblocked() */ @@ -470,19 +512,17 @@ void partial_lu_inplace(MatrixType& lu, TranspositionType& row_transpositions, t } // end namespace internal template<typename MatrixType> -template<typename InputType> -PartialPivLU<MatrixType>& PartialPivLU<MatrixType>::compute(const EigenBase<InputType>& matrix) +void PartialPivLU<MatrixType>::compute() { check_template_parameters(); // the row permutation is stored as int indices, so just to be sure: - eigen_assert(matrix.rows()<NumTraits<int>::highest()); + eigen_assert(m_lu.rows()<NumTraits<int>::highest()); - m_lu = matrix.derived(); m_l1_norm = m_lu.cwiseAbs().colwise().sum().maxCoeff(); - eigen_assert(matrix.rows() == matrix.cols() && "PartialPivLU is only for square (and moreover invertible) matrices"); - const Index size = matrix.rows(); + eigen_assert(m_lu.rows() == m_lu.cols() && "PartialPivLU is only for square (and moreover invertible) matrices"); + const Index size = m_lu.rows(); m_rowsTranspositions.resize(size); @@ -493,7 +533,6 @@ PartialPivLU<MatrixType>& PartialPivLU<MatrixType>::compute(const EigenBase<Inpu m_p = m_rowsTranspositions; m_isInitialized = true; - return *this; } template<typename MatrixType> diff --git a/Eigen/src/LU/PartialPivLU_MKL.h b/Eigen/src/LU/PartialPivLU_LAPACKE.h index 41692b9a1..755168a94 100644 --- a/Eigen/src/LU/PartialPivLU_MKL.h +++ b/Eigen/src/LU/PartialPivLU_LAPACKE.h @@ -25,7 +25,7 @@ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ******************************************************************************** - * Content : Eigen bindings to Intel(R) MKL + * Content : Eigen bindings to LAPACKe * LU decomposition with partial pivoting based on LAPACKE_?getrf function. ******************************************************************************** */ @@ -33,15 +33,13 @@ #ifndef EIGEN_PARTIALLU_LAPACK_H #define EIGEN_PARTIALLU_LAPACK_H -#include "Eigen/src/Core/util/MKL_support.h" - namespace Eigen { namespace internal { -/** \internal Specialization for the data types supported by MKL */ +/** \internal Specialization for the data types supported by LAPACKe */ -#define EIGEN_MKL_LU_PARTPIV(EIGTYPE, MKLTYPE, MKLPREFIX) \ +#define EIGEN_LAPACKE_LU_PARTPIV(EIGTYPE, LAPACKE_TYPE, LAPACKE_PREFIX) \ template<int StorageOrder> \ struct partial_lu_impl<EIGTYPE, StorageOrder, lapack_int> \ { \ @@ -61,7 +59,7 @@ struct partial_lu_impl<EIGTYPE, StorageOrder, lapack_int> \ n = convert_index<lapack_int>(cols); \ nb_transpositions = 0; \ \ - info = LAPACKE_##MKLPREFIX##getrf( matrix_order, m, n, (MKLTYPE*)a, lda, ipiv ); \ + info = LAPACKE_##LAPACKE_PREFIX##getrf( matrix_order, m, n, (LAPACKE_TYPE*)a, lda, ipiv ); \ \ for(int i=0;i<m;i++) { ipiv[i]--; if (ipiv[i]!=i) nb_transpositions++; } \ \ @@ -73,10 +71,10 @@ struct partial_lu_impl<EIGTYPE, StorageOrder, lapack_int> \ } \ }; -EIGEN_MKL_LU_PARTPIV(double, double, d) -EIGEN_MKL_LU_PARTPIV(float, float, s) -EIGEN_MKL_LU_PARTPIV(dcomplex, MKL_Complex16, z) -EIGEN_MKL_LU_PARTPIV(scomplex, MKL_Complex8, c) +EIGEN_LAPACKE_LU_PARTPIV(double, double, d) +EIGEN_LAPACKE_LU_PARTPIV(float, float, s) +EIGEN_LAPACKE_LU_PARTPIV(dcomplex, lapack_complex_double, z) +EIGEN_LAPACKE_LU_PARTPIV(scomplex, lapack_complex_float, c) } // end namespace internal diff --git a/Eigen/src/QR/ColPivHouseholderQR.h b/Eigen/src/QR/ColPivHouseholderQR.h index 525ee8c18..ee6989897 100644 --- a/Eigen/src/QR/ColPivHouseholderQR.h +++ b/Eigen/src/QR/ColPivHouseholderQR.h @@ -41,6 +41,8 @@ template<typename _MatrixType> struct traits<ColPivHouseholderQR<_MatrixType> > * This decomposition performs column pivoting in order to be rank-revealing and improve * numerical stability. It is slower than HouseholderQR, and faster than FullPivHouseholderQR. * + * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism. + * * \sa MatrixBase::colPivHouseholderQr() */ template<typename _MatrixType> class ColPivHouseholderQR @@ -51,7 +53,6 @@ template<typename _MatrixType> class ColPivHouseholderQR enum { RowsAtCompileTime = MatrixType::RowsAtCompileTime, ColsAtCompileTime = MatrixType::ColsAtCompileTime, - Options = MatrixType::Options, MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime }; @@ -59,7 +60,6 @@ template<typename _MatrixType> class ColPivHouseholderQR typedef typename MatrixType::RealScalar RealScalar; // FIXME should be int typedef typename MatrixType::StorageIndex StorageIndex; - typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, Options, MaxRowsAtCompileTime, MaxRowsAtCompileTime> MatrixQType; typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType; typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> PermutationType; typedef typename internal::plain_row_type<MatrixType, Index>::type IntRowVectorType; @@ -135,6 +135,27 @@ template<typename _MatrixType> class ColPivHouseholderQR compute(matrix.derived()); } + /** \brief Constructs a QR factorization from a given matrix + * + * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when \c MatrixType is a Eigen::Ref. + * + * \sa ColPivHouseholderQR(const EigenBase&) + */ + template<typename InputType> + explicit ColPivHouseholderQR(EigenBase<InputType>& matrix) + : m_qr(matrix.derived()), + m_hCoeffs((std::min)(matrix.rows(),matrix.cols())), + m_colsPermutation(PermIndexType(matrix.cols())), + m_colsTranspositions(matrix.cols()), + m_temp(matrix.cols()), + m_colNormsUpdated(matrix.cols()), + m_colNormsDirect(matrix.cols()), + m_isInitialized(false), + m_usePrescribedThreshold(false) + { + computeInPlace(); + } + /** This method finds a solution x to the equation Ax=b, where A is the matrix of which * *this is the QR decomposition, if any exists. * @@ -453,21 +474,19 @@ template<typename MatrixType> template<typename InputType> ColPivHouseholderQR<MatrixType>& ColPivHouseholderQR<MatrixType>::compute(const EigenBase<InputType>& matrix) { - check_template_parameters(); - - // the column permutation is stored as int indices, so just to be sure: - eigen_assert(matrix.cols()<=NumTraits<int>::highest()); - - m_qr = matrix; - + m_qr = matrix.derived(); computeInPlace(); - return *this; } template<typename MatrixType> void ColPivHouseholderQR<MatrixType>::computeInPlace() { + check_template_parameters(); + + // the column permutation is stored as int indices, so just to be sure: + eigen_assert(m_qr.cols()<=NumTraits<int>::highest()); + using std::abs; Index rows = m_qr.rows(); @@ -598,7 +617,7 @@ void ColPivHouseholderQR<_MatrixType>::_solve_impl(const RhsType &rhs, DstType & namespace internal { template<typename DstXprType, typename MatrixType, typename Scalar> -struct Assignment<DstXprType, Inverse<ColPivHouseholderQR<MatrixType> >, internal::assign_op<Scalar,Scalar>, Dense2Dense, Scalar> +struct Assignment<DstXprType, Inverse<ColPivHouseholderQR<MatrixType> >, internal::assign_op<Scalar,Scalar>, Dense2Dense> { typedef ColPivHouseholderQR<MatrixType> QrType; typedef Inverse<QrType> SrcXprType; diff --git a/Eigen/src/QR/ColPivHouseholderQR_MKL.h b/Eigen/src/QR/ColPivHouseholderQR_LAPACKE.h index 65391a5d2..4e9651f83 100644 --- a/Eigen/src/QR/ColPivHouseholderQR_MKL.h +++ b/Eigen/src/QR/ColPivHouseholderQR_LAPACKE.h @@ -25,22 +25,20 @@ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ******************************************************************************** - * Content : Eigen bindings to Intel(R) MKL + * Content : Eigen bindings to LAPACKe * Householder QR decomposition of a matrix with column pivoting based on * LAPACKE_?geqp3 function. ******************************************************************************** */ -#ifndef EIGEN_COLPIVOTINGHOUSEHOLDERQR_MKL_H -#define EIGEN_COLPIVOTINGHOUSEHOLDERQR_MKL_H - -#include "Eigen/src/Core/util/MKL_support.h" +#ifndef EIGEN_COLPIVOTINGHOUSEHOLDERQR_LAPACKE_H +#define EIGEN_COLPIVOTINGHOUSEHOLDERQR_LAPACKE_H namespace Eigen { -/** \internal Specialization for the data types supported by MKL */ +/** \internal Specialization for the data types supported by LAPACKe */ -#define EIGEN_MKL_QR_COLPIV(EIGTYPE, MKLTYPE, MKLPREFIX, EIGCOLROW, MKLCOLROW) \ +#define EIGEN_LAPACKE_QR_COLPIV(EIGTYPE, LAPACKE_TYPE, LAPACKE_PREFIX, EIGCOLROW, LAPACKE_COLROW) \ template<> template<typename InputType> inline \ ColPivHouseholderQR<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic> >& \ ColPivHouseholderQR<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic> >::compute( \ @@ -66,9 +64,9 @@ ColPivHouseholderQR<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynami m_colsPermutation.indices().setZero(); \ \ lapack_int lda = internal::convert_index<lapack_int,Index>(m_qr.outerStride()); \ - lapack_int matrix_order = MKLCOLROW; \ - LAPACKE_##MKLPREFIX##geqp3( matrix_order, internal::convert_index<lapack_int,Index>(rows), internal::convert_index<lapack_int,Index>(cols), \ - (MKLTYPE*)m_qr.data(), lda, (lapack_int*)m_colsPermutation.indices().data(), (MKLTYPE*)m_hCoeffs.data()); \ + lapack_int matrix_order = LAPACKE_COLROW; \ + LAPACKE_##LAPACKE_PREFIX##geqp3( matrix_order, internal::convert_index<lapack_int,Index>(rows), internal::convert_index<lapack_int,Index>(cols), \ + (LAPACKE_TYPE*)m_qr.data(), lda, (lapack_int*)m_colsPermutation.indices().data(), (LAPACKE_TYPE*)m_hCoeffs.data()); \ m_isInitialized = true; \ m_maxpivot=m_qr.diagonal().cwiseAbs().maxCoeff(); \ m_hCoeffs.adjointInPlace(); \ @@ -84,16 +82,16 @@ ColPivHouseholderQR<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynami return *this; \ } -EIGEN_MKL_QR_COLPIV(double, double, d, ColMajor, LAPACK_COL_MAJOR) -EIGEN_MKL_QR_COLPIV(float, float, s, ColMajor, LAPACK_COL_MAJOR) -EIGEN_MKL_QR_COLPIV(dcomplex, MKL_Complex16, z, ColMajor, LAPACK_COL_MAJOR) -EIGEN_MKL_QR_COLPIV(scomplex, MKL_Complex8, c, ColMajor, LAPACK_COL_MAJOR) +EIGEN_LAPACKE_QR_COLPIV(double, double, d, ColMajor, LAPACK_COL_MAJOR) +EIGEN_LAPACKE_QR_COLPIV(float, float, s, ColMajor, LAPACK_COL_MAJOR) +EIGEN_LAPACKE_QR_COLPIV(dcomplex, lapack_complex_double, z, ColMajor, LAPACK_COL_MAJOR) +EIGEN_LAPACKE_QR_COLPIV(scomplex, lapack_complex_float, c, ColMajor, LAPACK_COL_MAJOR) -EIGEN_MKL_QR_COLPIV(double, double, d, RowMajor, LAPACK_ROW_MAJOR) -EIGEN_MKL_QR_COLPIV(float, float, s, RowMajor, LAPACK_ROW_MAJOR) -EIGEN_MKL_QR_COLPIV(dcomplex, MKL_Complex16, z, RowMajor, LAPACK_ROW_MAJOR) -EIGEN_MKL_QR_COLPIV(scomplex, MKL_Complex8, c, RowMajor, LAPACK_ROW_MAJOR) +EIGEN_LAPACKE_QR_COLPIV(double, double, d, RowMajor, LAPACK_ROW_MAJOR) +EIGEN_LAPACKE_QR_COLPIV(float, float, s, RowMajor, LAPACK_ROW_MAJOR) +EIGEN_LAPACKE_QR_COLPIV(dcomplex, lapack_complex_double, z, RowMajor, LAPACK_ROW_MAJOR) +EIGEN_LAPACKE_QR_COLPIV(scomplex, lapack_complex_float, c, RowMajor, LAPACK_ROW_MAJOR) } // end namespace Eigen -#endif // EIGEN_COLPIVOTINGHOUSEHOLDERQR_MKL_H +#endif // EIGEN_COLPIVOTINGHOUSEHOLDERQR_LAPACKE_H diff --git a/Eigen/src/QR/CompleteOrthogonalDecomposition.h b/Eigen/src/QR/CompleteOrthogonalDecomposition.h index 52bcc2173..f299d3c00 100644 --- a/Eigen/src/QR/CompleteOrthogonalDecomposition.h +++ b/Eigen/src/QR/CompleteOrthogonalDecomposition.h @@ -29,16 +29,19 @@ struct traits<CompleteOrthogonalDecomposition<_MatrixType> > * * \param MatrixType the type of the matrix of which we are computing the COD. * - * This class performs a rank-revealing complete ortogonal decomposition of a + * This class performs a rank-revealing complete orthogonal decomposition of a * matrix \b A into matrices \b P, \b Q, \b T, and \b Z such that * \f[ - * \mathbf{A} \, \mathbf{P} = \mathbf{Q} \, \begin{matrix} \mathbf{T} & - * \mathbf{0} \\ \mathbf{0} & \mathbf{0} \end{matrix} \, \mathbf{Z} + * \mathbf{A} \, \mathbf{P} = \mathbf{Q} \, + * \begin{bmatrix} \mathbf{T} & \mathbf{0} \\ + * \mathbf{0} & \mathbf{0} \end{bmatrix} \, \mathbf{Z} * \f] * by using Householder transformations. Here, \b P is a permutation matrix, * \b Q and \b Z are unitary matrices and \b T an upper triangular matrix of * size rank-by-rank. \b A may be rank deficient. * + * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism. + * * \sa MatrixBase::completeOrthogonalDecomposition() */ template <typename _MatrixType> @@ -48,16 +51,12 @@ class CompleteOrthogonalDecomposition { enum { RowsAtCompileTime = MatrixType::RowsAtCompileTime, ColsAtCompileTime = MatrixType::ColsAtCompileTime, - Options = MatrixType::Options, MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime }; typedef typename MatrixType::Scalar Scalar; typedef typename MatrixType::RealScalar RealScalar; typedef typename MatrixType::StorageIndex StorageIndex; - typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, Options, - MaxRowsAtCompileTime, MaxRowsAtCompileTime> - MatrixQType; typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType; typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> PermutationType; @@ -114,12 +113,29 @@ class CompleteOrthogonalDecomposition { explicit CompleteOrthogonalDecomposition(const EigenBase<InputType>& matrix) : m_cpqr(matrix.rows(), matrix.cols()), m_zCoeffs((std::min)(matrix.rows(), matrix.cols())), - m_temp(matrix.cols()) { + m_temp(matrix.cols()) + { compute(matrix.derived()); } + /** \brief Constructs a complete orthogonal decomposition from a given matrix + * + * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when \c MatrixType is a Eigen::Ref. + * + * \sa CompleteOrthogonalDecomposition(const EigenBase&) + */ + template<typename InputType> + explicit CompleteOrthogonalDecomposition(EigenBase<InputType>& matrix) + : m_cpqr(matrix.derived()), + m_zCoeffs((std::min)(matrix.rows(), matrix.cols())), + m_temp(matrix.cols()) + { + computeInPlace(); + } + + /** This method computes the minimum-norm solution X to a least squares - * problem \f[\mathrm{minimize} ||A X - B|| \f], where \b A is the matrix of + * problem \f[\mathrm{minimize} \|A X - B\|, \f] where \b A is the matrix of * which \c *this is the complete orthogonal decomposition. * * \param B the right-hand sides of the problem to solve. @@ -165,7 +181,12 @@ class CompleteOrthogonalDecomposition { const MatrixType& matrixT() const { return m_cpqr.matrixQR(); } template <typename InputType> - CompleteOrthogonalDecomposition& compute(const EigenBase<InputType>& matrix); + CompleteOrthogonalDecomposition& compute(const EigenBase<InputType>& matrix) { + // Compute the column pivoted QR factorization A P = Q R. + m_cpqr.compute(matrix); + computeInPlace(); + return *this; + } /** \returns a const reference to the column permutation matrix */ const PermutationType& colsPermutation() const { @@ -354,6 +375,8 @@ class CompleteOrthogonalDecomposition { EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar); } + void computeInPlace(); + /** Overwrites \b rhs with \f$ \mathbf{Z}^* * \mathbf{rhs} \f$. */ template <typename Rhs> @@ -384,20 +407,16 @@ CompleteOrthogonalDecomposition<MatrixType>::logAbsDeterminant() const { * CompleteOrthogonalDecomposition(const MatrixType&) */ template <typename MatrixType> -template <typename InputType> -CompleteOrthogonalDecomposition<MatrixType>& CompleteOrthogonalDecomposition< - MatrixType>::compute(const EigenBase<InputType>& matrix) { +void CompleteOrthogonalDecomposition<MatrixType>::computeInPlace() +{ check_template_parameters(); // the column permutation is stored as int indices, so just to be sure: - eigen_assert(matrix.cols() <= NumTraits<int>::highest()); - - // Compute the column pivoted QR factorization A P = Q R. - m_cpqr.compute(matrix); + eigen_assert(m_cpqr.cols() <= NumTraits<int>::highest()); const Index rank = m_cpqr.rank(); - const Index cols = matrix.cols(); - const Index rows = matrix.rows(); + const Index cols = m_cpqr.cols(); + const Index rows = m_cpqr.rows(); m_zCoeffs.resize((std::min)(rows, cols)); m_temp.resize(cols); @@ -443,7 +462,6 @@ CompleteOrthogonalDecomposition<MatrixType>& CompleteOrthogonalDecomposition< } } } - return *this; } template <typename MatrixType> @@ -509,12 +527,12 @@ void CompleteOrthogonalDecomposition<_MatrixType>::_solve_impl( namespace internal { -template<typename DstXprType, typename MatrixType, typename Scalar> -struct Assignment<DstXprType, Inverse<CompleteOrthogonalDecomposition<MatrixType> >, internal::assign_op<Scalar,Scalar>, Dense2Dense, Scalar> +template<typename DstXprType, typename MatrixType> +struct Assignment<DstXprType, Inverse<CompleteOrthogonalDecomposition<MatrixType> >, internal::assign_op<typename DstXprType::Scalar,typename CompleteOrthogonalDecomposition<MatrixType>::Scalar>, Dense2Dense> { typedef CompleteOrthogonalDecomposition<MatrixType> CodType; typedef Inverse<CodType> SrcXprType; - static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &) + static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename CodType::Scalar> &) { dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.rows())); } diff --git a/Eigen/src/QR/FullPivHouseholderQR.h b/Eigen/src/QR/FullPivHouseholderQR.h index 4f55d52a5..4c85a4693 100644 --- a/Eigen/src/QR/FullPivHouseholderQR.h +++ b/Eigen/src/QR/FullPivHouseholderQR.h @@ -50,6 +50,8 @@ struct traits<FullPivHouseholderQRMatrixQReturnType<MatrixType> > * This decomposition performs a very prudent full pivoting in order to be rank-revealing and achieve optimal * numerical stability. The trade-off is that it is slower than HouseholderQR and ColPivHouseholderQR. * + * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism. + * * \sa MatrixBase::fullPivHouseholderQr() */ template<typename _MatrixType> class FullPivHouseholderQR @@ -60,7 +62,6 @@ template<typename _MatrixType> class FullPivHouseholderQR enum { RowsAtCompileTime = MatrixType::RowsAtCompileTime, ColsAtCompileTime = MatrixType::ColsAtCompileTime, - Options = MatrixType::Options, MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime }; @@ -135,6 +136,26 @@ template<typename _MatrixType> class FullPivHouseholderQR compute(matrix.derived()); } + /** \brief Constructs a QR factorization from a given matrix + * + * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when \c MatrixType is a Eigen::Ref. + * + * \sa FullPivHouseholderQR(const EigenBase&) + */ + template<typename InputType> + explicit FullPivHouseholderQR(EigenBase<InputType>& matrix) + : m_qr(matrix.derived()), + m_hCoeffs((std::min)(matrix.rows(), matrix.cols())), + m_rows_transpositions((std::min)(matrix.rows(), matrix.cols())), + m_cols_transpositions((std::min)(matrix.rows(), matrix.cols())), + m_cols_permutation(matrix.cols()), + m_temp(matrix.cols()), + m_isInitialized(false), + m_usePrescribedThreshold(false) + { + computeInPlace(); + } + /** This method finds a solution x to the equation Ax=b, where A is the matrix of which * \c *this is the QR decomposition. * @@ -430,18 +451,16 @@ template<typename MatrixType> template<typename InputType> FullPivHouseholderQR<MatrixType>& FullPivHouseholderQR<MatrixType>::compute(const EigenBase<InputType>& matrix) { - check_template_parameters(); - m_qr = matrix.derived(); - computeInPlace(); - return *this; } template<typename MatrixType> void FullPivHouseholderQR<MatrixType>::computeInPlace() { + check_template_parameters(); + using std::abs; Index rows = m_qr.rows(); Index cols = m_qr.cols(); @@ -560,7 +579,7 @@ void FullPivHouseholderQR<_MatrixType>::_solve_impl(const RhsType &rhs, DstType namespace internal { template<typename DstXprType, typename MatrixType, typename Scalar> -struct Assignment<DstXprType, Inverse<FullPivHouseholderQR<MatrixType> >, internal::assign_op<Scalar,Scalar>, Dense2Dense, Scalar> +struct Assignment<DstXprType, Inverse<FullPivHouseholderQR<MatrixType> >, internal::assign_op<Scalar,Scalar>, Dense2Dense> { typedef FullPivHouseholderQR<MatrixType> QrType; typedef Inverse<QrType> SrcXprType; diff --git a/Eigen/src/QR/HouseholderQR.h b/Eigen/src/QR/HouseholderQR.h index 03bc8e6cd..2e64fa7fe 100644 --- a/Eigen/src/QR/HouseholderQR.h +++ b/Eigen/src/QR/HouseholderQR.h @@ -37,6 +37,8 @@ namespace Eigen { * This Householder QR decomposition is faster, but less numerically stable and less feature-full than * FullPivHouseholderQR or ColPivHouseholderQR. * + * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism. + * * \sa MatrixBase::householderQr() */ template<typename _MatrixType> class HouseholderQR @@ -47,7 +49,6 @@ template<typename _MatrixType> class HouseholderQR enum { RowsAtCompileTime = MatrixType::RowsAtCompileTime, ColsAtCompileTime = MatrixType::ColsAtCompileTime, - Options = MatrixType::Options, MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime }; @@ -102,6 +103,24 @@ template<typename _MatrixType> class HouseholderQR compute(matrix.derived()); } + + /** \brief Constructs a QR factorization from a given matrix + * + * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when + * \c MatrixType is a Eigen::Ref. + * + * \sa HouseholderQR(const EigenBase&) + */ + template<typename InputType> + explicit HouseholderQR(EigenBase<InputType>& matrix) + : m_qr(matrix.derived()), + m_hCoeffs((std::min)(matrix.rows(),matrix.cols())), + m_temp(matrix.cols()), + m_isInitialized(false) + { + computeInPlace(); + } + /** This method finds a solution x to the equation Ax=b, where A is the matrix of which * *this is the QR decomposition, if any exists. * @@ -151,7 +170,11 @@ template<typename _MatrixType> class HouseholderQR } template<typename InputType> - HouseholderQR& compute(const EigenBase<InputType>& matrix); + HouseholderQR& compute(const EigenBase<InputType>& matrix) { + m_qr = matrix.derived(); + computeInPlace(); + return *this; + } /** \returns the absolute value of the determinant of the matrix of which * *this is the QR decomposition. It has only linear complexity @@ -203,6 +226,8 @@ template<typename _MatrixType> class HouseholderQR { EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar); } + + void computeInPlace(); MatrixType m_qr; HCoeffsType m_hCoeffs; @@ -354,16 +379,14 @@ void HouseholderQR<_MatrixType>::_solve_impl(const RhsType &rhs, DstType &dst) c * \sa class HouseholderQR, HouseholderQR(const MatrixType&) */ template<typename MatrixType> -template<typename InputType> -HouseholderQR<MatrixType>& HouseholderQR<MatrixType>::compute(const EigenBase<InputType>& matrix) +void HouseholderQR<MatrixType>::computeInPlace() { check_template_parameters(); - Index rows = matrix.rows(); - Index cols = matrix.cols(); + Index rows = m_qr.rows(); + Index cols = m_qr.cols(); Index size = (std::min)(rows,cols); - m_qr = matrix.derived(); m_hCoeffs.resize(size); m_temp.resize(cols); @@ -371,7 +394,6 @@ HouseholderQR<MatrixType>& HouseholderQR<MatrixType>::compute(const EigenBase<In internal::householder_qr_inplace_blocked<MatrixType, HCoeffsType>::run(m_qr, m_hCoeffs, 48, m_temp.data()); m_isInitialized = true; - return *this; } #ifndef __CUDACC__ diff --git a/Eigen/src/QR/HouseholderQR_MKL.h b/Eigen/src/QR/HouseholderQR_LAPACKE.h index 84ab640a1..1dc7d5363 100644 --- a/Eigen/src/QR/HouseholderQR_MKL.h +++ b/Eigen/src/QR/HouseholderQR_LAPACKE.h @@ -25,24 +25,22 @@ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ******************************************************************************** - * Content : Eigen bindings to Intel(R) MKL + * Content : Eigen bindings to LAPACKe * Householder QR decomposition of a matrix w/o pivoting based on * LAPACKE_?geqrf function. ******************************************************************************** */ -#ifndef EIGEN_QR_MKL_H -#define EIGEN_QR_MKL_H - -#include "../Core/util/MKL_support.h" +#ifndef EIGEN_QR_LAPACKE_H +#define EIGEN_QR_LAPACKE_H namespace Eigen { namespace internal { -/** \internal Specialization for the data types supported by MKL */ +/** \internal Specialization for the data types supported by LAPACKe */ -#define EIGEN_MKL_QR_NOPIV(EIGTYPE, MKLTYPE, MKLPREFIX) \ +#define EIGEN_LAPACKE_QR_NOPIV(EIGTYPE, LAPACKE_TYPE, LAPACKE_PREFIX) \ template<typename MatrixQR, typename HCoeffs> \ struct householder_qr_inplace_blocked<MatrixQR, HCoeffs, EIGTYPE, true> \ { \ @@ -53,18 +51,18 @@ struct householder_qr_inplace_blocked<MatrixQR, HCoeffs, EIGTYPE, true> \ lapack_int n = (lapack_int) mat.cols(); \ lapack_int lda = (lapack_int) mat.outerStride(); \ lapack_int matrix_order = (MatrixQR::IsRowMajor) ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR; \ - LAPACKE_##MKLPREFIX##geqrf( matrix_order, m, n, (MKLTYPE*)mat.data(), lda, (MKLTYPE*)hCoeffs.data()); \ + LAPACKE_##LAPACKE_PREFIX##geqrf( matrix_order, m, n, (LAPACKE_TYPE*)mat.data(), lda, (LAPACKE_TYPE*)hCoeffs.data()); \ hCoeffs.adjointInPlace(); \ } \ }; -EIGEN_MKL_QR_NOPIV(double, double, d) -EIGEN_MKL_QR_NOPIV(float, float, s) -EIGEN_MKL_QR_NOPIV(dcomplex, MKL_Complex16, z) -EIGEN_MKL_QR_NOPIV(scomplex, MKL_Complex8, c) +EIGEN_LAPACKE_QR_NOPIV(double, double, d) +EIGEN_LAPACKE_QR_NOPIV(float, float, s) +EIGEN_LAPACKE_QR_NOPIV(dcomplex, lapack_complex_double, z) +EIGEN_LAPACKE_QR_NOPIV(scomplex, lapack_complex_float, c) } // end namespace internal } // end namespace Eigen -#endif // EIGEN_QR_MKL_H +#endif // EIGEN_QR_LAPACKE_H diff --git a/Eigen/src/SVD/BDCSVD.h b/Eigen/src/SVD/BDCSVD.h index 799e81bd7..25fca6f4d 100644 --- a/Eigen/src/SVD/BDCSVD.h +++ b/Eigen/src/SVD/BDCSVD.h @@ -1052,7 +1052,7 @@ void BDCSVD<MatrixType>::deflation(Index firstCol, Index lastCol, Index k, Index const RealScalar considerZero = (std::numeric_limits<RealScalar>::min)(); RealScalar maxDiag = diag.tail((std::max)(Index(1),length-1)).cwiseAbs().maxCoeff(); - RealScalar epsilon_strict = numext::maxi(considerZero,NumTraits<RealScalar>::epsilon() * maxDiag); + RealScalar epsilon_strict = numext::maxi<RealScalar>(considerZero,NumTraits<RealScalar>::epsilon() * maxDiag); RealScalar epsilon_coarse = 8 * NumTraits<RealScalar>::epsilon() * numext::maxi<RealScalar>(col0.cwiseAbs().maxCoeff(), maxDiag); #ifdef EIGEN_BDCSVD_SANITY_CHECKS diff --git a/Eigen/src/SVD/JacobiSVD.h b/Eigen/src/SVD/JacobiSVD.h index b83fd7a4d..605c1a2a6 100644 --- a/Eigen/src/SVD/JacobiSVD.h +++ b/Eigen/src/SVD/JacobiSVD.h @@ -713,7 +713,7 @@ JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsig { finished = false; // perform SVD decomposition of 2x2 sub-matrix corresponding to indices p,q to make it diagonal - // the complex to real operation returns true is the updated 2x2 block is not already diagonal + // the complex to real operation returns true if the updated 2x2 block is not already diagonal if(internal::svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner>::run(m_workMatrix, *this, p, q, maxDiagEntry)) { JacobiRotation<RealScalar> j_left, j_right; @@ -727,7 +727,7 @@ JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsig if(computeV()) m_matrixV.applyOnTheRight(p,q,j_right); // keep track of the largest diagonal coefficient - maxDiagEntry = numext::maxi(maxDiagEntry,numext::maxi(abs(m_workMatrix.coeff(p,p)), abs(m_workMatrix.coeff(q,q)))); + maxDiagEntry = numext::maxi<RealScalar>(maxDiagEntry,numext::maxi(abs(m_workMatrix.coeff(p,p)), abs(m_workMatrix.coeff(q,q)))); } } } @@ -738,9 +738,22 @@ JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsig for(Index i = 0; i < m_diagSize; ++i) { - RealScalar a = abs(m_workMatrix.coeff(i,i)); - m_singularValues.coeffRef(i) = a; - if(computeU() && (a!=RealScalar(0))) m_matrixU.col(i) *= m_workMatrix.coeff(i,i)/a; + // For a complex matrix, some diagonal coefficients might note have been + // treated by svd_precondition_2x2_block_to_be_real, and the imaginary part + // of some diagonal entry might not be null. + if(NumTraits<Scalar>::IsComplex && abs(numext::imag(m_workMatrix.coeff(i,i)))>considerAsZero) + { + RealScalar a = abs(m_workMatrix.coeff(i,i)); + m_singularValues.coeffRef(i) = abs(a); + if(computeU()) m_matrixU.col(i) *= m_workMatrix.coeff(i,i)/a; + } + else + { + // m_workMatrix.coeff(i,i) is already real, no difficulty: + RealScalar a = numext::real(m_workMatrix.coeff(i,i)); + m_singularValues.coeffRef(i) = abs(a); + if(computeU() && (a<RealScalar(0))) m_matrixU.col(i) = -m_matrixU.col(i); + } } m_singularValues *= scale; diff --git a/Eigen/src/SVD/JacobiSVD_MKL.h b/Eigen/src/SVD/JacobiSVD_LAPACKE.h index 14e461c4e..50272154f 100644 --- a/Eigen/src/SVD/JacobiSVD_MKL.h +++ b/Eigen/src/SVD/JacobiSVD_LAPACKE.h @@ -25,21 +25,19 @@ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ******************************************************************************** - * Content : Eigen bindings to Intel(R) MKL + * Content : Eigen bindings to LAPACKe * Singular Value Decomposition - SVD. ******************************************************************************** */ -#ifndef EIGEN_JACOBISVD_MKL_H -#define EIGEN_JACOBISVD_MKL_H - -#include "Eigen/src/Core/util/MKL_support.h" +#ifndef EIGEN_JACOBISVD_LAPACKE_H +#define EIGEN_JACOBISVD_LAPACKE_H namespace Eigen { -/** \internal Specialization for the data types supported by MKL */ +/** \internal Specialization for the data types supported by LAPACKe */ -#define EIGEN_MKL_SVD(EIGTYPE, MKLTYPE, MKLRTYPE, MKLPREFIX, EIGCOLROW, MKLCOLROW) \ +#define EIGEN_LAPACKE_SVD(EIGTYPE, LAPACKE_TYPE, LAPACKE_RTYPE, LAPACKE_PREFIX, EIGCOLROW, LAPACKE_COLROW) \ template<> inline \ JacobiSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, ColPivHouseholderQRPreconditioner>& \ JacobiSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, ColPivHouseholderQRPreconditioner>::compute(const Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>& matrix, unsigned int computationOptions) \ @@ -52,41 +50,41 @@ JacobiSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, ColPiv /*const RealScalar precision = RealScalar(2) * NumTraits<Scalar>::epsilon();*/ \ m_nonzeroSingularValues = m_diagSize; \ \ - lapack_int lda = matrix.outerStride(), ldu, ldvt; \ - lapack_int matrix_order = MKLCOLROW; \ + lapack_int lda = internal::convert_index<lapack_int>(matrix.outerStride()), ldu, ldvt; \ + lapack_int matrix_order = LAPACKE_COLROW; \ char jobu, jobvt; \ - MKLTYPE *u, *vt, dummy; \ + LAPACKE_TYPE *u, *vt, dummy; \ jobu = (m_computeFullU) ? 'A' : (m_computeThinU) ? 'S' : 'N'; \ jobvt = (m_computeFullV) ? 'A' : (m_computeThinV) ? 'S' : 'N'; \ if (computeU()) { \ - ldu = m_matrixU.outerStride(); \ - u = (MKLTYPE*)m_matrixU.data(); \ + ldu = internal::convert_index<lapack_int>(m_matrixU.outerStride()); \ + u = (LAPACKE_TYPE*)m_matrixU.data(); \ } else { ldu=1; u=&dummy; }\ MatrixType localV; \ - ldvt = (m_computeFullV) ? m_cols : (m_computeThinV) ? m_diagSize : 1; \ + ldvt = (m_computeFullV) ? internal::convert_index<lapack_int>(m_cols) : (m_computeThinV) ? internal::convert_index<lapack_int>(m_diagSize) : 1; \ if (computeV()) { \ localV.resize(ldvt, m_cols); \ - vt = (MKLTYPE*)localV.data(); \ + vt = (LAPACKE_TYPE*)localV.data(); \ } else { ldvt=1; vt=&dummy; }\ - Matrix<MKLRTYPE, Dynamic, Dynamic> superb; superb.resize(m_diagSize, 1); \ + Matrix<LAPACKE_RTYPE, Dynamic, Dynamic> superb; superb.resize(m_diagSize, 1); \ MatrixType m_temp; m_temp = matrix; \ - LAPACKE_##MKLPREFIX##gesvd( matrix_order, jobu, jobvt, m_rows, m_cols, (MKLTYPE*)m_temp.data(), lda, (MKLRTYPE*)m_singularValues.data(), u, ldu, vt, ldvt, superb.data()); \ + LAPACKE_##LAPACKE_PREFIX##gesvd( matrix_order, jobu, jobvt, internal::convert_index<lapack_int>(m_rows), internal::convert_index<lapack_int>(m_cols), (LAPACKE_TYPE*)m_temp.data(), lda, (LAPACKE_RTYPE*)m_singularValues.data(), u, ldu, vt, ldvt, superb.data()); \ if (computeV()) m_matrixV = localV.adjoint(); \ /* for(int i=0;i<m_diagSize;i++) if (m_singularValues.coeffRef(i) < precision) { m_nonzeroSingularValues--; m_singularValues.coeffRef(i)=RealScalar(0);}*/ \ m_isInitialized = true; \ return *this; \ } -EIGEN_MKL_SVD(double, double, double, d, ColMajor, LAPACK_COL_MAJOR) -EIGEN_MKL_SVD(float, float, float , s, ColMajor, LAPACK_COL_MAJOR) -EIGEN_MKL_SVD(dcomplex, MKL_Complex16, double, z, ColMajor, LAPACK_COL_MAJOR) -EIGEN_MKL_SVD(scomplex, MKL_Complex8, float , c, ColMajor, LAPACK_COL_MAJOR) +EIGEN_LAPACKE_SVD(double, double, double, d, ColMajor, LAPACK_COL_MAJOR) +EIGEN_LAPACKE_SVD(float, float, float , s, ColMajor, LAPACK_COL_MAJOR) +EIGEN_LAPACKE_SVD(dcomplex, lapack_complex_double, double, z, ColMajor, LAPACK_COL_MAJOR) +EIGEN_LAPACKE_SVD(scomplex, lapack_complex_float, float , c, ColMajor, LAPACK_COL_MAJOR) -EIGEN_MKL_SVD(double, double, double, d, RowMajor, LAPACK_ROW_MAJOR) -EIGEN_MKL_SVD(float, float, float , s, RowMajor, LAPACK_ROW_MAJOR) -EIGEN_MKL_SVD(dcomplex, MKL_Complex16, double, z, RowMajor, LAPACK_ROW_MAJOR) -EIGEN_MKL_SVD(scomplex, MKL_Complex8, float , c, RowMajor, LAPACK_ROW_MAJOR) +EIGEN_LAPACKE_SVD(double, double, double, d, RowMajor, LAPACK_ROW_MAJOR) +EIGEN_LAPACKE_SVD(float, float, float , s, RowMajor, LAPACK_ROW_MAJOR) +EIGEN_LAPACKE_SVD(dcomplex, lapack_complex_double, double, z, RowMajor, LAPACK_ROW_MAJOR) +EIGEN_LAPACKE_SVD(scomplex, lapack_complex_float, float , c, RowMajor, LAPACK_ROW_MAJOR) } // end namespace Eigen -#endif // EIGEN_JACOBISVD_MKL_H +#endif // EIGEN_JACOBISVD_LAPACKE_H diff --git a/Eigen/src/SVD/SVDBase.h b/Eigen/src/SVD/SVDBase.h index e2d77a761..cc90a3b75 100644 --- a/Eigen/src/SVD/SVDBase.h +++ b/Eigen/src/SVD/SVDBase.h @@ -130,10 +130,9 @@ public: inline Index rank() const { using std::abs; - using std::max; eigen_assert(m_isInitialized && "JacobiSVD is not initialized."); if(m_singularValues.size()==0) return 0; - RealScalar premultiplied_threshold = (max)(m_singularValues.coeff(0) * threshold(), (std::numeric_limits<RealScalar>::min)()); + RealScalar premultiplied_threshold = numext::maxi<RealScalar>(m_singularValues.coeff(0) * threshold(), (std::numeric_limits<RealScalar>::min)()); Index i = m_nonzeroSingularValues-1; while(i>=0 && m_singularValues.coeff(i) < premultiplied_threshold) --i; return i+1; diff --git a/Eigen/src/SparseCore/SparseAssign.h b/Eigen/src/SparseCore/SparseAssign.h index b284fa9e4..fa5386599 100644 --- a/Eigen/src/SparseCore/SparseAssign.h +++ b/Eigen/src/SparseCore/SparseAssign.h @@ -124,8 +124,8 @@ void assign_sparse_to_sparse(DstXprType &dst, const SrcXprType &src) } // Generic Sparse to Sparse assignment -template< typename DstXprType, typename SrcXprType, typename Functor, typename Scalar> -struct Assignment<DstXprType, SrcXprType, Functor, Sparse2Sparse, Scalar> +template< typename DstXprType, typename SrcXprType, typename Functor> +struct Assignment<DstXprType, SrcXprType, Functor, Sparse2Sparse> { static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/) { @@ -134,8 +134,8 @@ struct Assignment<DstXprType, SrcXprType, Functor, Sparse2Sparse, Scalar> }; // Generic Sparse to Dense assignment -template< typename DstXprType, typename SrcXprType, typename Functor, typename Scalar> -struct Assignment<DstXprType, SrcXprType, Functor, Sparse2Dense, Scalar> +template< typename DstXprType, typename SrcXprType, typename Functor> +struct Assignment<DstXprType, SrcXprType, Functor, Sparse2Dense> { static void run(DstXprType &dst, const SrcXprType &src, const Functor &func) { @@ -156,7 +156,7 @@ struct Assignment<DstXprType, SrcXprType, Functor, Sparse2Dense, Scalar> // Specialization for "dst = dec.solve(rhs)" // NOTE we need to specialize it for Sparse2Sparse to avoid ambiguous specialization error template<typename DstXprType, typename DecType, typename RhsType, typename Scalar> -struct Assignment<DstXprType, Solve<DecType,RhsType>, internal::assign_op<Scalar,Scalar>, Sparse2Sparse, Scalar> +struct Assignment<DstXprType, Solve<DecType,RhsType>, internal::assign_op<Scalar,Scalar>, Sparse2Sparse> { typedef Solve<DecType,RhsType> SrcXprType; static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &) @@ -169,10 +169,11 @@ struct Diagonal2Sparse {}; template<> struct AssignmentKind<SparseShape,DiagonalShape> { typedef Diagonal2Sparse Kind; }; -template< typename DstXprType, typename SrcXprType, typename Functor, typename Scalar> -struct Assignment<DstXprType, SrcXprType, Functor, Diagonal2Sparse, Scalar> +template< typename DstXprType, typename SrcXprType, typename Functor> +struct Assignment<DstXprType, SrcXprType, Functor, Diagonal2Sparse> { typedef typename DstXprType::StorageIndex StorageIndex; + typedef typename DstXprType::Scalar Scalar; typedef Array<StorageIndex,Dynamic,1> ArrayXI; typedef Array<Scalar,Dynamic,1> ArrayXS; template<int Options> diff --git a/Eigen/src/SparseCore/SparseBlock.h b/Eigen/src/SparseCore/SparseBlock.h index 0e447f15f..13e8b0bf1 100644 --- a/Eigen/src/SparseCore/SparseBlock.h +++ b/Eigen/src/SparseCore/SparseBlock.h @@ -504,6 +504,7 @@ template<typename ArgType, int BlockRows, int BlockCols, bool InnerPanel> class unary_evaluator<Block<ArgType,BlockRows,BlockCols,InnerPanel>, IteratorBased>::InnerVectorInnerIterator
: public EvalIterator
{
+ enum { IsRowMajor = unary_evaluator::IsRowMajor };
const XprType& m_block;
Index m_end;
public:
@@ -528,6 +529,7 @@ public: template<typename ArgType, int BlockRows, int BlockCols, bool InnerPanel>
class unary_evaluator<Block<ArgType,BlockRows,BlockCols,InnerPanel>, IteratorBased>::OuterVectorInnerIterator
{
+ enum { IsRowMajor = unary_evaluator::IsRowMajor };
const unary_evaluator& m_eval;
Index m_outerPos;
Index m_innerIndex;
diff --git a/Eigen/src/SparseCore/SparseMap.h b/Eigen/src/SparseCore/SparseMap.h index d76f3b68f..f99be3379 100644 --- a/Eigen/src/SparseCore/SparseMap.h +++ b/Eigen/src/SparseCore/SparseMap.h @@ -186,7 +186,7 @@ class SparseMapBase<Derived,WriteAccessors> Index end = Base::isCompressed() ? Base::m_outerIndex[outer+1] : start + Base::m_innerNonZeros[outer]; eigen_assert(end>=start && "you probably called coeffRef on a non finalized matrix"); eigen_assert(end>start && "coeffRef cannot be called on a zero coefficient"); - Index* r = std::lower_bound(&Base::m_innerIndices[start],&Base::m_innerIndices[end],inner); + StorageIndex* r = std::lower_bound(&Base::m_innerIndices[start],&Base::m_innerIndices[end],inner); const Index id = r - &Base::m_innerIndices[0]; eigen_assert((*r==inner) && (id<end) && "coeffRef cannot be called on a zero coefficient"); return const_cast<Scalar*>(Base::m_values)[id]; diff --git a/Eigen/src/SparseCore/SparseProduct.h b/Eigen/src/SparseCore/SparseProduct.h index 84e69903b..7a5ad0635 100644 --- a/Eigen/src/SparseCore/SparseProduct.h +++ b/Eigen/src/SparseCore/SparseProduct.h @@ -45,7 +45,7 @@ struct generic_product_impl<Lhs, Rhs, SparseShape, SparseShape, ProductType> // dense += sparse * sparse template<typename Dest,typename ActualLhs> - static void addTo(Dest& dst, const ActualLhs& lhs, const Rhs& rhs, int* = typename enable_if<is_same<typename evaluator_traits<Dest>::Shape,DenseShape>::value,int*>::type(0) ) + static void addTo(Dest& dst, const ActualLhs& lhs, const Rhs& rhs, typename enable_if<is_same<typename evaluator_traits<Dest>::Shape,DenseShape>::value,int*>::type* = 0) { typedef typename nested_eval<ActualLhs,Dynamic>::type LhsNested; typedef typename nested_eval<Rhs,Dynamic>::type RhsNested; @@ -57,7 +57,7 @@ struct generic_product_impl<Lhs, Rhs, SparseShape, SparseShape, ProductType> // dense -= sparse * sparse template<typename Dest> - static void subTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, int* = typename enable_if<is_same<typename evaluator_traits<Dest>::Shape,DenseShape>::value,int*>::type(0) ) + static void subTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, typename enable_if<is_same<typename evaluator_traits<Dest>::Shape,DenseShape>::value,int*>::type* = 0) { addTo(dst, -lhs, rhs); } diff --git a/Eigen/src/SparseCore/SparseSelfAdjointView.h b/Eigen/src/SparseCore/SparseSelfAdjointView.h index 4f0c84d88..a48520c0c 100644 --- a/Eigen/src/SparseCore/SparseSelfAdjointView.h +++ b/Eigen/src/SparseCore/SparseSelfAdjointView.h @@ -218,8 +218,8 @@ struct SparseSelfAdjoint2Sparse {}; template<> struct AssignmentKind<SparseShape,SparseSelfAdjointShape> { typedef SparseSelfAdjoint2Sparse Kind; }; template<> struct AssignmentKind<SparseSelfAdjointShape,SparseShape> { typedef Sparse2Sparse Kind; }; -template< typename DstXprType, typename SrcXprType, typename Functor, typename Scalar> -struct Assignment<DstXprType, SrcXprType, Functor, SparseSelfAdjoint2Sparse, Scalar> +template< typename DstXprType, typename SrcXprType, typename Functor> +struct Assignment<DstXprType, SrcXprType, Functor, SparseSelfAdjoint2Sparse> { typedef typename DstXprType::StorageIndex StorageIndex; template<typename DestScalar,int StorageOrder> diff --git a/Eigen/src/SuperLUSupport/SuperLUSupport.h b/Eigen/src/SuperLUSupport/SuperLUSupport.h index 7e2efd452..88c44bcd0 100644 --- a/Eigen/src/SuperLUSupport/SuperLUSupport.h +++ b/Eigen/src/SuperLUSupport/SuperLUSupport.h @@ -10,15 +10,16 @@ #ifndef EIGEN_SUPERLUSUPPORT_H #define EIGEN_SUPERLUSUPPORT_H -namespace Eigen { +namespace Eigen { +#if defined(SUPERLU_MAJOR_VERSION) && (SUPERLU_MAJOR_VERSION >= 5) #define DECL_GSSVX(PREFIX,FLOATTYPE,KEYTYPE) \ extern "C" { \ extern void PREFIX##gssvx(superlu_options_t *, SuperMatrix *, int *, int *, int *, \ char *, FLOATTYPE *, FLOATTYPE *, SuperMatrix *, SuperMatrix *, \ void *, int, SuperMatrix *, SuperMatrix *, \ FLOATTYPE *, FLOATTYPE *, FLOATTYPE *, FLOATTYPE *, \ - mem_usage_t *, SuperLUStat_t *, int *); \ + GlobalLU_t *, mem_usage_t *, SuperLUStat_t *, int *); \ } \ inline float SuperLU_gssvx(superlu_options_t *options, SuperMatrix *A, \ int *perm_c, int *perm_r, int *etree, char *equed, \ @@ -28,12 +29,37 @@ namespace Eigen { FLOATTYPE *recip_pivot_growth, \ FLOATTYPE *rcond, FLOATTYPE *ferr, FLOATTYPE *berr, \ SuperLUStat_t *stats, int *info, KEYTYPE) { \ - mem_usage_t mem_usage; \ + mem_usage_t mem_usage; \ + GlobalLU_t gLU; \ + PREFIX##gssvx(options, A, perm_c, perm_r, etree, equed, R, C, L, \ + U, work, lwork, B, X, recip_pivot_growth, rcond, \ + ferr, berr, &gLU, &mem_usage, stats, info); \ + return mem_usage.for_lu; /* bytes used by the factor storage */ \ + } +#else // version < 5.0 +#define DECL_GSSVX(PREFIX,FLOATTYPE,KEYTYPE) \ + extern "C" { \ + extern void PREFIX##gssvx(superlu_options_t *, SuperMatrix *, int *, int *, int *, \ + char *, FLOATTYPE *, FLOATTYPE *, SuperMatrix *, SuperMatrix *, \ + void *, int, SuperMatrix *, SuperMatrix *, \ + FLOATTYPE *, FLOATTYPE *, FLOATTYPE *, FLOATTYPE *, \ + mem_usage_t *, SuperLUStat_t *, int *); \ + } \ + inline float SuperLU_gssvx(superlu_options_t *options, SuperMatrix *A, \ + int *perm_c, int *perm_r, int *etree, char *equed, \ + FLOATTYPE *R, FLOATTYPE *C, SuperMatrix *L, \ + SuperMatrix *U, void *work, int lwork, \ + SuperMatrix *B, SuperMatrix *X, \ + FLOATTYPE *recip_pivot_growth, \ + FLOATTYPE *rcond, FLOATTYPE *ferr, FLOATTYPE *berr, \ + SuperLUStat_t *stats, int *info, KEYTYPE) { \ + mem_usage_t mem_usage; \ PREFIX##gssvx(options, A, perm_c, perm_r, etree, equed, R, C, L, \ U, work, lwork, B, X, recip_pivot_growth, rcond, \ ferr, berr, &mem_usage, stats, info); \ return mem_usage.for_lu; /* bytes used by the factor storage */ \ } +#endif DECL_GSSVX(s,float,float) DECL_GSSVX(c,float,std::complex<float>) diff --git a/Eigen/src/misc/RealSvd2x2.h b/Eigen/src/misc/RealSvd2x2.h index dfaaa0b17..abb4d3c2f 100644 --- a/Eigen/src/misc/RealSvd2x2.h +++ b/Eigen/src/misc/RealSvd2x2.h @@ -28,7 +28,8 @@ void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q, JacobiRotation<RealScalar> rot1; RealScalar t = m.coeff(0,0) + m.coeff(1,1); RealScalar d = m.coeff(1,0) - m.coeff(0,1); - if(d == RealScalar(0)) + + if(abs(d) < (std::numeric_limits<RealScalar>::min)()) { rot1.s() = RealScalar(0); rot1.c() = RealScalar(1); diff --git a/Eigen/src/misc/lapacke.h b/Eigen/src/misc/lapacke.h new file mode 100755 index 000000000..8c7e79b03 --- /dev/null +++ b/Eigen/src/misc/lapacke.h @@ -0,0 +1,16291 @@ +/***************************************************************************** + Copyright (c) 2010, Intel Corp. + All rights reserved. + + Redistribution and use in source and binary forms, with or without + modification, are permitted provided that the following conditions are met: + + * Redistributions of source code must retain the above copyright notice, + this list of conditions and the following disclaimer. + * Redistributions in binary form must reproduce the above copyright + notice, this list of conditions and the following disclaimer in the + documentation and/or other materials provided with the distribution. + * Neither the name of Intel Corporation nor the names of its contributors + may be used to endorse or promote products derived from this software + without specific prior written permission. + + THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" + AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE + LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF + THE POSSIBILITY OF SUCH DAMAGE. +****************************************************************************** +* Contents: Native C interface to LAPACK +* Author: Intel Corporation +* Generated November, 2011 +*****************************************************************************/ + +#ifndef _MKL_LAPACKE_H_ + +#ifndef _LAPACKE_H_ +#define _LAPACKE_H_ + +/* +* Turn on HAVE_LAPACK_CONFIG_H to redefine C-LAPACK datatypes +*/ +#ifdef HAVE_LAPACK_CONFIG_H +#include "lapacke_config.h" +#endif + +#ifdef __cplusplus +extern "C" { +#endif /* __cplusplus */ + +#include <stdlib.h> + +#ifndef lapack_int +#define lapack_int int +#endif + +#ifndef lapack_logical +#define lapack_logical lapack_int +#endif + +/* Complex types are structures equivalent to the +* Fortran complex types COMPLEX(4) and COMPLEX(8). +* +* One can also redefine the types with his own types +* for example by including in the code definitions like +* +* #define lapack_complex_float std::complex<float> +* #define lapack_complex_double std::complex<double> +* +* or define these types in the command line: +* +* -Dlapack_complex_float="std::complex<float>" +* -Dlapack_complex_double="std::complex<double>" +*/ + +#ifndef LAPACK_COMPLEX_CUSTOM + +/* Complex type (single precision) */ +#ifndef lapack_complex_float +#include <complex.h> +#define lapack_complex_float float _Complex +#endif + +#ifndef lapack_complex_float_real +#define lapack_complex_float_real(z) (creal(z)) +#endif + +#ifndef lapack_complex_float_imag +#define lapack_complex_float_imag(z) (cimag(z)) +#endif + +lapack_complex_float lapack_make_complex_float( float re, float im ); + +/* Complex type (double precision) */ +#ifndef lapack_complex_double +#include <complex.h> +#define lapack_complex_double double _Complex +#endif + +#ifndef lapack_complex_double_real +#define lapack_complex_double_real(z) (creal(z)) +#endif + +#ifndef lapack_complex_double_imag +#define lapack_complex_double_imag(z) (cimag(z)) +#endif + +lapack_complex_double lapack_make_complex_double( double re, double im ); + +#endif + +#ifndef LAPACKE_malloc +#define LAPACKE_malloc( size ) malloc( size ) +#endif +#ifndef LAPACKE_free +#define LAPACKE_free( p ) free( p ) +#endif + +#define LAPACK_C2INT( x ) (lapack_int)(*((float*)&x )) +#define LAPACK_Z2INT( x ) (lapack_int)(*((double*)&x )) + +#define LAPACK_ROW_MAJOR 101 +#define LAPACK_COL_MAJOR 102 + +#define LAPACK_WORK_MEMORY_ERROR -1010 +#define LAPACK_TRANSPOSE_MEMORY_ERROR -1011 + +/* Callback logical functions of one, two, or three arguments are used +* to select eigenvalues to sort to the top left of the Schur form. +* The value is selected if function returns TRUE (non-zero). */ + +typedef lapack_logical (*LAPACK_S_SELECT2) ( const float*, const float* ); +typedef lapack_logical (*LAPACK_S_SELECT3) + ( const float*, const float*, const float* ); +typedef lapack_logical (*LAPACK_D_SELECT2) ( const double*, const double* ); +typedef lapack_logical (*LAPACK_D_SELECT3) + ( const double*, const double*, const double* ); + +typedef lapack_logical (*LAPACK_C_SELECT1) ( const lapack_complex_float* ); +typedef lapack_logical (*LAPACK_C_SELECT2) + ( const lapack_complex_float*, const lapack_complex_float* ); +typedef lapack_logical (*LAPACK_Z_SELECT1) ( const lapack_complex_double* ); +typedef lapack_logical (*LAPACK_Z_SELECT2) + ( const lapack_complex_double*, const lapack_complex_double* ); + +#include "lapacke_mangling.h" + +#define LAPACK_lsame LAPACK_GLOBAL(lsame,LSAME) +lapack_logical LAPACK_lsame( char* ca, char* cb, + lapack_int lca, lapack_int lcb ); + +/* C-LAPACK function prototypes */ + +lapack_int LAPACKE_sbdsdc( int matrix_order, char uplo, char compq, + lapack_int n, float* d, float* e, float* u, + lapack_int ldu, float* vt, lapack_int ldvt, float* q, + lapack_int* iq ); +lapack_int LAPACKE_dbdsdc( int matrix_order, char uplo, char compq, + lapack_int n, double* d, double* e, double* u, + lapack_int ldu, double* vt, lapack_int ldvt, + double* q, lapack_int* iq ); + +lapack_int LAPACKE_sbdsqr( int matrix_order, char uplo, lapack_int n, + lapack_int ncvt, lapack_int nru, lapack_int ncc, + float* d, float* e, float* vt, lapack_int ldvt, + float* u, lapack_int ldu, float* c, lapack_int ldc ); +lapack_int LAPACKE_dbdsqr( int matrix_order, char uplo, lapack_int n, + lapack_int ncvt, lapack_int nru, lapack_int ncc, + double* d, double* e, double* vt, lapack_int ldvt, + double* u, lapack_int ldu, double* c, + lapack_int ldc ); +lapack_int LAPACKE_cbdsqr( int matrix_order, char uplo, lapack_int n, + lapack_int ncvt, lapack_int nru, lapack_int ncc, + float* d, float* e, lapack_complex_float* vt, + lapack_int ldvt, lapack_complex_float* u, + lapack_int ldu, lapack_complex_float* c, + lapack_int ldc ); +lapack_int LAPACKE_zbdsqr( int matrix_order, char uplo, lapack_int n, + lapack_int ncvt, lapack_int nru, lapack_int ncc, + double* d, double* e, lapack_complex_double* vt, + lapack_int ldvt, lapack_complex_double* u, + lapack_int ldu, lapack_complex_double* c, + lapack_int ldc ); + +lapack_int LAPACKE_sdisna( char job, lapack_int m, lapack_int n, const float* d, + float* sep ); +lapack_int LAPACKE_ddisna( char job, lapack_int m, lapack_int n, + const double* d, double* sep ); + +lapack_int LAPACKE_sgbbrd( int matrix_order, char vect, lapack_int m, + lapack_int n, lapack_int ncc, lapack_int kl, + lapack_int ku, float* ab, lapack_int ldab, float* d, + float* e, float* q, lapack_int ldq, float* pt, + lapack_int ldpt, float* c, lapack_int ldc ); +lapack_int LAPACKE_dgbbrd( int matrix_order, char vect, lapack_int m, + lapack_int n, lapack_int ncc, lapack_int kl, + lapack_int ku, double* ab, lapack_int ldab, + double* d, double* e, double* q, lapack_int ldq, + double* pt, lapack_int ldpt, double* c, + lapack_int ldc ); +lapack_int LAPACKE_cgbbrd( int matrix_order, char vect, lapack_int m, + lapack_int n, lapack_int ncc, lapack_int kl, + lapack_int ku, lapack_complex_float* ab, + lapack_int ldab, float* d, float* e, + lapack_complex_float* q, lapack_int ldq, + lapack_complex_float* pt, lapack_int ldpt, + lapack_complex_float* c, lapack_int ldc ); +lapack_int LAPACKE_zgbbrd( int matrix_order, char vect, lapack_int m, + lapack_int n, lapack_int ncc, lapack_int kl, + lapack_int ku, lapack_complex_double* ab, + lapack_int ldab, double* d, double* e, + lapack_complex_double* q, lapack_int ldq, + lapack_complex_double* pt, lapack_int ldpt, + lapack_complex_double* c, lapack_int ldc ); + +lapack_int LAPACKE_sgbcon( int matrix_order, char norm, lapack_int n, + lapack_int kl, lapack_int ku, const float* ab, + lapack_int ldab, const lapack_int* ipiv, float anorm, + float* rcond ); +lapack_int LAPACKE_dgbcon( int matrix_order, char norm, lapack_int n, + lapack_int kl, lapack_int ku, const double* ab, + lapack_int ldab, const lapack_int* ipiv, + double anorm, double* rcond ); +lapack_int LAPACKE_cgbcon( int matrix_order, char norm, lapack_int n, + lapack_int kl, lapack_int ku, + const lapack_complex_float* ab, lapack_int ldab, + const lapack_int* ipiv, float anorm, float* rcond ); +lapack_int LAPACKE_zgbcon( int matrix_order, char norm, lapack_int n, + lapack_int kl, lapack_int ku, + const lapack_complex_double* ab, lapack_int ldab, + const lapack_int* ipiv, double anorm, + double* rcond ); + +lapack_int LAPACKE_sgbequ( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, const float* ab, + lapack_int ldab, float* r, float* c, float* rowcnd, + float* colcnd, float* amax ); +lapack_int LAPACKE_dgbequ( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, const double* ab, + lapack_int ldab, double* r, double* c, + double* rowcnd, double* colcnd, double* amax ); +lapack_int LAPACKE_cgbequ( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, + const lapack_complex_float* ab, lapack_int ldab, + float* r, float* c, float* rowcnd, float* colcnd, + float* amax ); +lapack_int LAPACKE_zgbequ( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, + const lapack_complex_double* ab, lapack_int ldab, + double* r, double* c, double* rowcnd, double* colcnd, + double* amax ); + +lapack_int LAPACKE_sgbequb( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, const float* ab, + lapack_int ldab, float* r, float* c, float* rowcnd, + float* colcnd, float* amax ); +lapack_int LAPACKE_dgbequb( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, const double* ab, + lapack_int ldab, double* r, double* c, + double* rowcnd, double* colcnd, double* amax ); +lapack_int LAPACKE_cgbequb( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, + const lapack_complex_float* ab, lapack_int ldab, + float* r, float* c, float* rowcnd, float* colcnd, + float* amax ); +lapack_int LAPACKE_zgbequb( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, + const lapack_complex_double* ab, lapack_int ldab, + double* r, double* c, double* rowcnd, + double* colcnd, double* amax ); + +lapack_int LAPACKE_sgbrfs( int matrix_order, char trans, lapack_int n, + lapack_int kl, lapack_int ku, lapack_int nrhs, + const float* ab, lapack_int ldab, const float* afb, + lapack_int ldafb, const lapack_int* ipiv, + const float* b, lapack_int ldb, float* x, + lapack_int ldx, float* ferr, float* berr ); +lapack_int LAPACKE_dgbrfs( int matrix_order, char trans, lapack_int n, + lapack_int kl, lapack_int ku, lapack_int nrhs, + const double* ab, lapack_int ldab, const double* afb, + lapack_int ldafb, const lapack_int* ipiv, + const double* b, lapack_int ldb, double* x, + lapack_int ldx, double* ferr, double* berr ); +lapack_int LAPACKE_cgbrfs( int matrix_order, char trans, lapack_int n, + lapack_int kl, lapack_int ku, lapack_int nrhs, + const lapack_complex_float* ab, lapack_int ldab, + const lapack_complex_float* afb, lapack_int ldafb, + const lapack_int* ipiv, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, float* ferr, + float* berr ); +lapack_int LAPACKE_zgbrfs( int matrix_order, char trans, lapack_int n, + lapack_int kl, lapack_int ku, lapack_int nrhs, + const lapack_complex_double* ab, lapack_int ldab, + const lapack_complex_double* afb, lapack_int ldafb, + const lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr ); + +lapack_int LAPACKE_sgbrfsx( int matrix_order, char trans, char equed, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, const float* ab, lapack_int ldab, + const float* afb, lapack_int ldafb, + const lapack_int* ipiv, const float* r, + const float* c, const float* b, lapack_int ldb, + float* x, lapack_int ldx, float* rcond, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params ); +lapack_int LAPACKE_dgbrfsx( int matrix_order, char trans, char equed, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, const double* ab, lapack_int ldab, + const double* afb, lapack_int ldafb, + const lapack_int* ipiv, const double* r, + const double* c, const double* b, lapack_int ldb, + double* x, lapack_int ldx, double* rcond, + double* berr, lapack_int n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int nparams, double* params ); +lapack_int LAPACKE_cgbrfsx( int matrix_order, char trans, char equed, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, const lapack_complex_float* ab, + lapack_int ldab, const lapack_complex_float* afb, + lapack_int ldafb, const lapack_int* ipiv, + const float* r, const float* c, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* berr, lapack_int n_err_bnds, + float* err_bnds_norm, float* err_bnds_comp, + lapack_int nparams, float* params ); +lapack_int LAPACKE_zgbrfsx( int matrix_order, char trans, char equed, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, const lapack_complex_double* ab, + lapack_int ldab, const lapack_complex_double* afb, + lapack_int ldafb, const lapack_int* ipiv, + const double* r, const double* c, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* berr, lapack_int n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int nparams, double* params ); + +lapack_int LAPACKE_sgbsv( int matrix_order, lapack_int n, lapack_int kl, + lapack_int ku, lapack_int nrhs, float* ab, + lapack_int ldab, lapack_int* ipiv, float* b, + lapack_int ldb ); +lapack_int LAPACKE_dgbsv( int matrix_order, lapack_int n, lapack_int kl, + lapack_int ku, lapack_int nrhs, double* ab, + lapack_int ldab, lapack_int* ipiv, double* b, + lapack_int ldb ); +lapack_int LAPACKE_cgbsv( int matrix_order, lapack_int n, lapack_int kl, + lapack_int ku, lapack_int nrhs, + lapack_complex_float* ab, lapack_int ldab, + lapack_int* ipiv, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zgbsv( int matrix_order, lapack_int n, lapack_int kl, + lapack_int ku, lapack_int nrhs, + lapack_complex_double* ab, lapack_int ldab, + lapack_int* ipiv, lapack_complex_double* b, + lapack_int ldb ); + +lapack_int LAPACKE_sgbsvx( int matrix_order, char fact, char trans, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, float* ab, lapack_int ldab, + float* afb, lapack_int ldafb, lapack_int* ipiv, + char* equed, float* r, float* c, float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* rcond, float* ferr, float* berr, + float* rpivot ); +lapack_int LAPACKE_dgbsvx( int matrix_order, char fact, char trans, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, double* ab, lapack_int ldab, + double* afb, lapack_int ldafb, lapack_int* ipiv, + char* equed, double* r, double* c, double* b, + lapack_int ldb, double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr, + double* rpivot ); +lapack_int LAPACKE_cgbsvx( int matrix_order, char fact, char trans, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, lapack_complex_float* ab, + lapack_int ldab, lapack_complex_float* afb, + lapack_int ldafb, lapack_int* ipiv, char* equed, + float* r, float* c, lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* x, + lapack_int ldx, float* rcond, float* ferr, + float* berr, float* rpivot ); +lapack_int LAPACKE_zgbsvx( int matrix_order, char fact, char trans, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, lapack_complex_double* ab, + lapack_int ldab, lapack_complex_double* afb, + lapack_int ldafb, lapack_int* ipiv, char* equed, + double* r, double* c, lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* x, + lapack_int ldx, double* rcond, double* ferr, + double* berr, double* rpivot ); + +lapack_int LAPACKE_sgbsvxx( int matrix_order, char fact, char trans, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, float* ab, lapack_int ldab, + float* afb, lapack_int ldafb, lapack_int* ipiv, + char* equed, float* r, float* c, float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* rcond, float* rpvgrw, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params ); +lapack_int LAPACKE_dgbsvxx( int matrix_order, char fact, char trans, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, double* ab, lapack_int ldab, + double* afb, lapack_int ldafb, lapack_int* ipiv, + char* equed, double* r, double* c, double* b, + lapack_int ldb, double* x, lapack_int ldx, + double* rcond, double* rpvgrw, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params ); +lapack_int LAPACKE_cgbsvxx( int matrix_order, char fact, char trans, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, lapack_complex_float* ab, + lapack_int ldab, lapack_complex_float* afb, + lapack_int ldafb, lapack_int* ipiv, char* equed, + float* r, float* c, lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* x, + lapack_int ldx, float* rcond, float* rpvgrw, + float* berr, lapack_int n_err_bnds, + float* err_bnds_norm, float* err_bnds_comp, + lapack_int nparams, float* params ); +lapack_int LAPACKE_zgbsvxx( int matrix_order, char fact, char trans, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, lapack_complex_double* ab, + lapack_int ldab, lapack_complex_double* afb, + lapack_int ldafb, lapack_int* ipiv, char* equed, + double* r, double* c, lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* x, + lapack_int ldx, double* rcond, double* rpvgrw, + double* berr, lapack_int n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int nparams, double* params ); + +lapack_int LAPACKE_sgbtrf( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, float* ab, + lapack_int ldab, lapack_int* ipiv ); +lapack_int LAPACKE_dgbtrf( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, double* ab, + lapack_int ldab, lapack_int* ipiv ); +lapack_int LAPACKE_cgbtrf( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, + lapack_complex_float* ab, lapack_int ldab, + lapack_int* ipiv ); +lapack_int LAPACKE_zgbtrf( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, + lapack_complex_double* ab, lapack_int ldab, + lapack_int* ipiv ); + +lapack_int LAPACKE_sgbtrs( int matrix_order, char trans, lapack_int n, + lapack_int kl, lapack_int ku, lapack_int nrhs, + const float* ab, lapack_int ldab, + const lapack_int* ipiv, float* b, lapack_int ldb ); +lapack_int LAPACKE_dgbtrs( int matrix_order, char trans, lapack_int n, + lapack_int kl, lapack_int ku, lapack_int nrhs, + const double* ab, lapack_int ldab, + const lapack_int* ipiv, double* b, lapack_int ldb ); +lapack_int LAPACKE_cgbtrs( int matrix_order, char trans, lapack_int n, + lapack_int kl, lapack_int ku, lapack_int nrhs, + const lapack_complex_float* ab, lapack_int ldab, + const lapack_int* ipiv, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zgbtrs( int matrix_order, char trans, lapack_int n, + lapack_int kl, lapack_int ku, lapack_int nrhs, + const lapack_complex_double* ab, lapack_int ldab, + const lapack_int* ipiv, lapack_complex_double* b, + lapack_int ldb ); + +lapack_int LAPACKE_sgebak( int matrix_order, char job, char side, lapack_int n, + lapack_int ilo, lapack_int ihi, const float* scale, + lapack_int m, float* v, lapack_int ldv ); +lapack_int LAPACKE_dgebak( int matrix_order, char job, char side, lapack_int n, + lapack_int ilo, lapack_int ihi, const double* scale, + lapack_int m, double* v, lapack_int ldv ); +lapack_int LAPACKE_cgebak( int matrix_order, char job, char side, lapack_int n, + lapack_int ilo, lapack_int ihi, const float* scale, + lapack_int m, lapack_complex_float* v, + lapack_int ldv ); +lapack_int LAPACKE_zgebak( int matrix_order, char job, char side, lapack_int n, + lapack_int ilo, lapack_int ihi, const double* scale, + lapack_int m, lapack_complex_double* v, + lapack_int ldv ); + +lapack_int LAPACKE_sgebal( int matrix_order, char job, lapack_int n, float* a, + lapack_int lda, lapack_int* ilo, lapack_int* ihi, + float* scale ); +lapack_int LAPACKE_dgebal( int matrix_order, char job, lapack_int n, double* a, + lapack_int lda, lapack_int* ilo, lapack_int* ihi, + double* scale ); +lapack_int LAPACKE_cgebal( int matrix_order, char job, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_int* ilo, lapack_int* ihi, float* scale ); +lapack_int LAPACKE_zgebal( int matrix_order, char job, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_int* ilo, lapack_int* ihi, double* scale ); + +lapack_int LAPACKE_sgebrd( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* d, float* e, + float* tauq, float* taup ); +lapack_int LAPACKE_dgebrd( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* d, double* e, + double* tauq, double* taup ); +lapack_int LAPACKE_cgebrd( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, float* d, + float* e, lapack_complex_float* tauq, + lapack_complex_float* taup ); +lapack_int LAPACKE_zgebrd( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, double* d, + double* e, lapack_complex_double* tauq, + lapack_complex_double* taup ); + +lapack_int LAPACKE_sgecon( int matrix_order, char norm, lapack_int n, + const float* a, lapack_int lda, float anorm, + float* rcond ); +lapack_int LAPACKE_dgecon( int matrix_order, char norm, lapack_int n, + const double* a, lapack_int lda, double anorm, + double* rcond ); +lapack_int LAPACKE_cgecon( int matrix_order, char norm, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + float anorm, float* rcond ); +lapack_int LAPACKE_zgecon( int matrix_order, char norm, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + double anorm, double* rcond ); + +lapack_int LAPACKE_sgeequ( int matrix_order, lapack_int m, lapack_int n, + const float* a, lapack_int lda, float* r, float* c, + float* rowcnd, float* colcnd, float* amax ); +lapack_int LAPACKE_dgeequ( int matrix_order, lapack_int m, lapack_int n, + const double* a, lapack_int lda, double* r, + double* c, double* rowcnd, double* colcnd, + double* amax ); +lapack_int LAPACKE_cgeequ( int matrix_order, lapack_int m, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + float* r, float* c, float* rowcnd, float* colcnd, + float* amax ); +lapack_int LAPACKE_zgeequ( int matrix_order, lapack_int m, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + double* r, double* c, double* rowcnd, double* colcnd, + double* amax ); + +lapack_int LAPACKE_sgeequb( int matrix_order, lapack_int m, lapack_int n, + const float* a, lapack_int lda, float* r, float* c, + float* rowcnd, float* colcnd, float* amax ); +lapack_int LAPACKE_dgeequb( int matrix_order, lapack_int m, lapack_int n, + const double* a, lapack_int lda, double* r, + double* c, double* rowcnd, double* colcnd, + double* amax ); +lapack_int LAPACKE_cgeequb( int matrix_order, lapack_int m, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + float* r, float* c, float* rowcnd, float* colcnd, + float* amax ); +lapack_int LAPACKE_zgeequb( int matrix_order, lapack_int m, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + double* r, double* c, double* rowcnd, + double* colcnd, double* amax ); + +lapack_int LAPACKE_sgees( int matrix_order, char jobvs, char sort, + LAPACK_S_SELECT2 select, lapack_int n, float* a, + lapack_int lda, lapack_int* sdim, float* wr, + float* wi, float* vs, lapack_int ldvs ); +lapack_int LAPACKE_dgees( int matrix_order, char jobvs, char sort, + LAPACK_D_SELECT2 select, lapack_int n, double* a, + lapack_int lda, lapack_int* sdim, double* wr, + double* wi, double* vs, lapack_int ldvs ); +lapack_int LAPACKE_cgees( int matrix_order, char jobvs, char sort, + LAPACK_C_SELECT1 select, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_int* sdim, lapack_complex_float* w, + lapack_complex_float* vs, lapack_int ldvs ); +lapack_int LAPACKE_zgees( int matrix_order, char jobvs, char sort, + LAPACK_Z_SELECT1 select, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_int* sdim, lapack_complex_double* w, + lapack_complex_double* vs, lapack_int ldvs ); + +lapack_int LAPACKE_sgeesx( int matrix_order, char jobvs, char sort, + LAPACK_S_SELECT2 select, char sense, lapack_int n, + float* a, lapack_int lda, lapack_int* sdim, + float* wr, float* wi, float* vs, lapack_int ldvs, + float* rconde, float* rcondv ); +lapack_int LAPACKE_dgeesx( int matrix_order, char jobvs, char sort, + LAPACK_D_SELECT2 select, char sense, lapack_int n, + double* a, lapack_int lda, lapack_int* sdim, + double* wr, double* wi, double* vs, lapack_int ldvs, + double* rconde, double* rcondv ); +lapack_int LAPACKE_cgeesx( int matrix_order, char jobvs, char sort, + LAPACK_C_SELECT1 select, char sense, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_int* sdim, lapack_complex_float* w, + lapack_complex_float* vs, lapack_int ldvs, + float* rconde, float* rcondv ); +lapack_int LAPACKE_zgeesx( int matrix_order, char jobvs, char sort, + LAPACK_Z_SELECT1 select, char sense, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_int* sdim, lapack_complex_double* w, + lapack_complex_double* vs, lapack_int ldvs, + double* rconde, double* rcondv ); + +lapack_int LAPACKE_sgeev( int matrix_order, char jobvl, char jobvr, + lapack_int n, float* a, lapack_int lda, float* wr, + float* wi, float* vl, lapack_int ldvl, float* vr, + lapack_int ldvr ); +lapack_int LAPACKE_dgeev( int matrix_order, char jobvl, char jobvr, + lapack_int n, double* a, lapack_int lda, double* wr, + double* wi, double* vl, lapack_int ldvl, double* vr, + lapack_int ldvr ); +lapack_int LAPACKE_cgeev( int matrix_order, char jobvl, char jobvr, + lapack_int n, lapack_complex_float* a, lapack_int lda, + lapack_complex_float* w, lapack_complex_float* vl, + lapack_int ldvl, lapack_complex_float* vr, + lapack_int ldvr ); +lapack_int LAPACKE_zgeev( int matrix_order, char jobvl, char jobvr, + lapack_int n, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* w, + lapack_complex_double* vl, lapack_int ldvl, + lapack_complex_double* vr, lapack_int ldvr ); + +lapack_int LAPACKE_sgeevx( int matrix_order, char balanc, char jobvl, + char jobvr, char sense, lapack_int n, float* a, + lapack_int lda, float* wr, float* wi, float* vl, + lapack_int ldvl, float* vr, lapack_int ldvr, + lapack_int* ilo, lapack_int* ihi, float* scale, + float* abnrm, float* rconde, float* rcondv ); +lapack_int LAPACKE_dgeevx( int matrix_order, char balanc, char jobvl, + char jobvr, char sense, lapack_int n, double* a, + lapack_int lda, double* wr, double* wi, double* vl, + lapack_int ldvl, double* vr, lapack_int ldvr, + lapack_int* ilo, lapack_int* ihi, double* scale, + double* abnrm, double* rconde, double* rcondv ); +lapack_int LAPACKE_cgeevx( int matrix_order, char balanc, char jobvl, + char jobvr, char sense, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* w, lapack_complex_float* vl, + lapack_int ldvl, lapack_complex_float* vr, + lapack_int ldvr, lapack_int* ilo, lapack_int* ihi, + float* scale, float* abnrm, float* rconde, + float* rcondv ); +lapack_int LAPACKE_zgeevx( int matrix_order, char balanc, char jobvl, + char jobvr, char sense, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* w, lapack_complex_double* vl, + lapack_int ldvl, lapack_complex_double* vr, + lapack_int ldvr, lapack_int* ilo, lapack_int* ihi, + double* scale, double* abnrm, double* rconde, + double* rcondv ); + +lapack_int LAPACKE_sgehrd( int matrix_order, lapack_int n, lapack_int ilo, + lapack_int ihi, float* a, lapack_int lda, + float* tau ); +lapack_int LAPACKE_dgehrd( int matrix_order, lapack_int n, lapack_int ilo, + lapack_int ihi, double* a, lapack_int lda, + double* tau ); +lapack_int LAPACKE_cgehrd( int matrix_order, lapack_int n, lapack_int ilo, + lapack_int ihi, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* tau ); +lapack_int LAPACKE_zgehrd( int matrix_order, lapack_int n, lapack_int ilo, + lapack_int ihi, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* tau ); + +lapack_int LAPACKE_sgejsv( int matrix_order, char joba, char jobu, char jobv, + char jobr, char jobt, char jobp, lapack_int m, + lapack_int n, float* a, lapack_int lda, float* sva, + float* u, lapack_int ldu, float* v, lapack_int ldv, + float* stat, lapack_int* istat ); +lapack_int LAPACKE_dgejsv( int matrix_order, char joba, char jobu, char jobv, + char jobr, char jobt, char jobp, lapack_int m, + lapack_int n, double* a, lapack_int lda, double* sva, + double* u, lapack_int ldu, double* v, lapack_int ldv, + double* stat, lapack_int* istat ); + +lapack_int LAPACKE_sgelq2( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* tau ); +lapack_int LAPACKE_dgelq2( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* tau ); +lapack_int LAPACKE_cgelq2( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* tau ); +lapack_int LAPACKE_zgelq2( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* tau ); + +lapack_int LAPACKE_sgelqf( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* tau ); +lapack_int LAPACKE_dgelqf( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* tau ); +lapack_int LAPACKE_cgelqf( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* tau ); +lapack_int LAPACKE_zgelqf( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* tau ); + +lapack_int LAPACKE_sgels( int matrix_order, char trans, lapack_int m, + lapack_int n, lapack_int nrhs, float* a, + lapack_int lda, float* b, lapack_int ldb ); +lapack_int LAPACKE_dgels( int matrix_order, char trans, lapack_int m, + lapack_int n, lapack_int nrhs, double* a, + lapack_int lda, double* b, lapack_int ldb ); +lapack_int LAPACKE_cgels( int matrix_order, char trans, lapack_int m, + lapack_int n, lapack_int nrhs, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zgels( int matrix_order, char trans, lapack_int m, + lapack_int n, lapack_int nrhs, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_sgelsd( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, float* a, lapack_int lda, float* b, + lapack_int ldb, float* s, float rcond, + lapack_int* rank ); +lapack_int LAPACKE_dgelsd( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, double* a, lapack_int lda, + double* b, lapack_int ldb, double* s, double rcond, + lapack_int* rank ); +lapack_int LAPACKE_cgelsd( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb, float* s, float rcond, + lapack_int* rank ); +lapack_int LAPACKE_zgelsd( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb, double* s, double rcond, + lapack_int* rank ); + +lapack_int LAPACKE_sgelss( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, float* a, lapack_int lda, float* b, + lapack_int ldb, float* s, float rcond, + lapack_int* rank ); +lapack_int LAPACKE_dgelss( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, double* a, lapack_int lda, + double* b, lapack_int ldb, double* s, double rcond, + lapack_int* rank ); +lapack_int LAPACKE_cgelss( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb, float* s, float rcond, + lapack_int* rank ); +lapack_int LAPACKE_zgelss( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb, double* s, double rcond, + lapack_int* rank ); + +lapack_int LAPACKE_sgelsy( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, float* a, lapack_int lda, float* b, + lapack_int ldb, lapack_int* jpvt, float rcond, + lapack_int* rank ); +lapack_int LAPACKE_dgelsy( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, double* a, lapack_int lda, + double* b, lapack_int ldb, lapack_int* jpvt, + double rcond, lapack_int* rank ); +lapack_int LAPACKE_cgelsy( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb, lapack_int* jpvt, float rcond, + lapack_int* rank ); +lapack_int LAPACKE_zgelsy( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb, lapack_int* jpvt, double rcond, + lapack_int* rank ); + +lapack_int LAPACKE_sgeqlf( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* tau ); +lapack_int LAPACKE_dgeqlf( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* tau ); +lapack_int LAPACKE_cgeqlf( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* tau ); +lapack_int LAPACKE_zgeqlf( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* tau ); + +lapack_int LAPACKE_sgeqp3( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, lapack_int* jpvt, + float* tau ); +lapack_int LAPACKE_dgeqp3( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, lapack_int* jpvt, + double* tau ); +lapack_int LAPACKE_cgeqp3( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_int* jpvt, lapack_complex_float* tau ); +lapack_int LAPACKE_zgeqp3( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_int* jpvt, lapack_complex_double* tau ); + +lapack_int LAPACKE_sgeqpf( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, lapack_int* jpvt, + float* tau ); +lapack_int LAPACKE_dgeqpf( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, lapack_int* jpvt, + double* tau ); +lapack_int LAPACKE_cgeqpf( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_int* jpvt, lapack_complex_float* tau ); +lapack_int LAPACKE_zgeqpf( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_int* jpvt, lapack_complex_double* tau ); + +lapack_int LAPACKE_sgeqr2( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* tau ); +lapack_int LAPACKE_dgeqr2( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* tau ); +lapack_int LAPACKE_cgeqr2( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* tau ); +lapack_int LAPACKE_zgeqr2( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* tau ); + +lapack_int LAPACKE_sgeqrf( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* tau ); +lapack_int LAPACKE_dgeqrf( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* tau ); +lapack_int LAPACKE_cgeqrf( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* tau ); +lapack_int LAPACKE_zgeqrf( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* tau ); + +lapack_int LAPACKE_sgeqrfp( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* tau ); +lapack_int LAPACKE_dgeqrfp( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* tau ); +lapack_int LAPACKE_cgeqrfp( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* tau ); +lapack_int LAPACKE_zgeqrfp( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* tau ); + +lapack_int LAPACKE_sgerfs( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const float* a, lapack_int lda, + const float* af, lapack_int ldaf, + const lapack_int* ipiv, const float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* ferr, float* berr ); +lapack_int LAPACKE_dgerfs( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const double* a, lapack_int lda, + const double* af, lapack_int ldaf, + const lapack_int* ipiv, const double* b, + lapack_int ldb, double* x, lapack_int ldx, + double* ferr, double* berr ); +lapack_int LAPACKE_cgerfs( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* af, + lapack_int ldaf, const lapack_int* ipiv, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, float* ferr, + float* berr ); +lapack_int LAPACKE_zgerfs( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, const lapack_complex_double* af, + lapack_int ldaf, const lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr ); + +lapack_int LAPACKE_sgerfsx( int matrix_order, char trans, char equed, + lapack_int n, lapack_int nrhs, const float* a, + lapack_int lda, const float* af, lapack_int ldaf, + const lapack_int* ipiv, const float* r, + const float* c, const float* b, lapack_int ldb, + float* x, lapack_int ldx, float* rcond, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params ); +lapack_int LAPACKE_dgerfsx( int matrix_order, char trans, char equed, + lapack_int n, lapack_int nrhs, const double* a, + lapack_int lda, const double* af, lapack_int ldaf, + const lapack_int* ipiv, const double* r, + const double* c, const double* b, lapack_int ldb, + double* x, lapack_int ldx, double* rcond, + double* berr, lapack_int n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int nparams, double* params ); +lapack_int LAPACKE_cgerfsx( int matrix_order, char trans, char equed, + lapack_int n, lapack_int nrhs, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* af, lapack_int ldaf, + const lapack_int* ipiv, const float* r, + const float* c, const lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* x, + lapack_int ldx, float* rcond, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params ); +lapack_int LAPACKE_zgerfsx( int matrix_order, char trans, char equed, + lapack_int n, lapack_int nrhs, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* af, lapack_int ldaf, + const lapack_int* ipiv, const double* r, + const double* c, const lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* x, + lapack_int ldx, double* rcond, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params ); + +lapack_int LAPACKE_sgerqf( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* tau ); +lapack_int LAPACKE_dgerqf( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* tau ); +lapack_int LAPACKE_cgerqf( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* tau ); +lapack_int LAPACKE_zgerqf( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* tau ); + +lapack_int LAPACKE_sgesdd( int matrix_order, char jobz, lapack_int m, + lapack_int n, float* a, lapack_int lda, float* s, + float* u, lapack_int ldu, float* vt, + lapack_int ldvt ); +lapack_int LAPACKE_dgesdd( int matrix_order, char jobz, lapack_int m, + lapack_int n, double* a, lapack_int lda, double* s, + double* u, lapack_int ldu, double* vt, + lapack_int ldvt ); +lapack_int LAPACKE_cgesdd( int matrix_order, char jobz, lapack_int m, + lapack_int n, lapack_complex_float* a, + lapack_int lda, float* s, lapack_complex_float* u, + lapack_int ldu, lapack_complex_float* vt, + lapack_int ldvt ); +lapack_int LAPACKE_zgesdd( int matrix_order, char jobz, lapack_int m, + lapack_int n, lapack_complex_double* a, + lapack_int lda, double* s, lapack_complex_double* u, + lapack_int ldu, lapack_complex_double* vt, + lapack_int ldvt ); + +lapack_int LAPACKE_sgesv( int matrix_order, lapack_int n, lapack_int nrhs, + float* a, lapack_int lda, lapack_int* ipiv, float* b, + lapack_int ldb ); +lapack_int LAPACKE_dgesv( int matrix_order, lapack_int n, lapack_int nrhs, + double* a, lapack_int lda, lapack_int* ipiv, + double* b, lapack_int ldb ); +lapack_int LAPACKE_cgesv( int matrix_order, lapack_int n, lapack_int nrhs, + lapack_complex_float* a, lapack_int lda, + lapack_int* ipiv, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zgesv( int matrix_order, lapack_int n, lapack_int nrhs, + lapack_complex_double* a, lapack_int lda, + lapack_int* ipiv, lapack_complex_double* b, + lapack_int ldb ); +lapack_int LAPACKE_dsgesv( int matrix_order, lapack_int n, lapack_int nrhs, + double* a, lapack_int lda, lapack_int* ipiv, + double* b, lapack_int ldb, double* x, lapack_int ldx, + lapack_int* iter ); +lapack_int LAPACKE_zcgesv( int matrix_order, lapack_int n, lapack_int nrhs, + lapack_complex_double* a, lapack_int lda, + lapack_int* ipiv, lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* x, + lapack_int ldx, lapack_int* iter ); + +lapack_int LAPACKE_sgesvd( int matrix_order, char jobu, char jobvt, + lapack_int m, lapack_int n, float* a, lapack_int lda, + float* s, float* u, lapack_int ldu, float* vt, + lapack_int ldvt, float* superb ); +lapack_int LAPACKE_dgesvd( int matrix_order, char jobu, char jobvt, + lapack_int m, lapack_int n, double* a, + lapack_int lda, double* s, double* u, lapack_int ldu, + double* vt, lapack_int ldvt, double* superb ); +lapack_int LAPACKE_cgesvd( int matrix_order, char jobu, char jobvt, + lapack_int m, lapack_int n, lapack_complex_float* a, + lapack_int lda, float* s, lapack_complex_float* u, + lapack_int ldu, lapack_complex_float* vt, + lapack_int ldvt, float* superb ); +lapack_int LAPACKE_zgesvd( int matrix_order, char jobu, char jobvt, + lapack_int m, lapack_int n, lapack_complex_double* a, + lapack_int lda, double* s, lapack_complex_double* u, + lapack_int ldu, lapack_complex_double* vt, + lapack_int ldvt, double* superb ); + +lapack_int LAPACKE_sgesvj( int matrix_order, char joba, char jobu, char jobv, + lapack_int m, lapack_int n, float* a, lapack_int lda, + float* sva, lapack_int mv, float* v, lapack_int ldv, + float* stat ); +lapack_int LAPACKE_dgesvj( int matrix_order, char joba, char jobu, char jobv, + lapack_int m, lapack_int n, double* a, + lapack_int lda, double* sva, lapack_int mv, + double* v, lapack_int ldv, double* stat ); + +lapack_int LAPACKE_sgesvx( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, float* a, + lapack_int lda, float* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, float* r, float* c, + float* b, lapack_int ldb, float* x, lapack_int ldx, + float* rcond, float* ferr, float* berr, + float* rpivot ); +lapack_int LAPACKE_dgesvx( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, double* a, + lapack_int lda, double* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, double* r, double* c, + double* b, lapack_int ldb, double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr, + double* rpivot ); +lapack_int LAPACKE_cgesvx( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, float* r, float* c, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* ferr, float* berr, + float* rpivot ); +lapack_int LAPACKE_zgesvx( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, double* r, double* c, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr, + double* rpivot ); + +lapack_int LAPACKE_sgesvxx( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, float* a, + lapack_int lda, float* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, float* r, float* c, + float* b, lapack_int ldb, float* x, lapack_int ldx, + float* rcond, float* rpvgrw, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params ); +lapack_int LAPACKE_dgesvxx( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, double* a, + lapack_int lda, double* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, double* r, double* c, + double* b, lapack_int ldb, double* x, + lapack_int ldx, double* rcond, double* rpvgrw, + double* berr, lapack_int n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int nparams, double* params ); +lapack_int LAPACKE_cgesvxx( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, float* r, float* c, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* rpvgrw, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params ); +lapack_int LAPACKE_zgesvxx( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, double* r, double* c, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* rpvgrw, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params ); + +lapack_int LAPACKE_sgetf2( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, lapack_int* ipiv ); +lapack_int LAPACKE_dgetf2( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, lapack_int* ipiv ); +lapack_int LAPACKE_cgetf2( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_int* ipiv ); +lapack_int LAPACKE_zgetf2( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_int* ipiv ); + +lapack_int LAPACKE_sgetrf( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, lapack_int* ipiv ); +lapack_int LAPACKE_dgetrf( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, lapack_int* ipiv ); +lapack_int LAPACKE_cgetrf( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_int* ipiv ); +lapack_int LAPACKE_zgetrf( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_int* ipiv ); + +lapack_int LAPACKE_sgetri( int matrix_order, lapack_int n, float* a, + lapack_int lda, const lapack_int* ipiv ); +lapack_int LAPACKE_dgetri( int matrix_order, lapack_int n, double* a, + lapack_int lda, const lapack_int* ipiv ); +lapack_int LAPACKE_cgetri( int matrix_order, lapack_int n, + lapack_complex_float* a, lapack_int lda, + const lapack_int* ipiv ); +lapack_int LAPACKE_zgetri( int matrix_order, lapack_int n, + lapack_complex_double* a, lapack_int lda, + const lapack_int* ipiv ); + +lapack_int LAPACKE_sgetrs( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const float* a, lapack_int lda, + const lapack_int* ipiv, float* b, lapack_int ldb ); +lapack_int LAPACKE_dgetrs( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const double* a, lapack_int lda, + const lapack_int* ipiv, double* b, lapack_int ldb ); +lapack_int LAPACKE_cgetrs( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zgetrs( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_sggbak( int matrix_order, char job, char side, lapack_int n, + lapack_int ilo, lapack_int ihi, const float* lscale, + const float* rscale, lapack_int m, float* v, + lapack_int ldv ); +lapack_int LAPACKE_dggbak( int matrix_order, char job, char side, lapack_int n, + lapack_int ilo, lapack_int ihi, const double* lscale, + const double* rscale, lapack_int m, double* v, + lapack_int ldv ); +lapack_int LAPACKE_cggbak( int matrix_order, char job, char side, lapack_int n, + lapack_int ilo, lapack_int ihi, const float* lscale, + const float* rscale, lapack_int m, + lapack_complex_float* v, lapack_int ldv ); +lapack_int LAPACKE_zggbak( int matrix_order, char job, char side, lapack_int n, + lapack_int ilo, lapack_int ihi, const double* lscale, + const double* rscale, lapack_int m, + lapack_complex_double* v, lapack_int ldv ); + +lapack_int LAPACKE_sggbal( int matrix_order, char job, lapack_int n, float* a, + lapack_int lda, float* b, lapack_int ldb, + lapack_int* ilo, lapack_int* ihi, float* lscale, + float* rscale ); +lapack_int LAPACKE_dggbal( int matrix_order, char job, lapack_int n, double* a, + lapack_int lda, double* b, lapack_int ldb, + lapack_int* ilo, lapack_int* ihi, double* lscale, + double* rscale ); +lapack_int LAPACKE_cggbal( int matrix_order, char job, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + lapack_int* ilo, lapack_int* ihi, float* lscale, + float* rscale ); +lapack_int LAPACKE_zggbal( int matrix_order, char job, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + lapack_int* ilo, lapack_int* ihi, double* lscale, + double* rscale ); + +lapack_int LAPACKE_sgges( int matrix_order, char jobvsl, char jobvsr, char sort, + LAPACK_S_SELECT3 selctg, lapack_int n, float* a, + lapack_int lda, float* b, lapack_int ldb, + lapack_int* sdim, float* alphar, float* alphai, + float* beta, float* vsl, lapack_int ldvsl, float* vsr, + lapack_int ldvsr ); +lapack_int LAPACKE_dgges( int matrix_order, char jobvsl, char jobvsr, char sort, + LAPACK_D_SELECT3 selctg, lapack_int n, double* a, + lapack_int lda, double* b, lapack_int ldb, + lapack_int* sdim, double* alphar, double* alphai, + double* beta, double* vsl, lapack_int ldvsl, + double* vsr, lapack_int ldvsr ); +lapack_int LAPACKE_cgges( int matrix_order, char jobvsl, char jobvsr, char sort, + LAPACK_C_SELECT2 selctg, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + lapack_int* sdim, lapack_complex_float* alpha, + lapack_complex_float* beta, lapack_complex_float* vsl, + lapack_int ldvsl, lapack_complex_float* vsr, + lapack_int ldvsr ); +lapack_int LAPACKE_zgges( int matrix_order, char jobvsl, char jobvsr, char sort, + LAPACK_Z_SELECT2 selctg, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + lapack_int* sdim, lapack_complex_double* alpha, + lapack_complex_double* beta, + lapack_complex_double* vsl, lapack_int ldvsl, + lapack_complex_double* vsr, lapack_int ldvsr ); + +lapack_int LAPACKE_sggesx( int matrix_order, char jobvsl, char jobvsr, + char sort, LAPACK_S_SELECT3 selctg, char sense, + lapack_int n, float* a, lapack_int lda, float* b, + lapack_int ldb, lapack_int* sdim, float* alphar, + float* alphai, float* beta, float* vsl, + lapack_int ldvsl, float* vsr, lapack_int ldvsr, + float* rconde, float* rcondv ); +lapack_int LAPACKE_dggesx( int matrix_order, char jobvsl, char jobvsr, + char sort, LAPACK_D_SELECT3 selctg, char sense, + lapack_int n, double* a, lapack_int lda, double* b, + lapack_int ldb, lapack_int* sdim, double* alphar, + double* alphai, double* beta, double* vsl, + lapack_int ldvsl, double* vsr, lapack_int ldvsr, + double* rconde, double* rcondv ); +lapack_int LAPACKE_cggesx( int matrix_order, char jobvsl, char jobvsr, + char sort, LAPACK_C_SELECT2 selctg, char sense, + lapack_int n, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb, lapack_int* sdim, + lapack_complex_float* alpha, + lapack_complex_float* beta, + lapack_complex_float* vsl, lapack_int ldvsl, + lapack_complex_float* vsr, lapack_int ldvsr, + float* rconde, float* rcondv ); +lapack_int LAPACKE_zggesx( int matrix_order, char jobvsl, char jobvsr, + char sort, LAPACK_Z_SELECT2 selctg, char sense, + lapack_int n, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb, lapack_int* sdim, + lapack_complex_double* alpha, + lapack_complex_double* beta, + lapack_complex_double* vsl, lapack_int ldvsl, + lapack_complex_double* vsr, lapack_int ldvsr, + double* rconde, double* rcondv ); + +lapack_int LAPACKE_sggev( int matrix_order, char jobvl, char jobvr, + lapack_int n, float* a, lapack_int lda, float* b, + lapack_int ldb, float* alphar, float* alphai, + float* beta, float* vl, lapack_int ldvl, float* vr, + lapack_int ldvr ); +lapack_int LAPACKE_dggev( int matrix_order, char jobvl, char jobvr, + lapack_int n, double* a, lapack_int lda, double* b, + lapack_int ldb, double* alphar, double* alphai, + double* beta, double* vl, lapack_int ldvl, double* vr, + lapack_int ldvr ); +lapack_int LAPACKE_cggev( int matrix_order, char jobvl, char jobvr, + lapack_int n, lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* alpha, + lapack_complex_float* beta, lapack_complex_float* vl, + lapack_int ldvl, lapack_complex_float* vr, + lapack_int ldvr ); +lapack_int LAPACKE_zggev( int matrix_order, char jobvl, char jobvr, + lapack_int n, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* alpha, + lapack_complex_double* beta, + lapack_complex_double* vl, lapack_int ldvl, + lapack_complex_double* vr, lapack_int ldvr ); + +lapack_int LAPACKE_sggevx( int matrix_order, char balanc, char jobvl, + char jobvr, char sense, lapack_int n, float* a, + lapack_int lda, float* b, lapack_int ldb, + float* alphar, float* alphai, float* beta, float* vl, + lapack_int ldvl, float* vr, lapack_int ldvr, + lapack_int* ilo, lapack_int* ihi, float* lscale, + float* rscale, float* abnrm, float* bbnrm, + float* rconde, float* rcondv ); +lapack_int LAPACKE_dggevx( int matrix_order, char balanc, char jobvl, + char jobvr, char sense, lapack_int n, double* a, + lapack_int lda, double* b, lapack_int ldb, + double* alphar, double* alphai, double* beta, + double* vl, lapack_int ldvl, double* vr, + lapack_int ldvr, lapack_int* ilo, lapack_int* ihi, + double* lscale, double* rscale, double* abnrm, + double* bbnrm, double* rconde, double* rcondv ); +lapack_int LAPACKE_cggevx( int matrix_order, char balanc, char jobvl, + char jobvr, char sense, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* alpha, + lapack_complex_float* beta, lapack_complex_float* vl, + lapack_int ldvl, lapack_complex_float* vr, + lapack_int ldvr, lapack_int* ilo, lapack_int* ihi, + float* lscale, float* rscale, float* abnrm, + float* bbnrm, float* rconde, float* rcondv ); +lapack_int LAPACKE_zggevx( int matrix_order, char balanc, char jobvl, + char jobvr, char sense, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* alpha, + lapack_complex_double* beta, + lapack_complex_double* vl, lapack_int ldvl, + lapack_complex_double* vr, lapack_int ldvr, + lapack_int* ilo, lapack_int* ihi, double* lscale, + double* rscale, double* abnrm, double* bbnrm, + double* rconde, double* rcondv ); + +lapack_int LAPACKE_sggglm( int matrix_order, lapack_int n, lapack_int m, + lapack_int p, float* a, lapack_int lda, float* b, + lapack_int ldb, float* d, float* x, float* y ); +lapack_int LAPACKE_dggglm( int matrix_order, lapack_int n, lapack_int m, + lapack_int p, double* a, lapack_int lda, double* b, + lapack_int ldb, double* d, double* x, double* y ); +lapack_int LAPACKE_cggglm( int matrix_order, lapack_int n, lapack_int m, + lapack_int p, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* d, + lapack_complex_float* x, lapack_complex_float* y ); +lapack_int LAPACKE_zggglm( int matrix_order, lapack_int n, lapack_int m, + lapack_int p, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* d, + lapack_complex_double* x, lapack_complex_double* y ); + +lapack_int LAPACKE_sgghrd( int matrix_order, char compq, char compz, + lapack_int n, lapack_int ilo, lapack_int ihi, + float* a, lapack_int lda, float* b, lapack_int ldb, + float* q, lapack_int ldq, float* z, lapack_int ldz ); +lapack_int LAPACKE_dgghrd( int matrix_order, char compq, char compz, + lapack_int n, lapack_int ilo, lapack_int ihi, + double* a, lapack_int lda, double* b, lapack_int ldb, + double* q, lapack_int ldq, double* z, + lapack_int ldz ); +lapack_int LAPACKE_cgghrd( int matrix_order, char compq, char compz, + lapack_int n, lapack_int ilo, lapack_int ihi, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* q, lapack_int ldq, + lapack_complex_float* z, lapack_int ldz ); +lapack_int LAPACKE_zgghrd( int matrix_order, char compq, char compz, + lapack_int n, lapack_int ilo, lapack_int ihi, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* q, lapack_int ldq, + lapack_complex_double* z, lapack_int ldz ); + +lapack_int LAPACKE_sgglse( int matrix_order, lapack_int m, lapack_int n, + lapack_int p, float* a, lapack_int lda, float* b, + lapack_int ldb, float* c, float* d, float* x ); +lapack_int LAPACKE_dgglse( int matrix_order, lapack_int m, lapack_int n, + lapack_int p, double* a, lapack_int lda, double* b, + lapack_int ldb, double* c, double* d, double* x ); +lapack_int LAPACKE_cgglse( int matrix_order, lapack_int m, lapack_int n, + lapack_int p, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* c, + lapack_complex_float* d, lapack_complex_float* x ); +lapack_int LAPACKE_zgglse( int matrix_order, lapack_int m, lapack_int n, + lapack_int p, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* c, + lapack_complex_double* d, lapack_complex_double* x ); + +lapack_int LAPACKE_sggqrf( int matrix_order, lapack_int n, lapack_int m, + lapack_int p, float* a, lapack_int lda, float* taua, + float* b, lapack_int ldb, float* taub ); +lapack_int LAPACKE_dggqrf( int matrix_order, lapack_int n, lapack_int m, + lapack_int p, double* a, lapack_int lda, + double* taua, double* b, lapack_int ldb, + double* taub ); +lapack_int LAPACKE_cggqrf( int matrix_order, lapack_int n, lapack_int m, + lapack_int p, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* taua, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* taub ); +lapack_int LAPACKE_zggqrf( int matrix_order, lapack_int n, lapack_int m, + lapack_int p, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* taua, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* taub ); + +lapack_int LAPACKE_sggrqf( int matrix_order, lapack_int m, lapack_int p, + lapack_int n, float* a, lapack_int lda, float* taua, + float* b, lapack_int ldb, float* taub ); +lapack_int LAPACKE_dggrqf( int matrix_order, lapack_int m, lapack_int p, + lapack_int n, double* a, lapack_int lda, + double* taua, double* b, lapack_int ldb, + double* taub ); +lapack_int LAPACKE_cggrqf( int matrix_order, lapack_int m, lapack_int p, + lapack_int n, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* taua, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* taub ); +lapack_int LAPACKE_zggrqf( int matrix_order, lapack_int m, lapack_int p, + lapack_int n, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* taua, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* taub ); + +lapack_int LAPACKE_sggsvd( int matrix_order, char jobu, char jobv, char jobq, + lapack_int m, lapack_int n, lapack_int p, + lapack_int* k, lapack_int* l, float* a, + lapack_int lda, float* b, lapack_int ldb, + float* alpha, float* beta, float* u, lapack_int ldu, + float* v, lapack_int ldv, float* q, lapack_int ldq, + lapack_int* iwork ); +lapack_int LAPACKE_dggsvd( int matrix_order, char jobu, char jobv, char jobq, + lapack_int m, lapack_int n, lapack_int p, + lapack_int* k, lapack_int* l, double* a, + lapack_int lda, double* b, lapack_int ldb, + double* alpha, double* beta, double* u, + lapack_int ldu, double* v, lapack_int ldv, double* q, + lapack_int ldq, lapack_int* iwork ); +lapack_int LAPACKE_cggsvd( int matrix_order, char jobu, char jobv, char jobq, + lapack_int m, lapack_int n, lapack_int p, + lapack_int* k, lapack_int* l, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + float* alpha, float* beta, lapack_complex_float* u, + lapack_int ldu, lapack_complex_float* v, + lapack_int ldv, lapack_complex_float* q, + lapack_int ldq, lapack_int* iwork ); +lapack_int LAPACKE_zggsvd( int matrix_order, char jobu, char jobv, char jobq, + lapack_int m, lapack_int n, lapack_int p, + lapack_int* k, lapack_int* l, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + double* alpha, double* beta, + lapack_complex_double* u, lapack_int ldu, + lapack_complex_double* v, lapack_int ldv, + lapack_complex_double* q, lapack_int ldq, + lapack_int* iwork ); + +lapack_int LAPACKE_sggsvp( int matrix_order, char jobu, char jobv, char jobq, + lapack_int m, lapack_int p, lapack_int n, float* a, + lapack_int lda, float* b, lapack_int ldb, float tola, + float tolb, lapack_int* k, lapack_int* l, float* u, + lapack_int ldu, float* v, lapack_int ldv, float* q, + lapack_int ldq ); +lapack_int LAPACKE_dggsvp( int matrix_order, char jobu, char jobv, char jobq, + lapack_int m, lapack_int p, lapack_int n, double* a, + lapack_int lda, double* b, lapack_int ldb, + double tola, double tolb, lapack_int* k, + lapack_int* l, double* u, lapack_int ldu, double* v, + lapack_int ldv, double* q, lapack_int ldq ); +lapack_int LAPACKE_cggsvp( int matrix_order, char jobu, char jobv, char jobq, + lapack_int m, lapack_int p, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, float tola, + float tolb, lapack_int* k, lapack_int* l, + lapack_complex_float* u, lapack_int ldu, + lapack_complex_float* v, lapack_int ldv, + lapack_complex_float* q, lapack_int ldq ); +lapack_int LAPACKE_zggsvp( int matrix_order, char jobu, char jobv, char jobq, + lapack_int m, lapack_int p, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + double tola, double tolb, lapack_int* k, + lapack_int* l, lapack_complex_double* u, + lapack_int ldu, lapack_complex_double* v, + lapack_int ldv, lapack_complex_double* q, + lapack_int ldq ); + +lapack_int LAPACKE_sgtcon( char norm, lapack_int n, const float* dl, + const float* d, const float* du, const float* du2, + const lapack_int* ipiv, float anorm, float* rcond ); +lapack_int LAPACKE_dgtcon( char norm, lapack_int n, const double* dl, + const double* d, const double* du, const double* du2, + const lapack_int* ipiv, double anorm, + double* rcond ); +lapack_int LAPACKE_cgtcon( char norm, lapack_int n, + const lapack_complex_float* dl, + const lapack_complex_float* d, + const lapack_complex_float* du, + const lapack_complex_float* du2, + const lapack_int* ipiv, float anorm, float* rcond ); +lapack_int LAPACKE_zgtcon( char norm, lapack_int n, + const lapack_complex_double* dl, + const lapack_complex_double* d, + const lapack_complex_double* du, + const lapack_complex_double* du2, + const lapack_int* ipiv, double anorm, + double* rcond ); + +lapack_int LAPACKE_sgtrfs( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const float* dl, const float* d, + const float* du, const float* dlf, const float* df, + const float* duf, const float* du2, + const lapack_int* ipiv, const float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* ferr, float* berr ); +lapack_int LAPACKE_dgtrfs( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const double* dl, const double* d, + const double* du, const double* dlf, + const double* df, const double* duf, + const double* du2, const lapack_int* ipiv, + const double* b, lapack_int ldb, double* x, + lapack_int ldx, double* ferr, double* berr ); +lapack_int LAPACKE_cgtrfs( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const lapack_complex_float* dl, + const lapack_complex_float* d, + const lapack_complex_float* du, + const lapack_complex_float* dlf, + const lapack_complex_float* df, + const lapack_complex_float* duf, + const lapack_complex_float* du2, + const lapack_int* ipiv, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, float* ferr, + float* berr ); +lapack_int LAPACKE_zgtrfs( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const lapack_complex_double* dl, + const lapack_complex_double* d, + const lapack_complex_double* du, + const lapack_complex_double* dlf, + const lapack_complex_double* df, + const lapack_complex_double* duf, + const lapack_complex_double* du2, + const lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr ); + +lapack_int LAPACKE_sgtsv( int matrix_order, lapack_int n, lapack_int nrhs, + float* dl, float* d, float* du, float* b, + lapack_int ldb ); +lapack_int LAPACKE_dgtsv( int matrix_order, lapack_int n, lapack_int nrhs, + double* dl, double* d, double* du, double* b, + lapack_int ldb ); +lapack_int LAPACKE_cgtsv( int matrix_order, lapack_int n, lapack_int nrhs, + lapack_complex_float* dl, lapack_complex_float* d, + lapack_complex_float* du, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zgtsv( int matrix_order, lapack_int n, lapack_int nrhs, + lapack_complex_double* dl, lapack_complex_double* d, + lapack_complex_double* du, lapack_complex_double* b, + lapack_int ldb ); + +lapack_int LAPACKE_sgtsvx( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, const float* dl, + const float* d, const float* du, float* dlf, + float* df, float* duf, float* du2, lapack_int* ipiv, + const float* b, lapack_int ldb, float* x, + lapack_int ldx, float* rcond, float* ferr, + float* berr ); +lapack_int LAPACKE_dgtsvx( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, const double* dl, + const double* d, const double* du, double* dlf, + double* df, double* duf, double* du2, + lapack_int* ipiv, const double* b, lapack_int ldb, + double* x, lapack_int ldx, double* rcond, + double* ferr, double* berr ); +lapack_int LAPACKE_cgtsvx( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, + const lapack_complex_float* dl, + const lapack_complex_float* d, + const lapack_complex_float* du, + lapack_complex_float* dlf, lapack_complex_float* df, + lapack_complex_float* duf, lapack_complex_float* du2, + lapack_int* ipiv, const lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* x, + lapack_int ldx, float* rcond, float* ferr, + float* berr ); +lapack_int LAPACKE_zgtsvx( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, + const lapack_complex_double* dl, + const lapack_complex_double* d, + const lapack_complex_double* du, + lapack_complex_double* dlf, + lapack_complex_double* df, + lapack_complex_double* duf, + lapack_complex_double* du2, lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr ); + +lapack_int LAPACKE_sgttrf( lapack_int n, float* dl, float* d, float* du, + float* du2, lapack_int* ipiv ); +lapack_int LAPACKE_dgttrf( lapack_int n, double* dl, double* d, double* du, + double* du2, lapack_int* ipiv ); +lapack_int LAPACKE_cgttrf( lapack_int n, lapack_complex_float* dl, + lapack_complex_float* d, lapack_complex_float* du, + lapack_complex_float* du2, lapack_int* ipiv ); +lapack_int LAPACKE_zgttrf( lapack_int n, lapack_complex_double* dl, + lapack_complex_double* d, lapack_complex_double* du, + lapack_complex_double* du2, lapack_int* ipiv ); + +lapack_int LAPACKE_sgttrs( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const float* dl, const float* d, + const float* du, const float* du2, + const lapack_int* ipiv, float* b, lapack_int ldb ); +lapack_int LAPACKE_dgttrs( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const double* dl, const double* d, + const double* du, const double* du2, + const lapack_int* ipiv, double* b, lapack_int ldb ); +lapack_int LAPACKE_cgttrs( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const lapack_complex_float* dl, + const lapack_complex_float* d, + const lapack_complex_float* du, + const lapack_complex_float* du2, + const lapack_int* ipiv, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zgttrs( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const lapack_complex_double* dl, + const lapack_complex_double* d, + const lapack_complex_double* du, + const lapack_complex_double* du2, + const lapack_int* ipiv, lapack_complex_double* b, + lapack_int ldb ); + +lapack_int LAPACKE_chbev( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_int kd, lapack_complex_float* ab, + lapack_int ldab, float* w, lapack_complex_float* z, + lapack_int ldz ); +lapack_int LAPACKE_zhbev( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_int kd, lapack_complex_double* ab, + lapack_int ldab, double* w, lapack_complex_double* z, + lapack_int ldz ); + +lapack_int LAPACKE_chbevd( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_int kd, lapack_complex_float* ab, + lapack_int ldab, float* w, lapack_complex_float* z, + lapack_int ldz ); +lapack_int LAPACKE_zhbevd( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_int kd, lapack_complex_double* ab, + lapack_int ldab, double* w, lapack_complex_double* z, + lapack_int ldz ); + +lapack_int LAPACKE_chbevx( int matrix_order, char jobz, char range, char uplo, + lapack_int n, lapack_int kd, + lapack_complex_float* ab, lapack_int ldab, + lapack_complex_float* q, lapack_int ldq, float vl, + float vu, lapack_int il, lapack_int iu, float abstol, + lapack_int* m, float* w, lapack_complex_float* z, + lapack_int ldz, lapack_int* ifail ); +lapack_int LAPACKE_zhbevx( int matrix_order, char jobz, char range, char uplo, + lapack_int n, lapack_int kd, + lapack_complex_double* ab, lapack_int ldab, + lapack_complex_double* q, lapack_int ldq, double vl, + double vu, lapack_int il, lapack_int iu, + double abstol, lapack_int* m, double* w, + lapack_complex_double* z, lapack_int ldz, + lapack_int* ifail ); + +lapack_int LAPACKE_chbgst( int matrix_order, char vect, char uplo, lapack_int n, + lapack_int ka, lapack_int kb, + lapack_complex_float* ab, lapack_int ldab, + const lapack_complex_float* bb, lapack_int ldbb, + lapack_complex_float* x, lapack_int ldx ); +lapack_int LAPACKE_zhbgst( int matrix_order, char vect, char uplo, lapack_int n, + lapack_int ka, lapack_int kb, + lapack_complex_double* ab, lapack_int ldab, + const lapack_complex_double* bb, lapack_int ldbb, + lapack_complex_double* x, lapack_int ldx ); + +lapack_int LAPACKE_chbgv( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_int ka, lapack_int kb, + lapack_complex_float* ab, lapack_int ldab, + lapack_complex_float* bb, lapack_int ldbb, float* w, + lapack_complex_float* z, lapack_int ldz ); +lapack_int LAPACKE_zhbgv( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_int ka, lapack_int kb, + lapack_complex_double* ab, lapack_int ldab, + lapack_complex_double* bb, lapack_int ldbb, double* w, + lapack_complex_double* z, lapack_int ldz ); + +lapack_int LAPACKE_chbgvd( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_int ka, lapack_int kb, + lapack_complex_float* ab, lapack_int ldab, + lapack_complex_float* bb, lapack_int ldbb, float* w, + lapack_complex_float* z, lapack_int ldz ); +lapack_int LAPACKE_zhbgvd( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_int ka, lapack_int kb, + lapack_complex_double* ab, lapack_int ldab, + lapack_complex_double* bb, lapack_int ldbb, + double* w, lapack_complex_double* z, + lapack_int ldz ); + +lapack_int LAPACKE_chbgvx( int matrix_order, char jobz, char range, char uplo, + lapack_int n, lapack_int ka, lapack_int kb, + lapack_complex_float* ab, lapack_int ldab, + lapack_complex_float* bb, lapack_int ldbb, + lapack_complex_float* q, lapack_int ldq, float vl, + float vu, lapack_int il, lapack_int iu, float abstol, + lapack_int* m, float* w, lapack_complex_float* z, + lapack_int ldz, lapack_int* ifail ); +lapack_int LAPACKE_zhbgvx( int matrix_order, char jobz, char range, char uplo, + lapack_int n, lapack_int ka, lapack_int kb, + lapack_complex_double* ab, lapack_int ldab, + lapack_complex_double* bb, lapack_int ldbb, + lapack_complex_double* q, lapack_int ldq, double vl, + double vu, lapack_int il, lapack_int iu, + double abstol, lapack_int* m, double* w, + lapack_complex_double* z, lapack_int ldz, + lapack_int* ifail ); + +lapack_int LAPACKE_chbtrd( int matrix_order, char vect, char uplo, lapack_int n, + lapack_int kd, lapack_complex_float* ab, + lapack_int ldab, float* d, float* e, + lapack_complex_float* q, lapack_int ldq ); +lapack_int LAPACKE_zhbtrd( int matrix_order, char vect, char uplo, lapack_int n, + lapack_int kd, lapack_complex_double* ab, + lapack_int ldab, double* d, double* e, + lapack_complex_double* q, lapack_int ldq ); + +lapack_int LAPACKE_checon( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + const lapack_int* ipiv, float anorm, float* rcond ); +lapack_int LAPACKE_zhecon( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + const lapack_int* ipiv, double anorm, + double* rcond ); + +lapack_int LAPACKE_cheequb( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + float* s, float* scond, float* amax ); +lapack_int LAPACKE_zheequb( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + double* s, double* scond, double* amax ); + +lapack_int LAPACKE_cheev( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, float* w ); +lapack_int LAPACKE_zheev( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, double* w ); + +lapack_int LAPACKE_cheevd( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, float* w ); +lapack_int LAPACKE_zheevd( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + double* w ); + +lapack_int LAPACKE_cheevr( int matrix_order, char jobz, char range, char uplo, + lapack_int n, lapack_complex_float* a, + lapack_int lda, float vl, float vu, lapack_int il, + lapack_int iu, float abstol, lapack_int* m, float* w, + lapack_complex_float* z, lapack_int ldz, + lapack_int* isuppz ); +lapack_int LAPACKE_zheevr( int matrix_order, char jobz, char range, char uplo, + lapack_int n, lapack_complex_double* a, + lapack_int lda, double vl, double vu, lapack_int il, + lapack_int iu, double abstol, lapack_int* m, + double* w, lapack_complex_double* z, lapack_int ldz, + lapack_int* isuppz ); + +lapack_int LAPACKE_cheevx( int matrix_order, char jobz, char range, char uplo, + lapack_int n, lapack_complex_float* a, + lapack_int lda, float vl, float vu, lapack_int il, + lapack_int iu, float abstol, lapack_int* m, float* w, + lapack_complex_float* z, lapack_int ldz, + lapack_int* ifail ); +lapack_int LAPACKE_zheevx( int matrix_order, char jobz, char range, char uplo, + lapack_int n, lapack_complex_double* a, + lapack_int lda, double vl, double vu, lapack_int il, + lapack_int iu, double abstol, lapack_int* m, + double* w, lapack_complex_double* z, lapack_int ldz, + lapack_int* ifail ); + +lapack_int LAPACKE_chegst( int matrix_order, lapack_int itype, char uplo, + lapack_int n, lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zhegst( int matrix_order, lapack_int itype, char uplo, + lapack_int n, lapack_complex_double* a, + lapack_int lda, const lapack_complex_double* b, + lapack_int ldb ); + +lapack_int LAPACKE_chegv( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb, float* w ); +lapack_int LAPACKE_zhegv( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb, double* w ); + +lapack_int LAPACKE_chegvd( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb, float* w ); +lapack_int LAPACKE_zhegvd( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb, double* w ); + +lapack_int LAPACKE_chegvx( int matrix_order, lapack_int itype, char jobz, + char range, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, float vl, + float vu, lapack_int il, lapack_int iu, float abstol, + lapack_int* m, float* w, lapack_complex_float* z, + lapack_int ldz, lapack_int* ifail ); +lapack_int LAPACKE_zhegvx( int matrix_order, lapack_int itype, char jobz, + char range, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, double vl, + double vu, lapack_int il, lapack_int iu, + double abstol, lapack_int* m, double* w, + lapack_complex_double* z, lapack_int ldz, + lapack_int* ifail ); + +lapack_int LAPACKE_cherfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* af, + lapack_int ldaf, const lapack_int* ipiv, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, float* ferr, + float* berr ); +lapack_int LAPACKE_zherfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, const lapack_complex_double* af, + lapack_int ldaf, const lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr ); + +lapack_int LAPACKE_cherfsx( int matrix_order, char uplo, char equed, + lapack_int n, lapack_int nrhs, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* af, lapack_int ldaf, + const lapack_int* ipiv, const float* s, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* berr, lapack_int n_err_bnds, + float* err_bnds_norm, float* err_bnds_comp, + lapack_int nparams, float* params ); +lapack_int LAPACKE_zherfsx( int matrix_order, char uplo, char equed, + lapack_int n, lapack_int nrhs, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* af, lapack_int ldaf, + const lapack_int* ipiv, const double* s, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* berr, lapack_int n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int nparams, double* params ); + +lapack_int LAPACKE_chesv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_float* a, + lapack_int lda, lapack_int* ipiv, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zhesv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_double* a, + lapack_int lda, lapack_int* ipiv, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_chesvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, lapack_complex_float* af, + lapack_int ldaf, lapack_int* ipiv, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* ferr, float* berr ); +lapack_int LAPACKE_zhesvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, lapack_complex_double* af, + lapack_int ldaf, lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr ); + +lapack_int LAPACKE_chesvxx( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, float* s, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* rpvgrw, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params ); +lapack_int LAPACKE_zhesvxx( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, double* s, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* rpvgrw, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params ); + +lapack_int LAPACKE_chetrd( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, float* d, + float* e, lapack_complex_float* tau ); +lapack_int LAPACKE_zhetrd( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, double* d, + double* e, lapack_complex_double* tau ); + +lapack_int LAPACKE_chetrf( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_int* ipiv ); +lapack_int LAPACKE_zhetrf( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_int* ipiv ); + +lapack_int LAPACKE_chetri( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + const lapack_int* ipiv ); +lapack_int LAPACKE_zhetri( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + const lapack_int* ipiv ); + +lapack_int LAPACKE_chetrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zhetrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_chfrk( int matrix_order, char transr, char uplo, char trans, + lapack_int n, lapack_int k, float alpha, + const lapack_complex_float* a, lapack_int lda, + float beta, lapack_complex_float* c ); +lapack_int LAPACKE_zhfrk( int matrix_order, char transr, char uplo, char trans, + lapack_int n, lapack_int k, double alpha, + const lapack_complex_double* a, lapack_int lda, + double beta, lapack_complex_double* c ); + +lapack_int LAPACKE_shgeqz( int matrix_order, char job, char compq, char compz, + lapack_int n, lapack_int ilo, lapack_int ihi, + float* h, lapack_int ldh, float* t, lapack_int ldt, + float* alphar, float* alphai, float* beta, float* q, + lapack_int ldq, float* z, lapack_int ldz ); +lapack_int LAPACKE_dhgeqz( int matrix_order, char job, char compq, char compz, + lapack_int n, lapack_int ilo, lapack_int ihi, + double* h, lapack_int ldh, double* t, lapack_int ldt, + double* alphar, double* alphai, double* beta, + double* q, lapack_int ldq, double* z, + lapack_int ldz ); +lapack_int LAPACKE_chgeqz( int matrix_order, char job, char compq, char compz, + lapack_int n, lapack_int ilo, lapack_int ihi, + lapack_complex_float* h, lapack_int ldh, + lapack_complex_float* t, lapack_int ldt, + lapack_complex_float* alpha, + lapack_complex_float* beta, lapack_complex_float* q, + lapack_int ldq, lapack_complex_float* z, + lapack_int ldz ); +lapack_int LAPACKE_zhgeqz( int matrix_order, char job, char compq, char compz, + lapack_int n, lapack_int ilo, lapack_int ihi, + lapack_complex_double* h, lapack_int ldh, + lapack_complex_double* t, lapack_int ldt, + lapack_complex_double* alpha, + lapack_complex_double* beta, + lapack_complex_double* q, lapack_int ldq, + lapack_complex_double* z, lapack_int ldz ); + +lapack_int LAPACKE_chpcon( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* ap, + const lapack_int* ipiv, float anorm, float* rcond ); +lapack_int LAPACKE_zhpcon( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* ap, + const lapack_int* ipiv, double anorm, + double* rcond ); + +lapack_int LAPACKE_chpev( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_complex_float* ap, float* w, + lapack_complex_float* z, lapack_int ldz ); +lapack_int LAPACKE_zhpev( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_complex_double* ap, double* w, + lapack_complex_double* z, lapack_int ldz ); + +lapack_int LAPACKE_chpevd( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_complex_float* ap, float* w, + lapack_complex_float* z, lapack_int ldz ); +lapack_int LAPACKE_zhpevd( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_complex_double* ap, double* w, + lapack_complex_double* z, lapack_int ldz ); + +lapack_int LAPACKE_chpevx( int matrix_order, char jobz, char range, char uplo, + lapack_int n, lapack_complex_float* ap, float vl, + float vu, lapack_int il, lapack_int iu, float abstol, + lapack_int* m, float* w, lapack_complex_float* z, + lapack_int ldz, lapack_int* ifail ); +lapack_int LAPACKE_zhpevx( int matrix_order, char jobz, char range, char uplo, + lapack_int n, lapack_complex_double* ap, double vl, + double vu, lapack_int il, lapack_int iu, + double abstol, lapack_int* m, double* w, + lapack_complex_double* z, lapack_int ldz, + lapack_int* ifail ); + +lapack_int LAPACKE_chpgst( int matrix_order, lapack_int itype, char uplo, + lapack_int n, lapack_complex_float* ap, + const lapack_complex_float* bp ); +lapack_int LAPACKE_zhpgst( int matrix_order, lapack_int itype, char uplo, + lapack_int n, lapack_complex_double* ap, + const lapack_complex_double* bp ); + +lapack_int LAPACKE_chpgv( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, lapack_complex_float* ap, + lapack_complex_float* bp, float* w, + lapack_complex_float* z, lapack_int ldz ); +lapack_int LAPACKE_zhpgv( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, lapack_complex_double* ap, + lapack_complex_double* bp, double* w, + lapack_complex_double* z, lapack_int ldz ); + +lapack_int LAPACKE_chpgvd( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, lapack_complex_float* ap, + lapack_complex_float* bp, float* w, + lapack_complex_float* z, lapack_int ldz ); +lapack_int LAPACKE_zhpgvd( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, lapack_complex_double* ap, + lapack_complex_double* bp, double* w, + lapack_complex_double* z, lapack_int ldz ); + +lapack_int LAPACKE_chpgvx( int matrix_order, lapack_int itype, char jobz, + char range, char uplo, lapack_int n, + lapack_complex_float* ap, lapack_complex_float* bp, + float vl, float vu, lapack_int il, lapack_int iu, + float abstol, lapack_int* m, float* w, + lapack_complex_float* z, lapack_int ldz, + lapack_int* ifail ); +lapack_int LAPACKE_zhpgvx( int matrix_order, lapack_int itype, char jobz, + char range, char uplo, lapack_int n, + lapack_complex_double* ap, lapack_complex_double* bp, + double vl, double vu, lapack_int il, lapack_int iu, + double abstol, lapack_int* m, double* w, + lapack_complex_double* z, lapack_int ldz, + lapack_int* ifail ); + +lapack_int LAPACKE_chprfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* ap, + const lapack_complex_float* afp, + const lapack_int* ipiv, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, float* ferr, + float* berr ); +lapack_int LAPACKE_zhprfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* ap, + const lapack_complex_double* afp, + const lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr ); + +lapack_int LAPACKE_chpsv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_float* ap, + lapack_int* ipiv, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zhpsv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_double* ap, + lapack_int* ipiv, lapack_complex_double* b, + lapack_int ldb ); + +lapack_int LAPACKE_chpsvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* ap, + lapack_complex_float* afp, lapack_int* ipiv, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* ferr, float* berr ); +lapack_int LAPACKE_zhpsvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* ap, + lapack_complex_double* afp, lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr ); + +lapack_int LAPACKE_chptrd( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* ap, float* d, float* e, + lapack_complex_float* tau ); +lapack_int LAPACKE_zhptrd( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* ap, double* d, double* e, + lapack_complex_double* tau ); + +lapack_int LAPACKE_chptrf( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* ap, lapack_int* ipiv ); +lapack_int LAPACKE_zhptrf( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* ap, lapack_int* ipiv ); + +lapack_int LAPACKE_chptri( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* ap, const lapack_int* ipiv ); +lapack_int LAPACKE_zhptri( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* ap, const lapack_int* ipiv ); + +lapack_int LAPACKE_chptrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* ap, + const lapack_int* ipiv, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zhptrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* ap, + const lapack_int* ipiv, lapack_complex_double* b, + lapack_int ldb ); + +lapack_int LAPACKE_shsein( int matrix_order, char job, char eigsrc, char initv, + lapack_logical* select, lapack_int n, const float* h, + lapack_int ldh, float* wr, const float* wi, + float* vl, lapack_int ldvl, float* vr, + lapack_int ldvr, lapack_int mm, lapack_int* m, + lapack_int* ifaill, lapack_int* ifailr ); +lapack_int LAPACKE_dhsein( int matrix_order, char job, char eigsrc, char initv, + lapack_logical* select, lapack_int n, + const double* h, lapack_int ldh, double* wr, + const double* wi, double* vl, lapack_int ldvl, + double* vr, lapack_int ldvr, lapack_int mm, + lapack_int* m, lapack_int* ifaill, + lapack_int* ifailr ); +lapack_int LAPACKE_chsein( int matrix_order, char job, char eigsrc, char initv, + const lapack_logical* select, lapack_int n, + const lapack_complex_float* h, lapack_int ldh, + lapack_complex_float* w, lapack_complex_float* vl, + lapack_int ldvl, lapack_complex_float* vr, + lapack_int ldvr, lapack_int mm, lapack_int* m, + lapack_int* ifaill, lapack_int* ifailr ); +lapack_int LAPACKE_zhsein( int matrix_order, char job, char eigsrc, char initv, + const lapack_logical* select, lapack_int n, + const lapack_complex_double* h, lapack_int ldh, + lapack_complex_double* w, lapack_complex_double* vl, + lapack_int ldvl, lapack_complex_double* vr, + lapack_int ldvr, lapack_int mm, lapack_int* m, + lapack_int* ifaill, lapack_int* ifailr ); + +lapack_int LAPACKE_shseqr( int matrix_order, char job, char compz, lapack_int n, + lapack_int ilo, lapack_int ihi, float* h, + lapack_int ldh, float* wr, float* wi, float* z, + lapack_int ldz ); +lapack_int LAPACKE_dhseqr( int matrix_order, char job, char compz, lapack_int n, + lapack_int ilo, lapack_int ihi, double* h, + lapack_int ldh, double* wr, double* wi, double* z, + lapack_int ldz ); +lapack_int LAPACKE_chseqr( int matrix_order, char job, char compz, lapack_int n, + lapack_int ilo, lapack_int ihi, + lapack_complex_float* h, lapack_int ldh, + lapack_complex_float* w, lapack_complex_float* z, + lapack_int ldz ); +lapack_int LAPACKE_zhseqr( int matrix_order, char job, char compz, lapack_int n, + lapack_int ilo, lapack_int ihi, + lapack_complex_double* h, lapack_int ldh, + lapack_complex_double* w, lapack_complex_double* z, + lapack_int ldz ); + +lapack_int LAPACKE_clacgv( lapack_int n, lapack_complex_float* x, + lapack_int incx ); +lapack_int LAPACKE_zlacgv( lapack_int n, lapack_complex_double* x, + lapack_int incx ); + +lapack_int LAPACKE_slacpy( int matrix_order, char uplo, lapack_int m, + lapack_int n, const float* a, lapack_int lda, float* b, + lapack_int ldb ); +lapack_int LAPACKE_dlacpy( int matrix_order, char uplo, lapack_int m, + lapack_int n, const double* a, lapack_int lda, double* b, + lapack_int ldb ); +lapack_int LAPACKE_clacpy( int matrix_order, char uplo, lapack_int m, + lapack_int n, const lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zlacpy( int matrix_order, char uplo, lapack_int m, + lapack_int n, const lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb ); + +lapack_int LAPACKE_zlag2c( int matrix_order, lapack_int m, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + lapack_complex_float* sa, lapack_int ldsa ); + +lapack_int LAPACKE_slag2d( int matrix_order, lapack_int m, lapack_int n, + const float* sa, lapack_int ldsa, double* a, + lapack_int lda ); + +lapack_int LAPACKE_dlag2s( int matrix_order, lapack_int m, lapack_int n, + const double* a, lapack_int lda, float* sa, + lapack_int ldsa ); + +lapack_int LAPACKE_clag2z( int matrix_order, lapack_int m, lapack_int n, + const lapack_complex_float* sa, lapack_int ldsa, + lapack_complex_double* a, lapack_int lda ); + +lapack_int LAPACKE_slagge( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, const float* d, + float* a, lapack_int lda, lapack_int* iseed ); +lapack_int LAPACKE_dlagge( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, const double* d, + double* a, lapack_int lda, lapack_int* iseed ); +lapack_int LAPACKE_clagge( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, const float* d, + lapack_complex_float* a, lapack_int lda, + lapack_int* iseed ); +lapack_int LAPACKE_zlagge( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, const double* d, + lapack_complex_double* a, lapack_int lda, + lapack_int* iseed ); + +float LAPACKE_slamch( char cmach ); +double LAPACKE_dlamch( char cmach ); + +float LAPACKE_slange( int matrix_order, char norm, lapack_int m, + lapack_int n, const float* a, lapack_int lda ); +double LAPACKE_dlange( int matrix_order, char norm, lapack_int m, + lapack_int n, const double* a, lapack_int lda ); +float LAPACKE_clange( int matrix_order, char norm, lapack_int m, + lapack_int n, const lapack_complex_float* a, + lapack_int lda ); +double LAPACKE_zlange( int matrix_order, char norm, lapack_int m, + lapack_int n, const lapack_complex_double* a, + lapack_int lda ); + +float LAPACKE_clanhe( int matrix_order, char norm, char uplo, lapack_int n, + const lapack_complex_float* a, lapack_int lda ); +double LAPACKE_zlanhe( int matrix_order, char norm, char uplo, lapack_int n, + const lapack_complex_double* a, lapack_int lda ); + +float LAPACKE_slansy( int matrix_order, char norm, char uplo, lapack_int n, + const float* a, lapack_int lda ); +double LAPACKE_dlansy( int matrix_order, char norm, char uplo, lapack_int n, + const double* a, lapack_int lda ); +float LAPACKE_clansy( int matrix_order, char norm, char uplo, lapack_int n, + const lapack_complex_float* a, lapack_int lda ); +double LAPACKE_zlansy( int matrix_order, char norm, char uplo, lapack_int n, + const lapack_complex_double* a, lapack_int lda ); + +float LAPACKE_slantr( int matrix_order, char norm, char uplo, char diag, + lapack_int m, lapack_int n, const float* a, + lapack_int lda ); +double LAPACKE_dlantr( int matrix_order, char norm, char uplo, char diag, + lapack_int m, lapack_int n, const double* a, + lapack_int lda ); +float LAPACKE_clantr( int matrix_order, char norm, char uplo, char diag, + lapack_int m, lapack_int n, const lapack_complex_float* a, + lapack_int lda ); +double LAPACKE_zlantr( int matrix_order, char norm, char uplo, char diag, + lapack_int m, lapack_int n, const lapack_complex_double* a, + lapack_int lda ); + + +lapack_int LAPACKE_slarfb( int matrix_order, char side, char trans, char direct, + char storev, lapack_int m, lapack_int n, + lapack_int k, const float* v, lapack_int ldv, + const float* t, lapack_int ldt, float* c, + lapack_int ldc ); +lapack_int LAPACKE_dlarfb( int matrix_order, char side, char trans, char direct, + char storev, lapack_int m, lapack_int n, + lapack_int k, const double* v, lapack_int ldv, + const double* t, lapack_int ldt, double* c, + lapack_int ldc ); +lapack_int LAPACKE_clarfb( int matrix_order, char side, char trans, char direct, + char storev, lapack_int m, lapack_int n, + lapack_int k, const lapack_complex_float* v, + lapack_int ldv, const lapack_complex_float* t, + lapack_int ldt, lapack_complex_float* c, + lapack_int ldc ); +lapack_int LAPACKE_zlarfb( int matrix_order, char side, char trans, char direct, + char storev, lapack_int m, lapack_int n, + lapack_int k, const lapack_complex_double* v, + lapack_int ldv, const lapack_complex_double* t, + lapack_int ldt, lapack_complex_double* c, + lapack_int ldc ); + +lapack_int LAPACKE_slarfg( lapack_int n, float* alpha, float* x, + lapack_int incx, float* tau ); +lapack_int LAPACKE_dlarfg( lapack_int n, double* alpha, double* x, + lapack_int incx, double* tau ); +lapack_int LAPACKE_clarfg( lapack_int n, lapack_complex_float* alpha, + lapack_complex_float* x, lapack_int incx, + lapack_complex_float* tau ); +lapack_int LAPACKE_zlarfg( lapack_int n, lapack_complex_double* alpha, + lapack_complex_double* x, lapack_int incx, + lapack_complex_double* tau ); + +lapack_int LAPACKE_slarft( int matrix_order, char direct, char storev, + lapack_int n, lapack_int k, const float* v, + lapack_int ldv, const float* tau, float* t, + lapack_int ldt ); +lapack_int LAPACKE_dlarft( int matrix_order, char direct, char storev, + lapack_int n, lapack_int k, const double* v, + lapack_int ldv, const double* tau, double* t, + lapack_int ldt ); +lapack_int LAPACKE_clarft( int matrix_order, char direct, char storev, + lapack_int n, lapack_int k, + const lapack_complex_float* v, lapack_int ldv, + const lapack_complex_float* tau, + lapack_complex_float* t, lapack_int ldt ); +lapack_int LAPACKE_zlarft( int matrix_order, char direct, char storev, + lapack_int n, lapack_int k, + const lapack_complex_double* v, lapack_int ldv, + const lapack_complex_double* tau, + lapack_complex_double* t, lapack_int ldt ); + +lapack_int LAPACKE_slarfx( int matrix_order, char side, lapack_int m, + lapack_int n, const float* v, float tau, float* c, + lapack_int ldc, float* work ); +lapack_int LAPACKE_dlarfx( int matrix_order, char side, lapack_int m, + lapack_int n, const double* v, double tau, double* c, + lapack_int ldc, double* work ); +lapack_int LAPACKE_clarfx( int matrix_order, char side, lapack_int m, + lapack_int n, const lapack_complex_float* v, + lapack_complex_float tau, lapack_complex_float* c, + lapack_int ldc, lapack_complex_float* work ); +lapack_int LAPACKE_zlarfx( int matrix_order, char side, lapack_int m, + lapack_int n, const lapack_complex_double* v, + lapack_complex_double tau, lapack_complex_double* c, + lapack_int ldc, lapack_complex_double* work ); + +lapack_int LAPACKE_slarnv( lapack_int idist, lapack_int* iseed, lapack_int n, + float* x ); +lapack_int LAPACKE_dlarnv( lapack_int idist, lapack_int* iseed, lapack_int n, + double* x ); +lapack_int LAPACKE_clarnv( lapack_int idist, lapack_int* iseed, lapack_int n, + lapack_complex_float* x ); +lapack_int LAPACKE_zlarnv( lapack_int idist, lapack_int* iseed, lapack_int n, + lapack_complex_double* x ); + +lapack_int LAPACKE_slaset( int matrix_order, char uplo, lapack_int m, + lapack_int n, float alpha, float beta, float* a, + lapack_int lda ); +lapack_int LAPACKE_dlaset( int matrix_order, char uplo, lapack_int m, + lapack_int n, double alpha, double beta, double* a, + lapack_int lda ); +lapack_int LAPACKE_claset( int matrix_order, char uplo, lapack_int m, + lapack_int n, lapack_complex_float alpha, + lapack_complex_float beta, lapack_complex_float* a, + lapack_int lda ); +lapack_int LAPACKE_zlaset( int matrix_order, char uplo, lapack_int m, + lapack_int n, lapack_complex_double alpha, + lapack_complex_double beta, lapack_complex_double* a, + lapack_int lda ); + +lapack_int LAPACKE_slasrt( char id, lapack_int n, float* d ); +lapack_int LAPACKE_dlasrt( char id, lapack_int n, double* d ); + +lapack_int LAPACKE_slaswp( int matrix_order, lapack_int n, float* a, + lapack_int lda, lapack_int k1, lapack_int k2, + const lapack_int* ipiv, lapack_int incx ); +lapack_int LAPACKE_dlaswp( int matrix_order, lapack_int n, double* a, + lapack_int lda, lapack_int k1, lapack_int k2, + const lapack_int* ipiv, lapack_int incx ); +lapack_int LAPACKE_claswp( int matrix_order, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_int k1, lapack_int k2, const lapack_int* ipiv, + lapack_int incx ); +lapack_int LAPACKE_zlaswp( int matrix_order, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_int k1, lapack_int k2, const lapack_int* ipiv, + lapack_int incx ); + +lapack_int LAPACKE_slatms( int matrix_order, lapack_int m, lapack_int n, + char dist, lapack_int* iseed, char sym, float* d, + lapack_int mode, float cond, float dmax, + lapack_int kl, lapack_int ku, char pack, float* a, + lapack_int lda ); +lapack_int LAPACKE_dlatms( int matrix_order, lapack_int m, lapack_int n, + char dist, lapack_int* iseed, char sym, double* d, + lapack_int mode, double cond, double dmax, + lapack_int kl, lapack_int ku, char pack, double* a, + lapack_int lda ); +lapack_int LAPACKE_clatms( int matrix_order, lapack_int m, lapack_int n, + char dist, lapack_int* iseed, char sym, float* d, + lapack_int mode, float cond, float dmax, + lapack_int kl, lapack_int ku, char pack, + lapack_complex_float* a, lapack_int lda ); +lapack_int LAPACKE_zlatms( int matrix_order, lapack_int m, lapack_int n, + char dist, lapack_int* iseed, char sym, double* d, + lapack_int mode, double cond, double dmax, + lapack_int kl, lapack_int ku, char pack, + lapack_complex_double* a, lapack_int lda ); + +lapack_int LAPACKE_slauum( int matrix_order, char uplo, lapack_int n, float* a, + lapack_int lda ); +lapack_int LAPACKE_dlauum( int matrix_order, char uplo, lapack_int n, double* a, + lapack_int lda ); +lapack_int LAPACKE_clauum( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda ); +lapack_int LAPACKE_zlauum( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda ); + +lapack_int LAPACKE_sopgtr( int matrix_order, char uplo, lapack_int n, + const float* ap, const float* tau, float* q, + lapack_int ldq ); +lapack_int LAPACKE_dopgtr( int matrix_order, char uplo, lapack_int n, + const double* ap, const double* tau, double* q, + lapack_int ldq ); + +lapack_int LAPACKE_sopmtr( int matrix_order, char side, char uplo, char trans, + lapack_int m, lapack_int n, const float* ap, + const float* tau, float* c, lapack_int ldc ); +lapack_int LAPACKE_dopmtr( int matrix_order, char side, char uplo, char trans, + lapack_int m, lapack_int n, const double* ap, + const double* tau, double* c, lapack_int ldc ); + +lapack_int LAPACKE_sorgbr( int matrix_order, char vect, lapack_int m, + lapack_int n, lapack_int k, float* a, lapack_int lda, + const float* tau ); +lapack_int LAPACKE_dorgbr( int matrix_order, char vect, lapack_int m, + lapack_int n, lapack_int k, double* a, + lapack_int lda, const double* tau ); + +lapack_int LAPACKE_sorghr( int matrix_order, lapack_int n, lapack_int ilo, + lapack_int ihi, float* a, lapack_int lda, + const float* tau ); +lapack_int LAPACKE_dorghr( int matrix_order, lapack_int n, lapack_int ilo, + lapack_int ihi, double* a, lapack_int lda, + const double* tau ); + +lapack_int LAPACKE_sorglq( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, float* a, lapack_int lda, + const float* tau ); +lapack_int LAPACKE_dorglq( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, double* a, lapack_int lda, + const double* tau ); + +lapack_int LAPACKE_sorgql( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, float* a, lapack_int lda, + const float* tau ); +lapack_int LAPACKE_dorgql( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, double* a, lapack_int lda, + const double* tau ); + +lapack_int LAPACKE_sorgqr( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, float* a, lapack_int lda, + const float* tau ); +lapack_int LAPACKE_dorgqr( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, double* a, lapack_int lda, + const double* tau ); + +lapack_int LAPACKE_sorgrq( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, float* a, lapack_int lda, + const float* tau ); +lapack_int LAPACKE_dorgrq( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, double* a, lapack_int lda, + const double* tau ); + +lapack_int LAPACKE_sorgtr( int matrix_order, char uplo, lapack_int n, float* a, + lapack_int lda, const float* tau ); +lapack_int LAPACKE_dorgtr( int matrix_order, char uplo, lapack_int n, double* a, + lapack_int lda, const double* tau ); + +lapack_int LAPACKE_sormbr( int matrix_order, char vect, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const float* a, lapack_int lda, const float* tau, + float* c, lapack_int ldc ); +lapack_int LAPACKE_dormbr( int matrix_order, char vect, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const double* a, lapack_int lda, const double* tau, + double* c, lapack_int ldc ); + +lapack_int LAPACKE_sormhr( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int ilo, + lapack_int ihi, const float* a, lapack_int lda, + const float* tau, float* c, lapack_int ldc ); +lapack_int LAPACKE_dormhr( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int ilo, + lapack_int ihi, const double* a, lapack_int lda, + const double* tau, double* c, lapack_int ldc ); + +lapack_int LAPACKE_sormlq( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const float* a, lapack_int lda, const float* tau, + float* c, lapack_int ldc ); +lapack_int LAPACKE_dormlq( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const double* a, lapack_int lda, const double* tau, + double* c, lapack_int ldc ); + +lapack_int LAPACKE_sormql( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const float* a, lapack_int lda, const float* tau, + float* c, lapack_int ldc ); +lapack_int LAPACKE_dormql( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const double* a, lapack_int lda, const double* tau, + double* c, lapack_int ldc ); + +lapack_int LAPACKE_sormqr( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const float* a, lapack_int lda, const float* tau, + float* c, lapack_int ldc ); +lapack_int LAPACKE_dormqr( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const double* a, lapack_int lda, const double* tau, + double* c, lapack_int ldc ); + +lapack_int LAPACKE_sormrq( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const float* a, lapack_int lda, const float* tau, + float* c, lapack_int ldc ); +lapack_int LAPACKE_dormrq( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const double* a, lapack_int lda, const double* tau, + double* c, lapack_int ldc ); + +lapack_int LAPACKE_sormrz( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int l, const float* a, lapack_int lda, + const float* tau, float* c, lapack_int ldc ); +lapack_int LAPACKE_dormrz( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int l, const double* a, lapack_int lda, + const double* tau, double* c, lapack_int ldc ); + +lapack_int LAPACKE_sormtr( int matrix_order, char side, char uplo, char trans, + lapack_int m, lapack_int n, const float* a, + lapack_int lda, const float* tau, float* c, + lapack_int ldc ); +lapack_int LAPACKE_dormtr( int matrix_order, char side, char uplo, char trans, + lapack_int m, lapack_int n, const double* a, + lapack_int lda, const double* tau, double* c, + lapack_int ldc ); + +lapack_int LAPACKE_spbcon( int matrix_order, char uplo, lapack_int n, + lapack_int kd, const float* ab, lapack_int ldab, + float anorm, float* rcond ); +lapack_int LAPACKE_dpbcon( int matrix_order, char uplo, lapack_int n, + lapack_int kd, const double* ab, lapack_int ldab, + double anorm, double* rcond ); +lapack_int LAPACKE_cpbcon( int matrix_order, char uplo, lapack_int n, + lapack_int kd, const lapack_complex_float* ab, + lapack_int ldab, float anorm, float* rcond ); +lapack_int LAPACKE_zpbcon( int matrix_order, char uplo, lapack_int n, + lapack_int kd, const lapack_complex_double* ab, + lapack_int ldab, double anorm, double* rcond ); + +lapack_int LAPACKE_spbequ( int matrix_order, char uplo, lapack_int n, + lapack_int kd, const float* ab, lapack_int ldab, + float* s, float* scond, float* amax ); +lapack_int LAPACKE_dpbequ( int matrix_order, char uplo, lapack_int n, + lapack_int kd, const double* ab, lapack_int ldab, + double* s, double* scond, double* amax ); +lapack_int LAPACKE_cpbequ( int matrix_order, char uplo, lapack_int n, + lapack_int kd, const lapack_complex_float* ab, + lapack_int ldab, float* s, float* scond, + float* amax ); +lapack_int LAPACKE_zpbequ( int matrix_order, char uplo, lapack_int n, + lapack_int kd, const lapack_complex_double* ab, + lapack_int ldab, double* s, double* scond, + double* amax ); + +lapack_int LAPACKE_spbrfs( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, const float* ab, + lapack_int ldab, const float* afb, lapack_int ldafb, + const float* b, lapack_int ldb, float* x, + lapack_int ldx, float* ferr, float* berr ); +lapack_int LAPACKE_dpbrfs( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, const double* ab, + lapack_int ldab, const double* afb, lapack_int ldafb, + const double* b, lapack_int ldb, double* x, + lapack_int ldx, double* ferr, double* berr ); +lapack_int LAPACKE_cpbrfs( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, + const lapack_complex_float* ab, lapack_int ldab, + const lapack_complex_float* afb, lapack_int ldafb, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, float* ferr, + float* berr ); +lapack_int LAPACKE_zpbrfs( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, + const lapack_complex_double* ab, lapack_int ldab, + const lapack_complex_double* afb, lapack_int ldafb, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr ); + +lapack_int LAPACKE_spbstf( int matrix_order, char uplo, lapack_int n, + lapack_int kb, float* bb, lapack_int ldbb ); +lapack_int LAPACKE_dpbstf( int matrix_order, char uplo, lapack_int n, + lapack_int kb, double* bb, lapack_int ldbb ); +lapack_int LAPACKE_cpbstf( int matrix_order, char uplo, lapack_int n, + lapack_int kb, lapack_complex_float* bb, + lapack_int ldbb ); +lapack_int LAPACKE_zpbstf( int matrix_order, char uplo, lapack_int n, + lapack_int kb, lapack_complex_double* bb, + lapack_int ldbb ); + +lapack_int LAPACKE_spbsv( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, float* ab, + lapack_int ldab, float* b, lapack_int ldb ); +lapack_int LAPACKE_dpbsv( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, double* ab, + lapack_int ldab, double* b, lapack_int ldb ); +lapack_int LAPACKE_cpbsv( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, + lapack_complex_float* ab, lapack_int ldab, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zpbsv( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, + lapack_complex_double* ab, lapack_int ldab, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_spbsvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, float* ab, + lapack_int ldab, float* afb, lapack_int ldafb, + char* equed, float* s, float* b, lapack_int ldb, + float* x, lapack_int ldx, float* rcond, float* ferr, + float* berr ); +lapack_int LAPACKE_dpbsvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, double* ab, + lapack_int ldab, double* afb, lapack_int ldafb, + char* equed, double* s, double* b, lapack_int ldb, + double* x, lapack_int ldx, double* rcond, + double* ferr, double* berr ); +lapack_int LAPACKE_cpbsvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, + lapack_complex_float* ab, lapack_int ldab, + lapack_complex_float* afb, lapack_int ldafb, + char* equed, float* s, lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* x, + lapack_int ldx, float* rcond, float* ferr, + float* berr ); +lapack_int LAPACKE_zpbsvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, + lapack_complex_double* ab, lapack_int ldab, + lapack_complex_double* afb, lapack_int ldafb, + char* equed, double* s, lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* x, + lapack_int ldx, double* rcond, double* ferr, + double* berr ); + +lapack_int LAPACKE_spbtrf( int matrix_order, char uplo, lapack_int n, + lapack_int kd, float* ab, lapack_int ldab ); +lapack_int LAPACKE_dpbtrf( int matrix_order, char uplo, lapack_int n, + lapack_int kd, double* ab, lapack_int ldab ); +lapack_int LAPACKE_cpbtrf( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_complex_float* ab, + lapack_int ldab ); +lapack_int LAPACKE_zpbtrf( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_complex_double* ab, + lapack_int ldab ); + +lapack_int LAPACKE_spbtrs( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, const float* ab, + lapack_int ldab, float* b, lapack_int ldb ); +lapack_int LAPACKE_dpbtrs( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, const double* ab, + lapack_int ldab, double* b, lapack_int ldb ); +lapack_int LAPACKE_cpbtrs( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, + const lapack_complex_float* ab, lapack_int ldab, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zpbtrs( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, + const lapack_complex_double* ab, lapack_int ldab, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_spftrf( int matrix_order, char transr, char uplo, + lapack_int n, float* a ); +lapack_int LAPACKE_dpftrf( int matrix_order, char transr, char uplo, + lapack_int n, double* a ); +lapack_int LAPACKE_cpftrf( int matrix_order, char transr, char uplo, + lapack_int n, lapack_complex_float* a ); +lapack_int LAPACKE_zpftrf( int matrix_order, char transr, char uplo, + lapack_int n, lapack_complex_double* a ); + +lapack_int LAPACKE_spftri( int matrix_order, char transr, char uplo, + lapack_int n, float* a ); +lapack_int LAPACKE_dpftri( int matrix_order, char transr, char uplo, + lapack_int n, double* a ); +lapack_int LAPACKE_cpftri( int matrix_order, char transr, char uplo, + lapack_int n, lapack_complex_float* a ); +lapack_int LAPACKE_zpftri( int matrix_order, char transr, char uplo, + lapack_int n, lapack_complex_double* a ); + +lapack_int LAPACKE_spftrs( int matrix_order, char transr, char uplo, + lapack_int n, lapack_int nrhs, const float* a, + float* b, lapack_int ldb ); +lapack_int LAPACKE_dpftrs( int matrix_order, char transr, char uplo, + lapack_int n, lapack_int nrhs, const double* a, + double* b, lapack_int ldb ); +lapack_int LAPACKE_cpftrs( int matrix_order, char transr, char uplo, + lapack_int n, lapack_int nrhs, + const lapack_complex_float* a, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zpftrs( int matrix_order, char transr, char uplo, + lapack_int n, lapack_int nrhs, + const lapack_complex_double* a, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_spocon( int matrix_order, char uplo, lapack_int n, + const float* a, lapack_int lda, float anorm, + float* rcond ); +lapack_int LAPACKE_dpocon( int matrix_order, char uplo, lapack_int n, + const double* a, lapack_int lda, double anorm, + double* rcond ); +lapack_int LAPACKE_cpocon( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + float anorm, float* rcond ); +lapack_int LAPACKE_zpocon( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + double anorm, double* rcond ); + +lapack_int LAPACKE_spoequ( int matrix_order, lapack_int n, const float* a, + lapack_int lda, float* s, float* scond, + float* amax ); +lapack_int LAPACKE_dpoequ( int matrix_order, lapack_int n, const double* a, + lapack_int lda, double* s, double* scond, + double* amax ); +lapack_int LAPACKE_cpoequ( int matrix_order, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + float* s, float* scond, float* amax ); +lapack_int LAPACKE_zpoequ( int matrix_order, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + double* s, double* scond, double* amax ); + +lapack_int LAPACKE_spoequb( int matrix_order, lapack_int n, const float* a, + lapack_int lda, float* s, float* scond, + float* amax ); +lapack_int LAPACKE_dpoequb( int matrix_order, lapack_int n, const double* a, + lapack_int lda, double* s, double* scond, + double* amax ); +lapack_int LAPACKE_cpoequb( int matrix_order, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + float* s, float* scond, float* amax ); +lapack_int LAPACKE_zpoequb( int matrix_order, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + double* s, double* scond, double* amax ); + +lapack_int LAPACKE_sporfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* a, lapack_int lda, + const float* af, lapack_int ldaf, const float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* ferr, float* berr ); +lapack_int LAPACKE_dporfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* a, lapack_int lda, + const double* af, lapack_int ldaf, const double* b, + lapack_int ldb, double* x, lapack_int ldx, + double* ferr, double* berr ); +lapack_int LAPACKE_cporfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* af, + lapack_int ldaf, const lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* x, + lapack_int ldx, float* ferr, float* berr ); +lapack_int LAPACKE_zporfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, const lapack_complex_double* af, + lapack_int ldaf, const lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* x, + lapack_int ldx, double* ferr, double* berr ); + +lapack_int LAPACKE_sporfsx( int matrix_order, char uplo, char equed, + lapack_int n, lapack_int nrhs, const float* a, + lapack_int lda, const float* af, lapack_int ldaf, + const float* s, const float* b, lapack_int ldb, + float* x, lapack_int ldx, float* rcond, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params ); +lapack_int LAPACKE_dporfsx( int matrix_order, char uplo, char equed, + lapack_int n, lapack_int nrhs, const double* a, + lapack_int lda, const double* af, lapack_int ldaf, + const double* s, const double* b, lapack_int ldb, + double* x, lapack_int ldx, double* rcond, + double* berr, lapack_int n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int nparams, double* params ); +lapack_int LAPACKE_cporfsx( int matrix_order, char uplo, char equed, + lapack_int n, lapack_int nrhs, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* af, lapack_int ldaf, + const float* s, const lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* x, + lapack_int ldx, float* rcond, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params ); +lapack_int LAPACKE_zporfsx( int matrix_order, char uplo, char equed, + lapack_int n, lapack_int nrhs, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* af, lapack_int ldaf, + const double* s, const lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* x, + lapack_int ldx, double* rcond, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params ); + +lapack_int LAPACKE_sposv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, float* a, lapack_int lda, float* b, + lapack_int ldb ); +lapack_int LAPACKE_dposv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, double* a, lapack_int lda, double* b, + lapack_int ldb ); +lapack_int LAPACKE_cposv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zposv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb ); +lapack_int LAPACKE_dsposv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, double* a, lapack_int lda, + double* b, lapack_int ldb, double* x, lapack_int ldx, + lapack_int* iter ); +lapack_int LAPACKE_zcposv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* x, + lapack_int ldx, lapack_int* iter ); + +lapack_int LAPACKE_sposvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int nrhs, float* a, lapack_int lda, float* af, + lapack_int ldaf, char* equed, float* s, float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* rcond, float* ferr, float* berr ); +lapack_int LAPACKE_dposvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int nrhs, double* a, lapack_int lda, + double* af, lapack_int ldaf, char* equed, double* s, + double* b, lapack_int ldb, double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr ); +lapack_int LAPACKE_cposvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* af, + lapack_int ldaf, char* equed, float* s, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* ferr, float* berr ); +lapack_int LAPACKE_zposvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* af, + lapack_int ldaf, char* equed, double* s, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr ); + +lapack_int LAPACKE_sposvxx( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, float* a, + lapack_int lda, float* af, lapack_int ldaf, + char* equed, float* s, float* b, lapack_int ldb, + float* x, lapack_int ldx, float* rcond, + float* rpvgrw, float* berr, lapack_int n_err_bnds, + float* err_bnds_norm, float* err_bnds_comp, + lapack_int nparams, float* params ); +lapack_int LAPACKE_dposvxx( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, double* a, + lapack_int lda, double* af, lapack_int ldaf, + char* equed, double* s, double* b, lapack_int ldb, + double* x, lapack_int ldx, double* rcond, + double* rpvgrw, double* berr, lapack_int n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int nparams, double* params ); +lapack_int LAPACKE_cposvxx( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* af, lapack_int ldaf, + char* equed, float* s, lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* x, + lapack_int ldx, float* rcond, float* rpvgrw, + float* berr, lapack_int n_err_bnds, + float* err_bnds_norm, float* err_bnds_comp, + lapack_int nparams, float* params ); +lapack_int LAPACKE_zposvxx( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* af, lapack_int ldaf, + char* equed, double* s, lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* x, + lapack_int ldx, double* rcond, double* rpvgrw, + double* berr, lapack_int n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int nparams, double* params ); + +lapack_int LAPACKE_spotrf( int matrix_order, char uplo, lapack_int n, float* a, + lapack_int lda ); +lapack_int LAPACKE_dpotrf( int matrix_order, char uplo, lapack_int n, double* a, + lapack_int lda ); +lapack_int LAPACKE_cpotrf( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda ); +lapack_int LAPACKE_zpotrf( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda ); + +lapack_int LAPACKE_spotri( int matrix_order, char uplo, lapack_int n, float* a, + lapack_int lda ); +lapack_int LAPACKE_dpotri( int matrix_order, char uplo, lapack_int n, double* a, + lapack_int lda ); +lapack_int LAPACKE_cpotri( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda ); +lapack_int LAPACKE_zpotri( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda ); + +lapack_int LAPACKE_spotrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* a, lapack_int lda, + float* b, lapack_int ldb ); +lapack_int LAPACKE_dpotrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* a, lapack_int lda, + double* b, lapack_int ldb ); +lapack_int LAPACKE_cpotrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zpotrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb ); + +lapack_int LAPACKE_sppcon( int matrix_order, char uplo, lapack_int n, + const float* ap, float anorm, float* rcond ); +lapack_int LAPACKE_dppcon( int matrix_order, char uplo, lapack_int n, + const double* ap, double anorm, double* rcond ); +lapack_int LAPACKE_cppcon( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* ap, float anorm, + float* rcond ); +lapack_int LAPACKE_zppcon( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* ap, double anorm, + double* rcond ); + +lapack_int LAPACKE_sppequ( int matrix_order, char uplo, lapack_int n, + const float* ap, float* s, float* scond, + float* amax ); +lapack_int LAPACKE_dppequ( int matrix_order, char uplo, lapack_int n, + const double* ap, double* s, double* scond, + double* amax ); +lapack_int LAPACKE_cppequ( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* ap, float* s, + float* scond, float* amax ); +lapack_int LAPACKE_zppequ( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* ap, double* s, + double* scond, double* amax ); + +lapack_int LAPACKE_spprfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* ap, const float* afp, + const float* b, lapack_int ldb, float* x, + lapack_int ldx, float* ferr, float* berr ); +lapack_int LAPACKE_dpprfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* ap, const double* afp, + const double* b, lapack_int ldb, double* x, + lapack_int ldx, double* ferr, double* berr ); +lapack_int LAPACKE_cpprfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* ap, + const lapack_complex_float* afp, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, float* ferr, + float* berr ); +lapack_int LAPACKE_zpprfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* ap, + const lapack_complex_double* afp, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr ); + +lapack_int LAPACKE_sppsv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, float* ap, float* b, + lapack_int ldb ); +lapack_int LAPACKE_dppsv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, double* ap, double* b, + lapack_int ldb ); +lapack_int LAPACKE_cppsv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_float* ap, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zppsv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_double* ap, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_sppsvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int nrhs, float* ap, float* afp, char* equed, + float* s, float* b, lapack_int ldb, float* x, + lapack_int ldx, float* rcond, float* ferr, + float* berr ); +lapack_int LAPACKE_dppsvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int nrhs, double* ap, double* afp, + char* equed, double* s, double* b, lapack_int ldb, + double* x, lapack_int ldx, double* rcond, + double* ferr, double* berr ); +lapack_int LAPACKE_cppsvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_float* ap, + lapack_complex_float* afp, char* equed, float* s, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* ferr, float* berr ); +lapack_int LAPACKE_zppsvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_double* ap, + lapack_complex_double* afp, char* equed, double* s, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr ); + +lapack_int LAPACKE_spptrf( int matrix_order, char uplo, lapack_int n, + float* ap ); +lapack_int LAPACKE_dpptrf( int matrix_order, char uplo, lapack_int n, + double* ap ); +lapack_int LAPACKE_cpptrf( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* ap ); +lapack_int LAPACKE_zpptrf( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* ap ); + +lapack_int LAPACKE_spptri( int matrix_order, char uplo, lapack_int n, + float* ap ); +lapack_int LAPACKE_dpptri( int matrix_order, char uplo, lapack_int n, + double* ap ); +lapack_int LAPACKE_cpptri( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* ap ); +lapack_int LAPACKE_zpptri( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* ap ); + +lapack_int LAPACKE_spptrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* ap, float* b, + lapack_int ldb ); +lapack_int LAPACKE_dpptrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* ap, double* b, + lapack_int ldb ); +lapack_int LAPACKE_cpptrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* ap, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zpptrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* ap, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_spstrf( int matrix_order, char uplo, lapack_int n, float* a, + lapack_int lda, lapack_int* piv, lapack_int* rank, + float tol ); +lapack_int LAPACKE_dpstrf( int matrix_order, char uplo, lapack_int n, double* a, + lapack_int lda, lapack_int* piv, lapack_int* rank, + double tol ); +lapack_int LAPACKE_cpstrf( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_int* piv, lapack_int* rank, float tol ); +lapack_int LAPACKE_zpstrf( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_int* piv, lapack_int* rank, double tol ); + +lapack_int LAPACKE_sptcon( lapack_int n, const float* d, const float* e, + float anorm, float* rcond ); +lapack_int LAPACKE_dptcon( lapack_int n, const double* d, const double* e, + double anorm, double* rcond ); +lapack_int LAPACKE_cptcon( lapack_int n, const float* d, + const lapack_complex_float* e, float anorm, + float* rcond ); +lapack_int LAPACKE_zptcon( lapack_int n, const double* d, + const lapack_complex_double* e, double anorm, + double* rcond ); + +lapack_int LAPACKE_spteqr( int matrix_order, char compz, lapack_int n, float* d, + float* e, float* z, lapack_int ldz ); +lapack_int LAPACKE_dpteqr( int matrix_order, char compz, lapack_int n, + double* d, double* e, double* z, lapack_int ldz ); +lapack_int LAPACKE_cpteqr( int matrix_order, char compz, lapack_int n, float* d, + float* e, lapack_complex_float* z, lapack_int ldz ); +lapack_int LAPACKE_zpteqr( int matrix_order, char compz, lapack_int n, + double* d, double* e, lapack_complex_double* z, + lapack_int ldz ); + +lapack_int LAPACKE_sptrfs( int matrix_order, lapack_int n, lapack_int nrhs, + const float* d, const float* e, const float* df, + const float* ef, const float* b, lapack_int ldb, + float* x, lapack_int ldx, float* ferr, float* berr ); +lapack_int LAPACKE_dptrfs( int matrix_order, lapack_int n, lapack_int nrhs, + const double* d, const double* e, const double* df, + const double* ef, const double* b, lapack_int ldb, + double* x, lapack_int ldx, double* ferr, + double* berr ); +lapack_int LAPACKE_cptrfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* d, + const lapack_complex_float* e, const float* df, + const lapack_complex_float* ef, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, float* ferr, + float* berr ); +lapack_int LAPACKE_zptrfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* d, + const lapack_complex_double* e, const double* df, + const lapack_complex_double* ef, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr ); + +lapack_int LAPACKE_sptsv( int matrix_order, lapack_int n, lapack_int nrhs, + float* d, float* e, float* b, lapack_int ldb ); +lapack_int LAPACKE_dptsv( int matrix_order, lapack_int n, lapack_int nrhs, + double* d, double* e, double* b, lapack_int ldb ); +lapack_int LAPACKE_cptsv( int matrix_order, lapack_int n, lapack_int nrhs, + float* d, lapack_complex_float* e, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zptsv( int matrix_order, lapack_int n, lapack_int nrhs, + double* d, lapack_complex_double* e, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_sptsvx( int matrix_order, char fact, lapack_int n, + lapack_int nrhs, const float* d, const float* e, + float* df, float* ef, const float* b, lapack_int ldb, + float* x, lapack_int ldx, float* rcond, float* ferr, + float* berr ); +lapack_int LAPACKE_dptsvx( int matrix_order, char fact, lapack_int n, + lapack_int nrhs, const double* d, const double* e, + double* df, double* ef, const double* b, + lapack_int ldb, double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr ); +lapack_int LAPACKE_cptsvx( int matrix_order, char fact, lapack_int n, + lapack_int nrhs, const float* d, + const lapack_complex_float* e, float* df, + lapack_complex_float* ef, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* ferr, float* berr ); +lapack_int LAPACKE_zptsvx( int matrix_order, char fact, lapack_int n, + lapack_int nrhs, const double* d, + const lapack_complex_double* e, double* df, + lapack_complex_double* ef, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr ); + +lapack_int LAPACKE_spttrf( lapack_int n, float* d, float* e ); +lapack_int LAPACKE_dpttrf( lapack_int n, double* d, double* e ); +lapack_int LAPACKE_cpttrf( lapack_int n, float* d, lapack_complex_float* e ); +lapack_int LAPACKE_zpttrf( lapack_int n, double* d, lapack_complex_double* e ); + +lapack_int LAPACKE_spttrs( int matrix_order, lapack_int n, lapack_int nrhs, + const float* d, const float* e, float* b, + lapack_int ldb ); +lapack_int LAPACKE_dpttrs( int matrix_order, lapack_int n, lapack_int nrhs, + const double* d, const double* e, double* b, + lapack_int ldb ); +lapack_int LAPACKE_cpttrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* d, + const lapack_complex_float* e, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zpttrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* d, + const lapack_complex_double* e, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_ssbev( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_int kd, float* ab, lapack_int ldab, float* w, + float* z, lapack_int ldz ); +lapack_int LAPACKE_dsbev( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_int kd, double* ab, lapack_int ldab, double* w, + double* z, lapack_int ldz ); + +lapack_int LAPACKE_ssbevd( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_int kd, float* ab, lapack_int ldab, float* w, + float* z, lapack_int ldz ); +lapack_int LAPACKE_dsbevd( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_int kd, double* ab, lapack_int ldab, + double* w, double* z, lapack_int ldz ); + +lapack_int LAPACKE_ssbevx( int matrix_order, char jobz, char range, char uplo, + lapack_int n, lapack_int kd, float* ab, + lapack_int ldab, float* q, lapack_int ldq, float vl, + float vu, lapack_int il, lapack_int iu, float abstol, + lapack_int* m, float* w, float* z, lapack_int ldz, + lapack_int* ifail ); +lapack_int LAPACKE_dsbevx( int matrix_order, char jobz, char range, char uplo, + lapack_int n, lapack_int kd, double* ab, + lapack_int ldab, double* q, lapack_int ldq, + double vl, double vu, lapack_int il, lapack_int iu, + double abstol, lapack_int* m, double* w, double* z, + lapack_int ldz, lapack_int* ifail ); + +lapack_int LAPACKE_ssbgst( int matrix_order, char vect, char uplo, lapack_int n, + lapack_int ka, lapack_int kb, float* ab, + lapack_int ldab, const float* bb, lapack_int ldbb, + float* x, lapack_int ldx ); +lapack_int LAPACKE_dsbgst( int matrix_order, char vect, char uplo, lapack_int n, + lapack_int ka, lapack_int kb, double* ab, + lapack_int ldab, const double* bb, lapack_int ldbb, + double* x, lapack_int ldx ); + +lapack_int LAPACKE_ssbgv( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_int ka, lapack_int kb, float* ab, + lapack_int ldab, float* bb, lapack_int ldbb, float* w, + float* z, lapack_int ldz ); +lapack_int LAPACKE_dsbgv( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_int ka, lapack_int kb, double* ab, + lapack_int ldab, double* bb, lapack_int ldbb, + double* w, double* z, lapack_int ldz ); + +lapack_int LAPACKE_ssbgvd( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_int ka, lapack_int kb, float* ab, + lapack_int ldab, float* bb, lapack_int ldbb, + float* w, float* z, lapack_int ldz ); +lapack_int LAPACKE_dsbgvd( int matrix_order, char jobz, char uplo, lapack_int n, + lapack_int ka, lapack_int kb, double* ab, + lapack_int ldab, double* bb, lapack_int ldbb, + double* w, double* z, lapack_int ldz ); + +lapack_int LAPACKE_ssbgvx( int matrix_order, char jobz, char range, char uplo, + lapack_int n, lapack_int ka, lapack_int kb, + float* ab, lapack_int ldab, float* bb, + lapack_int ldbb, float* q, lapack_int ldq, float vl, + float vu, lapack_int il, lapack_int iu, float abstol, + lapack_int* m, float* w, float* z, lapack_int ldz, + lapack_int* ifail ); +lapack_int LAPACKE_dsbgvx( int matrix_order, char jobz, char range, char uplo, + lapack_int n, lapack_int ka, lapack_int kb, + double* ab, lapack_int ldab, double* bb, + lapack_int ldbb, double* q, lapack_int ldq, + double vl, double vu, lapack_int il, lapack_int iu, + double abstol, lapack_int* m, double* w, double* z, + lapack_int ldz, lapack_int* ifail ); + +lapack_int LAPACKE_ssbtrd( int matrix_order, char vect, char uplo, lapack_int n, + lapack_int kd, float* ab, lapack_int ldab, float* d, + float* e, float* q, lapack_int ldq ); +lapack_int LAPACKE_dsbtrd( int matrix_order, char vect, char uplo, lapack_int n, + lapack_int kd, double* ab, lapack_int ldab, + double* d, double* e, double* q, lapack_int ldq ); + +lapack_int LAPACKE_ssfrk( int matrix_order, char transr, char uplo, char trans, + lapack_int n, lapack_int k, float alpha, + const float* a, lapack_int lda, float beta, + float* c ); +lapack_int LAPACKE_dsfrk( int matrix_order, char transr, char uplo, char trans, + lapack_int n, lapack_int k, double alpha, + const double* a, lapack_int lda, double beta, + double* c ); + +lapack_int LAPACKE_sspcon( int matrix_order, char uplo, lapack_int n, + const float* ap, const lapack_int* ipiv, float anorm, + float* rcond ); +lapack_int LAPACKE_dspcon( int matrix_order, char uplo, lapack_int n, + const double* ap, const lapack_int* ipiv, + double anorm, double* rcond ); +lapack_int LAPACKE_cspcon( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* ap, + const lapack_int* ipiv, float anorm, float* rcond ); +lapack_int LAPACKE_zspcon( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* ap, + const lapack_int* ipiv, double anorm, + double* rcond ); + +lapack_int LAPACKE_sspev( int matrix_order, char jobz, char uplo, lapack_int n, + float* ap, float* w, float* z, lapack_int ldz ); +lapack_int LAPACKE_dspev( int matrix_order, char jobz, char uplo, lapack_int n, + double* ap, double* w, double* z, lapack_int ldz ); + +lapack_int LAPACKE_sspevd( int matrix_order, char jobz, char uplo, lapack_int n, + float* ap, float* w, float* z, lapack_int ldz ); +lapack_int LAPACKE_dspevd( int matrix_order, char jobz, char uplo, lapack_int n, + double* ap, double* w, double* z, lapack_int ldz ); + +lapack_int LAPACKE_sspevx( int matrix_order, char jobz, char range, char uplo, + lapack_int n, float* ap, float vl, float vu, + lapack_int il, lapack_int iu, float abstol, + lapack_int* m, float* w, float* z, lapack_int ldz, + lapack_int* ifail ); +lapack_int LAPACKE_dspevx( int matrix_order, char jobz, char range, char uplo, + lapack_int n, double* ap, double vl, double vu, + lapack_int il, lapack_int iu, double abstol, + lapack_int* m, double* w, double* z, lapack_int ldz, + lapack_int* ifail ); + +lapack_int LAPACKE_sspgst( int matrix_order, lapack_int itype, char uplo, + lapack_int n, float* ap, const float* bp ); +lapack_int LAPACKE_dspgst( int matrix_order, lapack_int itype, char uplo, + lapack_int n, double* ap, const double* bp ); + +lapack_int LAPACKE_sspgv( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, float* ap, float* bp, + float* w, float* z, lapack_int ldz ); +lapack_int LAPACKE_dspgv( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, double* ap, double* bp, + double* w, double* z, lapack_int ldz ); + +lapack_int LAPACKE_sspgvd( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, float* ap, float* bp, + float* w, float* z, lapack_int ldz ); +lapack_int LAPACKE_dspgvd( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, double* ap, double* bp, + double* w, double* z, lapack_int ldz ); + +lapack_int LAPACKE_sspgvx( int matrix_order, lapack_int itype, char jobz, + char range, char uplo, lapack_int n, float* ap, + float* bp, float vl, float vu, lapack_int il, + lapack_int iu, float abstol, lapack_int* m, float* w, + float* z, lapack_int ldz, lapack_int* ifail ); +lapack_int LAPACKE_dspgvx( int matrix_order, lapack_int itype, char jobz, + char range, char uplo, lapack_int n, double* ap, + double* bp, double vl, double vu, lapack_int il, + lapack_int iu, double abstol, lapack_int* m, + double* w, double* z, lapack_int ldz, + lapack_int* ifail ); + +lapack_int LAPACKE_ssprfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* ap, const float* afp, + const lapack_int* ipiv, const float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* ferr, float* berr ); +lapack_int LAPACKE_dsprfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* ap, const double* afp, + const lapack_int* ipiv, const double* b, + lapack_int ldb, double* x, lapack_int ldx, + double* ferr, double* berr ); +lapack_int LAPACKE_csprfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* ap, + const lapack_complex_float* afp, + const lapack_int* ipiv, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, float* ferr, + float* berr ); +lapack_int LAPACKE_zsprfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* ap, + const lapack_complex_double* afp, + const lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr ); + +lapack_int LAPACKE_sspsv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, float* ap, lapack_int* ipiv, + float* b, lapack_int ldb ); +lapack_int LAPACKE_dspsv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, double* ap, lapack_int* ipiv, + double* b, lapack_int ldb ); +lapack_int LAPACKE_cspsv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_float* ap, + lapack_int* ipiv, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zspsv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_double* ap, + lapack_int* ipiv, lapack_complex_double* b, + lapack_int ldb ); + +lapack_int LAPACKE_sspsvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int nrhs, const float* ap, float* afp, + lapack_int* ipiv, const float* b, lapack_int ldb, + float* x, lapack_int ldx, float* rcond, float* ferr, + float* berr ); +lapack_int LAPACKE_dspsvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int nrhs, const double* ap, double* afp, + lapack_int* ipiv, const double* b, lapack_int ldb, + double* x, lapack_int ldx, double* rcond, + double* ferr, double* berr ); +lapack_int LAPACKE_cspsvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* ap, + lapack_complex_float* afp, lapack_int* ipiv, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* ferr, float* berr ); +lapack_int LAPACKE_zspsvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* ap, + lapack_complex_double* afp, lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr ); + +lapack_int LAPACKE_ssptrd( int matrix_order, char uplo, lapack_int n, float* ap, + float* d, float* e, float* tau ); +lapack_int LAPACKE_dsptrd( int matrix_order, char uplo, lapack_int n, + double* ap, double* d, double* e, double* tau ); + +lapack_int LAPACKE_ssptrf( int matrix_order, char uplo, lapack_int n, float* ap, + lapack_int* ipiv ); +lapack_int LAPACKE_dsptrf( int matrix_order, char uplo, lapack_int n, + double* ap, lapack_int* ipiv ); +lapack_int LAPACKE_csptrf( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* ap, lapack_int* ipiv ); +lapack_int LAPACKE_zsptrf( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* ap, lapack_int* ipiv ); + +lapack_int LAPACKE_ssptri( int matrix_order, char uplo, lapack_int n, float* ap, + const lapack_int* ipiv ); +lapack_int LAPACKE_dsptri( int matrix_order, char uplo, lapack_int n, + double* ap, const lapack_int* ipiv ); +lapack_int LAPACKE_csptri( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* ap, const lapack_int* ipiv ); +lapack_int LAPACKE_zsptri( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* ap, const lapack_int* ipiv ); + +lapack_int LAPACKE_ssptrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* ap, + const lapack_int* ipiv, float* b, lapack_int ldb ); +lapack_int LAPACKE_dsptrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* ap, + const lapack_int* ipiv, double* b, lapack_int ldb ); +lapack_int LAPACKE_csptrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* ap, + const lapack_int* ipiv, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zsptrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* ap, + const lapack_int* ipiv, lapack_complex_double* b, + lapack_int ldb ); + +lapack_int LAPACKE_sstebz( char range, char order, lapack_int n, float vl, + float vu, lapack_int il, lapack_int iu, float abstol, + const float* d, const float* e, lapack_int* m, + lapack_int* nsplit, float* w, lapack_int* iblock, + lapack_int* isplit ); +lapack_int LAPACKE_dstebz( char range, char order, lapack_int n, double vl, + double vu, lapack_int il, lapack_int iu, + double abstol, const double* d, const double* e, + lapack_int* m, lapack_int* nsplit, double* w, + lapack_int* iblock, lapack_int* isplit ); + +lapack_int LAPACKE_sstedc( int matrix_order, char compz, lapack_int n, float* d, + float* e, float* z, lapack_int ldz ); +lapack_int LAPACKE_dstedc( int matrix_order, char compz, lapack_int n, + double* d, double* e, double* z, lapack_int ldz ); +lapack_int LAPACKE_cstedc( int matrix_order, char compz, lapack_int n, float* d, + float* e, lapack_complex_float* z, lapack_int ldz ); +lapack_int LAPACKE_zstedc( int matrix_order, char compz, lapack_int n, + double* d, double* e, lapack_complex_double* z, + lapack_int ldz ); + +lapack_int LAPACKE_sstegr( int matrix_order, char jobz, char range, + lapack_int n, float* d, float* e, float vl, float vu, + lapack_int il, lapack_int iu, float abstol, + lapack_int* m, float* w, float* z, lapack_int ldz, + lapack_int* isuppz ); +lapack_int LAPACKE_dstegr( int matrix_order, char jobz, char range, + lapack_int n, double* d, double* e, double vl, + double vu, lapack_int il, lapack_int iu, + double abstol, lapack_int* m, double* w, double* z, + lapack_int ldz, lapack_int* isuppz ); +lapack_int LAPACKE_cstegr( int matrix_order, char jobz, char range, + lapack_int n, float* d, float* e, float vl, float vu, + lapack_int il, lapack_int iu, float abstol, + lapack_int* m, float* w, lapack_complex_float* z, + lapack_int ldz, lapack_int* isuppz ); +lapack_int LAPACKE_zstegr( int matrix_order, char jobz, char range, + lapack_int n, double* d, double* e, double vl, + double vu, lapack_int il, lapack_int iu, + double abstol, lapack_int* m, double* w, + lapack_complex_double* z, lapack_int ldz, + lapack_int* isuppz ); + +lapack_int LAPACKE_sstein( int matrix_order, lapack_int n, const float* d, + const float* e, lapack_int m, const float* w, + const lapack_int* iblock, const lapack_int* isplit, + float* z, lapack_int ldz, lapack_int* ifailv ); +lapack_int LAPACKE_dstein( int matrix_order, lapack_int n, const double* d, + const double* e, lapack_int m, const double* w, + const lapack_int* iblock, const lapack_int* isplit, + double* z, lapack_int ldz, lapack_int* ifailv ); +lapack_int LAPACKE_cstein( int matrix_order, lapack_int n, const float* d, + const float* e, lapack_int m, const float* w, + const lapack_int* iblock, const lapack_int* isplit, + lapack_complex_float* z, lapack_int ldz, + lapack_int* ifailv ); +lapack_int LAPACKE_zstein( int matrix_order, lapack_int n, const double* d, + const double* e, lapack_int m, const double* w, + const lapack_int* iblock, const lapack_int* isplit, + lapack_complex_double* z, lapack_int ldz, + lapack_int* ifailv ); + +lapack_int LAPACKE_sstemr( int matrix_order, char jobz, char range, + lapack_int n, float* d, float* e, float vl, float vu, + lapack_int il, lapack_int iu, lapack_int* m, + float* w, float* z, lapack_int ldz, lapack_int nzc, + lapack_int* isuppz, lapack_logical* tryrac ); +lapack_int LAPACKE_dstemr( int matrix_order, char jobz, char range, + lapack_int n, double* d, double* e, double vl, + double vu, lapack_int il, lapack_int iu, + lapack_int* m, double* w, double* z, lapack_int ldz, + lapack_int nzc, lapack_int* isuppz, + lapack_logical* tryrac ); +lapack_int LAPACKE_cstemr( int matrix_order, char jobz, char range, + lapack_int n, float* d, float* e, float vl, float vu, + lapack_int il, lapack_int iu, lapack_int* m, + float* w, lapack_complex_float* z, lapack_int ldz, + lapack_int nzc, lapack_int* isuppz, + lapack_logical* tryrac ); +lapack_int LAPACKE_zstemr( int matrix_order, char jobz, char range, + lapack_int n, double* d, double* e, double vl, + double vu, lapack_int il, lapack_int iu, + lapack_int* m, double* w, lapack_complex_double* z, + lapack_int ldz, lapack_int nzc, lapack_int* isuppz, + lapack_logical* tryrac ); + +lapack_int LAPACKE_ssteqr( int matrix_order, char compz, lapack_int n, float* d, + float* e, float* z, lapack_int ldz ); +lapack_int LAPACKE_dsteqr( int matrix_order, char compz, lapack_int n, + double* d, double* e, double* z, lapack_int ldz ); +lapack_int LAPACKE_csteqr( int matrix_order, char compz, lapack_int n, float* d, + float* e, lapack_complex_float* z, lapack_int ldz ); +lapack_int LAPACKE_zsteqr( int matrix_order, char compz, lapack_int n, + double* d, double* e, lapack_complex_double* z, + lapack_int ldz ); + +lapack_int LAPACKE_ssterf( lapack_int n, float* d, float* e ); +lapack_int LAPACKE_dsterf( lapack_int n, double* d, double* e ); + +lapack_int LAPACKE_sstev( int matrix_order, char jobz, lapack_int n, float* d, + float* e, float* z, lapack_int ldz ); +lapack_int LAPACKE_dstev( int matrix_order, char jobz, lapack_int n, double* d, + double* e, double* z, lapack_int ldz ); + +lapack_int LAPACKE_sstevd( int matrix_order, char jobz, lapack_int n, float* d, + float* e, float* z, lapack_int ldz ); +lapack_int LAPACKE_dstevd( int matrix_order, char jobz, lapack_int n, double* d, + double* e, double* z, lapack_int ldz ); + +lapack_int LAPACKE_sstevr( int matrix_order, char jobz, char range, + lapack_int n, float* d, float* e, float vl, float vu, + lapack_int il, lapack_int iu, float abstol, + lapack_int* m, float* w, float* z, lapack_int ldz, + lapack_int* isuppz ); +lapack_int LAPACKE_dstevr( int matrix_order, char jobz, char range, + lapack_int n, double* d, double* e, double vl, + double vu, lapack_int il, lapack_int iu, + double abstol, lapack_int* m, double* w, double* z, + lapack_int ldz, lapack_int* isuppz ); + +lapack_int LAPACKE_sstevx( int matrix_order, char jobz, char range, + lapack_int n, float* d, float* e, float vl, float vu, + lapack_int il, lapack_int iu, float abstol, + lapack_int* m, float* w, float* z, lapack_int ldz, + lapack_int* ifail ); +lapack_int LAPACKE_dstevx( int matrix_order, char jobz, char range, + lapack_int n, double* d, double* e, double vl, + double vu, lapack_int il, lapack_int iu, + double abstol, lapack_int* m, double* w, double* z, + lapack_int ldz, lapack_int* ifail ); + +lapack_int LAPACKE_ssycon( int matrix_order, char uplo, lapack_int n, + const float* a, lapack_int lda, + const lapack_int* ipiv, float anorm, float* rcond ); +lapack_int LAPACKE_dsycon( int matrix_order, char uplo, lapack_int n, + const double* a, lapack_int lda, + const lapack_int* ipiv, double anorm, + double* rcond ); +lapack_int LAPACKE_csycon( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + const lapack_int* ipiv, float anorm, float* rcond ); +lapack_int LAPACKE_zsycon( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + const lapack_int* ipiv, double anorm, + double* rcond ); + +lapack_int LAPACKE_ssyequb( int matrix_order, char uplo, lapack_int n, + const float* a, lapack_int lda, float* s, + float* scond, float* amax ); +lapack_int LAPACKE_dsyequb( int matrix_order, char uplo, lapack_int n, + const double* a, lapack_int lda, double* s, + double* scond, double* amax ); +lapack_int LAPACKE_csyequb( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + float* s, float* scond, float* amax ); +lapack_int LAPACKE_zsyequb( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + double* s, double* scond, double* amax ); + +lapack_int LAPACKE_ssyev( int matrix_order, char jobz, char uplo, lapack_int n, + float* a, lapack_int lda, float* w ); +lapack_int LAPACKE_dsyev( int matrix_order, char jobz, char uplo, lapack_int n, + double* a, lapack_int lda, double* w ); + +lapack_int LAPACKE_ssyevd( int matrix_order, char jobz, char uplo, lapack_int n, + float* a, lapack_int lda, float* w ); +lapack_int LAPACKE_dsyevd( int matrix_order, char jobz, char uplo, lapack_int n, + double* a, lapack_int lda, double* w ); + +lapack_int LAPACKE_ssyevr( int matrix_order, char jobz, char range, char uplo, + lapack_int n, float* a, lapack_int lda, float vl, + float vu, lapack_int il, lapack_int iu, float abstol, + lapack_int* m, float* w, float* z, lapack_int ldz, + lapack_int* isuppz ); +lapack_int LAPACKE_dsyevr( int matrix_order, char jobz, char range, char uplo, + lapack_int n, double* a, lapack_int lda, double vl, + double vu, lapack_int il, lapack_int iu, + double abstol, lapack_int* m, double* w, double* z, + lapack_int ldz, lapack_int* isuppz ); + +lapack_int LAPACKE_ssyevx( int matrix_order, char jobz, char range, char uplo, + lapack_int n, float* a, lapack_int lda, float vl, + float vu, lapack_int il, lapack_int iu, float abstol, + lapack_int* m, float* w, float* z, lapack_int ldz, + lapack_int* ifail ); +lapack_int LAPACKE_dsyevx( int matrix_order, char jobz, char range, char uplo, + lapack_int n, double* a, lapack_int lda, double vl, + double vu, lapack_int il, lapack_int iu, + double abstol, lapack_int* m, double* w, double* z, + lapack_int ldz, lapack_int* ifail ); + +lapack_int LAPACKE_ssygst( int matrix_order, lapack_int itype, char uplo, + lapack_int n, float* a, lapack_int lda, + const float* b, lapack_int ldb ); +lapack_int LAPACKE_dsygst( int matrix_order, lapack_int itype, char uplo, + lapack_int n, double* a, lapack_int lda, + const double* b, lapack_int ldb ); + +lapack_int LAPACKE_ssygv( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, float* a, lapack_int lda, + float* b, lapack_int ldb, float* w ); +lapack_int LAPACKE_dsygv( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, double* a, lapack_int lda, + double* b, lapack_int ldb, double* w ); + +lapack_int LAPACKE_ssygvd( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, float* a, lapack_int lda, + float* b, lapack_int ldb, float* w ); +lapack_int LAPACKE_dsygvd( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, double* a, lapack_int lda, + double* b, lapack_int ldb, double* w ); + +lapack_int LAPACKE_ssygvx( int matrix_order, lapack_int itype, char jobz, + char range, char uplo, lapack_int n, float* a, + lapack_int lda, float* b, lapack_int ldb, float vl, + float vu, lapack_int il, lapack_int iu, float abstol, + lapack_int* m, float* w, float* z, lapack_int ldz, + lapack_int* ifail ); +lapack_int LAPACKE_dsygvx( int matrix_order, lapack_int itype, char jobz, + char range, char uplo, lapack_int n, double* a, + lapack_int lda, double* b, lapack_int ldb, double vl, + double vu, lapack_int il, lapack_int iu, + double abstol, lapack_int* m, double* w, double* z, + lapack_int ldz, lapack_int* ifail ); + +lapack_int LAPACKE_ssyrfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* a, lapack_int lda, + const float* af, lapack_int ldaf, + const lapack_int* ipiv, const float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* ferr, float* berr ); +lapack_int LAPACKE_dsyrfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* a, lapack_int lda, + const double* af, lapack_int ldaf, + const lapack_int* ipiv, const double* b, + lapack_int ldb, double* x, lapack_int ldx, + double* ferr, double* berr ); +lapack_int LAPACKE_csyrfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* af, + lapack_int ldaf, const lapack_int* ipiv, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, float* ferr, + float* berr ); +lapack_int LAPACKE_zsyrfs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, const lapack_complex_double* af, + lapack_int ldaf, const lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr ); + +lapack_int LAPACKE_ssyrfsx( int matrix_order, char uplo, char equed, + lapack_int n, lapack_int nrhs, const float* a, + lapack_int lda, const float* af, lapack_int ldaf, + const lapack_int* ipiv, const float* s, + const float* b, lapack_int ldb, float* x, + lapack_int ldx, float* rcond, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params ); +lapack_int LAPACKE_dsyrfsx( int matrix_order, char uplo, char equed, + lapack_int n, lapack_int nrhs, const double* a, + lapack_int lda, const double* af, lapack_int ldaf, + const lapack_int* ipiv, const double* s, + const double* b, lapack_int ldb, double* x, + lapack_int ldx, double* rcond, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params ); +lapack_int LAPACKE_csyrfsx( int matrix_order, char uplo, char equed, + lapack_int n, lapack_int nrhs, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* af, lapack_int ldaf, + const lapack_int* ipiv, const float* s, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* berr, lapack_int n_err_bnds, + float* err_bnds_norm, float* err_bnds_comp, + lapack_int nparams, float* params ); +lapack_int LAPACKE_zsyrfsx( int matrix_order, char uplo, char equed, + lapack_int n, lapack_int nrhs, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* af, lapack_int ldaf, + const lapack_int* ipiv, const double* s, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* berr, lapack_int n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int nparams, double* params ); + +lapack_int LAPACKE_ssysv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, float* a, lapack_int lda, + lapack_int* ipiv, float* b, lapack_int ldb ); +lapack_int LAPACKE_dsysv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, double* a, lapack_int lda, + lapack_int* ipiv, double* b, lapack_int ldb ); +lapack_int LAPACKE_csysv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_float* a, + lapack_int lda, lapack_int* ipiv, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zsysv( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_double* a, + lapack_int lda, lapack_int* ipiv, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_ssysvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int nrhs, const float* a, lapack_int lda, + float* af, lapack_int ldaf, lapack_int* ipiv, + const float* b, lapack_int ldb, float* x, + lapack_int ldx, float* rcond, float* ferr, + float* berr ); +lapack_int LAPACKE_dsysvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int nrhs, const double* a, lapack_int lda, + double* af, lapack_int ldaf, lapack_int* ipiv, + const double* b, lapack_int ldb, double* x, + lapack_int ldx, double* rcond, double* ferr, + double* berr ); +lapack_int LAPACKE_csysvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, lapack_complex_float* af, + lapack_int ldaf, lapack_int* ipiv, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* ferr, float* berr ); +lapack_int LAPACKE_zsysvx( int matrix_order, char fact, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, lapack_complex_double* af, + lapack_int ldaf, lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr ); + +lapack_int LAPACKE_ssysvxx( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, float* a, + lapack_int lda, float* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, float* s, float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* rcond, float* rpvgrw, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params ); +lapack_int LAPACKE_dsysvxx( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, double* a, + lapack_int lda, double* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, double* s, double* b, + lapack_int ldb, double* x, lapack_int ldx, + double* rcond, double* rpvgrw, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params ); +lapack_int LAPACKE_csysvxx( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, float* s, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* rpvgrw, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params ); +lapack_int LAPACKE_zsysvxx( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, double* s, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* rpvgrw, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params ); + +lapack_int LAPACKE_ssytrd( int matrix_order, char uplo, lapack_int n, float* a, + lapack_int lda, float* d, float* e, float* tau ); +lapack_int LAPACKE_dsytrd( int matrix_order, char uplo, lapack_int n, double* a, + lapack_int lda, double* d, double* e, double* tau ); + +lapack_int LAPACKE_ssytrf( int matrix_order, char uplo, lapack_int n, float* a, + lapack_int lda, lapack_int* ipiv ); +lapack_int LAPACKE_dsytrf( int matrix_order, char uplo, lapack_int n, double* a, + lapack_int lda, lapack_int* ipiv ); +lapack_int LAPACKE_csytrf( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_int* ipiv ); +lapack_int LAPACKE_zsytrf( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_int* ipiv ); + +lapack_int LAPACKE_ssytri( int matrix_order, char uplo, lapack_int n, float* a, + lapack_int lda, const lapack_int* ipiv ); +lapack_int LAPACKE_dsytri( int matrix_order, char uplo, lapack_int n, double* a, + lapack_int lda, const lapack_int* ipiv ); +lapack_int LAPACKE_csytri( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + const lapack_int* ipiv ); +lapack_int LAPACKE_zsytri( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + const lapack_int* ipiv ); + +lapack_int LAPACKE_ssytrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* a, lapack_int lda, + const lapack_int* ipiv, float* b, lapack_int ldb ); +lapack_int LAPACKE_dsytrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* a, lapack_int lda, + const lapack_int* ipiv, double* b, lapack_int ldb ); +lapack_int LAPACKE_csytrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zsytrs( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_stbcon( int matrix_order, char norm, char uplo, char diag, + lapack_int n, lapack_int kd, const float* ab, + lapack_int ldab, float* rcond ); +lapack_int LAPACKE_dtbcon( int matrix_order, char norm, char uplo, char diag, + lapack_int n, lapack_int kd, const double* ab, + lapack_int ldab, double* rcond ); +lapack_int LAPACKE_ctbcon( int matrix_order, char norm, char uplo, char diag, + lapack_int n, lapack_int kd, + const lapack_complex_float* ab, lapack_int ldab, + float* rcond ); +lapack_int LAPACKE_ztbcon( int matrix_order, char norm, char uplo, char diag, + lapack_int n, lapack_int kd, + const lapack_complex_double* ab, lapack_int ldab, + double* rcond ); + +lapack_int LAPACKE_stbrfs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int kd, lapack_int nrhs, + const float* ab, lapack_int ldab, const float* b, + lapack_int ldb, const float* x, lapack_int ldx, + float* ferr, float* berr ); +lapack_int LAPACKE_dtbrfs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int kd, lapack_int nrhs, + const double* ab, lapack_int ldab, const double* b, + lapack_int ldb, const double* x, lapack_int ldx, + double* ferr, double* berr ); +lapack_int LAPACKE_ctbrfs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int kd, lapack_int nrhs, + const lapack_complex_float* ab, lapack_int ldab, + const lapack_complex_float* b, lapack_int ldb, + const lapack_complex_float* x, lapack_int ldx, + float* ferr, float* berr ); +lapack_int LAPACKE_ztbrfs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int kd, lapack_int nrhs, + const lapack_complex_double* ab, lapack_int ldab, + const lapack_complex_double* b, lapack_int ldb, + const lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr ); + +lapack_int LAPACKE_stbtrs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int kd, lapack_int nrhs, + const float* ab, lapack_int ldab, float* b, + lapack_int ldb ); +lapack_int LAPACKE_dtbtrs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int kd, lapack_int nrhs, + const double* ab, lapack_int ldab, double* b, + lapack_int ldb ); +lapack_int LAPACKE_ctbtrs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int kd, lapack_int nrhs, + const lapack_complex_float* ab, lapack_int ldab, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_ztbtrs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int kd, lapack_int nrhs, + const lapack_complex_double* ab, lapack_int ldab, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_stfsm( int matrix_order, char transr, char side, char uplo, + char trans, char diag, lapack_int m, lapack_int n, + float alpha, const float* a, float* b, + lapack_int ldb ); +lapack_int LAPACKE_dtfsm( int matrix_order, char transr, char side, char uplo, + char trans, char diag, lapack_int m, lapack_int n, + double alpha, const double* a, double* b, + lapack_int ldb ); +lapack_int LAPACKE_ctfsm( int matrix_order, char transr, char side, char uplo, + char trans, char diag, lapack_int m, lapack_int n, + lapack_complex_float alpha, + const lapack_complex_float* a, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_ztfsm( int matrix_order, char transr, char side, char uplo, + char trans, char diag, lapack_int m, lapack_int n, + lapack_complex_double alpha, + const lapack_complex_double* a, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_stftri( int matrix_order, char transr, char uplo, char diag, + lapack_int n, float* a ); +lapack_int LAPACKE_dtftri( int matrix_order, char transr, char uplo, char diag, + lapack_int n, double* a ); +lapack_int LAPACKE_ctftri( int matrix_order, char transr, char uplo, char diag, + lapack_int n, lapack_complex_float* a ); +lapack_int LAPACKE_ztftri( int matrix_order, char transr, char uplo, char diag, + lapack_int n, lapack_complex_double* a ); + +lapack_int LAPACKE_stfttp( int matrix_order, char transr, char uplo, + lapack_int n, const float* arf, float* ap ); +lapack_int LAPACKE_dtfttp( int matrix_order, char transr, char uplo, + lapack_int n, const double* arf, double* ap ); +lapack_int LAPACKE_ctfttp( int matrix_order, char transr, char uplo, + lapack_int n, const lapack_complex_float* arf, + lapack_complex_float* ap ); +lapack_int LAPACKE_ztfttp( int matrix_order, char transr, char uplo, + lapack_int n, const lapack_complex_double* arf, + lapack_complex_double* ap ); + +lapack_int LAPACKE_stfttr( int matrix_order, char transr, char uplo, + lapack_int n, const float* arf, float* a, + lapack_int lda ); +lapack_int LAPACKE_dtfttr( int matrix_order, char transr, char uplo, + lapack_int n, const double* arf, double* a, + lapack_int lda ); +lapack_int LAPACKE_ctfttr( int matrix_order, char transr, char uplo, + lapack_int n, const lapack_complex_float* arf, + lapack_complex_float* a, lapack_int lda ); +lapack_int LAPACKE_ztfttr( int matrix_order, char transr, char uplo, + lapack_int n, const lapack_complex_double* arf, + lapack_complex_double* a, lapack_int lda ); + +lapack_int LAPACKE_stgevc( int matrix_order, char side, char howmny, + const lapack_logical* select, lapack_int n, + const float* s, lapack_int lds, const float* p, + lapack_int ldp, float* vl, lapack_int ldvl, + float* vr, lapack_int ldvr, lapack_int mm, + lapack_int* m ); +lapack_int LAPACKE_dtgevc( int matrix_order, char side, char howmny, + const lapack_logical* select, lapack_int n, + const double* s, lapack_int lds, const double* p, + lapack_int ldp, double* vl, lapack_int ldvl, + double* vr, lapack_int ldvr, lapack_int mm, + lapack_int* m ); +lapack_int LAPACKE_ctgevc( int matrix_order, char side, char howmny, + const lapack_logical* select, lapack_int n, + const lapack_complex_float* s, lapack_int lds, + const lapack_complex_float* p, lapack_int ldp, + lapack_complex_float* vl, lapack_int ldvl, + lapack_complex_float* vr, lapack_int ldvr, + lapack_int mm, lapack_int* m ); +lapack_int LAPACKE_ztgevc( int matrix_order, char side, char howmny, + const lapack_logical* select, lapack_int n, + const lapack_complex_double* s, lapack_int lds, + const lapack_complex_double* p, lapack_int ldp, + lapack_complex_double* vl, lapack_int ldvl, + lapack_complex_double* vr, lapack_int ldvr, + lapack_int mm, lapack_int* m ); + +lapack_int LAPACKE_stgexc( int matrix_order, lapack_logical wantq, + lapack_logical wantz, lapack_int n, float* a, + lapack_int lda, float* b, lapack_int ldb, float* q, + lapack_int ldq, float* z, lapack_int ldz, + lapack_int* ifst, lapack_int* ilst ); +lapack_int LAPACKE_dtgexc( int matrix_order, lapack_logical wantq, + lapack_logical wantz, lapack_int n, double* a, + lapack_int lda, double* b, lapack_int ldb, double* q, + lapack_int ldq, double* z, lapack_int ldz, + lapack_int* ifst, lapack_int* ilst ); +lapack_int LAPACKE_ctgexc( int matrix_order, lapack_logical wantq, + lapack_logical wantz, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* q, lapack_int ldq, + lapack_complex_float* z, lapack_int ldz, + lapack_int ifst, lapack_int ilst ); +lapack_int LAPACKE_ztgexc( int matrix_order, lapack_logical wantq, + lapack_logical wantz, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* q, lapack_int ldq, + lapack_complex_double* z, lapack_int ldz, + lapack_int ifst, lapack_int ilst ); + +lapack_int LAPACKE_stgsen( int matrix_order, lapack_int ijob, + lapack_logical wantq, lapack_logical wantz, + const lapack_logical* select, lapack_int n, float* a, + lapack_int lda, float* b, lapack_int ldb, + float* alphar, float* alphai, float* beta, float* q, + lapack_int ldq, float* z, lapack_int ldz, + lapack_int* m, float* pl, float* pr, float* dif ); +lapack_int LAPACKE_dtgsen( int matrix_order, lapack_int ijob, + lapack_logical wantq, lapack_logical wantz, + const lapack_logical* select, lapack_int n, + double* a, lapack_int lda, double* b, lapack_int ldb, + double* alphar, double* alphai, double* beta, + double* q, lapack_int ldq, double* z, lapack_int ldz, + lapack_int* m, double* pl, double* pr, double* dif ); +lapack_int LAPACKE_ctgsen( int matrix_order, lapack_int ijob, + lapack_logical wantq, lapack_logical wantz, + const lapack_logical* select, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* alpha, + lapack_complex_float* beta, lapack_complex_float* q, + lapack_int ldq, lapack_complex_float* z, + lapack_int ldz, lapack_int* m, float* pl, float* pr, + float* dif ); +lapack_int LAPACKE_ztgsen( int matrix_order, lapack_int ijob, + lapack_logical wantq, lapack_logical wantz, + const lapack_logical* select, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* alpha, + lapack_complex_double* beta, + lapack_complex_double* q, lapack_int ldq, + lapack_complex_double* z, lapack_int ldz, + lapack_int* m, double* pl, double* pr, double* dif ); + +lapack_int LAPACKE_stgsja( int matrix_order, char jobu, char jobv, char jobq, + lapack_int m, lapack_int p, lapack_int n, + lapack_int k, lapack_int l, float* a, lapack_int lda, + float* b, lapack_int ldb, float tola, float tolb, + float* alpha, float* beta, float* u, lapack_int ldu, + float* v, lapack_int ldv, float* q, lapack_int ldq, + lapack_int* ncycle ); +lapack_int LAPACKE_dtgsja( int matrix_order, char jobu, char jobv, char jobq, + lapack_int m, lapack_int p, lapack_int n, + lapack_int k, lapack_int l, double* a, + lapack_int lda, double* b, lapack_int ldb, + double tola, double tolb, double* alpha, + double* beta, double* u, lapack_int ldu, double* v, + lapack_int ldv, double* q, lapack_int ldq, + lapack_int* ncycle ); +lapack_int LAPACKE_ctgsja( int matrix_order, char jobu, char jobv, char jobq, + lapack_int m, lapack_int p, lapack_int n, + lapack_int k, lapack_int l, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb, float tola, float tolb, float* alpha, + float* beta, lapack_complex_float* u, lapack_int ldu, + lapack_complex_float* v, lapack_int ldv, + lapack_complex_float* q, lapack_int ldq, + lapack_int* ncycle ); +lapack_int LAPACKE_ztgsja( int matrix_order, char jobu, char jobv, char jobq, + lapack_int m, lapack_int p, lapack_int n, + lapack_int k, lapack_int l, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb, double tola, double tolb, + double* alpha, double* beta, + lapack_complex_double* u, lapack_int ldu, + lapack_complex_double* v, lapack_int ldv, + lapack_complex_double* q, lapack_int ldq, + lapack_int* ncycle ); + +lapack_int LAPACKE_stgsna( int matrix_order, char job, char howmny, + const lapack_logical* select, lapack_int n, + const float* a, lapack_int lda, const float* b, + lapack_int ldb, const float* vl, lapack_int ldvl, + const float* vr, lapack_int ldvr, float* s, + float* dif, lapack_int mm, lapack_int* m ); +lapack_int LAPACKE_dtgsna( int matrix_order, char job, char howmny, + const lapack_logical* select, lapack_int n, + const double* a, lapack_int lda, const double* b, + lapack_int ldb, const double* vl, lapack_int ldvl, + const double* vr, lapack_int ldvr, double* s, + double* dif, lapack_int mm, lapack_int* m ); +lapack_int LAPACKE_ctgsna( int matrix_order, char job, char howmny, + const lapack_logical* select, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* b, lapack_int ldb, + const lapack_complex_float* vl, lapack_int ldvl, + const lapack_complex_float* vr, lapack_int ldvr, + float* s, float* dif, lapack_int mm, lapack_int* m ); +lapack_int LAPACKE_ztgsna( int matrix_order, char job, char howmny, + const lapack_logical* select, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* b, lapack_int ldb, + const lapack_complex_double* vl, lapack_int ldvl, + const lapack_complex_double* vr, lapack_int ldvr, + double* s, double* dif, lapack_int mm, + lapack_int* m ); + +lapack_int LAPACKE_stgsyl( int matrix_order, char trans, lapack_int ijob, + lapack_int m, lapack_int n, const float* a, + lapack_int lda, const float* b, lapack_int ldb, + float* c, lapack_int ldc, const float* d, + lapack_int ldd, const float* e, lapack_int lde, + float* f, lapack_int ldf, float* scale, float* dif ); +lapack_int LAPACKE_dtgsyl( int matrix_order, char trans, lapack_int ijob, + lapack_int m, lapack_int n, const double* a, + lapack_int lda, const double* b, lapack_int ldb, + double* c, lapack_int ldc, const double* d, + lapack_int ldd, const double* e, lapack_int lde, + double* f, lapack_int ldf, double* scale, + double* dif ); +lapack_int LAPACKE_ctgsyl( int matrix_order, char trans, lapack_int ijob, + lapack_int m, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* c, lapack_int ldc, + const lapack_complex_float* d, lapack_int ldd, + const lapack_complex_float* e, lapack_int lde, + lapack_complex_float* f, lapack_int ldf, + float* scale, float* dif ); +lapack_int LAPACKE_ztgsyl( int matrix_order, char trans, lapack_int ijob, + lapack_int m, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* c, lapack_int ldc, + const lapack_complex_double* d, lapack_int ldd, + const lapack_complex_double* e, lapack_int lde, + lapack_complex_double* f, lapack_int ldf, + double* scale, double* dif ); + +lapack_int LAPACKE_stpcon( int matrix_order, char norm, char uplo, char diag, + lapack_int n, const float* ap, float* rcond ); +lapack_int LAPACKE_dtpcon( int matrix_order, char norm, char uplo, char diag, + lapack_int n, const double* ap, double* rcond ); +lapack_int LAPACKE_ctpcon( int matrix_order, char norm, char uplo, char diag, + lapack_int n, const lapack_complex_float* ap, + float* rcond ); +lapack_int LAPACKE_ztpcon( int matrix_order, char norm, char uplo, char diag, + lapack_int n, const lapack_complex_double* ap, + double* rcond ); + +lapack_int LAPACKE_stprfs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int nrhs, const float* ap, + const float* b, lapack_int ldb, const float* x, + lapack_int ldx, float* ferr, float* berr ); +lapack_int LAPACKE_dtprfs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int nrhs, const double* ap, + const double* b, lapack_int ldb, const double* x, + lapack_int ldx, double* ferr, double* berr ); +lapack_int LAPACKE_ctprfs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int nrhs, + const lapack_complex_float* ap, + const lapack_complex_float* b, lapack_int ldb, + const lapack_complex_float* x, lapack_int ldx, + float* ferr, float* berr ); +lapack_int LAPACKE_ztprfs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int nrhs, + const lapack_complex_double* ap, + const lapack_complex_double* b, lapack_int ldb, + const lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr ); + +lapack_int LAPACKE_stptri( int matrix_order, char uplo, char diag, lapack_int n, + float* ap ); +lapack_int LAPACKE_dtptri( int matrix_order, char uplo, char diag, lapack_int n, + double* ap ); +lapack_int LAPACKE_ctptri( int matrix_order, char uplo, char diag, lapack_int n, + lapack_complex_float* ap ); +lapack_int LAPACKE_ztptri( int matrix_order, char uplo, char diag, lapack_int n, + lapack_complex_double* ap ); + +lapack_int LAPACKE_stptrs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int nrhs, const float* ap, + float* b, lapack_int ldb ); +lapack_int LAPACKE_dtptrs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int nrhs, const double* ap, + double* b, lapack_int ldb ); +lapack_int LAPACKE_ctptrs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int nrhs, + const lapack_complex_float* ap, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_ztptrs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int nrhs, + const lapack_complex_double* ap, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_stpttf( int matrix_order, char transr, char uplo, + lapack_int n, const float* ap, float* arf ); +lapack_int LAPACKE_dtpttf( int matrix_order, char transr, char uplo, + lapack_int n, const double* ap, double* arf ); +lapack_int LAPACKE_ctpttf( int matrix_order, char transr, char uplo, + lapack_int n, const lapack_complex_float* ap, + lapack_complex_float* arf ); +lapack_int LAPACKE_ztpttf( int matrix_order, char transr, char uplo, + lapack_int n, const lapack_complex_double* ap, + lapack_complex_double* arf ); + +lapack_int LAPACKE_stpttr( int matrix_order, char uplo, lapack_int n, + const float* ap, float* a, lapack_int lda ); +lapack_int LAPACKE_dtpttr( int matrix_order, char uplo, lapack_int n, + const double* ap, double* a, lapack_int lda ); +lapack_int LAPACKE_ctpttr( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* ap, + lapack_complex_float* a, lapack_int lda ); +lapack_int LAPACKE_ztpttr( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* ap, + lapack_complex_double* a, lapack_int lda ); + +lapack_int LAPACKE_strcon( int matrix_order, char norm, char uplo, char diag, + lapack_int n, const float* a, lapack_int lda, + float* rcond ); +lapack_int LAPACKE_dtrcon( int matrix_order, char norm, char uplo, char diag, + lapack_int n, const double* a, lapack_int lda, + double* rcond ); +lapack_int LAPACKE_ctrcon( int matrix_order, char norm, char uplo, char diag, + lapack_int n, const lapack_complex_float* a, + lapack_int lda, float* rcond ); +lapack_int LAPACKE_ztrcon( int matrix_order, char norm, char uplo, char diag, + lapack_int n, const lapack_complex_double* a, + lapack_int lda, double* rcond ); + +lapack_int LAPACKE_strevc( int matrix_order, char side, char howmny, + lapack_logical* select, lapack_int n, const float* t, + lapack_int ldt, float* vl, lapack_int ldvl, + float* vr, lapack_int ldvr, lapack_int mm, + lapack_int* m ); +lapack_int LAPACKE_dtrevc( int matrix_order, char side, char howmny, + lapack_logical* select, lapack_int n, + const double* t, lapack_int ldt, double* vl, + lapack_int ldvl, double* vr, lapack_int ldvr, + lapack_int mm, lapack_int* m ); +lapack_int LAPACKE_ctrevc( int matrix_order, char side, char howmny, + const lapack_logical* select, lapack_int n, + lapack_complex_float* t, lapack_int ldt, + lapack_complex_float* vl, lapack_int ldvl, + lapack_complex_float* vr, lapack_int ldvr, + lapack_int mm, lapack_int* m ); +lapack_int LAPACKE_ztrevc( int matrix_order, char side, char howmny, + const lapack_logical* select, lapack_int n, + lapack_complex_double* t, lapack_int ldt, + lapack_complex_double* vl, lapack_int ldvl, + lapack_complex_double* vr, lapack_int ldvr, + lapack_int mm, lapack_int* m ); + +lapack_int LAPACKE_strexc( int matrix_order, char compq, lapack_int n, float* t, + lapack_int ldt, float* q, lapack_int ldq, + lapack_int* ifst, lapack_int* ilst ); +lapack_int LAPACKE_dtrexc( int matrix_order, char compq, lapack_int n, + double* t, lapack_int ldt, double* q, lapack_int ldq, + lapack_int* ifst, lapack_int* ilst ); +lapack_int LAPACKE_ctrexc( int matrix_order, char compq, lapack_int n, + lapack_complex_float* t, lapack_int ldt, + lapack_complex_float* q, lapack_int ldq, + lapack_int ifst, lapack_int ilst ); +lapack_int LAPACKE_ztrexc( int matrix_order, char compq, lapack_int n, + lapack_complex_double* t, lapack_int ldt, + lapack_complex_double* q, lapack_int ldq, + lapack_int ifst, lapack_int ilst ); + +lapack_int LAPACKE_strrfs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int nrhs, const float* a, + lapack_int lda, const float* b, lapack_int ldb, + const float* x, lapack_int ldx, float* ferr, + float* berr ); +lapack_int LAPACKE_dtrrfs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int nrhs, const double* a, + lapack_int lda, const double* b, lapack_int ldb, + const double* x, lapack_int ldx, double* ferr, + double* berr ); +lapack_int LAPACKE_ctrrfs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int nrhs, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* b, lapack_int ldb, + const lapack_complex_float* x, lapack_int ldx, + float* ferr, float* berr ); +lapack_int LAPACKE_ztrrfs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int nrhs, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* b, lapack_int ldb, + const lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr ); + +lapack_int LAPACKE_strsen( int matrix_order, char job, char compq, + const lapack_logical* select, lapack_int n, float* t, + lapack_int ldt, float* q, lapack_int ldq, float* wr, + float* wi, lapack_int* m, float* s, float* sep ); +lapack_int LAPACKE_dtrsen( int matrix_order, char job, char compq, + const lapack_logical* select, lapack_int n, + double* t, lapack_int ldt, double* q, lapack_int ldq, + double* wr, double* wi, lapack_int* m, double* s, + double* sep ); +lapack_int LAPACKE_ctrsen( int matrix_order, char job, char compq, + const lapack_logical* select, lapack_int n, + lapack_complex_float* t, lapack_int ldt, + lapack_complex_float* q, lapack_int ldq, + lapack_complex_float* w, lapack_int* m, float* s, + float* sep ); +lapack_int LAPACKE_ztrsen( int matrix_order, char job, char compq, + const lapack_logical* select, lapack_int n, + lapack_complex_double* t, lapack_int ldt, + lapack_complex_double* q, lapack_int ldq, + lapack_complex_double* w, lapack_int* m, double* s, + double* sep ); + +lapack_int LAPACKE_strsna( int matrix_order, char job, char howmny, + const lapack_logical* select, lapack_int n, + const float* t, lapack_int ldt, const float* vl, + lapack_int ldvl, const float* vr, lapack_int ldvr, + float* s, float* sep, lapack_int mm, lapack_int* m ); +lapack_int LAPACKE_dtrsna( int matrix_order, char job, char howmny, + const lapack_logical* select, lapack_int n, + const double* t, lapack_int ldt, const double* vl, + lapack_int ldvl, const double* vr, lapack_int ldvr, + double* s, double* sep, lapack_int mm, + lapack_int* m ); +lapack_int LAPACKE_ctrsna( int matrix_order, char job, char howmny, + const lapack_logical* select, lapack_int n, + const lapack_complex_float* t, lapack_int ldt, + const lapack_complex_float* vl, lapack_int ldvl, + const lapack_complex_float* vr, lapack_int ldvr, + float* s, float* sep, lapack_int mm, lapack_int* m ); +lapack_int LAPACKE_ztrsna( int matrix_order, char job, char howmny, + const lapack_logical* select, lapack_int n, + const lapack_complex_double* t, lapack_int ldt, + const lapack_complex_double* vl, lapack_int ldvl, + const lapack_complex_double* vr, lapack_int ldvr, + double* s, double* sep, lapack_int mm, + lapack_int* m ); + +lapack_int LAPACKE_strsyl( int matrix_order, char trana, char tranb, + lapack_int isgn, lapack_int m, lapack_int n, + const float* a, lapack_int lda, const float* b, + lapack_int ldb, float* c, lapack_int ldc, + float* scale ); +lapack_int LAPACKE_dtrsyl( int matrix_order, char trana, char tranb, + lapack_int isgn, lapack_int m, lapack_int n, + const double* a, lapack_int lda, const double* b, + lapack_int ldb, double* c, lapack_int ldc, + double* scale ); +lapack_int LAPACKE_ctrsyl( int matrix_order, char trana, char tranb, + lapack_int isgn, lapack_int m, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* c, lapack_int ldc, + float* scale ); +lapack_int LAPACKE_ztrsyl( int matrix_order, char trana, char tranb, + lapack_int isgn, lapack_int m, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* c, lapack_int ldc, + double* scale ); + +lapack_int LAPACKE_strtri( int matrix_order, char uplo, char diag, lapack_int n, + float* a, lapack_int lda ); +lapack_int LAPACKE_dtrtri( int matrix_order, char uplo, char diag, lapack_int n, + double* a, lapack_int lda ); +lapack_int LAPACKE_ctrtri( int matrix_order, char uplo, char diag, lapack_int n, + lapack_complex_float* a, lapack_int lda ); +lapack_int LAPACKE_ztrtri( int matrix_order, char uplo, char diag, lapack_int n, + lapack_complex_double* a, lapack_int lda ); + +lapack_int LAPACKE_strtrs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int nrhs, const float* a, + lapack_int lda, float* b, lapack_int ldb ); +lapack_int LAPACKE_dtrtrs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int nrhs, const double* a, + lapack_int lda, double* b, lapack_int ldb ); +lapack_int LAPACKE_ctrtrs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int nrhs, + const lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_ztrtrs( int matrix_order, char uplo, char trans, char diag, + lapack_int n, lapack_int nrhs, + const lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_strttf( int matrix_order, char transr, char uplo, + lapack_int n, const float* a, lapack_int lda, + float* arf ); +lapack_int LAPACKE_dtrttf( int matrix_order, char transr, char uplo, + lapack_int n, const double* a, lapack_int lda, + double* arf ); +lapack_int LAPACKE_ctrttf( int matrix_order, char transr, char uplo, + lapack_int n, const lapack_complex_float* a, + lapack_int lda, lapack_complex_float* arf ); +lapack_int LAPACKE_ztrttf( int matrix_order, char transr, char uplo, + lapack_int n, const lapack_complex_double* a, + lapack_int lda, lapack_complex_double* arf ); + +lapack_int LAPACKE_strttp( int matrix_order, char uplo, lapack_int n, + const float* a, lapack_int lda, float* ap ); +lapack_int LAPACKE_dtrttp( int matrix_order, char uplo, lapack_int n, + const double* a, lapack_int lda, double* ap ); +lapack_int LAPACKE_ctrttp( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + lapack_complex_float* ap ); +lapack_int LAPACKE_ztrttp( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + lapack_complex_double* ap ); + +lapack_int LAPACKE_stzrzf( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* tau ); +lapack_int LAPACKE_dtzrzf( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* tau ); +lapack_int LAPACKE_ctzrzf( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* tau ); +lapack_int LAPACKE_ztzrzf( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* tau ); + +lapack_int LAPACKE_cungbr( int matrix_order, char vect, lapack_int m, + lapack_int n, lapack_int k, lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* tau ); +lapack_int LAPACKE_zungbr( int matrix_order, char vect, lapack_int m, + lapack_int n, lapack_int k, lapack_complex_double* a, + lapack_int lda, const lapack_complex_double* tau ); + +lapack_int LAPACKE_cunghr( int matrix_order, lapack_int n, lapack_int ilo, + lapack_int ihi, lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* tau ); +lapack_int LAPACKE_zunghr( int matrix_order, lapack_int n, lapack_int ilo, + lapack_int ihi, lapack_complex_double* a, + lapack_int lda, const lapack_complex_double* tau ); + +lapack_int LAPACKE_cunglq( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* tau ); +lapack_int LAPACKE_zunglq( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, lapack_complex_double* a, + lapack_int lda, const lapack_complex_double* tau ); + +lapack_int LAPACKE_cungql( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* tau ); +lapack_int LAPACKE_zungql( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, lapack_complex_double* a, + lapack_int lda, const lapack_complex_double* tau ); + +lapack_int LAPACKE_cungqr( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* tau ); +lapack_int LAPACKE_zungqr( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, lapack_complex_double* a, + lapack_int lda, const lapack_complex_double* tau ); + +lapack_int LAPACKE_cungrq( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* tau ); +lapack_int LAPACKE_zungrq( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, lapack_complex_double* a, + lapack_int lda, const lapack_complex_double* tau ); + +lapack_int LAPACKE_cungtr( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* tau ); +lapack_int LAPACKE_zungtr( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* tau ); + +lapack_int LAPACKE_cunmbr( int matrix_order, char vect, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int ldc ); +lapack_int LAPACKE_zunmbr( int matrix_order, char vect, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int ldc ); + +lapack_int LAPACKE_cunmhr( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int ilo, + lapack_int ihi, const lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int ldc ); +lapack_int LAPACKE_zunmhr( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int ilo, + lapack_int ihi, const lapack_complex_double* a, + lapack_int lda, const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int ldc ); + +lapack_int LAPACKE_cunmlq( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int ldc ); +lapack_int LAPACKE_zunmlq( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int ldc ); + +lapack_int LAPACKE_cunmql( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int ldc ); +lapack_int LAPACKE_zunmql( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int ldc ); + +lapack_int LAPACKE_cunmqr( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int ldc ); +lapack_int LAPACKE_zunmqr( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int ldc ); + +lapack_int LAPACKE_cunmrq( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int ldc ); +lapack_int LAPACKE_zunmrq( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int ldc ); + +lapack_int LAPACKE_cunmrz( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int l, const lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int ldc ); +lapack_int LAPACKE_zunmrz( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int l, const lapack_complex_double* a, + lapack_int lda, const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int ldc ); + +lapack_int LAPACKE_cunmtr( int matrix_order, char side, char uplo, char trans, + lapack_int m, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int ldc ); +lapack_int LAPACKE_zunmtr( int matrix_order, char side, char uplo, char trans, + lapack_int m, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int ldc ); + +lapack_int LAPACKE_cupgtr( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* ap, + const lapack_complex_float* tau, + lapack_complex_float* q, lapack_int ldq ); +lapack_int LAPACKE_zupgtr( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* ap, + const lapack_complex_double* tau, + lapack_complex_double* q, lapack_int ldq ); + +lapack_int LAPACKE_cupmtr( int matrix_order, char side, char uplo, char trans, + lapack_int m, lapack_int n, + const lapack_complex_float* ap, + const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int ldc ); +lapack_int LAPACKE_zupmtr( int matrix_order, char side, char uplo, char trans, + lapack_int m, lapack_int n, + const lapack_complex_double* ap, + const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int ldc ); + +lapack_int LAPACKE_sbdsdc_work( int matrix_order, char uplo, char compq, + lapack_int n, float* d, float* e, float* u, + lapack_int ldu, float* vt, lapack_int ldvt, + float* q, lapack_int* iq, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dbdsdc_work( int matrix_order, char uplo, char compq, + lapack_int n, double* d, double* e, double* u, + lapack_int ldu, double* vt, lapack_int ldvt, + double* q, lapack_int* iq, double* work, + lapack_int* iwork ); + +lapack_int LAPACKE_sbdsqr_work( int matrix_order, char uplo, lapack_int n, + lapack_int ncvt, lapack_int nru, lapack_int ncc, + float* d, float* e, float* vt, lapack_int ldvt, + float* u, lapack_int ldu, float* c, + lapack_int ldc, float* work ); +lapack_int LAPACKE_dbdsqr_work( int matrix_order, char uplo, lapack_int n, + lapack_int ncvt, lapack_int nru, lapack_int ncc, + double* d, double* e, double* vt, + lapack_int ldvt, double* u, lapack_int ldu, + double* c, lapack_int ldc, double* work ); +lapack_int LAPACKE_cbdsqr_work( int matrix_order, char uplo, lapack_int n, + lapack_int ncvt, lapack_int nru, lapack_int ncc, + float* d, float* e, lapack_complex_float* vt, + lapack_int ldvt, lapack_complex_float* u, + lapack_int ldu, lapack_complex_float* c, + lapack_int ldc, float* work ); +lapack_int LAPACKE_zbdsqr_work( int matrix_order, char uplo, lapack_int n, + lapack_int ncvt, lapack_int nru, lapack_int ncc, + double* d, double* e, lapack_complex_double* vt, + lapack_int ldvt, lapack_complex_double* u, + lapack_int ldu, lapack_complex_double* c, + lapack_int ldc, double* work ); + +lapack_int LAPACKE_sdisna_work( char job, lapack_int m, lapack_int n, + const float* d, float* sep ); +lapack_int LAPACKE_ddisna_work( char job, lapack_int m, lapack_int n, + const double* d, double* sep ); + +lapack_int LAPACKE_sgbbrd_work( int matrix_order, char vect, lapack_int m, + lapack_int n, lapack_int ncc, lapack_int kl, + lapack_int ku, float* ab, lapack_int ldab, + float* d, float* e, float* q, lapack_int ldq, + float* pt, lapack_int ldpt, float* c, + lapack_int ldc, float* work ); +lapack_int LAPACKE_dgbbrd_work( int matrix_order, char vect, lapack_int m, + lapack_int n, lapack_int ncc, lapack_int kl, + lapack_int ku, double* ab, lapack_int ldab, + double* d, double* e, double* q, lapack_int ldq, + double* pt, lapack_int ldpt, double* c, + lapack_int ldc, double* work ); +lapack_int LAPACKE_cgbbrd_work( int matrix_order, char vect, lapack_int m, + lapack_int n, lapack_int ncc, lapack_int kl, + lapack_int ku, lapack_complex_float* ab, + lapack_int ldab, float* d, float* e, + lapack_complex_float* q, lapack_int ldq, + lapack_complex_float* pt, lapack_int ldpt, + lapack_complex_float* c, lapack_int ldc, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zgbbrd_work( int matrix_order, char vect, lapack_int m, + lapack_int n, lapack_int ncc, lapack_int kl, + lapack_int ku, lapack_complex_double* ab, + lapack_int ldab, double* d, double* e, + lapack_complex_double* q, lapack_int ldq, + lapack_complex_double* pt, lapack_int ldpt, + lapack_complex_double* c, lapack_int ldc, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_sgbcon_work( int matrix_order, char norm, lapack_int n, + lapack_int kl, lapack_int ku, const float* ab, + lapack_int ldab, const lapack_int* ipiv, + float anorm, float* rcond, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dgbcon_work( int matrix_order, char norm, lapack_int n, + lapack_int kl, lapack_int ku, const double* ab, + lapack_int ldab, const lapack_int* ipiv, + double anorm, double* rcond, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_cgbcon_work( int matrix_order, char norm, lapack_int n, + lapack_int kl, lapack_int ku, + const lapack_complex_float* ab, lapack_int ldab, + const lapack_int* ipiv, float anorm, + float* rcond, lapack_complex_float* work, + float* rwork ); +lapack_int LAPACKE_zgbcon_work( int matrix_order, char norm, lapack_int n, + lapack_int kl, lapack_int ku, + const lapack_complex_double* ab, + lapack_int ldab, const lapack_int* ipiv, + double anorm, double* rcond, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_sgbequ_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, const float* ab, + lapack_int ldab, float* r, float* c, + float* rowcnd, float* colcnd, float* amax ); +lapack_int LAPACKE_dgbequ_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, const double* ab, + lapack_int ldab, double* r, double* c, + double* rowcnd, double* colcnd, double* amax ); +lapack_int LAPACKE_cgbequ_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, + const lapack_complex_float* ab, lapack_int ldab, + float* r, float* c, float* rowcnd, + float* colcnd, float* amax ); +lapack_int LAPACKE_zgbequ_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, + const lapack_complex_double* ab, + lapack_int ldab, double* r, double* c, + double* rowcnd, double* colcnd, double* amax ); + +lapack_int LAPACKE_sgbequb_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, const float* ab, + lapack_int ldab, float* r, float* c, + float* rowcnd, float* colcnd, float* amax ); +lapack_int LAPACKE_dgbequb_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, const double* ab, + lapack_int ldab, double* r, double* c, + double* rowcnd, double* colcnd, double* amax ); +lapack_int LAPACKE_cgbequb_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, + const lapack_complex_float* ab, + lapack_int ldab, float* r, float* c, + float* rowcnd, float* colcnd, float* amax ); +lapack_int LAPACKE_zgbequb_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, + const lapack_complex_double* ab, + lapack_int ldab, double* r, double* c, + double* rowcnd, double* colcnd, double* amax ); + +lapack_int LAPACKE_sgbrfs_work( int matrix_order, char trans, lapack_int n, + lapack_int kl, lapack_int ku, lapack_int nrhs, + const float* ab, lapack_int ldab, + const float* afb, lapack_int ldafb, + const lapack_int* ipiv, const float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* ferr, float* berr, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dgbrfs_work( int matrix_order, char trans, lapack_int n, + lapack_int kl, lapack_int ku, lapack_int nrhs, + const double* ab, lapack_int ldab, + const double* afb, lapack_int ldafb, + const lapack_int* ipiv, const double* b, + lapack_int ldb, double* x, lapack_int ldx, + double* ferr, double* berr, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_cgbrfs_work( int matrix_order, char trans, lapack_int n, + lapack_int kl, lapack_int ku, lapack_int nrhs, + const lapack_complex_float* ab, lapack_int ldab, + const lapack_complex_float* afb, + lapack_int ldafb, const lapack_int* ipiv, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* ferr, float* berr, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zgbrfs_work( int matrix_order, char trans, lapack_int n, + lapack_int kl, lapack_int ku, lapack_int nrhs, + const lapack_complex_double* ab, + lapack_int ldab, + const lapack_complex_double* afb, + lapack_int ldafb, const lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_sgbrfsx_work( int matrix_order, char trans, char equed, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, const float* ab, + lapack_int ldab, const float* afb, + lapack_int ldafb, const lapack_int* ipiv, + const float* r, const float* c, const float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* rcond, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dgbrfsx_work( int matrix_order, char trans, char equed, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, const double* ab, + lapack_int ldab, const double* afb, + lapack_int ldafb, const lapack_int* ipiv, + const double* r, const double* c, + const double* b, lapack_int ldb, double* x, + lapack_int ldx, double* rcond, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_cgbrfsx_work( int matrix_order, char trans, char equed, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, + const lapack_complex_float* ab, + lapack_int ldab, + const lapack_complex_float* afb, + lapack_int ldafb, const lapack_int* ipiv, + const float* r, const float* c, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params, lapack_complex_float* work, + float* rwork ); +lapack_int LAPACKE_zgbrfsx_work( int matrix_order, char trans, char equed, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, + const lapack_complex_double* ab, + lapack_int ldab, + const lapack_complex_double* afb, + lapack_int ldafb, const lapack_int* ipiv, + const double* r, const double* c, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params, lapack_complex_double* work, + double* rwork ); + +lapack_int LAPACKE_sgbsv_work( int matrix_order, lapack_int n, lapack_int kl, + lapack_int ku, lapack_int nrhs, float* ab, + lapack_int ldab, lapack_int* ipiv, float* b, + lapack_int ldb ); +lapack_int LAPACKE_dgbsv_work( int matrix_order, lapack_int n, lapack_int kl, + lapack_int ku, lapack_int nrhs, double* ab, + lapack_int ldab, lapack_int* ipiv, double* b, + lapack_int ldb ); +lapack_int LAPACKE_cgbsv_work( int matrix_order, lapack_int n, lapack_int kl, + lapack_int ku, lapack_int nrhs, + lapack_complex_float* ab, lapack_int ldab, + lapack_int* ipiv, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zgbsv_work( int matrix_order, lapack_int n, lapack_int kl, + lapack_int ku, lapack_int nrhs, + lapack_complex_double* ab, lapack_int ldab, + lapack_int* ipiv, lapack_complex_double* b, + lapack_int ldb ); + +lapack_int LAPACKE_sgbsvx_work( int matrix_order, char fact, char trans, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, float* ab, lapack_int ldab, + float* afb, lapack_int ldafb, lapack_int* ipiv, + char* equed, float* r, float* c, float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* rcond, float* ferr, float* berr, + float* work, lapack_int* iwork ); +lapack_int LAPACKE_dgbsvx_work( int matrix_order, char fact, char trans, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, double* ab, lapack_int ldab, + double* afb, lapack_int ldafb, lapack_int* ipiv, + char* equed, double* r, double* c, double* b, + lapack_int ldb, double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr, + double* work, lapack_int* iwork ); +lapack_int LAPACKE_cgbsvx_work( int matrix_order, char fact, char trans, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, lapack_complex_float* ab, + lapack_int ldab, lapack_complex_float* afb, + lapack_int ldafb, lapack_int* ipiv, char* equed, + float* r, float* c, lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* x, + lapack_int ldx, float* rcond, float* ferr, + float* berr, lapack_complex_float* work, + float* rwork ); +lapack_int LAPACKE_zgbsvx_work( int matrix_order, char fact, char trans, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, lapack_complex_double* ab, + lapack_int ldab, lapack_complex_double* afb, + lapack_int ldafb, lapack_int* ipiv, char* equed, + double* r, double* c, lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* x, + lapack_int ldx, double* rcond, double* ferr, + double* berr, lapack_complex_double* work, + double* rwork ); + +lapack_int LAPACKE_sgbsvxx_work( int matrix_order, char fact, char trans, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, float* ab, lapack_int ldab, + float* afb, lapack_int ldafb, lapack_int* ipiv, + char* equed, float* r, float* c, float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* rcond, float* rpvgrw, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dgbsvxx_work( int matrix_order, char fact, char trans, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, double* ab, lapack_int ldab, + double* afb, lapack_int ldafb, + lapack_int* ipiv, char* equed, double* r, + double* c, double* b, lapack_int ldb, + double* x, lapack_int ldx, double* rcond, + double* rpvgrw, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_cgbsvxx_work( int matrix_order, char fact, char trans, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, lapack_complex_float* ab, + lapack_int ldab, lapack_complex_float* afb, + lapack_int ldafb, lapack_int* ipiv, + char* equed, float* r, float* c, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* rpvgrw, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params, lapack_complex_float* work, + float* rwork ); +lapack_int LAPACKE_zgbsvxx_work( int matrix_order, char fact, char trans, + lapack_int n, lapack_int kl, lapack_int ku, + lapack_int nrhs, lapack_complex_double* ab, + lapack_int ldab, lapack_complex_double* afb, + lapack_int ldafb, lapack_int* ipiv, + char* equed, double* r, double* c, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* rpvgrw, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params, lapack_complex_double* work, + double* rwork ); + +lapack_int LAPACKE_sgbtrf_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, float* ab, + lapack_int ldab, lapack_int* ipiv ); +lapack_int LAPACKE_dgbtrf_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, double* ab, + lapack_int ldab, lapack_int* ipiv ); +lapack_int LAPACKE_cgbtrf_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, + lapack_complex_float* ab, lapack_int ldab, + lapack_int* ipiv ); +lapack_int LAPACKE_zgbtrf_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, + lapack_complex_double* ab, lapack_int ldab, + lapack_int* ipiv ); + +lapack_int LAPACKE_sgbtrs_work( int matrix_order, char trans, lapack_int n, + lapack_int kl, lapack_int ku, lapack_int nrhs, + const float* ab, lapack_int ldab, + const lapack_int* ipiv, float* b, + lapack_int ldb ); +lapack_int LAPACKE_dgbtrs_work( int matrix_order, char trans, lapack_int n, + lapack_int kl, lapack_int ku, lapack_int nrhs, + const double* ab, lapack_int ldab, + const lapack_int* ipiv, double* b, + lapack_int ldb ); +lapack_int LAPACKE_cgbtrs_work( int matrix_order, char trans, lapack_int n, + lapack_int kl, lapack_int ku, lapack_int nrhs, + const lapack_complex_float* ab, lapack_int ldab, + const lapack_int* ipiv, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zgbtrs_work( int matrix_order, char trans, lapack_int n, + lapack_int kl, lapack_int ku, lapack_int nrhs, + const lapack_complex_double* ab, + lapack_int ldab, const lapack_int* ipiv, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_sgebak_work( int matrix_order, char job, char side, + lapack_int n, lapack_int ilo, lapack_int ihi, + const float* scale, lapack_int m, float* v, + lapack_int ldv ); +lapack_int LAPACKE_dgebak_work( int matrix_order, char job, char side, + lapack_int n, lapack_int ilo, lapack_int ihi, + const double* scale, lapack_int m, double* v, + lapack_int ldv ); +lapack_int LAPACKE_cgebak_work( int matrix_order, char job, char side, + lapack_int n, lapack_int ilo, lapack_int ihi, + const float* scale, lapack_int m, + lapack_complex_float* v, lapack_int ldv ); +lapack_int LAPACKE_zgebak_work( int matrix_order, char job, char side, + lapack_int n, lapack_int ilo, lapack_int ihi, + const double* scale, lapack_int m, + lapack_complex_double* v, lapack_int ldv ); + +lapack_int LAPACKE_sgebal_work( int matrix_order, char job, lapack_int n, + float* a, lapack_int lda, lapack_int* ilo, + lapack_int* ihi, float* scale ); +lapack_int LAPACKE_dgebal_work( int matrix_order, char job, lapack_int n, + double* a, lapack_int lda, lapack_int* ilo, + lapack_int* ihi, double* scale ); +lapack_int LAPACKE_cgebal_work( int matrix_order, char job, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_int* ilo, lapack_int* ihi, + float* scale ); +lapack_int LAPACKE_zgebal_work( int matrix_order, char job, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_int* ilo, lapack_int* ihi, + double* scale ); + +lapack_int LAPACKE_sgebrd_work( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* d, float* e, + float* tauq, float* taup, float* work, + lapack_int lwork ); +lapack_int LAPACKE_dgebrd_work( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* d, double* e, + double* tauq, double* taup, double* work, + lapack_int lwork ); +lapack_int LAPACKE_cgebrd_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + float* d, float* e, lapack_complex_float* tauq, + lapack_complex_float* taup, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zgebrd_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + double* d, double* e, + lapack_complex_double* tauq, + lapack_complex_double* taup, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_sgecon_work( int matrix_order, char norm, lapack_int n, + const float* a, lapack_int lda, float anorm, + float* rcond, float* work, lapack_int* iwork ); +lapack_int LAPACKE_dgecon_work( int matrix_order, char norm, lapack_int n, + const double* a, lapack_int lda, double anorm, + double* rcond, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_cgecon_work( int matrix_order, char norm, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + float anorm, float* rcond, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zgecon_work( int matrix_order, char norm, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + double anorm, double* rcond, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_sgeequ_work( int matrix_order, lapack_int m, lapack_int n, + const float* a, lapack_int lda, float* r, + float* c, float* rowcnd, float* colcnd, + float* amax ); +lapack_int LAPACKE_dgeequ_work( int matrix_order, lapack_int m, lapack_int n, + const double* a, lapack_int lda, double* r, + double* c, double* rowcnd, double* colcnd, + double* amax ); +lapack_int LAPACKE_cgeequ_work( int matrix_order, lapack_int m, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + float* r, float* c, float* rowcnd, + float* colcnd, float* amax ); +lapack_int LAPACKE_zgeequ_work( int matrix_order, lapack_int m, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + double* r, double* c, double* rowcnd, + double* colcnd, double* amax ); + +lapack_int LAPACKE_sgeequb_work( int matrix_order, lapack_int m, lapack_int n, + const float* a, lapack_int lda, float* r, + float* c, float* rowcnd, float* colcnd, + float* amax ); +lapack_int LAPACKE_dgeequb_work( int matrix_order, lapack_int m, lapack_int n, + const double* a, lapack_int lda, double* r, + double* c, double* rowcnd, double* colcnd, + double* amax ); +lapack_int LAPACKE_cgeequb_work( int matrix_order, lapack_int m, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + float* r, float* c, float* rowcnd, + float* colcnd, float* amax ); +lapack_int LAPACKE_zgeequb_work( int matrix_order, lapack_int m, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + double* r, double* c, double* rowcnd, + double* colcnd, double* amax ); + +lapack_int LAPACKE_sgees_work( int matrix_order, char jobvs, char sort, + LAPACK_S_SELECT2 select, lapack_int n, float* a, + lapack_int lda, lapack_int* sdim, float* wr, + float* wi, float* vs, lapack_int ldvs, + float* work, lapack_int lwork, + lapack_logical* bwork ); +lapack_int LAPACKE_dgees_work( int matrix_order, char jobvs, char sort, + LAPACK_D_SELECT2 select, lapack_int n, double* a, + lapack_int lda, lapack_int* sdim, double* wr, + double* wi, double* vs, lapack_int ldvs, + double* work, lapack_int lwork, + lapack_logical* bwork ); +lapack_int LAPACKE_cgees_work( int matrix_order, char jobvs, char sort, + LAPACK_C_SELECT1 select, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_int* sdim, lapack_complex_float* w, + lapack_complex_float* vs, lapack_int ldvs, + lapack_complex_float* work, lapack_int lwork, + float* rwork, lapack_logical* bwork ); +lapack_int LAPACKE_zgees_work( int matrix_order, char jobvs, char sort, + LAPACK_Z_SELECT1 select, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_int* sdim, lapack_complex_double* w, + lapack_complex_double* vs, lapack_int ldvs, + lapack_complex_double* work, lapack_int lwork, + double* rwork, lapack_logical* bwork ); + +lapack_int LAPACKE_sgeesx_work( int matrix_order, char jobvs, char sort, + LAPACK_S_SELECT2 select, char sense, + lapack_int n, float* a, lapack_int lda, + lapack_int* sdim, float* wr, float* wi, + float* vs, lapack_int ldvs, float* rconde, + float* rcondv, float* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork, + lapack_logical* bwork ); +lapack_int LAPACKE_dgeesx_work( int matrix_order, char jobvs, char sort, + LAPACK_D_SELECT2 select, char sense, + lapack_int n, double* a, lapack_int lda, + lapack_int* sdim, double* wr, double* wi, + double* vs, lapack_int ldvs, double* rconde, + double* rcondv, double* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork, + lapack_logical* bwork ); +lapack_int LAPACKE_cgeesx_work( int matrix_order, char jobvs, char sort, + LAPACK_C_SELECT1 select, char sense, + lapack_int n, lapack_complex_float* a, + lapack_int lda, lapack_int* sdim, + lapack_complex_float* w, + lapack_complex_float* vs, lapack_int ldvs, + float* rconde, float* rcondv, + lapack_complex_float* work, lapack_int lwork, + float* rwork, lapack_logical* bwork ); +lapack_int LAPACKE_zgeesx_work( int matrix_order, char jobvs, char sort, + LAPACK_Z_SELECT1 select, char sense, + lapack_int n, lapack_complex_double* a, + lapack_int lda, lapack_int* sdim, + lapack_complex_double* w, + lapack_complex_double* vs, lapack_int ldvs, + double* rconde, double* rcondv, + lapack_complex_double* work, lapack_int lwork, + double* rwork, lapack_logical* bwork ); + +lapack_int LAPACKE_sgeev_work( int matrix_order, char jobvl, char jobvr, + lapack_int n, float* a, lapack_int lda, + float* wr, float* wi, float* vl, lapack_int ldvl, + float* vr, lapack_int ldvr, float* work, + lapack_int lwork ); +lapack_int LAPACKE_dgeev_work( int matrix_order, char jobvl, char jobvr, + lapack_int n, double* a, lapack_int lda, + double* wr, double* wi, double* vl, + lapack_int ldvl, double* vr, lapack_int ldvr, + double* work, lapack_int lwork ); +lapack_int LAPACKE_cgeev_work( int matrix_order, char jobvl, char jobvr, + lapack_int n, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* w, + lapack_complex_float* vl, lapack_int ldvl, + lapack_complex_float* vr, lapack_int ldvr, + lapack_complex_float* work, lapack_int lwork, + float* rwork ); +lapack_int LAPACKE_zgeev_work( int matrix_order, char jobvl, char jobvr, + lapack_int n, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* w, + lapack_complex_double* vl, lapack_int ldvl, + lapack_complex_double* vr, lapack_int ldvr, + lapack_complex_double* work, lapack_int lwork, + double* rwork ); + +lapack_int LAPACKE_sgeevx_work( int matrix_order, char balanc, char jobvl, + char jobvr, char sense, lapack_int n, float* a, + lapack_int lda, float* wr, float* wi, float* vl, + lapack_int ldvl, float* vr, lapack_int ldvr, + lapack_int* ilo, lapack_int* ihi, float* scale, + float* abnrm, float* rconde, float* rcondv, + float* work, lapack_int lwork, + lapack_int* iwork ); +lapack_int LAPACKE_dgeevx_work( int matrix_order, char balanc, char jobvl, + char jobvr, char sense, lapack_int n, double* a, + lapack_int lda, double* wr, double* wi, + double* vl, lapack_int ldvl, double* vr, + lapack_int ldvr, lapack_int* ilo, + lapack_int* ihi, double* scale, double* abnrm, + double* rconde, double* rcondv, double* work, + lapack_int lwork, lapack_int* iwork ); +lapack_int LAPACKE_cgeevx_work( int matrix_order, char balanc, char jobvl, + char jobvr, char sense, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* w, + lapack_complex_float* vl, lapack_int ldvl, + lapack_complex_float* vr, lapack_int ldvr, + lapack_int* ilo, lapack_int* ihi, float* scale, + float* abnrm, float* rconde, float* rcondv, + lapack_complex_float* work, lapack_int lwork, + float* rwork ); +lapack_int LAPACKE_zgeevx_work( int matrix_order, char balanc, char jobvl, + char jobvr, char sense, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* w, + lapack_complex_double* vl, lapack_int ldvl, + lapack_complex_double* vr, lapack_int ldvr, + lapack_int* ilo, lapack_int* ihi, double* scale, + double* abnrm, double* rconde, double* rcondv, + lapack_complex_double* work, lapack_int lwork, + double* rwork ); + +lapack_int LAPACKE_sgehrd_work( int matrix_order, lapack_int n, lapack_int ilo, + lapack_int ihi, float* a, lapack_int lda, + float* tau, float* work, lapack_int lwork ); +lapack_int LAPACKE_dgehrd_work( int matrix_order, lapack_int n, lapack_int ilo, + lapack_int ihi, double* a, lapack_int lda, + double* tau, double* work, lapack_int lwork ); +lapack_int LAPACKE_cgehrd_work( int matrix_order, lapack_int n, lapack_int ilo, + lapack_int ihi, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* tau, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zgehrd_work( int matrix_order, lapack_int n, lapack_int ilo, + lapack_int ihi, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* tau, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_sgejsv_work( int matrix_order, char joba, char jobu, + char jobv, char jobr, char jobt, char jobp, + lapack_int m, lapack_int n, float* a, + lapack_int lda, float* sva, float* u, + lapack_int ldu, float* v, lapack_int ldv, + float* work, lapack_int lwork, + lapack_int* iwork ); +lapack_int LAPACKE_dgejsv_work( int matrix_order, char joba, char jobu, + char jobv, char jobr, char jobt, char jobp, + lapack_int m, lapack_int n, double* a, + lapack_int lda, double* sva, double* u, + lapack_int ldu, double* v, lapack_int ldv, + double* work, lapack_int lwork, + lapack_int* iwork ); + +lapack_int LAPACKE_sgelq2_work( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* tau, + float* work ); +lapack_int LAPACKE_dgelq2_work( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* tau, + double* work ); +lapack_int LAPACKE_cgelq2_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* tau, + lapack_complex_float* work ); +lapack_int LAPACKE_zgelq2_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* tau, + lapack_complex_double* work ); + +lapack_int LAPACKE_sgelqf_work( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* tau, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dgelqf_work( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* tau, + double* work, lapack_int lwork ); +lapack_int LAPACKE_cgelqf_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* tau, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zgelqf_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* tau, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_sgels_work( int matrix_order, char trans, lapack_int m, + lapack_int n, lapack_int nrhs, float* a, + lapack_int lda, float* b, lapack_int ldb, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dgels_work( int matrix_order, char trans, lapack_int m, + lapack_int n, lapack_int nrhs, double* a, + lapack_int lda, double* b, lapack_int ldb, + double* work, lapack_int lwork ); +lapack_int LAPACKE_cgels_work( int matrix_order, char trans, lapack_int m, + lapack_int n, lapack_int nrhs, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zgels_work( int matrix_order, char trans, lapack_int m, + lapack_int n, lapack_int nrhs, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_sgelsd_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, float* a, lapack_int lda, + float* b, lapack_int ldb, float* s, float rcond, + lapack_int* rank, float* work, lapack_int lwork, + lapack_int* iwork ); +lapack_int LAPACKE_dgelsd_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, double* a, lapack_int lda, + double* b, lapack_int ldb, double* s, + double rcond, lapack_int* rank, double* work, + lapack_int lwork, lapack_int* iwork ); +lapack_int LAPACKE_cgelsd_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb, float* s, float rcond, + lapack_int* rank, lapack_complex_float* work, + lapack_int lwork, float* rwork, + lapack_int* iwork ); +lapack_int LAPACKE_zgelsd_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb, double* s, double rcond, + lapack_int* rank, lapack_complex_double* work, + lapack_int lwork, double* rwork, + lapack_int* iwork ); + +lapack_int LAPACKE_sgelss_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, float* a, lapack_int lda, + float* b, lapack_int ldb, float* s, float rcond, + lapack_int* rank, float* work, + lapack_int lwork ); +lapack_int LAPACKE_dgelss_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, double* a, lapack_int lda, + double* b, lapack_int ldb, double* s, + double rcond, lapack_int* rank, double* work, + lapack_int lwork ); +lapack_int LAPACKE_cgelss_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb, float* s, float rcond, + lapack_int* rank, lapack_complex_float* work, + lapack_int lwork, float* rwork ); +lapack_int LAPACKE_zgelss_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb, double* s, double rcond, + lapack_int* rank, lapack_complex_double* work, + lapack_int lwork, double* rwork ); + +lapack_int LAPACKE_sgelsy_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, float* a, lapack_int lda, + float* b, lapack_int ldb, lapack_int* jpvt, + float rcond, lapack_int* rank, float* work, + lapack_int lwork ); +lapack_int LAPACKE_dgelsy_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, double* a, lapack_int lda, + double* b, lapack_int ldb, lapack_int* jpvt, + double rcond, lapack_int* rank, double* work, + lapack_int lwork ); +lapack_int LAPACKE_cgelsy_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb, lapack_int* jpvt, float rcond, + lapack_int* rank, lapack_complex_float* work, + lapack_int lwork, float* rwork ); +lapack_int LAPACKE_zgelsy_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int nrhs, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb, lapack_int* jpvt, double rcond, + lapack_int* rank, lapack_complex_double* work, + lapack_int lwork, double* rwork ); + +lapack_int LAPACKE_sgeqlf_work( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* tau, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dgeqlf_work( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* tau, + double* work, lapack_int lwork ); +lapack_int LAPACKE_cgeqlf_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* tau, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zgeqlf_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* tau, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_sgeqp3_work( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, lapack_int* jpvt, + float* tau, float* work, lapack_int lwork ); +lapack_int LAPACKE_dgeqp3_work( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, lapack_int* jpvt, + double* tau, double* work, lapack_int lwork ); +lapack_int LAPACKE_cgeqp3_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_int* jpvt, lapack_complex_float* tau, + lapack_complex_float* work, lapack_int lwork, + float* rwork ); +lapack_int LAPACKE_zgeqp3_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_int* jpvt, lapack_complex_double* tau, + lapack_complex_double* work, lapack_int lwork, + double* rwork ); + +lapack_int LAPACKE_sgeqpf_work( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, lapack_int* jpvt, + float* tau, float* work ); +lapack_int LAPACKE_dgeqpf_work( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, lapack_int* jpvt, + double* tau, double* work ); +lapack_int LAPACKE_cgeqpf_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_int* jpvt, lapack_complex_float* tau, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zgeqpf_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_int* jpvt, lapack_complex_double* tau, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_sgeqr2_work( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* tau, + float* work ); +lapack_int LAPACKE_dgeqr2_work( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* tau, + double* work ); +lapack_int LAPACKE_cgeqr2_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* tau, + lapack_complex_float* work ); +lapack_int LAPACKE_zgeqr2_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* tau, + lapack_complex_double* work ); + +lapack_int LAPACKE_sgeqrf_work( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* tau, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dgeqrf_work( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* tau, + double* work, lapack_int lwork ); +lapack_int LAPACKE_cgeqrf_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* tau, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zgeqrf_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* tau, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_sgeqrfp_work( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* tau, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dgeqrfp_work( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* tau, + double* work, lapack_int lwork ); +lapack_int LAPACKE_cgeqrfp_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* tau, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zgeqrfp_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* tau, + lapack_complex_double* work, + lapack_int lwork ); + +lapack_int LAPACKE_sgerfs_work( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const float* a, lapack_int lda, + const float* af, lapack_int ldaf, + const lapack_int* ipiv, const float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* ferr, float* berr, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dgerfs_work( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const double* a, + lapack_int lda, const double* af, + lapack_int ldaf, const lapack_int* ipiv, + const double* b, lapack_int ldb, double* x, + lapack_int ldx, double* ferr, double* berr, + double* work, lapack_int* iwork ); +lapack_int LAPACKE_cgerfs_work( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* af, + lapack_int ldaf, const lapack_int* ipiv, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* ferr, float* berr, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zgerfs_work( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, const lapack_complex_double* af, + lapack_int ldaf, const lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_sgerfsx_work( int matrix_order, char trans, char equed, + lapack_int n, lapack_int nrhs, const float* a, + lapack_int lda, const float* af, + lapack_int ldaf, const lapack_int* ipiv, + const float* r, const float* c, const float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* rcond, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dgerfsx_work( int matrix_order, char trans, char equed, + lapack_int n, lapack_int nrhs, const double* a, + lapack_int lda, const double* af, + lapack_int ldaf, const lapack_int* ipiv, + const double* r, const double* c, + const double* b, lapack_int ldb, double* x, + lapack_int ldx, double* rcond, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_cgerfsx_work( int matrix_order, char trans, char equed, + lapack_int n, lapack_int nrhs, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* af, + lapack_int ldaf, const lapack_int* ipiv, + const float* r, const float* c, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params, lapack_complex_float* work, + float* rwork ); +lapack_int LAPACKE_zgerfsx_work( int matrix_order, char trans, char equed, + lapack_int n, lapack_int nrhs, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* af, + lapack_int ldaf, const lapack_int* ipiv, + const double* r, const double* c, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params, lapack_complex_double* work, + double* rwork ); + +lapack_int LAPACKE_sgerqf_work( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* tau, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dgerqf_work( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* tau, + double* work, lapack_int lwork ); +lapack_int LAPACKE_cgerqf_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* tau, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zgerqf_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* tau, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_sgesdd_work( int matrix_order, char jobz, lapack_int m, + lapack_int n, float* a, lapack_int lda, + float* s, float* u, lapack_int ldu, float* vt, + lapack_int ldvt, float* work, lapack_int lwork, + lapack_int* iwork ); +lapack_int LAPACKE_dgesdd_work( int matrix_order, char jobz, lapack_int m, + lapack_int n, double* a, lapack_int lda, + double* s, double* u, lapack_int ldu, + double* vt, lapack_int ldvt, double* work, + lapack_int lwork, lapack_int* iwork ); +lapack_int LAPACKE_cgesdd_work( int matrix_order, char jobz, lapack_int m, + lapack_int n, lapack_complex_float* a, + lapack_int lda, float* s, + lapack_complex_float* u, lapack_int ldu, + lapack_complex_float* vt, lapack_int ldvt, + lapack_complex_float* work, lapack_int lwork, + float* rwork, lapack_int* iwork ); +lapack_int LAPACKE_zgesdd_work( int matrix_order, char jobz, lapack_int m, + lapack_int n, lapack_complex_double* a, + lapack_int lda, double* s, + lapack_complex_double* u, lapack_int ldu, + lapack_complex_double* vt, lapack_int ldvt, + lapack_complex_double* work, lapack_int lwork, + double* rwork, lapack_int* iwork ); + +lapack_int LAPACKE_sgesv_work( int matrix_order, lapack_int n, lapack_int nrhs, + float* a, lapack_int lda, lapack_int* ipiv, + float* b, lapack_int ldb ); +lapack_int LAPACKE_dgesv_work( int matrix_order, lapack_int n, lapack_int nrhs, + double* a, lapack_int lda, lapack_int* ipiv, + double* b, lapack_int ldb ); +lapack_int LAPACKE_cgesv_work( int matrix_order, lapack_int n, lapack_int nrhs, + lapack_complex_float* a, lapack_int lda, + lapack_int* ipiv, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zgesv_work( int matrix_order, lapack_int n, lapack_int nrhs, + lapack_complex_double* a, lapack_int lda, + lapack_int* ipiv, lapack_complex_double* b, + lapack_int ldb ); +lapack_int LAPACKE_dsgesv_work( int matrix_order, lapack_int n, lapack_int nrhs, + double* a, lapack_int lda, lapack_int* ipiv, + double* b, lapack_int ldb, double* x, + lapack_int ldx, double* work, float* swork, + lapack_int* iter ); +lapack_int LAPACKE_zcgesv_work( int matrix_order, lapack_int n, lapack_int nrhs, + lapack_complex_double* a, lapack_int lda, + lapack_int* ipiv, lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* x, + lapack_int ldx, lapack_complex_double* work, + lapack_complex_float* swork, double* rwork, + lapack_int* iter ); + +lapack_int LAPACKE_sgesvd_work( int matrix_order, char jobu, char jobvt, + lapack_int m, lapack_int n, float* a, + lapack_int lda, float* s, float* u, + lapack_int ldu, float* vt, lapack_int ldvt, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dgesvd_work( int matrix_order, char jobu, char jobvt, + lapack_int m, lapack_int n, double* a, + lapack_int lda, double* s, double* u, + lapack_int ldu, double* vt, lapack_int ldvt, + double* work, lapack_int lwork ); +lapack_int LAPACKE_cgesvd_work( int matrix_order, char jobu, char jobvt, + lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + float* s, lapack_complex_float* u, + lapack_int ldu, lapack_complex_float* vt, + lapack_int ldvt, lapack_complex_float* work, + lapack_int lwork, float* rwork ); +lapack_int LAPACKE_zgesvd_work( int matrix_order, char jobu, char jobvt, + lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + double* s, lapack_complex_double* u, + lapack_int ldu, lapack_complex_double* vt, + lapack_int ldvt, lapack_complex_double* work, + lapack_int lwork, double* rwork ); + +lapack_int LAPACKE_sgesvj_work( int matrix_order, char joba, char jobu, + char jobv, lapack_int m, lapack_int n, float* a, + lapack_int lda, float* sva, lapack_int mv, + float* v, lapack_int ldv, float* work, + lapack_int lwork ); +lapack_int LAPACKE_dgesvj_work( int matrix_order, char joba, char jobu, + char jobv, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* sva, + lapack_int mv, double* v, lapack_int ldv, + double* work, lapack_int lwork ); + +lapack_int LAPACKE_sgesvx_work( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, float* a, + lapack_int lda, float* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, float* r, + float* c, float* b, lapack_int ldb, float* x, + lapack_int ldx, float* rcond, float* ferr, + float* berr, float* work, lapack_int* iwork ); +lapack_int LAPACKE_dgesvx_work( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, double* a, + lapack_int lda, double* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, double* r, + double* c, double* b, lapack_int ldb, double* x, + lapack_int ldx, double* rcond, double* ferr, + double* berr, double* work, lapack_int* iwork ); +lapack_int LAPACKE_cgesvx_work( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, float* r, + float* c, lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* x, + lapack_int ldx, float* rcond, float* ferr, + float* berr, lapack_complex_float* work, + float* rwork ); +lapack_int LAPACKE_zgesvx_work( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, double* r, + double* c, lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* x, + lapack_int ldx, double* rcond, double* ferr, + double* berr, lapack_complex_double* work, + double* rwork ); + +lapack_int LAPACKE_sgesvxx_work( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, float* a, + lapack_int lda, float* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, float* r, + float* c, float* b, lapack_int ldb, float* x, + lapack_int ldx, float* rcond, float* rpvgrw, + float* berr, lapack_int n_err_bnds, + float* err_bnds_norm, float* err_bnds_comp, + lapack_int nparams, float* params, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dgesvxx_work( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, double* a, + lapack_int lda, double* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, double* r, + double* c, double* b, lapack_int ldb, + double* x, lapack_int ldx, double* rcond, + double* rpvgrw, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_cgesvxx_work( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, float* r, + float* c, lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* x, + lapack_int ldx, float* rcond, float* rpvgrw, + float* berr, lapack_int n_err_bnds, + float* err_bnds_norm, float* err_bnds_comp, + lapack_int nparams, float* params, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zgesvxx_work( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, double* r, + double* c, lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* x, + lapack_int ldx, double* rcond, double* rpvgrw, + double* berr, lapack_int n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int nparams, double* params, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_sgetf2_work( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, lapack_int* ipiv ); +lapack_int LAPACKE_dgetf2_work( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, lapack_int* ipiv ); +lapack_int LAPACKE_cgetf2_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_int* ipiv ); +lapack_int LAPACKE_zgetf2_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_int* ipiv ); + +lapack_int LAPACKE_sgetrf_work( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, lapack_int* ipiv ); +lapack_int LAPACKE_dgetrf_work( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, lapack_int* ipiv ); +lapack_int LAPACKE_cgetrf_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_int* ipiv ); +lapack_int LAPACKE_zgetrf_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_int* ipiv ); + +lapack_int LAPACKE_sgetri_work( int matrix_order, lapack_int n, float* a, + lapack_int lda, const lapack_int* ipiv, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dgetri_work( int matrix_order, lapack_int n, double* a, + lapack_int lda, const lapack_int* ipiv, + double* work, lapack_int lwork ); +lapack_int LAPACKE_cgetri_work( int matrix_order, lapack_int n, + lapack_complex_float* a, lapack_int lda, + const lapack_int* ipiv, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zgetri_work( int matrix_order, lapack_int n, + lapack_complex_double* a, lapack_int lda, + const lapack_int* ipiv, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_sgetrs_work( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const float* a, lapack_int lda, + const lapack_int* ipiv, float* b, + lapack_int ldb ); +lapack_int LAPACKE_dgetrs_work( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const double* a, + lapack_int lda, const lapack_int* ipiv, + double* b, lapack_int ldb ); +lapack_int LAPACKE_cgetrs_work( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zgetrs_work( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_sggbak_work( int matrix_order, char job, char side, + lapack_int n, lapack_int ilo, lapack_int ihi, + const float* lscale, const float* rscale, + lapack_int m, float* v, lapack_int ldv ); +lapack_int LAPACKE_dggbak_work( int matrix_order, char job, char side, + lapack_int n, lapack_int ilo, lapack_int ihi, + const double* lscale, const double* rscale, + lapack_int m, double* v, lapack_int ldv ); +lapack_int LAPACKE_cggbak_work( int matrix_order, char job, char side, + lapack_int n, lapack_int ilo, lapack_int ihi, + const float* lscale, const float* rscale, + lapack_int m, lapack_complex_float* v, + lapack_int ldv ); +lapack_int LAPACKE_zggbak_work( int matrix_order, char job, char side, + lapack_int n, lapack_int ilo, lapack_int ihi, + const double* lscale, const double* rscale, + lapack_int m, lapack_complex_double* v, + lapack_int ldv ); + +lapack_int LAPACKE_sggbal_work( int matrix_order, char job, lapack_int n, + float* a, lapack_int lda, float* b, + lapack_int ldb, lapack_int* ilo, + lapack_int* ihi, float* lscale, float* rscale, + float* work ); +lapack_int LAPACKE_dggbal_work( int matrix_order, char job, lapack_int n, + double* a, lapack_int lda, double* b, + lapack_int ldb, lapack_int* ilo, + lapack_int* ihi, double* lscale, double* rscale, + double* work ); +lapack_int LAPACKE_cggbal_work( int matrix_order, char job, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + lapack_int* ilo, lapack_int* ihi, float* lscale, + float* rscale, float* work ); +lapack_int LAPACKE_zggbal_work( int matrix_order, char job, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + lapack_int* ilo, lapack_int* ihi, + double* lscale, double* rscale, double* work ); + +lapack_int LAPACKE_sgges_work( int matrix_order, char jobvsl, char jobvsr, + char sort, LAPACK_S_SELECT3 selctg, lapack_int n, + float* a, lapack_int lda, float* b, + lapack_int ldb, lapack_int* sdim, float* alphar, + float* alphai, float* beta, float* vsl, + lapack_int ldvsl, float* vsr, lapack_int ldvsr, + float* work, lapack_int lwork, + lapack_logical* bwork ); +lapack_int LAPACKE_dgges_work( int matrix_order, char jobvsl, char jobvsr, + char sort, LAPACK_D_SELECT3 selctg, lapack_int n, + double* a, lapack_int lda, double* b, + lapack_int ldb, lapack_int* sdim, double* alphar, + double* alphai, double* beta, double* vsl, + lapack_int ldvsl, double* vsr, lapack_int ldvsr, + double* work, lapack_int lwork, + lapack_logical* bwork ); +lapack_int LAPACKE_cgges_work( int matrix_order, char jobvsl, char jobvsr, + char sort, LAPACK_C_SELECT2 selctg, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + lapack_int* sdim, lapack_complex_float* alpha, + lapack_complex_float* beta, + lapack_complex_float* vsl, lapack_int ldvsl, + lapack_complex_float* vsr, lapack_int ldvsr, + lapack_complex_float* work, lapack_int lwork, + float* rwork, lapack_logical* bwork ); +lapack_int LAPACKE_zgges_work( int matrix_order, char jobvsl, char jobvsr, + char sort, LAPACK_Z_SELECT2 selctg, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + lapack_int* sdim, lapack_complex_double* alpha, + lapack_complex_double* beta, + lapack_complex_double* vsl, lapack_int ldvsl, + lapack_complex_double* vsr, lapack_int ldvsr, + lapack_complex_double* work, lapack_int lwork, + double* rwork, lapack_logical* bwork ); + +lapack_int LAPACKE_sggesx_work( int matrix_order, char jobvsl, char jobvsr, + char sort, LAPACK_S_SELECT3 selctg, char sense, + lapack_int n, float* a, lapack_int lda, + float* b, lapack_int ldb, lapack_int* sdim, + float* alphar, float* alphai, float* beta, + float* vsl, lapack_int ldvsl, float* vsr, + lapack_int ldvsr, float* rconde, float* rcondv, + float* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork, + lapack_logical* bwork ); +lapack_int LAPACKE_dggesx_work( int matrix_order, char jobvsl, char jobvsr, + char sort, LAPACK_D_SELECT3 selctg, char sense, + lapack_int n, double* a, lapack_int lda, + double* b, lapack_int ldb, lapack_int* sdim, + double* alphar, double* alphai, double* beta, + double* vsl, lapack_int ldvsl, double* vsr, + lapack_int ldvsr, double* rconde, + double* rcondv, double* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork, + lapack_logical* bwork ); +lapack_int LAPACKE_cggesx_work( int matrix_order, char jobvsl, char jobvsr, + char sort, LAPACK_C_SELECT2 selctg, char sense, + lapack_int n, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb, lapack_int* sdim, + lapack_complex_float* alpha, + lapack_complex_float* beta, + lapack_complex_float* vsl, lapack_int ldvsl, + lapack_complex_float* vsr, lapack_int ldvsr, + float* rconde, float* rcondv, + lapack_complex_float* work, lapack_int lwork, + float* rwork, lapack_int* iwork, + lapack_int liwork, lapack_logical* bwork ); +lapack_int LAPACKE_zggesx_work( int matrix_order, char jobvsl, char jobvsr, + char sort, LAPACK_Z_SELECT2 selctg, char sense, + lapack_int n, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb, lapack_int* sdim, + lapack_complex_double* alpha, + lapack_complex_double* beta, + lapack_complex_double* vsl, lapack_int ldvsl, + lapack_complex_double* vsr, lapack_int ldvsr, + double* rconde, double* rcondv, + lapack_complex_double* work, lapack_int lwork, + double* rwork, lapack_int* iwork, + lapack_int liwork, lapack_logical* bwork ); + +lapack_int LAPACKE_sggev_work( int matrix_order, char jobvl, char jobvr, + lapack_int n, float* a, lapack_int lda, float* b, + lapack_int ldb, float* alphar, float* alphai, + float* beta, float* vl, lapack_int ldvl, + float* vr, lapack_int ldvr, float* work, + lapack_int lwork ); +lapack_int LAPACKE_dggev_work( int matrix_order, char jobvl, char jobvr, + lapack_int n, double* a, lapack_int lda, + double* b, lapack_int ldb, double* alphar, + double* alphai, double* beta, double* vl, + lapack_int ldvl, double* vr, lapack_int ldvr, + double* work, lapack_int lwork ); +lapack_int LAPACKE_cggev_work( int matrix_order, char jobvl, char jobvr, + lapack_int n, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* alpha, + lapack_complex_float* beta, + lapack_complex_float* vl, lapack_int ldvl, + lapack_complex_float* vr, lapack_int ldvr, + lapack_complex_float* work, lapack_int lwork, + float* rwork ); +lapack_int LAPACKE_zggev_work( int matrix_order, char jobvl, char jobvr, + lapack_int n, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* alpha, + lapack_complex_double* beta, + lapack_complex_double* vl, lapack_int ldvl, + lapack_complex_double* vr, lapack_int ldvr, + lapack_complex_double* work, lapack_int lwork, + double* rwork ); + +lapack_int LAPACKE_sggevx_work( int matrix_order, char balanc, char jobvl, + char jobvr, char sense, lapack_int n, float* a, + lapack_int lda, float* b, lapack_int ldb, + float* alphar, float* alphai, float* beta, + float* vl, lapack_int ldvl, float* vr, + lapack_int ldvr, lapack_int* ilo, + lapack_int* ihi, float* lscale, float* rscale, + float* abnrm, float* bbnrm, float* rconde, + float* rcondv, float* work, lapack_int lwork, + lapack_int* iwork, lapack_logical* bwork ); +lapack_int LAPACKE_dggevx_work( int matrix_order, char balanc, char jobvl, + char jobvr, char sense, lapack_int n, double* a, + lapack_int lda, double* b, lapack_int ldb, + double* alphar, double* alphai, double* beta, + double* vl, lapack_int ldvl, double* vr, + lapack_int ldvr, lapack_int* ilo, + lapack_int* ihi, double* lscale, double* rscale, + double* abnrm, double* bbnrm, double* rconde, + double* rcondv, double* work, lapack_int lwork, + lapack_int* iwork, lapack_logical* bwork ); +lapack_int LAPACKE_cggevx_work( int matrix_order, char balanc, char jobvl, + char jobvr, char sense, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* alpha, + lapack_complex_float* beta, + lapack_complex_float* vl, lapack_int ldvl, + lapack_complex_float* vr, lapack_int ldvr, + lapack_int* ilo, lapack_int* ihi, float* lscale, + float* rscale, float* abnrm, float* bbnrm, + float* rconde, float* rcondv, + lapack_complex_float* work, lapack_int lwork, + float* rwork, lapack_int* iwork, + lapack_logical* bwork ); +lapack_int LAPACKE_zggevx_work( int matrix_order, char balanc, char jobvl, + char jobvr, char sense, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* alpha, + lapack_complex_double* beta, + lapack_complex_double* vl, lapack_int ldvl, + lapack_complex_double* vr, lapack_int ldvr, + lapack_int* ilo, lapack_int* ihi, + double* lscale, double* rscale, double* abnrm, + double* bbnrm, double* rconde, double* rcondv, + lapack_complex_double* work, lapack_int lwork, + double* rwork, lapack_int* iwork, + lapack_logical* bwork ); + +lapack_int LAPACKE_sggglm_work( int matrix_order, lapack_int n, lapack_int m, + lapack_int p, float* a, lapack_int lda, + float* b, lapack_int ldb, float* d, float* x, + float* y, float* work, lapack_int lwork ); +lapack_int LAPACKE_dggglm_work( int matrix_order, lapack_int n, lapack_int m, + lapack_int p, double* a, lapack_int lda, + double* b, lapack_int ldb, double* d, double* x, + double* y, double* work, lapack_int lwork ); +lapack_int LAPACKE_cggglm_work( int matrix_order, lapack_int n, lapack_int m, + lapack_int p, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* d, + lapack_complex_float* x, + lapack_complex_float* y, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zggglm_work( int matrix_order, lapack_int n, lapack_int m, + lapack_int p, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* d, + lapack_complex_double* x, + lapack_complex_double* y, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_sgghrd_work( int matrix_order, char compq, char compz, + lapack_int n, lapack_int ilo, lapack_int ihi, + float* a, lapack_int lda, float* b, + lapack_int ldb, float* q, lapack_int ldq, + float* z, lapack_int ldz ); +lapack_int LAPACKE_dgghrd_work( int matrix_order, char compq, char compz, + lapack_int n, lapack_int ilo, lapack_int ihi, + double* a, lapack_int lda, double* b, + lapack_int ldb, double* q, lapack_int ldq, + double* z, lapack_int ldz ); +lapack_int LAPACKE_cgghrd_work( int matrix_order, char compq, char compz, + lapack_int n, lapack_int ilo, lapack_int ihi, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* q, lapack_int ldq, + lapack_complex_float* z, lapack_int ldz ); +lapack_int LAPACKE_zgghrd_work( int matrix_order, char compq, char compz, + lapack_int n, lapack_int ilo, lapack_int ihi, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* q, lapack_int ldq, + lapack_complex_double* z, lapack_int ldz ); + +lapack_int LAPACKE_sgglse_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int p, float* a, lapack_int lda, + float* b, lapack_int ldb, float* c, float* d, + float* x, float* work, lapack_int lwork ); +lapack_int LAPACKE_dgglse_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int p, double* a, lapack_int lda, + double* b, lapack_int ldb, double* c, double* d, + double* x, double* work, lapack_int lwork ); +lapack_int LAPACKE_cgglse_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int p, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* c, + lapack_complex_float* d, + lapack_complex_float* x, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zgglse_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int p, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* c, + lapack_complex_double* d, + lapack_complex_double* x, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_sggqrf_work( int matrix_order, lapack_int n, lapack_int m, + lapack_int p, float* a, lapack_int lda, + float* taua, float* b, lapack_int ldb, + float* taub, float* work, lapack_int lwork ); +lapack_int LAPACKE_dggqrf_work( int matrix_order, lapack_int n, lapack_int m, + lapack_int p, double* a, lapack_int lda, + double* taua, double* b, lapack_int ldb, + double* taub, double* work, lapack_int lwork ); +lapack_int LAPACKE_cggqrf_work( int matrix_order, lapack_int n, lapack_int m, + lapack_int p, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* taua, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* taub, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zggqrf_work( int matrix_order, lapack_int n, lapack_int m, + lapack_int p, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* taua, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* taub, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_sggrqf_work( int matrix_order, lapack_int m, lapack_int p, + lapack_int n, float* a, lapack_int lda, + float* taua, float* b, lapack_int ldb, + float* taub, float* work, lapack_int lwork ); +lapack_int LAPACKE_dggrqf_work( int matrix_order, lapack_int m, lapack_int p, + lapack_int n, double* a, lapack_int lda, + double* taua, double* b, lapack_int ldb, + double* taub, double* work, lapack_int lwork ); +lapack_int LAPACKE_cggrqf_work( int matrix_order, lapack_int m, lapack_int p, + lapack_int n, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* taua, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* taub, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zggrqf_work( int matrix_order, lapack_int m, lapack_int p, + lapack_int n, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* taua, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* taub, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_sggsvd_work( int matrix_order, char jobu, char jobv, + char jobq, lapack_int m, lapack_int n, + lapack_int p, lapack_int* k, lapack_int* l, + float* a, lapack_int lda, float* b, + lapack_int ldb, float* alpha, float* beta, + float* u, lapack_int ldu, float* v, + lapack_int ldv, float* q, lapack_int ldq, + float* work, lapack_int* iwork ); +lapack_int LAPACKE_dggsvd_work( int matrix_order, char jobu, char jobv, + char jobq, lapack_int m, lapack_int n, + lapack_int p, lapack_int* k, lapack_int* l, + double* a, lapack_int lda, double* b, + lapack_int ldb, double* alpha, double* beta, + double* u, lapack_int ldu, double* v, + lapack_int ldv, double* q, lapack_int ldq, + double* work, lapack_int* iwork ); +lapack_int LAPACKE_cggsvd_work( int matrix_order, char jobu, char jobv, + char jobq, lapack_int m, lapack_int n, + lapack_int p, lapack_int* k, lapack_int* l, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + float* alpha, float* beta, + lapack_complex_float* u, lapack_int ldu, + lapack_complex_float* v, lapack_int ldv, + lapack_complex_float* q, lapack_int ldq, + lapack_complex_float* work, float* rwork, + lapack_int* iwork ); +lapack_int LAPACKE_zggsvd_work( int matrix_order, char jobu, char jobv, + char jobq, lapack_int m, lapack_int n, + lapack_int p, lapack_int* k, lapack_int* l, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + double* alpha, double* beta, + lapack_complex_double* u, lapack_int ldu, + lapack_complex_double* v, lapack_int ldv, + lapack_complex_double* q, lapack_int ldq, + lapack_complex_double* work, double* rwork, + lapack_int* iwork ); + +lapack_int LAPACKE_sggsvp_work( int matrix_order, char jobu, char jobv, + char jobq, lapack_int m, lapack_int p, + lapack_int n, float* a, lapack_int lda, + float* b, lapack_int ldb, float tola, + float tolb, lapack_int* k, lapack_int* l, + float* u, lapack_int ldu, float* v, + lapack_int ldv, float* q, lapack_int ldq, + lapack_int* iwork, float* tau, float* work ); +lapack_int LAPACKE_dggsvp_work( int matrix_order, char jobu, char jobv, + char jobq, lapack_int m, lapack_int p, + lapack_int n, double* a, lapack_int lda, + double* b, lapack_int ldb, double tola, + double tolb, lapack_int* k, lapack_int* l, + double* u, lapack_int ldu, double* v, + lapack_int ldv, double* q, lapack_int ldq, + lapack_int* iwork, double* tau, double* work ); +lapack_int LAPACKE_cggsvp_work( int matrix_order, char jobu, char jobv, + char jobq, lapack_int m, lapack_int p, + lapack_int n, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb, float tola, float tolb, + lapack_int* k, lapack_int* l, + lapack_complex_float* u, lapack_int ldu, + lapack_complex_float* v, lapack_int ldv, + lapack_complex_float* q, lapack_int ldq, + lapack_int* iwork, float* rwork, + lapack_complex_float* tau, + lapack_complex_float* work ); +lapack_int LAPACKE_zggsvp_work( int matrix_order, char jobu, char jobv, + char jobq, lapack_int m, lapack_int p, + lapack_int n, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb, double tola, double tolb, + lapack_int* k, lapack_int* l, + lapack_complex_double* u, lapack_int ldu, + lapack_complex_double* v, lapack_int ldv, + lapack_complex_double* q, lapack_int ldq, + lapack_int* iwork, double* rwork, + lapack_complex_double* tau, + lapack_complex_double* work ); + +lapack_int LAPACKE_sgtcon_work( char norm, lapack_int n, const float* dl, + const float* d, const float* du, + const float* du2, const lapack_int* ipiv, + float anorm, float* rcond, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dgtcon_work( char norm, lapack_int n, const double* dl, + const double* d, const double* du, + const double* du2, const lapack_int* ipiv, + double anorm, double* rcond, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_cgtcon_work( char norm, lapack_int n, + const lapack_complex_float* dl, + const lapack_complex_float* d, + const lapack_complex_float* du, + const lapack_complex_float* du2, + const lapack_int* ipiv, float anorm, + float* rcond, lapack_complex_float* work ); +lapack_int LAPACKE_zgtcon_work( char norm, lapack_int n, + const lapack_complex_double* dl, + const lapack_complex_double* d, + const lapack_complex_double* du, + const lapack_complex_double* du2, + const lapack_int* ipiv, double anorm, + double* rcond, lapack_complex_double* work ); + +lapack_int LAPACKE_sgtrfs_work( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const float* dl, + const float* d, const float* du, + const float* dlf, const float* df, + const float* duf, const float* du2, + const lapack_int* ipiv, const float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* ferr, float* berr, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dgtrfs_work( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const double* dl, + const double* d, const double* du, + const double* dlf, const double* df, + const double* duf, const double* du2, + const lapack_int* ipiv, const double* b, + lapack_int ldb, double* x, lapack_int ldx, + double* ferr, double* berr, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_cgtrfs_work( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const lapack_complex_float* dl, + const lapack_complex_float* d, + const lapack_complex_float* du, + const lapack_complex_float* dlf, + const lapack_complex_float* df, + const lapack_complex_float* duf, + const lapack_complex_float* du2, + const lapack_int* ipiv, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* ferr, float* berr, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zgtrfs_work( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, + const lapack_complex_double* dl, + const lapack_complex_double* d, + const lapack_complex_double* du, + const lapack_complex_double* dlf, + const lapack_complex_double* df, + const lapack_complex_double* duf, + const lapack_complex_double* du2, + const lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_sgtsv_work( int matrix_order, lapack_int n, lapack_int nrhs, + float* dl, float* d, float* du, float* b, + lapack_int ldb ); +lapack_int LAPACKE_dgtsv_work( int matrix_order, lapack_int n, lapack_int nrhs, + double* dl, double* d, double* du, double* b, + lapack_int ldb ); +lapack_int LAPACKE_cgtsv_work( int matrix_order, lapack_int n, lapack_int nrhs, + lapack_complex_float* dl, + lapack_complex_float* d, + lapack_complex_float* du, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zgtsv_work( int matrix_order, lapack_int n, lapack_int nrhs, + lapack_complex_double* dl, + lapack_complex_double* d, + lapack_complex_double* du, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_sgtsvx_work( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, const float* dl, + const float* d, const float* du, float* dlf, + float* df, float* duf, float* du2, + lapack_int* ipiv, const float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* rcond, float* ferr, float* berr, + float* work, lapack_int* iwork ); +lapack_int LAPACKE_dgtsvx_work( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, const double* dl, + const double* d, const double* du, double* dlf, + double* df, double* duf, double* du2, + lapack_int* ipiv, const double* b, + lapack_int ldb, double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr, + double* work, lapack_int* iwork ); +lapack_int LAPACKE_cgtsvx_work( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, + const lapack_complex_float* dl, + const lapack_complex_float* d, + const lapack_complex_float* du, + lapack_complex_float* dlf, + lapack_complex_float* df, + lapack_complex_float* duf, + lapack_complex_float* du2, lapack_int* ipiv, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* ferr, float* berr, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zgtsvx_work( int matrix_order, char fact, char trans, + lapack_int n, lapack_int nrhs, + const lapack_complex_double* dl, + const lapack_complex_double* d, + const lapack_complex_double* du, + lapack_complex_double* dlf, + lapack_complex_double* df, + lapack_complex_double* duf, + lapack_complex_double* du2, lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_sgttrf_work( lapack_int n, float* dl, float* d, float* du, + float* du2, lapack_int* ipiv ); +lapack_int LAPACKE_dgttrf_work( lapack_int n, double* dl, double* d, double* du, + double* du2, lapack_int* ipiv ); +lapack_int LAPACKE_cgttrf_work( lapack_int n, lapack_complex_float* dl, + lapack_complex_float* d, + lapack_complex_float* du, + lapack_complex_float* du2, lapack_int* ipiv ); +lapack_int LAPACKE_zgttrf_work( lapack_int n, lapack_complex_double* dl, + lapack_complex_double* d, + lapack_complex_double* du, + lapack_complex_double* du2, lapack_int* ipiv ); + +lapack_int LAPACKE_sgttrs_work( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const float* dl, + const float* d, const float* du, + const float* du2, const lapack_int* ipiv, + float* b, lapack_int ldb ); +lapack_int LAPACKE_dgttrs_work( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const double* dl, + const double* d, const double* du, + const double* du2, const lapack_int* ipiv, + double* b, lapack_int ldb ); +lapack_int LAPACKE_cgttrs_work( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, const lapack_complex_float* dl, + const lapack_complex_float* d, + const lapack_complex_float* du, + const lapack_complex_float* du2, + const lapack_int* ipiv, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zgttrs_work( int matrix_order, char trans, lapack_int n, + lapack_int nrhs, + const lapack_complex_double* dl, + const lapack_complex_double* d, + const lapack_complex_double* du, + const lapack_complex_double* du2, + const lapack_int* ipiv, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_chbev_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_int kd, + lapack_complex_float* ab, lapack_int ldab, + float* w, lapack_complex_float* z, + lapack_int ldz, lapack_complex_float* work, + float* rwork ); +lapack_int LAPACKE_zhbev_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_int kd, + lapack_complex_double* ab, lapack_int ldab, + double* w, lapack_complex_double* z, + lapack_int ldz, lapack_complex_double* work, + double* rwork ); + +lapack_int LAPACKE_chbevd_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_int kd, + lapack_complex_float* ab, lapack_int ldab, + float* w, lapack_complex_float* z, + lapack_int ldz, lapack_complex_float* work, + lapack_int lwork, float* rwork, + lapack_int lrwork, lapack_int* iwork, + lapack_int liwork ); +lapack_int LAPACKE_zhbevd_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_int kd, + lapack_complex_double* ab, lapack_int ldab, + double* w, lapack_complex_double* z, + lapack_int ldz, lapack_complex_double* work, + lapack_int lwork, double* rwork, + lapack_int lrwork, lapack_int* iwork, + lapack_int liwork ); + +lapack_int LAPACKE_chbevx_work( int matrix_order, char jobz, char range, + char uplo, lapack_int n, lapack_int kd, + lapack_complex_float* ab, lapack_int ldab, + lapack_complex_float* q, lapack_int ldq, + float vl, float vu, lapack_int il, + lapack_int iu, float abstol, lapack_int* m, + float* w, lapack_complex_float* z, + lapack_int ldz, lapack_complex_float* work, + float* rwork, lapack_int* iwork, + lapack_int* ifail ); +lapack_int LAPACKE_zhbevx_work( int matrix_order, char jobz, char range, + char uplo, lapack_int n, lapack_int kd, + lapack_complex_double* ab, lapack_int ldab, + lapack_complex_double* q, lapack_int ldq, + double vl, double vu, lapack_int il, + lapack_int iu, double abstol, lapack_int* m, + double* w, lapack_complex_double* z, + lapack_int ldz, lapack_complex_double* work, + double* rwork, lapack_int* iwork, + lapack_int* ifail ); + +lapack_int LAPACKE_chbgst_work( int matrix_order, char vect, char uplo, + lapack_int n, lapack_int ka, lapack_int kb, + lapack_complex_float* ab, lapack_int ldab, + const lapack_complex_float* bb, lapack_int ldbb, + lapack_complex_float* x, lapack_int ldx, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zhbgst_work( int matrix_order, char vect, char uplo, + lapack_int n, lapack_int ka, lapack_int kb, + lapack_complex_double* ab, lapack_int ldab, + const lapack_complex_double* bb, + lapack_int ldbb, lapack_complex_double* x, + lapack_int ldx, lapack_complex_double* work, + double* rwork ); + +lapack_int LAPACKE_chbgv_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_int ka, lapack_int kb, + lapack_complex_float* ab, lapack_int ldab, + lapack_complex_float* bb, lapack_int ldbb, + float* w, lapack_complex_float* z, + lapack_int ldz, lapack_complex_float* work, + float* rwork ); +lapack_int LAPACKE_zhbgv_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_int ka, lapack_int kb, + lapack_complex_double* ab, lapack_int ldab, + lapack_complex_double* bb, lapack_int ldbb, + double* w, lapack_complex_double* z, + lapack_int ldz, lapack_complex_double* work, + double* rwork ); + +lapack_int LAPACKE_chbgvd_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_int ka, lapack_int kb, + lapack_complex_float* ab, lapack_int ldab, + lapack_complex_float* bb, lapack_int ldbb, + float* w, lapack_complex_float* z, + lapack_int ldz, lapack_complex_float* work, + lapack_int lwork, float* rwork, + lapack_int lrwork, lapack_int* iwork, + lapack_int liwork ); +lapack_int LAPACKE_zhbgvd_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_int ka, lapack_int kb, + lapack_complex_double* ab, lapack_int ldab, + lapack_complex_double* bb, lapack_int ldbb, + double* w, lapack_complex_double* z, + lapack_int ldz, lapack_complex_double* work, + lapack_int lwork, double* rwork, + lapack_int lrwork, lapack_int* iwork, + lapack_int liwork ); + +lapack_int LAPACKE_chbgvx_work( int matrix_order, char jobz, char range, + char uplo, lapack_int n, lapack_int ka, + lapack_int kb, lapack_complex_float* ab, + lapack_int ldab, lapack_complex_float* bb, + lapack_int ldbb, lapack_complex_float* q, + lapack_int ldq, float vl, float vu, + lapack_int il, lapack_int iu, float abstol, + lapack_int* m, float* w, + lapack_complex_float* z, lapack_int ldz, + lapack_complex_float* work, float* rwork, + lapack_int* iwork, lapack_int* ifail ); +lapack_int LAPACKE_zhbgvx_work( int matrix_order, char jobz, char range, + char uplo, lapack_int n, lapack_int ka, + lapack_int kb, lapack_complex_double* ab, + lapack_int ldab, lapack_complex_double* bb, + lapack_int ldbb, lapack_complex_double* q, + lapack_int ldq, double vl, double vu, + lapack_int il, lapack_int iu, double abstol, + lapack_int* m, double* w, + lapack_complex_double* z, lapack_int ldz, + lapack_complex_double* work, double* rwork, + lapack_int* iwork, lapack_int* ifail ); + +lapack_int LAPACKE_chbtrd_work( int matrix_order, char vect, char uplo, + lapack_int n, lapack_int kd, + lapack_complex_float* ab, lapack_int ldab, + float* d, float* e, lapack_complex_float* q, + lapack_int ldq, lapack_complex_float* work ); +lapack_int LAPACKE_zhbtrd_work( int matrix_order, char vect, char uplo, + lapack_int n, lapack_int kd, + lapack_complex_double* ab, lapack_int ldab, + double* d, double* e, lapack_complex_double* q, + lapack_int ldq, lapack_complex_double* work ); + +lapack_int LAPACKE_checon_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + const lapack_int* ipiv, float anorm, + float* rcond, lapack_complex_float* work ); +lapack_int LAPACKE_zhecon_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + const lapack_int* ipiv, double anorm, + double* rcond, lapack_complex_double* work ); + +lapack_int LAPACKE_cheequb_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + float* s, float* scond, float* amax, + lapack_complex_float* work ); +lapack_int LAPACKE_zheequb_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + double* s, double* scond, double* amax, + lapack_complex_double* work ); + +lapack_int LAPACKE_cheev_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_complex_float* a, + lapack_int lda, float* w, + lapack_complex_float* work, lapack_int lwork, + float* rwork ); +lapack_int LAPACKE_zheev_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_complex_double* a, + lapack_int lda, double* w, + lapack_complex_double* work, lapack_int lwork, + double* rwork ); + +lapack_int LAPACKE_cheevd_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_complex_float* a, + lapack_int lda, float* w, + lapack_complex_float* work, lapack_int lwork, + float* rwork, lapack_int lrwork, + lapack_int* iwork, lapack_int liwork ); +lapack_int LAPACKE_zheevd_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_complex_double* a, + lapack_int lda, double* w, + lapack_complex_double* work, lapack_int lwork, + double* rwork, lapack_int lrwork, + lapack_int* iwork, lapack_int liwork ); + +lapack_int LAPACKE_cheevr_work( int matrix_order, char jobz, char range, + char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + float vl, float vu, lapack_int il, + lapack_int iu, float abstol, lapack_int* m, + float* w, lapack_complex_float* z, + lapack_int ldz, lapack_int* isuppz, + lapack_complex_float* work, lapack_int lwork, + float* rwork, lapack_int lrwork, + lapack_int* iwork, lapack_int liwork ); +lapack_int LAPACKE_zheevr_work( int matrix_order, char jobz, char range, + char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + double vl, double vu, lapack_int il, + lapack_int iu, double abstol, lapack_int* m, + double* w, lapack_complex_double* z, + lapack_int ldz, lapack_int* isuppz, + lapack_complex_double* work, lapack_int lwork, + double* rwork, lapack_int lrwork, + lapack_int* iwork, lapack_int liwork ); + +lapack_int LAPACKE_cheevx_work( int matrix_order, char jobz, char range, + char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + float vl, float vu, lapack_int il, + lapack_int iu, float abstol, lapack_int* m, + float* w, lapack_complex_float* z, + lapack_int ldz, lapack_complex_float* work, + lapack_int lwork, float* rwork, + lapack_int* iwork, lapack_int* ifail ); +lapack_int LAPACKE_zheevx_work( int matrix_order, char jobz, char range, + char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + double vl, double vu, lapack_int il, + lapack_int iu, double abstol, lapack_int* m, + double* w, lapack_complex_double* z, + lapack_int ldz, lapack_complex_double* work, + lapack_int lwork, double* rwork, + lapack_int* iwork, lapack_int* ifail ); + +lapack_int LAPACKE_chegst_work( int matrix_order, lapack_int itype, char uplo, + lapack_int n, lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zhegst_work( int matrix_order, lapack_int itype, char uplo, + lapack_int n, lapack_complex_double* a, + lapack_int lda, const lapack_complex_double* b, + lapack_int ldb ); + +lapack_int LAPACKE_chegv_work( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb, float* w, + lapack_complex_float* work, lapack_int lwork, + float* rwork ); +lapack_int LAPACKE_zhegv_work( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + double* w, lapack_complex_double* work, + lapack_int lwork, double* rwork ); + +lapack_int LAPACKE_chegvd_work( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + float* w, lapack_complex_float* work, + lapack_int lwork, float* rwork, + lapack_int lrwork, lapack_int* iwork, + lapack_int liwork ); +lapack_int LAPACKE_zhegvd_work( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + double* w, lapack_complex_double* work, + lapack_int lwork, double* rwork, + lapack_int lrwork, lapack_int* iwork, + lapack_int liwork ); + +lapack_int LAPACKE_chegvx_work( int matrix_order, lapack_int itype, char jobz, + char range, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + float vl, float vu, lapack_int il, + lapack_int iu, float abstol, lapack_int* m, + float* w, lapack_complex_float* z, + lapack_int ldz, lapack_complex_float* work, + lapack_int lwork, float* rwork, + lapack_int* iwork, lapack_int* ifail ); +lapack_int LAPACKE_zhegvx_work( int matrix_order, lapack_int itype, char jobz, + char range, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + double vl, double vu, lapack_int il, + lapack_int iu, double abstol, lapack_int* m, + double* w, lapack_complex_double* z, + lapack_int ldz, lapack_complex_double* work, + lapack_int lwork, double* rwork, + lapack_int* iwork, lapack_int* ifail ); + +lapack_int LAPACKE_cherfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* af, + lapack_int ldaf, const lapack_int* ipiv, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* ferr, float* berr, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zherfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, const lapack_complex_double* af, + lapack_int ldaf, const lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_cherfsx_work( int matrix_order, char uplo, char equed, + lapack_int n, lapack_int nrhs, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* af, + lapack_int ldaf, const lapack_int* ipiv, + const float* s, const lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* x, + lapack_int ldx, float* rcond, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params, lapack_complex_float* work, + float* rwork ); +lapack_int LAPACKE_zherfsx_work( int matrix_order, char uplo, char equed, + lapack_int n, lapack_int nrhs, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* af, + lapack_int ldaf, const lapack_int* ipiv, + const double* s, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params, lapack_complex_double* work, + double* rwork ); + +lapack_int LAPACKE_chesv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_float* a, + lapack_int lda, lapack_int* ipiv, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zhesv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_double* a, + lapack_int lda, lapack_int* ipiv, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_chesvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + const lapack_complex_float* a, lapack_int lda, + lapack_complex_float* af, lapack_int ldaf, + lapack_int* ipiv, const lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* x, + lapack_int ldx, float* rcond, float* ferr, + float* berr, lapack_complex_float* work, + lapack_int lwork, float* rwork ); +lapack_int LAPACKE_zhesvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + const lapack_complex_double* a, lapack_int lda, + lapack_complex_double* af, lapack_int ldaf, + lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr, + lapack_complex_double* work, lapack_int lwork, + double* rwork ); + +lapack_int LAPACKE_chesvxx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, float* s, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* rpvgrw, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params, lapack_complex_float* work, + float* rwork ); +lapack_int LAPACKE_zhesvxx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, double* s, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* rpvgrw, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params, lapack_complex_double* work, + double* rwork ); + +lapack_int LAPACKE_chetrd_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + float* d, float* e, lapack_complex_float* tau, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zhetrd_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + double* d, double* e, + lapack_complex_double* tau, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_chetrf_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_int* ipiv, lapack_complex_float* work, + lapack_int lwork ); +lapack_int LAPACKE_zhetrf_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_int* ipiv, lapack_complex_double* work, + lapack_int lwork ); + +lapack_int LAPACKE_chetri_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + const lapack_int* ipiv, + lapack_complex_float* work ); +lapack_int LAPACKE_zhetri_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + const lapack_int* ipiv, + lapack_complex_double* work ); + +lapack_int LAPACKE_chetrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zhetrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_chfrk_work( int matrix_order, char transr, char uplo, + char trans, lapack_int n, lapack_int k, + float alpha, const lapack_complex_float* a, + lapack_int lda, float beta, + lapack_complex_float* c ); +lapack_int LAPACKE_zhfrk_work( int matrix_order, char transr, char uplo, + char trans, lapack_int n, lapack_int k, + double alpha, const lapack_complex_double* a, + lapack_int lda, double beta, + lapack_complex_double* c ); + +lapack_int LAPACKE_shgeqz_work( int matrix_order, char job, char compq, + char compz, lapack_int n, lapack_int ilo, + lapack_int ihi, float* h, lapack_int ldh, + float* t, lapack_int ldt, float* alphar, + float* alphai, float* beta, float* q, + lapack_int ldq, float* z, lapack_int ldz, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dhgeqz_work( int matrix_order, char job, char compq, + char compz, lapack_int n, lapack_int ilo, + lapack_int ihi, double* h, lapack_int ldh, + double* t, lapack_int ldt, double* alphar, + double* alphai, double* beta, double* q, + lapack_int ldq, double* z, lapack_int ldz, + double* work, lapack_int lwork ); +lapack_int LAPACKE_chgeqz_work( int matrix_order, char job, char compq, + char compz, lapack_int n, lapack_int ilo, + lapack_int ihi, lapack_complex_float* h, + lapack_int ldh, lapack_complex_float* t, + lapack_int ldt, lapack_complex_float* alpha, + lapack_complex_float* beta, + lapack_complex_float* q, lapack_int ldq, + lapack_complex_float* z, lapack_int ldz, + lapack_complex_float* work, lapack_int lwork, + float* rwork ); +lapack_int LAPACKE_zhgeqz_work( int matrix_order, char job, char compq, + char compz, lapack_int n, lapack_int ilo, + lapack_int ihi, lapack_complex_double* h, + lapack_int ldh, lapack_complex_double* t, + lapack_int ldt, lapack_complex_double* alpha, + lapack_complex_double* beta, + lapack_complex_double* q, lapack_int ldq, + lapack_complex_double* z, lapack_int ldz, + lapack_complex_double* work, lapack_int lwork, + double* rwork ); + +lapack_int LAPACKE_chpcon_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* ap, + const lapack_int* ipiv, float anorm, + float* rcond, lapack_complex_float* work ); +lapack_int LAPACKE_zhpcon_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* ap, + const lapack_int* ipiv, double anorm, + double* rcond, lapack_complex_double* work ); + +lapack_int LAPACKE_chpev_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_complex_float* ap, float* w, + lapack_complex_float* z, lapack_int ldz, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zhpev_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_complex_double* ap, + double* w, lapack_complex_double* z, + lapack_int ldz, lapack_complex_double* work, + double* rwork ); + +lapack_int LAPACKE_chpevd_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_complex_float* ap, + float* w, lapack_complex_float* z, + lapack_int ldz, lapack_complex_float* work, + lapack_int lwork, float* rwork, + lapack_int lrwork, lapack_int* iwork, + lapack_int liwork ); +lapack_int LAPACKE_zhpevd_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_complex_double* ap, + double* w, lapack_complex_double* z, + lapack_int ldz, lapack_complex_double* work, + lapack_int lwork, double* rwork, + lapack_int lrwork, lapack_int* iwork, + lapack_int liwork ); + +lapack_int LAPACKE_chpevx_work( int matrix_order, char jobz, char range, + char uplo, lapack_int n, + lapack_complex_float* ap, float vl, float vu, + lapack_int il, lapack_int iu, float abstol, + lapack_int* m, float* w, + lapack_complex_float* z, lapack_int ldz, + lapack_complex_float* work, float* rwork, + lapack_int* iwork, lapack_int* ifail ); +lapack_int LAPACKE_zhpevx_work( int matrix_order, char jobz, char range, + char uplo, lapack_int n, + lapack_complex_double* ap, double vl, double vu, + lapack_int il, lapack_int iu, double abstol, + lapack_int* m, double* w, + lapack_complex_double* z, lapack_int ldz, + lapack_complex_double* work, double* rwork, + lapack_int* iwork, lapack_int* ifail ); + +lapack_int LAPACKE_chpgst_work( int matrix_order, lapack_int itype, char uplo, + lapack_int n, lapack_complex_float* ap, + const lapack_complex_float* bp ); +lapack_int LAPACKE_zhpgst_work( int matrix_order, lapack_int itype, char uplo, + lapack_int n, lapack_complex_double* ap, + const lapack_complex_double* bp ); + +lapack_int LAPACKE_chpgv_work( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, + lapack_complex_float* ap, + lapack_complex_float* bp, float* w, + lapack_complex_float* z, lapack_int ldz, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zhpgv_work( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, + lapack_complex_double* ap, + lapack_complex_double* bp, double* w, + lapack_complex_double* z, lapack_int ldz, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_chpgvd_work( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, + lapack_complex_float* ap, + lapack_complex_float* bp, float* w, + lapack_complex_float* z, lapack_int ldz, + lapack_complex_float* work, lapack_int lwork, + float* rwork, lapack_int lrwork, + lapack_int* iwork, lapack_int liwork ); +lapack_int LAPACKE_zhpgvd_work( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, + lapack_complex_double* ap, + lapack_complex_double* bp, double* w, + lapack_complex_double* z, lapack_int ldz, + lapack_complex_double* work, lapack_int lwork, + double* rwork, lapack_int lrwork, + lapack_int* iwork, lapack_int liwork ); + +lapack_int LAPACKE_chpgvx_work( int matrix_order, lapack_int itype, char jobz, + char range, char uplo, lapack_int n, + lapack_complex_float* ap, + lapack_complex_float* bp, float vl, float vu, + lapack_int il, lapack_int iu, float abstol, + lapack_int* m, float* w, + lapack_complex_float* z, lapack_int ldz, + lapack_complex_float* work, float* rwork, + lapack_int* iwork, lapack_int* ifail ); +lapack_int LAPACKE_zhpgvx_work( int matrix_order, lapack_int itype, char jobz, + char range, char uplo, lapack_int n, + lapack_complex_double* ap, + lapack_complex_double* bp, double vl, double vu, + lapack_int il, lapack_int iu, double abstol, + lapack_int* m, double* w, + lapack_complex_double* z, lapack_int ldz, + lapack_complex_double* work, double* rwork, + lapack_int* iwork, lapack_int* ifail ); + +lapack_int LAPACKE_chprfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* ap, + const lapack_complex_float* afp, + const lapack_int* ipiv, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* ferr, float* berr, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zhprfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, + const lapack_complex_double* ap, + const lapack_complex_double* afp, + const lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_chpsv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_float* ap, + lapack_int* ipiv, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zhpsv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_double* ap, + lapack_int* ipiv, lapack_complex_double* b, + lapack_int ldb ); + +lapack_int LAPACKE_chpsvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + const lapack_complex_float* ap, + lapack_complex_float* afp, lapack_int* ipiv, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* ferr, float* berr, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zhpsvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + const lapack_complex_double* ap, + lapack_complex_double* afp, lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_chptrd_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* ap, float* d, float* e, + lapack_complex_float* tau ); +lapack_int LAPACKE_zhptrd_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* ap, double* d, double* e, + lapack_complex_double* tau ); + +lapack_int LAPACKE_chptrf_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* ap, lapack_int* ipiv ); +lapack_int LAPACKE_zhptrf_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* ap, lapack_int* ipiv ); + +lapack_int LAPACKE_chptri_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* ap, + const lapack_int* ipiv, + lapack_complex_float* work ); +lapack_int LAPACKE_zhptri_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* ap, + const lapack_int* ipiv, + lapack_complex_double* work ); + +lapack_int LAPACKE_chptrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* ap, + const lapack_int* ipiv, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zhptrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, + const lapack_complex_double* ap, + const lapack_int* ipiv, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_shsein_work( int matrix_order, char job, char eigsrc, + char initv, lapack_logical* select, + lapack_int n, const float* h, lapack_int ldh, + float* wr, const float* wi, float* vl, + lapack_int ldvl, float* vr, lapack_int ldvr, + lapack_int mm, lapack_int* m, float* work, + lapack_int* ifaill, lapack_int* ifailr ); +lapack_int LAPACKE_dhsein_work( int matrix_order, char job, char eigsrc, + char initv, lapack_logical* select, + lapack_int n, const double* h, lapack_int ldh, + double* wr, const double* wi, double* vl, + lapack_int ldvl, double* vr, lapack_int ldvr, + lapack_int mm, lapack_int* m, double* work, + lapack_int* ifaill, lapack_int* ifailr ); +lapack_int LAPACKE_chsein_work( int matrix_order, char job, char eigsrc, + char initv, const lapack_logical* select, + lapack_int n, const lapack_complex_float* h, + lapack_int ldh, lapack_complex_float* w, + lapack_complex_float* vl, lapack_int ldvl, + lapack_complex_float* vr, lapack_int ldvr, + lapack_int mm, lapack_int* m, + lapack_complex_float* work, float* rwork, + lapack_int* ifaill, lapack_int* ifailr ); +lapack_int LAPACKE_zhsein_work( int matrix_order, char job, char eigsrc, + char initv, const lapack_logical* select, + lapack_int n, const lapack_complex_double* h, + lapack_int ldh, lapack_complex_double* w, + lapack_complex_double* vl, lapack_int ldvl, + lapack_complex_double* vr, lapack_int ldvr, + lapack_int mm, lapack_int* m, + lapack_complex_double* work, double* rwork, + lapack_int* ifaill, lapack_int* ifailr ); + +lapack_int LAPACKE_shseqr_work( int matrix_order, char job, char compz, + lapack_int n, lapack_int ilo, lapack_int ihi, + float* h, lapack_int ldh, float* wr, float* wi, + float* z, lapack_int ldz, float* work, + lapack_int lwork ); +lapack_int LAPACKE_dhseqr_work( int matrix_order, char job, char compz, + lapack_int n, lapack_int ilo, lapack_int ihi, + double* h, lapack_int ldh, double* wr, + double* wi, double* z, lapack_int ldz, + double* work, lapack_int lwork ); +lapack_int LAPACKE_chseqr_work( int matrix_order, char job, char compz, + lapack_int n, lapack_int ilo, lapack_int ihi, + lapack_complex_float* h, lapack_int ldh, + lapack_complex_float* w, + lapack_complex_float* z, lapack_int ldz, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zhseqr_work( int matrix_order, char job, char compz, + lapack_int n, lapack_int ilo, lapack_int ihi, + lapack_complex_double* h, lapack_int ldh, + lapack_complex_double* w, + lapack_complex_double* z, lapack_int ldz, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_clacgv_work( lapack_int n, lapack_complex_float* x, + lapack_int incx ); +lapack_int LAPACKE_zlacgv_work( lapack_int n, lapack_complex_double* x, + lapack_int incx ); + +lapack_int LAPACKE_slacpy_work( int matrix_order, char uplo, lapack_int m, + lapack_int n, const float* a, lapack_int lda, + float* b, lapack_int ldb ); +lapack_int LAPACKE_dlacpy_work( int matrix_order, char uplo, lapack_int m, + lapack_int n, const double* a, lapack_int lda, + double* b, lapack_int ldb ); +lapack_int LAPACKE_clacpy_work( int matrix_order, char uplo, lapack_int m, + lapack_int n, const lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zlacpy_work( int matrix_order, char uplo, lapack_int m, + lapack_int n, const lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb ); + +lapack_int LAPACKE_zlag2c_work( int matrix_order, lapack_int m, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + lapack_complex_float* sa, lapack_int ldsa ); + +lapack_int LAPACKE_slag2d_work( int matrix_order, lapack_int m, lapack_int n, + const float* sa, lapack_int ldsa, double* a, + lapack_int lda ); + +lapack_int LAPACKE_dlag2s_work( int matrix_order, lapack_int m, lapack_int n, + const double* a, lapack_int lda, float* sa, + lapack_int ldsa ); + +lapack_int LAPACKE_clag2z_work( int matrix_order, lapack_int m, lapack_int n, + const lapack_complex_float* sa, lapack_int ldsa, + lapack_complex_double* a, lapack_int lda ); + +lapack_int LAPACKE_slagge_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, const float* d, + float* a, lapack_int lda, lapack_int* iseed, + float* work ); +lapack_int LAPACKE_dlagge_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, const double* d, + double* a, lapack_int lda, lapack_int* iseed, + double* work ); +lapack_int LAPACKE_clagge_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, const float* d, + lapack_complex_float* a, lapack_int lda, + lapack_int* iseed, lapack_complex_float* work ); +lapack_int LAPACKE_zlagge_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int kl, lapack_int ku, const double* d, + lapack_complex_double* a, lapack_int lda, + lapack_int* iseed, + lapack_complex_double* work ); + +lapack_int LAPACKE_claghe_work( int matrix_order, lapack_int n, lapack_int k, + const float* d, lapack_complex_float* a, + lapack_int lda, lapack_int* iseed, + lapack_complex_float* work ); +lapack_int LAPACKE_zlaghe_work( int matrix_order, lapack_int n, lapack_int k, + const double* d, lapack_complex_double* a, + lapack_int lda, lapack_int* iseed, + lapack_complex_double* work ); + +lapack_int LAPACKE_slagsy_work( int matrix_order, lapack_int n, lapack_int k, + const float* d, float* a, lapack_int lda, + lapack_int* iseed, float* work ); +lapack_int LAPACKE_dlagsy_work( int matrix_order, lapack_int n, lapack_int k, + const double* d, double* a, lapack_int lda, + lapack_int* iseed, double* work ); +lapack_int LAPACKE_clagsy_work( int matrix_order, lapack_int n, lapack_int k, + const float* d, lapack_complex_float* a, + lapack_int lda, lapack_int* iseed, + lapack_complex_float* work ); +lapack_int LAPACKE_zlagsy_work( int matrix_order, lapack_int n, lapack_int k, + const double* d, lapack_complex_double* a, + lapack_int lda, lapack_int* iseed, + lapack_complex_double* work ); + +lapack_int LAPACKE_slapmr_work( int matrix_order, lapack_logical forwrd, + lapack_int m, lapack_int n, float* x, + lapack_int ldx, lapack_int* k ); +lapack_int LAPACKE_dlapmr_work( int matrix_order, lapack_logical forwrd, + lapack_int m, lapack_int n, double* x, + lapack_int ldx, lapack_int* k ); +lapack_int LAPACKE_clapmr_work( int matrix_order, lapack_logical forwrd, + lapack_int m, lapack_int n, + lapack_complex_float* x, lapack_int ldx, + lapack_int* k ); +lapack_int LAPACKE_zlapmr_work( int matrix_order, lapack_logical forwrd, + lapack_int m, lapack_int n, + lapack_complex_double* x, lapack_int ldx, + lapack_int* k ); + +lapack_int LAPACKE_slartgp_work( float f, float g, float* cs, float* sn, + float* r ); +lapack_int LAPACKE_dlartgp_work( double f, double g, double* cs, double* sn, + double* r ); + +lapack_int LAPACKE_slartgs_work( float x, float y, float sigma, float* cs, + float* sn ); +lapack_int LAPACKE_dlartgs_work( double x, double y, double sigma, double* cs, + double* sn ); + +float LAPACKE_slapy2_work( float x, float y ); +double LAPACKE_dlapy2_work( double x, double y ); + +float LAPACKE_slapy3_work( float x, float y, float z ); +double LAPACKE_dlapy3_work( double x, double y, double z ); + +float LAPACKE_slamch_work( char cmach ); +double LAPACKE_dlamch_work( char cmach ); + +float LAPACKE_slange_work( int matrix_order, char norm, lapack_int m, + lapack_int n, const float* a, lapack_int lda, + float* work ); +double LAPACKE_dlange_work( int matrix_order, char norm, lapack_int m, + lapack_int n, const double* a, lapack_int lda, + double* work ); +float LAPACKE_clange_work( int matrix_order, char norm, lapack_int m, + lapack_int n, const lapack_complex_float* a, + lapack_int lda, float* work ); +double LAPACKE_zlange_work( int matrix_order, char norm, lapack_int m, + lapack_int n, const lapack_complex_double* a, + lapack_int lda, double* work ); + +float LAPACKE_clanhe_work( int matrix_order, char norm, char uplo, + lapack_int n, const lapack_complex_float* a, + lapack_int lda, float* work ); +double LAPACKE_zlanhe_work( int matrix_order, char norm, char uplo, + lapack_int n, const lapack_complex_double* a, + lapack_int lda, double* work ); + +float LAPACKE_slansy_work( int matrix_order, char norm, char uplo, + lapack_int n, const float* a, lapack_int lda, + float* work ); +double LAPACKE_dlansy_work( int matrix_order, char norm, char uplo, + lapack_int n, const double* a, lapack_int lda, + double* work ); +float LAPACKE_clansy_work( int matrix_order, char norm, char uplo, + lapack_int n, const lapack_complex_float* a, + lapack_int lda, float* work ); +double LAPACKE_zlansy_work( int matrix_order, char norm, char uplo, + lapack_int n, const lapack_complex_double* a, + lapack_int lda, double* work ); + +float LAPACKE_slantr_work( int matrix_order, char norm, char uplo, + char diag, lapack_int m, lapack_int n, const float* a, + lapack_int lda, float* work ); +double LAPACKE_dlantr_work( int matrix_order, char norm, char uplo, + char diag, lapack_int m, lapack_int n, + const double* a, lapack_int lda, double* work ); +float LAPACKE_clantr_work( int matrix_order, char norm, char uplo, + char diag, lapack_int m, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + float* work ); +double LAPACKE_zlantr_work( int matrix_order, char norm, char uplo, + char diag, lapack_int m, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + double* work ); + +lapack_int LAPACKE_slarfb_work( int matrix_order, char side, char trans, + char direct, char storev, lapack_int m, + lapack_int n, lapack_int k, const float* v, + lapack_int ldv, const float* t, lapack_int ldt, + float* c, lapack_int ldc, float* work, + lapack_int ldwork ); +lapack_int LAPACKE_dlarfb_work( int matrix_order, char side, char trans, + char direct, char storev, lapack_int m, + lapack_int n, lapack_int k, const double* v, + lapack_int ldv, const double* t, lapack_int ldt, + double* c, lapack_int ldc, double* work, + lapack_int ldwork ); +lapack_int LAPACKE_clarfb_work( int matrix_order, char side, char trans, + char direct, char storev, lapack_int m, + lapack_int n, lapack_int k, + const lapack_complex_float* v, lapack_int ldv, + const lapack_complex_float* t, lapack_int ldt, + lapack_complex_float* c, lapack_int ldc, + lapack_complex_float* work, lapack_int ldwork ); +lapack_int LAPACKE_zlarfb_work( int matrix_order, char side, char trans, + char direct, char storev, lapack_int m, + lapack_int n, lapack_int k, + const lapack_complex_double* v, lapack_int ldv, + const lapack_complex_double* t, lapack_int ldt, + lapack_complex_double* c, lapack_int ldc, + lapack_complex_double* work, + lapack_int ldwork ); + +lapack_int LAPACKE_slarfg_work( lapack_int n, float* alpha, float* x, + lapack_int incx, float* tau ); +lapack_int LAPACKE_dlarfg_work( lapack_int n, double* alpha, double* x, + lapack_int incx, double* tau ); +lapack_int LAPACKE_clarfg_work( lapack_int n, lapack_complex_float* alpha, + lapack_complex_float* x, lapack_int incx, + lapack_complex_float* tau ); +lapack_int LAPACKE_zlarfg_work( lapack_int n, lapack_complex_double* alpha, + lapack_complex_double* x, lapack_int incx, + lapack_complex_double* tau ); + +lapack_int LAPACKE_slarft_work( int matrix_order, char direct, char storev, + lapack_int n, lapack_int k, const float* v, + lapack_int ldv, const float* tau, float* t, + lapack_int ldt ); +lapack_int LAPACKE_dlarft_work( int matrix_order, char direct, char storev, + lapack_int n, lapack_int k, const double* v, + lapack_int ldv, const double* tau, double* t, + lapack_int ldt ); +lapack_int LAPACKE_clarft_work( int matrix_order, char direct, char storev, + lapack_int n, lapack_int k, + const lapack_complex_float* v, lapack_int ldv, + const lapack_complex_float* tau, + lapack_complex_float* t, lapack_int ldt ); +lapack_int LAPACKE_zlarft_work( int matrix_order, char direct, char storev, + lapack_int n, lapack_int k, + const lapack_complex_double* v, lapack_int ldv, + const lapack_complex_double* tau, + lapack_complex_double* t, lapack_int ldt ); + +lapack_int LAPACKE_slarfx_work( int matrix_order, char side, lapack_int m, + lapack_int n, const float* v, float tau, + float* c, lapack_int ldc, float* work ); +lapack_int LAPACKE_dlarfx_work( int matrix_order, char side, lapack_int m, + lapack_int n, const double* v, double tau, + double* c, lapack_int ldc, double* work ); +lapack_int LAPACKE_clarfx_work( int matrix_order, char side, lapack_int m, + lapack_int n, const lapack_complex_float* v, + lapack_complex_float tau, + lapack_complex_float* c, lapack_int ldc, + lapack_complex_float* work ); +lapack_int LAPACKE_zlarfx_work( int matrix_order, char side, lapack_int m, + lapack_int n, const lapack_complex_double* v, + lapack_complex_double tau, + lapack_complex_double* c, lapack_int ldc, + lapack_complex_double* work ); + +lapack_int LAPACKE_slarnv_work( lapack_int idist, lapack_int* iseed, + lapack_int n, float* x ); +lapack_int LAPACKE_dlarnv_work( lapack_int idist, lapack_int* iseed, + lapack_int n, double* x ); +lapack_int LAPACKE_clarnv_work( lapack_int idist, lapack_int* iseed, + lapack_int n, lapack_complex_float* x ); +lapack_int LAPACKE_zlarnv_work( lapack_int idist, lapack_int* iseed, + lapack_int n, lapack_complex_double* x ); + +lapack_int LAPACKE_slaset_work( int matrix_order, char uplo, lapack_int m, + lapack_int n, float alpha, float beta, float* a, + lapack_int lda ); +lapack_int LAPACKE_dlaset_work( int matrix_order, char uplo, lapack_int m, + lapack_int n, double alpha, double beta, + double* a, lapack_int lda ); +lapack_int LAPACKE_claset_work( int matrix_order, char uplo, lapack_int m, + lapack_int n, lapack_complex_float alpha, + lapack_complex_float beta, + lapack_complex_float* a, lapack_int lda ); +lapack_int LAPACKE_zlaset_work( int matrix_order, char uplo, lapack_int m, + lapack_int n, lapack_complex_double alpha, + lapack_complex_double beta, + lapack_complex_double* a, lapack_int lda ); + +lapack_int LAPACKE_slasrt_work( char id, lapack_int n, float* d ); +lapack_int LAPACKE_dlasrt_work( char id, lapack_int n, double* d ); + +lapack_int LAPACKE_slaswp_work( int matrix_order, lapack_int n, float* a, + lapack_int lda, lapack_int k1, lapack_int k2, + const lapack_int* ipiv, lapack_int incx ); +lapack_int LAPACKE_dlaswp_work( int matrix_order, lapack_int n, double* a, + lapack_int lda, lapack_int k1, lapack_int k2, + const lapack_int* ipiv, lapack_int incx ); +lapack_int LAPACKE_claswp_work( int matrix_order, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_int k1, lapack_int k2, + const lapack_int* ipiv, lapack_int incx ); +lapack_int LAPACKE_zlaswp_work( int matrix_order, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_int k1, lapack_int k2, + const lapack_int* ipiv, lapack_int incx ); + +lapack_int LAPACKE_slatms_work( int matrix_order, lapack_int m, lapack_int n, + char dist, lapack_int* iseed, char sym, + float* d, lapack_int mode, float cond, + float dmax, lapack_int kl, lapack_int ku, + char pack, float* a, lapack_int lda, + float* work ); +lapack_int LAPACKE_dlatms_work( int matrix_order, lapack_int m, lapack_int n, + char dist, lapack_int* iseed, char sym, + double* d, lapack_int mode, double cond, + double dmax, lapack_int kl, lapack_int ku, + char pack, double* a, lapack_int lda, + double* work ); +lapack_int LAPACKE_clatms_work( int matrix_order, lapack_int m, lapack_int n, + char dist, lapack_int* iseed, char sym, + float* d, lapack_int mode, float cond, + float dmax, lapack_int kl, lapack_int ku, + char pack, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* work ); +lapack_int LAPACKE_zlatms_work( int matrix_order, lapack_int m, lapack_int n, + char dist, lapack_int* iseed, char sym, + double* d, lapack_int mode, double cond, + double dmax, lapack_int kl, lapack_int ku, + char pack, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* work ); + +lapack_int LAPACKE_slauum_work( int matrix_order, char uplo, lapack_int n, + float* a, lapack_int lda ); +lapack_int LAPACKE_dlauum_work( int matrix_order, char uplo, lapack_int n, + double* a, lapack_int lda ); +lapack_int LAPACKE_clauum_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda ); +lapack_int LAPACKE_zlauum_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda ); + +lapack_int LAPACKE_sopgtr_work( int matrix_order, char uplo, lapack_int n, + const float* ap, const float* tau, float* q, + lapack_int ldq, float* work ); +lapack_int LAPACKE_dopgtr_work( int matrix_order, char uplo, lapack_int n, + const double* ap, const double* tau, double* q, + lapack_int ldq, double* work ); + +lapack_int LAPACKE_sopmtr_work( int matrix_order, char side, char uplo, + char trans, lapack_int m, lapack_int n, + const float* ap, const float* tau, float* c, + lapack_int ldc, float* work ); +lapack_int LAPACKE_dopmtr_work( int matrix_order, char side, char uplo, + char trans, lapack_int m, lapack_int n, + const double* ap, const double* tau, double* c, + lapack_int ldc, double* work ); + +lapack_int LAPACKE_sorgbr_work( int matrix_order, char vect, lapack_int m, + lapack_int n, lapack_int k, float* a, + lapack_int lda, const float* tau, float* work, + lapack_int lwork ); +lapack_int LAPACKE_dorgbr_work( int matrix_order, char vect, lapack_int m, + lapack_int n, lapack_int k, double* a, + lapack_int lda, const double* tau, double* work, + lapack_int lwork ); + +lapack_int LAPACKE_sorghr_work( int matrix_order, lapack_int n, lapack_int ilo, + lapack_int ihi, float* a, lapack_int lda, + const float* tau, float* work, + lapack_int lwork ); +lapack_int LAPACKE_dorghr_work( int matrix_order, lapack_int n, lapack_int ilo, + lapack_int ihi, double* a, lapack_int lda, + const double* tau, double* work, + lapack_int lwork ); + +lapack_int LAPACKE_sorglq_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, float* a, lapack_int lda, + const float* tau, float* work, + lapack_int lwork ); +lapack_int LAPACKE_dorglq_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, double* a, lapack_int lda, + const double* tau, double* work, + lapack_int lwork ); + +lapack_int LAPACKE_sorgql_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, float* a, lapack_int lda, + const float* tau, float* work, + lapack_int lwork ); +lapack_int LAPACKE_dorgql_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, double* a, lapack_int lda, + const double* tau, double* work, + lapack_int lwork ); + +lapack_int LAPACKE_sorgqr_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, float* a, lapack_int lda, + const float* tau, float* work, + lapack_int lwork ); +lapack_int LAPACKE_dorgqr_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, double* a, lapack_int lda, + const double* tau, double* work, + lapack_int lwork ); + +lapack_int LAPACKE_sorgrq_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, float* a, lapack_int lda, + const float* tau, float* work, + lapack_int lwork ); +lapack_int LAPACKE_dorgrq_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, double* a, lapack_int lda, + const double* tau, double* work, + lapack_int lwork ); + +lapack_int LAPACKE_sorgtr_work( int matrix_order, char uplo, lapack_int n, + float* a, lapack_int lda, const float* tau, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dorgtr_work( int matrix_order, char uplo, lapack_int n, + double* a, lapack_int lda, const double* tau, + double* work, lapack_int lwork ); + +lapack_int LAPACKE_sormbr_work( int matrix_order, char vect, char side, + char trans, lapack_int m, lapack_int n, + lapack_int k, const float* a, lapack_int lda, + const float* tau, float* c, lapack_int ldc, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dormbr_work( int matrix_order, char vect, char side, + char trans, lapack_int m, lapack_int n, + lapack_int k, const double* a, lapack_int lda, + const double* tau, double* c, lapack_int ldc, + double* work, lapack_int lwork ); + +lapack_int LAPACKE_sormhr_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int ilo, + lapack_int ihi, const float* a, lapack_int lda, + const float* tau, float* c, lapack_int ldc, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dormhr_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int ilo, + lapack_int ihi, const double* a, lapack_int lda, + const double* tau, double* c, lapack_int ldc, + double* work, lapack_int lwork ); + +lapack_int LAPACKE_sormlq_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const float* a, lapack_int lda, + const float* tau, float* c, lapack_int ldc, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dormlq_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const double* a, lapack_int lda, + const double* tau, double* c, lapack_int ldc, + double* work, lapack_int lwork ); + +lapack_int LAPACKE_sormql_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const float* a, lapack_int lda, + const float* tau, float* c, lapack_int ldc, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dormql_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const double* a, lapack_int lda, + const double* tau, double* c, lapack_int ldc, + double* work, lapack_int lwork ); + +lapack_int LAPACKE_sormqr_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const float* a, lapack_int lda, + const float* tau, float* c, lapack_int ldc, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dormqr_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const double* a, lapack_int lda, + const double* tau, double* c, lapack_int ldc, + double* work, lapack_int lwork ); + +lapack_int LAPACKE_sormrq_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const float* a, lapack_int lda, + const float* tau, float* c, lapack_int ldc, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dormrq_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const double* a, lapack_int lda, + const double* tau, double* c, lapack_int ldc, + double* work, lapack_int lwork ); + +lapack_int LAPACKE_sormrz_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int l, const float* a, lapack_int lda, + const float* tau, float* c, lapack_int ldc, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dormrz_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int l, const double* a, lapack_int lda, + const double* tau, double* c, lapack_int ldc, + double* work, lapack_int lwork ); + +lapack_int LAPACKE_sormtr_work( int matrix_order, char side, char uplo, + char trans, lapack_int m, lapack_int n, + const float* a, lapack_int lda, + const float* tau, float* c, lapack_int ldc, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dormtr_work( int matrix_order, char side, char uplo, + char trans, lapack_int m, lapack_int n, + const double* a, lapack_int lda, + const double* tau, double* c, lapack_int ldc, + double* work, lapack_int lwork ); + +lapack_int LAPACKE_spbcon_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, const float* ab, lapack_int ldab, + float anorm, float* rcond, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dpbcon_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, const double* ab, + lapack_int ldab, double anorm, double* rcond, + double* work, lapack_int* iwork ); +lapack_int LAPACKE_cpbcon_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, const lapack_complex_float* ab, + lapack_int ldab, float anorm, float* rcond, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zpbcon_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, const lapack_complex_double* ab, + lapack_int ldab, double anorm, double* rcond, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_spbequ_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, const float* ab, lapack_int ldab, + float* s, float* scond, float* amax ); +lapack_int LAPACKE_dpbequ_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, const double* ab, + lapack_int ldab, double* s, double* scond, + double* amax ); +lapack_int LAPACKE_cpbequ_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, const lapack_complex_float* ab, + lapack_int ldab, float* s, float* scond, + float* amax ); +lapack_int LAPACKE_zpbequ_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, const lapack_complex_double* ab, + lapack_int ldab, double* s, double* scond, + double* amax ); + +lapack_int LAPACKE_spbrfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, const float* ab, + lapack_int ldab, const float* afb, + lapack_int ldafb, const float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* ferr, float* berr, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dpbrfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, + const double* ab, lapack_int ldab, + const double* afb, lapack_int ldafb, + const double* b, lapack_int ldb, double* x, + lapack_int ldx, double* ferr, double* berr, + double* work, lapack_int* iwork ); +lapack_int LAPACKE_cpbrfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, + const lapack_complex_float* ab, lapack_int ldab, + const lapack_complex_float* afb, + lapack_int ldafb, const lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* x, + lapack_int ldx, float* ferr, float* berr, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zpbrfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, + const lapack_complex_double* ab, + lapack_int ldab, + const lapack_complex_double* afb, + lapack_int ldafb, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_spbstf_work( int matrix_order, char uplo, lapack_int n, + lapack_int kb, float* bb, lapack_int ldbb ); +lapack_int LAPACKE_dpbstf_work( int matrix_order, char uplo, lapack_int n, + lapack_int kb, double* bb, lapack_int ldbb ); +lapack_int LAPACKE_cpbstf_work( int matrix_order, char uplo, lapack_int n, + lapack_int kb, lapack_complex_float* bb, + lapack_int ldbb ); +lapack_int LAPACKE_zpbstf_work( int matrix_order, char uplo, lapack_int n, + lapack_int kb, lapack_complex_double* bb, + lapack_int ldbb ); + +lapack_int LAPACKE_spbsv_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, float* ab, + lapack_int ldab, float* b, lapack_int ldb ); +lapack_int LAPACKE_dpbsv_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, double* ab, + lapack_int ldab, double* b, lapack_int ldb ); +lapack_int LAPACKE_cpbsv_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, + lapack_complex_float* ab, lapack_int ldab, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zpbsv_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, + lapack_complex_double* ab, lapack_int ldab, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_spbsvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int kd, lapack_int nrhs, + float* ab, lapack_int ldab, float* afb, + lapack_int ldafb, char* equed, float* s, + float* b, lapack_int ldb, float* x, + lapack_int ldx, float* rcond, float* ferr, + float* berr, float* work, lapack_int* iwork ); +lapack_int LAPACKE_dpbsvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int kd, lapack_int nrhs, + double* ab, lapack_int ldab, double* afb, + lapack_int ldafb, char* equed, double* s, + double* b, lapack_int ldb, double* x, + lapack_int ldx, double* rcond, double* ferr, + double* berr, double* work, lapack_int* iwork ); +lapack_int LAPACKE_cpbsvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int kd, lapack_int nrhs, + lapack_complex_float* ab, lapack_int ldab, + lapack_complex_float* afb, lapack_int ldafb, + char* equed, float* s, lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* x, + lapack_int ldx, float* rcond, float* ferr, + float* berr, lapack_complex_float* work, + float* rwork ); +lapack_int LAPACKE_zpbsvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int kd, lapack_int nrhs, + lapack_complex_double* ab, lapack_int ldab, + lapack_complex_double* afb, lapack_int ldafb, + char* equed, double* s, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_spbtrf_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, float* ab, lapack_int ldab ); +lapack_int LAPACKE_dpbtrf_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, double* ab, lapack_int ldab ); +lapack_int LAPACKE_cpbtrf_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_complex_float* ab, + lapack_int ldab ); +lapack_int LAPACKE_zpbtrf_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_complex_double* ab, + lapack_int ldab ); + +lapack_int LAPACKE_spbtrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, const float* ab, + lapack_int ldab, float* b, lapack_int ldb ); +lapack_int LAPACKE_dpbtrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, + const double* ab, lapack_int ldab, double* b, + lapack_int ldb ); +lapack_int LAPACKE_cpbtrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, + const lapack_complex_float* ab, lapack_int ldab, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zpbtrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int kd, lapack_int nrhs, + const lapack_complex_double* ab, + lapack_int ldab, lapack_complex_double* b, + lapack_int ldb ); + +lapack_int LAPACKE_spftrf_work( int matrix_order, char transr, char uplo, + lapack_int n, float* a ); +lapack_int LAPACKE_dpftrf_work( int matrix_order, char transr, char uplo, + lapack_int n, double* a ); +lapack_int LAPACKE_cpftrf_work( int matrix_order, char transr, char uplo, + lapack_int n, lapack_complex_float* a ); +lapack_int LAPACKE_zpftrf_work( int matrix_order, char transr, char uplo, + lapack_int n, lapack_complex_double* a ); + +lapack_int LAPACKE_spftri_work( int matrix_order, char transr, char uplo, + lapack_int n, float* a ); +lapack_int LAPACKE_dpftri_work( int matrix_order, char transr, char uplo, + lapack_int n, double* a ); +lapack_int LAPACKE_cpftri_work( int matrix_order, char transr, char uplo, + lapack_int n, lapack_complex_float* a ); +lapack_int LAPACKE_zpftri_work( int matrix_order, char transr, char uplo, + lapack_int n, lapack_complex_double* a ); + +lapack_int LAPACKE_spftrs_work( int matrix_order, char transr, char uplo, + lapack_int n, lapack_int nrhs, const float* a, + float* b, lapack_int ldb ); +lapack_int LAPACKE_dpftrs_work( int matrix_order, char transr, char uplo, + lapack_int n, lapack_int nrhs, const double* a, + double* b, lapack_int ldb ); +lapack_int LAPACKE_cpftrs_work( int matrix_order, char transr, char uplo, + lapack_int n, lapack_int nrhs, + const lapack_complex_float* a, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zpftrs_work( int matrix_order, char transr, char uplo, + lapack_int n, lapack_int nrhs, + const lapack_complex_double* a, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_spocon_work( int matrix_order, char uplo, lapack_int n, + const float* a, lapack_int lda, float anorm, + float* rcond, float* work, lapack_int* iwork ); +lapack_int LAPACKE_dpocon_work( int matrix_order, char uplo, lapack_int n, + const double* a, lapack_int lda, double anorm, + double* rcond, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_cpocon_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + float anorm, float* rcond, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zpocon_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + double anorm, double* rcond, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_spoequ_work( int matrix_order, lapack_int n, const float* a, + lapack_int lda, float* s, float* scond, + float* amax ); +lapack_int LAPACKE_dpoequ_work( int matrix_order, lapack_int n, const double* a, + lapack_int lda, double* s, double* scond, + double* amax ); +lapack_int LAPACKE_cpoequ_work( int matrix_order, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + float* s, float* scond, float* amax ); +lapack_int LAPACKE_zpoequ_work( int matrix_order, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + double* s, double* scond, double* amax ); + +lapack_int LAPACKE_spoequb_work( int matrix_order, lapack_int n, const float* a, + lapack_int lda, float* s, float* scond, + float* amax ); +lapack_int LAPACKE_dpoequb_work( int matrix_order, lapack_int n, + const double* a, lapack_int lda, double* s, + double* scond, double* amax ); +lapack_int LAPACKE_cpoequb_work( int matrix_order, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + float* s, float* scond, float* amax ); +lapack_int LAPACKE_zpoequb_work( int matrix_order, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + double* s, double* scond, double* amax ); + +lapack_int LAPACKE_sporfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* a, lapack_int lda, + const float* af, lapack_int ldaf, + const float* b, lapack_int ldb, float* x, + lapack_int ldx, float* ferr, float* berr, + float* work, lapack_int* iwork ); +lapack_int LAPACKE_dporfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* a, + lapack_int lda, const double* af, + lapack_int ldaf, const double* b, + lapack_int ldb, double* x, lapack_int ldx, + double* ferr, double* berr, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_cporfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* af, + lapack_int ldaf, const lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* x, + lapack_int ldx, float* ferr, float* berr, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zporfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, const lapack_complex_double* af, + lapack_int ldaf, const lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* x, + lapack_int ldx, double* ferr, double* berr, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_sporfsx_work( int matrix_order, char uplo, char equed, + lapack_int n, lapack_int nrhs, const float* a, + lapack_int lda, const float* af, + lapack_int ldaf, const float* s, + const float* b, lapack_int ldb, float* x, + lapack_int ldx, float* rcond, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dporfsx_work( int matrix_order, char uplo, char equed, + lapack_int n, lapack_int nrhs, const double* a, + lapack_int lda, const double* af, + lapack_int ldaf, const double* s, + const double* b, lapack_int ldb, double* x, + lapack_int ldx, double* rcond, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_cporfsx_work( int matrix_order, char uplo, char equed, + lapack_int n, lapack_int nrhs, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* af, + lapack_int ldaf, const float* s, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params, lapack_complex_float* work, + float* rwork ); +lapack_int LAPACKE_zporfsx_work( int matrix_order, char uplo, char equed, + lapack_int n, lapack_int nrhs, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* af, + lapack_int ldaf, const double* s, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params, lapack_complex_double* work, + double* rwork ); + +lapack_int LAPACKE_sposv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, float* a, lapack_int lda, + float* b, lapack_int ldb ); +lapack_int LAPACKE_dposv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, double* a, lapack_int lda, + double* b, lapack_int ldb ); +lapack_int LAPACKE_cposv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zposv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb ); +lapack_int LAPACKE_dsposv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, double* a, lapack_int lda, + double* b, lapack_int ldb, double* x, + lapack_int ldx, double* work, float* swork, + lapack_int* iter ); +lapack_int LAPACKE_zcposv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* x, + lapack_int ldx, lapack_complex_double* work, + lapack_complex_float* swork, double* rwork, + lapack_int* iter ); + +lapack_int LAPACKE_sposvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, float* a, + lapack_int lda, float* af, lapack_int ldaf, + char* equed, float* s, float* b, lapack_int ldb, + float* x, lapack_int ldx, float* rcond, + float* ferr, float* berr, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dposvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, double* a, + lapack_int lda, double* af, lapack_int ldaf, + char* equed, double* s, double* b, + lapack_int ldb, double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr, + double* work, lapack_int* iwork ); +lapack_int LAPACKE_cposvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* af, lapack_int ldaf, + char* equed, float* s, lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* x, + lapack_int ldx, float* rcond, float* ferr, + float* berr, lapack_complex_float* work, + float* rwork ); +lapack_int LAPACKE_zposvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* af, lapack_int ldaf, + char* equed, double* s, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_sposvxx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, float* a, + lapack_int lda, float* af, lapack_int ldaf, + char* equed, float* s, float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* rcond, float* rpvgrw, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dposvxx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, double* a, + lapack_int lda, double* af, lapack_int ldaf, + char* equed, double* s, double* b, + lapack_int ldb, double* x, lapack_int ldx, + double* rcond, double* rpvgrw, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_cposvxx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* af, lapack_int ldaf, + char* equed, float* s, lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* x, + lapack_int ldx, float* rcond, float* rpvgrw, + float* berr, lapack_int n_err_bnds, + float* err_bnds_norm, float* err_bnds_comp, + lapack_int nparams, float* params, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zposvxx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* af, lapack_int ldaf, + char* equed, double* s, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* rpvgrw, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params, lapack_complex_double* work, + double* rwork ); + +lapack_int LAPACKE_spotrf_work( int matrix_order, char uplo, lapack_int n, + float* a, lapack_int lda ); +lapack_int LAPACKE_dpotrf_work( int matrix_order, char uplo, lapack_int n, + double* a, lapack_int lda ); +lapack_int LAPACKE_cpotrf_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda ); +lapack_int LAPACKE_zpotrf_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda ); + +lapack_int LAPACKE_spotri_work( int matrix_order, char uplo, lapack_int n, + float* a, lapack_int lda ); +lapack_int LAPACKE_dpotri_work( int matrix_order, char uplo, lapack_int n, + double* a, lapack_int lda ); +lapack_int LAPACKE_cpotri_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda ); +lapack_int LAPACKE_zpotri_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda ); + +lapack_int LAPACKE_spotrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* a, lapack_int lda, + float* b, lapack_int ldb ); +lapack_int LAPACKE_dpotrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* a, + lapack_int lda, double* b, lapack_int ldb ); +lapack_int LAPACKE_cpotrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zpotrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, lapack_complex_double* b, + lapack_int ldb ); + +lapack_int LAPACKE_sppcon_work( int matrix_order, char uplo, lapack_int n, + const float* ap, float anorm, float* rcond, + float* work, lapack_int* iwork ); +lapack_int LAPACKE_dppcon_work( int matrix_order, char uplo, lapack_int n, + const double* ap, double anorm, double* rcond, + double* work, lapack_int* iwork ); +lapack_int LAPACKE_cppcon_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* ap, float anorm, + float* rcond, lapack_complex_float* work, + float* rwork ); +lapack_int LAPACKE_zppcon_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* ap, double anorm, + double* rcond, lapack_complex_double* work, + double* rwork ); + +lapack_int LAPACKE_sppequ_work( int matrix_order, char uplo, lapack_int n, + const float* ap, float* s, float* scond, + float* amax ); +lapack_int LAPACKE_dppequ_work( int matrix_order, char uplo, lapack_int n, + const double* ap, double* s, double* scond, + double* amax ); +lapack_int LAPACKE_cppequ_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* ap, float* s, + float* scond, float* amax ); +lapack_int LAPACKE_zppequ_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* ap, double* s, + double* scond, double* amax ); + +lapack_int LAPACKE_spprfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* ap, + const float* afp, const float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* ferr, float* berr, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dpprfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* ap, + const double* afp, const double* b, + lapack_int ldb, double* x, lapack_int ldx, + double* ferr, double* berr, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_cpprfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* ap, + const lapack_complex_float* afp, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* ferr, float* berr, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zpprfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, + const lapack_complex_double* ap, + const lapack_complex_double* afp, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_sppsv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, float* ap, float* b, + lapack_int ldb ); +lapack_int LAPACKE_dppsv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, double* ap, double* b, + lapack_int ldb ); +lapack_int LAPACKE_cppsv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_float* ap, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zppsv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_double* ap, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_sppsvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, float* ap, + float* afp, char* equed, float* s, float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* rcond, float* ferr, float* berr, + float* work, lapack_int* iwork ); +lapack_int LAPACKE_dppsvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, double* ap, + double* afp, char* equed, double* s, double* b, + lapack_int ldb, double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr, + double* work, lapack_int* iwork ); +lapack_int LAPACKE_cppsvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + lapack_complex_float* ap, + lapack_complex_float* afp, char* equed, + float* s, lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* x, + lapack_int ldx, float* rcond, float* ferr, + float* berr, lapack_complex_float* work, + float* rwork ); +lapack_int LAPACKE_zppsvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + lapack_complex_double* ap, + lapack_complex_double* afp, char* equed, + double* s, lapack_complex_double* b, + lapack_int ldb, lapack_complex_double* x, + lapack_int ldx, double* rcond, double* ferr, + double* berr, lapack_complex_double* work, + double* rwork ); + +lapack_int LAPACKE_spptrf_work( int matrix_order, char uplo, lapack_int n, + float* ap ); +lapack_int LAPACKE_dpptrf_work( int matrix_order, char uplo, lapack_int n, + double* ap ); +lapack_int LAPACKE_cpptrf_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* ap ); +lapack_int LAPACKE_zpptrf_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* ap ); + +lapack_int LAPACKE_spptri_work( int matrix_order, char uplo, lapack_int n, + float* ap ); +lapack_int LAPACKE_dpptri_work( int matrix_order, char uplo, lapack_int n, + double* ap ); +lapack_int LAPACKE_cpptri_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* ap ); +lapack_int LAPACKE_zpptri_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* ap ); + +lapack_int LAPACKE_spptrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* ap, float* b, + lapack_int ldb ); +lapack_int LAPACKE_dpptrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* ap, double* b, + lapack_int ldb ); +lapack_int LAPACKE_cpptrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* ap, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zpptrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, + const lapack_complex_double* ap, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_spstrf_work( int matrix_order, char uplo, lapack_int n, + float* a, lapack_int lda, lapack_int* piv, + lapack_int* rank, float tol, float* work ); +lapack_int LAPACKE_dpstrf_work( int matrix_order, char uplo, lapack_int n, + double* a, lapack_int lda, lapack_int* piv, + lapack_int* rank, double tol, double* work ); +lapack_int LAPACKE_cpstrf_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_int* piv, lapack_int* rank, float tol, + float* work ); +lapack_int LAPACKE_zpstrf_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_int* piv, lapack_int* rank, double tol, + double* work ); + +lapack_int LAPACKE_sptcon_work( lapack_int n, const float* d, const float* e, + float anorm, float* rcond, float* work ); +lapack_int LAPACKE_dptcon_work( lapack_int n, const double* d, const double* e, + double anorm, double* rcond, double* work ); +lapack_int LAPACKE_cptcon_work( lapack_int n, const float* d, + const lapack_complex_float* e, float anorm, + float* rcond, float* work ); +lapack_int LAPACKE_zptcon_work( lapack_int n, const double* d, + const lapack_complex_double* e, double anorm, + double* rcond, double* work ); + +lapack_int LAPACKE_spteqr_work( int matrix_order, char compz, lapack_int n, + float* d, float* e, float* z, lapack_int ldz, + float* work ); +lapack_int LAPACKE_dpteqr_work( int matrix_order, char compz, lapack_int n, + double* d, double* e, double* z, lapack_int ldz, + double* work ); +lapack_int LAPACKE_cpteqr_work( int matrix_order, char compz, lapack_int n, + float* d, float* e, lapack_complex_float* z, + lapack_int ldz, float* work ); +lapack_int LAPACKE_zpteqr_work( int matrix_order, char compz, lapack_int n, + double* d, double* e, lapack_complex_double* z, + lapack_int ldz, double* work ); + +lapack_int LAPACKE_sptrfs_work( int matrix_order, lapack_int n, lapack_int nrhs, + const float* d, const float* e, const float* df, + const float* ef, const float* b, lapack_int ldb, + float* x, lapack_int ldx, float* ferr, + float* berr, float* work ); +lapack_int LAPACKE_dptrfs_work( int matrix_order, lapack_int n, lapack_int nrhs, + const double* d, const double* e, + const double* df, const double* ef, + const double* b, lapack_int ldb, double* x, + lapack_int ldx, double* ferr, double* berr, + double* work ); +lapack_int LAPACKE_cptrfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* d, + const lapack_complex_float* e, const float* df, + const lapack_complex_float* ef, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* ferr, float* berr, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zptrfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* d, + const lapack_complex_double* e, + const double* df, + const lapack_complex_double* ef, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_sptsv_work( int matrix_order, lapack_int n, lapack_int nrhs, + float* d, float* e, float* b, lapack_int ldb ); +lapack_int LAPACKE_dptsv_work( int matrix_order, lapack_int n, lapack_int nrhs, + double* d, double* e, double* b, + lapack_int ldb ); +lapack_int LAPACKE_cptsv_work( int matrix_order, lapack_int n, lapack_int nrhs, + float* d, lapack_complex_float* e, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zptsv_work( int matrix_order, lapack_int n, lapack_int nrhs, + double* d, lapack_complex_double* e, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_sptsvx_work( int matrix_order, char fact, lapack_int n, + lapack_int nrhs, const float* d, const float* e, + float* df, float* ef, const float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* rcond, float* ferr, float* berr, + float* work ); +lapack_int LAPACKE_dptsvx_work( int matrix_order, char fact, lapack_int n, + lapack_int nrhs, const double* d, + const double* e, double* df, double* ef, + const double* b, lapack_int ldb, double* x, + lapack_int ldx, double* rcond, double* ferr, + double* berr, double* work ); +lapack_int LAPACKE_cptsvx_work( int matrix_order, char fact, lapack_int n, + lapack_int nrhs, const float* d, + const lapack_complex_float* e, float* df, + lapack_complex_float* ef, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* ferr, float* berr, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zptsvx_work( int matrix_order, char fact, lapack_int n, + lapack_int nrhs, const double* d, + const lapack_complex_double* e, double* df, + lapack_complex_double* ef, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_spttrf_work( lapack_int n, float* d, float* e ); +lapack_int LAPACKE_dpttrf_work( lapack_int n, double* d, double* e ); +lapack_int LAPACKE_cpttrf_work( lapack_int n, float* d, + lapack_complex_float* e ); +lapack_int LAPACKE_zpttrf_work( lapack_int n, double* d, + lapack_complex_double* e ); + +lapack_int LAPACKE_spttrs_work( int matrix_order, lapack_int n, lapack_int nrhs, + const float* d, const float* e, float* b, + lapack_int ldb ); +lapack_int LAPACKE_dpttrs_work( int matrix_order, lapack_int n, lapack_int nrhs, + const double* d, const double* e, double* b, + lapack_int ldb ); +lapack_int LAPACKE_cpttrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* d, + const lapack_complex_float* e, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zpttrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* d, + const lapack_complex_double* e, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_ssbev_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_int kd, float* ab, + lapack_int ldab, float* w, float* z, + lapack_int ldz, float* work ); +lapack_int LAPACKE_dsbev_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_int kd, double* ab, + lapack_int ldab, double* w, double* z, + lapack_int ldz, double* work ); + +lapack_int LAPACKE_ssbevd_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_int kd, float* ab, + lapack_int ldab, float* w, float* z, + lapack_int ldz, float* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); +lapack_int LAPACKE_dsbevd_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_int kd, double* ab, + lapack_int ldab, double* w, double* z, + lapack_int ldz, double* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); + +lapack_int LAPACKE_ssbevx_work( int matrix_order, char jobz, char range, + char uplo, lapack_int n, lapack_int kd, + float* ab, lapack_int ldab, float* q, + lapack_int ldq, float vl, float vu, + lapack_int il, lapack_int iu, float abstol, + lapack_int* m, float* w, float* z, + lapack_int ldz, float* work, lapack_int* iwork, + lapack_int* ifail ); +lapack_int LAPACKE_dsbevx_work( int matrix_order, char jobz, char range, + char uplo, lapack_int n, lapack_int kd, + double* ab, lapack_int ldab, double* q, + lapack_int ldq, double vl, double vu, + lapack_int il, lapack_int iu, double abstol, + lapack_int* m, double* w, double* z, + lapack_int ldz, double* work, lapack_int* iwork, + lapack_int* ifail ); + +lapack_int LAPACKE_ssbgst_work( int matrix_order, char vect, char uplo, + lapack_int n, lapack_int ka, lapack_int kb, + float* ab, lapack_int ldab, const float* bb, + lapack_int ldbb, float* x, lapack_int ldx, + float* work ); +lapack_int LAPACKE_dsbgst_work( int matrix_order, char vect, char uplo, + lapack_int n, lapack_int ka, lapack_int kb, + double* ab, lapack_int ldab, const double* bb, + lapack_int ldbb, double* x, lapack_int ldx, + double* work ); + +lapack_int LAPACKE_ssbgv_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_int ka, lapack_int kb, + float* ab, lapack_int ldab, float* bb, + lapack_int ldbb, float* w, float* z, + lapack_int ldz, float* work ); +lapack_int LAPACKE_dsbgv_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_int ka, lapack_int kb, + double* ab, lapack_int ldab, double* bb, + lapack_int ldbb, double* w, double* z, + lapack_int ldz, double* work ); + +lapack_int LAPACKE_ssbgvd_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_int ka, lapack_int kb, + float* ab, lapack_int ldab, float* bb, + lapack_int ldbb, float* w, float* z, + lapack_int ldz, float* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); +lapack_int LAPACKE_dsbgvd_work( int matrix_order, char jobz, char uplo, + lapack_int n, lapack_int ka, lapack_int kb, + double* ab, lapack_int ldab, double* bb, + lapack_int ldbb, double* w, double* z, + lapack_int ldz, double* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); + +lapack_int LAPACKE_ssbgvx_work( int matrix_order, char jobz, char range, + char uplo, lapack_int n, lapack_int ka, + lapack_int kb, float* ab, lapack_int ldab, + float* bb, lapack_int ldbb, float* q, + lapack_int ldq, float vl, float vu, + lapack_int il, lapack_int iu, float abstol, + lapack_int* m, float* w, float* z, + lapack_int ldz, float* work, lapack_int* iwork, + lapack_int* ifail ); +lapack_int LAPACKE_dsbgvx_work( int matrix_order, char jobz, char range, + char uplo, lapack_int n, lapack_int ka, + lapack_int kb, double* ab, lapack_int ldab, + double* bb, lapack_int ldbb, double* q, + lapack_int ldq, double vl, double vu, + lapack_int il, lapack_int iu, double abstol, + lapack_int* m, double* w, double* z, + lapack_int ldz, double* work, lapack_int* iwork, + lapack_int* ifail ); + +lapack_int LAPACKE_ssbtrd_work( int matrix_order, char vect, char uplo, + lapack_int n, lapack_int kd, float* ab, + lapack_int ldab, float* d, float* e, float* q, + lapack_int ldq, float* work ); +lapack_int LAPACKE_dsbtrd_work( int matrix_order, char vect, char uplo, + lapack_int n, lapack_int kd, double* ab, + lapack_int ldab, double* d, double* e, + double* q, lapack_int ldq, double* work ); + +lapack_int LAPACKE_ssfrk_work( int matrix_order, char transr, char uplo, + char trans, lapack_int n, lapack_int k, + float alpha, const float* a, lapack_int lda, + float beta, float* c ); +lapack_int LAPACKE_dsfrk_work( int matrix_order, char transr, char uplo, + char trans, lapack_int n, lapack_int k, + double alpha, const double* a, lapack_int lda, + double beta, double* c ); + +lapack_int LAPACKE_sspcon_work( int matrix_order, char uplo, lapack_int n, + const float* ap, const lapack_int* ipiv, + float anorm, float* rcond, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dspcon_work( int matrix_order, char uplo, lapack_int n, + const double* ap, const lapack_int* ipiv, + double anorm, double* rcond, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_cspcon_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* ap, + const lapack_int* ipiv, float anorm, + float* rcond, lapack_complex_float* work ); +lapack_int LAPACKE_zspcon_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* ap, + const lapack_int* ipiv, double anorm, + double* rcond, lapack_complex_double* work ); + +lapack_int LAPACKE_sspev_work( int matrix_order, char jobz, char uplo, + lapack_int n, float* ap, float* w, float* z, + lapack_int ldz, float* work ); +lapack_int LAPACKE_dspev_work( int matrix_order, char jobz, char uplo, + lapack_int n, double* ap, double* w, double* z, + lapack_int ldz, double* work ); + +lapack_int LAPACKE_sspevd_work( int matrix_order, char jobz, char uplo, + lapack_int n, float* ap, float* w, float* z, + lapack_int ldz, float* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); +lapack_int LAPACKE_dspevd_work( int matrix_order, char jobz, char uplo, + lapack_int n, double* ap, double* w, double* z, + lapack_int ldz, double* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); + +lapack_int LAPACKE_sspevx_work( int matrix_order, char jobz, char range, + char uplo, lapack_int n, float* ap, float vl, + float vu, lapack_int il, lapack_int iu, + float abstol, lapack_int* m, float* w, float* z, + lapack_int ldz, float* work, lapack_int* iwork, + lapack_int* ifail ); +lapack_int LAPACKE_dspevx_work( int matrix_order, char jobz, char range, + char uplo, lapack_int n, double* ap, double vl, + double vu, lapack_int il, lapack_int iu, + double abstol, lapack_int* m, double* w, + double* z, lapack_int ldz, double* work, + lapack_int* iwork, lapack_int* ifail ); + +lapack_int LAPACKE_sspgst_work( int matrix_order, lapack_int itype, char uplo, + lapack_int n, float* ap, const float* bp ); +lapack_int LAPACKE_dspgst_work( int matrix_order, lapack_int itype, char uplo, + lapack_int n, double* ap, const double* bp ); + +lapack_int LAPACKE_sspgv_work( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, float* ap, float* bp, + float* w, float* z, lapack_int ldz, + float* work ); +lapack_int LAPACKE_dspgv_work( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, double* ap, double* bp, + double* w, double* z, lapack_int ldz, + double* work ); + +lapack_int LAPACKE_sspgvd_work( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, float* ap, float* bp, + float* w, float* z, lapack_int ldz, float* work, + lapack_int lwork, lapack_int* iwork, + lapack_int liwork ); +lapack_int LAPACKE_dspgvd_work( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, double* ap, double* bp, + double* w, double* z, lapack_int ldz, + double* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); + +lapack_int LAPACKE_sspgvx_work( int matrix_order, lapack_int itype, char jobz, + char range, char uplo, lapack_int n, float* ap, + float* bp, float vl, float vu, lapack_int il, + lapack_int iu, float abstol, lapack_int* m, + float* w, float* z, lapack_int ldz, float* work, + lapack_int* iwork, lapack_int* ifail ); +lapack_int LAPACKE_dspgvx_work( int matrix_order, lapack_int itype, char jobz, + char range, char uplo, lapack_int n, double* ap, + double* bp, double vl, double vu, lapack_int il, + lapack_int iu, double abstol, lapack_int* m, + double* w, double* z, lapack_int ldz, + double* work, lapack_int* iwork, + lapack_int* ifail ); + +lapack_int LAPACKE_ssprfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* ap, + const float* afp, const lapack_int* ipiv, + const float* b, lapack_int ldb, float* x, + lapack_int ldx, float* ferr, float* berr, + float* work, lapack_int* iwork ); +lapack_int LAPACKE_dsprfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* ap, + const double* afp, const lapack_int* ipiv, + const double* b, lapack_int ldb, double* x, + lapack_int ldx, double* ferr, double* berr, + double* work, lapack_int* iwork ); +lapack_int LAPACKE_csprfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* ap, + const lapack_complex_float* afp, + const lapack_int* ipiv, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* ferr, float* berr, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zsprfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, + const lapack_complex_double* ap, + const lapack_complex_double* afp, + const lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_sspsv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, float* ap, lapack_int* ipiv, + float* b, lapack_int ldb ); +lapack_int LAPACKE_dspsv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, double* ap, lapack_int* ipiv, + double* b, lapack_int ldb ); +lapack_int LAPACKE_cspsv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_float* ap, + lapack_int* ipiv, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zspsv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_double* ap, + lapack_int* ipiv, lapack_complex_double* b, + lapack_int ldb ); + +lapack_int LAPACKE_sspsvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, const float* ap, + float* afp, lapack_int* ipiv, const float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* rcond, float* ferr, float* berr, + float* work, lapack_int* iwork ); +lapack_int LAPACKE_dspsvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, const double* ap, + double* afp, lapack_int* ipiv, const double* b, + lapack_int ldb, double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr, + double* work, lapack_int* iwork ); +lapack_int LAPACKE_cspsvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + const lapack_complex_float* ap, + lapack_complex_float* afp, lapack_int* ipiv, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* ferr, float* berr, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zspsvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + const lapack_complex_double* ap, + lapack_complex_double* afp, lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_ssptrd_work( int matrix_order, char uplo, lapack_int n, + float* ap, float* d, float* e, float* tau ); +lapack_int LAPACKE_dsptrd_work( int matrix_order, char uplo, lapack_int n, + double* ap, double* d, double* e, double* tau ); + +lapack_int LAPACKE_ssptrf_work( int matrix_order, char uplo, lapack_int n, + float* ap, lapack_int* ipiv ); +lapack_int LAPACKE_dsptrf_work( int matrix_order, char uplo, lapack_int n, + double* ap, lapack_int* ipiv ); +lapack_int LAPACKE_csptrf_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* ap, lapack_int* ipiv ); +lapack_int LAPACKE_zsptrf_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* ap, lapack_int* ipiv ); + +lapack_int LAPACKE_ssptri_work( int matrix_order, char uplo, lapack_int n, + float* ap, const lapack_int* ipiv, + float* work ); +lapack_int LAPACKE_dsptri_work( int matrix_order, char uplo, lapack_int n, + double* ap, const lapack_int* ipiv, + double* work ); +lapack_int LAPACKE_csptri_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* ap, + const lapack_int* ipiv, + lapack_complex_float* work ); +lapack_int LAPACKE_zsptri_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* ap, + const lapack_int* ipiv, + lapack_complex_double* work ); + +lapack_int LAPACKE_ssptrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* ap, + const lapack_int* ipiv, float* b, + lapack_int ldb ); +lapack_int LAPACKE_dsptrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* ap, + const lapack_int* ipiv, double* b, + lapack_int ldb ); +lapack_int LAPACKE_csptrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* ap, + const lapack_int* ipiv, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_zsptrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, + const lapack_complex_double* ap, + const lapack_int* ipiv, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_sstebz_work( char range, char order, lapack_int n, float vl, + float vu, lapack_int il, lapack_int iu, + float abstol, const float* d, const float* e, + lapack_int* m, lapack_int* nsplit, float* w, + lapack_int* iblock, lapack_int* isplit, + float* work, lapack_int* iwork ); +lapack_int LAPACKE_dstebz_work( char range, char order, lapack_int n, double vl, + double vu, lapack_int il, lapack_int iu, + double abstol, const double* d, const double* e, + lapack_int* m, lapack_int* nsplit, double* w, + lapack_int* iblock, lapack_int* isplit, + double* work, lapack_int* iwork ); + +lapack_int LAPACKE_sstedc_work( int matrix_order, char compz, lapack_int n, + float* d, float* e, float* z, lapack_int ldz, + float* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); +lapack_int LAPACKE_dstedc_work( int matrix_order, char compz, lapack_int n, + double* d, double* e, double* z, lapack_int ldz, + double* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); +lapack_int LAPACKE_cstedc_work( int matrix_order, char compz, lapack_int n, + float* d, float* e, lapack_complex_float* z, + lapack_int ldz, lapack_complex_float* work, + lapack_int lwork, float* rwork, + lapack_int lrwork, lapack_int* iwork, + lapack_int liwork ); +lapack_int LAPACKE_zstedc_work( int matrix_order, char compz, lapack_int n, + double* d, double* e, lapack_complex_double* z, + lapack_int ldz, lapack_complex_double* work, + lapack_int lwork, double* rwork, + lapack_int lrwork, lapack_int* iwork, + lapack_int liwork ); + +lapack_int LAPACKE_sstegr_work( int matrix_order, char jobz, char range, + lapack_int n, float* d, float* e, float vl, + float vu, lapack_int il, lapack_int iu, + float abstol, lapack_int* m, float* w, float* z, + lapack_int ldz, lapack_int* isuppz, float* work, + lapack_int lwork, lapack_int* iwork, + lapack_int liwork ); +lapack_int LAPACKE_dstegr_work( int matrix_order, char jobz, char range, + lapack_int n, double* d, double* e, double vl, + double vu, lapack_int il, lapack_int iu, + double abstol, lapack_int* m, double* w, + double* z, lapack_int ldz, lapack_int* isuppz, + double* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); +lapack_int LAPACKE_cstegr_work( int matrix_order, char jobz, char range, + lapack_int n, float* d, float* e, float vl, + float vu, lapack_int il, lapack_int iu, + float abstol, lapack_int* m, float* w, + lapack_complex_float* z, lapack_int ldz, + lapack_int* isuppz, float* work, + lapack_int lwork, lapack_int* iwork, + lapack_int liwork ); +lapack_int LAPACKE_zstegr_work( int matrix_order, char jobz, char range, + lapack_int n, double* d, double* e, double vl, + double vu, lapack_int il, lapack_int iu, + double abstol, lapack_int* m, double* w, + lapack_complex_double* z, lapack_int ldz, + lapack_int* isuppz, double* work, + lapack_int lwork, lapack_int* iwork, + lapack_int liwork ); + +lapack_int LAPACKE_sstein_work( int matrix_order, lapack_int n, const float* d, + const float* e, lapack_int m, const float* w, + const lapack_int* iblock, + const lapack_int* isplit, float* z, + lapack_int ldz, float* work, lapack_int* iwork, + lapack_int* ifailv ); +lapack_int LAPACKE_dstein_work( int matrix_order, lapack_int n, const double* d, + const double* e, lapack_int m, const double* w, + const lapack_int* iblock, + const lapack_int* isplit, double* z, + lapack_int ldz, double* work, lapack_int* iwork, + lapack_int* ifailv ); +lapack_int LAPACKE_cstein_work( int matrix_order, lapack_int n, const float* d, + const float* e, lapack_int m, const float* w, + const lapack_int* iblock, + const lapack_int* isplit, + lapack_complex_float* z, lapack_int ldz, + float* work, lapack_int* iwork, + lapack_int* ifailv ); +lapack_int LAPACKE_zstein_work( int matrix_order, lapack_int n, const double* d, + const double* e, lapack_int m, const double* w, + const lapack_int* iblock, + const lapack_int* isplit, + lapack_complex_double* z, lapack_int ldz, + double* work, lapack_int* iwork, + lapack_int* ifailv ); + +lapack_int LAPACKE_sstemr_work( int matrix_order, char jobz, char range, + lapack_int n, float* d, float* e, float vl, + float vu, lapack_int il, lapack_int iu, + lapack_int* m, float* w, float* z, + lapack_int ldz, lapack_int nzc, + lapack_int* isuppz, lapack_logical* tryrac, + float* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); +lapack_int LAPACKE_dstemr_work( int matrix_order, char jobz, char range, + lapack_int n, double* d, double* e, double vl, + double vu, lapack_int il, lapack_int iu, + lapack_int* m, double* w, double* z, + lapack_int ldz, lapack_int nzc, + lapack_int* isuppz, lapack_logical* tryrac, + double* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); +lapack_int LAPACKE_cstemr_work( int matrix_order, char jobz, char range, + lapack_int n, float* d, float* e, float vl, + float vu, lapack_int il, lapack_int iu, + lapack_int* m, float* w, + lapack_complex_float* z, lapack_int ldz, + lapack_int nzc, lapack_int* isuppz, + lapack_logical* tryrac, float* work, + lapack_int lwork, lapack_int* iwork, + lapack_int liwork ); +lapack_int LAPACKE_zstemr_work( int matrix_order, char jobz, char range, + lapack_int n, double* d, double* e, double vl, + double vu, lapack_int il, lapack_int iu, + lapack_int* m, double* w, + lapack_complex_double* z, lapack_int ldz, + lapack_int nzc, lapack_int* isuppz, + lapack_logical* tryrac, double* work, + lapack_int lwork, lapack_int* iwork, + lapack_int liwork ); + +lapack_int LAPACKE_ssteqr_work( int matrix_order, char compz, lapack_int n, + float* d, float* e, float* z, lapack_int ldz, + float* work ); +lapack_int LAPACKE_dsteqr_work( int matrix_order, char compz, lapack_int n, + double* d, double* e, double* z, lapack_int ldz, + double* work ); +lapack_int LAPACKE_csteqr_work( int matrix_order, char compz, lapack_int n, + float* d, float* e, lapack_complex_float* z, + lapack_int ldz, float* work ); +lapack_int LAPACKE_zsteqr_work( int matrix_order, char compz, lapack_int n, + double* d, double* e, lapack_complex_double* z, + lapack_int ldz, double* work ); + +lapack_int LAPACKE_ssterf_work( lapack_int n, float* d, float* e ); +lapack_int LAPACKE_dsterf_work( lapack_int n, double* d, double* e ); + +lapack_int LAPACKE_sstev_work( int matrix_order, char jobz, lapack_int n, + float* d, float* e, float* z, lapack_int ldz, + float* work ); +lapack_int LAPACKE_dstev_work( int matrix_order, char jobz, lapack_int n, + double* d, double* e, double* z, lapack_int ldz, + double* work ); + +lapack_int LAPACKE_sstevd_work( int matrix_order, char jobz, lapack_int n, + float* d, float* e, float* z, lapack_int ldz, + float* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); +lapack_int LAPACKE_dstevd_work( int matrix_order, char jobz, lapack_int n, + double* d, double* e, double* z, lapack_int ldz, + double* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); + +lapack_int LAPACKE_sstevr_work( int matrix_order, char jobz, char range, + lapack_int n, float* d, float* e, float vl, + float vu, lapack_int il, lapack_int iu, + float abstol, lapack_int* m, float* w, float* z, + lapack_int ldz, lapack_int* isuppz, float* work, + lapack_int lwork, lapack_int* iwork, + lapack_int liwork ); +lapack_int LAPACKE_dstevr_work( int matrix_order, char jobz, char range, + lapack_int n, double* d, double* e, double vl, + double vu, lapack_int il, lapack_int iu, + double abstol, lapack_int* m, double* w, + double* z, lapack_int ldz, lapack_int* isuppz, + double* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); + +lapack_int LAPACKE_sstevx_work( int matrix_order, char jobz, char range, + lapack_int n, float* d, float* e, float vl, + float vu, lapack_int il, lapack_int iu, + float abstol, lapack_int* m, float* w, float* z, + lapack_int ldz, float* work, lapack_int* iwork, + lapack_int* ifail ); +lapack_int LAPACKE_dstevx_work( int matrix_order, char jobz, char range, + lapack_int n, double* d, double* e, double vl, + double vu, lapack_int il, lapack_int iu, + double abstol, lapack_int* m, double* w, + double* z, lapack_int ldz, double* work, + lapack_int* iwork, lapack_int* ifail ); + +lapack_int LAPACKE_ssycon_work( int matrix_order, char uplo, lapack_int n, + const float* a, lapack_int lda, + const lapack_int* ipiv, float anorm, + float* rcond, float* work, lapack_int* iwork ); +lapack_int LAPACKE_dsycon_work( int matrix_order, char uplo, lapack_int n, + const double* a, lapack_int lda, + const lapack_int* ipiv, double anorm, + double* rcond, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_csycon_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + const lapack_int* ipiv, float anorm, + float* rcond, lapack_complex_float* work ); +lapack_int LAPACKE_zsycon_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + const lapack_int* ipiv, double anorm, + double* rcond, lapack_complex_double* work ); + +lapack_int LAPACKE_ssyequb_work( int matrix_order, char uplo, lapack_int n, + const float* a, lapack_int lda, float* s, + float* scond, float* amax, float* work ); +lapack_int LAPACKE_dsyequb_work( int matrix_order, char uplo, lapack_int n, + const double* a, lapack_int lda, double* s, + double* scond, double* amax, double* work ); +lapack_int LAPACKE_csyequb_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + float* s, float* scond, float* amax, + lapack_complex_float* work ); +lapack_int LAPACKE_zsyequb_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + double* s, double* scond, double* amax, + lapack_complex_double* work ); + +lapack_int LAPACKE_ssyev_work( int matrix_order, char jobz, char uplo, + lapack_int n, float* a, lapack_int lda, float* w, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dsyev_work( int matrix_order, char jobz, char uplo, + lapack_int n, double* a, lapack_int lda, + double* w, double* work, lapack_int lwork ); + +lapack_int LAPACKE_ssyevd_work( int matrix_order, char jobz, char uplo, + lapack_int n, float* a, lapack_int lda, + float* w, float* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); +lapack_int LAPACKE_dsyevd_work( int matrix_order, char jobz, char uplo, + lapack_int n, double* a, lapack_int lda, + double* w, double* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); + +lapack_int LAPACKE_ssyevr_work( int matrix_order, char jobz, char range, + char uplo, lapack_int n, float* a, + lapack_int lda, float vl, float vu, + lapack_int il, lapack_int iu, float abstol, + lapack_int* m, float* w, float* z, + lapack_int ldz, lapack_int* isuppz, float* work, + lapack_int lwork, lapack_int* iwork, + lapack_int liwork ); +lapack_int LAPACKE_dsyevr_work( int matrix_order, char jobz, char range, + char uplo, lapack_int n, double* a, + lapack_int lda, double vl, double vu, + lapack_int il, lapack_int iu, double abstol, + lapack_int* m, double* w, double* z, + lapack_int ldz, lapack_int* isuppz, + double* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); + +lapack_int LAPACKE_ssyevx_work( int matrix_order, char jobz, char range, + char uplo, lapack_int n, float* a, + lapack_int lda, float vl, float vu, + lapack_int il, lapack_int iu, float abstol, + lapack_int* m, float* w, float* z, + lapack_int ldz, float* work, lapack_int lwork, + lapack_int* iwork, lapack_int* ifail ); +lapack_int LAPACKE_dsyevx_work( int matrix_order, char jobz, char range, + char uplo, lapack_int n, double* a, + lapack_int lda, double vl, double vu, + lapack_int il, lapack_int iu, double abstol, + lapack_int* m, double* w, double* z, + lapack_int ldz, double* work, lapack_int lwork, + lapack_int* iwork, lapack_int* ifail ); + +lapack_int LAPACKE_ssygst_work( int matrix_order, lapack_int itype, char uplo, + lapack_int n, float* a, lapack_int lda, + const float* b, lapack_int ldb ); +lapack_int LAPACKE_dsygst_work( int matrix_order, lapack_int itype, char uplo, + lapack_int n, double* a, lapack_int lda, + const double* b, lapack_int ldb ); + +lapack_int LAPACKE_ssygv_work( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, float* a, + lapack_int lda, float* b, lapack_int ldb, + float* w, float* work, lapack_int lwork ); +lapack_int LAPACKE_dsygv_work( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, double* a, + lapack_int lda, double* b, lapack_int ldb, + double* w, double* work, lapack_int lwork ); + +lapack_int LAPACKE_ssygvd_work( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, float* a, + lapack_int lda, float* b, lapack_int ldb, + float* w, float* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); +lapack_int LAPACKE_dsygvd_work( int matrix_order, lapack_int itype, char jobz, + char uplo, lapack_int n, double* a, + lapack_int lda, double* b, lapack_int ldb, + double* w, double* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); + +lapack_int LAPACKE_ssygvx_work( int matrix_order, lapack_int itype, char jobz, + char range, char uplo, lapack_int n, float* a, + lapack_int lda, float* b, lapack_int ldb, + float vl, float vu, lapack_int il, + lapack_int iu, float abstol, lapack_int* m, + float* w, float* z, lapack_int ldz, float* work, + lapack_int lwork, lapack_int* iwork, + lapack_int* ifail ); +lapack_int LAPACKE_dsygvx_work( int matrix_order, lapack_int itype, char jobz, + char range, char uplo, lapack_int n, double* a, + lapack_int lda, double* b, lapack_int ldb, + double vl, double vu, lapack_int il, + lapack_int iu, double abstol, lapack_int* m, + double* w, double* z, lapack_int ldz, + double* work, lapack_int lwork, + lapack_int* iwork, lapack_int* ifail ); + +lapack_int LAPACKE_ssyrfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* a, lapack_int lda, + const float* af, lapack_int ldaf, + const lapack_int* ipiv, const float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* ferr, float* berr, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dsyrfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* a, + lapack_int lda, const double* af, + lapack_int ldaf, const lapack_int* ipiv, + const double* b, lapack_int ldb, double* x, + lapack_int ldx, double* ferr, double* berr, + double* work, lapack_int* iwork ); +lapack_int LAPACKE_csyrfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* af, + lapack_int ldaf, const lapack_int* ipiv, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* ferr, float* berr, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_zsyrfs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, const lapack_complex_double* af, + lapack_int ldaf, const lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_ssyrfsx_work( int matrix_order, char uplo, char equed, + lapack_int n, lapack_int nrhs, const float* a, + lapack_int lda, const float* af, + lapack_int ldaf, const lapack_int* ipiv, + const float* s, const float* b, lapack_int ldb, + float* x, lapack_int ldx, float* rcond, + float* berr, lapack_int n_err_bnds, + float* err_bnds_norm, float* err_bnds_comp, + lapack_int nparams, float* params, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dsyrfsx_work( int matrix_order, char uplo, char equed, + lapack_int n, lapack_int nrhs, const double* a, + lapack_int lda, const double* af, + lapack_int ldaf, const lapack_int* ipiv, + const double* s, const double* b, + lapack_int ldb, double* x, lapack_int ldx, + double* rcond, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_csyrfsx_work( int matrix_order, char uplo, char equed, + lapack_int n, lapack_int nrhs, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* af, + lapack_int ldaf, const lapack_int* ipiv, + const float* s, const lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* x, + lapack_int ldx, float* rcond, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params, lapack_complex_float* work, + float* rwork ); +lapack_int LAPACKE_zsyrfsx_work( int matrix_order, char uplo, char equed, + lapack_int n, lapack_int nrhs, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* af, + lapack_int ldaf, const lapack_int* ipiv, + const double* s, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params, lapack_complex_double* work, + double* rwork ); + +lapack_int LAPACKE_ssysv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, float* a, lapack_int lda, + lapack_int* ipiv, float* b, lapack_int ldb, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dsysv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, double* a, lapack_int lda, + lapack_int* ipiv, double* b, lapack_int ldb, + double* work, lapack_int lwork ); +lapack_int LAPACKE_csysv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_float* a, + lapack_int lda, lapack_int* ipiv, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zsysv_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, lapack_complex_double* a, + lapack_int lda, lapack_int* ipiv, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_ssysvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, const float* a, + lapack_int lda, float* af, lapack_int ldaf, + lapack_int* ipiv, const float* b, + lapack_int ldb, float* x, lapack_int ldx, + float* rcond, float* ferr, float* berr, + float* work, lapack_int lwork, + lapack_int* iwork ); +lapack_int LAPACKE_dsysvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, const double* a, + lapack_int lda, double* af, lapack_int ldaf, + lapack_int* ipiv, const double* b, + lapack_int ldb, double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr, + double* work, lapack_int lwork, + lapack_int* iwork ); +lapack_int LAPACKE_csysvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + const lapack_complex_float* a, lapack_int lda, + lapack_complex_float* af, lapack_int ldaf, + lapack_int* ipiv, const lapack_complex_float* b, + lapack_int ldb, lapack_complex_float* x, + lapack_int ldx, float* rcond, float* ferr, + float* berr, lapack_complex_float* work, + lapack_int lwork, float* rwork ); +lapack_int LAPACKE_zsysvx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + const lapack_complex_double* a, lapack_int lda, + lapack_complex_double* af, lapack_int ldaf, + lapack_int* ipiv, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* ferr, double* berr, + lapack_complex_double* work, lapack_int lwork, + double* rwork ); + +lapack_int LAPACKE_ssysvxx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, float* a, + lapack_int lda, float* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, float* s, + float* b, lapack_int ldb, float* x, + lapack_int ldx, float* rcond, float* rpvgrw, + float* berr, lapack_int n_err_bnds, + float* err_bnds_norm, float* err_bnds_comp, + lapack_int nparams, float* params, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dsysvxx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, double* a, + lapack_int lda, double* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, double* s, + double* b, lapack_int ldb, double* x, + lapack_int ldx, double* rcond, double* rpvgrw, + double* berr, lapack_int n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int nparams, double* params, + double* work, lapack_int* iwork ); +lapack_int LAPACKE_csysvxx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, float* s, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* x, lapack_int ldx, + float* rcond, float* rpvgrw, float* berr, + lapack_int n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int nparams, + float* params, lapack_complex_float* work, + float* rwork ); +lapack_int LAPACKE_zsysvxx_work( int matrix_order, char fact, char uplo, + lapack_int n, lapack_int nrhs, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* af, lapack_int ldaf, + lapack_int* ipiv, char* equed, double* s, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* x, lapack_int ldx, + double* rcond, double* rpvgrw, double* berr, + lapack_int n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int nparams, + double* params, lapack_complex_double* work, + double* rwork ); + +lapack_int LAPACKE_ssytrd_work( int matrix_order, char uplo, lapack_int n, + float* a, lapack_int lda, float* d, float* e, + float* tau, float* work, lapack_int lwork ); +lapack_int LAPACKE_dsytrd_work( int matrix_order, char uplo, lapack_int n, + double* a, lapack_int lda, double* d, double* e, + double* tau, double* work, lapack_int lwork ); + +lapack_int LAPACKE_ssytrf_work( int matrix_order, char uplo, lapack_int n, + float* a, lapack_int lda, lapack_int* ipiv, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dsytrf_work( int matrix_order, char uplo, lapack_int n, + double* a, lapack_int lda, lapack_int* ipiv, + double* work, lapack_int lwork ); +lapack_int LAPACKE_csytrf_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_int* ipiv, lapack_complex_float* work, + lapack_int lwork ); +lapack_int LAPACKE_zsytrf_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_int* ipiv, lapack_complex_double* work, + lapack_int lwork ); + +lapack_int LAPACKE_ssytri_work( int matrix_order, char uplo, lapack_int n, + float* a, lapack_int lda, + const lapack_int* ipiv, float* work ); +lapack_int LAPACKE_dsytri_work( int matrix_order, char uplo, lapack_int n, + double* a, lapack_int lda, + const lapack_int* ipiv, double* work ); +lapack_int LAPACKE_csytri_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + const lapack_int* ipiv, + lapack_complex_float* work ); +lapack_int LAPACKE_zsytri_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + const lapack_int* ipiv, + lapack_complex_double* work ); + +lapack_int LAPACKE_ssytrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* a, lapack_int lda, + const lapack_int* ipiv, float* b, + lapack_int ldb ); +lapack_int LAPACKE_dsytrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* a, + lapack_int lda, const lapack_int* ipiv, + double* b, lapack_int ldb ); +lapack_int LAPACKE_csytrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_zsytrs_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_stbcon_work( int matrix_order, char norm, char uplo, + char diag, lapack_int n, lapack_int kd, + const float* ab, lapack_int ldab, float* rcond, + float* work, lapack_int* iwork ); +lapack_int LAPACKE_dtbcon_work( int matrix_order, char norm, char uplo, + char diag, lapack_int n, lapack_int kd, + const double* ab, lapack_int ldab, + double* rcond, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_ctbcon_work( int matrix_order, char norm, char uplo, + char diag, lapack_int n, lapack_int kd, + const lapack_complex_float* ab, lapack_int ldab, + float* rcond, lapack_complex_float* work, + float* rwork ); +lapack_int LAPACKE_ztbcon_work( int matrix_order, char norm, char uplo, + char diag, lapack_int n, lapack_int kd, + const lapack_complex_double* ab, + lapack_int ldab, double* rcond, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_stbrfs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int kd, + lapack_int nrhs, const float* ab, + lapack_int ldab, const float* b, lapack_int ldb, + const float* x, lapack_int ldx, float* ferr, + float* berr, float* work, lapack_int* iwork ); +lapack_int LAPACKE_dtbrfs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int kd, + lapack_int nrhs, const double* ab, + lapack_int ldab, const double* b, + lapack_int ldb, const double* x, lapack_int ldx, + double* ferr, double* berr, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_ctbrfs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int kd, + lapack_int nrhs, const lapack_complex_float* ab, + lapack_int ldab, const lapack_complex_float* b, + lapack_int ldb, const lapack_complex_float* x, + lapack_int ldx, float* ferr, float* berr, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_ztbrfs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int kd, + lapack_int nrhs, + const lapack_complex_double* ab, + lapack_int ldab, const lapack_complex_double* b, + lapack_int ldb, const lapack_complex_double* x, + lapack_int ldx, double* ferr, double* berr, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_stbtrs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int kd, + lapack_int nrhs, const float* ab, + lapack_int ldab, float* b, lapack_int ldb ); +lapack_int LAPACKE_dtbtrs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int kd, + lapack_int nrhs, const double* ab, + lapack_int ldab, double* b, lapack_int ldb ); +lapack_int LAPACKE_ctbtrs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int kd, + lapack_int nrhs, const lapack_complex_float* ab, + lapack_int ldab, lapack_complex_float* b, + lapack_int ldb ); +lapack_int LAPACKE_ztbtrs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int kd, + lapack_int nrhs, + const lapack_complex_double* ab, + lapack_int ldab, lapack_complex_double* b, + lapack_int ldb ); + +lapack_int LAPACKE_stfsm_work( int matrix_order, char transr, char side, + char uplo, char trans, char diag, lapack_int m, + lapack_int n, float alpha, const float* a, + float* b, lapack_int ldb ); +lapack_int LAPACKE_dtfsm_work( int matrix_order, char transr, char side, + char uplo, char trans, char diag, lapack_int m, + lapack_int n, double alpha, const double* a, + double* b, lapack_int ldb ); +lapack_int LAPACKE_ctfsm_work( int matrix_order, char transr, char side, + char uplo, char trans, char diag, lapack_int m, + lapack_int n, lapack_complex_float alpha, + const lapack_complex_float* a, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_ztfsm_work( int matrix_order, char transr, char side, + char uplo, char trans, char diag, lapack_int m, + lapack_int n, lapack_complex_double alpha, + const lapack_complex_double* a, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_stftri_work( int matrix_order, char transr, char uplo, + char diag, lapack_int n, float* a ); +lapack_int LAPACKE_dtftri_work( int matrix_order, char transr, char uplo, + char diag, lapack_int n, double* a ); +lapack_int LAPACKE_ctftri_work( int matrix_order, char transr, char uplo, + char diag, lapack_int n, + lapack_complex_float* a ); +lapack_int LAPACKE_ztftri_work( int matrix_order, char transr, char uplo, + char diag, lapack_int n, + lapack_complex_double* a ); + +lapack_int LAPACKE_stfttp_work( int matrix_order, char transr, char uplo, + lapack_int n, const float* arf, float* ap ); +lapack_int LAPACKE_dtfttp_work( int matrix_order, char transr, char uplo, + lapack_int n, const double* arf, double* ap ); +lapack_int LAPACKE_ctfttp_work( int matrix_order, char transr, char uplo, + lapack_int n, const lapack_complex_float* arf, + lapack_complex_float* ap ); +lapack_int LAPACKE_ztfttp_work( int matrix_order, char transr, char uplo, + lapack_int n, const lapack_complex_double* arf, + lapack_complex_double* ap ); + +lapack_int LAPACKE_stfttr_work( int matrix_order, char transr, char uplo, + lapack_int n, const float* arf, float* a, + lapack_int lda ); +lapack_int LAPACKE_dtfttr_work( int matrix_order, char transr, char uplo, + lapack_int n, const double* arf, double* a, + lapack_int lda ); +lapack_int LAPACKE_ctfttr_work( int matrix_order, char transr, char uplo, + lapack_int n, const lapack_complex_float* arf, + lapack_complex_float* a, lapack_int lda ); +lapack_int LAPACKE_ztfttr_work( int matrix_order, char transr, char uplo, + lapack_int n, const lapack_complex_double* arf, + lapack_complex_double* a, lapack_int lda ); + +lapack_int LAPACKE_stgevc_work( int matrix_order, char side, char howmny, + const lapack_logical* select, lapack_int n, + const float* s, lapack_int lds, const float* p, + lapack_int ldp, float* vl, lapack_int ldvl, + float* vr, lapack_int ldvr, lapack_int mm, + lapack_int* m, float* work ); +lapack_int LAPACKE_dtgevc_work( int matrix_order, char side, char howmny, + const lapack_logical* select, lapack_int n, + const double* s, lapack_int lds, + const double* p, lapack_int ldp, double* vl, + lapack_int ldvl, double* vr, lapack_int ldvr, + lapack_int mm, lapack_int* m, double* work ); +lapack_int LAPACKE_ctgevc_work( int matrix_order, char side, char howmny, + const lapack_logical* select, lapack_int n, + const lapack_complex_float* s, lapack_int lds, + const lapack_complex_float* p, lapack_int ldp, + lapack_complex_float* vl, lapack_int ldvl, + lapack_complex_float* vr, lapack_int ldvr, + lapack_int mm, lapack_int* m, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_ztgevc_work( int matrix_order, char side, char howmny, + const lapack_logical* select, lapack_int n, + const lapack_complex_double* s, lapack_int lds, + const lapack_complex_double* p, lapack_int ldp, + lapack_complex_double* vl, lapack_int ldvl, + lapack_complex_double* vr, lapack_int ldvr, + lapack_int mm, lapack_int* m, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_stgexc_work( int matrix_order, lapack_logical wantq, + lapack_logical wantz, lapack_int n, float* a, + lapack_int lda, float* b, lapack_int ldb, + float* q, lapack_int ldq, float* z, + lapack_int ldz, lapack_int* ifst, + lapack_int* ilst, float* work, + lapack_int lwork ); +lapack_int LAPACKE_dtgexc_work( int matrix_order, lapack_logical wantq, + lapack_logical wantz, lapack_int n, double* a, + lapack_int lda, double* b, lapack_int ldb, + double* q, lapack_int ldq, double* z, + lapack_int ldz, lapack_int* ifst, + lapack_int* ilst, double* work, + lapack_int lwork ); +lapack_int LAPACKE_ctgexc_work( int matrix_order, lapack_logical wantq, + lapack_logical wantz, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* q, lapack_int ldq, + lapack_complex_float* z, lapack_int ldz, + lapack_int ifst, lapack_int ilst ); +lapack_int LAPACKE_ztgexc_work( int matrix_order, lapack_logical wantq, + lapack_logical wantz, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* q, lapack_int ldq, + lapack_complex_double* z, lapack_int ldz, + lapack_int ifst, lapack_int ilst ); + +lapack_int LAPACKE_stgsen_work( int matrix_order, lapack_int ijob, + lapack_logical wantq, lapack_logical wantz, + const lapack_logical* select, lapack_int n, + float* a, lapack_int lda, float* b, + lapack_int ldb, float* alphar, float* alphai, + float* beta, float* q, lapack_int ldq, float* z, + lapack_int ldz, lapack_int* m, float* pl, + float* pr, float* dif, float* work, + lapack_int lwork, lapack_int* iwork, + lapack_int liwork ); +lapack_int LAPACKE_dtgsen_work( int matrix_order, lapack_int ijob, + lapack_logical wantq, lapack_logical wantz, + const lapack_logical* select, lapack_int n, + double* a, lapack_int lda, double* b, + lapack_int ldb, double* alphar, double* alphai, + double* beta, double* q, lapack_int ldq, + double* z, lapack_int ldz, lapack_int* m, + double* pl, double* pr, double* dif, + double* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); +lapack_int LAPACKE_ctgsen_work( int matrix_order, lapack_int ijob, + lapack_logical wantq, lapack_logical wantz, + const lapack_logical* select, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* alpha, + lapack_complex_float* beta, + lapack_complex_float* q, lapack_int ldq, + lapack_complex_float* z, lapack_int ldz, + lapack_int* m, float* pl, float* pr, float* dif, + lapack_complex_float* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); +lapack_int LAPACKE_ztgsen_work( int matrix_order, lapack_int ijob, + lapack_logical wantq, lapack_logical wantz, + const lapack_logical* select, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* alpha, + lapack_complex_double* beta, + lapack_complex_double* q, lapack_int ldq, + lapack_complex_double* z, lapack_int ldz, + lapack_int* m, double* pl, double* pr, + double* dif, lapack_complex_double* work, + lapack_int lwork, lapack_int* iwork, + lapack_int liwork ); + +lapack_int LAPACKE_stgsja_work( int matrix_order, char jobu, char jobv, + char jobq, lapack_int m, lapack_int p, + lapack_int n, lapack_int k, lapack_int l, + float* a, lapack_int lda, float* b, + lapack_int ldb, float tola, float tolb, + float* alpha, float* beta, float* u, + lapack_int ldu, float* v, lapack_int ldv, + float* q, lapack_int ldq, float* work, + lapack_int* ncycle ); +lapack_int LAPACKE_dtgsja_work( int matrix_order, char jobu, char jobv, + char jobq, lapack_int m, lapack_int p, + lapack_int n, lapack_int k, lapack_int l, + double* a, lapack_int lda, double* b, + lapack_int ldb, double tola, double tolb, + double* alpha, double* beta, double* u, + lapack_int ldu, double* v, lapack_int ldv, + double* q, lapack_int ldq, double* work, + lapack_int* ncycle ); +lapack_int LAPACKE_ctgsja_work( int matrix_order, char jobu, char jobv, + char jobq, lapack_int m, lapack_int p, + lapack_int n, lapack_int k, lapack_int l, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + float tola, float tolb, float* alpha, + float* beta, lapack_complex_float* u, + lapack_int ldu, lapack_complex_float* v, + lapack_int ldv, lapack_complex_float* q, + lapack_int ldq, lapack_complex_float* work, + lapack_int* ncycle ); +lapack_int LAPACKE_ztgsja_work( int matrix_order, char jobu, char jobv, + char jobq, lapack_int m, lapack_int p, + lapack_int n, lapack_int k, lapack_int l, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + double tola, double tolb, double* alpha, + double* beta, lapack_complex_double* u, + lapack_int ldu, lapack_complex_double* v, + lapack_int ldv, lapack_complex_double* q, + lapack_int ldq, lapack_complex_double* work, + lapack_int* ncycle ); + +lapack_int LAPACKE_stgsna_work( int matrix_order, char job, char howmny, + const lapack_logical* select, lapack_int n, + const float* a, lapack_int lda, const float* b, + lapack_int ldb, const float* vl, + lapack_int ldvl, const float* vr, + lapack_int ldvr, float* s, float* dif, + lapack_int mm, lapack_int* m, float* work, + lapack_int lwork, lapack_int* iwork ); +lapack_int LAPACKE_dtgsna_work( int matrix_order, char job, char howmny, + const lapack_logical* select, lapack_int n, + const double* a, lapack_int lda, + const double* b, lapack_int ldb, + const double* vl, lapack_int ldvl, + const double* vr, lapack_int ldvr, double* s, + double* dif, lapack_int mm, lapack_int* m, + double* work, lapack_int lwork, + lapack_int* iwork ); +lapack_int LAPACKE_ctgsna_work( int matrix_order, char job, char howmny, + const lapack_logical* select, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* b, lapack_int ldb, + const lapack_complex_float* vl, lapack_int ldvl, + const lapack_complex_float* vr, lapack_int ldvr, + float* s, float* dif, lapack_int mm, + lapack_int* m, lapack_complex_float* work, + lapack_int lwork, lapack_int* iwork ); +lapack_int LAPACKE_ztgsna_work( int matrix_order, char job, char howmny, + const lapack_logical* select, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* b, lapack_int ldb, + const lapack_complex_double* vl, + lapack_int ldvl, + const lapack_complex_double* vr, + lapack_int ldvr, double* s, double* dif, + lapack_int mm, lapack_int* m, + lapack_complex_double* work, lapack_int lwork, + lapack_int* iwork ); + +lapack_int LAPACKE_stgsyl_work( int matrix_order, char trans, lapack_int ijob, + lapack_int m, lapack_int n, const float* a, + lapack_int lda, const float* b, lapack_int ldb, + float* c, lapack_int ldc, const float* d, + lapack_int ldd, const float* e, lapack_int lde, + float* f, lapack_int ldf, float* scale, + float* dif, float* work, lapack_int lwork, + lapack_int* iwork ); +lapack_int LAPACKE_dtgsyl_work( int matrix_order, char trans, lapack_int ijob, + lapack_int m, lapack_int n, const double* a, + lapack_int lda, const double* b, lapack_int ldb, + double* c, lapack_int ldc, const double* d, + lapack_int ldd, const double* e, lapack_int lde, + double* f, lapack_int ldf, double* scale, + double* dif, double* work, lapack_int lwork, + lapack_int* iwork ); +lapack_int LAPACKE_ctgsyl_work( int matrix_order, char trans, lapack_int ijob, + lapack_int m, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* c, lapack_int ldc, + const lapack_complex_float* d, lapack_int ldd, + const lapack_complex_float* e, lapack_int lde, + lapack_complex_float* f, lapack_int ldf, + float* scale, float* dif, + lapack_complex_float* work, lapack_int lwork, + lapack_int* iwork ); +lapack_int LAPACKE_ztgsyl_work( int matrix_order, char trans, lapack_int ijob, + lapack_int m, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* c, lapack_int ldc, + const lapack_complex_double* d, lapack_int ldd, + const lapack_complex_double* e, lapack_int lde, + lapack_complex_double* f, lapack_int ldf, + double* scale, double* dif, + lapack_complex_double* work, lapack_int lwork, + lapack_int* iwork ); + +lapack_int LAPACKE_stpcon_work( int matrix_order, char norm, char uplo, + char diag, lapack_int n, const float* ap, + float* rcond, float* work, lapack_int* iwork ); +lapack_int LAPACKE_dtpcon_work( int matrix_order, char norm, char uplo, + char diag, lapack_int n, const double* ap, + double* rcond, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_ctpcon_work( int matrix_order, char norm, char uplo, + char diag, lapack_int n, + const lapack_complex_float* ap, float* rcond, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_ztpcon_work( int matrix_order, char norm, char uplo, + char diag, lapack_int n, + const lapack_complex_double* ap, double* rcond, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_stprfs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int nrhs, + const float* ap, const float* b, lapack_int ldb, + const float* x, lapack_int ldx, float* ferr, + float* berr, float* work, lapack_int* iwork ); +lapack_int LAPACKE_dtprfs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int nrhs, + const double* ap, const double* b, + lapack_int ldb, const double* x, lapack_int ldx, + double* ferr, double* berr, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_ctprfs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int nrhs, + const lapack_complex_float* ap, + const lapack_complex_float* b, lapack_int ldb, + const lapack_complex_float* x, lapack_int ldx, + float* ferr, float* berr, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_ztprfs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int nrhs, + const lapack_complex_double* ap, + const lapack_complex_double* b, lapack_int ldb, + const lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_stptri_work( int matrix_order, char uplo, char diag, + lapack_int n, float* ap ); +lapack_int LAPACKE_dtptri_work( int matrix_order, char uplo, char diag, + lapack_int n, double* ap ); +lapack_int LAPACKE_ctptri_work( int matrix_order, char uplo, char diag, + lapack_int n, lapack_complex_float* ap ); +lapack_int LAPACKE_ztptri_work( int matrix_order, char uplo, char diag, + lapack_int n, lapack_complex_double* ap ); + +lapack_int LAPACKE_stptrs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int nrhs, + const float* ap, float* b, lapack_int ldb ); +lapack_int LAPACKE_dtptrs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int nrhs, + const double* ap, double* b, lapack_int ldb ); +lapack_int LAPACKE_ctptrs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int nrhs, + const lapack_complex_float* ap, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_ztptrs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int nrhs, + const lapack_complex_double* ap, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_stpttf_work( int matrix_order, char transr, char uplo, + lapack_int n, const float* ap, float* arf ); +lapack_int LAPACKE_dtpttf_work( int matrix_order, char transr, char uplo, + lapack_int n, const double* ap, double* arf ); +lapack_int LAPACKE_ctpttf_work( int matrix_order, char transr, char uplo, + lapack_int n, const lapack_complex_float* ap, + lapack_complex_float* arf ); +lapack_int LAPACKE_ztpttf_work( int matrix_order, char transr, char uplo, + lapack_int n, const lapack_complex_double* ap, + lapack_complex_double* arf ); + +lapack_int LAPACKE_stpttr_work( int matrix_order, char uplo, lapack_int n, + const float* ap, float* a, lapack_int lda ); +lapack_int LAPACKE_dtpttr_work( int matrix_order, char uplo, lapack_int n, + const double* ap, double* a, lapack_int lda ); +lapack_int LAPACKE_ctpttr_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* ap, + lapack_complex_float* a, lapack_int lda ); +lapack_int LAPACKE_ztpttr_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* ap, + lapack_complex_double* a, lapack_int lda ); + +lapack_int LAPACKE_strcon_work( int matrix_order, char norm, char uplo, + char diag, lapack_int n, const float* a, + lapack_int lda, float* rcond, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dtrcon_work( int matrix_order, char norm, char uplo, + char diag, lapack_int n, const double* a, + lapack_int lda, double* rcond, double* work, + lapack_int* iwork ); +lapack_int LAPACKE_ctrcon_work( int matrix_order, char norm, char uplo, + char diag, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + float* rcond, lapack_complex_float* work, + float* rwork ); +lapack_int LAPACKE_ztrcon_work( int matrix_order, char norm, char uplo, + char diag, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + double* rcond, lapack_complex_double* work, + double* rwork ); + +lapack_int LAPACKE_strevc_work( int matrix_order, char side, char howmny, + lapack_logical* select, lapack_int n, + const float* t, lapack_int ldt, float* vl, + lapack_int ldvl, float* vr, lapack_int ldvr, + lapack_int mm, lapack_int* m, float* work ); +lapack_int LAPACKE_dtrevc_work( int matrix_order, char side, char howmny, + lapack_logical* select, lapack_int n, + const double* t, lapack_int ldt, double* vl, + lapack_int ldvl, double* vr, lapack_int ldvr, + lapack_int mm, lapack_int* m, double* work ); +lapack_int LAPACKE_ctrevc_work( int matrix_order, char side, char howmny, + const lapack_logical* select, lapack_int n, + lapack_complex_float* t, lapack_int ldt, + lapack_complex_float* vl, lapack_int ldvl, + lapack_complex_float* vr, lapack_int ldvr, + lapack_int mm, lapack_int* m, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_ztrevc_work( int matrix_order, char side, char howmny, + const lapack_logical* select, lapack_int n, + lapack_complex_double* t, lapack_int ldt, + lapack_complex_double* vl, lapack_int ldvl, + lapack_complex_double* vr, lapack_int ldvr, + lapack_int mm, lapack_int* m, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_strexc_work( int matrix_order, char compq, lapack_int n, + float* t, lapack_int ldt, float* q, + lapack_int ldq, lapack_int* ifst, + lapack_int* ilst, float* work ); +lapack_int LAPACKE_dtrexc_work( int matrix_order, char compq, lapack_int n, + double* t, lapack_int ldt, double* q, + lapack_int ldq, lapack_int* ifst, + lapack_int* ilst, double* work ); +lapack_int LAPACKE_ctrexc_work( int matrix_order, char compq, lapack_int n, + lapack_complex_float* t, lapack_int ldt, + lapack_complex_float* q, lapack_int ldq, + lapack_int ifst, lapack_int ilst ); +lapack_int LAPACKE_ztrexc_work( int matrix_order, char compq, lapack_int n, + lapack_complex_double* t, lapack_int ldt, + lapack_complex_double* q, lapack_int ldq, + lapack_int ifst, lapack_int ilst ); + +lapack_int LAPACKE_strrfs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int nrhs, + const float* a, lapack_int lda, const float* b, + lapack_int ldb, const float* x, lapack_int ldx, + float* ferr, float* berr, float* work, + lapack_int* iwork ); +lapack_int LAPACKE_dtrrfs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int nrhs, + const double* a, lapack_int lda, + const double* b, lapack_int ldb, + const double* x, lapack_int ldx, double* ferr, + double* berr, double* work, lapack_int* iwork ); +lapack_int LAPACKE_ctrrfs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int nrhs, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* b, lapack_int ldb, + const lapack_complex_float* x, lapack_int ldx, + float* ferr, float* berr, + lapack_complex_float* work, float* rwork ); +lapack_int LAPACKE_ztrrfs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int nrhs, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* b, lapack_int ldb, + const lapack_complex_double* x, lapack_int ldx, + double* ferr, double* berr, + lapack_complex_double* work, double* rwork ); + +lapack_int LAPACKE_strsen_work( int matrix_order, char job, char compq, + const lapack_logical* select, lapack_int n, + float* t, lapack_int ldt, float* q, + lapack_int ldq, float* wr, float* wi, + lapack_int* m, float* s, float* sep, + float* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); +lapack_int LAPACKE_dtrsen_work( int matrix_order, char job, char compq, + const lapack_logical* select, lapack_int n, + double* t, lapack_int ldt, double* q, + lapack_int ldq, double* wr, double* wi, + lapack_int* m, double* s, double* sep, + double* work, lapack_int lwork, + lapack_int* iwork, lapack_int liwork ); +lapack_int LAPACKE_ctrsen_work( int matrix_order, char job, char compq, + const lapack_logical* select, lapack_int n, + lapack_complex_float* t, lapack_int ldt, + lapack_complex_float* q, lapack_int ldq, + lapack_complex_float* w, lapack_int* m, + float* s, float* sep, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_ztrsen_work( int matrix_order, char job, char compq, + const lapack_logical* select, lapack_int n, + lapack_complex_double* t, lapack_int ldt, + lapack_complex_double* q, lapack_int ldq, + lapack_complex_double* w, lapack_int* m, + double* s, double* sep, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_strsna_work( int matrix_order, char job, char howmny, + const lapack_logical* select, lapack_int n, + const float* t, lapack_int ldt, const float* vl, + lapack_int ldvl, const float* vr, + lapack_int ldvr, float* s, float* sep, + lapack_int mm, lapack_int* m, float* work, + lapack_int ldwork, lapack_int* iwork ); +lapack_int LAPACKE_dtrsna_work( int matrix_order, char job, char howmny, + const lapack_logical* select, lapack_int n, + const double* t, lapack_int ldt, + const double* vl, lapack_int ldvl, + const double* vr, lapack_int ldvr, double* s, + double* sep, lapack_int mm, lapack_int* m, + double* work, lapack_int ldwork, + lapack_int* iwork ); +lapack_int LAPACKE_ctrsna_work( int matrix_order, char job, char howmny, + const lapack_logical* select, lapack_int n, + const lapack_complex_float* t, lapack_int ldt, + const lapack_complex_float* vl, lapack_int ldvl, + const lapack_complex_float* vr, lapack_int ldvr, + float* s, float* sep, lapack_int mm, + lapack_int* m, lapack_complex_float* work, + lapack_int ldwork, float* rwork ); +lapack_int LAPACKE_ztrsna_work( int matrix_order, char job, char howmny, + const lapack_logical* select, lapack_int n, + const lapack_complex_double* t, lapack_int ldt, + const lapack_complex_double* vl, + lapack_int ldvl, + const lapack_complex_double* vr, + lapack_int ldvr, double* s, double* sep, + lapack_int mm, lapack_int* m, + lapack_complex_double* work, lapack_int ldwork, + double* rwork ); + +lapack_int LAPACKE_strsyl_work( int matrix_order, char trana, char tranb, + lapack_int isgn, lapack_int m, lapack_int n, + const float* a, lapack_int lda, const float* b, + lapack_int ldb, float* c, lapack_int ldc, + float* scale ); +lapack_int LAPACKE_dtrsyl_work( int matrix_order, char trana, char tranb, + lapack_int isgn, lapack_int m, lapack_int n, + const double* a, lapack_int lda, + const double* b, lapack_int ldb, double* c, + lapack_int ldc, double* scale ); +lapack_int LAPACKE_ctrsyl_work( int matrix_order, char trana, char tranb, + lapack_int isgn, lapack_int m, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* c, lapack_int ldc, + float* scale ); +lapack_int LAPACKE_ztrsyl_work( int matrix_order, char trana, char tranb, + lapack_int isgn, lapack_int m, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* c, lapack_int ldc, + double* scale ); + +lapack_int LAPACKE_strtri_work( int matrix_order, char uplo, char diag, + lapack_int n, float* a, lapack_int lda ); +lapack_int LAPACKE_dtrtri_work( int matrix_order, char uplo, char diag, + lapack_int n, double* a, lapack_int lda ); +lapack_int LAPACKE_ctrtri_work( int matrix_order, char uplo, char diag, + lapack_int n, lapack_complex_float* a, + lapack_int lda ); +lapack_int LAPACKE_ztrtri_work( int matrix_order, char uplo, char diag, + lapack_int n, lapack_complex_double* a, + lapack_int lda ); + +lapack_int LAPACKE_strtrs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int nrhs, + const float* a, lapack_int lda, float* b, + lapack_int ldb ); +lapack_int LAPACKE_dtrtrs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int nrhs, + const double* a, lapack_int lda, double* b, + lapack_int ldb ); +lapack_int LAPACKE_ctrtrs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int nrhs, + const lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_ztrtrs_work( int matrix_order, char uplo, char trans, + char diag, lapack_int n, lapack_int nrhs, + const lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_strttf_work( int matrix_order, char transr, char uplo, + lapack_int n, const float* a, lapack_int lda, + float* arf ); +lapack_int LAPACKE_dtrttf_work( int matrix_order, char transr, char uplo, + lapack_int n, const double* a, lapack_int lda, + double* arf ); +lapack_int LAPACKE_ctrttf_work( int matrix_order, char transr, char uplo, + lapack_int n, const lapack_complex_float* a, + lapack_int lda, lapack_complex_float* arf ); +lapack_int LAPACKE_ztrttf_work( int matrix_order, char transr, char uplo, + lapack_int n, const lapack_complex_double* a, + lapack_int lda, lapack_complex_double* arf ); + +lapack_int LAPACKE_strttp_work( int matrix_order, char uplo, lapack_int n, + const float* a, lapack_int lda, float* ap ); +lapack_int LAPACKE_dtrttp_work( int matrix_order, char uplo, lapack_int n, + const double* a, lapack_int lda, double* ap ); +lapack_int LAPACKE_ctrttp_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + lapack_complex_float* ap ); +lapack_int LAPACKE_ztrttp_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + lapack_complex_double* ap ); + +lapack_int LAPACKE_stzrzf_work( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* tau, + float* work, lapack_int lwork ); +lapack_int LAPACKE_dtzrzf_work( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* tau, + double* work, lapack_int lwork ); +lapack_int LAPACKE_ctzrzf_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* tau, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_ztzrzf_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* tau, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_cungbr_work( int matrix_order, char vect, lapack_int m, + lapack_int n, lapack_int k, + lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* tau, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zungbr_work( int matrix_order, char vect, lapack_int m, + lapack_int n, lapack_int k, + lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* tau, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_cunghr_work( int matrix_order, lapack_int n, lapack_int ilo, + lapack_int ihi, lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* tau, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zunghr_work( int matrix_order, lapack_int n, lapack_int ilo, + lapack_int ihi, lapack_complex_double* a, + lapack_int lda, + const lapack_complex_double* tau, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_cunglq_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* tau, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zunglq_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, lapack_complex_double* a, + lapack_int lda, + const lapack_complex_double* tau, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_cungql_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* tau, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zungql_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, lapack_complex_double* a, + lapack_int lda, + const lapack_complex_double* tau, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_cungqr_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* tau, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zungqr_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, lapack_complex_double* a, + lapack_int lda, + const lapack_complex_double* tau, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_cungrq_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* tau, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zungrq_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int k, lapack_complex_double* a, + lapack_int lda, + const lapack_complex_double* tau, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_cungtr_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* tau, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zungtr_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* tau, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_cunmbr_work( int matrix_order, char vect, char side, + char trans, lapack_int m, lapack_int n, + lapack_int k, const lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int ldc, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zunmbr_work( int matrix_order, char vect, char side, + char trans, lapack_int m, lapack_int n, + lapack_int k, const lapack_complex_double* a, + lapack_int lda, + const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int ldc, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_cunmhr_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int ilo, + lapack_int ihi, const lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int ldc, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zunmhr_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int ilo, + lapack_int ihi, const lapack_complex_double* a, + lapack_int lda, + const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int ldc, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_cunmlq_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int ldc, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zunmlq_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int ldc, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_cunmql_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int ldc, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zunmql_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int ldc, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_cunmqr_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int ldc, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zunmqr_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int ldc, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_cunmrq_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int ldc, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zunmrq_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int ldc, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_cunmrz_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int l, const lapack_complex_float* a, + lapack_int lda, const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int ldc, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zunmrz_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int l, const lapack_complex_double* a, + lapack_int lda, + const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int ldc, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_cunmtr_work( int matrix_order, char side, char uplo, + char trans, lapack_int m, lapack_int n, + const lapack_complex_float* a, lapack_int lda, + const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int ldc, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_zunmtr_work( int matrix_order, char side, char uplo, + char trans, lapack_int m, lapack_int n, + const lapack_complex_double* a, lapack_int lda, + const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int ldc, + lapack_complex_double* work, lapack_int lwork ); + +lapack_int LAPACKE_cupgtr_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_float* ap, + const lapack_complex_float* tau, + lapack_complex_float* q, lapack_int ldq, + lapack_complex_float* work ); +lapack_int LAPACKE_zupgtr_work( int matrix_order, char uplo, lapack_int n, + const lapack_complex_double* ap, + const lapack_complex_double* tau, + lapack_complex_double* q, lapack_int ldq, + lapack_complex_double* work ); + +lapack_int LAPACKE_cupmtr_work( int matrix_order, char side, char uplo, + char trans, lapack_int m, lapack_int n, + const lapack_complex_float* ap, + const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int ldc, + lapack_complex_float* work ); +lapack_int LAPACKE_zupmtr_work( int matrix_order, char side, char uplo, + char trans, lapack_int m, lapack_int n, + const lapack_complex_double* ap, + const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int ldc, + lapack_complex_double* work ); + +lapack_int LAPACKE_claghe( int matrix_order, lapack_int n, lapack_int k, + const float* d, lapack_complex_float* a, + lapack_int lda, lapack_int* iseed ); +lapack_int LAPACKE_zlaghe( int matrix_order, lapack_int n, lapack_int k, + const double* d, lapack_complex_double* a, + lapack_int lda, lapack_int* iseed ); + +lapack_int LAPACKE_slagsy( int matrix_order, lapack_int n, lapack_int k, + const float* d, float* a, lapack_int lda, + lapack_int* iseed ); +lapack_int LAPACKE_dlagsy( int matrix_order, lapack_int n, lapack_int k, + const double* d, double* a, lapack_int lda, + lapack_int* iseed ); +lapack_int LAPACKE_clagsy( int matrix_order, lapack_int n, lapack_int k, + const float* d, lapack_complex_float* a, + lapack_int lda, lapack_int* iseed ); +lapack_int LAPACKE_zlagsy( int matrix_order, lapack_int n, lapack_int k, + const double* d, lapack_complex_double* a, + lapack_int lda, lapack_int* iseed ); + +lapack_int LAPACKE_slapmr( int matrix_order, lapack_logical forwrd, + lapack_int m, lapack_int n, float* x, lapack_int ldx, + lapack_int* k ); +lapack_int LAPACKE_dlapmr( int matrix_order, lapack_logical forwrd, + lapack_int m, lapack_int n, double* x, + lapack_int ldx, lapack_int* k ); +lapack_int LAPACKE_clapmr( int matrix_order, lapack_logical forwrd, + lapack_int m, lapack_int n, lapack_complex_float* x, + lapack_int ldx, lapack_int* k ); +lapack_int LAPACKE_zlapmr( int matrix_order, lapack_logical forwrd, + lapack_int m, lapack_int n, lapack_complex_double* x, + lapack_int ldx, lapack_int* k ); + + +float LAPACKE_slapy2( float x, float y ); +double LAPACKE_dlapy2( double x, double y ); + +float LAPACKE_slapy3( float x, float y, float z ); +double LAPACKE_dlapy3( double x, double y, double z ); + +lapack_int LAPACKE_slartgp( float f, float g, float* cs, float* sn, float* r ); +lapack_int LAPACKE_dlartgp( double f, double g, double* cs, double* sn, + double* r ); + +lapack_int LAPACKE_slartgs( float x, float y, float sigma, float* cs, + float* sn ); +lapack_int LAPACKE_dlartgs( double x, double y, double sigma, double* cs, + double* sn ); + + +//LAPACK 3.3.0 +lapack_int LAPACKE_cbbcsd( int matrix_order, char jobu1, char jobu2, + char jobv1t, char jobv2t, char trans, lapack_int m, + lapack_int p, lapack_int q, float* theta, float* phi, + lapack_complex_float* u1, lapack_int ldu1, + lapack_complex_float* u2, lapack_int ldu2, + lapack_complex_float* v1t, lapack_int ldv1t, + lapack_complex_float* v2t, lapack_int ldv2t, + float* b11d, float* b11e, float* b12d, float* b12e, + float* b21d, float* b21e, float* b22d, float* b22e ); +lapack_int LAPACKE_cbbcsd_work( int matrix_order, char jobu1, char jobu2, + char jobv1t, char jobv2t, char trans, + lapack_int m, lapack_int p, lapack_int q, + float* theta, float* phi, + lapack_complex_float* u1, lapack_int ldu1, + lapack_complex_float* u2, lapack_int ldu2, + lapack_complex_float* v1t, lapack_int ldv1t, + lapack_complex_float* v2t, lapack_int ldv2t, + float* b11d, float* b11e, float* b12d, + float* b12e, float* b21d, float* b21e, + float* b22d, float* b22e, float* rwork, + lapack_int lrwork ); +lapack_int LAPACKE_cheswapr( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int i1, + lapack_int i2 ); +lapack_int LAPACKE_cheswapr_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int i1, + lapack_int i2 ); +lapack_int LAPACKE_chetri2( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + const lapack_int* ipiv ); +lapack_int LAPACKE_chetri2_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + const lapack_int* ipiv, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_chetri2x( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + const lapack_int* ipiv, lapack_int nb ); +lapack_int LAPACKE_chetri2x_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + const lapack_int* ipiv, + lapack_complex_float* work, lapack_int nb ); +lapack_int LAPACKE_chetrs2( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_chetrs2_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* work ); +lapack_int LAPACKE_csyconv( int matrix_order, char uplo, char way, lapack_int n, + lapack_complex_float* a, lapack_int lda, + const lapack_int* ipiv ); +lapack_int LAPACKE_csyconv_work( int matrix_order, char uplo, char way, + lapack_int n, lapack_complex_float* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_float* work ); +lapack_int LAPACKE_csyswapr( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int i1, + lapack_int i2 ); +lapack_int LAPACKE_csyswapr_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int i1, + lapack_int i2 ); +lapack_int LAPACKE_csytri2( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + const lapack_int* ipiv ); +lapack_int LAPACKE_csytri2_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + const lapack_int* ipiv, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_csytri2x( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + const lapack_int* ipiv, lapack_int nb ); +lapack_int LAPACKE_csytri2x_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float* a, lapack_int lda, + const lapack_int* ipiv, + lapack_complex_float* work, lapack_int nb ); +lapack_int LAPACKE_csytrs2( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_csytrs2_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_float* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* work ); +lapack_int LAPACKE_cunbdb( int matrix_order, char trans, char signs, + lapack_int m, lapack_int p, lapack_int q, + lapack_complex_float* x11, lapack_int ldx11, + lapack_complex_float* x12, lapack_int ldx12, + lapack_complex_float* x21, lapack_int ldx21, + lapack_complex_float* x22, lapack_int ldx22, + float* theta, float* phi, + lapack_complex_float* taup1, + lapack_complex_float* taup2, + lapack_complex_float* tauq1, + lapack_complex_float* tauq2 ); +lapack_int LAPACKE_cunbdb_work( int matrix_order, char trans, char signs, + lapack_int m, lapack_int p, lapack_int q, + lapack_complex_float* x11, lapack_int ldx11, + lapack_complex_float* x12, lapack_int ldx12, + lapack_complex_float* x21, lapack_int ldx21, + lapack_complex_float* x22, lapack_int ldx22, + float* theta, float* phi, + lapack_complex_float* taup1, + lapack_complex_float* taup2, + lapack_complex_float* tauq1, + lapack_complex_float* tauq2, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_cuncsd( int matrix_order, char jobu1, char jobu2, + char jobv1t, char jobv2t, char trans, char signs, + lapack_int m, lapack_int p, lapack_int q, + lapack_complex_float* x11, lapack_int ldx11, + lapack_complex_float* x12, lapack_int ldx12, + lapack_complex_float* x21, lapack_int ldx21, + lapack_complex_float* x22, lapack_int ldx22, + float* theta, lapack_complex_float* u1, + lapack_int ldu1, lapack_complex_float* u2, + lapack_int ldu2, lapack_complex_float* v1t, + lapack_int ldv1t, lapack_complex_float* v2t, + lapack_int ldv2t ); +lapack_int LAPACKE_cuncsd_work( int matrix_order, char jobu1, char jobu2, + char jobv1t, char jobv2t, char trans, + char signs, lapack_int m, lapack_int p, + lapack_int q, lapack_complex_float* x11, + lapack_int ldx11, lapack_complex_float* x12, + lapack_int ldx12, lapack_complex_float* x21, + lapack_int ldx21, lapack_complex_float* x22, + lapack_int ldx22, float* theta, + lapack_complex_float* u1, lapack_int ldu1, + lapack_complex_float* u2, lapack_int ldu2, + lapack_complex_float* v1t, lapack_int ldv1t, + lapack_complex_float* v2t, lapack_int ldv2t, + lapack_complex_float* work, lapack_int lwork, + float* rwork, lapack_int lrwork, + lapack_int* iwork ); +lapack_int LAPACKE_dbbcsd( int matrix_order, char jobu1, char jobu2, + char jobv1t, char jobv2t, char trans, lapack_int m, + lapack_int p, lapack_int q, double* theta, + double* phi, double* u1, lapack_int ldu1, double* u2, + lapack_int ldu2, double* v1t, lapack_int ldv1t, + double* v2t, lapack_int ldv2t, double* b11d, + double* b11e, double* b12d, double* b12e, + double* b21d, double* b21e, double* b22d, + double* b22e ); +lapack_int LAPACKE_dbbcsd_work( int matrix_order, char jobu1, char jobu2, + char jobv1t, char jobv2t, char trans, + lapack_int m, lapack_int p, lapack_int q, + double* theta, double* phi, double* u1, + lapack_int ldu1, double* u2, lapack_int ldu2, + double* v1t, lapack_int ldv1t, double* v2t, + lapack_int ldv2t, double* b11d, double* b11e, + double* b12d, double* b12e, double* b21d, + double* b21e, double* b22d, double* b22e, + double* work, lapack_int lwork ); +lapack_int LAPACKE_dorbdb( int matrix_order, char trans, char signs, + lapack_int m, lapack_int p, lapack_int q, + double* x11, lapack_int ldx11, double* x12, + lapack_int ldx12, double* x21, lapack_int ldx21, + double* x22, lapack_int ldx22, double* theta, + double* phi, double* taup1, double* taup2, + double* tauq1, double* tauq2 ); +lapack_int LAPACKE_dorbdb_work( int matrix_order, char trans, char signs, + lapack_int m, lapack_int p, lapack_int q, + double* x11, lapack_int ldx11, double* x12, + lapack_int ldx12, double* x21, lapack_int ldx21, + double* x22, lapack_int ldx22, double* theta, + double* phi, double* taup1, double* taup2, + double* tauq1, double* tauq2, double* work, + lapack_int lwork ); +lapack_int LAPACKE_dorcsd( int matrix_order, char jobu1, char jobu2, + char jobv1t, char jobv2t, char trans, char signs, + lapack_int m, lapack_int p, lapack_int q, + double* x11, lapack_int ldx11, double* x12, + lapack_int ldx12, double* x21, lapack_int ldx21, + double* x22, lapack_int ldx22, double* theta, + double* u1, lapack_int ldu1, double* u2, + lapack_int ldu2, double* v1t, lapack_int ldv1t, + double* v2t, lapack_int ldv2t ); +lapack_int LAPACKE_dorcsd_work( int matrix_order, char jobu1, char jobu2, + char jobv1t, char jobv2t, char trans, + char signs, lapack_int m, lapack_int p, + lapack_int q, double* x11, lapack_int ldx11, + double* x12, lapack_int ldx12, double* x21, + lapack_int ldx21, double* x22, lapack_int ldx22, + double* theta, double* u1, lapack_int ldu1, + double* u2, lapack_int ldu2, double* v1t, + lapack_int ldv1t, double* v2t, lapack_int ldv2t, + double* work, lapack_int lwork, + lapack_int* iwork ); +lapack_int LAPACKE_dsyconv( int matrix_order, char uplo, char way, lapack_int n, + double* a, lapack_int lda, const lapack_int* ipiv ); +lapack_int LAPACKE_dsyconv_work( int matrix_order, char uplo, char way, + lapack_int n, double* a, lapack_int lda, + const lapack_int* ipiv, double* work ); +lapack_int LAPACKE_dsyswapr( int matrix_order, char uplo, lapack_int n, + double* a, lapack_int i1, lapack_int i2 ); +lapack_int LAPACKE_dsyswapr_work( int matrix_order, char uplo, lapack_int n, + double* a, lapack_int i1, lapack_int i2 ); +lapack_int LAPACKE_dsytri2( int matrix_order, char uplo, lapack_int n, + double* a, lapack_int lda, const lapack_int* ipiv ); +lapack_int LAPACKE_dsytri2_work( int matrix_order, char uplo, lapack_int n, + double* a, lapack_int lda, + const lapack_int* ipiv, + lapack_complex_double* work, lapack_int lwork ); +lapack_int LAPACKE_dsytri2x( int matrix_order, char uplo, lapack_int n, + double* a, lapack_int lda, const lapack_int* ipiv, + lapack_int nb ); +lapack_int LAPACKE_dsytri2x_work( int matrix_order, char uplo, lapack_int n, + double* a, lapack_int lda, + const lapack_int* ipiv, double* work, + lapack_int nb ); +lapack_int LAPACKE_dsytrs2( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* a, lapack_int lda, + const lapack_int* ipiv, double* b, lapack_int ldb ); +lapack_int LAPACKE_dsytrs2_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const double* a, + lapack_int lda, const lapack_int* ipiv, + double* b, lapack_int ldb, double* work ); +lapack_int LAPACKE_sbbcsd( int matrix_order, char jobu1, char jobu2, + char jobv1t, char jobv2t, char trans, lapack_int m, + lapack_int p, lapack_int q, float* theta, float* phi, + float* u1, lapack_int ldu1, float* u2, + lapack_int ldu2, float* v1t, lapack_int ldv1t, + float* v2t, lapack_int ldv2t, float* b11d, + float* b11e, float* b12d, float* b12e, float* b21d, + float* b21e, float* b22d, float* b22e ); +lapack_int LAPACKE_sbbcsd_work( int matrix_order, char jobu1, char jobu2, + char jobv1t, char jobv2t, char trans, + lapack_int m, lapack_int p, lapack_int q, + float* theta, float* phi, float* u1, + lapack_int ldu1, float* u2, lapack_int ldu2, + float* v1t, lapack_int ldv1t, float* v2t, + lapack_int ldv2t, float* b11d, float* b11e, + float* b12d, float* b12e, float* b21d, + float* b21e, float* b22d, float* b22e, + float* work, lapack_int lwork ); +lapack_int LAPACKE_sorbdb( int matrix_order, char trans, char signs, + lapack_int m, lapack_int p, lapack_int q, float* x11, + lapack_int ldx11, float* x12, lapack_int ldx12, + float* x21, lapack_int ldx21, float* x22, + lapack_int ldx22, float* theta, float* phi, + float* taup1, float* taup2, float* tauq1, + float* tauq2 ); +lapack_int LAPACKE_sorbdb_work( int matrix_order, char trans, char signs, + lapack_int m, lapack_int p, lapack_int q, + float* x11, lapack_int ldx11, float* x12, + lapack_int ldx12, float* x21, lapack_int ldx21, + float* x22, lapack_int ldx22, float* theta, + float* phi, float* taup1, float* taup2, + float* tauq1, float* tauq2, float* work, + lapack_int lwork ); +lapack_int LAPACKE_sorcsd( int matrix_order, char jobu1, char jobu2, + char jobv1t, char jobv2t, char trans, char signs, + lapack_int m, lapack_int p, lapack_int q, float* x11, + lapack_int ldx11, float* x12, lapack_int ldx12, + float* x21, lapack_int ldx21, float* x22, + lapack_int ldx22, float* theta, float* u1, + lapack_int ldu1, float* u2, lapack_int ldu2, + float* v1t, lapack_int ldv1t, float* v2t, + lapack_int ldv2t ); +lapack_int LAPACKE_sorcsd_work( int matrix_order, char jobu1, char jobu2, + char jobv1t, char jobv2t, char trans, + char signs, lapack_int m, lapack_int p, + lapack_int q, float* x11, lapack_int ldx11, + float* x12, lapack_int ldx12, float* x21, + lapack_int ldx21, float* x22, lapack_int ldx22, + float* theta, float* u1, lapack_int ldu1, + float* u2, lapack_int ldu2, float* v1t, + lapack_int ldv1t, float* v2t, lapack_int ldv2t, + float* work, lapack_int lwork, + lapack_int* iwork ); +lapack_int LAPACKE_ssyconv( int matrix_order, char uplo, char way, lapack_int n, + float* a, lapack_int lda, const lapack_int* ipiv ); +lapack_int LAPACKE_ssyconv_work( int matrix_order, char uplo, char way, + lapack_int n, float* a, lapack_int lda, + const lapack_int* ipiv, float* work ); +lapack_int LAPACKE_ssyswapr( int matrix_order, char uplo, lapack_int n, + float* a, lapack_int i1, lapack_int i2 ); +lapack_int LAPACKE_ssyswapr_work( int matrix_order, char uplo, lapack_int n, + float* a, lapack_int i1, lapack_int i2 ); +lapack_int LAPACKE_ssytri2( int matrix_order, char uplo, lapack_int n, float* a, + lapack_int lda, const lapack_int* ipiv ); +lapack_int LAPACKE_ssytri2_work( int matrix_order, char uplo, lapack_int n, + float* a, lapack_int lda, + const lapack_int* ipiv, + lapack_complex_float* work, lapack_int lwork ); +lapack_int LAPACKE_ssytri2x( int matrix_order, char uplo, lapack_int n, + float* a, lapack_int lda, const lapack_int* ipiv, + lapack_int nb ); +lapack_int LAPACKE_ssytri2x_work( int matrix_order, char uplo, lapack_int n, + float* a, lapack_int lda, + const lapack_int* ipiv, float* work, + lapack_int nb ); +lapack_int LAPACKE_ssytrs2( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* a, lapack_int lda, + const lapack_int* ipiv, float* b, lapack_int ldb ); +lapack_int LAPACKE_ssytrs2_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const float* a, + lapack_int lda, const lapack_int* ipiv, + float* b, lapack_int ldb, float* work ); +lapack_int LAPACKE_zbbcsd( int matrix_order, char jobu1, char jobu2, + char jobv1t, char jobv2t, char trans, lapack_int m, + lapack_int p, lapack_int q, double* theta, + double* phi, lapack_complex_double* u1, + lapack_int ldu1, lapack_complex_double* u2, + lapack_int ldu2, lapack_complex_double* v1t, + lapack_int ldv1t, lapack_complex_double* v2t, + lapack_int ldv2t, double* b11d, double* b11e, + double* b12d, double* b12e, double* b21d, + double* b21e, double* b22d, double* b22e ); +lapack_int LAPACKE_zbbcsd_work( int matrix_order, char jobu1, char jobu2, + char jobv1t, char jobv2t, char trans, + lapack_int m, lapack_int p, lapack_int q, + double* theta, double* phi, + lapack_complex_double* u1, lapack_int ldu1, + lapack_complex_double* u2, lapack_int ldu2, + lapack_complex_double* v1t, lapack_int ldv1t, + lapack_complex_double* v2t, lapack_int ldv2t, + double* b11d, double* b11e, double* b12d, + double* b12e, double* b21d, double* b21e, + double* b22d, double* b22e, double* rwork, + lapack_int lrwork ); +lapack_int LAPACKE_zheswapr( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int i1, + lapack_int i2 ); +lapack_int LAPACKE_zheswapr_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int i1, + lapack_int i2 ); +lapack_int LAPACKE_zhetri2( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + const lapack_int* ipiv ); +lapack_int LAPACKE_zhetri2_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + const lapack_int* ipiv, + lapack_complex_double* work, lapack_int lwork ); +lapack_int LAPACKE_zhetri2x( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + const lapack_int* ipiv, lapack_int nb ); +lapack_int LAPACKE_zhetri2x_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + const lapack_int* ipiv, + lapack_complex_double* work, lapack_int nb ); +lapack_int LAPACKE_zhetrs2( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_double* b, lapack_int ldb ); +lapack_int LAPACKE_zhetrs2_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* work ); +lapack_int LAPACKE_zsyconv( int matrix_order, char uplo, char way, lapack_int n, + lapack_complex_double* a, lapack_int lda, + const lapack_int* ipiv ); +lapack_int LAPACKE_zsyconv_work( int matrix_order, char uplo, char way, + lapack_int n, lapack_complex_double* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_double* work ); +lapack_int LAPACKE_zsyswapr( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int i1, + lapack_int i2 ); +lapack_int LAPACKE_zsyswapr_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int i1, + lapack_int i2 ); +lapack_int LAPACKE_zsytri2( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + const lapack_int* ipiv ); +lapack_int LAPACKE_zsytri2_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + const lapack_int* ipiv, + lapack_complex_double* work, lapack_int lwork ); +lapack_int LAPACKE_zsytri2x( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + const lapack_int* ipiv, lapack_int nb ); +lapack_int LAPACKE_zsytri2x_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double* a, lapack_int lda, + const lapack_int* ipiv, + lapack_complex_double* work, lapack_int nb ); +lapack_int LAPACKE_zsytrs2( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_double* b, lapack_int ldb ); +lapack_int LAPACKE_zsytrs2_work( int matrix_order, char uplo, lapack_int n, + lapack_int nrhs, const lapack_complex_double* a, + lapack_int lda, const lapack_int* ipiv, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* work ); +lapack_int LAPACKE_zunbdb( int matrix_order, char trans, char signs, + lapack_int m, lapack_int p, lapack_int q, + lapack_complex_double* x11, lapack_int ldx11, + lapack_complex_double* x12, lapack_int ldx12, + lapack_complex_double* x21, lapack_int ldx21, + lapack_complex_double* x22, lapack_int ldx22, + double* theta, double* phi, + lapack_complex_double* taup1, + lapack_complex_double* taup2, + lapack_complex_double* tauq1, + lapack_complex_double* tauq2 ); +lapack_int LAPACKE_zunbdb_work( int matrix_order, char trans, char signs, + lapack_int m, lapack_int p, lapack_int q, + lapack_complex_double* x11, lapack_int ldx11, + lapack_complex_double* x12, lapack_int ldx12, + lapack_complex_double* x21, lapack_int ldx21, + lapack_complex_double* x22, lapack_int ldx22, + double* theta, double* phi, + lapack_complex_double* taup1, + lapack_complex_double* taup2, + lapack_complex_double* tauq1, + lapack_complex_double* tauq2, + lapack_complex_double* work, lapack_int lwork ); +lapack_int LAPACKE_zuncsd( int matrix_order, char jobu1, char jobu2, + char jobv1t, char jobv2t, char trans, char signs, + lapack_int m, lapack_int p, lapack_int q, + lapack_complex_double* x11, lapack_int ldx11, + lapack_complex_double* x12, lapack_int ldx12, + lapack_complex_double* x21, lapack_int ldx21, + lapack_complex_double* x22, lapack_int ldx22, + double* theta, lapack_complex_double* u1, + lapack_int ldu1, lapack_complex_double* u2, + lapack_int ldu2, lapack_complex_double* v1t, + lapack_int ldv1t, lapack_complex_double* v2t, + lapack_int ldv2t ); +lapack_int LAPACKE_zuncsd_work( int matrix_order, char jobu1, char jobu2, + char jobv1t, char jobv2t, char trans, + char signs, lapack_int m, lapack_int p, + lapack_int q, lapack_complex_double* x11, + lapack_int ldx11, lapack_complex_double* x12, + lapack_int ldx12, lapack_complex_double* x21, + lapack_int ldx21, lapack_complex_double* x22, + lapack_int ldx22, double* theta, + lapack_complex_double* u1, lapack_int ldu1, + lapack_complex_double* u2, lapack_int ldu2, + lapack_complex_double* v1t, lapack_int ldv1t, + lapack_complex_double* v2t, lapack_int ldv2t, + lapack_complex_double* work, lapack_int lwork, + double* rwork, lapack_int lrwork, + lapack_int* iwork ); +//LAPACK 3.4.0 +lapack_int LAPACKE_sgemqrt( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int nb, const float* v, lapack_int ldv, + const float* t, lapack_int ldt, float* c, + lapack_int ldc ); +lapack_int LAPACKE_dgemqrt( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int nb, const double* v, lapack_int ldv, + const double* t, lapack_int ldt, double* c, + lapack_int ldc ); +lapack_int LAPACKE_cgemqrt( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int nb, const lapack_complex_float* v, + lapack_int ldv, const lapack_complex_float* t, + lapack_int ldt, lapack_complex_float* c, + lapack_int ldc ); +lapack_int LAPACKE_zgemqrt( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int nb, const lapack_complex_double* v, + lapack_int ldv, const lapack_complex_double* t, + lapack_int ldt, lapack_complex_double* c, + lapack_int ldc ); + +lapack_int LAPACKE_sgeqrt( int matrix_order, lapack_int m, lapack_int n, + lapack_int nb, float* a, lapack_int lda, float* t, + lapack_int ldt ); +lapack_int LAPACKE_dgeqrt( int matrix_order, lapack_int m, lapack_int n, + lapack_int nb, double* a, lapack_int lda, double* t, + lapack_int ldt ); +lapack_int LAPACKE_cgeqrt( int matrix_order, lapack_int m, lapack_int n, + lapack_int nb, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* t, + lapack_int ldt ); +lapack_int LAPACKE_zgeqrt( int matrix_order, lapack_int m, lapack_int n, + lapack_int nb, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* t, + lapack_int ldt ); + +lapack_int LAPACKE_sgeqrt2( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* t, + lapack_int ldt ); +lapack_int LAPACKE_dgeqrt2( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* t, + lapack_int ldt ); +lapack_int LAPACKE_cgeqrt2( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* t, lapack_int ldt ); +lapack_int LAPACKE_zgeqrt2( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* t, lapack_int ldt ); + +lapack_int LAPACKE_sgeqrt3( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* t, + lapack_int ldt ); +lapack_int LAPACKE_dgeqrt3( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* t, + lapack_int ldt ); +lapack_int LAPACKE_cgeqrt3( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* t, lapack_int ldt ); +lapack_int LAPACKE_zgeqrt3( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* t, lapack_int ldt ); + +lapack_int LAPACKE_stpmqrt( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int l, lapack_int nb, const float* v, + lapack_int ldv, const float* t, lapack_int ldt, + float* a, lapack_int lda, float* b, + lapack_int ldb ); +lapack_int LAPACKE_dtpmqrt( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int l, lapack_int nb, const double* v, + lapack_int ldv, const double* t, lapack_int ldt, + double* a, lapack_int lda, double* b, + lapack_int ldb ); +lapack_int LAPACKE_ctpmqrt( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int l, lapack_int nb, + const lapack_complex_float* v, lapack_int ldv, + const lapack_complex_float* t, lapack_int ldt, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb ); +lapack_int LAPACKE_ztpmqrt( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int l, lapack_int nb, + const lapack_complex_double* v, lapack_int ldv, + const lapack_complex_double* t, lapack_int ldt, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb ); + +lapack_int LAPACKE_dtpqrt( int matrix_order, lapack_int m, lapack_int n, + lapack_int l, lapack_int nb, double* a, + lapack_int lda, double* b, lapack_int ldb, double* t, + lapack_int ldt ); +lapack_int LAPACKE_ctpqrt( int matrix_order, lapack_int m, lapack_int n, + lapack_int l, lapack_int nb, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* t, + lapack_complex_float* b, lapack_int ldb, + lapack_int ldt ); +lapack_int LAPACKE_ztpqrt( int matrix_order, lapack_int m, lapack_int n, + lapack_int l, lapack_int nb, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* t, lapack_int ldt ); + +lapack_int LAPACKE_stpqrt2( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* b, lapack_int ldb, + float* t, lapack_int ldt ); +lapack_int LAPACKE_dtpqrt2( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* b, + lapack_int ldb, double* t, lapack_int ldt ); +lapack_int LAPACKE_ctpqrt2( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* t, lapack_int ldt ); +lapack_int LAPACKE_ztpqrt2( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* t, lapack_int ldt ); + +lapack_int LAPACKE_stprfb( int matrix_order, char side, char trans, char direct, + char storev, lapack_int m, lapack_int n, + lapack_int k, lapack_int l, const float* v, + lapack_int ldv, const float* t, lapack_int ldt, + float* a, lapack_int lda, float* b, lapack_int ldb, + lapack_int myldwork ); +lapack_int LAPACKE_dtprfb( int matrix_order, char side, char trans, char direct, + char storev, lapack_int m, lapack_int n, + lapack_int k, lapack_int l, const double* v, + lapack_int ldv, const double* t, lapack_int ldt, + double* a, lapack_int lda, double* b, lapack_int ldb, + lapack_int myldwork ); +lapack_int LAPACKE_ctprfb( int matrix_order, char side, char trans, char direct, + char storev, lapack_int m, lapack_int n, + lapack_int k, lapack_int l, + const lapack_complex_float* v, lapack_int ldv, + const lapack_complex_float* t, lapack_int ldt, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + lapack_int myldwork ); +lapack_int LAPACKE_ztprfb( int matrix_order, char side, char trans, char direct, + char storev, lapack_int m, lapack_int n, + lapack_int k, lapack_int l, + const lapack_complex_double* v, lapack_int ldv, + const lapack_complex_double* t, lapack_int ldt, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + lapack_int myldwork ); + +lapack_int LAPACKE_sgemqrt_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int nb, const float* v, lapack_int ldv, + const float* t, lapack_int ldt, float* c, + lapack_int ldc, float* work ); +lapack_int LAPACKE_dgemqrt_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int nb, const double* v, lapack_int ldv, + const double* t, lapack_int ldt, double* c, + lapack_int ldc, double* work ); +lapack_int LAPACKE_cgemqrt_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int nb, const lapack_complex_float* v, + lapack_int ldv, const lapack_complex_float* t, + lapack_int ldt, lapack_complex_float* c, + lapack_int ldc, lapack_complex_float* work ); +lapack_int LAPACKE_zgemqrt_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int nb, const lapack_complex_double* v, + lapack_int ldv, const lapack_complex_double* t, + lapack_int ldt, lapack_complex_double* c, + lapack_int ldc, lapack_complex_double* work ); + +lapack_int LAPACKE_sgeqrt_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int nb, float* a, lapack_int lda, + float* t, lapack_int ldt, float* work ); +lapack_int LAPACKE_dgeqrt_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int nb, double* a, lapack_int lda, + double* t, lapack_int ldt, double* work ); +lapack_int LAPACKE_cgeqrt_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int nb, lapack_complex_float* a, + lapack_int lda, lapack_complex_float* t, + lapack_int ldt, lapack_complex_float* work ); +lapack_int LAPACKE_zgeqrt_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int nb, lapack_complex_double* a, + lapack_int lda, lapack_complex_double* t, + lapack_int ldt, lapack_complex_double* work ); + +lapack_int LAPACKE_sgeqrt2_work( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* t, + lapack_int ldt ); +lapack_int LAPACKE_dgeqrt2_work( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* t, + lapack_int ldt ); +lapack_int LAPACKE_cgeqrt2_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* t, lapack_int ldt ); +lapack_int LAPACKE_zgeqrt2_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* t, lapack_int ldt ); + +lapack_int LAPACKE_sgeqrt3_work( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* t, + lapack_int ldt ); +lapack_int LAPACKE_dgeqrt3_work( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* t, + lapack_int ldt ); +lapack_int LAPACKE_cgeqrt3_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* t, lapack_int ldt ); +lapack_int LAPACKE_zgeqrt3_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* t, lapack_int ldt ); + +lapack_int LAPACKE_stpmqrt_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int l, lapack_int nb, const float* v, + lapack_int ldv, const float* t, lapack_int ldt, + float* a, lapack_int lda, float* b, + lapack_int ldb, float* work ); +lapack_int LAPACKE_dtpmqrt_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int l, lapack_int nb, const double* v, + lapack_int ldv, const double* t, + lapack_int ldt, double* a, lapack_int lda, + double* b, lapack_int ldb, double* work ); +lapack_int LAPACKE_ctpmqrt_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int l, lapack_int nb, + const lapack_complex_float* v, lapack_int ldv, + const lapack_complex_float* t, lapack_int ldt, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* work ); +lapack_int LAPACKE_ztpmqrt_work( int matrix_order, char side, char trans, + lapack_int m, lapack_int n, lapack_int k, + lapack_int l, lapack_int nb, + const lapack_complex_double* v, lapack_int ldv, + const lapack_complex_double* t, lapack_int ldt, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* work ); + +lapack_int LAPACKE_dtpqrt_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int l, lapack_int nb, double* a, + lapack_int lda, double* b, lapack_int ldb, + double* t, lapack_int ldt, double* work ); +lapack_int LAPACKE_ctpqrt_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int l, lapack_int nb, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* t, + lapack_complex_float* b, lapack_int ldb, + lapack_int ldt, lapack_complex_float* work ); +lapack_int LAPACKE_ztpqrt_work( int matrix_order, lapack_int m, lapack_int n, + lapack_int l, lapack_int nb, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* t, lapack_int ldt, + lapack_complex_double* work ); + +lapack_int LAPACKE_stpqrt2_work( int matrix_order, lapack_int m, lapack_int n, + float* a, lapack_int lda, float* b, + lapack_int ldb, float* t, lapack_int ldt ); +lapack_int LAPACKE_dtpqrt2_work( int matrix_order, lapack_int m, lapack_int n, + double* a, lapack_int lda, double* b, + lapack_int ldb, double* t, lapack_int ldt ); +lapack_int LAPACKE_ctpqrt2_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + lapack_complex_float* t, lapack_int ldt ); +lapack_int LAPACKE_ztpqrt2_work( int matrix_order, lapack_int m, lapack_int n, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + lapack_complex_double* t, lapack_int ldt ); + +lapack_int LAPACKE_stprfb_work( int matrix_order, char side, char trans, + char direct, char storev, lapack_int m, + lapack_int n, lapack_int k, lapack_int l, + const float* v, lapack_int ldv, const float* t, + lapack_int ldt, float* a, lapack_int lda, + float* b, lapack_int ldb, const float* mywork, + lapack_int myldwork ); +lapack_int LAPACKE_dtprfb_work( int matrix_order, char side, char trans, + char direct, char storev, lapack_int m, + lapack_int n, lapack_int k, lapack_int l, + const double* v, lapack_int ldv, + const double* t, lapack_int ldt, double* a, + lapack_int lda, double* b, lapack_int ldb, + const double* mywork, lapack_int myldwork ); +lapack_int LAPACKE_ctprfb_work( int matrix_order, char side, char trans, + char direct, char storev, lapack_int m, + lapack_int n, lapack_int k, lapack_int l, + const lapack_complex_float* v, lapack_int ldv, + const lapack_complex_float* t, lapack_int ldt, + lapack_complex_float* a, lapack_int lda, + lapack_complex_float* b, lapack_int ldb, + const float* mywork, lapack_int myldwork ); +lapack_int LAPACKE_ztprfb_work( int matrix_order, char side, char trans, + char direct, char storev, lapack_int m, + lapack_int n, lapack_int k, lapack_int l, + const lapack_complex_double* v, lapack_int ldv, + const lapack_complex_double* t, lapack_int ldt, + lapack_complex_double* a, lapack_int lda, + lapack_complex_double* b, lapack_int ldb, + const double* mywork, lapack_int myldwork ); +//LAPACK 3.X.X +lapack_int LAPACKE_csyr( int matrix_order, char uplo, lapack_int n, + lapack_complex_float alpha, + const lapack_complex_float* x, lapack_int incx, + lapack_complex_float* a, lapack_int lda ); +lapack_int LAPACKE_zsyr( int matrix_order, char uplo, lapack_int n, + lapack_complex_double alpha, + const lapack_complex_double* x, lapack_int incx, + lapack_complex_double* a, lapack_int lda ); + +lapack_int LAPACKE_csyr_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_float alpha, + const lapack_complex_float* x, + lapack_int incx, lapack_complex_float* a, + lapack_int lda ); +lapack_int LAPACKE_zsyr_work( int matrix_order, char uplo, lapack_int n, + lapack_complex_double alpha, + const lapack_complex_double* x, + lapack_int incx, lapack_complex_double* a, + lapack_int lda ); + + + +#define LAPACK_sgetrf LAPACK_GLOBAL(sgetrf,SGETRF) +#define LAPACK_dgetrf LAPACK_GLOBAL(dgetrf,DGETRF) +#define LAPACK_cgetrf LAPACK_GLOBAL(cgetrf,CGETRF) +#define LAPACK_zgetrf LAPACK_GLOBAL(zgetrf,ZGETRF) +#define LAPACK_sgbtrf LAPACK_GLOBAL(sgbtrf,SGBTRF) +#define LAPACK_dgbtrf LAPACK_GLOBAL(dgbtrf,DGBTRF) +#define LAPACK_cgbtrf LAPACK_GLOBAL(cgbtrf,CGBTRF) +#define LAPACK_zgbtrf LAPACK_GLOBAL(zgbtrf,ZGBTRF) +#define LAPACK_sgttrf LAPACK_GLOBAL(sgttrf,SGTTRF) +#define LAPACK_dgttrf LAPACK_GLOBAL(dgttrf,DGTTRF) +#define LAPACK_cgttrf LAPACK_GLOBAL(cgttrf,CGTTRF) +#define LAPACK_zgttrf LAPACK_GLOBAL(zgttrf,ZGTTRF) +#define LAPACK_spotrf LAPACK_GLOBAL(spotrf,SPOTRF) +#define LAPACK_dpotrf LAPACK_GLOBAL(dpotrf,DPOTRF) +#define LAPACK_cpotrf LAPACK_GLOBAL(cpotrf,CPOTRF) +#define LAPACK_zpotrf LAPACK_GLOBAL(zpotrf,ZPOTRF) +#define LAPACK_dpstrf LAPACK_GLOBAL(dpstrf,DPSTRF) +#define LAPACK_spstrf LAPACK_GLOBAL(spstrf,SPSTRF) +#define LAPACK_zpstrf LAPACK_GLOBAL(zpstrf,ZPSTRF) +#define LAPACK_cpstrf LAPACK_GLOBAL(cpstrf,CPSTRF) +#define LAPACK_dpftrf LAPACK_GLOBAL(dpftrf,DPFTRF) +#define LAPACK_spftrf LAPACK_GLOBAL(spftrf,SPFTRF) +#define LAPACK_zpftrf LAPACK_GLOBAL(zpftrf,ZPFTRF) +#define LAPACK_cpftrf LAPACK_GLOBAL(cpftrf,CPFTRF) +#define LAPACK_spptrf LAPACK_GLOBAL(spptrf,SPPTRF) +#define LAPACK_dpptrf LAPACK_GLOBAL(dpptrf,DPPTRF) +#define LAPACK_cpptrf LAPACK_GLOBAL(cpptrf,CPPTRF) +#define LAPACK_zpptrf LAPACK_GLOBAL(zpptrf,ZPPTRF) +#define LAPACK_spbtrf LAPACK_GLOBAL(spbtrf,SPBTRF) +#define LAPACK_dpbtrf LAPACK_GLOBAL(dpbtrf,DPBTRF) +#define LAPACK_cpbtrf LAPACK_GLOBAL(cpbtrf,CPBTRF) +#define LAPACK_zpbtrf LAPACK_GLOBAL(zpbtrf,ZPBTRF) +#define LAPACK_spttrf LAPACK_GLOBAL(spttrf,SPTTRF) +#define LAPACK_dpttrf LAPACK_GLOBAL(dpttrf,DPTTRF) +#define LAPACK_cpttrf LAPACK_GLOBAL(cpttrf,CPTTRF) +#define LAPACK_zpttrf LAPACK_GLOBAL(zpttrf,ZPTTRF) +#define LAPACK_ssytrf LAPACK_GLOBAL(ssytrf,SSYTRF) +#define LAPACK_dsytrf LAPACK_GLOBAL(dsytrf,DSYTRF) +#define LAPACK_csytrf LAPACK_GLOBAL(csytrf,CSYTRF) +#define LAPACK_zsytrf LAPACK_GLOBAL(zsytrf,ZSYTRF) +#define LAPACK_chetrf LAPACK_GLOBAL(chetrf,CHETRF) +#define LAPACK_zhetrf LAPACK_GLOBAL(zhetrf,ZHETRF) +#define LAPACK_ssptrf LAPACK_GLOBAL(ssptrf,SSPTRF) +#define LAPACK_dsptrf LAPACK_GLOBAL(dsptrf,DSPTRF) +#define LAPACK_csptrf LAPACK_GLOBAL(csptrf,CSPTRF) +#define LAPACK_zsptrf LAPACK_GLOBAL(zsptrf,ZSPTRF) +#define LAPACK_chptrf LAPACK_GLOBAL(chptrf,CHPTRF) +#define LAPACK_zhptrf LAPACK_GLOBAL(zhptrf,ZHPTRF) +#define LAPACK_sgetrs LAPACK_GLOBAL(sgetrs,SGETRS) +#define LAPACK_dgetrs LAPACK_GLOBAL(dgetrs,DGETRS) +#define LAPACK_cgetrs LAPACK_GLOBAL(cgetrs,CGETRS) +#define LAPACK_zgetrs LAPACK_GLOBAL(zgetrs,ZGETRS) +#define LAPACK_sgbtrs LAPACK_GLOBAL(sgbtrs,SGBTRS) +#define LAPACK_dgbtrs LAPACK_GLOBAL(dgbtrs,DGBTRS) +#define LAPACK_cgbtrs LAPACK_GLOBAL(cgbtrs,CGBTRS) +#define LAPACK_zgbtrs LAPACK_GLOBAL(zgbtrs,ZGBTRS) +#define LAPACK_sgttrs LAPACK_GLOBAL(sgttrs,SGTTRS) +#define LAPACK_dgttrs LAPACK_GLOBAL(dgttrs,DGTTRS) +#define LAPACK_cgttrs LAPACK_GLOBAL(cgttrs,CGTTRS) +#define LAPACK_zgttrs LAPACK_GLOBAL(zgttrs,ZGTTRS) +#define LAPACK_spotrs LAPACK_GLOBAL(spotrs,SPOTRS) +#define LAPACK_dpotrs LAPACK_GLOBAL(dpotrs,DPOTRS) +#define LAPACK_cpotrs LAPACK_GLOBAL(cpotrs,CPOTRS) +#define LAPACK_zpotrs LAPACK_GLOBAL(zpotrs,ZPOTRS) +#define LAPACK_dpftrs LAPACK_GLOBAL(dpftrs,DPFTRS) +#define LAPACK_spftrs LAPACK_GLOBAL(spftrs,SPFTRS) +#define LAPACK_zpftrs LAPACK_GLOBAL(zpftrs,ZPFTRS) +#define LAPACK_cpftrs LAPACK_GLOBAL(cpftrs,CPFTRS) +#define LAPACK_spptrs LAPACK_GLOBAL(spptrs,SPPTRS) +#define LAPACK_dpptrs LAPACK_GLOBAL(dpptrs,DPPTRS) +#define LAPACK_cpptrs LAPACK_GLOBAL(cpptrs,CPPTRS) +#define LAPACK_zpptrs LAPACK_GLOBAL(zpptrs,ZPPTRS) +#define LAPACK_spbtrs LAPACK_GLOBAL(spbtrs,SPBTRS) +#define LAPACK_dpbtrs LAPACK_GLOBAL(dpbtrs,DPBTRS) +#define LAPACK_cpbtrs LAPACK_GLOBAL(cpbtrs,CPBTRS) +#define LAPACK_zpbtrs LAPACK_GLOBAL(zpbtrs,ZPBTRS) +#define LAPACK_spttrs LAPACK_GLOBAL(spttrs,SPTTRS) +#define LAPACK_dpttrs LAPACK_GLOBAL(dpttrs,DPTTRS) +#define LAPACK_cpttrs LAPACK_GLOBAL(cpttrs,CPTTRS) +#define LAPACK_zpttrs LAPACK_GLOBAL(zpttrs,ZPTTRS) +#define LAPACK_ssytrs LAPACK_GLOBAL(ssytrs,SSYTRS) +#define LAPACK_dsytrs LAPACK_GLOBAL(dsytrs,DSYTRS) +#define LAPACK_csytrs LAPACK_GLOBAL(csytrs,CSYTRS) +#define LAPACK_zsytrs LAPACK_GLOBAL(zsytrs,ZSYTRS) +#define LAPACK_chetrs LAPACK_GLOBAL(chetrs,CHETRS) +#define LAPACK_zhetrs LAPACK_GLOBAL(zhetrs,ZHETRS) +#define LAPACK_ssptrs LAPACK_GLOBAL(ssptrs,SSPTRS) +#define LAPACK_dsptrs LAPACK_GLOBAL(dsptrs,DSPTRS) +#define LAPACK_csptrs LAPACK_GLOBAL(csptrs,CSPTRS) +#define LAPACK_zsptrs LAPACK_GLOBAL(zsptrs,ZSPTRS) +#define LAPACK_chptrs LAPACK_GLOBAL(chptrs,CHPTRS) +#define LAPACK_zhptrs LAPACK_GLOBAL(zhptrs,ZHPTRS) +#define LAPACK_strtrs LAPACK_GLOBAL(strtrs,STRTRS) +#define LAPACK_dtrtrs LAPACK_GLOBAL(dtrtrs,DTRTRS) +#define LAPACK_ctrtrs LAPACK_GLOBAL(ctrtrs,CTRTRS) +#define LAPACK_ztrtrs LAPACK_GLOBAL(ztrtrs,ZTRTRS) +#define LAPACK_stptrs LAPACK_GLOBAL(stptrs,STPTRS) +#define LAPACK_dtptrs LAPACK_GLOBAL(dtptrs,DTPTRS) +#define LAPACK_ctptrs LAPACK_GLOBAL(ctptrs,CTPTRS) +#define LAPACK_ztptrs LAPACK_GLOBAL(ztptrs,ZTPTRS) +#define LAPACK_stbtrs LAPACK_GLOBAL(stbtrs,STBTRS) +#define LAPACK_dtbtrs LAPACK_GLOBAL(dtbtrs,DTBTRS) +#define LAPACK_ctbtrs LAPACK_GLOBAL(ctbtrs,CTBTRS) +#define LAPACK_ztbtrs LAPACK_GLOBAL(ztbtrs,ZTBTRS) +#define LAPACK_sgecon LAPACK_GLOBAL(sgecon,SGECON) +#define LAPACK_dgecon LAPACK_GLOBAL(dgecon,DGECON) +#define LAPACK_cgecon LAPACK_GLOBAL(cgecon,CGECON) +#define LAPACK_zgecon LAPACK_GLOBAL(zgecon,ZGECON) +#define LAPACK_sgbcon LAPACK_GLOBAL(sgbcon,SGBCON) +#define LAPACK_dgbcon LAPACK_GLOBAL(dgbcon,DGBCON) +#define LAPACK_cgbcon LAPACK_GLOBAL(cgbcon,CGBCON) +#define LAPACK_zgbcon LAPACK_GLOBAL(zgbcon,ZGBCON) +#define LAPACK_sgtcon LAPACK_GLOBAL(sgtcon,SGTCON) +#define LAPACK_dgtcon LAPACK_GLOBAL(dgtcon,DGTCON) +#define LAPACK_cgtcon LAPACK_GLOBAL(cgtcon,CGTCON) +#define LAPACK_zgtcon LAPACK_GLOBAL(zgtcon,ZGTCON) +#define LAPACK_spocon LAPACK_GLOBAL(spocon,SPOCON) +#define LAPACK_dpocon LAPACK_GLOBAL(dpocon,DPOCON) +#define LAPACK_cpocon LAPACK_GLOBAL(cpocon,CPOCON) +#define LAPACK_zpocon LAPACK_GLOBAL(zpocon,ZPOCON) +#define LAPACK_sppcon LAPACK_GLOBAL(sppcon,SPPCON) +#define LAPACK_dppcon LAPACK_GLOBAL(dppcon,DPPCON) +#define LAPACK_cppcon LAPACK_GLOBAL(cppcon,CPPCON) +#define LAPACK_zppcon LAPACK_GLOBAL(zppcon,ZPPCON) +#define LAPACK_spbcon LAPACK_GLOBAL(spbcon,SPBCON) +#define LAPACK_dpbcon LAPACK_GLOBAL(dpbcon,DPBCON) +#define LAPACK_cpbcon LAPACK_GLOBAL(cpbcon,CPBCON) +#define LAPACK_zpbcon LAPACK_GLOBAL(zpbcon,ZPBCON) +#define LAPACK_sptcon LAPACK_GLOBAL(sptcon,SPTCON) +#define LAPACK_dptcon LAPACK_GLOBAL(dptcon,DPTCON) +#define LAPACK_cptcon LAPACK_GLOBAL(cptcon,CPTCON) +#define LAPACK_zptcon LAPACK_GLOBAL(zptcon,ZPTCON) +#define LAPACK_ssycon LAPACK_GLOBAL(ssycon,SSYCON) +#define LAPACK_dsycon LAPACK_GLOBAL(dsycon,DSYCON) +#define LAPACK_csycon LAPACK_GLOBAL(csycon,CSYCON) +#define LAPACK_zsycon LAPACK_GLOBAL(zsycon,ZSYCON) +#define LAPACK_checon LAPACK_GLOBAL(checon,CHECON) +#define LAPACK_zhecon LAPACK_GLOBAL(zhecon,ZHECON) +#define LAPACK_sspcon LAPACK_GLOBAL(sspcon,SSPCON) +#define LAPACK_dspcon LAPACK_GLOBAL(dspcon,DSPCON) +#define LAPACK_cspcon LAPACK_GLOBAL(cspcon,CSPCON) +#define LAPACK_zspcon LAPACK_GLOBAL(zspcon,ZSPCON) +#define LAPACK_chpcon LAPACK_GLOBAL(chpcon,CHPCON) +#define LAPACK_zhpcon LAPACK_GLOBAL(zhpcon,ZHPCON) +#define LAPACK_strcon LAPACK_GLOBAL(strcon,STRCON) +#define LAPACK_dtrcon LAPACK_GLOBAL(dtrcon,DTRCON) +#define LAPACK_ctrcon LAPACK_GLOBAL(ctrcon,CTRCON) +#define LAPACK_ztrcon LAPACK_GLOBAL(ztrcon,ZTRCON) +#define LAPACK_stpcon LAPACK_GLOBAL(stpcon,STPCON) +#define LAPACK_dtpcon LAPACK_GLOBAL(dtpcon,DTPCON) +#define LAPACK_ctpcon LAPACK_GLOBAL(ctpcon,CTPCON) +#define LAPACK_ztpcon LAPACK_GLOBAL(ztpcon,ZTPCON) +#define LAPACK_stbcon LAPACK_GLOBAL(stbcon,STBCON) +#define LAPACK_dtbcon LAPACK_GLOBAL(dtbcon,DTBCON) +#define LAPACK_ctbcon LAPACK_GLOBAL(ctbcon,CTBCON) +#define LAPACK_ztbcon LAPACK_GLOBAL(ztbcon,ZTBCON) +#define LAPACK_sgerfs LAPACK_GLOBAL(sgerfs,SGERFS) +#define LAPACK_dgerfs LAPACK_GLOBAL(dgerfs,DGERFS) +#define LAPACK_cgerfs LAPACK_GLOBAL(cgerfs,CGERFS) +#define LAPACK_zgerfs LAPACK_GLOBAL(zgerfs,ZGERFS) +#define LAPACK_dgerfsx LAPACK_GLOBAL(dgerfsx,DGERFSX) +#define LAPACK_sgerfsx LAPACK_GLOBAL(sgerfsx,SGERFSX) +#define LAPACK_zgerfsx LAPACK_GLOBAL(zgerfsx,ZGERFSX) +#define LAPACK_cgerfsx LAPACK_GLOBAL(cgerfsx,CGERFSX) +#define LAPACK_sgbrfs LAPACK_GLOBAL(sgbrfs,SGBRFS) +#define LAPACK_dgbrfs LAPACK_GLOBAL(dgbrfs,DGBRFS) +#define LAPACK_cgbrfs LAPACK_GLOBAL(cgbrfs,CGBRFS) +#define LAPACK_zgbrfs LAPACK_GLOBAL(zgbrfs,ZGBRFS) +#define LAPACK_dgbrfsx LAPACK_GLOBAL(dgbrfsx,DGBRFSX) +#define LAPACK_sgbrfsx LAPACK_GLOBAL(sgbrfsx,SGBRFSX) +#define LAPACK_zgbrfsx LAPACK_GLOBAL(zgbrfsx,ZGBRFSX) +#define LAPACK_cgbrfsx LAPACK_GLOBAL(cgbrfsx,CGBRFSX) +#define LAPACK_sgtrfs LAPACK_GLOBAL(sgtrfs,SGTRFS) +#define LAPACK_dgtrfs LAPACK_GLOBAL(dgtrfs,DGTRFS) +#define LAPACK_cgtrfs LAPACK_GLOBAL(cgtrfs,CGTRFS) +#define LAPACK_zgtrfs LAPACK_GLOBAL(zgtrfs,ZGTRFS) +#define LAPACK_sporfs LAPACK_GLOBAL(sporfs,SPORFS) +#define LAPACK_dporfs LAPACK_GLOBAL(dporfs,DPORFS) +#define LAPACK_cporfs LAPACK_GLOBAL(cporfs,CPORFS) +#define LAPACK_zporfs LAPACK_GLOBAL(zporfs,ZPORFS) +#define LAPACK_dporfsx LAPACK_GLOBAL(dporfsx,DPORFSX) +#define LAPACK_sporfsx LAPACK_GLOBAL(sporfsx,SPORFSX) +#define LAPACK_zporfsx LAPACK_GLOBAL(zporfsx,ZPORFSX) +#define LAPACK_cporfsx LAPACK_GLOBAL(cporfsx,CPORFSX) +#define LAPACK_spprfs LAPACK_GLOBAL(spprfs,SPPRFS) +#define LAPACK_dpprfs LAPACK_GLOBAL(dpprfs,DPPRFS) +#define LAPACK_cpprfs LAPACK_GLOBAL(cpprfs,CPPRFS) +#define LAPACK_zpprfs LAPACK_GLOBAL(zpprfs,ZPPRFS) +#define LAPACK_spbrfs LAPACK_GLOBAL(spbrfs,SPBRFS) +#define LAPACK_dpbrfs LAPACK_GLOBAL(dpbrfs,DPBRFS) +#define LAPACK_cpbrfs LAPACK_GLOBAL(cpbrfs,CPBRFS) +#define LAPACK_zpbrfs LAPACK_GLOBAL(zpbrfs,ZPBRFS) +#define LAPACK_sptrfs LAPACK_GLOBAL(sptrfs,SPTRFS) +#define LAPACK_dptrfs LAPACK_GLOBAL(dptrfs,DPTRFS) +#define LAPACK_cptrfs LAPACK_GLOBAL(cptrfs,CPTRFS) +#define LAPACK_zptrfs LAPACK_GLOBAL(zptrfs,ZPTRFS) +#define LAPACK_ssyrfs LAPACK_GLOBAL(ssyrfs,SSYRFS) +#define LAPACK_dsyrfs LAPACK_GLOBAL(dsyrfs,DSYRFS) +#define LAPACK_csyrfs LAPACK_GLOBAL(csyrfs,CSYRFS) +#define LAPACK_zsyrfs LAPACK_GLOBAL(zsyrfs,ZSYRFS) +#define LAPACK_dsyrfsx LAPACK_GLOBAL(dsyrfsx,DSYRFSX) +#define LAPACK_ssyrfsx LAPACK_GLOBAL(ssyrfsx,SSYRFSX) +#define LAPACK_zsyrfsx LAPACK_GLOBAL(zsyrfsx,ZSYRFSX) +#define LAPACK_csyrfsx LAPACK_GLOBAL(csyrfsx,CSYRFSX) +#define LAPACK_cherfs LAPACK_GLOBAL(cherfs,CHERFS) +#define LAPACK_zherfs LAPACK_GLOBAL(zherfs,ZHERFS) +#define LAPACK_zherfsx LAPACK_GLOBAL(zherfsx,ZHERFSX) +#define LAPACK_cherfsx LAPACK_GLOBAL(cherfsx,CHERFSX) +#define LAPACK_ssprfs LAPACK_GLOBAL(ssprfs,SSPRFS) +#define LAPACK_dsprfs LAPACK_GLOBAL(dsprfs,DSPRFS) +#define LAPACK_csprfs LAPACK_GLOBAL(csprfs,CSPRFS) +#define LAPACK_zsprfs LAPACK_GLOBAL(zsprfs,ZSPRFS) +#define LAPACK_chprfs LAPACK_GLOBAL(chprfs,CHPRFS) +#define LAPACK_zhprfs LAPACK_GLOBAL(zhprfs,ZHPRFS) +#define LAPACK_strrfs LAPACK_GLOBAL(strrfs,STRRFS) +#define LAPACK_dtrrfs LAPACK_GLOBAL(dtrrfs,DTRRFS) +#define LAPACK_ctrrfs LAPACK_GLOBAL(ctrrfs,CTRRFS) +#define LAPACK_ztrrfs LAPACK_GLOBAL(ztrrfs,ZTRRFS) +#define LAPACK_stprfs LAPACK_GLOBAL(stprfs,STPRFS) +#define LAPACK_dtprfs LAPACK_GLOBAL(dtprfs,DTPRFS) +#define LAPACK_ctprfs LAPACK_GLOBAL(ctprfs,CTPRFS) +#define LAPACK_ztprfs LAPACK_GLOBAL(ztprfs,ZTPRFS) +#define LAPACK_stbrfs LAPACK_GLOBAL(stbrfs,STBRFS) +#define LAPACK_dtbrfs LAPACK_GLOBAL(dtbrfs,DTBRFS) +#define LAPACK_ctbrfs LAPACK_GLOBAL(ctbrfs,CTBRFS) +#define LAPACK_ztbrfs LAPACK_GLOBAL(ztbrfs,ZTBRFS) +#define LAPACK_sgetri LAPACK_GLOBAL(sgetri,SGETRI) +#define LAPACK_dgetri LAPACK_GLOBAL(dgetri,DGETRI) +#define LAPACK_cgetri LAPACK_GLOBAL(cgetri,CGETRI) +#define LAPACK_zgetri LAPACK_GLOBAL(zgetri,ZGETRI) +#define LAPACK_spotri LAPACK_GLOBAL(spotri,SPOTRI) +#define LAPACK_dpotri LAPACK_GLOBAL(dpotri,DPOTRI) +#define LAPACK_cpotri LAPACK_GLOBAL(cpotri,CPOTRI) +#define LAPACK_zpotri LAPACK_GLOBAL(zpotri,ZPOTRI) +#define LAPACK_dpftri LAPACK_GLOBAL(dpftri,DPFTRI) +#define LAPACK_spftri LAPACK_GLOBAL(spftri,SPFTRI) +#define LAPACK_zpftri LAPACK_GLOBAL(zpftri,ZPFTRI) +#define LAPACK_cpftri LAPACK_GLOBAL(cpftri,CPFTRI) +#define LAPACK_spptri LAPACK_GLOBAL(spptri,SPPTRI) +#define LAPACK_dpptri LAPACK_GLOBAL(dpptri,DPPTRI) +#define LAPACK_cpptri LAPACK_GLOBAL(cpptri,CPPTRI) +#define LAPACK_zpptri LAPACK_GLOBAL(zpptri,ZPPTRI) +#define LAPACK_ssytri LAPACK_GLOBAL(ssytri,SSYTRI) +#define LAPACK_dsytri LAPACK_GLOBAL(dsytri,DSYTRI) +#define LAPACK_csytri LAPACK_GLOBAL(csytri,CSYTRI) +#define LAPACK_zsytri LAPACK_GLOBAL(zsytri,ZSYTRI) +#define LAPACK_chetri LAPACK_GLOBAL(chetri,CHETRI) +#define LAPACK_zhetri LAPACK_GLOBAL(zhetri,ZHETRI) +#define LAPACK_ssptri LAPACK_GLOBAL(ssptri,SSPTRI) +#define LAPACK_dsptri LAPACK_GLOBAL(dsptri,DSPTRI) +#define LAPACK_csptri LAPACK_GLOBAL(csptri,CSPTRI) +#define LAPACK_zsptri LAPACK_GLOBAL(zsptri,ZSPTRI) +#define LAPACK_chptri LAPACK_GLOBAL(chptri,CHPTRI) +#define LAPACK_zhptri LAPACK_GLOBAL(zhptri,ZHPTRI) +#define LAPACK_strtri LAPACK_GLOBAL(strtri,STRTRI) +#define LAPACK_dtrtri LAPACK_GLOBAL(dtrtri,DTRTRI) +#define LAPACK_ctrtri LAPACK_GLOBAL(ctrtri,CTRTRI) +#define LAPACK_ztrtri LAPACK_GLOBAL(ztrtri,ZTRTRI) +#define LAPACK_dtftri LAPACK_GLOBAL(dtftri,DTFTRI) +#define LAPACK_stftri LAPACK_GLOBAL(stftri,STFTRI) +#define LAPACK_ztftri LAPACK_GLOBAL(ztftri,ZTFTRI) +#define LAPACK_ctftri LAPACK_GLOBAL(ctftri,CTFTRI) +#define LAPACK_stptri LAPACK_GLOBAL(stptri,STPTRI) +#define LAPACK_dtptri LAPACK_GLOBAL(dtptri,DTPTRI) +#define LAPACK_ctptri LAPACK_GLOBAL(ctptri,CTPTRI) +#define LAPACK_ztptri LAPACK_GLOBAL(ztptri,ZTPTRI) +#define LAPACK_sgeequ LAPACK_GLOBAL(sgeequ,SGEEQU) +#define LAPACK_dgeequ LAPACK_GLOBAL(dgeequ,DGEEQU) +#define LAPACK_cgeequ LAPACK_GLOBAL(cgeequ,CGEEQU) +#define LAPACK_zgeequ LAPACK_GLOBAL(zgeequ,ZGEEQU) +#define LAPACK_dgeequb LAPACK_GLOBAL(dgeequb,DGEEQUB) +#define LAPACK_sgeequb LAPACK_GLOBAL(sgeequb,SGEEQUB) +#define LAPACK_zgeequb LAPACK_GLOBAL(zgeequb,ZGEEQUB) +#define LAPACK_cgeequb LAPACK_GLOBAL(cgeequb,CGEEQUB) +#define LAPACK_sgbequ LAPACK_GLOBAL(sgbequ,SGBEQU) +#define LAPACK_dgbequ LAPACK_GLOBAL(dgbequ,DGBEQU) +#define LAPACK_cgbequ LAPACK_GLOBAL(cgbequ,CGBEQU) +#define LAPACK_zgbequ LAPACK_GLOBAL(zgbequ,ZGBEQU) +#define LAPACK_dgbequb LAPACK_GLOBAL(dgbequb,DGBEQUB) +#define LAPACK_sgbequb LAPACK_GLOBAL(sgbequb,SGBEQUB) +#define LAPACK_zgbequb LAPACK_GLOBAL(zgbequb,ZGBEQUB) +#define LAPACK_cgbequb LAPACK_GLOBAL(cgbequb,CGBEQUB) +#define LAPACK_spoequ LAPACK_GLOBAL(spoequ,SPOEQU) +#define LAPACK_dpoequ LAPACK_GLOBAL(dpoequ,DPOEQU) +#define LAPACK_cpoequ LAPACK_GLOBAL(cpoequ,CPOEQU) +#define LAPACK_zpoequ LAPACK_GLOBAL(zpoequ,ZPOEQU) +#define LAPACK_dpoequb LAPACK_GLOBAL(dpoequb,DPOEQUB) +#define LAPACK_spoequb LAPACK_GLOBAL(spoequb,SPOEQUB) +#define LAPACK_zpoequb LAPACK_GLOBAL(zpoequb,ZPOEQUB) +#define LAPACK_cpoequb LAPACK_GLOBAL(cpoequb,CPOEQUB) +#define LAPACK_sppequ LAPACK_GLOBAL(sppequ,SPPEQU) +#define LAPACK_dppequ LAPACK_GLOBAL(dppequ,DPPEQU) +#define LAPACK_cppequ LAPACK_GLOBAL(cppequ,CPPEQU) +#define LAPACK_zppequ LAPACK_GLOBAL(zppequ,ZPPEQU) +#define LAPACK_spbequ LAPACK_GLOBAL(spbequ,SPBEQU) +#define LAPACK_dpbequ LAPACK_GLOBAL(dpbequ,DPBEQU) +#define LAPACK_cpbequ LAPACK_GLOBAL(cpbequ,CPBEQU) +#define LAPACK_zpbequ LAPACK_GLOBAL(zpbequ,ZPBEQU) +#define LAPACK_dsyequb LAPACK_GLOBAL(dsyequb,DSYEQUB) +#define LAPACK_ssyequb LAPACK_GLOBAL(ssyequb,SSYEQUB) +#define LAPACK_zsyequb LAPACK_GLOBAL(zsyequb,ZSYEQUB) +#define LAPACK_csyequb LAPACK_GLOBAL(csyequb,CSYEQUB) +#define LAPACK_zheequb LAPACK_GLOBAL(zheequb,ZHEEQUB) +#define LAPACK_cheequb LAPACK_GLOBAL(cheequb,CHEEQUB) +#define LAPACK_sgesv LAPACK_GLOBAL(sgesv,SGESV) +#define LAPACK_dgesv LAPACK_GLOBAL(dgesv,DGESV) +#define LAPACK_cgesv LAPACK_GLOBAL(cgesv,CGESV) +#define LAPACK_zgesv LAPACK_GLOBAL(zgesv,ZGESV) +#define LAPACK_dsgesv LAPACK_GLOBAL(dsgesv,DSGESV) +#define LAPACK_zcgesv LAPACK_GLOBAL(zcgesv,ZCGESV) +#define LAPACK_sgesvx LAPACK_GLOBAL(sgesvx,SGESVX) +#define LAPACK_dgesvx LAPACK_GLOBAL(dgesvx,DGESVX) +#define LAPACK_cgesvx LAPACK_GLOBAL(cgesvx,CGESVX) +#define LAPACK_zgesvx LAPACK_GLOBAL(zgesvx,ZGESVX) +#define LAPACK_dgesvxx LAPACK_GLOBAL(dgesvxx,DGESVXX) +#define LAPACK_sgesvxx LAPACK_GLOBAL(sgesvxx,SGESVXX) +#define LAPACK_zgesvxx LAPACK_GLOBAL(zgesvxx,ZGESVXX) +#define LAPACK_cgesvxx LAPACK_GLOBAL(cgesvxx,CGESVXX) +#define LAPACK_sgbsv LAPACK_GLOBAL(sgbsv,SGBSV) +#define LAPACK_dgbsv LAPACK_GLOBAL(dgbsv,DGBSV) +#define LAPACK_cgbsv LAPACK_GLOBAL(cgbsv,CGBSV) +#define LAPACK_zgbsv LAPACK_GLOBAL(zgbsv,ZGBSV) +#define LAPACK_sgbsvx LAPACK_GLOBAL(sgbsvx,SGBSVX) +#define LAPACK_dgbsvx LAPACK_GLOBAL(dgbsvx,DGBSVX) +#define LAPACK_cgbsvx LAPACK_GLOBAL(cgbsvx,CGBSVX) +#define LAPACK_zgbsvx LAPACK_GLOBAL(zgbsvx,ZGBSVX) +#define LAPACK_dgbsvxx LAPACK_GLOBAL(dgbsvxx,DGBSVXX) +#define LAPACK_sgbsvxx LAPACK_GLOBAL(sgbsvxx,SGBSVXX) +#define LAPACK_zgbsvxx LAPACK_GLOBAL(zgbsvxx,ZGBSVXX) +#define LAPACK_cgbsvxx LAPACK_GLOBAL(cgbsvxx,CGBSVXX) +#define LAPACK_sgtsv LAPACK_GLOBAL(sgtsv,SGTSV) +#define LAPACK_dgtsv LAPACK_GLOBAL(dgtsv,DGTSV) +#define LAPACK_cgtsv LAPACK_GLOBAL(cgtsv,CGTSV) +#define LAPACK_zgtsv LAPACK_GLOBAL(zgtsv,ZGTSV) +#define LAPACK_sgtsvx LAPACK_GLOBAL(sgtsvx,SGTSVX) +#define LAPACK_dgtsvx LAPACK_GLOBAL(dgtsvx,DGTSVX) +#define LAPACK_cgtsvx LAPACK_GLOBAL(cgtsvx,CGTSVX) +#define LAPACK_zgtsvx LAPACK_GLOBAL(zgtsvx,ZGTSVX) +#define LAPACK_sposv LAPACK_GLOBAL(sposv,SPOSV) +#define LAPACK_dposv LAPACK_GLOBAL(dposv,DPOSV) +#define LAPACK_cposv LAPACK_GLOBAL(cposv,CPOSV) +#define LAPACK_zposv LAPACK_GLOBAL(zposv,ZPOSV) +#define LAPACK_dsposv LAPACK_GLOBAL(dsposv,DSPOSV) +#define LAPACK_zcposv LAPACK_GLOBAL(zcposv,ZCPOSV) +#define LAPACK_sposvx LAPACK_GLOBAL(sposvx,SPOSVX) +#define LAPACK_dposvx LAPACK_GLOBAL(dposvx,DPOSVX) +#define LAPACK_cposvx LAPACK_GLOBAL(cposvx,CPOSVX) +#define LAPACK_zposvx LAPACK_GLOBAL(zposvx,ZPOSVX) +#define LAPACK_dposvxx LAPACK_GLOBAL(dposvxx,DPOSVXX) +#define LAPACK_sposvxx LAPACK_GLOBAL(sposvxx,SPOSVXX) +#define LAPACK_zposvxx LAPACK_GLOBAL(zposvxx,ZPOSVXX) +#define LAPACK_cposvxx LAPACK_GLOBAL(cposvxx,CPOSVXX) +#define LAPACK_sppsv LAPACK_GLOBAL(sppsv,SPPSV) +#define LAPACK_dppsv LAPACK_GLOBAL(dppsv,DPPSV) +#define LAPACK_cppsv LAPACK_GLOBAL(cppsv,CPPSV) +#define LAPACK_zppsv LAPACK_GLOBAL(zppsv,ZPPSV) +#define LAPACK_sppsvx LAPACK_GLOBAL(sppsvx,SPPSVX) +#define LAPACK_dppsvx LAPACK_GLOBAL(dppsvx,DPPSVX) +#define LAPACK_cppsvx LAPACK_GLOBAL(cppsvx,CPPSVX) +#define LAPACK_zppsvx LAPACK_GLOBAL(zppsvx,ZPPSVX) +#define LAPACK_spbsv LAPACK_GLOBAL(spbsv,SPBSV) +#define LAPACK_dpbsv LAPACK_GLOBAL(dpbsv,DPBSV) +#define LAPACK_cpbsv LAPACK_GLOBAL(cpbsv,CPBSV) +#define LAPACK_zpbsv LAPACK_GLOBAL(zpbsv,ZPBSV) +#define LAPACK_spbsvx LAPACK_GLOBAL(spbsvx,SPBSVX) +#define LAPACK_dpbsvx LAPACK_GLOBAL(dpbsvx,DPBSVX) +#define LAPACK_cpbsvx LAPACK_GLOBAL(cpbsvx,CPBSVX) +#define LAPACK_zpbsvx LAPACK_GLOBAL(zpbsvx,ZPBSVX) +#define LAPACK_sptsv LAPACK_GLOBAL(sptsv,SPTSV) +#define LAPACK_dptsv LAPACK_GLOBAL(dptsv,DPTSV) +#define LAPACK_cptsv LAPACK_GLOBAL(cptsv,CPTSV) +#define LAPACK_zptsv LAPACK_GLOBAL(zptsv,ZPTSV) +#define LAPACK_sptsvx LAPACK_GLOBAL(sptsvx,SPTSVX) +#define LAPACK_dptsvx LAPACK_GLOBAL(dptsvx,DPTSVX) +#define LAPACK_cptsvx LAPACK_GLOBAL(cptsvx,CPTSVX) +#define LAPACK_zptsvx LAPACK_GLOBAL(zptsvx,ZPTSVX) +#define LAPACK_ssysv LAPACK_GLOBAL(ssysv,SSYSV) +#define LAPACK_dsysv LAPACK_GLOBAL(dsysv,DSYSV) +#define LAPACK_csysv LAPACK_GLOBAL(csysv,CSYSV) +#define LAPACK_zsysv LAPACK_GLOBAL(zsysv,ZSYSV) +#define LAPACK_ssysvx LAPACK_GLOBAL(ssysvx,SSYSVX) +#define LAPACK_dsysvx LAPACK_GLOBAL(dsysvx,DSYSVX) +#define LAPACK_csysvx LAPACK_GLOBAL(csysvx,CSYSVX) +#define LAPACK_zsysvx LAPACK_GLOBAL(zsysvx,ZSYSVX) +#define LAPACK_dsysvxx LAPACK_GLOBAL(dsysvxx,DSYSVXX) +#define LAPACK_ssysvxx LAPACK_GLOBAL(ssysvxx,SSYSVXX) +#define LAPACK_zsysvxx LAPACK_GLOBAL(zsysvxx,ZSYSVXX) +#define LAPACK_csysvxx LAPACK_GLOBAL(csysvxx,CSYSVXX) +#define LAPACK_chesv LAPACK_GLOBAL(chesv,CHESV) +#define LAPACK_zhesv LAPACK_GLOBAL(zhesv,ZHESV) +#define LAPACK_chesvx LAPACK_GLOBAL(chesvx,CHESVX) +#define LAPACK_zhesvx LAPACK_GLOBAL(zhesvx,ZHESVX) +#define LAPACK_zhesvxx LAPACK_GLOBAL(zhesvxx,ZHESVXX) +#define LAPACK_chesvxx LAPACK_GLOBAL(chesvxx,CHESVXX) +#define LAPACK_sspsv LAPACK_GLOBAL(sspsv,SSPSV) +#define LAPACK_dspsv LAPACK_GLOBAL(dspsv,DSPSV) +#define LAPACK_cspsv LAPACK_GLOBAL(cspsv,CSPSV) +#define LAPACK_zspsv LAPACK_GLOBAL(zspsv,ZSPSV) +#define LAPACK_sspsvx LAPACK_GLOBAL(sspsvx,SSPSVX) +#define LAPACK_dspsvx LAPACK_GLOBAL(dspsvx,DSPSVX) +#define LAPACK_cspsvx LAPACK_GLOBAL(cspsvx,CSPSVX) +#define LAPACK_zspsvx LAPACK_GLOBAL(zspsvx,ZSPSVX) +#define LAPACK_chpsv LAPACK_GLOBAL(chpsv,CHPSV) +#define LAPACK_zhpsv LAPACK_GLOBAL(zhpsv,ZHPSV) +#define LAPACK_chpsvx LAPACK_GLOBAL(chpsvx,CHPSVX) +#define LAPACK_zhpsvx LAPACK_GLOBAL(zhpsvx,ZHPSVX) +#define LAPACK_sgeqrf LAPACK_GLOBAL(sgeqrf,SGEQRF) +#define LAPACK_dgeqrf LAPACK_GLOBAL(dgeqrf,DGEQRF) +#define LAPACK_cgeqrf LAPACK_GLOBAL(cgeqrf,CGEQRF) +#define LAPACK_zgeqrf LAPACK_GLOBAL(zgeqrf,ZGEQRF) +#define LAPACK_sgeqpf LAPACK_GLOBAL(sgeqpf,SGEQPF) +#define LAPACK_dgeqpf LAPACK_GLOBAL(dgeqpf,DGEQPF) +#define LAPACK_cgeqpf LAPACK_GLOBAL(cgeqpf,CGEQPF) +#define LAPACK_zgeqpf LAPACK_GLOBAL(zgeqpf,ZGEQPF) +#define LAPACK_sgeqp3 LAPACK_GLOBAL(sgeqp3,SGEQP3) +#define LAPACK_dgeqp3 LAPACK_GLOBAL(dgeqp3,DGEQP3) +#define LAPACK_cgeqp3 LAPACK_GLOBAL(cgeqp3,CGEQP3) +#define LAPACK_zgeqp3 LAPACK_GLOBAL(zgeqp3,ZGEQP3) +#define LAPACK_sorgqr LAPACK_GLOBAL(sorgqr,SORGQR) +#define LAPACK_dorgqr LAPACK_GLOBAL(dorgqr,DORGQR) +#define LAPACK_sormqr LAPACK_GLOBAL(sormqr,SORMQR) +#define LAPACK_dormqr LAPACK_GLOBAL(dormqr,DORMQR) +#define LAPACK_cungqr LAPACK_GLOBAL(cungqr,CUNGQR) +#define LAPACK_zungqr LAPACK_GLOBAL(zungqr,ZUNGQR) +#define LAPACK_cunmqr LAPACK_GLOBAL(cunmqr,CUNMQR) +#define LAPACK_zunmqr LAPACK_GLOBAL(zunmqr,ZUNMQR) +#define LAPACK_sgelqf LAPACK_GLOBAL(sgelqf,SGELQF) +#define LAPACK_dgelqf LAPACK_GLOBAL(dgelqf,DGELQF) +#define LAPACK_cgelqf LAPACK_GLOBAL(cgelqf,CGELQF) +#define LAPACK_zgelqf LAPACK_GLOBAL(zgelqf,ZGELQF) +#define LAPACK_sorglq LAPACK_GLOBAL(sorglq,SORGLQ) +#define LAPACK_dorglq LAPACK_GLOBAL(dorglq,DORGLQ) +#define LAPACK_sormlq LAPACK_GLOBAL(sormlq,SORMLQ) +#define LAPACK_dormlq LAPACK_GLOBAL(dormlq,DORMLQ) +#define LAPACK_cunglq LAPACK_GLOBAL(cunglq,CUNGLQ) +#define LAPACK_zunglq LAPACK_GLOBAL(zunglq,ZUNGLQ) +#define LAPACK_cunmlq LAPACK_GLOBAL(cunmlq,CUNMLQ) +#define LAPACK_zunmlq LAPACK_GLOBAL(zunmlq,ZUNMLQ) +#define LAPACK_sgeqlf LAPACK_GLOBAL(sgeqlf,SGEQLF) +#define LAPACK_dgeqlf LAPACK_GLOBAL(dgeqlf,DGEQLF) +#define LAPACK_cgeqlf LAPACK_GLOBAL(cgeqlf,CGEQLF) +#define LAPACK_zgeqlf LAPACK_GLOBAL(zgeqlf,ZGEQLF) +#define LAPACK_sorgql LAPACK_GLOBAL(sorgql,SORGQL) +#define LAPACK_dorgql LAPACK_GLOBAL(dorgql,DORGQL) +#define LAPACK_cungql LAPACK_GLOBAL(cungql,CUNGQL) +#define LAPACK_zungql LAPACK_GLOBAL(zungql,ZUNGQL) +#define LAPACK_sormql LAPACK_GLOBAL(sormql,SORMQL) +#define LAPACK_dormql LAPACK_GLOBAL(dormql,DORMQL) +#define LAPACK_cunmql LAPACK_GLOBAL(cunmql,CUNMQL) +#define LAPACK_zunmql LAPACK_GLOBAL(zunmql,ZUNMQL) +#define LAPACK_sgerqf LAPACK_GLOBAL(sgerqf,SGERQF) +#define LAPACK_dgerqf LAPACK_GLOBAL(dgerqf,DGERQF) +#define LAPACK_cgerqf LAPACK_GLOBAL(cgerqf,CGERQF) +#define LAPACK_zgerqf LAPACK_GLOBAL(zgerqf,ZGERQF) +#define LAPACK_sorgrq LAPACK_GLOBAL(sorgrq,SORGRQ) +#define LAPACK_dorgrq LAPACK_GLOBAL(dorgrq,DORGRQ) +#define LAPACK_cungrq LAPACK_GLOBAL(cungrq,CUNGRQ) +#define LAPACK_zungrq LAPACK_GLOBAL(zungrq,ZUNGRQ) +#define LAPACK_sormrq LAPACK_GLOBAL(sormrq,SORMRQ) +#define LAPACK_dormrq LAPACK_GLOBAL(dormrq,DORMRQ) +#define LAPACK_cunmrq LAPACK_GLOBAL(cunmrq,CUNMRQ) +#define LAPACK_zunmrq LAPACK_GLOBAL(zunmrq,ZUNMRQ) +#define LAPACK_stzrzf LAPACK_GLOBAL(stzrzf,STZRZF) +#define LAPACK_dtzrzf LAPACK_GLOBAL(dtzrzf,DTZRZF) +#define LAPACK_ctzrzf LAPACK_GLOBAL(ctzrzf,CTZRZF) +#define LAPACK_ztzrzf LAPACK_GLOBAL(ztzrzf,ZTZRZF) +#define LAPACK_sormrz LAPACK_GLOBAL(sormrz,SORMRZ) +#define LAPACK_dormrz LAPACK_GLOBAL(dormrz,DORMRZ) +#define LAPACK_cunmrz LAPACK_GLOBAL(cunmrz,CUNMRZ) +#define LAPACK_zunmrz LAPACK_GLOBAL(zunmrz,ZUNMRZ) +#define LAPACK_sggqrf LAPACK_GLOBAL(sggqrf,SGGQRF) +#define LAPACK_dggqrf LAPACK_GLOBAL(dggqrf,DGGQRF) +#define LAPACK_cggqrf LAPACK_GLOBAL(cggqrf,CGGQRF) +#define LAPACK_zggqrf LAPACK_GLOBAL(zggqrf,ZGGQRF) +#define LAPACK_sggrqf LAPACK_GLOBAL(sggrqf,SGGRQF) +#define LAPACK_dggrqf LAPACK_GLOBAL(dggrqf,DGGRQF) +#define LAPACK_cggrqf LAPACK_GLOBAL(cggrqf,CGGRQF) +#define LAPACK_zggrqf LAPACK_GLOBAL(zggrqf,ZGGRQF) +#define LAPACK_sgebrd LAPACK_GLOBAL(sgebrd,SGEBRD) +#define LAPACK_dgebrd LAPACK_GLOBAL(dgebrd,DGEBRD) +#define LAPACK_cgebrd LAPACK_GLOBAL(cgebrd,CGEBRD) +#define LAPACK_zgebrd LAPACK_GLOBAL(zgebrd,ZGEBRD) +#define LAPACK_sgbbrd LAPACK_GLOBAL(sgbbrd,SGBBRD) +#define LAPACK_dgbbrd LAPACK_GLOBAL(dgbbrd,DGBBRD) +#define LAPACK_cgbbrd LAPACK_GLOBAL(cgbbrd,CGBBRD) +#define LAPACK_zgbbrd LAPACK_GLOBAL(zgbbrd,ZGBBRD) +#define LAPACK_sorgbr LAPACK_GLOBAL(sorgbr,SORGBR) +#define LAPACK_dorgbr LAPACK_GLOBAL(dorgbr,DORGBR) +#define LAPACK_sormbr LAPACK_GLOBAL(sormbr,SORMBR) +#define LAPACK_dormbr LAPACK_GLOBAL(dormbr,DORMBR) +#define LAPACK_cungbr LAPACK_GLOBAL(cungbr,CUNGBR) +#define LAPACK_zungbr LAPACK_GLOBAL(zungbr,ZUNGBR) +#define LAPACK_cunmbr LAPACK_GLOBAL(cunmbr,CUNMBR) +#define LAPACK_zunmbr LAPACK_GLOBAL(zunmbr,ZUNMBR) +#define LAPACK_sbdsqr LAPACK_GLOBAL(sbdsqr,SBDSQR) +#define LAPACK_dbdsqr LAPACK_GLOBAL(dbdsqr,DBDSQR) +#define LAPACK_cbdsqr LAPACK_GLOBAL(cbdsqr,CBDSQR) +#define LAPACK_zbdsqr LAPACK_GLOBAL(zbdsqr,ZBDSQR) +#define LAPACK_sbdsdc LAPACK_GLOBAL(sbdsdc,SBDSDC) +#define LAPACK_dbdsdc LAPACK_GLOBAL(dbdsdc,DBDSDC) +#define LAPACK_ssytrd LAPACK_GLOBAL(ssytrd,SSYTRD) +#define LAPACK_dsytrd LAPACK_GLOBAL(dsytrd,DSYTRD) +#define LAPACK_sorgtr LAPACK_GLOBAL(sorgtr,SORGTR) +#define LAPACK_dorgtr LAPACK_GLOBAL(dorgtr,DORGTR) +#define LAPACK_sormtr LAPACK_GLOBAL(sormtr,SORMTR) +#define LAPACK_dormtr LAPACK_GLOBAL(dormtr,DORMTR) +#define LAPACK_chetrd LAPACK_GLOBAL(chetrd,CHETRD) +#define LAPACK_zhetrd LAPACK_GLOBAL(zhetrd,ZHETRD) +#define LAPACK_cungtr LAPACK_GLOBAL(cungtr,CUNGTR) +#define LAPACK_zungtr LAPACK_GLOBAL(zungtr,ZUNGTR) +#define LAPACK_cunmtr LAPACK_GLOBAL(cunmtr,CUNMTR) +#define LAPACK_zunmtr LAPACK_GLOBAL(zunmtr,ZUNMTR) +#define LAPACK_ssptrd LAPACK_GLOBAL(ssptrd,SSPTRD) +#define LAPACK_dsptrd LAPACK_GLOBAL(dsptrd,DSPTRD) +#define LAPACK_sopgtr LAPACK_GLOBAL(sopgtr,SOPGTR) +#define LAPACK_dopgtr LAPACK_GLOBAL(dopgtr,DOPGTR) +#define LAPACK_sopmtr LAPACK_GLOBAL(sopmtr,SOPMTR) +#define LAPACK_dopmtr LAPACK_GLOBAL(dopmtr,DOPMTR) +#define LAPACK_chptrd LAPACK_GLOBAL(chptrd,CHPTRD) +#define LAPACK_zhptrd LAPACK_GLOBAL(zhptrd,ZHPTRD) +#define LAPACK_cupgtr LAPACK_GLOBAL(cupgtr,CUPGTR) +#define LAPACK_zupgtr LAPACK_GLOBAL(zupgtr,ZUPGTR) +#define LAPACK_cupmtr LAPACK_GLOBAL(cupmtr,CUPMTR) +#define LAPACK_zupmtr LAPACK_GLOBAL(zupmtr,ZUPMTR) +#define LAPACK_ssbtrd LAPACK_GLOBAL(ssbtrd,SSBTRD) +#define LAPACK_dsbtrd LAPACK_GLOBAL(dsbtrd,DSBTRD) +#define LAPACK_chbtrd LAPACK_GLOBAL(chbtrd,CHBTRD) +#define LAPACK_zhbtrd LAPACK_GLOBAL(zhbtrd,ZHBTRD) +#define LAPACK_ssterf LAPACK_GLOBAL(ssterf,SSTERF) +#define LAPACK_dsterf LAPACK_GLOBAL(dsterf,DSTERF) +#define LAPACK_ssteqr LAPACK_GLOBAL(ssteqr,SSTEQR) +#define LAPACK_dsteqr LAPACK_GLOBAL(dsteqr,DSTEQR) +#define LAPACK_csteqr LAPACK_GLOBAL(csteqr,CSTEQR) +#define LAPACK_zsteqr LAPACK_GLOBAL(zsteqr,ZSTEQR) +#define LAPACK_sstemr LAPACK_GLOBAL(sstemr,SSTEMR) +#define LAPACK_dstemr LAPACK_GLOBAL(dstemr,DSTEMR) +#define LAPACK_cstemr LAPACK_GLOBAL(cstemr,CSTEMR) +#define LAPACK_zstemr LAPACK_GLOBAL(zstemr,ZSTEMR) +#define LAPACK_sstedc LAPACK_GLOBAL(sstedc,SSTEDC) +#define LAPACK_dstedc LAPACK_GLOBAL(dstedc,DSTEDC) +#define LAPACK_cstedc LAPACK_GLOBAL(cstedc,CSTEDC) +#define LAPACK_zstedc LAPACK_GLOBAL(zstedc,ZSTEDC) +#define LAPACK_sstegr LAPACK_GLOBAL(sstegr,SSTEGR) +#define LAPACK_dstegr LAPACK_GLOBAL(dstegr,DSTEGR) +#define LAPACK_cstegr LAPACK_GLOBAL(cstegr,CSTEGR) +#define LAPACK_zstegr LAPACK_GLOBAL(zstegr,ZSTEGR) +#define LAPACK_spteqr LAPACK_GLOBAL(spteqr,SPTEQR) +#define LAPACK_dpteqr LAPACK_GLOBAL(dpteqr,DPTEQR) +#define LAPACK_cpteqr LAPACK_GLOBAL(cpteqr,CPTEQR) +#define LAPACK_zpteqr LAPACK_GLOBAL(zpteqr,ZPTEQR) +#define LAPACK_sstebz LAPACK_GLOBAL(sstebz,SSTEBZ) +#define LAPACK_dstebz LAPACK_GLOBAL(dstebz,DSTEBZ) +#define LAPACK_sstein LAPACK_GLOBAL(sstein,SSTEIN) +#define LAPACK_dstein LAPACK_GLOBAL(dstein,DSTEIN) +#define LAPACK_cstein LAPACK_GLOBAL(cstein,CSTEIN) +#define LAPACK_zstein LAPACK_GLOBAL(zstein,ZSTEIN) +#define LAPACK_sdisna LAPACK_GLOBAL(sdisna,SDISNA) +#define LAPACK_ddisna LAPACK_GLOBAL(ddisna,DDISNA) +#define LAPACK_ssygst LAPACK_GLOBAL(ssygst,SSYGST) +#define LAPACK_dsygst LAPACK_GLOBAL(dsygst,DSYGST) +#define LAPACK_chegst LAPACK_GLOBAL(chegst,CHEGST) +#define LAPACK_zhegst LAPACK_GLOBAL(zhegst,ZHEGST) +#define LAPACK_sspgst LAPACK_GLOBAL(sspgst,SSPGST) +#define LAPACK_dspgst LAPACK_GLOBAL(dspgst,DSPGST) +#define LAPACK_chpgst LAPACK_GLOBAL(chpgst,CHPGST) +#define LAPACK_zhpgst LAPACK_GLOBAL(zhpgst,ZHPGST) +#define LAPACK_ssbgst LAPACK_GLOBAL(ssbgst,SSBGST) +#define LAPACK_dsbgst LAPACK_GLOBAL(dsbgst,DSBGST) +#define LAPACK_chbgst LAPACK_GLOBAL(chbgst,CHBGST) +#define LAPACK_zhbgst LAPACK_GLOBAL(zhbgst,ZHBGST) +#define LAPACK_spbstf LAPACK_GLOBAL(spbstf,SPBSTF) +#define LAPACK_dpbstf LAPACK_GLOBAL(dpbstf,DPBSTF) +#define LAPACK_cpbstf LAPACK_GLOBAL(cpbstf,CPBSTF) +#define LAPACK_zpbstf LAPACK_GLOBAL(zpbstf,ZPBSTF) +#define LAPACK_sgehrd LAPACK_GLOBAL(sgehrd,SGEHRD) +#define LAPACK_dgehrd LAPACK_GLOBAL(dgehrd,DGEHRD) +#define LAPACK_cgehrd LAPACK_GLOBAL(cgehrd,CGEHRD) +#define LAPACK_zgehrd LAPACK_GLOBAL(zgehrd,ZGEHRD) +#define LAPACK_sorghr LAPACK_GLOBAL(sorghr,SORGHR) +#define LAPACK_dorghr LAPACK_GLOBAL(dorghr,DORGHR) +#define LAPACK_sormhr LAPACK_GLOBAL(sormhr,SORMHR) +#define LAPACK_dormhr LAPACK_GLOBAL(dormhr,DORMHR) +#define LAPACK_cunghr LAPACK_GLOBAL(cunghr,CUNGHR) +#define LAPACK_zunghr LAPACK_GLOBAL(zunghr,ZUNGHR) +#define LAPACK_cunmhr LAPACK_GLOBAL(cunmhr,CUNMHR) +#define LAPACK_zunmhr LAPACK_GLOBAL(zunmhr,ZUNMHR) +#define LAPACK_sgebal LAPACK_GLOBAL(sgebal,SGEBAL) +#define LAPACK_dgebal LAPACK_GLOBAL(dgebal,DGEBAL) +#define LAPACK_cgebal LAPACK_GLOBAL(cgebal,CGEBAL) +#define LAPACK_zgebal LAPACK_GLOBAL(zgebal,ZGEBAL) +#define LAPACK_sgebak LAPACK_GLOBAL(sgebak,SGEBAK) +#define LAPACK_dgebak LAPACK_GLOBAL(dgebak,DGEBAK) +#define LAPACK_cgebak LAPACK_GLOBAL(cgebak,CGEBAK) +#define LAPACK_zgebak LAPACK_GLOBAL(zgebak,ZGEBAK) +#define LAPACK_shseqr LAPACK_GLOBAL(shseqr,SHSEQR) +#define LAPACK_dhseqr LAPACK_GLOBAL(dhseqr,DHSEQR) +#define LAPACK_chseqr LAPACK_GLOBAL(chseqr,CHSEQR) +#define LAPACK_zhseqr LAPACK_GLOBAL(zhseqr,ZHSEQR) +#define LAPACK_shsein LAPACK_GLOBAL(shsein,SHSEIN) +#define LAPACK_dhsein LAPACK_GLOBAL(dhsein,DHSEIN) +#define LAPACK_chsein LAPACK_GLOBAL(chsein,CHSEIN) +#define LAPACK_zhsein LAPACK_GLOBAL(zhsein,ZHSEIN) +#define LAPACK_strevc LAPACK_GLOBAL(strevc,STREVC) +#define LAPACK_dtrevc LAPACK_GLOBAL(dtrevc,DTREVC) +#define LAPACK_ctrevc LAPACK_GLOBAL(ctrevc,CTREVC) +#define LAPACK_ztrevc LAPACK_GLOBAL(ztrevc,ZTREVC) +#define LAPACK_strsna LAPACK_GLOBAL(strsna,STRSNA) +#define LAPACK_dtrsna LAPACK_GLOBAL(dtrsna,DTRSNA) +#define LAPACK_ctrsna LAPACK_GLOBAL(ctrsna,CTRSNA) +#define LAPACK_ztrsna LAPACK_GLOBAL(ztrsna,ZTRSNA) +#define LAPACK_strexc LAPACK_GLOBAL(strexc,STREXC) +#define LAPACK_dtrexc LAPACK_GLOBAL(dtrexc,DTREXC) +#define LAPACK_ctrexc LAPACK_GLOBAL(ctrexc,CTREXC) +#define LAPACK_ztrexc LAPACK_GLOBAL(ztrexc,ZTREXC) +#define LAPACK_strsen LAPACK_GLOBAL(strsen,STRSEN) +#define LAPACK_dtrsen LAPACK_GLOBAL(dtrsen,DTRSEN) +#define LAPACK_ctrsen LAPACK_GLOBAL(ctrsen,CTRSEN) +#define LAPACK_ztrsen LAPACK_GLOBAL(ztrsen,ZTRSEN) +#define LAPACK_strsyl LAPACK_GLOBAL(strsyl,STRSYL) +#define LAPACK_dtrsyl LAPACK_GLOBAL(dtrsyl,DTRSYL) +#define LAPACK_ctrsyl LAPACK_GLOBAL(ctrsyl,CTRSYL) +#define LAPACK_ztrsyl LAPACK_GLOBAL(ztrsyl,ZTRSYL) +#define LAPACK_sgghrd LAPACK_GLOBAL(sgghrd,SGGHRD) +#define LAPACK_dgghrd LAPACK_GLOBAL(dgghrd,DGGHRD) +#define LAPACK_cgghrd LAPACK_GLOBAL(cgghrd,CGGHRD) +#define LAPACK_zgghrd LAPACK_GLOBAL(zgghrd,ZGGHRD) +#define LAPACK_sggbal LAPACK_GLOBAL(sggbal,SGGBAL) +#define LAPACK_dggbal LAPACK_GLOBAL(dggbal,DGGBAL) +#define LAPACK_cggbal LAPACK_GLOBAL(cggbal,CGGBAL) +#define LAPACK_zggbal LAPACK_GLOBAL(zggbal,ZGGBAL) +#define LAPACK_sggbak LAPACK_GLOBAL(sggbak,SGGBAK) +#define LAPACK_dggbak LAPACK_GLOBAL(dggbak,DGGBAK) +#define LAPACK_cggbak LAPACK_GLOBAL(cggbak,CGGBAK) +#define LAPACK_zggbak LAPACK_GLOBAL(zggbak,ZGGBAK) +#define LAPACK_shgeqz LAPACK_GLOBAL(shgeqz,SHGEQZ) +#define LAPACK_dhgeqz LAPACK_GLOBAL(dhgeqz,DHGEQZ) +#define LAPACK_chgeqz LAPACK_GLOBAL(chgeqz,CHGEQZ) +#define LAPACK_zhgeqz LAPACK_GLOBAL(zhgeqz,ZHGEQZ) +#define LAPACK_stgevc LAPACK_GLOBAL(stgevc,STGEVC) +#define LAPACK_dtgevc LAPACK_GLOBAL(dtgevc,DTGEVC) +#define LAPACK_ctgevc LAPACK_GLOBAL(ctgevc,CTGEVC) +#define LAPACK_ztgevc LAPACK_GLOBAL(ztgevc,ZTGEVC) +#define LAPACK_stgexc LAPACK_GLOBAL(stgexc,STGEXC) +#define LAPACK_dtgexc LAPACK_GLOBAL(dtgexc,DTGEXC) +#define LAPACK_ctgexc LAPACK_GLOBAL(ctgexc,CTGEXC) +#define LAPACK_ztgexc LAPACK_GLOBAL(ztgexc,ZTGEXC) +#define LAPACK_stgsen LAPACK_GLOBAL(stgsen,STGSEN) +#define LAPACK_dtgsen LAPACK_GLOBAL(dtgsen,DTGSEN) +#define LAPACK_ctgsen LAPACK_GLOBAL(ctgsen,CTGSEN) +#define LAPACK_ztgsen LAPACK_GLOBAL(ztgsen,ZTGSEN) +#define LAPACK_stgsyl LAPACK_GLOBAL(stgsyl,STGSYL) +#define LAPACK_dtgsyl LAPACK_GLOBAL(dtgsyl,DTGSYL) +#define LAPACK_ctgsyl LAPACK_GLOBAL(ctgsyl,CTGSYL) +#define LAPACK_ztgsyl LAPACK_GLOBAL(ztgsyl,ZTGSYL) +#define LAPACK_stgsna LAPACK_GLOBAL(stgsna,STGSNA) +#define LAPACK_dtgsna LAPACK_GLOBAL(dtgsna,DTGSNA) +#define LAPACK_ctgsna LAPACK_GLOBAL(ctgsna,CTGSNA) +#define LAPACK_ztgsna LAPACK_GLOBAL(ztgsna,ZTGSNA) +#define LAPACK_sggsvp LAPACK_GLOBAL(sggsvp,SGGSVP) +#define LAPACK_dggsvp LAPACK_GLOBAL(dggsvp,DGGSVP) +#define LAPACK_cggsvp LAPACK_GLOBAL(cggsvp,CGGSVP) +#define LAPACK_zggsvp LAPACK_GLOBAL(zggsvp,ZGGSVP) +#define LAPACK_stgsja LAPACK_GLOBAL(stgsja,STGSJA) +#define LAPACK_dtgsja LAPACK_GLOBAL(dtgsja,DTGSJA) +#define LAPACK_ctgsja LAPACK_GLOBAL(ctgsja,CTGSJA) +#define LAPACK_ztgsja LAPACK_GLOBAL(ztgsja,ZTGSJA) +#define LAPACK_sgels LAPACK_GLOBAL(sgels,SGELS) +#define LAPACK_dgels LAPACK_GLOBAL(dgels,DGELS) +#define LAPACK_cgels LAPACK_GLOBAL(cgels,CGELS) +#define LAPACK_zgels LAPACK_GLOBAL(zgels,ZGELS) +#define LAPACK_sgelsy LAPACK_GLOBAL(sgelsy,SGELSY) +#define LAPACK_dgelsy LAPACK_GLOBAL(dgelsy,DGELSY) +#define LAPACK_cgelsy LAPACK_GLOBAL(cgelsy,CGELSY) +#define LAPACK_zgelsy LAPACK_GLOBAL(zgelsy,ZGELSY) +#define LAPACK_sgelss LAPACK_GLOBAL(sgelss,SGELSS) +#define LAPACK_dgelss LAPACK_GLOBAL(dgelss,DGELSS) +#define LAPACK_cgelss LAPACK_GLOBAL(cgelss,CGELSS) +#define LAPACK_zgelss LAPACK_GLOBAL(zgelss,ZGELSS) +#define LAPACK_sgelsd LAPACK_GLOBAL(sgelsd,SGELSD) +#define LAPACK_dgelsd LAPACK_GLOBAL(dgelsd,DGELSD) +#define LAPACK_cgelsd LAPACK_GLOBAL(cgelsd,CGELSD) +#define LAPACK_zgelsd LAPACK_GLOBAL(zgelsd,ZGELSD) +#define LAPACK_sgglse LAPACK_GLOBAL(sgglse,SGGLSE) +#define LAPACK_dgglse LAPACK_GLOBAL(dgglse,DGGLSE) +#define LAPACK_cgglse LAPACK_GLOBAL(cgglse,CGGLSE) +#define LAPACK_zgglse LAPACK_GLOBAL(zgglse,ZGGLSE) +#define LAPACK_sggglm LAPACK_GLOBAL(sggglm,SGGGLM) +#define LAPACK_dggglm LAPACK_GLOBAL(dggglm,DGGGLM) +#define LAPACK_cggglm LAPACK_GLOBAL(cggglm,CGGGLM) +#define LAPACK_zggglm LAPACK_GLOBAL(zggglm,ZGGGLM) +#define LAPACK_ssyev LAPACK_GLOBAL(ssyev,SSYEV) +#define LAPACK_dsyev LAPACK_GLOBAL(dsyev,DSYEV) +#define LAPACK_cheev LAPACK_GLOBAL(cheev,CHEEV) +#define LAPACK_zheev LAPACK_GLOBAL(zheev,ZHEEV) +#define LAPACK_ssyevd LAPACK_GLOBAL(ssyevd,SSYEVD) +#define LAPACK_dsyevd LAPACK_GLOBAL(dsyevd,DSYEVD) +#define LAPACK_cheevd LAPACK_GLOBAL(cheevd,CHEEVD) +#define LAPACK_zheevd LAPACK_GLOBAL(zheevd,ZHEEVD) +#define LAPACK_ssyevx LAPACK_GLOBAL(ssyevx,SSYEVX) +#define LAPACK_dsyevx LAPACK_GLOBAL(dsyevx,DSYEVX) +#define LAPACK_cheevx LAPACK_GLOBAL(cheevx,CHEEVX) +#define LAPACK_zheevx LAPACK_GLOBAL(zheevx,ZHEEVX) +#define LAPACK_ssyevr LAPACK_GLOBAL(ssyevr,SSYEVR) +#define LAPACK_dsyevr LAPACK_GLOBAL(dsyevr,DSYEVR) +#define LAPACK_cheevr LAPACK_GLOBAL(cheevr,CHEEVR) +#define LAPACK_zheevr LAPACK_GLOBAL(zheevr,ZHEEVR) +#define LAPACK_sspev LAPACK_GLOBAL(sspev,SSPEV) +#define LAPACK_dspev LAPACK_GLOBAL(dspev,DSPEV) +#define LAPACK_chpev LAPACK_GLOBAL(chpev,CHPEV) +#define LAPACK_zhpev LAPACK_GLOBAL(zhpev,ZHPEV) +#define LAPACK_sspevd LAPACK_GLOBAL(sspevd,SSPEVD) +#define LAPACK_dspevd LAPACK_GLOBAL(dspevd,DSPEVD) +#define LAPACK_chpevd LAPACK_GLOBAL(chpevd,CHPEVD) +#define LAPACK_zhpevd LAPACK_GLOBAL(zhpevd,ZHPEVD) +#define LAPACK_sspevx LAPACK_GLOBAL(sspevx,SSPEVX) +#define LAPACK_dspevx LAPACK_GLOBAL(dspevx,DSPEVX) +#define LAPACK_chpevx LAPACK_GLOBAL(chpevx,CHPEVX) +#define LAPACK_zhpevx LAPACK_GLOBAL(zhpevx,ZHPEVX) +#define LAPACK_ssbev LAPACK_GLOBAL(ssbev,SSBEV) +#define LAPACK_dsbev LAPACK_GLOBAL(dsbev,DSBEV) +#define LAPACK_chbev LAPACK_GLOBAL(chbev,CHBEV) +#define LAPACK_zhbev LAPACK_GLOBAL(zhbev,ZHBEV) +#define LAPACK_ssbevd LAPACK_GLOBAL(ssbevd,SSBEVD) +#define LAPACK_dsbevd LAPACK_GLOBAL(dsbevd,DSBEVD) +#define LAPACK_chbevd LAPACK_GLOBAL(chbevd,CHBEVD) +#define LAPACK_zhbevd LAPACK_GLOBAL(zhbevd,ZHBEVD) +#define LAPACK_ssbevx LAPACK_GLOBAL(ssbevx,SSBEVX) +#define LAPACK_dsbevx LAPACK_GLOBAL(dsbevx,DSBEVX) +#define LAPACK_chbevx LAPACK_GLOBAL(chbevx,CHBEVX) +#define LAPACK_zhbevx LAPACK_GLOBAL(zhbevx,ZHBEVX) +#define LAPACK_sstev LAPACK_GLOBAL(sstev,SSTEV) +#define LAPACK_dstev LAPACK_GLOBAL(dstev,DSTEV) +#define LAPACK_sstevd LAPACK_GLOBAL(sstevd,SSTEVD) +#define LAPACK_dstevd LAPACK_GLOBAL(dstevd,DSTEVD) +#define LAPACK_sstevx LAPACK_GLOBAL(sstevx,SSTEVX) +#define LAPACK_dstevx LAPACK_GLOBAL(dstevx,DSTEVX) +#define LAPACK_sstevr LAPACK_GLOBAL(sstevr,SSTEVR) +#define LAPACK_dstevr LAPACK_GLOBAL(dstevr,DSTEVR) +#define LAPACK_sgees LAPACK_GLOBAL(sgees,SGEES) +#define LAPACK_dgees LAPACK_GLOBAL(dgees,DGEES) +#define LAPACK_cgees LAPACK_GLOBAL(cgees,CGEES) +#define LAPACK_zgees LAPACK_GLOBAL(zgees,ZGEES) +#define LAPACK_sgeesx LAPACK_GLOBAL(sgeesx,SGEESX) +#define LAPACK_dgeesx LAPACK_GLOBAL(dgeesx,DGEESX) +#define LAPACK_cgeesx LAPACK_GLOBAL(cgeesx,CGEESX) +#define LAPACK_zgeesx LAPACK_GLOBAL(zgeesx,ZGEESX) +#define LAPACK_sgeev LAPACK_GLOBAL(sgeev,SGEEV) +#define LAPACK_dgeev LAPACK_GLOBAL(dgeev,DGEEV) +#define LAPACK_cgeev LAPACK_GLOBAL(cgeev,CGEEV) +#define LAPACK_zgeev LAPACK_GLOBAL(zgeev,ZGEEV) +#define LAPACK_sgeevx LAPACK_GLOBAL(sgeevx,SGEEVX) +#define LAPACK_dgeevx LAPACK_GLOBAL(dgeevx,DGEEVX) +#define LAPACK_cgeevx LAPACK_GLOBAL(cgeevx,CGEEVX) +#define LAPACK_zgeevx LAPACK_GLOBAL(zgeevx,ZGEEVX) +#define LAPACK_sgesvd LAPACK_GLOBAL(sgesvd,SGESVD) +#define LAPACK_dgesvd LAPACK_GLOBAL(dgesvd,DGESVD) +#define LAPACK_cgesvd LAPACK_GLOBAL(cgesvd,CGESVD) +#define LAPACK_zgesvd LAPACK_GLOBAL(zgesvd,ZGESVD) +#define LAPACK_sgesdd LAPACK_GLOBAL(sgesdd,SGESDD) +#define LAPACK_dgesdd LAPACK_GLOBAL(dgesdd,DGESDD) +#define LAPACK_cgesdd LAPACK_GLOBAL(cgesdd,CGESDD) +#define LAPACK_zgesdd LAPACK_GLOBAL(zgesdd,ZGESDD) +#define LAPACK_dgejsv LAPACK_GLOBAL(dgejsv,DGEJSV) +#define LAPACK_sgejsv LAPACK_GLOBAL(sgejsv,SGEJSV) +#define LAPACK_dgesvj LAPACK_GLOBAL(dgesvj,DGESVJ) +#define LAPACK_sgesvj LAPACK_GLOBAL(sgesvj,SGESVJ) +#define LAPACK_sggsvd LAPACK_GLOBAL(sggsvd,SGGSVD) +#define LAPACK_dggsvd LAPACK_GLOBAL(dggsvd,DGGSVD) +#define LAPACK_cggsvd LAPACK_GLOBAL(cggsvd,CGGSVD) +#define LAPACK_zggsvd LAPACK_GLOBAL(zggsvd,ZGGSVD) +#define LAPACK_ssygv LAPACK_GLOBAL(ssygv,SSYGV) +#define LAPACK_dsygv LAPACK_GLOBAL(dsygv,DSYGV) +#define LAPACK_chegv LAPACK_GLOBAL(chegv,CHEGV) +#define LAPACK_zhegv LAPACK_GLOBAL(zhegv,ZHEGV) +#define LAPACK_ssygvd LAPACK_GLOBAL(ssygvd,SSYGVD) +#define LAPACK_dsygvd LAPACK_GLOBAL(dsygvd,DSYGVD) +#define LAPACK_chegvd LAPACK_GLOBAL(chegvd,CHEGVD) +#define LAPACK_zhegvd LAPACK_GLOBAL(zhegvd,ZHEGVD) +#define LAPACK_ssygvx LAPACK_GLOBAL(ssygvx,SSYGVX) +#define LAPACK_dsygvx LAPACK_GLOBAL(dsygvx,DSYGVX) +#define LAPACK_chegvx LAPACK_GLOBAL(chegvx,CHEGVX) +#define LAPACK_zhegvx LAPACK_GLOBAL(zhegvx,ZHEGVX) +#define LAPACK_sspgv LAPACK_GLOBAL(sspgv,SSPGV) +#define LAPACK_dspgv LAPACK_GLOBAL(dspgv,DSPGV) +#define LAPACK_chpgv LAPACK_GLOBAL(chpgv,CHPGV) +#define LAPACK_zhpgv LAPACK_GLOBAL(zhpgv,ZHPGV) +#define LAPACK_sspgvd LAPACK_GLOBAL(sspgvd,SSPGVD) +#define LAPACK_dspgvd LAPACK_GLOBAL(dspgvd,DSPGVD) +#define LAPACK_chpgvd LAPACK_GLOBAL(chpgvd,CHPGVD) +#define LAPACK_zhpgvd LAPACK_GLOBAL(zhpgvd,ZHPGVD) +#define LAPACK_sspgvx LAPACK_GLOBAL(sspgvx,SSPGVX) +#define LAPACK_dspgvx LAPACK_GLOBAL(dspgvx,DSPGVX) +#define LAPACK_chpgvx LAPACK_GLOBAL(chpgvx,CHPGVX) +#define LAPACK_zhpgvx LAPACK_GLOBAL(zhpgvx,ZHPGVX) +#define LAPACK_ssbgv LAPACK_GLOBAL(ssbgv,SSBGV) +#define LAPACK_dsbgv LAPACK_GLOBAL(dsbgv,DSBGV) +#define LAPACK_chbgv LAPACK_GLOBAL(chbgv,CHBGV) +#define LAPACK_zhbgv LAPACK_GLOBAL(zhbgv,ZHBGV) +#define LAPACK_ssbgvd LAPACK_GLOBAL(ssbgvd,SSBGVD) +#define LAPACK_dsbgvd LAPACK_GLOBAL(dsbgvd,DSBGVD) +#define LAPACK_chbgvd LAPACK_GLOBAL(chbgvd,CHBGVD) +#define LAPACK_zhbgvd LAPACK_GLOBAL(zhbgvd,ZHBGVD) +#define LAPACK_ssbgvx LAPACK_GLOBAL(ssbgvx,SSBGVX) +#define LAPACK_dsbgvx LAPACK_GLOBAL(dsbgvx,DSBGVX) +#define LAPACK_chbgvx LAPACK_GLOBAL(chbgvx,CHBGVX) +#define LAPACK_zhbgvx LAPACK_GLOBAL(zhbgvx,ZHBGVX) +#define LAPACK_sgges LAPACK_GLOBAL(sgges,SGGES) +#define LAPACK_dgges LAPACK_GLOBAL(dgges,DGGES) +#define LAPACK_cgges LAPACK_GLOBAL(cgges,CGGES) +#define LAPACK_zgges LAPACK_GLOBAL(zgges,ZGGES) +#define LAPACK_sggesx LAPACK_GLOBAL(sggesx,SGGESX) +#define LAPACK_dggesx LAPACK_GLOBAL(dggesx,DGGESX) +#define LAPACK_cggesx LAPACK_GLOBAL(cggesx,CGGESX) +#define LAPACK_zggesx LAPACK_GLOBAL(zggesx,ZGGESX) +#define LAPACK_sggev LAPACK_GLOBAL(sggev,SGGEV) +#define LAPACK_dggev LAPACK_GLOBAL(dggev,DGGEV) +#define LAPACK_cggev LAPACK_GLOBAL(cggev,CGGEV) +#define LAPACK_zggev LAPACK_GLOBAL(zggev,ZGGEV) +#define LAPACK_sggevx LAPACK_GLOBAL(sggevx,SGGEVX) +#define LAPACK_dggevx LAPACK_GLOBAL(dggevx,DGGEVX) +#define LAPACK_cggevx LAPACK_GLOBAL(cggevx,CGGEVX) +#define LAPACK_zggevx LAPACK_GLOBAL(zggevx,ZGGEVX) +#define LAPACK_dsfrk LAPACK_GLOBAL(dsfrk,DSFRK) +#define LAPACK_ssfrk LAPACK_GLOBAL(ssfrk,SSFRK) +#define LAPACK_zhfrk LAPACK_GLOBAL(zhfrk,ZHFRK) +#define LAPACK_chfrk LAPACK_GLOBAL(chfrk,CHFRK) +#define LAPACK_dtfsm LAPACK_GLOBAL(dtfsm,DTFSM) +#define LAPACK_stfsm LAPACK_GLOBAL(stfsm,STFSM) +#define LAPACK_ztfsm LAPACK_GLOBAL(ztfsm,ZTFSM) +#define LAPACK_ctfsm LAPACK_GLOBAL(ctfsm,CTFSM) +#define LAPACK_dtfttp LAPACK_GLOBAL(dtfttp,DTFTTP) +#define LAPACK_stfttp LAPACK_GLOBAL(stfttp,STFTTP) +#define LAPACK_ztfttp LAPACK_GLOBAL(ztfttp,ZTFTTP) +#define LAPACK_ctfttp LAPACK_GLOBAL(ctfttp,CTFTTP) +#define LAPACK_dtfttr LAPACK_GLOBAL(dtfttr,DTFTTR) +#define LAPACK_stfttr LAPACK_GLOBAL(stfttr,STFTTR) +#define LAPACK_ztfttr LAPACK_GLOBAL(ztfttr,ZTFTTR) +#define LAPACK_ctfttr LAPACK_GLOBAL(ctfttr,CTFTTR) +#define LAPACK_dtpttf LAPACK_GLOBAL(dtpttf,DTPTTF) +#define LAPACK_stpttf LAPACK_GLOBAL(stpttf,STPTTF) +#define LAPACK_ztpttf LAPACK_GLOBAL(ztpttf,ZTPTTF) +#define LAPACK_ctpttf LAPACK_GLOBAL(ctpttf,CTPTTF) +#define LAPACK_dtpttr LAPACK_GLOBAL(dtpttr,DTPTTR) +#define LAPACK_stpttr LAPACK_GLOBAL(stpttr,STPTTR) +#define LAPACK_ztpttr LAPACK_GLOBAL(ztpttr,ZTPTTR) +#define LAPACK_ctpttr LAPACK_GLOBAL(ctpttr,CTPTTR) +#define LAPACK_dtrttf LAPACK_GLOBAL(dtrttf,DTRTTF) +#define LAPACK_strttf LAPACK_GLOBAL(strttf,STRTTF) +#define LAPACK_ztrttf LAPACK_GLOBAL(ztrttf,ZTRTTF) +#define LAPACK_ctrttf LAPACK_GLOBAL(ctrttf,CTRTTF) +#define LAPACK_dtrttp LAPACK_GLOBAL(dtrttp,DTRTTP) +#define LAPACK_strttp LAPACK_GLOBAL(strttp,STRTTP) +#define LAPACK_ztrttp LAPACK_GLOBAL(ztrttp,ZTRTTP) +#define LAPACK_ctrttp LAPACK_GLOBAL(ctrttp,CTRTTP) +#define LAPACK_sgeqrfp LAPACK_GLOBAL(sgeqrfp,SGEQRFP) +#define LAPACK_dgeqrfp LAPACK_GLOBAL(dgeqrfp,DGEQRFP) +#define LAPACK_cgeqrfp LAPACK_GLOBAL(cgeqrfp,CGEQRFP) +#define LAPACK_zgeqrfp LAPACK_GLOBAL(zgeqrfp,ZGEQRFP) +#define LAPACK_clacgv LAPACK_GLOBAL(clacgv,CLACGV) +#define LAPACK_zlacgv LAPACK_GLOBAL(zlacgv,ZLACGV) +#define LAPACK_slarnv LAPACK_GLOBAL(slarnv,SLARNV) +#define LAPACK_dlarnv LAPACK_GLOBAL(dlarnv,DLARNV) +#define LAPACK_clarnv LAPACK_GLOBAL(clarnv,CLARNV) +#define LAPACK_zlarnv LAPACK_GLOBAL(zlarnv,ZLARNV) +#define LAPACK_sgeqr2 LAPACK_GLOBAL(sgeqr2,SGEQR2) +#define LAPACK_dgeqr2 LAPACK_GLOBAL(dgeqr2,DGEQR2) +#define LAPACK_cgeqr2 LAPACK_GLOBAL(cgeqr2,CGEQR2) +#define LAPACK_zgeqr2 LAPACK_GLOBAL(zgeqr2,ZGEQR2) +#define LAPACK_slacpy LAPACK_GLOBAL(slacpy,SLACPY) +#define LAPACK_dlacpy LAPACK_GLOBAL(dlacpy,DLACPY) +#define LAPACK_clacpy LAPACK_GLOBAL(clacpy,CLACPY) +#define LAPACK_zlacpy LAPACK_GLOBAL(zlacpy,ZLACPY) +#define LAPACK_sgetf2 LAPACK_GLOBAL(sgetf2,SGETF2) +#define LAPACK_dgetf2 LAPACK_GLOBAL(dgetf2,DGETF2) +#define LAPACK_cgetf2 LAPACK_GLOBAL(cgetf2,CGETF2) +#define LAPACK_zgetf2 LAPACK_GLOBAL(zgetf2,ZGETF2) +#define LAPACK_slaswp LAPACK_GLOBAL(slaswp,SLASWP) +#define LAPACK_dlaswp LAPACK_GLOBAL(dlaswp,DLASWP) +#define LAPACK_claswp LAPACK_GLOBAL(claswp,CLASWP) +#define LAPACK_zlaswp LAPACK_GLOBAL(zlaswp,ZLASWP) +#define LAPACK_slange LAPACK_GLOBAL(slange,SLANGE) +#define LAPACK_dlange LAPACK_GLOBAL(dlange,DLANGE) +#define LAPACK_clange LAPACK_GLOBAL(clange,CLANGE) +#define LAPACK_zlange LAPACK_GLOBAL(zlange,ZLANGE) +#define LAPACK_clanhe LAPACK_GLOBAL(clanhe,CLANHE) +#define LAPACK_zlanhe LAPACK_GLOBAL(zlanhe,ZLANHE) +#define LAPACK_slansy LAPACK_GLOBAL(slansy,SLANSY) +#define LAPACK_dlansy LAPACK_GLOBAL(dlansy,DLANSY) +#define LAPACK_clansy LAPACK_GLOBAL(clansy,CLANSY) +#define LAPACK_zlansy LAPACK_GLOBAL(zlansy,ZLANSY) +#define LAPACK_slantr LAPACK_GLOBAL(slantr,SLANTR) +#define LAPACK_dlantr LAPACK_GLOBAL(dlantr,DLANTR) +#define LAPACK_clantr LAPACK_GLOBAL(clantr,CLANTR) +#define LAPACK_zlantr LAPACK_GLOBAL(zlantr,ZLANTR) +#define LAPACK_slamch LAPACK_GLOBAL(slamch,SLAMCH) +#define LAPACK_dlamch LAPACK_GLOBAL(dlamch,DLAMCH) +#define LAPACK_sgelq2 LAPACK_GLOBAL(sgelq2,SGELQ2) +#define LAPACK_dgelq2 LAPACK_GLOBAL(dgelq2,DGELQ2) +#define LAPACK_cgelq2 LAPACK_GLOBAL(cgelq2,CGELQ2) +#define LAPACK_zgelq2 LAPACK_GLOBAL(zgelq2,ZGELQ2) +#define LAPACK_slarfb LAPACK_GLOBAL(slarfb,SLARFB) +#define LAPACK_dlarfb LAPACK_GLOBAL(dlarfb,DLARFB) +#define LAPACK_clarfb LAPACK_GLOBAL(clarfb,CLARFB) +#define LAPACK_zlarfb LAPACK_GLOBAL(zlarfb,ZLARFB) +#define LAPACK_slarfg LAPACK_GLOBAL(slarfg,SLARFG) +#define LAPACK_dlarfg LAPACK_GLOBAL(dlarfg,DLARFG) +#define LAPACK_clarfg LAPACK_GLOBAL(clarfg,CLARFG) +#define LAPACK_zlarfg LAPACK_GLOBAL(zlarfg,ZLARFG) +#define LAPACK_slarft LAPACK_GLOBAL(slarft,SLARFT) +#define LAPACK_dlarft LAPACK_GLOBAL(dlarft,DLARFT) +#define LAPACK_clarft LAPACK_GLOBAL(clarft,CLARFT) +#define LAPACK_zlarft LAPACK_GLOBAL(zlarft,ZLARFT) +#define LAPACK_slarfx LAPACK_GLOBAL(slarfx,SLARFX) +#define LAPACK_dlarfx LAPACK_GLOBAL(dlarfx,DLARFX) +#define LAPACK_clarfx LAPACK_GLOBAL(clarfx,CLARFX) +#define LAPACK_zlarfx LAPACK_GLOBAL(zlarfx,ZLARFX) +#define LAPACK_slatms LAPACK_GLOBAL(slatms,SLATMS) +#define LAPACK_dlatms LAPACK_GLOBAL(dlatms,DLATMS) +#define LAPACK_clatms LAPACK_GLOBAL(clatms,CLATMS) +#define LAPACK_zlatms LAPACK_GLOBAL(zlatms,ZLATMS) +#define LAPACK_slag2d LAPACK_GLOBAL(slag2d,SLAG2D) +#define LAPACK_dlag2s LAPACK_GLOBAL(dlag2s,DLAG2S) +#define LAPACK_clag2z LAPACK_GLOBAL(clag2z,CLAG2Z) +#define LAPACK_zlag2c LAPACK_GLOBAL(zlag2c,ZLAG2C) +#define LAPACK_slauum LAPACK_GLOBAL(slauum,SLAUUM) +#define LAPACK_dlauum LAPACK_GLOBAL(dlauum,DLAUUM) +#define LAPACK_clauum LAPACK_GLOBAL(clauum,CLAUUM) +#define LAPACK_zlauum LAPACK_GLOBAL(zlauum,ZLAUUM) +#define LAPACK_slagge LAPACK_GLOBAL(slagge,SLAGGE) +#define LAPACK_dlagge LAPACK_GLOBAL(dlagge,DLAGGE) +#define LAPACK_clagge LAPACK_GLOBAL(clagge,CLAGGE) +#define LAPACK_zlagge LAPACK_GLOBAL(zlagge,ZLAGGE) +#define LAPACK_slaset LAPACK_GLOBAL(slaset,SLASET) +#define LAPACK_dlaset LAPACK_GLOBAL(dlaset,DLASET) +#define LAPACK_claset LAPACK_GLOBAL(claset,CLASET) +#define LAPACK_zlaset LAPACK_GLOBAL(zlaset,ZLASET) +#define LAPACK_slasrt LAPACK_GLOBAL(slasrt,SLASRT) +#define LAPACK_dlasrt LAPACK_GLOBAL(dlasrt,DLASRT) +#define LAPACK_slagsy LAPACK_GLOBAL(slagsy,SLAGSY) +#define LAPACK_dlagsy LAPACK_GLOBAL(dlagsy,DLAGSY) +#define LAPACK_clagsy LAPACK_GLOBAL(clagsy,CLAGSY) +#define LAPACK_zlagsy LAPACK_GLOBAL(zlagsy,ZLAGSY) +#define LAPACK_claghe LAPACK_GLOBAL(claghe,CLAGHE) +#define LAPACK_zlaghe LAPACK_GLOBAL(zlaghe,ZLAGHE) +#define LAPACK_slapmr LAPACK_GLOBAL(slapmr,SLAPMR) +#define LAPACK_dlapmr LAPACK_GLOBAL(dlapmr,DLAPMR) +#define LAPACK_clapmr LAPACK_GLOBAL(clapmr,CLAPMR) +#define LAPACK_zlapmr LAPACK_GLOBAL(zlapmr,ZLAPMR) +#define LAPACK_slapy2 LAPACK_GLOBAL(slapy2,SLAPY2) +#define LAPACK_dlapy2 LAPACK_GLOBAL(dlapy2,DLAPY2) +#define LAPACK_slapy3 LAPACK_GLOBAL(slapy3,SLAPY3) +#define LAPACK_dlapy3 LAPACK_GLOBAL(dlapy3,DLAPY3) +#define LAPACK_slartgp LAPACK_GLOBAL(slartgp,SLARTGP) +#define LAPACK_dlartgp LAPACK_GLOBAL(dlartgp,DLARTGP) +#define LAPACK_slartgs LAPACK_GLOBAL(slartgs,SLARTGS) +#define LAPACK_dlartgs LAPACK_GLOBAL(dlartgs,DLARTGS) +// LAPACK 3.3.0 +#define LAPACK_cbbcsd LAPACK_GLOBAL(cbbcsd,CBBCSD) +#define LAPACK_cheswapr LAPACK_GLOBAL(cheswapr,CHESWAPR) +#define LAPACK_chetri2 LAPACK_GLOBAL(chetri2,CHETRI2) +#define LAPACK_chetri2x LAPACK_GLOBAL(chetri2x,CHETRI2X) +#define LAPACK_chetrs2 LAPACK_GLOBAL(chetrs2,CHETRS2) +#define LAPACK_csyconv LAPACK_GLOBAL(csyconv,CSYCONV) +#define LAPACK_csyswapr LAPACK_GLOBAL(csyswapr,CSYSWAPR) +#define LAPACK_csytri2 LAPACK_GLOBAL(csytri2,CSYTRI2) +#define LAPACK_csytri2x LAPACK_GLOBAL(csytri2x,CSYTRI2X) +#define LAPACK_csytrs2 LAPACK_GLOBAL(csytrs2,CSYTRS2) +#define LAPACK_cunbdb LAPACK_GLOBAL(cunbdb,CUNBDB) +#define LAPACK_cuncsd LAPACK_GLOBAL(cuncsd,CUNCSD) +#define LAPACK_dbbcsd LAPACK_GLOBAL(dbbcsd,DBBCSD) +#define LAPACK_dorbdb LAPACK_GLOBAL(dorbdb,DORBDB) +#define LAPACK_dorcsd LAPACK_GLOBAL(dorcsd,DORCSD) +#define LAPACK_dsyconv LAPACK_GLOBAL(dsyconv,DSYCONV) +#define LAPACK_dsyswapr LAPACK_GLOBAL(dsyswapr,DSYSWAPR) +#define LAPACK_dsytri2 LAPACK_GLOBAL(dsytri2,DSYTRI2) +#define LAPACK_dsytri2x LAPACK_GLOBAL(dsytri2x,DSYTRI2X) +#define LAPACK_dsytrs2 LAPACK_GLOBAL(dsytrs2,DSYTRS2) +#define LAPACK_sbbcsd LAPACK_GLOBAL(sbbcsd,SBBCSD) +#define LAPACK_sorbdb LAPACK_GLOBAL(sorbdb,SORBDB) +#define LAPACK_sorcsd LAPACK_GLOBAL(sorcsd,SORCSD) +#define LAPACK_ssyconv LAPACK_GLOBAL(ssyconv,SSYCONV) +#define LAPACK_ssyswapr LAPACK_GLOBAL(ssyswapr,SSYSWAPR) +#define LAPACK_ssytri2 LAPACK_GLOBAL(ssytri2,SSYTRI2) +#define LAPACK_ssytri2x LAPACK_GLOBAL(ssytri2x,SSYTRI2X) +#define LAPACK_ssytrs2 LAPACK_GLOBAL(ssytrs2,SSYTRS2) +#define LAPACK_zbbcsd LAPACK_GLOBAL(zbbcsd,ZBBCSD) +#define LAPACK_zheswapr LAPACK_GLOBAL(zheswapr,ZHESWAPR) +#define LAPACK_zhetri2 LAPACK_GLOBAL(zhetri2,ZHETRI2) +#define LAPACK_zhetri2x LAPACK_GLOBAL(zhetri2x,ZHETRI2X) +#define LAPACK_zhetrs2 LAPACK_GLOBAL(zhetrs2,ZHETRS2) +#define LAPACK_zsyconv LAPACK_GLOBAL(zsyconv,ZSYCONV) +#define LAPACK_zsyswapr LAPACK_GLOBAL(zsyswapr,ZSYSWAPR) +#define LAPACK_zsytri2 LAPACK_GLOBAL(zsytri2,ZSYTRI2) +#define LAPACK_zsytri2x LAPACK_GLOBAL(zsytri2x,ZSYTRI2X) +#define LAPACK_zsytrs2 LAPACK_GLOBAL(zsytrs2,ZSYTRS2) +#define LAPACK_zunbdb LAPACK_GLOBAL(zunbdb,ZUNBDB) +#define LAPACK_zuncsd LAPACK_GLOBAL(zuncsd,ZUNCSD) +// LAPACK 3.4.0 +#define LAPACK_sgemqrt LAPACK_GLOBAL(sgemqrt,SGEMQRT) +#define LAPACK_dgemqrt LAPACK_GLOBAL(dgemqrt,DGEMQRT) +#define LAPACK_cgemqrt LAPACK_GLOBAL(cgemqrt,CGEMQRT) +#define LAPACK_zgemqrt LAPACK_GLOBAL(zgemqrt,ZGEMQRT) +#define LAPACK_sgeqrt LAPACK_GLOBAL(sgeqrt,SGEQRT) +#define LAPACK_dgeqrt LAPACK_GLOBAL(dgeqrt,DGEQRT) +#define LAPACK_cgeqrt LAPACK_GLOBAL(cgeqrt,CGEQRT) +#define LAPACK_zgeqrt LAPACK_GLOBAL(zgeqrt,ZGEQRT) +#define LAPACK_sgeqrt2 LAPACK_GLOBAL(sgeqrt2,SGEQRT2) +#define LAPACK_dgeqrt2 LAPACK_GLOBAL(dgeqrt2,DGEQRT2) +#define LAPACK_cgeqrt2 LAPACK_GLOBAL(cgeqrt2,CGEQRT2) +#define LAPACK_zgeqrt2 LAPACK_GLOBAL(zgeqrt2,ZGEQRT2) +#define LAPACK_sgeqrt3 LAPACK_GLOBAL(sgeqrt3,SGEQRT3) +#define LAPACK_dgeqrt3 LAPACK_GLOBAL(dgeqrt3,DGEQRT3) +#define LAPACK_cgeqrt3 LAPACK_GLOBAL(cgeqrt3,CGEQRT3) +#define LAPACK_zgeqrt3 LAPACK_GLOBAL(zgeqrt3,ZGEQRT3) +#define LAPACK_stpmqrt LAPACK_GLOBAL(stpmqrt,STPMQRT) +#define LAPACK_dtpmqrt LAPACK_GLOBAL(dtpmqrt,DTPMQRT) +#define LAPACK_ctpmqrt LAPACK_GLOBAL(ctpmqrt,CTPMQRT) +#define LAPACK_ztpmqrt LAPACK_GLOBAL(ztpmqrt,ZTPMQRT) +#define LAPACK_dtpqrt LAPACK_GLOBAL(dtpqrt,DTPQRT) +#define LAPACK_ctpqrt LAPACK_GLOBAL(ctpqrt,CTPQRT) +#define LAPACK_ztpqrt LAPACK_GLOBAL(ztpqrt,ZTPQRT) +#define LAPACK_stpqrt2 LAPACK_GLOBAL(stpqrt2,STPQRT2) +#define LAPACK_dtpqrt2 LAPACK_GLOBAL(dtpqrt2,DTPQRT2) +#define LAPACK_ctpqrt2 LAPACK_GLOBAL(ctpqrt2,CTPQRT2) +#define LAPACK_ztpqrt2 LAPACK_GLOBAL(ztpqrt2,ZTPQRT2) +#define LAPACK_stprfb LAPACK_GLOBAL(stprfb,STPRFB) +#define LAPACK_dtprfb LAPACK_GLOBAL(dtprfb,DTPRFB) +#define LAPACK_ctprfb LAPACK_GLOBAL(ctprfb,CTPRFB) +#define LAPACK_ztprfb LAPACK_GLOBAL(ztprfb,ZTPRFB) +// LAPACK 3.X.X +#define LAPACK_csyr LAPACK_GLOBAL(csyr,CSYR) +#define LAPACK_zsyr LAPACK_GLOBAL(zsyr,ZSYR) + + +void LAPACK_sgetrf( lapack_int* m, lapack_int* n, float* a, lapack_int* lda, + lapack_int* ipiv, lapack_int *info ); +void LAPACK_dgetrf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda, + lapack_int* ipiv, lapack_int *info ); +void LAPACK_cgetrf( lapack_int* m, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_int* ipiv, lapack_int *info ); +void LAPACK_zgetrf( lapack_int* m, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_int* ipiv, lapack_int *info ); +void LAPACK_sgbtrf( lapack_int* m, lapack_int* n, lapack_int* kl, + lapack_int* ku, float* ab, lapack_int* ldab, + lapack_int* ipiv, lapack_int *info ); +void LAPACK_dgbtrf( lapack_int* m, lapack_int* n, lapack_int* kl, + lapack_int* ku, double* ab, lapack_int* ldab, + lapack_int* ipiv, lapack_int *info ); +void LAPACK_cgbtrf( lapack_int* m, lapack_int* n, lapack_int* kl, + lapack_int* ku, lapack_complex_float* ab, lapack_int* ldab, + lapack_int* ipiv, lapack_int *info ); +void LAPACK_zgbtrf( lapack_int* m, lapack_int* n, lapack_int* kl, + lapack_int* ku, lapack_complex_double* ab, lapack_int* ldab, + lapack_int* ipiv, lapack_int *info ); +void LAPACK_sgttrf( lapack_int* n, float* dl, float* d, float* du, float* du2, + lapack_int* ipiv, lapack_int *info ); +void LAPACK_dgttrf( lapack_int* n, double* dl, double* d, double* du, + double* du2, lapack_int* ipiv, lapack_int *info ); +void LAPACK_cgttrf( lapack_int* n, lapack_complex_float* dl, + lapack_complex_float* d, lapack_complex_float* du, + lapack_complex_float* du2, lapack_int* ipiv, + lapack_int *info ); +void LAPACK_zgttrf( lapack_int* n, lapack_complex_double* dl, + lapack_complex_double* d, lapack_complex_double* du, + lapack_complex_double* du2, lapack_int* ipiv, + lapack_int *info ); +void LAPACK_spotrf( char* uplo, lapack_int* n, float* a, lapack_int* lda, + lapack_int *info ); +void LAPACK_dpotrf( char* uplo, lapack_int* n, double* a, lapack_int* lda, + lapack_int *info ); +void LAPACK_cpotrf( char* uplo, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_int *info ); +void LAPACK_zpotrf( char* uplo, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_int *info ); +void LAPACK_dpstrf( char* uplo, lapack_int* n, double* a, lapack_int* lda, + lapack_int* piv, lapack_int* rank, double* tol, + double* work, lapack_int *info ); +void LAPACK_spstrf( char* uplo, lapack_int* n, float* a, lapack_int* lda, + lapack_int* piv, lapack_int* rank, float* tol, float* work, + lapack_int *info ); +void LAPACK_zpstrf( char* uplo, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_int* piv, lapack_int* rank, + double* tol, double* work, lapack_int *info ); +void LAPACK_cpstrf( char* uplo, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_int* piv, lapack_int* rank, + float* tol, float* work, lapack_int *info ); +void LAPACK_dpftrf( char* transr, char* uplo, lapack_int* n, double* a, + lapack_int *info ); +void LAPACK_spftrf( char* transr, char* uplo, lapack_int* n, float* a, + lapack_int *info ); +void LAPACK_zpftrf( char* transr, char* uplo, lapack_int* n, + lapack_complex_double* a, lapack_int *info ); +void LAPACK_cpftrf( char* transr, char* uplo, lapack_int* n, + lapack_complex_float* a, lapack_int *info ); +void LAPACK_spptrf( char* uplo, lapack_int* n, float* ap, lapack_int *info ); +void LAPACK_dpptrf( char* uplo, lapack_int* n, double* ap, lapack_int *info ); +void LAPACK_cpptrf( char* uplo, lapack_int* n, lapack_complex_float* ap, + lapack_int *info ); +void LAPACK_zpptrf( char* uplo, lapack_int* n, lapack_complex_double* ap, + lapack_int *info ); +void LAPACK_spbtrf( char* uplo, lapack_int* n, lapack_int* kd, float* ab, + lapack_int* ldab, lapack_int *info ); +void LAPACK_dpbtrf( char* uplo, lapack_int* n, lapack_int* kd, double* ab, + lapack_int* ldab, lapack_int *info ); +void LAPACK_cpbtrf( char* uplo, lapack_int* n, lapack_int* kd, + lapack_complex_float* ab, lapack_int* ldab, + lapack_int *info ); +void LAPACK_zpbtrf( char* uplo, lapack_int* n, lapack_int* kd, + lapack_complex_double* ab, lapack_int* ldab, + lapack_int *info ); +void LAPACK_spttrf( lapack_int* n, float* d, float* e, lapack_int *info ); +void LAPACK_dpttrf( lapack_int* n, double* d, double* e, lapack_int *info ); +void LAPACK_cpttrf( lapack_int* n, float* d, lapack_complex_float* e, + lapack_int *info ); +void LAPACK_zpttrf( lapack_int* n, double* d, lapack_complex_double* e, + lapack_int *info ); +void LAPACK_ssytrf( char* uplo, lapack_int* n, float* a, lapack_int* lda, + lapack_int* ipiv, float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_dsytrf( char* uplo, lapack_int* n, double* a, lapack_int* lda, + lapack_int* ipiv, double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_csytrf( char* uplo, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_int* ipiv, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_zsytrf( char* uplo, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_int* ipiv, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_chetrf( char* uplo, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_int* ipiv, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_zhetrf( char* uplo, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_int* ipiv, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_ssptrf( char* uplo, lapack_int* n, float* ap, lapack_int* ipiv, + lapack_int *info ); +void LAPACK_dsptrf( char* uplo, lapack_int* n, double* ap, lapack_int* ipiv, + lapack_int *info ); +void LAPACK_csptrf( char* uplo, lapack_int* n, lapack_complex_float* ap, + lapack_int* ipiv, lapack_int *info ); +void LAPACK_zsptrf( char* uplo, lapack_int* n, lapack_complex_double* ap, + lapack_int* ipiv, lapack_int *info ); +void LAPACK_chptrf( char* uplo, lapack_int* n, lapack_complex_float* ap, + lapack_int* ipiv, lapack_int *info ); +void LAPACK_zhptrf( char* uplo, lapack_int* n, lapack_complex_double* ap, + lapack_int* ipiv, lapack_int *info ); +void LAPACK_sgetrs( char* trans, lapack_int* n, lapack_int* nrhs, + const float* a, lapack_int* lda, const lapack_int* ipiv, + float* b, lapack_int* ldb, lapack_int *info ); +void LAPACK_dgetrs( char* trans, lapack_int* n, lapack_int* nrhs, + const double* a, lapack_int* lda, const lapack_int* ipiv, + double* b, lapack_int* ldb, lapack_int *info ); +void LAPACK_cgetrs( char* trans, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* a, lapack_int* lda, + const lapack_int* ipiv, lapack_complex_float* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_zgetrs( char* trans, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* a, lapack_int* lda, + const lapack_int* ipiv, lapack_complex_double* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_sgbtrs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku, + lapack_int* nrhs, const float* ab, lapack_int* ldab, + const lapack_int* ipiv, float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_dgbtrs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku, + lapack_int* nrhs, const double* ab, lapack_int* ldab, + const lapack_int* ipiv, double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_cgbtrs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku, + lapack_int* nrhs, const lapack_complex_float* ab, + lapack_int* ldab, const lapack_int* ipiv, + lapack_complex_float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_zgbtrs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku, + lapack_int* nrhs, const lapack_complex_double* ab, + lapack_int* ldab, const lapack_int* ipiv, + lapack_complex_double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_sgttrs( char* trans, lapack_int* n, lapack_int* nrhs, + const float* dl, const float* d, const float* du, + const float* du2, const lapack_int* ipiv, float* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_dgttrs( char* trans, lapack_int* n, lapack_int* nrhs, + const double* dl, const double* d, const double* du, + const double* du2, const lapack_int* ipiv, double* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_cgttrs( char* trans, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* dl, + const lapack_complex_float* d, + const lapack_complex_float* du, + const lapack_complex_float* du2, const lapack_int* ipiv, + lapack_complex_float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_zgttrs( char* trans, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* dl, + const lapack_complex_double* d, + const lapack_complex_double* du, + const lapack_complex_double* du2, const lapack_int* ipiv, + lapack_complex_double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_spotrs( char* uplo, lapack_int* n, lapack_int* nrhs, const float* a, + lapack_int* lda, float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_dpotrs( char* uplo, lapack_int* n, lapack_int* nrhs, + const double* a, lapack_int* lda, double* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_cpotrs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_zpotrs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_dpftrs( char* transr, char* uplo, lapack_int* n, lapack_int* nrhs, + const double* a, double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_spftrs( char* transr, char* uplo, lapack_int* n, lapack_int* nrhs, + const float* a, float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_zpftrs( char* transr, char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* a, lapack_complex_double* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_cpftrs( char* transr, char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* a, lapack_complex_float* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_spptrs( char* uplo, lapack_int* n, lapack_int* nrhs, + const float* ap, float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_dpptrs( char* uplo, lapack_int* n, lapack_int* nrhs, + const double* ap, double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_cpptrs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* ap, lapack_complex_float* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_zpptrs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* ap, lapack_complex_double* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_spbtrs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs, + const float* ab, lapack_int* ldab, float* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_dpbtrs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs, + const double* ab, lapack_int* ldab, double* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_cpbtrs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs, + const lapack_complex_float* ab, lapack_int* ldab, + lapack_complex_float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_zpbtrs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs, + const lapack_complex_double* ab, lapack_int* ldab, + lapack_complex_double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_spttrs( lapack_int* n, lapack_int* nrhs, const float* d, + const float* e, float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_dpttrs( lapack_int* n, lapack_int* nrhs, const double* d, + const double* e, double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_cpttrs( char* uplo, lapack_int* n, lapack_int* nrhs, const float* d, + const lapack_complex_float* e, lapack_complex_float* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_zpttrs( char* uplo, lapack_int* n, lapack_int* nrhs, + const double* d, const lapack_complex_double* e, + lapack_complex_double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_ssytrs( char* uplo, lapack_int* n, lapack_int* nrhs, const float* a, + lapack_int* lda, const lapack_int* ipiv, float* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_dsytrs( char* uplo, lapack_int* n, lapack_int* nrhs, + const double* a, lapack_int* lda, const lapack_int* ipiv, + double* b, lapack_int* ldb, lapack_int *info ); +void LAPACK_csytrs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* a, lapack_int* lda, + const lapack_int* ipiv, lapack_complex_float* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_zsytrs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* a, lapack_int* lda, + const lapack_int* ipiv, lapack_complex_double* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_chetrs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* a, lapack_int* lda, + const lapack_int* ipiv, lapack_complex_float* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_zhetrs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* a, lapack_int* lda, + const lapack_int* ipiv, lapack_complex_double* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_ssptrs( char* uplo, lapack_int* n, lapack_int* nrhs, + const float* ap, const lapack_int* ipiv, float* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_dsptrs( char* uplo, lapack_int* n, lapack_int* nrhs, + const double* ap, const lapack_int* ipiv, double* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_csptrs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* ap, const lapack_int* ipiv, + lapack_complex_float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_zsptrs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* ap, const lapack_int* ipiv, + lapack_complex_double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_chptrs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* ap, const lapack_int* ipiv, + lapack_complex_float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_zhptrs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* ap, const lapack_int* ipiv, + lapack_complex_double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_strtrs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* nrhs, const float* a, lapack_int* lda, float* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_dtrtrs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* nrhs, const double* a, lapack_int* lda, + double* b, lapack_int* ldb, lapack_int *info ); +void LAPACK_ctrtrs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* nrhs, const lapack_complex_float* a, + lapack_int* lda, lapack_complex_float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_ztrtrs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* nrhs, const lapack_complex_double* a, + lapack_int* lda, lapack_complex_double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_stptrs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* nrhs, const float* ap, float* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_dtptrs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* nrhs, const double* ap, double* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_ctptrs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* nrhs, const lapack_complex_float* ap, + lapack_complex_float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_ztptrs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* nrhs, const lapack_complex_double* ap, + lapack_complex_double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_stbtrs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* kd, lapack_int* nrhs, const float* ab, + lapack_int* ldab, float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_dtbtrs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* kd, lapack_int* nrhs, const double* ab, + lapack_int* ldab, double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_ctbtrs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* kd, lapack_int* nrhs, + const lapack_complex_float* ab, lapack_int* ldab, + lapack_complex_float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_ztbtrs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* kd, lapack_int* nrhs, + const lapack_complex_double* ab, lapack_int* ldab, + lapack_complex_double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_sgecon( char* norm, lapack_int* n, const float* a, lapack_int* lda, + float* anorm, float* rcond, float* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_dgecon( char* norm, lapack_int* n, const double* a, lapack_int* lda, + double* anorm, double* rcond, double* work, + lapack_int* iwork, lapack_int *info ); +void LAPACK_cgecon( char* norm, lapack_int* n, const lapack_complex_float* a, + lapack_int* lda, float* anorm, float* rcond, + lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_zgecon( char* norm, lapack_int* n, const lapack_complex_double* a, + lapack_int* lda, double* anorm, double* rcond, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_sgbcon( char* norm, lapack_int* n, lapack_int* kl, lapack_int* ku, + const float* ab, lapack_int* ldab, const lapack_int* ipiv, + float* anorm, float* rcond, float* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_dgbcon( char* norm, lapack_int* n, lapack_int* kl, lapack_int* ku, + const double* ab, lapack_int* ldab, const lapack_int* ipiv, + double* anorm, double* rcond, double* work, + lapack_int* iwork, lapack_int *info ); +void LAPACK_cgbcon( char* norm, lapack_int* n, lapack_int* kl, lapack_int* ku, + const lapack_complex_float* ab, lapack_int* ldab, + const lapack_int* ipiv, float* anorm, float* rcond, + lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_zgbcon( char* norm, lapack_int* n, lapack_int* kl, lapack_int* ku, + const lapack_complex_double* ab, lapack_int* ldab, + const lapack_int* ipiv, double* anorm, double* rcond, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_sgtcon( char* norm, lapack_int* n, const float* dl, const float* d, + const float* du, const float* du2, const lapack_int* ipiv, + float* anorm, float* rcond, float* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_dgtcon( char* norm, lapack_int* n, const double* dl, + const double* d, const double* du, const double* du2, + const lapack_int* ipiv, double* anorm, double* rcond, + double* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_cgtcon( char* norm, lapack_int* n, const lapack_complex_float* dl, + const lapack_complex_float* d, + const lapack_complex_float* du, + const lapack_complex_float* du2, const lapack_int* ipiv, + float* anorm, float* rcond, lapack_complex_float* work, + lapack_int *info ); +void LAPACK_zgtcon( char* norm, lapack_int* n, const lapack_complex_double* dl, + const lapack_complex_double* d, + const lapack_complex_double* du, + const lapack_complex_double* du2, const lapack_int* ipiv, + double* anorm, double* rcond, lapack_complex_double* work, + lapack_int *info ); +void LAPACK_spocon( char* uplo, lapack_int* n, const float* a, lapack_int* lda, + float* anorm, float* rcond, float* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_dpocon( char* uplo, lapack_int* n, const double* a, lapack_int* lda, + double* anorm, double* rcond, double* work, + lapack_int* iwork, lapack_int *info ); +void LAPACK_cpocon( char* uplo, lapack_int* n, const lapack_complex_float* a, + lapack_int* lda, float* anorm, float* rcond, + lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_zpocon( char* uplo, lapack_int* n, const lapack_complex_double* a, + lapack_int* lda, double* anorm, double* rcond, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_sppcon( char* uplo, lapack_int* n, const float* ap, float* anorm, + float* rcond, float* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_dppcon( char* uplo, lapack_int* n, const double* ap, double* anorm, + double* rcond, double* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_cppcon( char* uplo, lapack_int* n, const lapack_complex_float* ap, + float* anorm, float* rcond, lapack_complex_float* work, + float* rwork, lapack_int *info ); +void LAPACK_zppcon( char* uplo, lapack_int* n, const lapack_complex_double* ap, + double* anorm, double* rcond, lapack_complex_double* work, + double* rwork, lapack_int *info ); +void LAPACK_spbcon( char* uplo, lapack_int* n, lapack_int* kd, const float* ab, + lapack_int* ldab, float* anorm, float* rcond, float* work, + lapack_int* iwork, lapack_int *info ); +void LAPACK_dpbcon( char* uplo, lapack_int* n, lapack_int* kd, const double* ab, + lapack_int* ldab, double* anorm, double* rcond, + double* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_cpbcon( char* uplo, lapack_int* n, lapack_int* kd, + const lapack_complex_float* ab, lapack_int* ldab, + float* anorm, float* rcond, lapack_complex_float* work, + float* rwork, lapack_int *info ); +void LAPACK_zpbcon( char* uplo, lapack_int* n, lapack_int* kd, + const lapack_complex_double* ab, lapack_int* ldab, + double* anorm, double* rcond, lapack_complex_double* work, + double* rwork, lapack_int *info ); +void LAPACK_sptcon( lapack_int* n, const float* d, const float* e, float* anorm, + float* rcond, float* work, lapack_int *info ); +void LAPACK_dptcon( lapack_int* n, const double* d, const double* e, + double* anorm, double* rcond, double* work, + lapack_int *info ); +void LAPACK_cptcon( lapack_int* n, const float* d, + const lapack_complex_float* e, float* anorm, float* rcond, + float* work, lapack_int *info ); +void LAPACK_zptcon( lapack_int* n, const double* d, + const lapack_complex_double* e, double* anorm, + double* rcond, double* work, lapack_int *info ); +void LAPACK_ssycon( char* uplo, lapack_int* n, const float* a, lapack_int* lda, + const lapack_int* ipiv, float* anorm, float* rcond, + float* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_dsycon( char* uplo, lapack_int* n, const double* a, lapack_int* lda, + const lapack_int* ipiv, double* anorm, double* rcond, + double* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_csycon( char* uplo, lapack_int* n, const lapack_complex_float* a, + lapack_int* lda, const lapack_int* ipiv, float* anorm, + float* rcond, lapack_complex_float* work, + lapack_int *info ); +void LAPACK_zsycon( char* uplo, lapack_int* n, const lapack_complex_double* a, + lapack_int* lda, const lapack_int* ipiv, double* anorm, + double* rcond, lapack_complex_double* work, + lapack_int *info ); +void LAPACK_checon( char* uplo, lapack_int* n, const lapack_complex_float* a, + lapack_int* lda, const lapack_int* ipiv, float* anorm, + float* rcond, lapack_complex_float* work, + lapack_int *info ); +void LAPACK_zhecon( char* uplo, lapack_int* n, const lapack_complex_double* a, + lapack_int* lda, const lapack_int* ipiv, double* anorm, + double* rcond, lapack_complex_double* work, + lapack_int *info ); +void LAPACK_sspcon( char* uplo, lapack_int* n, const float* ap, + const lapack_int* ipiv, float* anorm, float* rcond, + float* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_dspcon( char* uplo, lapack_int* n, const double* ap, + const lapack_int* ipiv, double* anorm, double* rcond, + double* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_cspcon( char* uplo, lapack_int* n, const lapack_complex_float* ap, + const lapack_int* ipiv, float* anorm, float* rcond, + lapack_complex_float* work, lapack_int *info ); +void LAPACK_zspcon( char* uplo, lapack_int* n, const lapack_complex_double* ap, + const lapack_int* ipiv, double* anorm, double* rcond, + lapack_complex_double* work, lapack_int *info ); +void LAPACK_chpcon( char* uplo, lapack_int* n, const lapack_complex_float* ap, + const lapack_int* ipiv, float* anorm, float* rcond, + lapack_complex_float* work, lapack_int *info ); +void LAPACK_zhpcon( char* uplo, lapack_int* n, const lapack_complex_double* ap, + const lapack_int* ipiv, double* anorm, double* rcond, + lapack_complex_double* work, lapack_int *info ); +void LAPACK_strcon( char* norm, char* uplo, char* diag, lapack_int* n, + const float* a, lapack_int* lda, float* rcond, float* work, + lapack_int* iwork, lapack_int *info ); +void LAPACK_dtrcon( char* norm, char* uplo, char* diag, lapack_int* n, + const double* a, lapack_int* lda, double* rcond, + double* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_ctrcon( char* norm, char* uplo, char* diag, lapack_int* n, + const lapack_complex_float* a, lapack_int* lda, + float* rcond, lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_ztrcon( char* norm, char* uplo, char* diag, lapack_int* n, + const lapack_complex_double* a, lapack_int* lda, + double* rcond, lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_stpcon( char* norm, char* uplo, char* diag, lapack_int* n, + const float* ap, float* rcond, float* work, + lapack_int* iwork, lapack_int *info ); +void LAPACK_dtpcon( char* norm, char* uplo, char* diag, lapack_int* n, + const double* ap, double* rcond, double* work, + lapack_int* iwork, lapack_int *info ); +void LAPACK_ctpcon( char* norm, char* uplo, char* diag, lapack_int* n, + const lapack_complex_float* ap, float* rcond, + lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_ztpcon( char* norm, char* uplo, char* diag, lapack_int* n, + const lapack_complex_double* ap, double* rcond, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_stbcon( char* norm, char* uplo, char* diag, lapack_int* n, + lapack_int* kd, const float* ab, lapack_int* ldab, + float* rcond, float* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_dtbcon( char* norm, char* uplo, char* diag, lapack_int* n, + lapack_int* kd, const double* ab, lapack_int* ldab, + double* rcond, double* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_ctbcon( char* norm, char* uplo, char* diag, lapack_int* n, + lapack_int* kd, const lapack_complex_float* ab, + lapack_int* ldab, float* rcond, lapack_complex_float* work, + float* rwork, lapack_int *info ); +void LAPACK_ztbcon( char* norm, char* uplo, char* diag, lapack_int* n, + lapack_int* kd, const lapack_complex_double* ab, + lapack_int* ldab, double* rcond, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_sgerfs( char* trans, lapack_int* n, lapack_int* nrhs, + const float* a, lapack_int* lda, const float* af, + lapack_int* ldaf, const lapack_int* ipiv, const float* b, + lapack_int* ldb, float* x, lapack_int* ldx, float* ferr, + float* berr, float* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_dgerfs( char* trans, lapack_int* n, lapack_int* nrhs, + const double* a, lapack_int* lda, const double* af, + lapack_int* ldaf, const lapack_int* ipiv, const double* b, + lapack_int* ldb, double* x, lapack_int* ldx, double* ferr, + double* berr, double* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_cgerfs( char* trans, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* a, lapack_int* lda, + const lapack_complex_float* af, lapack_int* ldaf, + const lapack_int* ipiv, const lapack_complex_float* b, + lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx, + float* ferr, float* berr, lapack_complex_float* work, + float* rwork, lapack_int *info ); +void LAPACK_zgerfs( char* trans, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* a, lapack_int* lda, + const lapack_complex_double* af, lapack_int* ldaf, + const lapack_int* ipiv, const lapack_complex_double* b, + lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx, + double* ferr, double* berr, lapack_complex_double* work, + double* rwork, lapack_int *info ); +void LAPACK_dgerfsx( char* trans, char* equed, lapack_int* n, lapack_int* nrhs, + const double* a, lapack_int* lda, const double* af, + lapack_int* ldaf, const lapack_int* ipiv, const double* r, + const double* c, const double* b, lapack_int* ldb, + double* x, lapack_int* ldx, double* rcond, double* berr, + lapack_int* n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int* nparams, double* params, + double* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_sgerfsx( char* trans, char* equed, lapack_int* n, lapack_int* nrhs, + const float* a, lapack_int* lda, const float* af, + lapack_int* ldaf, const lapack_int* ipiv, const float* r, + const float* c, const float* b, lapack_int* ldb, float* x, + lapack_int* ldx, float* rcond, float* berr, + lapack_int* n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int* nparams, float* params, + float* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_zgerfsx( char* trans, char* equed, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* a, lapack_int* lda, + const lapack_complex_double* af, lapack_int* ldaf, + const lapack_int* ipiv, const double* r, const double* c, + const lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* rcond, + double* berr, lapack_int* n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int* nparams, double* params, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_cgerfsx( char* trans, char* equed, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* a, lapack_int* lda, + const lapack_complex_float* af, lapack_int* ldaf, + const lapack_int* ipiv, const float* r, const float* c, + const lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* rcond, + float* berr, lapack_int* n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int* nparams, float* params, + lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_sgbrfs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku, + lapack_int* nrhs, const float* ab, lapack_int* ldab, + const float* afb, lapack_int* ldafb, const lapack_int* ipiv, + const float* b, lapack_int* ldb, float* x, lapack_int* ldx, + float* ferr, float* berr, float* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_dgbrfs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku, + lapack_int* nrhs, const double* ab, lapack_int* ldab, + const double* afb, lapack_int* ldafb, + const lapack_int* ipiv, const double* b, lapack_int* ldb, + double* x, lapack_int* ldx, double* ferr, double* berr, + double* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_cgbrfs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku, + lapack_int* nrhs, const lapack_complex_float* ab, + lapack_int* ldab, const lapack_complex_float* afb, + lapack_int* ldafb, const lapack_int* ipiv, + const lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* ferr, + float* berr, lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_zgbrfs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku, + lapack_int* nrhs, const lapack_complex_double* ab, + lapack_int* ldab, const lapack_complex_double* afb, + lapack_int* ldafb, const lapack_int* ipiv, + const lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* ferr, + double* berr, lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_dgbrfsx( char* trans, char* equed, lapack_int* n, lapack_int* kl, + lapack_int* ku, lapack_int* nrhs, const double* ab, + lapack_int* ldab, const double* afb, lapack_int* ldafb, + const lapack_int* ipiv, const double* r, const double* c, + const double* b, lapack_int* ldb, double* x, + lapack_int* ldx, double* rcond, double* berr, + lapack_int* n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int* nparams, double* params, + double* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_sgbrfsx( char* trans, char* equed, lapack_int* n, lapack_int* kl, + lapack_int* ku, lapack_int* nrhs, const float* ab, + lapack_int* ldab, const float* afb, lapack_int* ldafb, + const lapack_int* ipiv, const float* r, const float* c, + const float* b, lapack_int* ldb, float* x, lapack_int* ldx, + float* rcond, float* berr, lapack_int* n_err_bnds, + float* err_bnds_norm, float* err_bnds_comp, + lapack_int* nparams, float* params, float* work, + lapack_int* iwork, lapack_int *info ); +void LAPACK_zgbrfsx( char* trans, char* equed, lapack_int* n, lapack_int* kl, + lapack_int* ku, lapack_int* nrhs, + const lapack_complex_double* ab, lapack_int* ldab, + const lapack_complex_double* afb, lapack_int* ldafb, + const lapack_int* ipiv, const double* r, const double* c, + const lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* rcond, + double* berr, lapack_int* n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int* nparams, double* params, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_cgbrfsx( char* trans, char* equed, lapack_int* n, lapack_int* kl, + lapack_int* ku, lapack_int* nrhs, + const lapack_complex_float* ab, lapack_int* ldab, + const lapack_complex_float* afb, lapack_int* ldafb, + const lapack_int* ipiv, const float* r, const float* c, + const lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* rcond, + float* berr, lapack_int* n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int* nparams, float* params, + lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_sgtrfs( char* trans, lapack_int* n, lapack_int* nrhs, + const float* dl, const float* d, const float* du, + const float* dlf, const float* df, const float* duf, + const float* du2, const lapack_int* ipiv, const float* b, + lapack_int* ldb, float* x, lapack_int* ldx, float* ferr, + float* berr, float* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_dgtrfs( char* trans, lapack_int* n, lapack_int* nrhs, + const double* dl, const double* d, const double* du, + const double* dlf, const double* df, const double* duf, + const double* du2, const lapack_int* ipiv, const double* b, + lapack_int* ldb, double* x, lapack_int* ldx, double* ferr, + double* berr, double* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_cgtrfs( char* trans, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* dl, + const lapack_complex_float* d, + const lapack_complex_float* du, + const lapack_complex_float* dlf, + const lapack_complex_float* df, + const lapack_complex_float* duf, + const lapack_complex_float* du2, const lapack_int* ipiv, + const lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* ferr, + float* berr, lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_zgtrfs( char* trans, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* dl, + const lapack_complex_double* d, + const lapack_complex_double* du, + const lapack_complex_double* dlf, + const lapack_complex_double* df, + const lapack_complex_double* duf, + const lapack_complex_double* du2, const lapack_int* ipiv, + const lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* ferr, + double* berr, lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_sporfs( char* uplo, lapack_int* n, lapack_int* nrhs, const float* a, + lapack_int* lda, const float* af, lapack_int* ldaf, + const float* b, lapack_int* ldb, float* x, lapack_int* ldx, + float* ferr, float* berr, float* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_dporfs( char* uplo, lapack_int* n, lapack_int* nrhs, + const double* a, lapack_int* lda, const double* af, + lapack_int* ldaf, const double* b, lapack_int* ldb, + double* x, lapack_int* ldx, double* ferr, double* berr, + double* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_cporfs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* a, lapack_int* lda, + const lapack_complex_float* af, lapack_int* ldaf, + const lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* ferr, + float* berr, lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_zporfs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* a, lapack_int* lda, + const lapack_complex_double* af, lapack_int* ldaf, + const lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* ferr, + double* berr, lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_dporfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs, + const double* a, lapack_int* lda, const double* af, + lapack_int* ldaf, const double* s, const double* b, + lapack_int* ldb, double* x, lapack_int* ldx, double* rcond, + double* berr, lapack_int* n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int* nparams, double* params, double* work, + lapack_int* iwork, lapack_int *info ); +void LAPACK_sporfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs, + const float* a, lapack_int* lda, const float* af, + lapack_int* ldaf, const float* s, const float* b, + lapack_int* ldb, float* x, lapack_int* ldx, float* rcond, + float* berr, lapack_int* n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int* nparams, float* params, + float* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_zporfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* a, lapack_int* lda, + const lapack_complex_double* af, lapack_int* ldaf, + const double* s, const lapack_complex_double* b, + lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx, + double* rcond, double* berr, lapack_int* n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int* nparams, double* params, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_cporfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* a, lapack_int* lda, + const lapack_complex_float* af, lapack_int* ldaf, + const float* s, const lapack_complex_float* b, + lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx, + float* rcond, float* berr, lapack_int* n_err_bnds, + float* err_bnds_norm, float* err_bnds_comp, + lapack_int* nparams, float* params, + lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_spprfs( char* uplo, lapack_int* n, lapack_int* nrhs, + const float* ap, const float* afp, const float* b, + lapack_int* ldb, float* x, lapack_int* ldx, float* ferr, + float* berr, float* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_dpprfs( char* uplo, lapack_int* n, lapack_int* nrhs, + const double* ap, const double* afp, const double* b, + lapack_int* ldb, double* x, lapack_int* ldx, double* ferr, + double* berr, double* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_cpprfs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* ap, + const lapack_complex_float* afp, + const lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* ferr, + float* berr, lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_zpprfs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* ap, + const lapack_complex_double* afp, + const lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* ferr, + double* berr, lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_spbrfs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs, + const float* ab, lapack_int* ldab, const float* afb, + lapack_int* ldafb, const float* b, lapack_int* ldb, + float* x, lapack_int* ldx, float* ferr, float* berr, + float* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_dpbrfs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs, + const double* ab, lapack_int* ldab, const double* afb, + lapack_int* ldafb, const double* b, lapack_int* ldb, + double* x, lapack_int* ldx, double* ferr, double* berr, + double* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_cpbrfs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs, + const lapack_complex_float* ab, lapack_int* ldab, + const lapack_complex_float* afb, lapack_int* ldafb, + const lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* ferr, + float* berr, lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_zpbrfs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs, + const lapack_complex_double* ab, lapack_int* ldab, + const lapack_complex_double* afb, lapack_int* ldafb, + const lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* ferr, + double* berr, lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_sptrfs( lapack_int* n, lapack_int* nrhs, const float* d, + const float* e, const float* df, const float* ef, + const float* b, lapack_int* ldb, float* x, lapack_int* ldx, + float* ferr, float* berr, float* work, lapack_int *info ); +void LAPACK_dptrfs( lapack_int* n, lapack_int* nrhs, const double* d, + const double* e, const double* df, const double* ef, + const double* b, lapack_int* ldb, double* x, + lapack_int* ldx, double* ferr, double* berr, double* work, + lapack_int *info ); +void LAPACK_cptrfs( char* uplo, lapack_int* n, lapack_int* nrhs, const float* d, + const lapack_complex_float* e, const float* df, + const lapack_complex_float* ef, + const lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* ferr, + float* berr, lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_zptrfs( char* uplo, lapack_int* n, lapack_int* nrhs, + const double* d, const lapack_complex_double* e, + const double* df, const lapack_complex_double* ef, + const lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* ferr, + double* berr, lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_ssyrfs( char* uplo, lapack_int* n, lapack_int* nrhs, const float* a, + lapack_int* lda, const float* af, lapack_int* ldaf, + const lapack_int* ipiv, const float* b, lapack_int* ldb, + float* x, lapack_int* ldx, float* ferr, float* berr, + float* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_dsyrfs( char* uplo, lapack_int* n, lapack_int* nrhs, + const double* a, lapack_int* lda, const double* af, + lapack_int* ldaf, const lapack_int* ipiv, const double* b, + lapack_int* ldb, double* x, lapack_int* ldx, double* ferr, + double* berr, double* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_csyrfs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* a, lapack_int* lda, + const lapack_complex_float* af, lapack_int* ldaf, + const lapack_int* ipiv, const lapack_complex_float* b, + lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx, + float* ferr, float* berr, lapack_complex_float* work, + float* rwork, lapack_int *info ); +void LAPACK_zsyrfs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* a, lapack_int* lda, + const lapack_complex_double* af, lapack_int* ldaf, + const lapack_int* ipiv, const lapack_complex_double* b, + lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx, + double* ferr, double* berr, lapack_complex_double* work, + double* rwork, lapack_int *info ); +void LAPACK_dsyrfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs, + const double* a, lapack_int* lda, const double* af, + lapack_int* ldaf, const lapack_int* ipiv, const double* s, + const double* b, lapack_int* ldb, double* x, + lapack_int* ldx, double* rcond, double* berr, + lapack_int* n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int* nparams, double* params, + double* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_ssyrfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs, + const float* a, lapack_int* lda, const float* af, + lapack_int* ldaf, const lapack_int* ipiv, const float* s, + const float* b, lapack_int* ldb, float* x, lapack_int* ldx, + float* rcond, float* berr, lapack_int* n_err_bnds, + float* err_bnds_norm, float* err_bnds_comp, + lapack_int* nparams, float* params, float* work, + lapack_int* iwork, lapack_int *info ); +void LAPACK_zsyrfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* a, lapack_int* lda, + const lapack_complex_double* af, lapack_int* ldaf, + const lapack_int* ipiv, const double* s, + const lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* rcond, + double* berr, lapack_int* n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int* nparams, double* params, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_csyrfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* a, lapack_int* lda, + const lapack_complex_float* af, lapack_int* ldaf, + const lapack_int* ipiv, const float* s, + const lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* rcond, + float* berr, lapack_int* n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int* nparams, float* params, + lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_cherfs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* a, lapack_int* lda, + const lapack_complex_float* af, lapack_int* ldaf, + const lapack_int* ipiv, const lapack_complex_float* b, + lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx, + float* ferr, float* berr, lapack_complex_float* work, + float* rwork, lapack_int *info ); +void LAPACK_zherfs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* a, lapack_int* lda, + const lapack_complex_double* af, lapack_int* ldaf, + const lapack_int* ipiv, const lapack_complex_double* b, + lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx, + double* ferr, double* berr, lapack_complex_double* work, + double* rwork, lapack_int *info ); +void LAPACK_zherfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* a, lapack_int* lda, + const lapack_complex_double* af, lapack_int* ldaf, + const lapack_int* ipiv, const double* s, + const lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* rcond, + double* berr, lapack_int* n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int* nparams, double* params, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_cherfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* a, lapack_int* lda, + const lapack_complex_float* af, lapack_int* ldaf, + const lapack_int* ipiv, const float* s, + const lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* rcond, + float* berr, lapack_int* n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int* nparams, float* params, + lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_ssprfs( char* uplo, lapack_int* n, lapack_int* nrhs, + const float* ap, const float* afp, const lapack_int* ipiv, + const float* b, lapack_int* ldb, float* x, lapack_int* ldx, + float* ferr, float* berr, float* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_dsprfs( char* uplo, lapack_int* n, lapack_int* nrhs, + const double* ap, const double* afp, const lapack_int* ipiv, + const double* b, lapack_int* ldb, double* x, + lapack_int* ldx, double* ferr, double* berr, double* work, + lapack_int* iwork, lapack_int *info ); +void LAPACK_csprfs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* ap, + const lapack_complex_float* afp, const lapack_int* ipiv, + const lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* ferr, + float* berr, lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_zsprfs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* ap, + const lapack_complex_double* afp, const lapack_int* ipiv, + const lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* ferr, + double* berr, lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_chprfs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* ap, + const lapack_complex_float* afp, const lapack_int* ipiv, + const lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* ferr, + float* berr, lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_zhprfs( char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* ap, + const lapack_complex_double* afp, const lapack_int* ipiv, + const lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* ferr, + double* berr, lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_strrfs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* nrhs, const float* a, lapack_int* lda, + const float* b, lapack_int* ldb, const float* x, + lapack_int* ldx, float* ferr, float* berr, float* work, + lapack_int* iwork, lapack_int *info ); +void LAPACK_dtrrfs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* nrhs, const double* a, lapack_int* lda, + const double* b, lapack_int* ldb, const double* x, + lapack_int* ldx, double* ferr, double* berr, double* work, + lapack_int* iwork, lapack_int *info ); +void LAPACK_ctrrfs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* nrhs, const lapack_complex_float* a, + lapack_int* lda, const lapack_complex_float* b, + lapack_int* ldb, const lapack_complex_float* x, + lapack_int* ldx, float* ferr, float* berr, + lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_ztrrfs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* nrhs, const lapack_complex_double* a, + lapack_int* lda, const lapack_complex_double* b, + lapack_int* ldb, const lapack_complex_double* x, + lapack_int* ldx, double* ferr, double* berr, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_stprfs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* nrhs, const float* ap, const float* b, + lapack_int* ldb, const float* x, lapack_int* ldx, + float* ferr, float* berr, float* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_dtprfs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* nrhs, const double* ap, const double* b, + lapack_int* ldb, const double* x, lapack_int* ldx, + double* ferr, double* berr, double* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_ctprfs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* nrhs, const lapack_complex_float* ap, + const lapack_complex_float* b, lapack_int* ldb, + const lapack_complex_float* x, lapack_int* ldx, float* ferr, + float* berr, lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_ztprfs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* nrhs, const lapack_complex_double* ap, + const lapack_complex_double* b, lapack_int* ldb, + const lapack_complex_double* x, lapack_int* ldx, + double* ferr, double* berr, lapack_complex_double* work, + double* rwork, lapack_int *info ); +void LAPACK_stbrfs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* kd, lapack_int* nrhs, const float* ab, + lapack_int* ldab, const float* b, lapack_int* ldb, + const float* x, lapack_int* ldx, float* ferr, float* berr, + float* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_dtbrfs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* kd, lapack_int* nrhs, const double* ab, + lapack_int* ldab, const double* b, lapack_int* ldb, + const double* x, lapack_int* ldx, double* ferr, + double* berr, double* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_ctbrfs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* kd, lapack_int* nrhs, + const lapack_complex_float* ab, lapack_int* ldab, + const lapack_complex_float* b, lapack_int* ldb, + const lapack_complex_float* x, lapack_int* ldx, float* ferr, + float* berr, lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_ztbrfs( char* uplo, char* trans, char* diag, lapack_int* n, + lapack_int* kd, lapack_int* nrhs, + const lapack_complex_double* ab, lapack_int* ldab, + const lapack_complex_double* b, lapack_int* ldb, + const lapack_complex_double* x, lapack_int* ldx, + double* ferr, double* berr, lapack_complex_double* work, + double* rwork, lapack_int *info ); +void LAPACK_sgetri( lapack_int* n, float* a, lapack_int* lda, + const lapack_int* ipiv, float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_dgetri( lapack_int* n, double* a, lapack_int* lda, + const lapack_int* ipiv, double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_cgetri( lapack_int* n, lapack_complex_float* a, lapack_int* lda, + const lapack_int* ipiv, lapack_complex_float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_zgetri( lapack_int* n, lapack_complex_double* a, lapack_int* lda, + const lapack_int* ipiv, lapack_complex_double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_spotri( char* uplo, lapack_int* n, float* a, lapack_int* lda, + lapack_int *info ); +void LAPACK_dpotri( char* uplo, lapack_int* n, double* a, lapack_int* lda, + lapack_int *info ); +void LAPACK_cpotri( char* uplo, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_int *info ); +void LAPACK_zpotri( char* uplo, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_int *info ); +void LAPACK_dpftri( char* transr, char* uplo, lapack_int* n, double* a, + lapack_int *info ); +void LAPACK_spftri( char* transr, char* uplo, lapack_int* n, float* a, + lapack_int *info ); +void LAPACK_zpftri( char* transr, char* uplo, lapack_int* n, + lapack_complex_double* a, lapack_int *info ); +void LAPACK_cpftri( char* transr, char* uplo, lapack_int* n, + lapack_complex_float* a, lapack_int *info ); +void LAPACK_spptri( char* uplo, lapack_int* n, float* ap, lapack_int *info ); +void LAPACK_dpptri( char* uplo, lapack_int* n, double* ap, lapack_int *info ); +void LAPACK_cpptri( char* uplo, lapack_int* n, lapack_complex_float* ap, + lapack_int *info ); +void LAPACK_zpptri( char* uplo, lapack_int* n, lapack_complex_double* ap, + lapack_int *info ); +void LAPACK_ssytri( char* uplo, lapack_int* n, float* a, lapack_int* lda, + const lapack_int* ipiv, float* work, lapack_int *info ); +void LAPACK_dsytri( char* uplo, lapack_int* n, double* a, lapack_int* lda, + const lapack_int* ipiv, double* work, lapack_int *info ); +void LAPACK_csytri( char* uplo, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, const lapack_int* ipiv, + lapack_complex_float* work, lapack_int *info ); +void LAPACK_zsytri( char* uplo, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, const lapack_int* ipiv, + lapack_complex_double* work, lapack_int *info ); +void LAPACK_chetri( char* uplo, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, const lapack_int* ipiv, + lapack_complex_float* work, lapack_int *info ); +void LAPACK_zhetri( char* uplo, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, const lapack_int* ipiv, + lapack_complex_double* work, lapack_int *info ); +void LAPACK_ssptri( char* uplo, lapack_int* n, float* ap, + const lapack_int* ipiv, float* work, lapack_int *info ); +void LAPACK_dsptri( char* uplo, lapack_int* n, double* ap, + const lapack_int* ipiv, double* work, lapack_int *info ); +void LAPACK_csptri( char* uplo, lapack_int* n, lapack_complex_float* ap, + const lapack_int* ipiv, lapack_complex_float* work, + lapack_int *info ); +void LAPACK_zsptri( char* uplo, lapack_int* n, lapack_complex_double* ap, + const lapack_int* ipiv, lapack_complex_double* work, + lapack_int *info ); +void LAPACK_chptri( char* uplo, lapack_int* n, lapack_complex_float* ap, + const lapack_int* ipiv, lapack_complex_float* work, + lapack_int *info ); +void LAPACK_zhptri( char* uplo, lapack_int* n, lapack_complex_double* ap, + const lapack_int* ipiv, lapack_complex_double* work, + lapack_int *info ); +void LAPACK_strtri( char* uplo, char* diag, lapack_int* n, float* a, + lapack_int* lda, lapack_int *info ); +void LAPACK_dtrtri( char* uplo, char* diag, lapack_int* n, double* a, + lapack_int* lda, lapack_int *info ); +void LAPACK_ctrtri( char* uplo, char* diag, lapack_int* n, + lapack_complex_float* a, lapack_int* lda, + lapack_int *info ); +void LAPACK_ztrtri( char* uplo, char* diag, lapack_int* n, + lapack_complex_double* a, lapack_int* lda, + lapack_int *info ); +void LAPACK_dtftri( char* transr, char* uplo, char* diag, lapack_int* n, + double* a, lapack_int *info ); +void LAPACK_stftri( char* transr, char* uplo, char* diag, lapack_int* n, + float* a, lapack_int *info ); +void LAPACK_ztftri( char* transr, char* uplo, char* diag, lapack_int* n, + lapack_complex_double* a, lapack_int *info ); +void LAPACK_ctftri( char* transr, char* uplo, char* diag, lapack_int* n, + lapack_complex_float* a, lapack_int *info ); +void LAPACK_stptri( char* uplo, char* diag, lapack_int* n, float* ap, + lapack_int *info ); +void LAPACK_dtptri( char* uplo, char* diag, lapack_int* n, double* ap, + lapack_int *info ); +void LAPACK_ctptri( char* uplo, char* diag, lapack_int* n, + lapack_complex_float* ap, lapack_int *info ); +void LAPACK_ztptri( char* uplo, char* diag, lapack_int* n, + lapack_complex_double* ap, lapack_int *info ); +void LAPACK_sgeequ( lapack_int* m, lapack_int* n, const float* a, + lapack_int* lda, float* r, float* c, float* rowcnd, + float* colcnd, float* amax, lapack_int *info ); +void LAPACK_dgeequ( lapack_int* m, lapack_int* n, const double* a, + lapack_int* lda, double* r, double* c, double* rowcnd, + double* colcnd, double* amax, lapack_int *info ); +void LAPACK_cgeequ( lapack_int* m, lapack_int* n, const lapack_complex_float* a, + lapack_int* lda, float* r, float* c, float* rowcnd, + float* colcnd, float* amax, lapack_int *info ); +void LAPACK_zgeequ( lapack_int* m, lapack_int* n, + const lapack_complex_double* a, lapack_int* lda, double* r, + double* c, double* rowcnd, double* colcnd, double* amax, + lapack_int *info ); +void LAPACK_dgeequb( lapack_int* m, lapack_int* n, const double* a, + lapack_int* lda, double* r, double* c, double* rowcnd, + double* colcnd, double* amax, lapack_int *info ); +void LAPACK_sgeequb( lapack_int* m, lapack_int* n, const float* a, + lapack_int* lda, float* r, float* c, float* rowcnd, + float* colcnd, float* amax, lapack_int *info ); +void LAPACK_zgeequb( lapack_int* m, lapack_int* n, + const lapack_complex_double* a, lapack_int* lda, double* r, + double* c, double* rowcnd, double* colcnd, double* amax, + lapack_int *info ); +void LAPACK_cgeequb( lapack_int* m, lapack_int* n, + const lapack_complex_float* a, lapack_int* lda, float* r, + float* c, float* rowcnd, float* colcnd, float* amax, + lapack_int *info ); +void LAPACK_sgbequ( lapack_int* m, lapack_int* n, lapack_int* kl, + lapack_int* ku, const float* ab, lapack_int* ldab, float* r, + float* c, float* rowcnd, float* colcnd, float* amax, + lapack_int *info ); +void LAPACK_dgbequ( lapack_int* m, lapack_int* n, lapack_int* kl, + lapack_int* ku, const double* ab, lapack_int* ldab, + double* r, double* c, double* rowcnd, double* colcnd, + double* amax, lapack_int *info ); +void LAPACK_cgbequ( lapack_int* m, lapack_int* n, lapack_int* kl, + lapack_int* ku, const lapack_complex_float* ab, + lapack_int* ldab, float* r, float* c, float* rowcnd, + float* colcnd, float* amax, lapack_int *info ); +void LAPACK_zgbequ( lapack_int* m, lapack_int* n, lapack_int* kl, + lapack_int* ku, const lapack_complex_double* ab, + lapack_int* ldab, double* r, double* c, double* rowcnd, + double* colcnd, double* amax, lapack_int *info ); +void LAPACK_dgbequb( lapack_int* m, lapack_int* n, lapack_int* kl, + lapack_int* ku, const double* ab, lapack_int* ldab, + double* r, double* c, double* rowcnd, double* colcnd, + double* amax, lapack_int *info ); +void LAPACK_sgbequb( lapack_int* m, lapack_int* n, lapack_int* kl, + lapack_int* ku, const float* ab, lapack_int* ldab, + float* r, float* c, float* rowcnd, float* colcnd, + float* amax, lapack_int *info ); +void LAPACK_zgbequb( lapack_int* m, lapack_int* n, lapack_int* kl, + lapack_int* ku, const lapack_complex_double* ab, + lapack_int* ldab, double* r, double* c, double* rowcnd, + double* colcnd, double* amax, lapack_int *info ); +void LAPACK_cgbequb( lapack_int* m, lapack_int* n, lapack_int* kl, + lapack_int* ku, const lapack_complex_float* ab, + lapack_int* ldab, float* r, float* c, float* rowcnd, + float* colcnd, float* amax, lapack_int *info ); +void LAPACK_spoequ( lapack_int* n, const float* a, lapack_int* lda, float* s, + float* scond, float* amax, lapack_int *info ); +void LAPACK_dpoequ( lapack_int* n, const double* a, lapack_int* lda, double* s, + double* scond, double* amax, lapack_int *info ); +void LAPACK_cpoequ( lapack_int* n, const lapack_complex_float* a, + lapack_int* lda, float* s, float* scond, float* amax, + lapack_int *info ); +void LAPACK_zpoequ( lapack_int* n, const lapack_complex_double* a, + lapack_int* lda, double* s, double* scond, double* amax, + lapack_int *info ); +void LAPACK_dpoequb( lapack_int* n, const double* a, lapack_int* lda, double* s, + double* scond, double* amax, lapack_int *info ); +void LAPACK_spoequb( lapack_int* n, const float* a, lapack_int* lda, float* s, + float* scond, float* amax, lapack_int *info ); +void LAPACK_zpoequb( lapack_int* n, const lapack_complex_double* a, + lapack_int* lda, double* s, double* scond, double* amax, + lapack_int *info ); +void LAPACK_cpoequb( lapack_int* n, const lapack_complex_float* a, + lapack_int* lda, float* s, float* scond, float* amax, + lapack_int *info ); +void LAPACK_sppequ( char* uplo, lapack_int* n, const float* ap, float* s, + float* scond, float* amax, lapack_int *info ); +void LAPACK_dppequ( char* uplo, lapack_int* n, const double* ap, double* s, + double* scond, double* amax, lapack_int *info ); +void LAPACK_cppequ( char* uplo, lapack_int* n, const lapack_complex_float* ap, + float* s, float* scond, float* amax, lapack_int *info ); +void LAPACK_zppequ( char* uplo, lapack_int* n, const lapack_complex_double* ap, + double* s, double* scond, double* amax, lapack_int *info ); +void LAPACK_spbequ( char* uplo, lapack_int* n, lapack_int* kd, const float* ab, + lapack_int* ldab, float* s, float* scond, float* amax, + lapack_int *info ); +void LAPACK_dpbequ( char* uplo, lapack_int* n, lapack_int* kd, const double* ab, + lapack_int* ldab, double* s, double* scond, double* amax, + lapack_int *info ); +void LAPACK_cpbequ( char* uplo, lapack_int* n, lapack_int* kd, + const lapack_complex_float* ab, lapack_int* ldab, float* s, + float* scond, float* amax, lapack_int *info ); +void LAPACK_zpbequ( char* uplo, lapack_int* n, lapack_int* kd, + const lapack_complex_double* ab, lapack_int* ldab, + double* s, double* scond, double* amax, lapack_int *info ); +void LAPACK_dsyequb( char* uplo, lapack_int* n, const double* a, + lapack_int* lda, double* s, double* scond, double* amax, + double* work, lapack_int *info ); +void LAPACK_ssyequb( char* uplo, lapack_int* n, const float* a, lapack_int* lda, + float* s, float* scond, float* amax, float* work, + lapack_int *info ); +void LAPACK_zsyequb( char* uplo, lapack_int* n, const lapack_complex_double* a, + lapack_int* lda, double* s, double* scond, double* amax, + lapack_complex_double* work, lapack_int *info ); +void LAPACK_csyequb( char* uplo, lapack_int* n, const lapack_complex_float* a, + lapack_int* lda, float* s, float* scond, float* amax, + lapack_complex_float* work, lapack_int *info ); +void LAPACK_zheequb( char* uplo, lapack_int* n, const lapack_complex_double* a, + lapack_int* lda, double* s, double* scond, double* amax, + lapack_complex_double* work, lapack_int *info ); +void LAPACK_cheequb( char* uplo, lapack_int* n, const lapack_complex_float* a, + lapack_int* lda, float* s, float* scond, float* amax, + lapack_complex_float* work, lapack_int *info ); +void LAPACK_sgesv( lapack_int* n, lapack_int* nrhs, float* a, lapack_int* lda, + lapack_int* ipiv, float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_dgesv( lapack_int* n, lapack_int* nrhs, double* a, lapack_int* lda, + lapack_int* ipiv, double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_cgesv( lapack_int* n, lapack_int* nrhs, lapack_complex_float* a, + lapack_int* lda, lapack_int* ipiv, lapack_complex_float* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_zgesv( lapack_int* n, lapack_int* nrhs, lapack_complex_double* a, + lapack_int* lda, lapack_int* ipiv, lapack_complex_double* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_dsgesv( lapack_int* n, lapack_int* nrhs, double* a, lapack_int* lda, + lapack_int* ipiv, double* b, lapack_int* ldb, double* x, + lapack_int* ldx, double* work, float* swork, + lapack_int* iter, lapack_int *info ); +void LAPACK_zcgesv( lapack_int* n, lapack_int* nrhs, lapack_complex_double* a, + lapack_int* lda, lapack_int* ipiv, lapack_complex_double* b, + lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx, + lapack_complex_double* work, lapack_complex_float* swork, + double* rwork, lapack_int* iter, lapack_int *info ); +void LAPACK_sgesvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs, + float* a, lapack_int* lda, float* af, lapack_int* ldaf, + lapack_int* ipiv, char* equed, float* r, float* c, float* b, + lapack_int* ldb, float* x, lapack_int* ldx, float* rcond, + float* ferr, float* berr, float* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_dgesvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs, + double* a, lapack_int* lda, double* af, lapack_int* ldaf, + lapack_int* ipiv, char* equed, double* r, double* c, + double* b, lapack_int* ldb, double* x, lapack_int* ldx, + double* rcond, double* ferr, double* berr, double* work, + lapack_int* iwork, lapack_int *info ); +void LAPACK_cgesvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* af, lapack_int* ldaf, + lapack_int* ipiv, char* equed, float* r, float* c, + lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* rcond, + float* ferr, float* berr, lapack_complex_float* work, + float* rwork, lapack_int *info ); +void LAPACK_zgesvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* af, lapack_int* ldaf, + lapack_int* ipiv, char* equed, double* r, double* c, + lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* rcond, + double* ferr, double* berr, lapack_complex_double* work, + double* rwork, lapack_int *info ); +void LAPACK_dgesvxx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs, + double* a, lapack_int* lda, double* af, lapack_int* ldaf, + lapack_int* ipiv, char* equed, double* r, double* c, + double* b, lapack_int* ldb, double* x, lapack_int* ldx, + double* rcond, double* rpvgrw, double* berr, + lapack_int* n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int* nparams, double* params, + double* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_sgesvxx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs, + float* a, lapack_int* lda, float* af, lapack_int* ldaf, + lapack_int* ipiv, char* equed, float* r, float* c, + float* b, lapack_int* ldb, float* x, lapack_int* ldx, + float* rcond, float* rpvgrw, float* berr, + lapack_int* n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int* nparams, float* params, + float* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_zgesvxx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* af, lapack_int* ldaf, + lapack_int* ipiv, char* equed, double* r, double* c, + lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* rcond, + double* rpvgrw, double* berr, lapack_int* n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int* nparams, double* params, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_cgesvxx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* af, lapack_int* ldaf, + lapack_int* ipiv, char* equed, float* r, float* c, + lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* rcond, + float* rpvgrw, float* berr, lapack_int* n_err_bnds, + float* err_bnds_norm, float* err_bnds_comp, + lapack_int* nparams, float* params, + lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_sgbsv( lapack_int* n, lapack_int* kl, lapack_int* ku, + lapack_int* nrhs, float* ab, lapack_int* ldab, + lapack_int* ipiv, float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_dgbsv( lapack_int* n, lapack_int* kl, lapack_int* ku, + lapack_int* nrhs, double* ab, lapack_int* ldab, + lapack_int* ipiv, double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_cgbsv( lapack_int* n, lapack_int* kl, lapack_int* ku, + lapack_int* nrhs, lapack_complex_float* ab, lapack_int* ldab, + lapack_int* ipiv, lapack_complex_float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_zgbsv( lapack_int* n, lapack_int* kl, lapack_int* ku, + lapack_int* nrhs, lapack_complex_double* ab, + lapack_int* ldab, lapack_int* ipiv, lapack_complex_double* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_sgbsvx( char* fact, char* trans, lapack_int* n, lapack_int* kl, + lapack_int* ku, lapack_int* nrhs, float* ab, + lapack_int* ldab, float* afb, lapack_int* ldafb, + lapack_int* ipiv, char* equed, float* r, float* c, float* b, + lapack_int* ldb, float* x, lapack_int* ldx, float* rcond, + float* ferr, float* berr, float* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_dgbsvx( char* fact, char* trans, lapack_int* n, lapack_int* kl, + lapack_int* ku, lapack_int* nrhs, double* ab, + lapack_int* ldab, double* afb, lapack_int* ldafb, + lapack_int* ipiv, char* equed, double* r, double* c, + double* b, lapack_int* ldb, double* x, lapack_int* ldx, + double* rcond, double* ferr, double* berr, double* work, + lapack_int* iwork, lapack_int *info ); +void LAPACK_cgbsvx( char* fact, char* trans, lapack_int* n, lapack_int* kl, + lapack_int* ku, lapack_int* nrhs, lapack_complex_float* ab, + lapack_int* ldab, lapack_complex_float* afb, + lapack_int* ldafb, lapack_int* ipiv, char* equed, float* r, + float* c, lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* rcond, + float* ferr, float* berr, lapack_complex_float* work, + float* rwork, lapack_int *info ); +void LAPACK_zgbsvx( char* fact, char* trans, lapack_int* n, lapack_int* kl, + lapack_int* ku, lapack_int* nrhs, lapack_complex_double* ab, + lapack_int* ldab, lapack_complex_double* afb, + lapack_int* ldafb, lapack_int* ipiv, char* equed, double* r, + double* c, lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* rcond, + double* ferr, double* berr, lapack_complex_double* work, + double* rwork, lapack_int *info ); +void LAPACK_dgbsvxx( char* fact, char* trans, lapack_int* n, lapack_int* kl, + lapack_int* ku, lapack_int* nrhs, double* ab, + lapack_int* ldab, double* afb, lapack_int* ldafb, + lapack_int* ipiv, char* equed, double* r, double* c, + double* b, lapack_int* ldb, double* x, lapack_int* ldx, + double* rcond, double* rpvgrw, double* berr, + lapack_int* n_err_bnds, double* err_bnds_norm, + double* err_bnds_comp, lapack_int* nparams, double* params, + double* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_sgbsvxx( char* fact, char* trans, lapack_int* n, lapack_int* kl, + lapack_int* ku, lapack_int* nrhs, float* ab, + lapack_int* ldab, float* afb, lapack_int* ldafb, + lapack_int* ipiv, char* equed, float* r, float* c, + float* b, lapack_int* ldb, float* x, lapack_int* ldx, + float* rcond, float* rpvgrw, float* berr, + lapack_int* n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int* nparams, float* params, + float* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_zgbsvxx( char* fact, char* trans, lapack_int* n, lapack_int* kl, + lapack_int* ku, lapack_int* nrhs, + lapack_complex_double* ab, lapack_int* ldab, + lapack_complex_double* afb, lapack_int* ldafb, + lapack_int* ipiv, char* equed, double* r, double* c, + lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* rcond, + double* rpvgrw, double* berr, lapack_int* n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int* nparams, double* params, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_cgbsvxx( char* fact, char* trans, lapack_int* n, lapack_int* kl, + lapack_int* ku, lapack_int* nrhs, lapack_complex_float* ab, + lapack_int* ldab, lapack_complex_float* afb, + lapack_int* ldafb, lapack_int* ipiv, char* equed, float* r, + float* c, lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* rcond, + float* rpvgrw, float* berr, lapack_int* n_err_bnds, + float* err_bnds_norm, float* err_bnds_comp, + lapack_int* nparams, float* params, + lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_sgtsv( lapack_int* n, lapack_int* nrhs, float* dl, float* d, + float* du, float* b, lapack_int* ldb, lapack_int *info ); +void LAPACK_dgtsv( lapack_int* n, lapack_int* nrhs, double* dl, double* d, + double* du, double* b, lapack_int* ldb, lapack_int *info ); +void LAPACK_cgtsv( lapack_int* n, lapack_int* nrhs, lapack_complex_float* dl, + lapack_complex_float* d, lapack_complex_float* du, + lapack_complex_float* b, lapack_int* ldb, lapack_int *info ); +void LAPACK_zgtsv( lapack_int* n, lapack_int* nrhs, lapack_complex_double* dl, + lapack_complex_double* d, lapack_complex_double* du, + lapack_complex_double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_sgtsvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs, + const float* dl, const float* d, const float* du, + float* dlf, float* df, float* duf, float* du2, + lapack_int* ipiv, const float* b, lapack_int* ldb, float* x, + lapack_int* ldx, float* rcond, float* ferr, float* berr, + float* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_dgtsvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs, + const double* dl, const double* d, const double* du, + double* dlf, double* df, double* duf, double* du2, + lapack_int* ipiv, const double* b, lapack_int* ldb, + double* x, lapack_int* ldx, double* rcond, double* ferr, + double* berr, double* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_cgtsvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* dl, + const lapack_complex_float* d, + const lapack_complex_float* du, lapack_complex_float* dlf, + lapack_complex_float* df, lapack_complex_float* duf, + lapack_complex_float* du2, lapack_int* ipiv, + const lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* rcond, + float* ferr, float* berr, lapack_complex_float* work, + float* rwork, lapack_int *info ); +void LAPACK_zgtsvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* dl, + const lapack_complex_double* d, + const lapack_complex_double* du, lapack_complex_double* dlf, + lapack_complex_double* df, lapack_complex_double* duf, + lapack_complex_double* du2, lapack_int* ipiv, + const lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* rcond, + double* ferr, double* berr, lapack_complex_double* work, + double* rwork, lapack_int *info ); +void LAPACK_sposv( char* uplo, lapack_int* n, lapack_int* nrhs, float* a, + lapack_int* lda, float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_dposv( char* uplo, lapack_int* n, lapack_int* nrhs, double* a, + lapack_int* lda, double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_cposv( char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, lapack_int *info ); +void LAPACK_zposv( char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_dsposv( char* uplo, lapack_int* n, lapack_int* nrhs, double* a, + lapack_int* lda, double* b, lapack_int* ldb, double* x, + lapack_int* ldx, double* work, float* swork, + lapack_int* iter, lapack_int *info ); +void LAPACK_zcposv( char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, + lapack_complex_double* work, lapack_complex_float* swork, + double* rwork, lapack_int* iter, lapack_int *info ); +void LAPACK_sposvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + float* a, lapack_int* lda, float* af, lapack_int* ldaf, + char* equed, float* s, float* b, lapack_int* ldb, float* x, + lapack_int* ldx, float* rcond, float* ferr, float* berr, + float* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_dposvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + double* a, lapack_int* lda, double* af, lapack_int* ldaf, + char* equed, double* s, double* b, lapack_int* ldb, + double* x, lapack_int* ldx, double* rcond, double* ferr, + double* berr, double* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_cposvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* af, lapack_int* ldaf, char* equed, + float* s, lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* rcond, + float* ferr, float* berr, lapack_complex_float* work, + float* rwork, lapack_int *info ); +void LAPACK_zposvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* af, lapack_int* ldaf, char* equed, + double* s, lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* rcond, + double* ferr, double* berr, lapack_complex_double* work, + double* rwork, lapack_int *info ); +void LAPACK_dposvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + double* a, lapack_int* lda, double* af, lapack_int* ldaf, + char* equed, double* s, double* b, lapack_int* ldb, + double* x, lapack_int* ldx, double* rcond, double* rpvgrw, + double* berr, lapack_int* n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int* nparams, double* params, double* work, + lapack_int* iwork, lapack_int *info ); +void LAPACK_sposvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + float* a, lapack_int* lda, float* af, lapack_int* ldaf, + char* equed, float* s, float* b, lapack_int* ldb, float* x, + lapack_int* ldx, float* rcond, float* rpvgrw, float* berr, + lapack_int* n_err_bnds, float* err_bnds_norm, + float* err_bnds_comp, lapack_int* nparams, float* params, + float* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_zposvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* af, lapack_int* ldaf, char* equed, + double* s, lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* rcond, + double* rpvgrw, double* berr, lapack_int* n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int* nparams, double* params, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_cposvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* af, lapack_int* ldaf, char* equed, + float* s, lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* rcond, + float* rpvgrw, float* berr, lapack_int* n_err_bnds, + float* err_bnds_norm, float* err_bnds_comp, + lapack_int* nparams, float* params, + lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_sppsv( char* uplo, lapack_int* n, lapack_int* nrhs, float* ap, + float* b, lapack_int* ldb, lapack_int *info ); +void LAPACK_dppsv( char* uplo, lapack_int* n, lapack_int* nrhs, double* ap, + double* b, lapack_int* ldb, lapack_int *info ); +void LAPACK_cppsv( char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_float* ap, lapack_complex_float* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_zppsv( char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_double* ap, lapack_complex_double* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_sppsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + float* ap, float* afp, char* equed, float* s, float* b, + lapack_int* ldb, float* x, lapack_int* ldx, float* rcond, + float* ferr, float* berr, float* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_dppsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + double* ap, double* afp, char* equed, double* s, double* b, + lapack_int* ldb, double* x, lapack_int* ldx, double* rcond, + double* ferr, double* berr, double* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_cppsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_float* ap, lapack_complex_float* afp, + char* equed, float* s, lapack_complex_float* b, + lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx, + float* rcond, float* ferr, float* berr, + lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_zppsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_double* ap, lapack_complex_double* afp, + char* equed, double* s, lapack_complex_double* b, + lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx, + double* rcond, double* ferr, double* berr, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_spbsv( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs, + float* ab, lapack_int* ldab, float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_dpbsv( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs, + double* ab, lapack_int* ldab, double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_cpbsv( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs, + lapack_complex_float* ab, lapack_int* ldab, + lapack_complex_float* b, lapack_int* ldb, lapack_int *info ); +void LAPACK_zpbsv( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs, + lapack_complex_double* ab, lapack_int* ldab, + lapack_complex_double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_spbsvx( char* fact, char* uplo, lapack_int* n, lapack_int* kd, + lapack_int* nrhs, float* ab, lapack_int* ldab, float* afb, + lapack_int* ldafb, char* equed, float* s, float* b, + lapack_int* ldb, float* x, lapack_int* ldx, float* rcond, + float* ferr, float* berr, float* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_dpbsvx( char* fact, char* uplo, lapack_int* n, lapack_int* kd, + lapack_int* nrhs, double* ab, lapack_int* ldab, double* afb, + lapack_int* ldafb, char* equed, double* s, double* b, + lapack_int* ldb, double* x, lapack_int* ldx, double* rcond, + double* ferr, double* berr, double* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_cpbsvx( char* fact, char* uplo, lapack_int* n, lapack_int* kd, + lapack_int* nrhs, lapack_complex_float* ab, + lapack_int* ldab, lapack_complex_float* afb, + lapack_int* ldafb, char* equed, float* s, + lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* rcond, + float* ferr, float* berr, lapack_complex_float* work, + float* rwork, lapack_int *info ); +void LAPACK_zpbsvx( char* fact, char* uplo, lapack_int* n, lapack_int* kd, + lapack_int* nrhs, lapack_complex_double* ab, + lapack_int* ldab, lapack_complex_double* afb, + lapack_int* ldafb, char* equed, double* s, + lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* rcond, + double* ferr, double* berr, lapack_complex_double* work, + double* rwork, lapack_int *info ); +void LAPACK_sptsv( lapack_int* n, lapack_int* nrhs, float* d, float* e, + float* b, lapack_int* ldb, lapack_int *info ); +void LAPACK_dptsv( lapack_int* n, lapack_int* nrhs, double* d, double* e, + double* b, lapack_int* ldb, lapack_int *info ); +void LAPACK_cptsv( lapack_int* n, lapack_int* nrhs, float* d, + lapack_complex_float* e, lapack_complex_float* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_zptsv( lapack_int* n, lapack_int* nrhs, double* d, + lapack_complex_double* e, lapack_complex_double* b, + lapack_int* ldb, lapack_int *info ); +void LAPACK_sptsvx( char* fact, lapack_int* n, lapack_int* nrhs, const float* d, + const float* e, float* df, float* ef, const float* b, + lapack_int* ldb, float* x, lapack_int* ldx, float* rcond, + float* ferr, float* berr, float* work, lapack_int *info ); +void LAPACK_dptsvx( char* fact, lapack_int* n, lapack_int* nrhs, + const double* d, const double* e, double* df, double* ef, + const double* b, lapack_int* ldb, double* x, + lapack_int* ldx, double* rcond, double* ferr, double* berr, + double* work, lapack_int *info ); +void LAPACK_cptsvx( char* fact, lapack_int* n, lapack_int* nrhs, const float* d, + const lapack_complex_float* e, float* df, + lapack_complex_float* ef, const lapack_complex_float* b, + lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx, + float* rcond, float* ferr, float* berr, + lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_zptsvx( char* fact, lapack_int* n, lapack_int* nrhs, + const double* d, const lapack_complex_double* e, double* df, + lapack_complex_double* ef, const lapack_complex_double* b, + lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx, + double* rcond, double* ferr, double* berr, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_ssysv( char* uplo, lapack_int* n, lapack_int* nrhs, float* a, + lapack_int* lda, lapack_int* ipiv, float* b, lapack_int* ldb, + float* work, lapack_int* lwork, lapack_int *info ); +void LAPACK_dsysv( char* uplo, lapack_int* n, lapack_int* nrhs, double* a, + lapack_int* lda, lapack_int* ipiv, double* b, + lapack_int* ldb, double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_csysv( char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_float* a, lapack_int* lda, lapack_int* ipiv, + lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_zsysv( char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_double* a, lapack_int* lda, lapack_int* ipiv, + lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_ssysvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + const float* a, lapack_int* lda, float* af, + lapack_int* ldaf, lapack_int* ipiv, const float* b, + lapack_int* ldb, float* x, lapack_int* ldx, float* rcond, + float* ferr, float* berr, float* work, lapack_int* lwork, + lapack_int* iwork, lapack_int *info ); +void LAPACK_dsysvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + const double* a, lapack_int* lda, double* af, + lapack_int* ldaf, lapack_int* ipiv, const double* b, + lapack_int* ldb, double* x, lapack_int* ldx, double* rcond, + double* ferr, double* berr, double* work, lapack_int* lwork, + lapack_int* iwork, lapack_int *info ); +void LAPACK_csysvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* af, lapack_int* ldaf, + lapack_int* ipiv, const lapack_complex_float* b, + lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx, + float* rcond, float* ferr, float* berr, + lapack_complex_float* work, lapack_int* lwork, float* rwork, + lapack_int *info ); +void LAPACK_zsysvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* af, lapack_int* ldaf, + lapack_int* ipiv, const lapack_complex_double* b, + lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx, + double* rcond, double* ferr, double* berr, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_int *info ); +void LAPACK_dsysvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + double* a, lapack_int* lda, double* af, lapack_int* ldaf, + lapack_int* ipiv, char* equed, double* s, double* b, + lapack_int* ldb, double* x, lapack_int* ldx, double* rcond, + double* rpvgrw, double* berr, lapack_int* n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int* nparams, double* params, double* work, + lapack_int* iwork, lapack_int *info ); +void LAPACK_ssysvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + float* a, lapack_int* lda, float* af, lapack_int* ldaf, + lapack_int* ipiv, char* equed, float* s, float* b, + lapack_int* ldb, float* x, lapack_int* ldx, float* rcond, + float* rpvgrw, float* berr, lapack_int* n_err_bnds, + float* err_bnds_norm, float* err_bnds_comp, + lapack_int* nparams, float* params, float* work, + lapack_int* iwork, lapack_int *info ); +void LAPACK_zsysvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* af, lapack_int* ldaf, + lapack_int* ipiv, char* equed, double* s, + lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* rcond, + double* rpvgrw, double* berr, lapack_int* n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int* nparams, double* params, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_csysvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* af, lapack_int* ldaf, + lapack_int* ipiv, char* equed, float* s, + lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* rcond, + float* rpvgrw, float* berr, lapack_int* n_err_bnds, + float* err_bnds_norm, float* err_bnds_comp, + lapack_int* nparams, float* params, + lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_chesv( char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_float* a, lapack_int* lda, lapack_int* ipiv, + lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_zhesv( char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_double* a, lapack_int* lda, lapack_int* ipiv, + lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_chesvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* af, lapack_int* ldaf, + lapack_int* ipiv, const lapack_complex_float* b, + lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx, + float* rcond, float* ferr, float* berr, + lapack_complex_float* work, lapack_int* lwork, float* rwork, + lapack_int *info ); +void LAPACK_zhesvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* af, lapack_int* ldaf, + lapack_int* ipiv, const lapack_complex_double* b, + lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx, + double* rcond, double* ferr, double* berr, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_int *info ); +void LAPACK_zhesvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* af, lapack_int* ldaf, + lapack_int* ipiv, char* equed, double* s, + lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* x, lapack_int* ldx, double* rcond, + double* rpvgrw, double* berr, lapack_int* n_err_bnds, + double* err_bnds_norm, double* err_bnds_comp, + lapack_int* nparams, double* params, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_chesvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* af, lapack_int* ldaf, + lapack_int* ipiv, char* equed, float* s, + lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* x, lapack_int* ldx, float* rcond, + float* rpvgrw, float* berr, lapack_int* n_err_bnds, + float* err_bnds_norm, float* err_bnds_comp, + lapack_int* nparams, float* params, + lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_sspsv( char* uplo, lapack_int* n, lapack_int* nrhs, float* ap, + lapack_int* ipiv, float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_dspsv( char* uplo, lapack_int* n, lapack_int* nrhs, double* ap, + lapack_int* ipiv, double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_cspsv( char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_float* ap, lapack_int* ipiv, + lapack_complex_float* b, lapack_int* ldb, lapack_int *info ); +void LAPACK_zspsv( char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_double* ap, lapack_int* ipiv, + lapack_complex_double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_sspsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + const float* ap, float* afp, lapack_int* ipiv, + const float* b, lapack_int* ldb, float* x, lapack_int* ldx, + float* rcond, float* ferr, float* berr, float* work, + lapack_int* iwork, lapack_int *info ); +void LAPACK_dspsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + const double* ap, double* afp, lapack_int* ipiv, + const double* b, lapack_int* ldb, double* x, + lapack_int* ldx, double* rcond, double* ferr, double* berr, + double* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_cspsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* ap, lapack_complex_float* afp, + lapack_int* ipiv, const lapack_complex_float* b, + lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx, + float* rcond, float* ferr, float* berr, + lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_zspsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* ap, lapack_complex_double* afp, + lapack_int* ipiv, const lapack_complex_double* b, + lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx, + double* rcond, double* ferr, double* berr, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_chpsv( char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_float* ap, lapack_int* ipiv, + lapack_complex_float* b, lapack_int* ldb, lapack_int *info ); +void LAPACK_zhpsv( char* uplo, lapack_int* n, lapack_int* nrhs, + lapack_complex_double* ap, lapack_int* ipiv, + lapack_complex_double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_chpsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_float* ap, lapack_complex_float* afp, + lapack_int* ipiv, const lapack_complex_float* b, + lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx, + float* rcond, float* ferr, float* berr, + lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_zhpsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs, + const lapack_complex_double* ap, lapack_complex_double* afp, + lapack_int* ipiv, const lapack_complex_double* b, + lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx, + double* rcond, double* ferr, double* berr, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_sgeqrf( lapack_int* m, lapack_int* n, float* a, lapack_int* lda, + float* tau, float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_dgeqrf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda, + double* tau, double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_cgeqrf( lapack_int* m, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_complex_float* tau, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_zgeqrf( lapack_int* m, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_complex_double* tau, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_sgeqpf( lapack_int* m, lapack_int* n, float* a, lapack_int* lda, + lapack_int* jpvt, float* tau, float* work, + lapack_int *info ); +void LAPACK_dgeqpf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda, + lapack_int* jpvt, double* tau, double* work, + lapack_int *info ); +void LAPACK_cgeqpf( lapack_int* m, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_int* jpvt, + lapack_complex_float* tau, lapack_complex_float* work, + float* rwork, lapack_int *info ); +void LAPACK_zgeqpf( lapack_int* m, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_int* jpvt, + lapack_complex_double* tau, lapack_complex_double* work, + double* rwork, lapack_int *info ); +void LAPACK_sgeqp3( lapack_int* m, lapack_int* n, float* a, lapack_int* lda, + lapack_int* jpvt, float* tau, float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_dgeqp3( lapack_int* m, lapack_int* n, double* a, lapack_int* lda, + lapack_int* jpvt, double* tau, double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_cgeqp3( lapack_int* m, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_int* jpvt, + lapack_complex_float* tau, lapack_complex_float* work, + lapack_int* lwork, float* rwork, lapack_int *info ); +void LAPACK_zgeqp3( lapack_int* m, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_int* jpvt, + lapack_complex_double* tau, lapack_complex_double* work, + lapack_int* lwork, double* rwork, lapack_int *info ); +void LAPACK_sorgqr( lapack_int* m, lapack_int* n, lapack_int* k, float* a, + lapack_int* lda, const float* tau, float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_dorgqr( lapack_int* m, lapack_int* n, lapack_int* k, double* a, + lapack_int* lda, const double* tau, double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_sormqr( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, const float* a, lapack_int* lda, + const float* tau, float* c, lapack_int* ldc, float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_dormqr( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, const double* a, lapack_int* lda, + const double* tau, double* c, lapack_int* ldc, double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_cungqr( lapack_int* m, lapack_int* n, lapack_int* k, + lapack_complex_float* a, lapack_int* lda, + const lapack_complex_float* tau, lapack_complex_float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_zungqr( lapack_int* m, lapack_int* n, lapack_int* k, + lapack_complex_double* a, lapack_int* lda, + const lapack_complex_double* tau, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_cunmqr( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, const lapack_complex_float* a, + lapack_int* lda, const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int* ldc, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_zunmqr( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, const lapack_complex_double* a, + lapack_int* lda, const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int* ldc, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_sgelqf( lapack_int* m, lapack_int* n, float* a, lapack_int* lda, + float* tau, float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_dgelqf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda, + double* tau, double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_cgelqf( lapack_int* m, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_complex_float* tau, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_zgelqf( lapack_int* m, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_complex_double* tau, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_sorglq( lapack_int* m, lapack_int* n, lapack_int* k, float* a, + lapack_int* lda, const float* tau, float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_dorglq( lapack_int* m, lapack_int* n, lapack_int* k, double* a, + lapack_int* lda, const double* tau, double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_sormlq( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, const float* a, lapack_int* lda, + const float* tau, float* c, lapack_int* ldc, float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_dormlq( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, const double* a, lapack_int* lda, + const double* tau, double* c, lapack_int* ldc, double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_cunglq( lapack_int* m, lapack_int* n, lapack_int* k, + lapack_complex_float* a, lapack_int* lda, + const lapack_complex_float* tau, lapack_complex_float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_zunglq( lapack_int* m, lapack_int* n, lapack_int* k, + lapack_complex_double* a, lapack_int* lda, + const lapack_complex_double* tau, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_cunmlq( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, const lapack_complex_float* a, + lapack_int* lda, const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int* ldc, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_zunmlq( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, const lapack_complex_double* a, + lapack_int* lda, const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int* ldc, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_sgeqlf( lapack_int* m, lapack_int* n, float* a, lapack_int* lda, + float* tau, float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_dgeqlf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda, + double* tau, double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_cgeqlf( lapack_int* m, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_complex_float* tau, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_zgeqlf( lapack_int* m, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_complex_double* tau, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_sorgql( lapack_int* m, lapack_int* n, lapack_int* k, float* a, + lapack_int* lda, const float* tau, float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_dorgql( lapack_int* m, lapack_int* n, lapack_int* k, double* a, + lapack_int* lda, const double* tau, double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_cungql( lapack_int* m, lapack_int* n, lapack_int* k, + lapack_complex_float* a, lapack_int* lda, + const lapack_complex_float* tau, lapack_complex_float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_zungql( lapack_int* m, lapack_int* n, lapack_int* k, + lapack_complex_double* a, lapack_int* lda, + const lapack_complex_double* tau, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_sormql( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, const float* a, lapack_int* lda, + const float* tau, float* c, lapack_int* ldc, float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_dormql( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, const double* a, lapack_int* lda, + const double* tau, double* c, lapack_int* ldc, double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_cunmql( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, const lapack_complex_float* a, + lapack_int* lda, const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int* ldc, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_zunmql( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, const lapack_complex_double* a, + lapack_int* lda, const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int* ldc, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_sgerqf( lapack_int* m, lapack_int* n, float* a, lapack_int* lda, + float* tau, float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_dgerqf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda, + double* tau, double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_cgerqf( lapack_int* m, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_complex_float* tau, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_zgerqf( lapack_int* m, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_complex_double* tau, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_sorgrq( lapack_int* m, lapack_int* n, lapack_int* k, float* a, + lapack_int* lda, const float* tau, float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_dorgrq( lapack_int* m, lapack_int* n, lapack_int* k, double* a, + lapack_int* lda, const double* tau, double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_cungrq( lapack_int* m, lapack_int* n, lapack_int* k, + lapack_complex_float* a, lapack_int* lda, + const lapack_complex_float* tau, lapack_complex_float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_zungrq( lapack_int* m, lapack_int* n, lapack_int* k, + lapack_complex_double* a, lapack_int* lda, + const lapack_complex_double* tau, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_sormrq( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, const float* a, lapack_int* lda, + const float* tau, float* c, lapack_int* ldc, float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_dormrq( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, const double* a, lapack_int* lda, + const double* tau, double* c, lapack_int* ldc, double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_cunmrq( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, const lapack_complex_float* a, + lapack_int* lda, const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int* ldc, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_zunmrq( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, const lapack_complex_double* a, + lapack_int* lda, const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int* ldc, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_stzrzf( lapack_int* m, lapack_int* n, float* a, lapack_int* lda, + float* tau, float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_dtzrzf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda, + double* tau, double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_ctzrzf( lapack_int* m, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_complex_float* tau, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_ztzrzf( lapack_int* m, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_complex_double* tau, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_sormrz( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, lapack_int* l, const float* a, + lapack_int* lda, const float* tau, float* c, + lapack_int* ldc, float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_dormrz( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, lapack_int* l, const double* a, + lapack_int* lda, const double* tau, double* c, + lapack_int* ldc, double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_cunmrz( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, lapack_int* l, const lapack_complex_float* a, + lapack_int* lda, const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int* ldc, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_zunmrz( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, lapack_int* l, + const lapack_complex_double* a, lapack_int* lda, + const lapack_complex_double* tau, lapack_complex_double* c, + lapack_int* ldc, lapack_complex_double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_sggqrf( lapack_int* n, lapack_int* m, lapack_int* p, float* a, + lapack_int* lda, float* taua, float* b, lapack_int* ldb, + float* taub, float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_dggqrf( lapack_int* n, lapack_int* m, lapack_int* p, double* a, + lapack_int* lda, double* taua, double* b, lapack_int* ldb, + double* taub, double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_cggqrf( lapack_int* n, lapack_int* m, lapack_int* p, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* taua, lapack_complex_float* b, + lapack_int* ldb, lapack_complex_float* taub, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_zggqrf( lapack_int* n, lapack_int* m, lapack_int* p, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* taua, lapack_complex_double* b, + lapack_int* ldb, lapack_complex_double* taub, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_sggrqf( lapack_int* m, lapack_int* p, lapack_int* n, float* a, + lapack_int* lda, float* taua, float* b, lapack_int* ldb, + float* taub, float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_dggrqf( lapack_int* m, lapack_int* p, lapack_int* n, double* a, + lapack_int* lda, double* taua, double* b, lapack_int* ldb, + double* taub, double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_cggrqf( lapack_int* m, lapack_int* p, lapack_int* n, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* taua, lapack_complex_float* b, + lapack_int* ldb, lapack_complex_float* taub, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_zggrqf( lapack_int* m, lapack_int* p, lapack_int* n, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* taua, lapack_complex_double* b, + lapack_int* ldb, lapack_complex_double* taub, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_sgebrd( lapack_int* m, lapack_int* n, float* a, lapack_int* lda, + float* d, float* e, float* tauq, float* taup, float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_dgebrd( lapack_int* m, lapack_int* n, double* a, lapack_int* lda, + double* d, double* e, double* tauq, double* taup, + double* work, lapack_int* lwork, lapack_int *info ); +void LAPACK_cgebrd( lapack_int* m, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, float* d, float* e, + lapack_complex_float* tauq, lapack_complex_float* taup, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_zgebrd( lapack_int* m, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, double* d, double* e, + lapack_complex_double* tauq, lapack_complex_double* taup, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_sgbbrd( char* vect, lapack_int* m, lapack_int* n, lapack_int* ncc, + lapack_int* kl, lapack_int* ku, float* ab, lapack_int* ldab, + float* d, float* e, float* q, lapack_int* ldq, float* pt, + lapack_int* ldpt, float* c, lapack_int* ldc, float* work, + lapack_int *info ); +void LAPACK_dgbbrd( char* vect, lapack_int* m, lapack_int* n, lapack_int* ncc, + lapack_int* kl, lapack_int* ku, double* ab, + lapack_int* ldab, double* d, double* e, double* q, + lapack_int* ldq, double* pt, lapack_int* ldpt, double* c, + lapack_int* ldc, double* work, lapack_int *info ); +void LAPACK_cgbbrd( char* vect, lapack_int* m, lapack_int* n, lapack_int* ncc, + lapack_int* kl, lapack_int* ku, lapack_complex_float* ab, + lapack_int* ldab, float* d, float* e, + lapack_complex_float* q, lapack_int* ldq, + lapack_complex_float* pt, lapack_int* ldpt, + lapack_complex_float* c, lapack_int* ldc, + lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_zgbbrd( char* vect, lapack_int* m, lapack_int* n, lapack_int* ncc, + lapack_int* kl, lapack_int* ku, lapack_complex_double* ab, + lapack_int* ldab, double* d, double* e, + lapack_complex_double* q, lapack_int* ldq, + lapack_complex_double* pt, lapack_int* ldpt, + lapack_complex_double* c, lapack_int* ldc, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_sorgbr( char* vect, lapack_int* m, lapack_int* n, lapack_int* k, + float* a, lapack_int* lda, const float* tau, float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_dorgbr( char* vect, lapack_int* m, lapack_int* n, lapack_int* k, + double* a, lapack_int* lda, const double* tau, double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_sormbr( char* vect, char* side, char* trans, lapack_int* m, + lapack_int* n, lapack_int* k, const float* a, + lapack_int* lda, const float* tau, float* c, + lapack_int* ldc, float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_dormbr( char* vect, char* side, char* trans, lapack_int* m, + lapack_int* n, lapack_int* k, const double* a, + lapack_int* lda, const double* tau, double* c, + lapack_int* ldc, double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_cungbr( char* vect, lapack_int* m, lapack_int* n, lapack_int* k, + lapack_complex_float* a, lapack_int* lda, + const lapack_complex_float* tau, lapack_complex_float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_zungbr( char* vect, lapack_int* m, lapack_int* n, lapack_int* k, + lapack_complex_double* a, lapack_int* lda, + const lapack_complex_double* tau, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_cunmbr( char* vect, char* side, char* trans, lapack_int* m, + lapack_int* n, lapack_int* k, const lapack_complex_float* a, + lapack_int* lda, const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int* ldc, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_zunmbr( char* vect, char* side, char* trans, lapack_int* m, + lapack_int* n, lapack_int* k, + const lapack_complex_double* a, lapack_int* lda, + const lapack_complex_double* tau, lapack_complex_double* c, + lapack_int* ldc, lapack_complex_double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_sbdsqr( char* uplo, lapack_int* n, lapack_int* ncvt, + lapack_int* nru, lapack_int* ncc, float* d, float* e, + float* vt, lapack_int* ldvt, float* u, lapack_int* ldu, + float* c, lapack_int* ldc, float* work, lapack_int *info ); +void LAPACK_dbdsqr( char* uplo, lapack_int* n, lapack_int* ncvt, + lapack_int* nru, lapack_int* ncc, double* d, double* e, + double* vt, lapack_int* ldvt, double* u, lapack_int* ldu, + double* c, lapack_int* ldc, double* work, + lapack_int *info ); +void LAPACK_cbdsqr( char* uplo, lapack_int* n, lapack_int* ncvt, + lapack_int* nru, lapack_int* ncc, float* d, float* e, + lapack_complex_float* vt, lapack_int* ldvt, + lapack_complex_float* u, lapack_int* ldu, + lapack_complex_float* c, lapack_int* ldc, float* work, + lapack_int *info ); +void LAPACK_zbdsqr( char* uplo, lapack_int* n, lapack_int* ncvt, + lapack_int* nru, lapack_int* ncc, double* d, double* e, + lapack_complex_double* vt, lapack_int* ldvt, + lapack_complex_double* u, lapack_int* ldu, + lapack_complex_double* c, lapack_int* ldc, double* work, + lapack_int *info ); +void LAPACK_sbdsdc( char* uplo, char* compq, lapack_int* n, float* d, float* e, + float* u, lapack_int* ldu, float* vt, lapack_int* ldvt, + float* q, lapack_int* iq, float* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_dbdsdc( char* uplo, char* compq, lapack_int* n, double* d, + double* e, double* u, lapack_int* ldu, double* vt, + lapack_int* ldvt, double* q, lapack_int* iq, double* work, + lapack_int* iwork, lapack_int *info ); +void LAPACK_ssytrd( char* uplo, lapack_int* n, float* a, lapack_int* lda, + float* d, float* e, float* tau, float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_dsytrd( char* uplo, lapack_int* n, double* a, lapack_int* lda, + double* d, double* e, double* tau, double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_sorgtr( char* uplo, lapack_int* n, float* a, lapack_int* lda, + const float* tau, float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_dorgtr( char* uplo, lapack_int* n, double* a, lapack_int* lda, + const double* tau, double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_sormtr( char* side, char* uplo, char* trans, lapack_int* m, + lapack_int* n, const float* a, lapack_int* lda, + const float* tau, float* c, lapack_int* ldc, float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_dormtr( char* side, char* uplo, char* trans, lapack_int* m, + lapack_int* n, const double* a, lapack_int* lda, + const double* tau, double* c, lapack_int* ldc, double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_chetrd( char* uplo, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, float* d, float* e, + lapack_complex_float* tau, lapack_complex_float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_zhetrd( char* uplo, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, double* d, double* e, + lapack_complex_double* tau, lapack_complex_double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_cungtr( char* uplo, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, const lapack_complex_float* tau, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_zungtr( char* uplo, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, const lapack_complex_double* tau, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_cunmtr( char* side, char* uplo, char* trans, lapack_int* m, + lapack_int* n, const lapack_complex_float* a, + lapack_int* lda, const lapack_complex_float* tau, + lapack_complex_float* c, lapack_int* ldc, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_zunmtr( char* side, char* uplo, char* trans, lapack_int* m, + lapack_int* n, const lapack_complex_double* a, + lapack_int* lda, const lapack_complex_double* tau, + lapack_complex_double* c, lapack_int* ldc, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_ssptrd( char* uplo, lapack_int* n, float* ap, float* d, float* e, + float* tau, lapack_int *info ); +void LAPACK_dsptrd( char* uplo, lapack_int* n, double* ap, double* d, double* e, + double* tau, lapack_int *info ); +void LAPACK_sopgtr( char* uplo, lapack_int* n, const float* ap, + const float* tau, float* q, lapack_int* ldq, float* work, + lapack_int *info ); +void LAPACK_dopgtr( char* uplo, lapack_int* n, const double* ap, + const double* tau, double* q, lapack_int* ldq, double* work, + lapack_int *info ); +void LAPACK_sopmtr( char* side, char* uplo, char* trans, lapack_int* m, + lapack_int* n, const float* ap, const float* tau, float* c, + lapack_int* ldc, float* work, lapack_int *info ); +void LAPACK_dopmtr( char* side, char* uplo, char* trans, lapack_int* m, + lapack_int* n, const double* ap, const double* tau, + double* c, lapack_int* ldc, double* work, + lapack_int *info ); +void LAPACK_chptrd( char* uplo, lapack_int* n, lapack_complex_float* ap, + float* d, float* e, lapack_complex_float* tau, + lapack_int *info ); +void LAPACK_zhptrd( char* uplo, lapack_int* n, lapack_complex_double* ap, + double* d, double* e, lapack_complex_double* tau, + lapack_int *info ); +void LAPACK_cupgtr( char* uplo, lapack_int* n, const lapack_complex_float* ap, + const lapack_complex_float* tau, lapack_complex_float* q, + lapack_int* ldq, lapack_complex_float* work, + lapack_int *info ); +void LAPACK_zupgtr( char* uplo, lapack_int* n, const lapack_complex_double* ap, + const lapack_complex_double* tau, lapack_complex_double* q, + lapack_int* ldq, lapack_complex_double* work, + lapack_int *info ); +void LAPACK_cupmtr( char* side, char* uplo, char* trans, lapack_int* m, + lapack_int* n, const lapack_complex_float* ap, + const lapack_complex_float* tau, lapack_complex_float* c, + lapack_int* ldc, lapack_complex_float* work, + lapack_int *info ); +void LAPACK_zupmtr( char* side, char* uplo, char* trans, lapack_int* m, + lapack_int* n, const lapack_complex_double* ap, + const lapack_complex_double* tau, lapack_complex_double* c, + lapack_int* ldc, lapack_complex_double* work, + lapack_int *info ); +void LAPACK_ssbtrd( char* vect, char* uplo, lapack_int* n, lapack_int* kd, + float* ab, lapack_int* ldab, float* d, float* e, float* q, + lapack_int* ldq, float* work, lapack_int *info ); +void LAPACK_dsbtrd( char* vect, char* uplo, lapack_int* n, lapack_int* kd, + double* ab, lapack_int* ldab, double* d, double* e, + double* q, lapack_int* ldq, double* work, + lapack_int *info ); +void LAPACK_chbtrd( char* vect, char* uplo, lapack_int* n, lapack_int* kd, + lapack_complex_float* ab, lapack_int* ldab, float* d, + float* e, lapack_complex_float* q, lapack_int* ldq, + lapack_complex_float* work, lapack_int *info ); +void LAPACK_zhbtrd( char* vect, char* uplo, lapack_int* n, lapack_int* kd, + lapack_complex_double* ab, lapack_int* ldab, double* d, + double* e, lapack_complex_double* q, lapack_int* ldq, + lapack_complex_double* work, lapack_int *info ); +void LAPACK_ssterf( lapack_int* n, float* d, float* e, lapack_int *info ); +void LAPACK_dsterf( lapack_int* n, double* d, double* e, lapack_int *info ); +void LAPACK_ssteqr( char* compz, lapack_int* n, float* d, float* e, float* z, + lapack_int* ldz, float* work, lapack_int *info ); +void LAPACK_dsteqr( char* compz, lapack_int* n, double* d, double* e, double* z, + lapack_int* ldz, double* work, lapack_int *info ); +void LAPACK_csteqr( char* compz, lapack_int* n, float* d, float* e, + lapack_complex_float* z, lapack_int* ldz, float* work, + lapack_int *info ); +void LAPACK_zsteqr( char* compz, lapack_int* n, double* d, double* e, + lapack_complex_double* z, lapack_int* ldz, double* work, + lapack_int *info ); +void LAPACK_sstemr( char* jobz, char* range, lapack_int* n, float* d, float* e, + float* vl, float* vu, lapack_int* il, lapack_int* iu, + lapack_int* m, float* w, float* z, lapack_int* ldz, + lapack_int* nzc, lapack_int* isuppz, lapack_logical* tryrac, + float* work, lapack_int* lwork, lapack_int* iwork, + lapack_int* liwork, lapack_int *info ); +void LAPACK_dstemr( char* jobz, char* range, lapack_int* n, double* d, + double* e, double* vl, double* vu, lapack_int* il, + lapack_int* iu, lapack_int* m, double* w, double* z, + lapack_int* ldz, lapack_int* nzc, lapack_int* isuppz, + lapack_logical* tryrac, double* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_cstemr( char* jobz, char* range, lapack_int* n, float* d, float* e, + float* vl, float* vu, lapack_int* il, lapack_int* iu, + lapack_int* m, float* w, lapack_complex_float* z, + lapack_int* ldz, lapack_int* nzc, lapack_int* isuppz, + lapack_logical* tryrac, float* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_zstemr( char* jobz, char* range, lapack_int* n, double* d, + double* e, double* vl, double* vu, lapack_int* il, + lapack_int* iu, lapack_int* m, double* w, + lapack_complex_double* z, lapack_int* ldz, lapack_int* nzc, + lapack_int* isuppz, lapack_logical* tryrac, double* work, + lapack_int* lwork, lapack_int* iwork, lapack_int* liwork, + lapack_int *info ); +void LAPACK_sstedc( char* compz, lapack_int* n, float* d, float* e, float* z, + lapack_int* ldz, float* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_dstedc( char* compz, lapack_int* n, double* d, double* e, double* z, + lapack_int* ldz, double* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_cstedc( char* compz, lapack_int* n, float* d, float* e, + lapack_complex_float* z, lapack_int* ldz, + lapack_complex_float* work, lapack_int* lwork, float* rwork, + lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork, + lapack_int *info ); +void LAPACK_zstedc( char* compz, lapack_int* n, double* d, double* e, + lapack_complex_double* z, lapack_int* ldz, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_int* lrwork, lapack_int* iwork, + lapack_int* liwork, lapack_int *info ); +void LAPACK_sstegr( char* jobz, char* range, lapack_int* n, float* d, float* e, + float* vl, float* vu, lapack_int* il, lapack_int* iu, + float* abstol, lapack_int* m, float* w, float* z, + lapack_int* ldz, lapack_int* isuppz, float* work, + lapack_int* lwork, lapack_int* iwork, lapack_int* liwork, + lapack_int *info ); +void LAPACK_dstegr( char* jobz, char* range, lapack_int* n, double* d, + double* e, double* vl, double* vu, lapack_int* il, + lapack_int* iu, double* abstol, lapack_int* m, double* w, + double* z, lapack_int* ldz, lapack_int* isuppz, + double* work, lapack_int* lwork, lapack_int* iwork, + lapack_int* liwork, lapack_int *info ); +void LAPACK_cstegr( char* jobz, char* range, lapack_int* n, float* d, float* e, + float* vl, float* vu, lapack_int* il, lapack_int* iu, + float* abstol, lapack_int* m, float* w, + lapack_complex_float* z, lapack_int* ldz, + lapack_int* isuppz, float* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_zstegr( char* jobz, char* range, lapack_int* n, double* d, + double* e, double* vl, double* vu, lapack_int* il, + lapack_int* iu, double* abstol, lapack_int* m, double* w, + lapack_complex_double* z, lapack_int* ldz, + lapack_int* isuppz, double* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_spteqr( char* compz, lapack_int* n, float* d, float* e, float* z, + lapack_int* ldz, float* work, lapack_int *info ); +void LAPACK_dpteqr( char* compz, lapack_int* n, double* d, double* e, double* z, + lapack_int* ldz, double* work, lapack_int *info ); +void LAPACK_cpteqr( char* compz, lapack_int* n, float* d, float* e, + lapack_complex_float* z, lapack_int* ldz, float* work, + lapack_int *info ); +void LAPACK_zpteqr( char* compz, lapack_int* n, double* d, double* e, + lapack_complex_double* z, lapack_int* ldz, double* work, + lapack_int *info ); +void LAPACK_sstebz( char* range, char* order, lapack_int* n, float* vl, + float* vu, lapack_int* il, lapack_int* iu, float* abstol, + const float* d, const float* e, lapack_int* m, + lapack_int* nsplit, float* w, lapack_int* iblock, + lapack_int* isplit, float* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_dstebz( char* range, char* order, lapack_int* n, double* vl, + double* vu, lapack_int* il, lapack_int* iu, double* abstol, + const double* d, const double* e, lapack_int* m, + lapack_int* nsplit, double* w, lapack_int* iblock, + lapack_int* isplit, double* work, lapack_int* iwork, + lapack_int *info ); +void LAPACK_sstein( lapack_int* n, const float* d, const float* e, + lapack_int* m, const float* w, const lapack_int* iblock, + const lapack_int* isplit, float* z, lapack_int* ldz, + float* work, lapack_int* iwork, lapack_int* ifailv, + lapack_int *info ); +void LAPACK_dstein( lapack_int* n, const double* d, const double* e, + lapack_int* m, const double* w, const lapack_int* iblock, + const lapack_int* isplit, double* z, lapack_int* ldz, + double* work, lapack_int* iwork, lapack_int* ifailv, + lapack_int *info ); +void LAPACK_cstein( lapack_int* n, const float* d, const float* e, + lapack_int* m, const float* w, const lapack_int* iblock, + const lapack_int* isplit, lapack_complex_float* z, + lapack_int* ldz, float* work, lapack_int* iwork, + lapack_int* ifailv, lapack_int *info ); +void LAPACK_zstein( lapack_int* n, const double* d, const double* e, + lapack_int* m, const double* w, const lapack_int* iblock, + const lapack_int* isplit, lapack_complex_double* z, + lapack_int* ldz, double* work, lapack_int* iwork, + lapack_int* ifailv, lapack_int *info ); +void LAPACK_sdisna( char* job, lapack_int* m, lapack_int* n, const float* d, + float* sep, lapack_int *info ); +void LAPACK_ddisna( char* job, lapack_int* m, lapack_int* n, const double* d, + double* sep, lapack_int *info ); +void LAPACK_ssygst( lapack_int* itype, char* uplo, lapack_int* n, float* a, + lapack_int* lda, const float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_dsygst( lapack_int* itype, char* uplo, lapack_int* n, double* a, + lapack_int* lda, const double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_chegst( lapack_int* itype, char* uplo, lapack_int* n, + lapack_complex_float* a, lapack_int* lda, + const lapack_complex_float* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_zhegst( lapack_int* itype, char* uplo, lapack_int* n, + lapack_complex_double* a, lapack_int* lda, + const lapack_complex_double* b, lapack_int* ldb, + lapack_int *info ); +void LAPACK_sspgst( lapack_int* itype, char* uplo, lapack_int* n, float* ap, + const float* bp, lapack_int *info ); +void LAPACK_dspgst( lapack_int* itype, char* uplo, lapack_int* n, double* ap, + const double* bp, lapack_int *info ); +void LAPACK_chpgst( lapack_int* itype, char* uplo, lapack_int* n, + lapack_complex_float* ap, const lapack_complex_float* bp, + lapack_int *info ); +void LAPACK_zhpgst( lapack_int* itype, char* uplo, lapack_int* n, + lapack_complex_double* ap, const lapack_complex_double* bp, + lapack_int *info ); +void LAPACK_ssbgst( char* vect, char* uplo, lapack_int* n, lapack_int* ka, + lapack_int* kb, float* ab, lapack_int* ldab, + const float* bb, lapack_int* ldbb, float* x, + lapack_int* ldx, float* work, lapack_int *info ); +void LAPACK_dsbgst( char* vect, char* uplo, lapack_int* n, lapack_int* ka, + lapack_int* kb, double* ab, lapack_int* ldab, + const double* bb, lapack_int* ldbb, double* x, + lapack_int* ldx, double* work, lapack_int *info ); +void LAPACK_chbgst( char* vect, char* uplo, lapack_int* n, lapack_int* ka, + lapack_int* kb, lapack_complex_float* ab, lapack_int* ldab, + const lapack_complex_float* bb, lapack_int* ldbb, + lapack_complex_float* x, lapack_int* ldx, + lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_zhbgst( char* vect, char* uplo, lapack_int* n, lapack_int* ka, + lapack_int* kb, lapack_complex_double* ab, lapack_int* ldab, + const lapack_complex_double* bb, lapack_int* ldbb, + lapack_complex_double* x, lapack_int* ldx, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_spbstf( char* uplo, lapack_int* n, lapack_int* kb, float* bb, + lapack_int* ldbb, lapack_int *info ); +void LAPACK_dpbstf( char* uplo, lapack_int* n, lapack_int* kb, double* bb, + lapack_int* ldbb, lapack_int *info ); +void LAPACK_cpbstf( char* uplo, lapack_int* n, lapack_int* kb, + lapack_complex_float* bb, lapack_int* ldbb, + lapack_int *info ); +void LAPACK_zpbstf( char* uplo, lapack_int* n, lapack_int* kb, + lapack_complex_double* bb, lapack_int* ldbb, + lapack_int *info ); +void LAPACK_sgehrd( lapack_int* n, lapack_int* ilo, lapack_int* ihi, float* a, + lapack_int* lda, float* tau, float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_dgehrd( lapack_int* n, lapack_int* ilo, lapack_int* ihi, double* a, + lapack_int* lda, double* tau, double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_cgehrd( lapack_int* n, lapack_int* ilo, lapack_int* ihi, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* tau, lapack_complex_float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_zgehrd( lapack_int* n, lapack_int* ilo, lapack_int* ihi, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* tau, lapack_complex_double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_sorghr( lapack_int* n, lapack_int* ilo, lapack_int* ihi, float* a, + lapack_int* lda, const float* tau, float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_dorghr( lapack_int* n, lapack_int* ilo, lapack_int* ihi, double* a, + lapack_int* lda, const double* tau, double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_sormhr( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* ilo, lapack_int* ihi, const float* a, + lapack_int* lda, const float* tau, float* c, + lapack_int* ldc, float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_dormhr( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* ilo, lapack_int* ihi, const double* a, + lapack_int* lda, const double* tau, double* c, + lapack_int* ldc, double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_cunghr( lapack_int* n, lapack_int* ilo, lapack_int* ihi, + lapack_complex_float* a, lapack_int* lda, + const lapack_complex_float* tau, lapack_complex_float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_zunghr( lapack_int* n, lapack_int* ilo, lapack_int* ihi, + lapack_complex_double* a, lapack_int* lda, + const lapack_complex_double* tau, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_cunmhr( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* ilo, lapack_int* ihi, + const lapack_complex_float* a, lapack_int* lda, + const lapack_complex_float* tau, lapack_complex_float* c, + lapack_int* ldc, lapack_complex_float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_zunmhr( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* ilo, lapack_int* ihi, + const lapack_complex_double* a, lapack_int* lda, + const lapack_complex_double* tau, lapack_complex_double* c, + lapack_int* ldc, lapack_complex_double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_sgebal( char* job, lapack_int* n, float* a, lapack_int* lda, + lapack_int* ilo, lapack_int* ihi, float* scale, + lapack_int *info ); +void LAPACK_dgebal( char* job, lapack_int* n, double* a, lapack_int* lda, + lapack_int* ilo, lapack_int* ihi, double* scale, + lapack_int *info ); +void LAPACK_cgebal( char* job, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_int* ilo, lapack_int* ihi, + float* scale, lapack_int *info ); +void LAPACK_zgebal( char* job, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_int* ilo, lapack_int* ihi, + double* scale, lapack_int *info ); +void LAPACK_sgebak( char* job, char* side, lapack_int* n, lapack_int* ilo, + lapack_int* ihi, const float* scale, lapack_int* m, + float* v, lapack_int* ldv, lapack_int *info ); +void LAPACK_dgebak( char* job, char* side, lapack_int* n, lapack_int* ilo, + lapack_int* ihi, const double* scale, lapack_int* m, + double* v, lapack_int* ldv, lapack_int *info ); +void LAPACK_cgebak( char* job, char* side, lapack_int* n, lapack_int* ilo, + lapack_int* ihi, const float* scale, lapack_int* m, + lapack_complex_float* v, lapack_int* ldv, + lapack_int *info ); +void LAPACK_zgebak( char* job, char* side, lapack_int* n, lapack_int* ilo, + lapack_int* ihi, const double* scale, lapack_int* m, + lapack_complex_double* v, lapack_int* ldv, + lapack_int *info ); +void LAPACK_shseqr( char* job, char* compz, lapack_int* n, lapack_int* ilo, + lapack_int* ihi, float* h, lapack_int* ldh, float* wr, + float* wi, float* z, lapack_int* ldz, float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_dhseqr( char* job, char* compz, lapack_int* n, lapack_int* ilo, + lapack_int* ihi, double* h, lapack_int* ldh, double* wr, + double* wi, double* z, lapack_int* ldz, double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_chseqr( char* job, char* compz, lapack_int* n, lapack_int* ilo, + lapack_int* ihi, lapack_complex_float* h, lapack_int* ldh, + lapack_complex_float* w, lapack_complex_float* z, + lapack_int* ldz, lapack_complex_float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_zhseqr( char* job, char* compz, lapack_int* n, lapack_int* ilo, + lapack_int* ihi, lapack_complex_double* h, lapack_int* ldh, + lapack_complex_double* w, lapack_complex_double* z, + lapack_int* ldz, lapack_complex_double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_shsein( char* job, char* eigsrc, char* initv, + lapack_logical* select, lapack_int* n, const float* h, + lapack_int* ldh, float* wr, const float* wi, float* vl, + lapack_int* ldvl, float* vr, lapack_int* ldvr, + lapack_int* mm, lapack_int* m, float* work, + lapack_int* ifaill, lapack_int* ifailr, lapack_int *info ); +void LAPACK_dhsein( char* job, char* eigsrc, char* initv, + lapack_logical* select, lapack_int* n, const double* h, + lapack_int* ldh, double* wr, const double* wi, double* vl, + lapack_int* ldvl, double* vr, lapack_int* ldvr, + lapack_int* mm, lapack_int* m, double* work, + lapack_int* ifaill, lapack_int* ifailr, lapack_int *info ); +void LAPACK_chsein( char* job, char* eigsrc, char* initv, + const lapack_logical* select, lapack_int* n, + const lapack_complex_float* h, lapack_int* ldh, + lapack_complex_float* w, lapack_complex_float* vl, + lapack_int* ldvl, lapack_complex_float* vr, + lapack_int* ldvr, lapack_int* mm, lapack_int* m, + lapack_complex_float* work, float* rwork, + lapack_int* ifaill, lapack_int* ifailr, lapack_int *info ); +void LAPACK_zhsein( char* job, char* eigsrc, char* initv, + const lapack_logical* select, lapack_int* n, + const lapack_complex_double* h, lapack_int* ldh, + lapack_complex_double* w, lapack_complex_double* vl, + lapack_int* ldvl, lapack_complex_double* vr, + lapack_int* ldvr, lapack_int* mm, lapack_int* m, + lapack_complex_double* work, double* rwork, + lapack_int* ifaill, lapack_int* ifailr, lapack_int *info ); +void LAPACK_strevc( char* side, char* howmny, lapack_logical* select, + lapack_int* n, const float* t, lapack_int* ldt, float* vl, + lapack_int* ldvl, float* vr, lapack_int* ldvr, + lapack_int* mm, lapack_int* m, float* work, + lapack_int *info ); +void LAPACK_dtrevc( char* side, char* howmny, lapack_logical* select, + lapack_int* n, const double* t, lapack_int* ldt, double* vl, + lapack_int* ldvl, double* vr, lapack_int* ldvr, + lapack_int* mm, lapack_int* m, double* work, + lapack_int *info ); +void LAPACK_ctrevc( char* side, char* howmny, const lapack_logical* select, + lapack_int* n, lapack_complex_float* t, lapack_int* ldt, + lapack_complex_float* vl, lapack_int* ldvl, + lapack_complex_float* vr, lapack_int* ldvr, lapack_int* mm, + lapack_int* m, lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_ztrevc( char* side, char* howmny, const lapack_logical* select, + lapack_int* n, lapack_complex_double* t, lapack_int* ldt, + lapack_complex_double* vl, lapack_int* ldvl, + lapack_complex_double* vr, lapack_int* ldvr, lapack_int* mm, + lapack_int* m, lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_strsna( char* job, char* howmny, const lapack_logical* select, + lapack_int* n, const float* t, lapack_int* ldt, + const float* vl, lapack_int* ldvl, const float* vr, + lapack_int* ldvr, float* s, float* sep, lapack_int* mm, + lapack_int* m, float* work, lapack_int* ldwork, + lapack_int* iwork, lapack_int *info ); +void LAPACK_dtrsna( char* job, char* howmny, const lapack_logical* select, + lapack_int* n, const double* t, lapack_int* ldt, + const double* vl, lapack_int* ldvl, const double* vr, + lapack_int* ldvr, double* s, double* sep, lapack_int* mm, + lapack_int* m, double* work, lapack_int* ldwork, + lapack_int* iwork, lapack_int *info ); +void LAPACK_ctrsna( char* job, char* howmny, const lapack_logical* select, + lapack_int* n, const lapack_complex_float* t, + lapack_int* ldt, const lapack_complex_float* vl, + lapack_int* ldvl, const lapack_complex_float* vr, + lapack_int* ldvr, float* s, float* sep, lapack_int* mm, + lapack_int* m, lapack_complex_float* work, + lapack_int* ldwork, float* rwork, lapack_int *info ); +void LAPACK_ztrsna( char* job, char* howmny, const lapack_logical* select, + lapack_int* n, const lapack_complex_double* t, + lapack_int* ldt, const lapack_complex_double* vl, + lapack_int* ldvl, const lapack_complex_double* vr, + lapack_int* ldvr, double* s, double* sep, lapack_int* mm, + lapack_int* m, lapack_complex_double* work, + lapack_int* ldwork, double* rwork, lapack_int *info ); +void LAPACK_strexc( char* compq, lapack_int* n, float* t, lapack_int* ldt, + float* q, lapack_int* ldq, lapack_int* ifst, + lapack_int* ilst, float* work, lapack_int *info ); +void LAPACK_dtrexc( char* compq, lapack_int* n, double* t, lapack_int* ldt, + double* q, lapack_int* ldq, lapack_int* ifst, + lapack_int* ilst, double* work, lapack_int *info ); +void LAPACK_ctrexc( char* compq, lapack_int* n, lapack_complex_float* t, + lapack_int* ldt, lapack_complex_float* q, lapack_int* ldq, + lapack_int* ifst, lapack_int* ilst, lapack_int *info ); +void LAPACK_ztrexc( char* compq, lapack_int* n, lapack_complex_double* t, + lapack_int* ldt, lapack_complex_double* q, lapack_int* ldq, + lapack_int* ifst, lapack_int* ilst, lapack_int *info ); +void LAPACK_strsen( char* job, char* compq, const lapack_logical* select, + lapack_int* n, float* t, lapack_int* ldt, float* q, + lapack_int* ldq, float* wr, float* wi, lapack_int* m, + float* s, float* sep, float* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_dtrsen( char* job, char* compq, const lapack_logical* select, + lapack_int* n, double* t, lapack_int* ldt, double* q, + lapack_int* ldq, double* wr, double* wi, lapack_int* m, + double* s, double* sep, double* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_ctrsen( char* job, char* compq, const lapack_logical* select, + lapack_int* n, lapack_complex_float* t, lapack_int* ldt, + lapack_complex_float* q, lapack_int* ldq, + lapack_complex_float* w, lapack_int* m, float* s, + float* sep, lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_ztrsen( char* job, char* compq, const lapack_logical* select, + lapack_int* n, lapack_complex_double* t, lapack_int* ldt, + lapack_complex_double* q, lapack_int* ldq, + lapack_complex_double* w, lapack_int* m, double* s, + double* sep, lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_strsyl( char* trana, char* tranb, lapack_int* isgn, lapack_int* m, + lapack_int* n, const float* a, lapack_int* lda, + const float* b, lapack_int* ldb, float* c, lapack_int* ldc, + float* scale, lapack_int *info ); +void LAPACK_dtrsyl( char* trana, char* tranb, lapack_int* isgn, lapack_int* m, + lapack_int* n, const double* a, lapack_int* lda, + const double* b, lapack_int* ldb, double* c, + lapack_int* ldc, double* scale, lapack_int *info ); +void LAPACK_ctrsyl( char* trana, char* tranb, lapack_int* isgn, lapack_int* m, + lapack_int* n, const lapack_complex_float* a, + lapack_int* lda, const lapack_complex_float* b, + lapack_int* ldb, lapack_complex_float* c, lapack_int* ldc, + float* scale, lapack_int *info ); +void LAPACK_ztrsyl( char* trana, char* tranb, lapack_int* isgn, lapack_int* m, + lapack_int* n, const lapack_complex_double* a, + lapack_int* lda, const lapack_complex_double* b, + lapack_int* ldb, lapack_complex_double* c, lapack_int* ldc, + double* scale, lapack_int *info ); +void LAPACK_sgghrd( char* compq, char* compz, lapack_int* n, lapack_int* ilo, + lapack_int* ihi, float* a, lapack_int* lda, float* b, + lapack_int* ldb, float* q, lapack_int* ldq, float* z, + lapack_int* ldz, lapack_int *info ); +void LAPACK_dgghrd( char* compq, char* compz, lapack_int* n, lapack_int* ilo, + lapack_int* ihi, double* a, lapack_int* lda, double* b, + lapack_int* ldb, double* q, lapack_int* ldq, double* z, + lapack_int* ldz, lapack_int *info ); +void LAPACK_cgghrd( char* compq, char* compz, lapack_int* n, lapack_int* ilo, + lapack_int* ihi, lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* q, lapack_int* ldq, + lapack_complex_float* z, lapack_int* ldz, + lapack_int *info ); +void LAPACK_zgghrd( char* compq, char* compz, lapack_int* n, lapack_int* ilo, + lapack_int* ihi, lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* q, lapack_int* ldq, + lapack_complex_double* z, lapack_int* ldz, + lapack_int *info ); +void LAPACK_sggbal( char* job, lapack_int* n, float* a, lapack_int* lda, + float* b, lapack_int* ldb, lapack_int* ilo, lapack_int* ihi, + float* lscale, float* rscale, float* work, + lapack_int *info ); +void LAPACK_dggbal( char* job, lapack_int* n, double* a, lapack_int* lda, + double* b, lapack_int* ldb, lapack_int* ilo, + lapack_int* ihi, double* lscale, double* rscale, + double* work, lapack_int *info ); +void LAPACK_cggbal( char* job, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_complex_float* b, lapack_int* ldb, + lapack_int* ilo, lapack_int* ihi, float* lscale, + float* rscale, float* work, lapack_int *info ); +void LAPACK_zggbal( char* job, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_complex_double* b, lapack_int* ldb, + lapack_int* ilo, lapack_int* ihi, double* lscale, + double* rscale, double* work, lapack_int *info ); +void LAPACK_sggbak( char* job, char* side, lapack_int* n, lapack_int* ilo, + lapack_int* ihi, const float* lscale, const float* rscale, + lapack_int* m, float* v, lapack_int* ldv, + lapack_int *info ); +void LAPACK_dggbak( char* job, char* side, lapack_int* n, lapack_int* ilo, + lapack_int* ihi, const double* lscale, const double* rscale, + lapack_int* m, double* v, lapack_int* ldv, + lapack_int *info ); +void LAPACK_cggbak( char* job, char* side, lapack_int* n, lapack_int* ilo, + lapack_int* ihi, const float* lscale, const float* rscale, + lapack_int* m, lapack_complex_float* v, lapack_int* ldv, + lapack_int *info ); +void LAPACK_zggbak( char* job, char* side, lapack_int* n, lapack_int* ilo, + lapack_int* ihi, const double* lscale, const double* rscale, + lapack_int* m, lapack_complex_double* v, lapack_int* ldv, + lapack_int *info ); +void LAPACK_shgeqz( char* job, char* compq, char* compz, lapack_int* n, + lapack_int* ilo, lapack_int* ihi, float* h, lapack_int* ldh, + float* t, lapack_int* ldt, float* alphar, float* alphai, + float* beta, float* q, lapack_int* ldq, float* z, + lapack_int* ldz, float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_dhgeqz( char* job, char* compq, char* compz, lapack_int* n, + lapack_int* ilo, lapack_int* ihi, double* h, + lapack_int* ldh, double* t, lapack_int* ldt, double* alphar, + double* alphai, double* beta, double* q, lapack_int* ldq, + double* z, lapack_int* ldz, double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_chgeqz( char* job, char* compq, char* compz, lapack_int* n, + lapack_int* ilo, lapack_int* ihi, lapack_complex_float* h, + lapack_int* ldh, lapack_complex_float* t, lapack_int* ldt, + lapack_complex_float* alpha, lapack_complex_float* beta, + lapack_complex_float* q, lapack_int* ldq, + lapack_complex_float* z, lapack_int* ldz, + lapack_complex_float* work, lapack_int* lwork, float* rwork, + lapack_int *info ); +void LAPACK_zhgeqz( char* job, char* compq, char* compz, lapack_int* n, + lapack_int* ilo, lapack_int* ihi, lapack_complex_double* h, + lapack_int* ldh, lapack_complex_double* t, lapack_int* ldt, + lapack_complex_double* alpha, lapack_complex_double* beta, + lapack_complex_double* q, lapack_int* ldq, + lapack_complex_double* z, lapack_int* ldz, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_int *info ); +void LAPACK_stgevc( char* side, char* howmny, const lapack_logical* select, + lapack_int* n, const float* s, lapack_int* lds, + const float* p, lapack_int* ldp, float* vl, + lapack_int* ldvl, float* vr, lapack_int* ldvr, + lapack_int* mm, lapack_int* m, float* work, + lapack_int *info ); +void LAPACK_dtgevc( char* side, char* howmny, const lapack_logical* select, + lapack_int* n, const double* s, lapack_int* lds, + const double* p, lapack_int* ldp, double* vl, + lapack_int* ldvl, double* vr, lapack_int* ldvr, + lapack_int* mm, lapack_int* m, double* work, + lapack_int *info ); +void LAPACK_ctgevc( char* side, char* howmny, const lapack_logical* select, + lapack_int* n, const lapack_complex_float* s, + lapack_int* lds, const lapack_complex_float* p, + lapack_int* ldp, lapack_complex_float* vl, lapack_int* ldvl, + lapack_complex_float* vr, lapack_int* ldvr, lapack_int* mm, + lapack_int* m, lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_ztgevc( char* side, char* howmny, const lapack_logical* select, + lapack_int* n, const lapack_complex_double* s, + lapack_int* lds, const lapack_complex_double* p, + lapack_int* ldp, lapack_complex_double* vl, + lapack_int* ldvl, lapack_complex_double* vr, + lapack_int* ldvr, lapack_int* mm, lapack_int* m, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_stgexc( lapack_logical* wantq, lapack_logical* wantz, lapack_int* n, + float* a, lapack_int* lda, float* b, lapack_int* ldb, + float* q, lapack_int* ldq, float* z, lapack_int* ldz, + lapack_int* ifst, lapack_int* ilst, float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_dtgexc( lapack_logical* wantq, lapack_logical* wantz, lapack_int* n, + double* a, lapack_int* lda, double* b, lapack_int* ldb, + double* q, lapack_int* ldq, double* z, lapack_int* ldz, + lapack_int* ifst, lapack_int* ilst, double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_ctgexc( lapack_logical* wantq, lapack_logical* wantz, lapack_int* n, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* q, lapack_int* ldq, + lapack_complex_float* z, lapack_int* ldz, lapack_int* ifst, + lapack_int* ilst, lapack_int *info ); +void LAPACK_ztgexc( lapack_logical* wantq, lapack_logical* wantz, lapack_int* n, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* q, lapack_int* ldq, + lapack_complex_double* z, lapack_int* ldz, lapack_int* ifst, + lapack_int* ilst, lapack_int *info ); +void LAPACK_stgsen( lapack_int* ijob, lapack_logical* wantq, + lapack_logical* wantz, const lapack_logical* select, + lapack_int* n, float* a, lapack_int* lda, float* b, + lapack_int* ldb, float* alphar, float* alphai, float* beta, + float* q, lapack_int* ldq, float* z, lapack_int* ldz, + lapack_int* m, float* pl, float* pr, float* dif, + float* work, lapack_int* lwork, lapack_int* iwork, + lapack_int* liwork, lapack_int *info ); +void LAPACK_dtgsen( lapack_int* ijob, lapack_logical* wantq, + lapack_logical* wantz, const lapack_logical* select, + lapack_int* n, double* a, lapack_int* lda, double* b, + lapack_int* ldb, double* alphar, double* alphai, + double* beta, double* q, lapack_int* ldq, double* z, + lapack_int* ldz, lapack_int* m, double* pl, double* pr, + double* dif, double* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_ctgsen( lapack_int* ijob, lapack_logical* wantq, + lapack_logical* wantz, const lapack_logical* select, + lapack_int* n, lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* alpha, lapack_complex_float* beta, + lapack_complex_float* q, lapack_int* ldq, + lapack_complex_float* z, lapack_int* ldz, lapack_int* m, + float* pl, float* pr, float* dif, + lapack_complex_float* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_ztgsen( lapack_int* ijob, lapack_logical* wantq, + lapack_logical* wantz, const lapack_logical* select, + lapack_int* n, lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* alpha, lapack_complex_double* beta, + lapack_complex_double* q, lapack_int* ldq, + lapack_complex_double* z, lapack_int* ldz, lapack_int* m, + double* pl, double* pr, double* dif, + lapack_complex_double* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_stgsyl( char* trans, lapack_int* ijob, lapack_int* m, lapack_int* n, + const float* a, lapack_int* lda, const float* b, + lapack_int* ldb, float* c, lapack_int* ldc, const float* d, + lapack_int* ldd, const float* e, lapack_int* lde, float* f, + lapack_int* ldf, float* scale, float* dif, float* work, + lapack_int* lwork, lapack_int* iwork, lapack_int *info ); +void LAPACK_dtgsyl( char* trans, lapack_int* ijob, lapack_int* m, lapack_int* n, + const double* a, lapack_int* lda, const double* b, + lapack_int* ldb, double* c, lapack_int* ldc, + const double* d, lapack_int* ldd, const double* e, + lapack_int* lde, double* f, lapack_int* ldf, double* scale, + double* dif, double* work, lapack_int* lwork, + lapack_int* iwork, lapack_int *info ); +void LAPACK_ctgsyl( char* trans, lapack_int* ijob, lapack_int* m, lapack_int* n, + const lapack_complex_float* a, lapack_int* lda, + const lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* c, lapack_int* ldc, + const lapack_complex_float* d, lapack_int* ldd, + const lapack_complex_float* e, lapack_int* lde, + lapack_complex_float* f, lapack_int* ldf, float* scale, + float* dif, lapack_complex_float* work, lapack_int* lwork, + lapack_int* iwork, lapack_int *info ); +void LAPACK_ztgsyl( char* trans, lapack_int* ijob, lapack_int* m, lapack_int* n, + const lapack_complex_double* a, lapack_int* lda, + const lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* c, lapack_int* ldc, + const lapack_complex_double* d, lapack_int* ldd, + const lapack_complex_double* e, lapack_int* lde, + lapack_complex_double* f, lapack_int* ldf, double* scale, + double* dif, lapack_complex_double* work, lapack_int* lwork, + lapack_int* iwork, lapack_int *info ); +void LAPACK_stgsna( char* job, char* howmny, const lapack_logical* select, + lapack_int* n, const float* a, lapack_int* lda, + const float* b, lapack_int* ldb, const float* vl, + lapack_int* ldvl, const float* vr, lapack_int* ldvr, + float* s, float* dif, lapack_int* mm, lapack_int* m, + float* work, lapack_int* lwork, lapack_int* iwork, + lapack_int *info ); +void LAPACK_dtgsna( char* job, char* howmny, const lapack_logical* select, + lapack_int* n, const double* a, lapack_int* lda, + const double* b, lapack_int* ldb, const double* vl, + lapack_int* ldvl, const double* vr, lapack_int* ldvr, + double* s, double* dif, lapack_int* mm, lapack_int* m, + double* work, lapack_int* lwork, lapack_int* iwork, + lapack_int *info ); +void LAPACK_ctgsna( char* job, char* howmny, const lapack_logical* select, + lapack_int* n, const lapack_complex_float* a, + lapack_int* lda, const lapack_complex_float* b, + lapack_int* ldb, const lapack_complex_float* vl, + lapack_int* ldvl, const lapack_complex_float* vr, + lapack_int* ldvr, float* s, float* dif, lapack_int* mm, + lapack_int* m, lapack_complex_float* work, + lapack_int* lwork, lapack_int* iwork, lapack_int *info ); +void LAPACK_ztgsna( char* job, char* howmny, const lapack_logical* select, + lapack_int* n, const lapack_complex_double* a, + lapack_int* lda, const lapack_complex_double* b, + lapack_int* ldb, const lapack_complex_double* vl, + lapack_int* ldvl, const lapack_complex_double* vr, + lapack_int* ldvr, double* s, double* dif, lapack_int* mm, + lapack_int* m, lapack_complex_double* work, + lapack_int* lwork, lapack_int* iwork, lapack_int *info ); +void LAPACK_sggsvp( char* jobu, char* jobv, char* jobq, lapack_int* m, + lapack_int* p, lapack_int* n, float* a, lapack_int* lda, + float* b, lapack_int* ldb, float* tola, float* tolb, + lapack_int* k, lapack_int* l, float* u, lapack_int* ldu, + float* v, lapack_int* ldv, float* q, lapack_int* ldq, + lapack_int* iwork, float* tau, float* work, + lapack_int *info ); +void LAPACK_dggsvp( char* jobu, char* jobv, char* jobq, lapack_int* m, + lapack_int* p, lapack_int* n, double* a, lapack_int* lda, + double* b, lapack_int* ldb, double* tola, double* tolb, + lapack_int* k, lapack_int* l, double* u, lapack_int* ldu, + double* v, lapack_int* ldv, double* q, lapack_int* ldq, + lapack_int* iwork, double* tau, double* work, + lapack_int *info ); +void LAPACK_cggsvp( char* jobu, char* jobv, char* jobq, lapack_int* m, + lapack_int* p, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_complex_float* b, lapack_int* ldb, + float* tola, float* tolb, lapack_int* k, lapack_int* l, + lapack_complex_float* u, lapack_int* ldu, + lapack_complex_float* v, lapack_int* ldv, + lapack_complex_float* q, lapack_int* ldq, lapack_int* iwork, + float* rwork, lapack_complex_float* tau, + lapack_complex_float* work, lapack_int *info ); +void LAPACK_zggsvp( char* jobu, char* jobv, char* jobq, lapack_int* m, + lapack_int* p, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_complex_double* b, lapack_int* ldb, + double* tola, double* tolb, lapack_int* k, lapack_int* l, + lapack_complex_double* u, lapack_int* ldu, + lapack_complex_double* v, lapack_int* ldv, + lapack_complex_double* q, lapack_int* ldq, + lapack_int* iwork, double* rwork, + lapack_complex_double* tau, lapack_complex_double* work, + lapack_int *info ); +void LAPACK_stgsja( char* jobu, char* jobv, char* jobq, lapack_int* m, + lapack_int* p, lapack_int* n, lapack_int* k, lapack_int* l, + float* a, lapack_int* lda, float* b, lapack_int* ldb, + float* tola, float* tolb, float* alpha, float* beta, + float* u, lapack_int* ldu, float* v, lapack_int* ldv, + float* q, lapack_int* ldq, float* work, lapack_int* ncycle, + lapack_int *info ); +void LAPACK_dtgsja( char* jobu, char* jobv, char* jobq, lapack_int* m, + lapack_int* p, lapack_int* n, lapack_int* k, lapack_int* l, + double* a, lapack_int* lda, double* b, lapack_int* ldb, + double* tola, double* tolb, double* alpha, double* beta, + double* u, lapack_int* ldu, double* v, lapack_int* ldv, + double* q, lapack_int* ldq, double* work, + lapack_int* ncycle, lapack_int *info ); +void LAPACK_ctgsja( char* jobu, char* jobv, char* jobq, lapack_int* m, + lapack_int* p, lapack_int* n, lapack_int* k, lapack_int* l, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, float* tola, + float* tolb, float* alpha, float* beta, + lapack_complex_float* u, lapack_int* ldu, + lapack_complex_float* v, lapack_int* ldv, + lapack_complex_float* q, lapack_int* ldq, + lapack_complex_float* work, lapack_int* ncycle, + lapack_int *info ); +void LAPACK_ztgsja( char* jobu, char* jobv, char* jobq, lapack_int* m, + lapack_int* p, lapack_int* n, lapack_int* k, lapack_int* l, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, double* tola, + double* tolb, double* alpha, double* beta, + lapack_complex_double* u, lapack_int* ldu, + lapack_complex_double* v, lapack_int* ldv, + lapack_complex_double* q, lapack_int* ldq, + lapack_complex_double* work, lapack_int* ncycle, + lapack_int *info ); +void LAPACK_sgels( char* trans, lapack_int* m, lapack_int* n, lapack_int* nrhs, + float* a, lapack_int* lda, float* b, lapack_int* ldb, + float* work, lapack_int* lwork, lapack_int *info ); +void LAPACK_dgels( char* trans, lapack_int* m, lapack_int* n, lapack_int* nrhs, + double* a, lapack_int* lda, double* b, lapack_int* ldb, + double* work, lapack_int* lwork, lapack_int *info ); +void LAPACK_cgels( char* trans, lapack_int* m, lapack_int* n, lapack_int* nrhs, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_zgels( char* trans, lapack_int* m, lapack_int* n, lapack_int* nrhs, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_sgelsy( lapack_int* m, lapack_int* n, lapack_int* nrhs, float* a, + lapack_int* lda, float* b, lapack_int* ldb, + lapack_int* jpvt, float* rcond, lapack_int* rank, + float* work, lapack_int* lwork, lapack_int *info ); +void LAPACK_dgelsy( lapack_int* m, lapack_int* n, lapack_int* nrhs, double* a, + lapack_int* lda, double* b, lapack_int* ldb, + lapack_int* jpvt, double* rcond, lapack_int* rank, + double* work, lapack_int* lwork, lapack_int *info ); +void LAPACK_cgelsy( lapack_int* m, lapack_int* n, lapack_int* nrhs, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, lapack_int* jpvt, + float* rcond, lapack_int* rank, lapack_complex_float* work, + lapack_int* lwork, float* rwork, lapack_int *info ); +void LAPACK_zgelsy( lapack_int* m, lapack_int* n, lapack_int* nrhs, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, lapack_int* jpvt, + double* rcond, lapack_int* rank, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_int *info ); +void LAPACK_sgelss( lapack_int* m, lapack_int* n, lapack_int* nrhs, float* a, + lapack_int* lda, float* b, lapack_int* ldb, float* s, + float* rcond, lapack_int* rank, float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_dgelss( lapack_int* m, lapack_int* n, lapack_int* nrhs, double* a, + lapack_int* lda, double* b, lapack_int* ldb, double* s, + double* rcond, lapack_int* rank, double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_cgelss( lapack_int* m, lapack_int* n, lapack_int* nrhs, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, float* s, + float* rcond, lapack_int* rank, lapack_complex_float* work, + lapack_int* lwork, float* rwork, lapack_int *info ); +void LAPACK_zgelss( lapack_int* m, lapack_int* n, lapack_int* nrhs, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, double* s, + double* rcond, lapack_int* rank, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_int *info ); +void LAPACK_sgelsd( lapack_int* m, lapack_int* n, lapack_int* nrhs, float* a, + lapack_int* lda, float* b, lapack_int* ldb, float* s, + float* rcond, lapack_int* rank, float* work, + lapack_int* lwork, lapack_int* iwork, lapack_int *info ); +void LAPACK_dgelsd( lapack_int* m, lapack_int* n, lapack_int* nrhs, double* a, + lapack_int* lda, double* b, lapack_int* ldb, double* s, + double* rcond, lapack_int* rank, double* work, + lapack_int* lwork, lapack_int* iwork, lapack_int *info ); +void LAPACK_cgelsd( lapack_int* m, lapack_int* n, lapack_int* nrhs, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, float* s, + float* rcond, lapack_int* rank, lapack_complex_float* work, + lapack_int* lwork, float* rwork, lapack_int* iwork, + lapack_int *info ); +void LAPACK_zgelsd( lapack_int* m, lapack_int* n, lapack_int* nrhs, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, double* s, + double* rcond, lapack_int* rank, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_int* iwork, lapack_int *info ); +void LAPACK_sgglse( lapack_int* m, lapack_int* n, lapack_int* p, float* a, + lapack_int* lda, float* b, lapack_int* ldb, float* c, + float* d, float* x, float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_dgglse( lapack_int* m, lapack_int* n, lapack_int* p, double* a, + lapack_int* lda, double* b, lapack_int* ldb, double* c, + double* d, double* x, double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_cgglse( lapack_int* m, lapack_int* n, lapack_int* p, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* c, lapack_complex_float* d, + lapack_complex_float* x, lapack_complex_float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_zgglse( lapack_int* m, lapack_int* n, lapack_int* p, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* c, lapack_complex_double* d, + lapack_complex_double* x, lapack_complex_double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_sggglm( lapack_int* n, lapack_int* m, lapack_int* p, float* a, + lapack_int* lda, float* b, lapack_int* ldb, float* d, + float* x, float* y, float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_dggglm( lapack_int* n, lapack_int* m, lapack_int* p, double* a, + lapack_int* lda, double* b, lapack_int* ldb, double* d, + double* x, double* y, double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_cggglm( lapack_int* n, lapack_int* m, lapack_int* p, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* d, lapack_complex_float* x, + lapack_complex_float* y, lapack_complex_float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_zggglm( lapack_int* n, lapack_int* m, lapack_int* p, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* d, lapack_complex_double* x, + lapack_complex_double* y, lapack_complex_double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_ssyev( char* jobz, char* uplo, lapack_int* n, float* a, + lapack_int* lda, float* w, float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_dsyev( char* jobz, char* uplo, lapack_int* n, double* a, + lapack_int* lda, double* w, double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_cheev( char* jobz, char* uplo, lapack_int* n, + lapack_complex_float* a, lapack_int* lda, float* w, + lapack_complex_float* work, lapack_int* lwork, float* rwork, + lapack_int *info ); +void LAPACK_zheev( char* jobz, char* uplo, lapack_int* n, + lapack_complex_double* a, lapack_int* lda, double* w, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_int *info ); +void LAPACK_ssyevd( char* jobz, char* uplo, lapack_int* n, float* a, + lapack_int* lda, float* w, float* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_dsyevd( char* jobz, char* uplo, lapack_int* n, double* a, + lapack_int* lda, double* w, double* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_cheevd( char* jobz, char* uplo, lapack_int* n, + lapack_complex_float* a, lapack_int* lda, float* w, + lapack_complex_float* work, lapack_int* lwork, float* rwork, + lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork, + lapack_int *info ); +void LAPACK_zheevd( char* jobz, char* uplo, lapack_int* n, + lapack_complex_double* a, lapack_int* lda, double* w, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_int* lrwork, lapack_int* iwork, + lapack_int* liwork, lapack_int *info ); +void LAPACK_ssyevx( char* jobz, char* range, char* uplo, lapack_int* n, + float* a, lapack_int* lda, float* vl, float* vu, + lapack_int* il, lapack_int* iu, float* abstol, + lapack_int* m, float* w, float* z, lapack_int* ldz, + float* work, lapack_int* lwork, lapack_int* iwork, + lapack_int* ifail, lapack_int *info ); +void LAPACK_dsyevx( char* jobz, char* range, char* uplo, lapack_int* n, + double* a, lapack_int* lda, double* vl, double* vu, + lapack_int* il, lapack_int* iu, double* abstol, + lapack_int* m, double* w, double* z, lapack_int* ldz, + double* work, lapack_int* lwork, lapack_int* iwork, + lapack_int* ifail, lapack_int *info ); +void LAPACK_cheevx( char* jobz, char* range, char* uplo, lapack_int* n, + lapack_complex_float* a, lapack_int* lda, float* vl, + float* vu, lapack_int* il, lapack_int* iu, float* abstol, + lapack_int* m, float* w, lapack_complex_float* z, + lapack_int* ldz, lapack_complex_float* work, + lapack_int* lwork, float* rwork, lapack_int* iwork, + lapack_int* ifail, lapack_int *info ); +void LAPACK_zheevx( char* jobz, char* range, char* uplo, lapack_int* n, + lapack_complex_double* a, lapack_int* lda, double* vl, + double* vu, lapack_int* il, lapack_int* iu, double* abstol, + lapack_int* m, double* w, lapack_complex_double* z, + lapack_int* ldz, lapack_complex_double* work, + lapack_int* lwork, double* rwork, lapack_int* iwork, + lapack_int* ifail, lapack_int *info ); +void LAPACK_ssyevr( char* jobz, char* range, char* uplo, lapack_int* n, + float* a, lapack_int* lda, float* vl, float* vu, + lapack_int* il, lapack_int* iu, float* abstol, + lapack_int* m, float* w, float* z, lapack_int* ldz, + lapack_int* isuppz, float* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_dsyevr( char* jobz, char* range, char* uplo, lapack_int* n, + double* a, lapack_int* lda, double* vl, double* vu, + lapack_int* il, lapack_int* iu, double* abstol, + lapack_int* m, double* w, double* z, lapack_int* ldz, + lapack_int* isuppz, double* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_cheevr( char* jobz, char* range, char* uplo, lapack_int* n, + lapack_complex_float* a, lapack_int* lda, float* vl, + float* vu, lapack_int* il, lapack_int* iu, float* abstol, + lapack_int* m, float* w, lapack_complex_float* z, + lapack_int* ldz, lapack_int* isuppz, + lapack_complex_float* work, lapack_int* lwork, float* rwork, + lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork, + lapack_int *info ); +void LAPACK_zheevr( char* jobz, char* range, char* uplo, lapack_int* n, + lapack_complex_double* a, lapack_int* lda, double* vl, + double* vu, lapack_int* il, lapack_int* iu, double* abstol, + lapack_int* m, double* w, lapack_complex_double* z, + lapack_int* ldz, lapack_int* isuppz, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_int* lrwork, lapack_int* iwork, + lapack_int* liwork, lapack_int *info ); +void LAPACK_sspev( char* jobz, char* uplo, lapack_int* n, float* ap, float* w, + float* z, lapack_int* ldz, float* work, lapack_int *info ); +void LAPACK_dspev( char* jobz, char* uplo, lapack_int* n, double* ap, double* w, + double* z, lapack_int* ldz, double* work, lapack_int *info ); +void LAPACK_chpev( char* jobz, char* uplo, lapack_int* n, + lapack_complex_float* ap, float* w, lapack_complex_float* z, + lapack_int* ldz, lapack_complex_float* work, float* rwork, + lapack_int *info ); +void LAPACK_zhpev( char* jobz, char* uplo, lapack_int* n, + lapack_complex_double* ap, double* w, + lapack_complex_double* z, lapack_int* ldz, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_sspevd( char* jobz, char* uplo, lapack_int* n, float* ap, float* w, + float* z, lapack_int* ldz, float* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_dspevd( char* jobz, char* uplo, lapack_int* n, double* ap, + double* w, double* z, lapack_int* ldz, double* work, + lapack_int* lwork, lapack_int* iwork, lapack_int* liwork, + lapack_int *info ); +void LAPACK_chpevd( char* jobz, char* uplo, lapack_int* n, + lapack_complex_float* ap, float* w, lapack_complex_float* z, + lapack_int* ldz, lapack_complex_float* work, + lapack_int* lwork, float* rwork, lapack_int* lrwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_zhpevd( char* jobz, char* uplo, lapack_int* n, + lapack_complex_double* ap, double* w, + lapack_complex_double* z, lapack_int* ldz, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_int* lrwork, lapack_int* iwork, + lapack_int* liwork, lapack_int *info ); +void LAPACK_sspevx( char* jobz, char* range, char* uplo, lapack_int* n, + float* ap, float* vl, float* vu, lapack_int* il, + lapack_int* iu, float* abstol, lapack_int* m, float* w, + float* z, lapack_int* ldz, float* work, lapack_int* iwork, + lapack_int* ifail, lapack_int *info ); +void LAPACK_dspevx( char* jobz, char* range, char* uplo, lapack_int* n, + double* ap, double* vl, double* vu, lapack_int* il, + lapack_int* iu, double* abstol, lapack_int* m, double* w, + double* z, lapack_int* ldz, double* work, lapack_int* iwork, + lapack_int* ifail, lapack_int *info ); +void LAPACK_chpevx( char* jobz, char* range, char* uplo, lapack_int* n, + lapack_complex_float* ap, float* vl, float* vu, + lapack_int* il, lapack_int* iu, float* abstol, + lapack_int* m, float* w, lapack_complex_float* z, + lapack_int* ldz, lapack_complex_float* work, float* rwork, + lapack_int* iwork, lapack_int* ifail, lapack_int *info ); +void LAPACK_zhpevx( char* jobz, char* range, char* uplo, lapack_int* n, + lapack_complex_double* ap, double* vl, double* vu, + lapack_int* il, lapack_int* iu, double* abstol, + lapack_int* m, double* w, lapack_complex_double* z, + lapack_int* ldz, lapack_complex_double* work, double* rwork, + lapack_int* iwork, lapack_int* ifail, lapack_int *info ); +void LAPACK_ssbev( char* jobz, char* uplo, lapack_int* n, lapack_int* kd, + float* ab, lapack_int* ldab, float* w, float* z, + lapack_int* ldz, float* work, lapack_int *info ); +void LAPACK_dsbev( char* jobz, char* uplo, lapack_int* n, lapack_int* kd, + double* ab, lapack_int* ldab, double* w, double* z, + lapack_int* ldz, double* work, lapack_int *info ); +void LAPACK_chbev( char* jobz, char* uplo, lapack_int* n, lapack_int* kd, + lapack_complex_float* ab, lapack_int* ldab, float* w, + lapack_complex_float* z, lapack_int* ldz, + lapack_complex_float* work, float* rwork, lapack_int *info ); +void LAPACK_zhbev( char* jobz, char* uplo, lapack_int* n, lapack_int* kd, + lapack_complex_double* ab, lapack_int* ldab, double* w, + lapack_complex_double* z, lapack_int* ldz, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_ssbevd( char* jobz, char* uplo, lapack_int* n, lapack_int* kd, + float* ab, lapack_int* ldab, float* w, float* z, + lapack_int* ldz, float* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_dsbevd( char* jobz, char* uplo, lapack_int* n, lapack_int* kd, + double* ab, lapack_int* ldab, double* w, double* z, + lapack_int* ldz, double* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_chbevd( char* jobz, char* uplo, lapack_int* n, lapack_int* kd, + lapack_complex_float* ab, lapack_int* ldab, float* w, + lapack_complex_float* z, lapack_int* ldz, + lapack_complex_float* work, lapack_int* lwork, float* rwork, + lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork, + lapack_int *info ); +void LAPACK_zhbevd( char* jobz, char* uplo, lapack_int* n, lapack_int* kd, + lapack_complex_double* ab, lapack_int* ldab, double* w, + lapack_complex_double* z, lapack_int* ldz, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_int* lrwork, lapack_int* iwork, + lapack_int* liwork, lapack_int *info ); +void LAPACK_ssbevx( char* jobz, char* range, char* uplo, lapack_int* n, + lapack_int* kd, float* ab, lapack_int* ldab, float* q, + lapack_int* ldq, float* vl, float* vu, lapack_int* il, + lapack_int* iu, float* abstol, lapack_int* m, float* w, + float* z, lapack_int* ldz, float* work, lapack_int* iwork, + lapack_int* ifail, lapack_int *info ); +void LAPACK_dsbevx( char* jobz, char* range, char* uplo, lapack_int* n, + lapack_int* kd, double* ab, lapack_int* ldab, double* q, + lapack_int* ldq, double* vl, double* vu, lapack_int* il, + lapack_int* iu, double* abstol, lapack_int* m, double* w, + double* z, lapack_int* ldz, double* work, lapack_int* iwork, + lapack_int* ifail, lapack_int *info ); +void LAPACK_chbevx( char* jobz, char* range, char* uplo, lapack_int* n, + lapack_int* kd, lapack_complex_float* ab, lapack_int* ldab, + lapack_complex_float* q, lapack_int* ldq, float* vl, + float* vu, lapack_int* il, lapack_int* iu, float* abstol, + lapack_int* m, float* w, lapack_complex_float* z, + lapack_int* ldz, lapack_complex_float* work, float* rwork, + lapack_int* iwork, lapack_int* ifail, lapack_int *info ); +void LAPACK_zhbevx( char* jobz, char* range, char* uplo, lapack_int* n, + lapack_int* kd, lapack_complex_double* ab, lapack_int* ldab, + lapack_complex_double* q, lapack_int* ldq, double* vl, + double* vu, lapack_int* il, lapack_int* iu, double* abstol, + lapack_int* m, double* w, lapack_complex_double* z, + lapack_int* ldz, lapack_complex_double* work, double* rwork, + lapack_int* iwork, lapack_int* ifail, lapack_int *info ); +void LAPACK_sstev( char* jobz, lapack_int* n, float* d, float* e, float* z, + lapack_int* ldz, float* work, lapack_int *info ); +void LAPACK_dstev( char* jobz, lapack_int* n, double* d, double* e, double* z, + lapack_int* ldz, double* work, lapack_int *info ); +void LAPACK_sstevd( char* jobz, lapack_int* n, float* d, float* e, float* z, + lapack_int* ldz, float* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_dstevd( char* jobz, lapack_int* n, double* d, double* e, double* z, + lapack_int* ldz, double* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_sstevx( char* jobz, char* range, lapack_int* n, float* d, float* e, + float* vl, float* vu, lapack_int* il, lapack_int* iu, + float* abstol, lapack_int* m, float* w, float* z, + lapack_int* ldz, float* work, lapack_int* iwork, + lapack_int* ifail, lapack_int *info ); +void LAPACK_dstevx( char* jobz, char* range, lapack_int* n, double* d, + double* e, double* vl, double* vu, lapack_int* il, + lapack_int* iu, double* abstol, lapack_int* m, double* w, + double* z, lapack_int* ldz, double* work, lapack_int* iwork, + lapack_int* ifail, lapack_int *info ); +void LAPACK_sstevr( char* jobz, char* range, lapack_int* n, float* d, float* e, + float* vl, float* vu, lapack_int* il, lapack_int* iu, + float* abstol, lapack_int* m, float* w, float* z, + lapack_int* ldz, lapack_int* isuppz, float* work, + lapack_int* lwork, lapack_int* iwork, lapack_int* liwork, + lapack_int *info ); +void LAPACK_dstevr( char* jobz, char* range, lapack_int* n, double* d, + double* e, double* vl, double* vu, lapack_int* il, + lapack_int* iu, double* abstol, lapack_int* m, double* w, + double* z, lapack_int* ldz, lapack_int* isuppz, + double* work, lapack_int* lwork, lapack_int* iwork, + lapack_int* liwork, lapack_int *info ); +void LAPACK_sgees( char* jobvs, char* sort, LAPACK_S_SELECT2 select, + lapack_int* n, float* a, lapack_int* lda, lapack_int* sdim, + float* wr, float* wi, float* vs, lapack_int* ldvs, + float* work, lapack_int* lwork, lapack_logical* bwork, + lapack_int *info ); +void LAPACK_dgees( char* jobvs, char* sort, LAPACK_D_SELECT2 select, + lapack_int* n, double* a, lapack_int* lda, lapack_int* sdim, + double* wr, double* wi, double* vs, lapack_int* ldvs, + double* work, lapack_int* lwork, lapack_logical* bwork, + lapack_int *info ); +void LAPACK_cgees( char* jobvs, char* sort, LAPACK_C_SELECT1 select, + lapack_int* n, lapack_complex_float* a, lapack_int* lda, + lapack_int* sdim, lapack_complex_float* w, + lapack_complex_float* vs, lapack_int* ldvs, + lapack_complex_float* work, lapack_int* lwork, float* rwork, + lapack_logical* bwork, lapack_int *info ); +void LAPACK_zgees( char* jobvs, char* sort, LAPACK_Z_SELECT1 select, + lapack_int* n, lapack_complex_double* a, lapack_int* lda, + lapack_int* sdim, lapack_complex_double* w, + lapack_complex_double* vs, lapack_int* ldvs, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_logical* bwork, lapack_int *info ); +void LAPACK_sgeesx( char* jobvs, char* sort, LAPACK_S_SELECT2 select, + char* sense, lapack_int* n, float* a, lapack_int* lda, + lapack_int* sdim, float* wr, float* wi, float* vs, + lapack_int* ldvs, float* rconde, float* rcondv, float* work, + lapack_int* lwork, lapack_int* iwork, lapack_int* liwork, + lapack_logical* bwork, lapack_int *info ); +void LAPACK_dgeesx( char* jobvs, char* sort, LAPACK_D_SELECT2 select, + char* sense, lapack_int* n, double* a, lapack_int* lda, + lapack_int* sdim, double* wr, double* wi, double* vs, + lapack_int* ldvs, double* rconde, double* rcondv, + double* work, lapack_int* lwork, lapack_int* iwork, + lapack_int* liwork, lapack_logical* bwork, + lapack_int *info ); +void LAPACK_cgeesx( char* jobvs, char* sort, LAPACK_C_SELECT1 select, + char* sense, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_int* sdim, lapack_complex_float* w, + lapack_complex_float* vs, lapack_int* ldvs, float* rconde, + float* rcondv, lapack_complex_float* work, + lapack_int* lwork, float* rwork, lapack_logical* bwork, + lapack_int *info ); +void LAPACK_zgeesx( char* jobvs, char* sort, LAPACK_Z_SELECT1 select, + char* sense, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_int* sdim, lapack_complex_double* w, + lapack_complex_double* vs, lapack_int* ldvs, double* rconde, + double* rcondv, lapack_complex_double* work, + lapack_int* lwork, double* rwork, lapack_logical* bwork, + lapack_int *info ); +void LAPACK_sgeev( char* jobvl, char* jobvr, lapack_int* n, float* a, + lapack_int* lda, float* wr, float* wi, float* vl, + lapack_int* ldvl, float* vr, lapack_int* ldvr, float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_dgeev( char* jobvl, char* jobvr, lapack_int* n, double* a, + lapack_int* lda, double* wr, double* wi, double* vl, + lapack_int* ldvl, double* vr, lapack_int* ldvr, double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_cgeev( char* jobvl, char* jobvr, lapack_int* n, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* w, lapack_complex_float* vl, + lapack_int* ldvl, lapack_complex_float* vr, lapack_int* ldvr, + lapack_complex_float* work, lapack_int* lwork, float* rwork, + lapack_int *info ); +void LAPACK_zgeev( char* jobvl, char* jobvr, lapack_int* n, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* w, lapack_complex_double* vl, + lapack_int* ldvl, lapack_complex_double* vr, + lapack_int* ldvr, lapack_complex_double* work, + lapack_int* lwork, double* rwork, lapack_int *info ); +void LAPACK_sgeevx( char* balanc, char* jobvl, char* jobvr, char* sense, + lapack_int* n, float* a, lapack_int* lda, float* wr, + float* wi, float* vl, lapack_int* ldvl, float* vr, + lapack_int* ldvr, lapack_int* ilo, lapack_int* ihi, + float* scale, float* abnrm, float* rconde, float* rcondv, + float* work, lapack_int* lwork, lapack_int* iwork, + lapack_int *info ); +void LAPACK_dgeevx( char* balanc, char* jobvl, char* jobvr, char* sense, + lapack_int* n, double* a, lapack_int* lda, double* wr, + double* wi, double* vl, lapack_int* ldvl, double* vr, + lapack_int* ldvr, lapack_int* ilo, lapack_int* ihi, + double* scale, double* abnrm, double* rconde, + double* rcondv, double* work, lapack_int* lwork, + lapack_int* iwork, lapack_int *info ); +void LAPACK_cgeevx( char* balanc, char* jobvl, char* jobvr, char* sense, + lapack_int* n, lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* w, lapack_complex_float* vl, + lapack_int* ldvl, lapack_complex_float* vr, + lapack_int* ldvr, lapack_int* ilo, lapack_int* ihi, + float* scale, float* abnrm, float* rconde, float* rcondv, + lapack_complex_float* work, lapack_int* lwork, float* rwork, + lapack_int *info ); +void LAPACK_zgeevx( char* balanc, char* jobvl, char* jobvr, char* sense, + lapack_int* n, lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* w, lapack_complex_double* vl, + lapack_int* ldvl, lapack_complex_double* vr, + lapack_int* ldvr, lapack_int* ilo, lapack_int* ihi, + double* scale, double* abnrm, double* rconde, + double* rcondv, lapack_complex_double* work, + lapack_int* lwork, double* rwork, lapack_int *info ); +void LAPACK_sgesvd( char* jobu, char* jobvt, lapack_int* m, lapack_int* n, + float* a, lapack_int* lda, float* s, float* u, + lapack_int* ldu, float* vt, lapack_int* ldvt, float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_dgesvd( char* jobu, char* jobvt, lapack_int* m, lapack_int* n, + double* a, lapack_int* lda, double* s, double* u, + lapack_int* ldu, double* vt, lapack_int* ldvt, double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_cgesvd( char* jobu, char* jobvt, lapack_int* m, lapack_int* n, + lapack_complex_float* a, lapack_int* lda, float* s, + lapack_complex_float* u, lapack_int* ldu, + lapack_complex_float* vt, lapack_int* ldvt, + lapack_complex_float* work, lapack_int* lwork, float* rwork, + lapack_int *info ); +void LAPACK_zgesvd( char* jobu, char* jobvt, lapack_int* m, lapack_int* n, + lapack_complex_double* a, lapack_int* lda, double* s, + lapack_complex_double* u, lapack_int* ldu, + lapack_complex_double* vt, lapack_int* ldvt, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_int *info ); +void LAPACK_sgesdd( char* jobz, lapack_int* m, lapack_int* n, float* a, + lapack_int* lda, float* s, float* u, lapack_int* ldu, + float* vt, lapack_int* ldvt, float* work, lapack_int* lwork, + lapack_int* iwork, lapack_int *info ); +void LAPACK_dgesdd( char* jobz, lapack_int* m, lapack_int* n, double* a, + lapack_int* lda, double* s, double* u, lapack_int* ldu, + double* vt, lapack_int* ldvt, double* work, + lapack_int* lwork, lapack_int* iwork, lapack_int *info ); +void LAPACK_cgesdd( char* jobz, lapack_int* m, lapack_int* n, + lapack_complex_float* a, lapack_int* lda, float* s, + lapack_complex_float* u, lapack_int* ldu, + lapack_complex_float* vt, lapack_int* ldvt, + lapack_complex_float* work, lapack_int* lwork, float* rwork, + lapack_int* iwork, lapack_int *info ); +void LAPACK_zgesdd( char* jobz, lapack_int* m, lapack_int* n, + lapack_complex_double* a, lapack_int* lda, double* s, + lapack_complex_double* u, lapack_int* ldu, + lapack_complex_double* vt, lapack_int* ldvt, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_int* iwork, lapack_int *info ); +void LAPACK_dgejsv( char* joba, char* jobu, char* jobv, char* jobr, char* jobt, + char* jobp, lapack_int* m, lapack_int* n, double* a, + lapack_int* lda, double* sva, double* u, lapack_int* ldu, + double* v, lapack_int* ldv, double* work, lapack_int* lwork, + lapack_int* iwork, lapack_int *info ); +void LAPACK_sgejsv( char* joba, char* jobu, char* jobv, char* jobr, char* jobt, + char* jobp, lapack_int* m, lapack_int* n, float* a, + lapack_int* lda, float* sva, float* u, lapack_int* ldu, + float* v, lapack_int* ldv, float* work, lapack_int* lwork, + lapack_int* iwork, lapack_int *info ); +void LAPACK_dgesvj( char* joba, char* jobu, char* jobv, lapack_int* m, + lapack_int* n, double* a, lapack_int* lda, double* sva, + lapack_int* mv, double* v, lapack_int* ldv, double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_sgesvj( char* joba, char* jobu, char* jobv, lapack_int* m, + lapack_int* n, float* a, lapack_int* lda, float* sva, + lapack_int* mv, float* v, lapack_int* ldv, float* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_sggsvd( char* jobu, char* jobv, char* jobq, lapack_int* m, + lapack_int* n, lapack_int* p, lapack_int* k, lapack_int* l, + float* a, lapack_int* lda, float* b, lapack_int* ldb, + float* alpha, float* beta, float* u, lapack_int* ldu, + float* v, lapack_int* ldv, float* q, lapack_int* ldq, + float* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_dggsvd( char* jobu, char* jobv, char* jobq, lapack_int* m, + lapack_int* n, lapack_int* p, lapack_int* k, lapack_int* l, + double* a, lapack_int* lda, double* b, lapack_int* ldb, + double* alpha, double* beta, double* u, lapack_int* ldu, + double* v, lapack_int* ldv, double* q, lapack_int* ldq, + double* work, lapack_int* iwork, lapack_int *info ); +void LAPACK_cggsvd( char* jobu, char* jobv, char* jobq, lapack_int* m, + lapack_int* n, lapack_int* p, lapack_int* k, lapack_int* l, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, float* alpha, + float* beta, lapack_complex_float* u, lapack_int* ldu, + lapack_complex_float* v, lapack_int* ldv, + lapack_complex_float* q, lapack_int* ldq, + lapack_complex_float* work, float* rwork, lapack_int* iwork, + lapack_int *info ); +void LAPACK_zggsvd( char* jobu, char* jobv, char* jobq, lapack_int* m, + lapack_int* n, lapack_int* p, lapack_int* k, lapack_int* l, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, double* alpha, + double* beta, lapack_complex_double* u, lapack_int* ldu, + lapack_complex_double* v, lapack_int* ldv, + lapack_complex_double* q, lapack_int* ldq, + lapack_complex_double* work, double* rwork, + lapack_int* iwork, lapack_int *info ); +void LAPACK_ssygv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n, + float* a, lapack_int* lda, float* b, lapack_int* ldb, + float* w, float* work, lapack_int* lwork, lapack_int *info ); +void LAPACK_dsygv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n, + double* a, lapack_int* lda, double* b, lapack_int* ldb, + double* w, double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_chegv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, float* w, + lapack_complex_float* work, lapack_int* lwork, float* rwork, + lapack_int *info ); +void LAPACK_zhegv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, double* w, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_int *info ); +void LAPACK_ssygvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n, + float* a, lapack_int* lda, float* b, lapack_int* ldb, + float* w, float* work, lapack_int* lwork, lapack_int* iwork, + lapack_int* liwork, lapack_int *info ); +void LAPACK_dsygvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n, + double* a, lapack_int* lda, double* b, lapack_int* ldb, + double* w, double* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_chegvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, float* w, + lapack_complex_float* work, lapack_int* lwork, float* rwork, + lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork, + lapack_int *info ); +void LAPACK_zhegvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, double* w, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_int* lrwork, lapack_int* iwork, + lapack_int* liwork, lapack_int *info ); +void LAPACK_ssygvx( lapack_int* itype, char* jobz, char* range, char* uplo, + lapack_int* n, float* a, lapack_int* lda, float* b, + lapack_int* ldb, float* vl, float* vu, lapack_int* il, + lapack_int* iu, float* abstol, lapack_int* m, float* w, + float* z, lapack_int* ldz, float* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* ifail, lapack_int *info ); +void LAPACK_dsygvx( lapack_int* itype, char* jobz, char* range, char* uplo, + lapack_int* n, double* a, lapack_int* lda, double* b, + lapack_int* ldb, double* vl, double* vu, lapack_int* il, + lapack_int* iu, double* abstol, lapack_int* m, double* w, + double* z, lapack_int* ldz, double* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* ifail, lapack_int *info ); +void LAPACK_chegvx( lapack_int* itype, char* jobz, char* range, char* uplo, + lapack_int* n, lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, float* vl, + float* vu, lapack_int* il, lapack_int* iu, float* abstol, + lapack_int* m, float* w, lapack_complex_float* z, + lapack_int* ldz, lapack_complex_float* work, + lapack_int* lwork, float* rwork, lapack_int* iwork, + lapack_int* ifail, lapack_int *info ); +void LAPACK_zhegvx( lapack_int* itype, char* jobz, char* range, char* uplo, + lapack_int* n, lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, double* vl, + double* vu, lapack_int* il, lapack_int* iu, double* abstol, + lapack_int* m, double* w, lapack_complex_double* z, + lapack_int* ldz, lapack_complex_double* work, + lapack_int* lwork, double* rwork, lapack_int* iwork, + lapack_int* ifail, lapack_int *info ); +void LAPACK_sspgv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n, + float* ap, float* bp, float* w, float* z, lapack_int* ldz, + float* work, lapack_int *info ); +void LAPACK_dspgv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n, + double* ap, double* bp, double* w, double* z, + lapack_int* ldz, double* work, lapack_int *info ); +void LAPACK_chpgv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n, + lapack_complex_float* ap, lapack_complex_float* bp, float* w, + lapack_complex_float* z, lapack_int* ldz, + lapack_complex_float* work, float* rwork, lapack_int *info ); +void LAPACK_zhpgv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n, + lapack_complex_double* ap, lapack_complex_double* bp, + double* w, lapack_complex_double* z, lapack_int* ldz, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_sspgvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n, + float* ap, float* bp, float* w, float* z, lapack_int* ldz, + float* work, lapack_int* lwork, lapack_int* iwork, + lapack_int* liwork, lapack_int *info ); +void LAPACK_dspgvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n, + double* ap, double* bp, double* w, double* z, + lapack_int* ldz, double* work, lapack_int* lwork, + lapack_int* iwork, lapack_int* liwork, lapack_int *info ); +void LAPACK_chpgvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n, + lapack_complex_float* ap, lapack_complex_float* bp, + float* w, lapack_complex_float* z, lapack_int* ldz, + lapack_complex_float* work, lapack_int* lwork, float* rwork, + lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork, + lapack_int *info ); +void LAPACK_zhpgvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n, + lapack_complex_double* ap, lapack_complex_double* bp, + double* w, lapack_complex_double* z, lapack_int* ldz, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_int* lrwork, lapack_int* iwork, + lapack_int* liwork, lapack_int *info ); +void LAPACK_sspgvx( lapack_int* itype, char* jobz, char* range, char* uplo, + lapack_int* n, float* ap, float* bp, float* vl, float* vu, + lapack_int* il, lapack_int* iu, float* abstol, + lapack_int* m, float* w, float* z, lapack_int* ldz, + float* work, lapack_int* iwork, lapack_int* ifail, + lapack_int *info ); +void LAPACK_dspgvx( lapack_int* itype, char* jobz, char* range, char* uplo, + lapack_int* n, double* ap, double* bp, double* vl, + double* vu, lapack_int* il, lapack_int* iu, double* abstol, + lapack_int* m, double* w, double* z, lapack_int* ldz, + double* work, lapack_int* iwork, lapack_int* ifail, + lapack_int *info ); +void LAPACK_chpgvx( lapack_int* itype, char* jobz, char* range, char* uplo, + lapack_int* n, lapack_complex_float* ap, + lapack_complex_float* bp, float* vl, float* vu, + lapack_int* il, lapack_int* iu, float* abstol, + lapack_int* m, float* w, lapack_complex_float* z, + lapack_int* ldz, lapack_complex_float* work, float* rwork, + lapack_int* iwork, lapack_int* ifail, lapack_int *info ); +void LAPACK_zhpgvx( lapack_int* itype, char* jobz, char* range, char* uplo, + lapack_int* n, lapack_complex_double* ap, + lapack_complex_double* bp, double* vl, double* vu, + lapack_int* il, lapack_int* iu, double* abstol, + lapack_int* m, double* w, lapack_complex_double* z, + lapack_int* ldz, lapack_complex_double* work, double* rwork, + lapack_int* iwork, lapack_int* ifail, lapack_int *info ); +void LAPACK_ssbgv( char* jobz, char* uplo, lapack_int* n, lapack_int* ka, + lapack_int* kb, float* ab, lapack_int* ldab, float* bb, + lapack_int* ldbb, float* w, float* z, lapack_int* ldz, + float* work, lapack_int *info ); +void LAPACK_dsbgv( char* jobz, char* uplo, lapack_int* n, lapack_int* ka, + lapack_int* kb, double* ab, lapack_int* ldab, double* bb, + lapack_int* ldbb, double* w, double* z, lapack_int* ldz, + double* work, lapack_int *info ); +void LAPACK_chbgv( char* jobz, char* uplo, lapack_int* n, lapack_int* ka, + lapack_int* kb, lapack_complex_float* ab, lapack_int* ldab, + lapack_complex_float* bb, lapack_int* ldbb, float* w, + lapack_complex_float* z, lapack_int* ldz, + lapack_complex_float* work, float* rwork, lapack_int *info ); +void LAPACK_zhbgv( char* jobz, char* uplo, lapack_int* n, lapack_int* ka, + lapack_int* kb, lapack_complex_double* ab, lapack_int* ldab, + lapack_complex_double* bb, lapack_int* ldbb, double* w, + lapack_complex_double* z, lapack_int* ldz, + lapack_complex_double* work, double* rwork, + lapack_int *info ); +void LAPACK_ssbgvd( char* jobz, char* uplo, lapack_int* n, lapack_int* ka, + lapack_int* kb, float* ab, lapack_int* ldab, float* bb, + lapack_int* ldbb, float* w, float* z, lapack_int* ldz, + float* work, lapack_int* lwork, lapack_int* iwork, + lapack_int* liwork, lapack_int *info ); +void LAPACK_dsbgvd( char* jobz, char* uplo, lapack_int* n, lapack_int* ka, + lapack_int* kb, double* ab, lapack_int* ldab, double* bb, + lapack_int* ldbb, double* w, double* z, lapack_int* ldz, + double* work, lapack_int* lwork, lapack_int* iwork, + lapack_int* liwork, lapack_int *info ); +void LAPACK_chbgvd( char* jobz, char* uplo, lapack_int* n, lapack_int* ka, + lapack_int* kb, lapack_complex_float* ab, lapack_int* ldab, + lapack_complex_float* bb, lapack_int* ldbb, float* w, + lapack_complex_float* z, lapack_int* ldz, + lapack_complex_float* work, lapack_int* lwork, float* rwork, + lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork, + lapack_int *info ); +void LAPACK_zhbgvd( char* jobz, char* uplo, lapack_int* n, lapack_int* ka, + lapack_int* kb, lapack_complex_double* ab, lapack_int* ldab, + lapack_complex_double* bb, lapack_int* ldbb, double* w, + lapack_complex_double* z, lapack_int* ldz, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_int* lrwork, lapack_int* iwork, + lapack_int* liwork, lapack_int *info ); +void LAPACK_ssbgvx( char* jobz, char* range, char* uplo, lapack_int* n, + lapack_int* ka, lapack_int* kb, float* ab, lapack_int* ldab, + float* bb, lapack_int* ldbb, float* q, lapack_int* ldq, + float* vl, float* vu, lapack_int* il, lapack_int* iu, + float* abstol, lapack_int* m, float* w, float* z, + lapack_int* ldz, float* work, lapack_int* iwork, + lapack_int* ifail, lapack_int *info ); +void LAPACK_dsbgvx( char* jobz, char* range, char* uplo, lapack_int* n, + lapack_int* ka, lapack_int* kb, double* ab, + lapack_int* ldab, double* bb, lapack_int* ldbb, double* q, + lapack_int* ldq, double* vl, double* vu, lapack_int* il, + lapack_int* iu, double* abstol, lapack_int* m, double* w, + double* z, lapack_int* ldz, double* work, lapack_int* iwork, + lapack_int* ifail, lapack_int *info ); +void LAPACK_chbgvx( char* jobz, char* range, char* uplo, lapack_int* n, + lapack_int* ka, lapack_int* kb, lapack_complex_float* ab, + lapack_int* ldab, lapack_complex_float* bb, + lapack_int* ldbb, lapack_complex_float* q, lapack_int* ldq, + float* vl, float* vu, lapack_int* il, lapack_int* iu, + float* abstol, lapack_int* m, float* w, + lapack_complex_float* z, lapack_int* ldz, + lapack_complex_float* work, float* rwork, lapack_int* iwork, + lapack_int* ifail, lapack_int *info ); +void LAPACK_zhbgvx( char* jobz, char* range, char* uplo, lapack_int* n, + lapack_int* ka, lapack_int* kb, lapack_complex_double* ab, + lapack_int* ldab, lapack_complex_double* bb, + lapack_int* ldbb, lapack_complex_double* q, lapack_int* ldq, + double* vl, double* vu, lapack_int* il, lapack_int* iu, + double* abstol, lapack_int* m, double* w, + lapack_complex_double* z, lapack_int* ldz, + lapack_complex_double* work, double* rwork, + lapack_int* iwork, lapack_int* ifail, lapack_int *info ); +void LAPACK_sgges( char* jobvsl, char* jobvsr, char* sort, + LAPACK_S_SELECT3 selctg, lapack_int* n, float* a, + lapack_int* lda, float* b, lapack_int* ldb, lapack_int* sdim, + float* alphar, float* alphai, float* beta, float* vsl, + lapack_int* ldvsl, float* vsr, lapack_int* ldvsr, + float* work, lapack_int* lwork, lapack_logical* bwork, + lapack_int *info ); +void LAPACK_dgges( char* jobvsl, char* jobvsr, char* sort, + LAPACK_D_SELECT3 selctg, lapack_int* n, double* a, + lapack_int* lda, double* b, lapack_int* ldb, + lapack_int* sdim, double* alphar, double* alphai, + double* beta, double* vsl, lapack_int* ldvsl, double* vsr, + lapack_int* ldvsr, double* work, lapack_int* lwork, + lapack_logical* bwork, lapack_int *info ); +void LAPACK_cgges( char* jobvsl, char* jobvsr, char* sort, + LAPACK_C_SELECT2 selctg, lapack_int* n, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, lapack_int* sdim, + lapack_complex_float* alpha, lapack_complex_float* beta, + lapack_complex_float* vsl, lapack_int* ldvsl, + lapack_complex_float* vsr, lapack_int* ldvsr, + lapack_complex_float* work, lapack_int* lwork, float* rwork, + lapack_logical* bwork, lapack_int *info ); +void LAPACK_zgges( char* jobvsl, char* jobvsr, char* sort, + LAPACK_Z_SELECT2 selctg, lapack_int* n, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, lapack_int* sdim, + lapack_complex_double* alpha, lapack_complex_double* beta, + lapack_complex_double* vsl, lapack_int* ldvsl, + lapack_complex_double* vsr, lapack_int* ldvsr, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_logical* bwork, lapack_int *info ); +void LAPACK_sggesx( char* jobvsl, char* jobvsr, char* sort, + LAPACK_S_SELECT3 selctg, char* sense, lapack_int* n, + float* a, lapack_int* lda, float* b, lapack_int* ldb, + lapack_int* sdim, float* alphar, float* alphai, float* beta, + float* vsl, lapack_int* ldvsl, float* vsr, + lapack_int* ldvsr, float* rconde, float* rcondv, + float* work, lapack_int* lwork, lapack_int* iwork, + lapack_int* liwork, lapack_logical* bwork, + lapack_int *info ); +void LAPACK_dggesx( char* jobvsl, char* jobvsr, char* sort, + LAPACK_D_SELECT3 selctg, char* sense, lapack_int* n, + double* a, lapack_int* lda, double* b, lapack_int* ldb, + lapack_int* sdim, double* alphar, double* alphai, + double* beta, double* vsl, lapack_int* ldvsl, double* vsr, + lapack_int* ldvsr, double* rconde, double* rcondv, + double* work, lapack_int* lwork, lapack_int* iwork, + lapack_int* liwork, lapack_logical* bwork, + lapack_int *info ); +void LAPACK_cggesx( char* jobvsl, char* jobvsr, char* sort, + LAPACK_C_SELECT2 selctg, char* sense, lapack_int* n, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, lapack_int* sdim, + lapack_complex_float* alpha, lapack_complex_float* beta, + lapack_complex_float* vsl, lapack_int* ldvsl, + lapack_complex_float* vsr, lapack_int* ldvsr, float* rconde, + float* rcondv, lapack_complex_float* work, + lapack_int* lwork, float* rwork, lapack_int* iwork, + lapack_int* liwork, lapack_logical* bwork, + lapack_int *info ); +void LAPACK_zggesx( char* jobvsl, char* jobvsr, char* sort, + LAPACK_Z_SELECT2 selctg, char* sense, lapack_int* n, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, lapack_int* sdim, + lapack_complex_double* alpha, lapack_complex_double* beta, + lapack_complex_double* vsl, lapack_int* ldvsl, + lapack_complex_double* vsr, lapack_int* ldvsr, + double* rconde, double* rcondv, lapack_complex_double* work, + lapack_int* lwork, double* rwork, lapack_int* iwork, + lapack_int* liwork, lapack_logical* bwork, + lapack_int *info ); +void LAPACK_sggev( char* jobvl, char* jobvr, lapack_int* n, float* a, + lapack_int* lda, float* b, lapack_int* ldb, float* alphar, + float* alphai, float* beta, float* vl, lapack_int* ldvl, + float* vr, lapack_int* ldvr, float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_dggev( char* jobvl, char* jobvr, lapack_int* n, double* a, + lapack_int* lda, double* b, lapack_int* ldb, double* alphar, + double* alphai, double* beta, double* vl, lapack_int* ldvl, + double* vr, lapack_int* ldvr, double* work, + lapack_int* lwork, lapack_int *info ); +void LAPACK_cggev( char* jobvl, char* jobvr, lapack_int* n, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* alpha, lapack_complex_float* beta, + lapack_complex_float* vl, lapack_int* ldvl, + lapack_complex_float* vr, lapack_int* ldvr, + lapack_complex_float* work, lapack_int* lwork, float* rwork, + lapack_int *info ); +void LAPACK_zggev( char* jobvl, char* jobvr, lapack_int* n, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* alpha, lapack_complex_double* beta, + lapack_complex_double* vl, lapack_int* ldvl, + lapack_complex_double* vr, lapack_int* ldvr, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_int *info ); +void LAPACK_sggevx( char* balanc, char* jobvl, char* jobvr, char* sense, + lapack_int* n, float* a, lapack_int* lda, float* b, + lapack_int* ldb, float* alphar, float* alphai, float* beta, + float* vl, lapack_int* ldvl, float* vr, lapack_int* ldvr, + lapack_int* ilo, lapack_int* ihi, float* lscale, + float* rscale, float* abnrm, float* bbnrm, float* rconde, + float* rcondv, float* work, lapack_int* lwork, + lapack_int* iwork, lapack_logical* bwork, + lapack_int *info ); +void LAPACK_dggevx( char* balanc, char* jobvl, char* jobvr, char* sense, + lapack_int* n, double* a, lapack_int* lda, double* b, + lapack_int* ldb, double* alphar, double* alphai, + double* beta, double* vl, lapack_int* ldvl, double* vr, + lapack_int* ldvr, lapack_int* ilo, lapack_int* ihi, + double* lscale, double* rscale, double* abnrm, + double* bbnrm, double* rconde, double* rcondv, double* work, + lapack_int* lwork, lapack_int* iwork, lapack_logical* bwork, + lapack_int *info ); +void LAPACK_cggevx( char* balanc, char* jobvl, char* jobvr, char* sense, + lapack_int* n, lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* alpha, lapack_complex_float* beta, + lapack_complex_float* vl, lapack_int* ldvl, + lapack_complex_float* vr, lapack_int* ldvr, lapack_int* ilo, + lapack_int* ihi, float* lscale, float* rscale, float* abnrm, + float* bbnrm, float* rconde, float* rcondv, + lapack_complex_float* work, lapack_int* lwork, float* rwork, + lapack_int* iwork, lapack_logical* bwork, + lapack_int *info ); +void LAPACK_zggevx( char* balanc, char* jobvl, char* jobvr, char* sense, + lapack_int* n, lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* alpha, lapack_complex_double* beta, + lapack_complex_double* vl, lapack_int* ldvl, + lapack_complex_double* vr, lapack_int* ldvr, + lapack_int* ilo, lapack_int* ihi, double* lscale, + double* rscale, double* abnrm, double* bbnrm, + double* rconde, double* rcondv, lapack_complex_double* work, + lapack_int* lwork, double* rwork, lapack_int* iwork, + lapack_logical* bwork, lapack_int *info ); +void LAPACK_dsfrk( char* transr, char* uplo, char* trans, lapack_int* n, + lapack_int* k, double* alpha, const double* a, + lapack_int* lda, double* beta, double* c ); +void LAPACK_ssfrk( char* transr, char* uplo, char* trans, lapack_int* n, + lapack_int* k, float* alpha, const float* a, lapack_int* lda, + float* beta, float* c ); +void LAPACK_zhfrk( char* transr, char* uplo, char* trans, lapack_int* n, + lapack_int* k, double* alpha, const lapack_complex_double* a, + lapack_int* lda, double* beta, lapack_complex_double* c ); +void LAPACK_chfrk( char* transr, char* uplo, char* trans, lapack_int* n, + lapack_int* k, float* alpha, const lapack_complex_float* a, + lapack_int* lda, float* beta, lapack_complex_float* c ); +void LAPACK_dtfsm( char* transr, char* side, char* uplo, char* trans, + char* diag, lapack_int* m, lapack_int* n, double* alpha, + const double* a, double* b, lapack_int* ldb ); +void LAPACK_stfsm( char* transr, char* side, char* uplo, char* trans, + char* diag, lapack_int* m, lapack_int* n, float* alpha, + const float* a, float* b, lapack_int* ldb ); +void LAPACK_ztfsm( char* transr, char* side, char* uplo, char* trans, + char* diag, lapack_int* m, lapack_int* n, + lapack_complex_double* alpha, const lapack_complex_double* a, + lapack_complex_double* b, lapack_int* ldb ); +void LAPACK_ctfsm( char* transr, char* side, char* uplo, char* trans, + char* diag, lapack_int* m, lapack_int* n, + lapack_complex_float* alpha, const lapack_complex_float* a, + lapack_complex_float* b, lapack_int* ldb ); +void LAPACK_dtfttp( char* transr, char* uplo, lapack_int* n, const double* arf, + double* ap, lapack_int *info ); +void LAPACK_stfttp( char* transr, char* uplo, lapack_int* n, const float* arf, + float* ap, lapack_int *info ); +void LAPACK_ztfttp( char* transr, char* uplo, lapack_int* n, + const lapack_complex_double* arf, lapack_complex_double* ap, + lapack_int *info ); +void LAPACK_ctfttp( char* transr, char* uplo, lapack_int* n, + const lapack_complex_float* arf, lapack_complex_float* ap, + lapack_int *info ); +void LAPACK_dtfttr( char* transr, char* uplo, lapack_int* n, const double* arf, + double* a, lapack_int* lda, lapack_int *info ); +void LAPACK_stfttr( char* transr, char* uplo, lapack_int* n, const float* arf, + float* a, lapack_int* lda, lapack_int *info ); +void LAPACK_ztfttr( char* transr, char* uplo, lapack_int* n, + const lapack_complex_double* arf, lapack_complex_double* a, + lapack_int* lda, lapack_int *info ); +void LAPACK_ctfttr( char* transr, char* uplo, lapack_int* n, + const lapack_complex_float* arf, lapack_complex_float* a, + lapack_int* lda, lapack_int *info ); +void LAPACK_dtpttf( char* transr, char* uplo, lapack_int* n, const double* ap, + double* arf, lapack_int *info ); +void LAPACK_stpttf( char* transr, char* uplo, lapack_int* n, const float* ap, + float* arf, lapack_int *info ); +void LAPACK_ztpttf( char* transr, char* uplo, lapack_int* n, + const lapack_complex_double* ap, lapack_complex_double* arf, + lapack_int *info ); +void LAPACK_ctpttf( char* transr, char* uplo, lapack_int* n, + const lapack_complex_float* ap, lapack_complex_float* arf, + lapack_int *info ); +void LAPACK_dtpttr( char* uplo, lapack_int* n, const double* ap, double* a, + lapack_int* lda, lapack_int *info ); +void LAPACK_stpttr( char* uplo, lapack_int* n, const float* ap, float* a, + lapack_int* lda, lapack_int *info ); +void LAPACK_ztpttr( char* uplo, lapack_int* n, const lapack_complex_double* ap, + lapack_complex_double* a, lapack_int* lda, + lapack_int *info ); +void LAPACK_ctpttr( char* uplo, lapack_int* n, const lapack_complex_float* ap, + lapack_complex_float* a, lapack_int* lda, + lapack_int *info ); +void LAPACK_dtrttf( char* transr, char* uplo, lapack_int* n, const double* a, + lapack_int* lda, double* arf, lapack_int *info ); +void LAPACK_strttf( char* transr, char* uplo, lapack_int* n, const float* a, + lapack_int* lda, float* arf, lapack_int *info ); +void LAPACK_ztrttf( char* transr, char* uplo, lapack_int* n, + const lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* arf, lapack_int *info ); +void LAPACK_ctrttf( char* transr, char* uplo, lapack_int* n, + const lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* arf, lapack_int *info ); +void LAPACK_dtrttp( char* uplo, lapack_int* n, const double* a, lapack_int* lda, + double* ap, lapack_int *info ); +void LAPACK_strttp( char* uplo, lapack_int* n, const float* a, lapack_int* lda, + float* ap, lapack_int *info ); +void LAPACK_ztrttp( char* uplo, lapack_int* n, const lapack_complex_double* a, + lapack_int* lda, lapack_complex_double* ap, + lapack_int *info ); +void LAPACK_ctrttp( char* uplo, lapack_int* n, const lapack_complex_float* a, + lapack_int* lda, lapack_complex_float* ap, + lapack_int *info ); +void LAPACK_sgeqrfp( lapack_int* m, lapack_int* n, float* a, lapack_int* lda, + float* tau, float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_dgeqrfp( lapack_int* m, lapack_int* n, double* a, lapack_int* lda, + double* tau, double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_cgeqrfp( lapack_int* m, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_complex_float* tau, + lapack_complex_float* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_zgeqrfp( lapack_int* m, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_complex_double* tau, + lapack_complex_double* work, lapack_int* lwork, + lapack_int *info ); +void LAPACK_clacgv( lapack_int* n, lapack_complex_float* x, lapack_int* incx ); +void LAPACK_zlacgv( lapack_int* n, lapack_complex_double* x, lapack_int* incx ); +void LAPACK_slarnv( lapack_int* idist, lapack_int* iseed, lapack_int* n, + float* x ); +void LAPACK_dlarnv( lapack_int* idist, lapack_int* iseed, lapack_int* n, + double* x ); +void LAPACK_clarnv( lapack_int* idist, lapack_int* iseed, lapack_int* n, + lapack_complex_float* x ); +void LAPACK_zlarnv( lapack_int* idist, lapack_int* iseed, lapack_int* n, + lapack_complex_double* x ); +void LAPACK_sgeqr2( lapack_int* m, lapack_int* n, float* a, lapack_int* lda, + float* tau, float* work, lapack_int *info ); +void LAPACK_dgeqr2( lapack_int* m, lapack_int* n, double* a, lapack_int* lda, + double* tau, double* work, lapack_int *info ); +void LAPACK_cgeqr2( lapack_int* m, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_complex_float* tau, + lapack_complex_float* work, lapack_int *info ); +void LAPACK_zgeqr2( lapack_int* m, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_complex_double* tau, + lapack_complex_double* work, lapack_int *info ); +void LAPACK_slacpy( char* uplo, lapack_int* m, lapack_int* n, const float* a, + lapack_int* lda, float* b, lapack_int* ldb ); +void LAPACK_dlacpy( char* uplo, lapack_int* m, lapack_int* n, const double* a, + lapack_int* lda, double* b, lapack_int* ldb ); +void LAPACK_clacpy( char* uplo, lapack_int* m, lapack_int* n, + const lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb ); +void LAPACK_zlacpy( char* uplo, lapack_int* m, lapack_int* n, + const lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb ); +void LAPACK_sgetf2( lapack_int* m, lapack_int* n, float* a, lapack_int* lda, + lapack_int* ipiv, lapack_int *info ); +void LAPACK_dgetf2( lapack_int* m, lapack_int* n, double* a, lapack_int* lda, + lapack_int* ipiv, lapack_int *info ); +void LAPACK_cgetf2( lapack_int* m, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_int* ipiv, lapack_int *info ); +void LAPACK_zgetf2( lapack_int* m, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_int* ipiv, lapack_int *info ); +void LAPACK_slaswp( lapack_int* n, float* a, lapack_int* lda, lapack_int* k1, + lapack_int* k2, const lapack_int* ipiv, lapack_int* incx ); +void LAPACK_dlaswp( lapack_int* n, double* a, lapack_int* lda, lapack_int* k1, + lapack_int* k2, const lapack_int* ipiv, lapack_int* incx ); +void LAPACK_claswp( lapack_int* n, lapack_complex_float* a, lapack_int* lda, + lapack_int* k1, lapack_int* k2, const lapack_int* ipiv, + lapack_int* incx ); +void LAPACK_zlaswp( lapack_int* n, lapack_complex_double* a, lapack_int* lda, + lapack_int* k1, lapack_int* k2, const lapack_int* ipiv, + lapack_int* incx ); +float LAPACK_slange( char* norm, lapack_int* m, lapack_int* n, const float* a, + lapack_int* lda, float* work ); +double LAPACK_dlange( char* norm, lapack_int* m, lapack_int* n, const double* a, + lapack_int* lda, double* work ); +float LAPACK_clange( char* norm, lapack_int* m, lapack_int* n, + const lapack_complex_float* a, lapack_int* lda, float* work ); +double LAPACK_zlange( char* norm, lapack_int* m, lapack_int* n, + const lapack_complex_double* a, lapack_int* lda, double* work ); +float LAPACK_clanhe( char* norm, char* uplo, lapack_int* n, + const lapack_complex_float* a, lapack_int* lda, float* work ); +double LAPACK_zlanhe( char* norm, char* uplo, lapack_int* n, + const lapack_complex_double* a, lapack_int* lda, double* work ); +float LAPACK_slansy( char* norm, char* uplo, lapack_int* n, const float* a, + lapack_int* lda, float* work ); +double LAPACK_dlansy( char* norm, char* uplo, lapack_int* n, const double* a, + lapack_int* lda, double* work ); +float LAPACK_clansy( char* norm, char* uplo, lapack_int* n, + const lapack_complex_float* a, lapack_int* lda, float* work ); +double LAPACK_zlansy( char* norm, char* uplo, lapack_int* n, + const lapack_complex_double* a, lapack_int* lda, double* work ); +float LAPACK_slantr( char* norm, char* uplo, char* diag, lapack_int* m, + lapack_int* n, const float* a, lapack_int* lda, float* work ); +double LAPACK_dlantr( char* norm, char* uplo, char* diag, lapack_int* m, + lapack_int* n, const double* a, lapack_int* lda, double* work ); +float LAPACK_clantr( char* norm, char* uplo, char* diag, lapack_int* m, + lapack_int* n, const lapack_complex_float* a, lapack_int* lda, + float* work ); +double LAPACK_zlantr( char* norm, char* uplo, char* diag, lapack_int* m, + lapack_int* n, const lapack_complex_double* a, lapack_int* lda, + double* work ); +float LAPACK_slamch( char* cmach ); +double LAPACK_dlamch( char* cmach ); +void LAPACK_sgelq2( lapack_int* m, lapack_int* n, float* a, lapack_int* lda, + float* tau, float* work, lapack_int *info ); +void LAPACK_dgelq2( lapack_int* m, lapack_int* n, double* a, lapack_int* lda, + double* tau, double* work, lapack_int *info ); +void LAPACK_cgelq2( lapack_int* m, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_complex_float* tau, + lapack_complex_float* work, lapack_int *info ); +void LAPACK_zgelq2( lapack_int* m, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_complex_double* tau, + lapack_complex_double* work, lapack_int *info ); +void LAPACK_slarfb( char* side, char* trans, char* direct, char* storev, + lapack_int* m, lapack_int* n, lapack_int* k, const float* v, + lapack_int* ldv, const float* t, lapack_int* ldt, float* c, + lapack_int* ldc, float* work, lapack_int* ldwork ); +void LAPACK_dlarfb( char* side, char* trans, char* direct, char* storev, + lapack_int* m, lapack_int* n, lapack_int* k, + const double* v, lapack_int* ldv, const double* t, + lapack_int* ldt, double* c, lapack_int* ldc, double* work, + lapack_int* ldwork ); +void LAPACK_clarfb( char* side, char* trans, char* direct, char* storev, + lapack_int* m, lapack_int* n, lapack_int* k, + const lapack_complex_float* v, lapack_int* ldv, + const lapack_complex_float* t, lapack_int* ldt, + lapack_complex_float* c, lapack_int* ldc, + lapack_complex_float* work, lapack_int* ldwork ); +void LAPACK_zlarfb( char* side, char* trans, char* direct, char* storev, + lapack_int* m, lapack_int* n, lapack_int* k, + const lapack_complex_double* v, lapack_int* ldv, + const lapack_complex_double* t, lapack_int* ldt, + lapack_complex_double* c, lapack_int* ldc, + lapack_complex_double* work, lapack_int* ldwork ); +void LAPACK_slarfg( lapack_int* n, float* alpha, float* x, lapack_int* incx, + float* tau ); +void LAPACK_dlarfg( lapack_int* n, double* alpha, double* x, lapack_int* incx, + double* tau ); +void LAPACK_clarfg( lapack_int* n, lapack_complex_float* alpha, + lapack_complex_float* x, lapack_int* incx, + lapack_complex_float* tau ); +void LAPACK_zlarfg( lapack_int* n, lapack_complex_double* alpha, + lapack_complex_double* x, lapack_int* incx, + lapack_complex_double* tau ); +void LAPACK_slarft( char* direct, char* storev, lapack_int* n, lapack_int* k, + const float* v, lapack_int* ldv, const float* tau, float* t, + lapack_int* ldt ); +void LAPACK_dlarft( char* direct, char* storev, lapack_int* n, lapack_int* k, + const double* v, lapack_int* ldv, const double* tau, + double* t, lapack_int* ldt ); +void LAPACK_clarft( char* direct, char* storev, lapack_int* n, lapack_int* k, + const lapack_complex_float* v, lapack_int* ldv, + const lapack_complex_float* tau, lapack_complex_float* t, + lapack_int* ldt ); +void LAPACK_zlarft( char* direct, char* storev, lapack_int* n, lapack_int* k, + const lapack_complex_double* v, lapack_int* ldv, + const lapack_complex_double* tau, lapack_complex_double* t, + lapack_int* ldt ); +void LAPACK_slarfx( char* side, lapack_int* m, lapack_int* n, const float* v, + float* tau, float* c, lapack_int* ldc, float* work ); +void LAPACK_dlarfx( char* side, lapack_int* m, lapack_int* n, const double* v, + double* tau, double* c, lapack_int* ldc, double* work ); +void LAPACK_clarfx( char* side, lapack_int* m, lapack_int* n, + const lapack_complex_float* v, lapack_complex_float* tau, + lapack_complex_float* c, lapack_int* ldc, + lapack_complex_float* work ); +void LAPACK_zlarfx( char* side, lapack_int* m, lapack_int* n, + const lapack_complex_double* v, lapack_complex_double* tau, + lapack_complex_double* c, lapack_int* ldc, + lapack_complex_double* work ); +void LAPACK_slatms( lapack_int* m, lapack_int* n, char* dist, lapack_int* iseed, + char* sym, float* d, lapack_int* mode, float* cond, + float* dmax, lapack_int* kl, lapack_int* ku, char* pack, + float* a, lapack_int* lda, float* work, lapack_int *info ); +void LAPACK_dlatms( lapack_int* m, lapack_int* n, char* dist, lapack_int* iseed, + char* sym, double* d, lapack_int* mode, double* cond, + double* dmax, lapack_int* kl, lapack_int* ku, char* pack, + double* a, lapack_int* lda, double* work, + lapack_int *info ); +void LAPACK_clatms( lapack_int* m, lapack_int* n, char* dist, lapack_int* iseed, + char* sym, float* d, lapack_int* mode, float* cond, + float* dmax, lapack_int* kl, lapack_int* ku, char* pack, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* work, lapack_int *info ); +void LAPACK_zlatms( lapack_int* m, lapack_int* n, char* dist, lapack_int* iseed, + char* sym, double* d, lapack_int* mode, double* cond, + double* dmax, lapack_int* kl, lapack_int* ku, char* pack, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* work, lapack_int *info ); +void LAPACK_slag2d( lapack_int* m, lapack_int* n, const float* sa, + lapack_int* ldsa, double* a, lapack_int* lda, + lapack_int *info ); +void LAPACK_dlag2s( lapack_int* m, lapack_int* n, const double* a, + lapack_int* lda, float* sa, lapack_int* ldsa, + lapack_int *info ); +void LAPACK_clag2z( lapack_int* m, lapack_int* n, + const lapack_complex_float* sa, lapack_int* ldsa, + lapack_complex_double* a, lapack_int* lda, + lapack_int *info ); +void LAPACK_zlag2c( lapack_int* m, lapack_int* n, + const lapack_complex_double* a, lapack_int* lda, + lapack_complex_float* sa, lapack_int* ldsa, + lapack_int *info ); +void LAPACK_slauum( char* uplo, lapack_int* n, float* a, lapack_int* lda, + lapack_int *info ); +void LAPACK_dlauum( char* uplo, lapack_int* n, double* a, lapack_int* lda, + lapack_int *info ); +void LAPACK_clauum( char* uplo, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_int *info ); +void LAPACK_zlauum( char* uplo, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_int *info ); +void LAPACK_slagge( lapack_int* m, lapack_int* n, lapack_int* kl, + lapack_int* ku, const float* d, float* a, lapack_int* lda, + lapack_int* iseed, float* work, lapack_int *info ); +void LAPACK_dlagge( lapack_int* m, lapack_int* n, lapack_int* kl, + lapack_int* ku, const double* d, double* a, lapack_int* lda, + lapack_int* iseed, double* work, lapack_int *info ); +void LAPACK_clagge( lapack_int* m, lapack_int* n, lapack_int* kl, + lapack_int* ku, const float* d, lapack_complex_float* a, + lapack_int* lda, lapack_int* iseed, + lapack_complex_float* work, lapack_int *info ); +void LAPACK_zlagge( lapack_int* m, lapack_int* n, lapack_int* kl, + lapack_int* ku, const double* d, lapack_complex_double* a, + lapack_int* lda, lapack_int* iseed, + lapack_complex_double* work, lapack_int *info ); +void LAPACK_slaset( char* uplo, lapack_int* m, lapack_int* n, float* alpha, + float* beta, float* a, lapack_int* lda ); +void LAPACK_dlaset( char* uplo, lapack_int* m, lapack_int* n, double* alpha, + double* beta, double* a, lapack_int* lda ); +void LAPACK_claset( char* uplo, lapack_int* m, lapack_int* n, + lapack_complex_float* alpha, lapack_complex_float* beta, + lapack_complex_float* a, lapack_int* lda ); +void LAPACK_zlaset( char* uplo, lapack_int* m, lapack_int* n, + lapack_complex_double* alpha, lapack_complex_double* beta, + lapack_complex_double* a, lapack_int* lda ); +void LAPACK_slasrt( char* id, lapack_int* n, float* d, lapack_int *info ); +void LAPACK_dlasrt( char* id, lapack_int* n, double* d, lapack_int *info ); +void LAPACK_claghe( lapack_int* n, lapack_int* k, const float* d, + lapack_complex_float* a, lapack_int* lda, lapack_int* iseed, + lapack_complex_float* work, lapack_int *info ); +void LAPACK_zlaghe( lapack_int* n, lapack_int* k, const double* d, + lapack_complex_double* a, lapack_int* lda, + lapack_int* iseed, lapack_complex_double* work, + lapack_int *info ); +void LAPACK_slagsy( lapack_int* n, lapack_int* k, const float* d, float* a, + lapack_int* lda, lapack_int* iseed, float* work, + lapack_int *info ); +void LAPACK_dlagsy( lapack_int* n, lapack_int* k, const double* d, double* a, + lapack_int* lda, lapack_int* iseed, double* work, + lapack_int *info ); +void LAPACK_clagsy( lapack_int* n, lapack_int* k, const float* d, + lapack_complex_float* a, lapack_int* lda, lapack_int* iseed, + lapack_complex_float* work, lapack_int *info ); +void LAPACK_zlagsy( lapack_int* n, lapack_int* k, const double* d, + lapack_complex_double* a, lapack_int* lda, + lapack_int* iseed, lapack_complex_double* work, + lapack_int *info ); +void LAPACK_slapmr( lapack_logical* forwrd, lapack_int* m, lapack_int* n, + float* x, lapack_int* ldx, lapack_int* k ); +void LAPACK_dlapmr( lapack_logical* forwrd, lapack_int* m, lapack_int* n, + double* x, lapack_int* ldx, lapack_int* k ); +void LAPACK_clapmr( lapack_logical* forwrd, lapack_int* m, lapack_int* n, + lapack_complex_float* x, lapack_int* ldx, lapack_int* k ); +void LAPACK_zlapmr( lapack_logical* forwrd, lapack_int* m, lapack_int* n, + lapack_complex_double* x, lapack_int* ldx, lapack_int* k ); +float LAPACK_slapy2( float* x, float* y ); +double LAPACK_dlapy2( double* x, double* y ); +float LAPACK_slapy3( float* x, float* y, float* z ); +double LAPACK_dlapy3( double* x, double* y, double* z ); +void LAPACK_slartgp( float* f, float* g, float* cs, float* sn, float* r ); +void LAPACK_dlartgp( double* f, double* g, double* cs, double* sn, double* r ); +void LAPACK_slartgs( float* x, float* y, float* sigma, float* cs, float* sn ); +void LAPACK_dlartgs( double* x, double* y, double* sigma, double* cs, + double* sn ); +// LAPACK 3.3.0 +void LAPACK_cbbcsd( char* jobu1, char* jobu2, + char* jobv1t, char* jobv2t, char* trans, + lapack_int* m, lapack_int* p, lapack_int* q, + float* theta, float* phi, + lapack_complex_float* u1, lapack_int* ldu1, + lapack_complex_float* u2, lapack_int* ldu2, + lapack_complex_float* v1t, lapack_int* ldv1t, + lapack_complex_float* v2t, lapack_int* ldv2t, + float* b11d, float* b11e, float* b12d, + float* b12e, float* b21d, float* b21e, + float* b22d, float* b22e, float* rwork, + lapack_int* lrwork , lapack_int *info ); +void LAPACK_cheswapr( char* uplo, lapack_int* n, + lapack_complex_float* a, lapack_int* i1, + lapack_int* i2 ); +void LAPACK_chetri2( char* uplo, lapack_int* n, + lapack_complex_float* a, lapack_int* lda, + const lapack_int* ipiv, + lapack_complex_float* work, lapack_int* lwork , lapack_int *info ); +void LAPACK_chetri2x( char* uplo, lapack_int* n, + lapack_complex_float* a, lapack_int* lda, + const lapack_int* ipiv, + lapack_complex_float* work, lapack_int* nb , lapack_int *info ); +void LAPACK_chetrs2( char* uplo, lapack_int* n, + lapack_int* nrhs, const lapack_complex_float* a, + lapack_int* lda, const lapack_int* ipiv, + lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* work , lapack_int *info ); +void LAPACK_csyconv( char* uplo, char* way, + lapack_int* n, lapack_complex_float* a, + lapack_int* lda, const lapack_int* ipiv, + lapack_complex_float* work , lapack_int *info ); +void LAPACK_csyswapr( char* uplo, lapack_int* n, + lapack_complex_float* a, lapack_int* i1, + lapack_int* i2 ); +void LAPACK_csytri2( char* uplo, lapack_int* n, + lapack_complex_float* a, lapack_int* lda, + const lapack_int* ipiv, + lapack_complex_float* work, lapack_int* lwork , lapack_int *info ); +void LAPACK_csytri2x( char* uplo, lapack_int* n, + lapack_complex_float* a, lapack_int* lda, + const lapack_int* ipiv, + lapack_complex_float* work, lapack_int* nb , lapack_int *info ); +void LAPACK_csytrs2( char* uplo, lapack_int* n, + lapack_int* nrhs, const lapack_complex_float* a, + lapack_int* lda, const lapack_int* ipiv, + lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* work , lapack_int *info ); +void LAPACK_cunbdb( char* trans, char* signs, + lapack_int* m, lapack_int* p, lapack_int* q, + lapack_complex_float* x11, lapack_int* ldx11, + lapack_complex_float* x12, lapack_int* ldx12, + lapack_complex_float* x21, lapack_int* ldx21, + lapack_complex_float* x22, lapack_int* ldx22, + float* theta, float* phi, + lapack_complex_float* taup1, + lapack_complex_float* taup2, + lapack_complex_float* tauq1, + lapack_complex_float* tauq2, + lapack_complex_float* work, lapack_int* lwork , lapack_int *info ); +void LAPACK_cuncsd( char* jobu1, char* jobu2, + char* jobv1t, char* jobv2t, char* trans, + char* signs, lapack_int* m, lapack_int* p, + lapack_int* q, lapack_complex_float* x11, + lapack_int* ldx11, lapack_complex_float* x12, + lapack_int* ldx12, lapack_complex_float* x21, + lapack_int* ldx21, lapack_complex_float* x22, + lapack_int* ldx22, float* theta, + lapack_complex_float* u1, lapack_int* ldu1, + lapack_complex_float* u2, lapack_int* ldu2, + lapack_complex_float* v1t, lapack_int* ldv1t, + lapack_complex_float* v2t, lapack_int* ldv2t, + lapack_complex_float* work, lapack_int* lwork, + float* rwork, lapack_int* lrwork, + lapack_int* iwork , lapack_int *info ); +void LAPACK_dbbcsd( char* jobu1, char* jobu2, + char* jobv1t, char* jobv2t, char* trans, + lapack_int* m, lapack_int* p, lapack_int* q, + double* theta, double* phi, double* u1, + lapack_int* ldu1, double* u2, lapack_int* ldu2, + double* v1t, lapack_int* ldv1t, double* v2t, + lapack_int* ldv2t, double* b11d, double* b11e, + double* b12d, double* b12e, double* b21d, + double* b21e, double* b22d, double* b22e, + double* work, lapack_int* lwork , lapack_int *info ); +void LAPACK_dorbdb( char* trans, char* signs, + lapack_int* m, lapack_int* p, lapack_int* q, + double* x11, lapack_int* ldx11, double* x12, + lapack_int* ldx12, double* x21, lapack_int* ldx21, + double* x22, lapack_int* ldx22, double* theta, + double* phi, double* taup1, double* taup2, + double* tauq1, double* tauq2, double* work, + lapack_int* lwork , lapack_int *info ); +void LAPACK_dorcsd( char* jobu1, char* jobu2, + char* jobv1t, char* jobv2t, char* trans, + char* signs, lapack_int* m, lapack_int* p, + lapack_int* q, double* x11, lapack_int* ldx11, + double* x12, lapack_int* ldx12, double* x21, + lapack_int* ldx21, double* x22, lapack_int* ldx22, + double* theta, double* u1, lapack_int* ldu1, + double* u2, lapack_int* ldu2, double* v1t, + lapack_int* ldv1t, double* v2t, lapack_int* ldv2t, + double* work, lapack_int* lwork, + lapack_int* iwork , lapack_int *info ); +void LAPACK_dsyconv( char* uplo, char* way, + lapack_int* n, double* a, lapack_int* lda, + const lapack_int* ipiv, double* work , lapack_int *info ); +void LAPACK_dsyswapr( char* uplo, lapack_int* n, + double* a, lapack_int* i1, lapack_int* i2 ); +void LAPACK_dsytri2( char* uplo, lapack_int* n, + double* a, lapack_int* lda, + const lapack_int* ipiv, + lapack_complex_double* work, lapack_int* lwork , lapack_int *info ); +void LAPACK_dsytri2x( char* uplo, lapack_int* n, + double* a, lapack_int* lda, + const lapack_int* ipiv, double* work, + lapack_int* nb , lapack_int *info ); +void LAPACK_dsytrs2( char* uplo, lapack_int* n, + lapack_int* nrhs, const double* a, + lapack_int* lda, const lapack_int* ipiv, + double* b, lapack_int* ldb, double* work , lapack_int *info ); +void LAPACK_sbbcsd( char* jobu1, char* jobu2, + char* jobv1t, char* jobv2t, char* trans, + lapack_int* m, lapack_int* p, lapack_int* q, + float* theta, float* phi, float* u1, + lapack_int* ldu1, float* u2, lapack_int* ldu2, + float* v1t, lapack_int* ldv1t, float* v2t, + lapack_int* ldv2t, float* b11d, float* b11e, + float* b12d, float* b12e, float* b21d, + float* b21e, float* b22d, float* b22e, + float* work, lapack_int* lwork , lapack_int *info ); +void LAPACK_sorbdb( char* trans, char* signs, + lapack_int* m, lapack_int* p, lapack_int* q, + float* x11, lapack_int* ldx11, float* x12, + lapack_int* ldx12, float* x21, lapack_int* ldx21, + float* x22, lapack_int* ldx22, float* theta, + float* phi, float* taup1, float* taup2, + float* tauq1, float* tauq2, float* work, + lapack_int* lwork , lapack_int *info ); +void LAPACK_sorcsd( char* jobu1, char* jobu2, + char* jobv1t, char* jobv2t, char* trans, + char* signs, lapack_int* m, lapack_int* p, + lapack_int* q, float* x11, lapack_int* ldx11, + float* x12, lapack_int* ldx12, float* x21, + lapack_int* ldx21, float* x22, lapack_int* ldx22, + float* theta, float* u1, lapack_int* ldu1, + float* u2, lapack_int* ldu2, float* v1t, + lapack_int* ldv1t, float* v2t, lapack_int* ldv2t, + float* work, lapack_int* lwork, + lapack_int* iwork , lapack_int *info ); +void LAPACK_ssyconv( char* uplo, char* way, + lapack_int* n, float* a, lapack_int* lda, + const lapack_int* ipiv, float* work , lapack_int *info ); +void LAPACK_ssyswapr( char* uplo, lapack_int* n, + float* a, lapack_int* i1, lapack_int* i2 ); +void LAPACK_ssytri2( char* uplo, lapack_int* n, + float* a, lapack_int* lda, + const lapack_int* ipiv, + lapack_complex_float* work, lapack_int* lwork , lapack_int *info ); +void LAPACK_ssytri2x( char* uplo, lapack_int* n, + float* a, lapack_int* lda, + const lapack_int* ipiv, float* work, + lapack_int* nb , lapack_int *info ); +void LAPACK_ssytrs2( char* uplo, lapack_int* n, + lapack_int* nrhs, const float* a, + lapack_int* lda, const lapack_int* ipiv, + float* b, lapack_int* ldb, float* work , lapack_int *info ); +void LAPACK_zbbcsd( char* jobu1, char* jobu2, + char* jobv1t, char* jobv2t, char* trans, + lapack_int* m, lapack_int* p, lapack_int* q, + double* theta, double* phi, + lapack_complex_double* u1, lapack_int* ldu1, + lapack_complex_double* u2, lapack_int* ldu2, + lapack_complex_double* v1t, lapack_int* ldv1t, + lapack_complex_double* v2t, lapack_int* ldv2t, + double* b11d, double* b11e, double* b12d, + double* b12e, double* b21d, double* b21e, + double* b22d, double* b22e, double* rwork, + lapack_int* lrwork , lapack_int *info ); +void LAPACK_zheswapr( char* uplo, lapack_int* n, + lapack_complex_double* a, lapack_int* i1, + lapack_int* i2 ); +void LAPACK_zhetri2( char* uplo, lapack_int* n, + lapack_complex_double* a, lapack_int* lda, + const lapack_int* ipiv, + lapack_complex_double* work, lapack_int* lwork , lapack_int *info ); +void LAPACK_zhetri2x( char* uplo, lapack_int* n, + lapack_complex_double* a, lapack_int* lda, + const lapack_int* ipiv, + lapack_complex_double* work, lapack_int* nb , lapack_int *info ); +void LAPACK_zhetrs2( char* uplo, lapack_int* n, + lapack_int* nrhs, + const lapack_complex_double* a, lapack_int* lda, + const lapack_int* ipiv, + lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* work , lapack_int *info ); +void LAPACK_zsyconv( char* uplo, char* way, + lapack_int* n, lapack_complex_double* a, + lapack_int* lda, const lapack_int* ipiv, + lapack_complex_double* work , lapack_int *info ); +void LAPACK_zsyswapr( char* uplo, lapack_int* n, + lapack_complex_double* a, lapack_int* i1, + lapack_int* i2 ); +void LAPACK_zsytri2( char* uplo, lapack_int* n, + lapack_complex_double* a, lapack_int* lda, + const lapack_int* ipiv, + lapack_complex_double* work, lapack_int* lwork , lapack_int *info ); +void LAPACK_zsytri2x( char* uplo, lapack_int* n, + lapack_complex_double* a, lapack_int* lda, + const lapack_int* ipiv, + lapack_complex_double* work, lapack_int* nb , lapack_int *info ); +void LAPACK_zsytrs2( char* uplo, lapack_int* n, + lapack_int* nrhs, + const lapack_complex_double* a, lapack_int* lda, + const lapack_int* ipiv, + lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* work , lapack_int *info ); +void LAPACK_zunbdb( char* trans, char* signs, + lapack_int* m, lapack_int* p, lapack_int* q, + lapack_complex_double* x11, lapack_int* ldx11, + lapack_complex_double* x12, lapack_int* ldx12, + lapack_complex_double* x21, lapack_int* ldx21, + lapack_complex_double* x22, lapack_int* ldx22, + double* theta, double* phi, + lapack_complex_double* taup1, + lapack_complex_double* taup2, + lapack_complex_double* tauq1, + lapack_complex_double* tauq2, + lapack_complex_double* work, lapack_int* lwork , lapack_int *info ); +void LAPACK_zuncsd( char* jobu1, char* jobu2, + char* jobv1t, char* jobv2t, char* trans, + char* signs, lapack_int* m, lapack_int* p, + lapack_int* q, lapack_complex_double* x11, + lapack_int* ldx11, lapack_complex_double* x12, + lapack_int* ldx12, lapack_complex_double* x21, + lapack_int* ldx21, lapack_complex_double* x22, + lapack_int* ldx22, double* theta, + lapack_complex_double* u1, lapack_int* ldu1, + lapack_complex_double* u2, lapack_int* ldu2, + lapack_complex_double* v1t, lapack_int* ldv1t, + lapack_complex_double* v2t, lapack_int* ldv2t, + lapack_complex_double* work, lapack_int* lwork, + double* rwork, lapack_int* lrwork, + lapack_int* iwork , lapack_int *info ); +// LAPACK 3.4.0 +void LAPACK_sgemqrt( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, lapack_int* nb, const float* v, + lapack_int* ldv, const float* t, lapack_int* ldt, float* c, + lapack_int* ldc, float* work, lapack_int *info ); +void LAPACK_dgemqrt( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, lapack_int* nb, const double* v, + lapack_int* ldv, const double* t, lapack_int* ldt, + double* c, lapack_int* ldc, double* work, + lapack_int *info ); +void LAPACK_cgemqrt( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, lapack_int* nb, + const lapack_complex_float* v, lapack_int* ldv, + const lapack_complex_float* t, lapack_int* ldt, + lapack_complex_float* c, lapack_int* ldc, + lapack_complex_float* work, lapack_int *info ); +void LAPACK_zgemqrt( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, lapack_int* nb, + const lapack_complex_double* v, lapack_int* ldv, + const lapack_complex_double* t, lapack_int* ldt, + lapack_complex_double* c, lapack_int* ldc, + lapack_complex_double* work, lapack_int *info ); +void LAPACK_sgeqrt( lapack_int* m, lapack_int* n, lapack_int* nb, float* a, + lapack_int* lda, float* t, lapack_int* ldt, float* work, + lapack_int *info ); +void LAPACK_dgeqrt( lapack_int* m, lapack_int* n, lapack_int* nb, double* a, + lapack_int* lda, double* t, lapack_int* ldt, double* work, + lapack_int *info ); +void LAPACK_cgeqrt( lapack_int* m, lapack_int* n, lapack_int* nb, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* t, lapack_int* ldt, + lapack_complex_float* work, lapack_int *info ); +void LAPACK_zgeqrt( lapack_int* m, lapack_int* n, lapack_int* nb, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* t, lapack_int* ldt, + lapack_complex_double* work, lapack_int *info ); +void LAPACK_sgeqrt2( lapack_int* m, lapack_int* n, float* a, lapack_int* lda, + float* t, lapack_int* ldt, lapack_int *info ); +void LAPACK_dgeqrt2( lapack_int* m, lapack_int* n, double* a, lapack_int* lda, + double* t, lapack_int* ldt, lapack_int *info ); +void LAPACK_cgeqrt2( lapack_int* m, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_complex_float* t, lapack_int* ldt, + lapack_int *info ); +void LAPACK_zgeqrt2( lapack_int* m, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_complex_double* t, lapack_int* ldt, + lapack_int *info ); +void LAPACK_sgeqrt3( lapack_int* m, lapack_int* n, float* a, lapack_int* lda, + float* t, lapack_int* ldt, lapack_int *info ); +void LAPACK_dgeqrt3( lapack_int* m, lapack_int* n, double* a, lapack_int* lda, + double* t, lapack_int* ldt, lapack_int *info ); +void LAPACK_cgeqrt3( lapack_int* m, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_complex_float* t, lapack_int* ldt, + lapack_int *info ); +void LAPACK_zgeqrt3( lapack_int* m, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_complex_double* t, lapack_int* ldt, + lapack_int *info ); +void LAPACK_stpmqrt( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, lapack_int* l, lapack_int* nb, + const float* v, lapack_int* ldv, const float* t, + lapack_int* ldt, float* a, lapack_int* lda, float* b, + lapack_int* ldb, float* work, lapack_int *info ); +void LAPACK_dtpmqrt( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, lapack_int* l, lapack_int* nb, + const double* v, lapack_int* ldv, const double* t, + lapack_int* ldt, double* a, lapack_int* lda, double* b, + lapack_int* ldb, double* work, lapack_int *info ); +void LAPACK_ctpmqrt( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, lapack_int* l, lapack_int* nb, + const lapack_complex_float* v, lapack_int* ldv, + const lapack_complex_float* t, lapack_int* ldt, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* work, lapack_int *info ); +void LAPACK_ztpmqrt( char* side, char* trans, lapack_int* m, lapack_int* n, + lapack_int* k, lapack_int* l, lapack_int* nb, + const lapack_complex_double* v, lapack_int* ldv, + const lapack_complex_double* t, lapack_int* ldt, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* work, lapack_int *info ); +void LAPACK_dtpqrt( lapack_int* m, lapack_int* n, lapack_int* l, lapack_int* nb, + double* a, lapack_int* lda, double* b, lapack_int* ldb, + double* t, lapack_int* ldt, double* work, + lapack_int *info ); +void LAPACK_ctpqrt( lapack_int* m, lapack_int* n, lapack_int* l, lapack_int* nb, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* t, lapack_complex_float* b, + lapack_int* ldb, lapack_int* ldt, + lapack_complex_float* work, lapack_int *info ); +void LAPACK_ztpqrt( lapack_int* m, lapack_int* n, lapack_int* l, lapack_int* nb, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* t, lapack_int* ldt, + lapack_complex_double* work, lapack_int *info ); +void LAPACK_stpqrt2( lapack_int* m, lapack_int* n, float* a, lapack_int* lda, + float* b, lapack_int* ldb, float* t, lapack_int* ldt, + lapack_int *info ); +void LAPACK_dtpqrt2( lapack_int* m, lapack_int* n, double* a, lapack_int* lda, + double* b, lapack_int* ldb, double* t, lapack_int* ldt, + lapack_int *info ); +void LAPACK_ctpqrt2( lapack_int* m, lapack_int* n, lapack_complex_float* a, + lapack_int* lda, lapack_complex_float* b, lapack_int* ldb, + lapack_complex_float* t, lapack_int* ldt, + lapack_int *info ); +void LAPACK_ztpqrt2( lapack_int* m, lapack_int* n, lapack_complex_double* a, + lapack_int* lda, lapack_complex_double* b, lapack_int* ldb, + lapack_complex_double* t, lapack_int* ldt, + lapack_int *info ); +void LAPACK_stprfb( char* side, char* trans, char* direct, char* storev, + lapack_int* m, lapack_int* n, lapack_int* k, lapack_int* l, + const float* v, lapack_int* ldv, const float* t, + lapack_int* ldt, float* a, lapack_int* lda, float* b, + lapack_int* ldb, const float* mywork, + lapack_int* myldwork ); +void LAPACK_dtprfb( char* side, char* trans, char* direct, char* storev, + lapack_int* m, lapack_int* n, lapack_int* k, lapack_int* l, + const double* v, lapack_int* ldv, const double* t, + lapack_int* ldt, double* a, lapack_int* lda, double* b, + lapack_int* ldb, const double* mywork, + lapack_int* myldwork ); +void LAPACK_ctprfb( char* side, char* trans, char* direct, char* storev, + lapack_int* m, lapack_int* n, lapack_int* k, lapack_int* l, + const lapack_complex_float* v, lapack_int* ldv, + const lapack_complex_float* t, lapack_int* ldt, + lapack_complex_float* a, lapack_int* lda, + lapack_complex_float* b, lapack_int* ldb, + const float* mywork, lapack_int* myldwork ); +void LAPACK_ztprfb( char* side, char* trans, char* direct, char* storev, + lapack_int* m, lapack_int* n, lapack_int* k, lapack_int* l, + const lapack_complex_double* v, lapack_int* ldv, + const lapack_complex_double* t, lapack_int* ldt, + lapack_complex_double* a, lapack_int* lda, + lapack_complex_double* b, lapack_int* ldb, + const double* mywork, lapack_int* myldwork ); +// LAPACK 3.X.X +void LAPACK_csyr( char* uplo, lapack_int* n, lapack_complex_float* alpha, + const lapack_complex_float* x, lapack_int* incx, + lapack_complex_float* a, lapack_int* lda ); +void LAPACK_zsyr( char* uplo, lapack_int* n, lapack_complex_double* alpha, + const lapack_complex_double* x, lapack_int* incx, + lapack_complex_double* a, lapack_int* lda ); + +#ifdef __cplusplus +} +#endif /* __cplusplus */ + +#endif /* _LAPACKE_H_ */ + +#endif /* _MKL_LAPACKE_H_ */ diff --git a/Eigen/src/misc/lapacke_mangling.h b/Eigen/src/misc/lapacke_mangling.h new file mode 100644 index 000000000..6211fd144 --- /dev/null +++ b/Eigen/src/misc/lapacke_mangling.h @@ -0,0 +1,17 @@ +#ifndef LAPACK_HEADER_INCLUDED +#define LAPACK_HEADER_INCLUDED + +#ifndef LAPACK_GLOBAL +#if defined(LAPACK_GLOBAL_PATTERN_LC) || defined(ADD_) +#define LAPACK_GLOBAL(lcname,UCNAME) lcname##_ +#elif defined(LAPACK_GLOBAL_PATTERN_UC) || defined(UPPER) +#define LAPACK_GLOBAL(lcname,UCNAME) UCNAME +#elif defined(LAPACK_GLOBAL_PATTERN_MC) || defined(NOCHANGE) +#define LAPACK_GLOBAL(lcname,UCNAME) lcname +#else +#define LAPACK_GLOBAL(lcname,UCNAME) lcname##_ +#endif +#endif + +#endif + diff --git a/Eigen/src/plugins/ArrayCwiseBinaryOps.h b/Eigen/src/plugins/ArrayCwiseBinaryOps.h index 19e25ab62..62fb303d9 100644 --- a/Eigen/src/plugins/ArrayCwiseBinaryOps.h +++ b/Eigen/src/plugins/ArrayCwiseBinaryOps.h @@ -330,6 +330,8 @@ operator^(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const #if 0 /** \cpp11 \returns an expression of the coefficient-wise polygamma function. * + * \specialfunctions_module + * * It returns the \a n -th derivative of the digamma(psi) evaluated at \c *this. * * \warning Be careful with the order of the parameters: x.polygamma(n) is equivalent to polygamma(n,x) @@ -346,6 +348,8 @@ polygamma(const EIGEN_CURRENT_STORAGE_BASE_CLASS<DerivedN> &n) const /** \returns an expression of the coefficient-wise zeta function. * + * \specialfunctions_module + * * It returns the Riemann zeta function of two arguments \c *this and \a q: * * \param *this is the exposent, it must be > 1 diff --git a/Eigen/src/plugins/ArrayCwiseUnaryOps.h b/Eigen/src/plugins/ArrayCwiseUnaryOps.h index 9e42bb540..ebaa3f192 100644 --- a/Eigen/src/plugins/ArrayCwiseUnaryOps.h +++ b/Eigen/src/plugins/ArrayCwiseUnaryOps.h @@ -22,10 +22,6 @@ typedef CwiseUnaryOp<internal::scalar_atan_op<Scalar>, const Derived> AtanReturn typedef CwiseUnaryOp<internal::scalar_tanh_op<Scalar>, const Derived> TanhReturnType; typedef CwiseUnaryOp<internal::scalar_sinh_op<Scalar>, const Derived> SinhReturnType; typedef CwiseUnaryOp<internal::scalar_cosh_op<Scalar>, const Derived> CoshReturnType; -typedef CwiseUnaryOp<internal::scalar_lgamma_op<Scalar>, const Derived> LgammaReturnType; -typedef CwiseUnaryOp<internal::scalar_digamma_op<Scalar>, const Derived> DigammaReturnType; -typedef CwiseUnaryOp<internal::scalar_erf_op<Scalar>, const Derived> ErfReturnType; -typedef CwiseUnaryOp<internal::scalar_erfc_op<Scalar>, const Derived> ErfcReturnType; typedef CwiseUnaryOp<internal::scalar_square_op<Scalar>, const Derived> SquareReturnType; typedef CwiseUnaryOp<internal::scalar_cube_op<Scalar>, const Derived> CubeReturnType; typedef CwiseUnaryOp<internal::scalar_round_op<Scalar>, const Derived> RoundReturnType; @@ -40,7 +36,7 @@ typedef CwiseUnaryOp<internal::scalar_isfinite_op<Scalar>, const Derived> IsFini * Example: \include Cwise_abs.cpp * Output: \verbinclude Cwise_abs.out * - * \sa abs2() + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_abs">Math functions</a>, abs2() */ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const AbsReturnType @@ -68,7 +64,7 @@ arg() const * Example: \include Cwise_abs2.cpp * Output: \verbinclude Cwise_abs2.out * - * \sa abs(), square() + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_abs2">Math functions</a>, abs(), square() */ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Abs2ReturnType @@ -85,7 +81,7 @@ abs2() const * Example: \include Cwise_exp.cpp * Output: \verbinclude Cwise_exp.out * - * \sa pow(), log(), sin(), cos() + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_exp">Math functions</a>, pow(), log(), sin(), cos() */ EIGEN_DEVICE_FUNC inline const ExpReturnType @@ -102,7 +98,7 @@ exp() const * Example: \include Cwise_log.cpp * Output: \verbinclude Cwise_log.out * - * \sa exp() + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_log">Math functions</a>, exp() */ EIGEN_DEVICE_FUNC inline const LogReturnType @@ -116,7 +112,7 @@ log() const * In exact arithmetic, \c x.log() is equivalent to \c (x+1).log(), * however, with finite precision, this function is much more accurate when \c x is close to zero. * - * \sa log() + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_log1p">Math functions</a>, log() */ EIGEN_DEVICE_FUNC inline const Log1pReturnType @@ -132,7 +128,7 @@ log1p() const * Example: \include Cwise_log10.cpp * Output: \verbinclude Cwise_log10.out * - * \sa log() + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_log10">Math functions</a>, log() */ EIGEN_DEVICE_FUNC inline const Log10ReturnType @@ -149,7 +145,7 @@ log10() const * Example: \include Cwise_sqrt.cpp * Output: \verbinclude Cwise_sqrt.out * - * \sa pow(), square() + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_sqrt">Math functions</a>, pow(), square() */ EIGEN_DEVICE_FUNC inline const SqrtReturnType @@ -199,7 +195,7 @@ sign() const * Example: \include Cwise_cos.cpp * Output: \verbinclude Cwise_cos.out * - * \sa sin(), acos() + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_cos">Math functions</a>, sin(), acos() */ EIGEN_DEVICE_FUNC inline const CosReturnType @@ -217,7 +213,7 @@ cos() const * Example: \include Cwise_sin.cpp * Output: \verbinclude Cwise_sin.out * - * \sa cos(), asin() + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_sin">Math functions</a>, cos(), asin() */ EIGEN_DEVICE_FUNC inline const SinReturnType @@ -231,7 +227,7 @@ sin() const * Example: \include Cwise_tan.cpp * Output: \verbinclude Cwise_tan.out * - * \sa cos(), sin() + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_tan">Math functions</a>, cos(), sin() */ EIGEN_DEVICE_FUNC inline const TanReturnType @@ -245,7 +241,7 @@ tan() const * Example: \include Cwise_atan.cpp * Output: \verbinclude Cwise_atan.out * - * \sa tan(), asin(), acos() + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_atan">Math functions</a>, tan(), asin(), acos() */ EIGEN_DEVICE_FUNC inline const AtanReturnType @@ -259,7 +255,7 @@ atan() const * Example: \include Cwise_acos.cpp * Output: \verbinclude Cwise_acos.out * - * \sa cos(), asin() + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_acos">Math functions</a>, cos(), asin() */ EIGEN_DEVICE_FUNC inline const AcosReturnType @@ -273,7 +269,7 @@ acos() const * Example: \include Cwise_asin.cpp * Output: \verbinclude Cwise_asin.out * - * \sa sin(), acos() + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_asin">Math functions</a>, sin(), acos() */ EIGEN_DEVICE_FUNC inline const AsinReturnType @@ -287,7 +283,7 @@ asin() const * Example: \include Cwise_tanh.cpp * Output: \verbinclude Cwise_tanh.out * - * \sa tan(), sinh(), cosh() + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_tanh">Math functions</a>, tan(), sinh(), cosh() */ EIGEN_DEVICE_FUNC inline const TanhReturnType @@ -301,7 +297,7 @@ tanh() const * Example: \include Cwise_sinh.cpp * Output: \verbinclude Cwise_sinh.out * - * \sa sin(), tanh(), cosh() + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_sinh">Math functions</a>, sin(), tanh(), cosh() */ EIGEN_DEVICE_FUNC inline const SinhReturnType @@ -315,7 +311,7 @@ sinh() const * Example: \include Cwise_cosh.cpp * Output: \verbinclude Cwise_cosh.out * - * \sa tan(), sinh(), cosh() + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_cosh">Math functions</a>, tan(), sinh(), cosh() */ EIGEN_DEVICE_FUNC inline const CoshReturnType @@ -324,77 +320,6 @@ cosh() const return CoshReturnType(derived()); } -/** \cpp11 \returns an expression of the coefficient-wise ln(|gamma(*this)|). - * - * Example: \include Cwise_lgamma.cpp - * Output: \verbinclude Cwise_lgamma.out - * - * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types, - * or float/double in non c++11 mode, the user has to provide implementations of lgamma(T) for any scalar - * type T to be supported. - * - * \sa digamma() - */ -EIGEN_DEVICE_FUNC -inline const LgammaReturnType -lgamma() const -{ - return LgammaReturnType(derived()); -} - -/** \returns an expression of the coefficient-wise digamma (psi, derivative of lgamma). - * - * \note This function supports only float and double scalar types. To support other scalar types, - * the user has to provide implementations of digamma(T) for any scalar - * type T to be supported. - * - * \sa Eigen::digamma(), Eigen::polygamma(), lgamma() - */ -EIGEN_DEVICE_FUNC -inline const DigammaReturnType -digamma() const -{ - return DigammaReturnType(derived()); -} - -/** \cpp11 \returns an expression of the coefficient-wise Gauss error - * function of *this. - * - * Example: \include Cwise_erf.cpp - * Output: \verbinclude Cwise_erf.out - * - * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types, - * or float/double in non c++11 mode, the user has to provide implementations of erf(T) for any scalar - * type T to be supported. - * - * \sa erfc() - */ -EIGEN_DEVICE_FUNC -inline const ErfReturnType -erf() const -{ - return ErfReturnType(derived()); -} - -/** \cpp11 \returns an expression of the coefficient-wise Complementary error - * function of *this. - * - * Example: \include Cwise_erfc.cpp - * Output: \verbinclude Cwise_erfc.out - * - * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types, - * or float/double in non c++11 mode, the user has to provide implementations of erfc(T) for any scalar - * type T to be supported. - * - * \sa erf() - */ -EIGEN_DEVICE_FUNC -inline const ErfcReturnType -erfc() const -{ - return ErfcReturnType(derived()); -} - /** \returns an expression of the coefficient-wise inverse of *this. * * Example: \include Cwise_inverse.cpp @@ -414,7 +339,7 @@ inverse() const * Example: \include Cwise_square.cpp * Output: \verbinclude Cwise_square.out * - * \sa operator/(), operator*(), abs2() + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_squareE">Math functions</a>, abs2(), cube(), pow() */ EIGEN_DEVICE_FUNC inline const SquareReturnType @@ -428,7 +353,7 @@ square() const * Example: \include Cwise_cube.cpp * Output: \verbinclude Cwise_cube.out * - * \sa square(), pow() + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_cube">Math functions</a>, square(), pow() */ EIGEN_DEVICE_FUNC inline const CubeReturnType @@ -442,7 +367,7 @@ cube() const * Example: \include Cwise_round.cpp * Output: \verbinclude Cwise_round.out * - * \sa ceil(), floor() + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_round">Math functions</a>, ceil(), floor() */ EIGEN_DEVICE_FUNC inline const RoundReturnType @@ -456,7 +381,7 @@ round() const * Example: \include Cwise_floor.cpp * Output: \verbinclude Cwise_floor.out * - * \sa ceil(), round() + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_floor">Math functions</a>, ceil(), round() */ EIGEN_DEVICE_FUNC inline const FloorReturnType @@ -470,7 +395,7 @@ floor() const * Example: \include Cwise_ceil.cpp * Output: \verbinclude Cwise_ceil.out * - * \sa floor(), round() + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_ceil">Math functions</a>, floor(), round() */ EIGEN_DEVICE_FUNC inline const CeilReturnType @@ -538,3 +463,90 @@ operator!() const THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_OF_BOOL); return BooleanNotReturnType(derived()); } + + +// --- SpecialFunctions module --- + +typedef CwiseUnaryOp<internal::scalar_lgamma_op<Scalar>, const Derived> LgammaReturnType; +typedef CwiseUnaryOp<internal::scalar_digamma_op<Scalar>, const Derived> DigammaReturnType; +typedef CwiseUnaryOp<internal::scalar_erf_op<Scalar>, const Derived> ErfReturnType; +typedef CwiseUnaryOp<internal::scalar_erfc_op<Scalar>, const Derived> ErfcReturnType; + +/** \cpp11 \returns an expression of the coefficient-wise ln(|gamma(*this)|). + * + * \specialfunctions_module + * + * Example: \include Cwise_lgamma.cpp + * Output: \verbinclude Cwise_lgamma.out + * + * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types, + * or float/double in non c++11 mode, the user has to provide implementations of lgamma(T) for any scalar + * type T to be supported. + * + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_lgamma">Math functions</a>, digamma() + */ +EIGEN_DEVICE_FUNC +inline const LgammaReturnType +lgamma() const +{ + return LgammaReturnType(derived()); +} + +/** \returns an expression of the coefficient-wise digamma (psi, derivative of lgamma). + * + * \specialfunctions_module + * + * \note This function supports only float and double scalar types. To support other scalar types, + * the user has to provide implementations of digamma(T) for any scalar + * type T to be supported. + * + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_digamma">Math functions</a>, Eigen::digamma(), Eigen::polygamma(), lgamma() + */ +EIGEN_DEVICE_FUNC +inline const DigammaReturnType +digamma() const +{ + return DigammaReturnType(derived()); +} + +/** \cpp11 \returns an expression of the coefficient-wise Gauss error + * function of *this. + * + * \specialfunctions_module + * + * Example: \include Cwise_erf.cpp + * Output: \verbinclude Cwise_erf.out + * + * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types, + * or float/double in non c++11 mode, the user has to provide implementations of erf(T) for any scalar + * type T to be supported. + * + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_erf">Math functions</a>, erfc() + */ +EIGEN_DEVICE_FUNC +inline const ErfReturnType +erf() const +{ + return ErfReturnType(derived()); +} + +/** \cpp11 \returns an expression of the coefficient-wise Complementary error + * function of *this. + * + * \specialfunctions_module + * + * Example: \include Cwise_erfc.cpp + * Output: \verbinclude Cwise_erfc.out + * + * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types, + * or float/double in non c++11 mode, the user has to provide implementations of erfc(T) for any scalar + * type T to be supported. + * + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_erfc">Math functions</a>, erf() + */ +EIGEN_DEVICE_FUNC +inline const ErfcReturnType +erfc() const +{ + return ErfcReturnType(derived()); +} diff --git a/Eigen/src/plugins/CommonCwiseUnaryOps.h b/Eigen/src/plugins/CommonCwiseUnaryOps.h index 6cd5479a0..5719c6b10 100644 --- a/Eigen/src/plugins/CommonCwiseUnaryOps.h +++ b/Eigen/src/plugins/CommonCwiseUnaryOps.h @@ -62,7 +62,7 @@ cast() const /** \returns an expression of the complex conjugate of \c *this. * - * \sa adjoint() */ + * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_conj">Math functions</a>, MatrixBase::adjoint() */ EIGEN_DEVICE_FUNC inline ConjugateReturnType conjugate() const diff --git a/bench/benchCholesky.cpp b/bench/benchCholesky.cpp index 42b3e1285..9a8e7cf63 100644 --- a/bench/benchCholesky.cpp +++ b/bench/benchCholesky.cpp @@ -31,7 +31,7 @@ __attribute__ ((noinline)) void benchLLT(const MatrixType& m) int rows = m.rows(); int cols = m.cols(); - int cost = 0; + double cost = 0; for (int j=0; j<rows; ++j) { int r = std::max(rows - j -1,0); @@ -78,10 +78,10 @@ __attribute__ ((noinline)) void benchLLT(const MatrixType& m) else std::cout << "fixed "; std::cout << covMat.rows() << " \t" - << (timerNoSqrt.value() * REPEAT) / repeats << "s " - << "(" << 1e-6 * cost*repeats/timerNoSqrt.value() << " MFLOPS)\t" - << (timerSqrt.value() * REPEAT) / repeats << "s " - << "(" << 1e-6 * cost*repeats/timerSqrt.value() << " MFLOPS)\n"; + << (timerNoSqrt.best()) / repeats << "s " + << "(" << 1e-9 * cost*repeats/timerNoSqrt.best() << " GFLOPS)\t" + << (timerSqrt.best()) / repeats << "s " + << "(" << 1e-9 * cost*repeats/timerSqrt.best() << " GFLOPS)\n"; #ifdef BENCH_GSL @@ -119,13 +119,13 @@ __attribute__ ((noinline)) void benchLLT(const MatrixType& m) int main(int argc, char* argv[]) { - const int dynsizes[] = {4,6,8,16,24,32,49,64,128,256,512,900,0}; - std::cout << "size no sqrt standard"; + const int dynsizes[] = {4,6,8,16,24,32,49,64,128,256,512,900,1500,0}; + std::cout << "size LDLT LLT"; // #ifdef BENCH_GSL // std::cout << " GSL (standard + double + ATLAS) "; // #endif std::cout << "\n"; - for (uint i=0; dynsizes[i]>0; ++i) + for (int i=0; dynsizes[i]>0; ++i) benchLLT(Matrix<Scalar,Dynamic,Dynamic>(dynsizes[i],dynsizes[i])); benchLLT(Matrix<Scalar,2,2>()); diff --git a/bench/dense_solvers.cpp b/bench/dense_solvers.cpp index aa4ff011f..24343dcd8 100644 --- a/bench/dense_solvers.cpp +++ b/bench/dense_solvers.cpp @@ -2,47 +2,74 @@ #include "BenchTimer.h" #include <Eigen/Dense> #include <map> +#include <vector> #include <string> +#include <sstream> using namespace Eigen; -std::map<std::string,Array<float,1,4> > results; +std::map<std::string,Array<float,1,8,DontAlign|RowMajor> > results; +std::vector<std::string> labels; +std::vector<Array2i> sizes; + +template<typename Solver,typename MatrixType> +EIGEN_DONT_INLINE +void compute_norm_equation(Solver &solver, const MatrixType &A) { + if(A.rows()!=A.cols()) + solver.compute(A.transpose()*A); + else + solver.compute(A); +} + +template<typename Solver,typename MatrixType> +EIGEN_DONT_INLINE +void compute(Solver &solver, const MatrixType &A) { + solver.compute(A); +} template<typename Scalar,int Size> -void bench(int id, int size = Size) +void bench(int id, int rows, int size = Size) { - typedef Matrix<Scalar,Size,Size> Mat; - Mat A(size,size); + typedef Matrix<Scalar,Dynamic,Size> Mat; + typedef Matrix<Scalar,Dynamic,Dynamic> MatDyn; + typedef Matrix<Scalar,Size,Size> MatSquare; + Mat A(rows,size); A.setRandom(); - A = A*A.adjoint(); + if(rows==size) + A = A*A.adjoint(); BenchTimer t_llt, t_ldlt, t_lu, t_fplu, t_qr, t_cpqr, t_cod, t_fpqr, t_jsvd, t_bdcsvd; + + int svd_opt = ComputeThinU|ComputeThinV; - int tries = 3; + int tries = 5; int rep = 1000/size; if(rep==0) rep = 1; // rep = rep*rep; - LLT<Mat> llt(A); - LDLT<Mat> ldlt(A); - PartialPivLU<Mat> lu(A); - FullPivLU<Mat> fplu(A); - HouseholderQR<Mat> qr(A); - ColPivHouseholderQR<Mat> cpqr(A); - CompleteOrthogonalDecomposition<Mat> cod(A); - FullPivHouseholderQR<Mat> fpqr(A); - JacobiSVD<Mat> jsvd(A.rows(),A.cols()); - BDCSVD<Mat> bdcsvd(A.rows(),A.cols()); + LLT<MatSquare> llt(size); + LDLT<MatSquare> ldlt(size); + PartialPivLU<MatSquare> lu(size); + FullPivLU<MatSquare> fplu(size,size); + HouseholderQR<Mat> qr(A.rows(),A.cols()); + ColPivHouseholderQR<Mat> cpqr(A.rows(),A.cols()); + CompleteOrthogonalDecomposition<Mat> cod(A.rows(),A.cols()); + FullPivHouseholderQR<Mat> fpqr(A.rows(),A.cols()); + JacobiSVD<MatDyn> jsvd(A.rows(),A.cols()); + BDCSVD<MatDyn> bdcsvd(A.rows(),A.cols()); - BENCH(t_llt, tries, rep, llt.compute(A)); - BENCH(t_ldlt, tries, rep, ldlt.compute(A)); - BENCH(t_lu, tries, rep, lu.compute(A)); - BENCH(t_fplu, tries, rep, fplu.compute(A)); - BENCH(t_qr, tries, rep, qr.compute(A)); - BENCH(t_cpqr, tries, rep, cpqr.compute(A)); - BENCH(t_cod, tries, rep, cod.compute(A)); - BENCH(t_fpqr, tries, rep, fpqr.compute(A)); + BENCH(t_llt, tries, rep, compute_norm_equation(llt,A)); + BENCH(t_ldlt, tries, rep, compute_norm_equation(ldlt,A)); + BENCH(t_lu, tries, rep, compute_norm_equation(lu,A)); + if(size<=1000) + BENCH(t_fplu, tries, rep, compute_norm_equation(fplu,A)); + BENCH(t_qr, tries, rep, compute(qr,A)); + BENCH(t_cpqr, tries, rep, compute(cpqr,A)); + BENCH(t_cod, tries, rep, compute(cod,A)); + if(size*rows<=10000000) + BENCH(t_fpqr, tries, rep, compute(fpqr,A)); if(size<500) // JacobiSVD is really too slow for too large matrices - BENCH(t_jsvd, tries, rep, jsvd.compute(A,ComputeFullU|ComputeFullV)); - BENCH(t_bdcsvd, tries, rep, bdcsvd.compute(A,ComputeFullU|ComputeFullV)); + BENCH(t_jsvd, tries, rep, jsvd.compute(A,svd_opt)); +// if(size*rows<=20000000) + BENCH(t_bdcsvd, tries, rep, bdcsvd.compute(A,svd_opt)); results["LLT"][id] = t_llt.best(); results["LDLT"][id] = t_ldlt.best(); @@ -52,33 +79,108 @@ void bench(int id, int size = Size) results["ColPivHouseholderQR"][id] = t_cpqr.best(); results["CompleteOrthogonalDecomposition"][id] = t_cod.best(); results["FullPivHouseholderQR"][id] = t_fpqr.best(); - results["JacobiSVD"][id] = size<500 ? t_jsvd.best() : 0; + results["JacobiSVD"][id] = t_jsvd.best(); results["BDCSVD"][id] = t_bdcsvd.best(); } + int main() { + labels.push_back("LLT"); + labels.push_back("LDLT"); + labels.push_back("PartialPivLU"); + labels.push_back("FullPivLU"); + labels.push_back("HouseholderQR"); + labels.push_back("ColPivHouseholderQR"); + labels.push_back("CompleteOrthogonalDecomposition"); + labels.push_back("FullPivHouseholderQR"); + labels.push_back("JacobiSVD"); + labels.push_back("BDCSVD"); + + for(int i=0; i<labels.size(); ++i) + results[labels[i]].fill(-1); + const int small = 8; - const int medium = 100; - const int large = 1000; - const int xl = 4000; - - bench<float,small>(0); - bench<float,Dynamic>(1,medium); - bench<float,Dynamic>(2,large); - bench<float,Dynamic>(3,xl); - - IOFormat fmt(3, 0, " \t", "\n", "", ""); - - std::cout << "solver/size " << small << "\t" << medium << "\t" << large << "\t" << xl << "\n"; - std::cout << "LLT (ms) " << (results["LLT"]/1000.).format(fmt) << "\n"; - std::cout << "LDLT (%) " << (results["LDLT"]/results["LLT"]).format(fmt) << "\n"; - std::cout << "PartialPivLU (%) " << (results["PartialPivLU"]/results["LLT"]).format(fmt) << "\n"; - std::cout << "FullPivLU (%) " << (results["FullPivLU"]/results["LLT"]).format(fmt) << "\n"; - std::cout << "HouseholderQR (%) " << (results["HouseholderQR"]/results["LLT"]).format(fmt) << "\n"; - std::cout << "ColPivHouseholderQR (%) " << (results["ColPivHouseholderQR"]/results["LLT"]).format(fmt) << "\n"; - std::cout << "CompleteOrthogonalDecomposition (%) " << (results["CompleteOrthogonalDecomposition"]/results["LLT"]).format(fmt) << "\n"; - std::cout << "FullPivHouseholderQR (%) " << (results["FullPivHouseholderQR"]/results["LLT"]).format(fmt) << "\n"; - std::cout << "JacobiSVD (%) " << (results["JacobiSVD"]/results["LLT"]).format(fmt) << "\n"; - std::cout << "BDCSVD (%) " << (results["BDCSVD"]/results["LLT"]).format(fmt) << "\n"; + sizes.push_back(Array2i(small,small)); + sizes.push_back(Array2i(100,100)); + sizes.push_back(Array2i(1000,1000)); + sizes.push_back(Array2i(4000,4000)); + sizes.push_back(Array2i(10000,small)); + sizes.push_back(Array2i(10000,100)); + sizes.push_back(Array2i(10000,1000)); + sizes.push_back(Array2i(10000,4000)); + + using namespace std; + + for(int k=0; k<sizes.size(); ++k) + { + cout << sizes[k](0) << "x" << sizes[k](1) << "...\n"; + bench<float,Dynamic>(k,sizes[k](0),sizes[k](1)); + } + + cout.width(32); + cout << "solver/size"; + cout << " "; + for(int k=0; k<sizes.size(); ++k) + { + std::stringstream ss; + ss << sizes[k](0) << "x" << sizes[k](1); + cout.width(10); cout << ss.str(); cout << " "; + } + cout << endl; + + + for(int i=0; i<labels.size(); ++i) + { + cout.width(32); cout << labels[i]; cout << " "; + ArrayXf r = (results[labels[i]]*100000.f).floor()/100.f; + for(int k=0; k<sizes.size(); ++k) + { + cout.width(10); + if(r(k)>=1e6) cout << "-"; + else cout << r(k); + cout << " "; + } + cout << endl; + } + + // HTML output + cout << "<table class=\"manual\">" << endl; + cout << "<tr><th>solver/size</th>" << endl; + for(int k=0; k<sizes.size(); ++k) + cout << " <th>" << sizes[k](0) << "x" << sizes[k](1) << "</th>"; + cout << "</tr>" << endl; + for(int i=0; i<labels.size(); ++i) + { + cout << "<tr"; + if(i%2==1) cout << " class=\"alt\""; + cout << "><td>" << labels[i] << "</td>"; + ArrayXf r = (results[labels[i]]*100000.f).floor()/100.f; + for(int k=0; k<sizes.size(); ++k) + { + if(r(k)>=1e6) cout << "<td>-</td>"; + else + { + cout << "<td>" << r(k); + if(i>0) + cout << " (x" << numext::round(10.f*results[labels[i]](k)/results["LLT"](k))/10.f << ")"; + if(i<4 && sizes[k](0)!=sizes[k](1)) + cout << " <sup><a href=\"#note_ls\">*</a></sup>"; + cout << "</td>"; + } + } + cout << "</tr>" << endl; + } + cout << "</table>" << endl; + +// cout << "LLT (ms) " << (results["LLT"]*1000.).format(fmt) << "\n"; +// cout << "LDLT (%) " << (results["LDLT"]/results["LLT"]).format(fmt) << "\n"; +// cout << "PartialPivLU (%) " << (results["PartialPivLU"]/results["LLT"]).format(fmt) << "\n"; +// cout << "FullPivLU (%) " << (results["FullPivLU"]/results["LLT"]).format(fmt) << "\n"; +// cout << "HouseholderQR (%) " << (results["HouseholderQR"]/results["LLT"]).format(fmt) << "\n"; +// cout << "ColPivHouseholderQR (%) " << (results["ColPivHouseholderQR"]/results["LLT"]).format(fmt) << "\n"; +// cout << "CompleteOrthogonalDecomposition (%) " << (results["CompleteOrthogonalDecomposition"]/results["LLT"]).format(fmt) << "\n"; +// cout << "FullPivHouseholderQR (%) " << (results["FullPivHouseholderQR"]/results["LLT"]).format(fmt) << "\n"; +// cout << "JacobiSVD (%) " << (results["JacobiSVD"]/results["LLT"]).format(fmt) << "\n"; +// cout << "BDCSVD (%) " << (results["BDCSVD"]/results["LLT"]).format(fmt) << "\n"; } diff --git a/bench/perf_monitoring/gemm/changesets.txt b/bench/perf_monitoring/gemm/changesets.txt index d00b4603a..af8eb9b8f 100644 --- a/bench/perf_monitoring/gemm/changesets.txt +++ b/bench/perf_monitoring/gemm/changesets.txt @@ -42,10 +42,20 @@ before-evaluators 6984:45f26866c091 # rm dynamic loop swapping, adjust lhs's micro panel height to fully exploit L1 cache 6986:a675d05b6f8f # blocking heuristic: block on the rhs in L1 if the lhs fit in L1. 7013:f875e75f07e5 # organize a little our default cache sizes, and use a saner default L1 outside of x86 (10% faster on Nexus 5) +7015:8aad8f35c955 # Refactor computeProductBlockingSizes to make room for the possibility of using lookup tables +7016:a58d253e8c91 # Polish lookup tables generation +7018:9b27294a8186 # actual_panel_rows computation should always be resilient to parameters not consistent with the known L1 cache size, see comment +7019:c758b1e2c073 # Provide a empirical lookup table for blocking sizes measured on a Nexus 5. Only for float, only for Android on ARM 32bit for now. +7085:627e039fba68 # Bug 986: add support for coefficient-based product with 0 depth. +7098:b6f1db9cf9ec # Bug 992: don't select a 3p GEMM path with non-vectorizable scalar types, this hits unsupported paths in symm/triangular products code 7591:09a8e2186610 # 3.3-alpha1 7650:b0f3c8f43025 # help clang inlining -8744:74b789ada92a # Improved the matrix multiplication blocking in the case where mr is not a power of 2 (e.g on Haswell CPUs) +#8744:74b789ada92a # Improved the matrix multiplication blocking in the case where mr is not a power of 2 (e.g on Haswell CPUs) 8789:efcb912e4356 # Made the index type a template parameter to evaluateProductBlockingSizes. Use numext::mini and numext::maxi instead of std::min/std::max to compute blocking sizes 8972:81d53c711775 # Don't optimize the processing of the last rows of a matrix matrix product in cases that violate the assumptions made by the optimized code path 8985:d935df21a082 # Remove the rotating kernel. - +8988:6c2dc56e73b3 # Bug 256: enable vectorization with unaligned loads/stores. +9148:b8b8c421e36c # Relax mixing-type constraints for binary coefficient-wise operators +9174:d228bc282ac9 # merge +9212:c90098affa7b # Fix performance regression introduced in changeset 8aad8f35c955 +9213:9f1c14e4694b # Fix performance regression in dgemm introduced by changeset 81d53c711775 diff --git a/bench/perf_monitoring/gemm/lazy_gemm.cpp b/bench/perf_monitoring/gemm/lazy_gemm.cpp index b443218d7..6dc370155 100644 --- a/bench/perf_monitoring/gemm/lazy_gemm.cpp +++ b/bench/perf_monitoring/gemm/lazy_gemm.cpp @@ -12,12 +12,13 @@ using namespace Eigen; typedef SCALAR Scalar; template<typename MatA, typename MatB, typename MatC> -inline void lazy_gemm(const MatA &A, const MatB &B, MatC &C) +EIGEN_DONT_INLINE +void lazy_gemm(const MatA &A, const MatB &B, MatC &C) { - escape((void*)A.data()); - escape((void*)B.data()); +// escape((void*)A.data()); +// escape((void*)B.data()); C.noalias() += A.lazyProduct(B); - escape((void*)C.data()); +// escape((void*)C.data()); } template<int m, int n, int k, int TA> diff --git a/bench/perf_monitoring/gemm/make_plot.sh b/bench/perf_monitoring/gemm/make_plot.sh index 4d6053501..cd3214ac9 100755 --- a/bench/perf_monitoring/gemm/make_plot.sh +++ b/bench/perf_monitoring/gemm/make_plot.sh @@ -25,7 +25,7 @@ echo "set xtics rotate 1" >> $WHAT.gnuplot echo "set term pdf color rounded enhanced fontscale 0.35 size 7in,5in" >> $WHAT.gnuplot echo set output "'"$WHAT.pdf"'" >> $WHAT.gnuplot -col=`cat settings.txt | wc -l` +col=`cat $bench"_settings.txt" | wc -l` echo "plot for [col=2:$col+1] '$WHAT.out.header' using 0:col:xticlabels(1) with lines" >> $WHAT.gnuplot echo " " >> $WHAT.gnuplot diff --git a/bench/perf_monitoring/gemm/run.sh b/bench/perf_monitoring/gemm/run.sh index bfb4ecfac..9d6ee40bc 100755 --- a/bench/perf_monitoring/gemm/run.sh +++ b/bench/perf_monitoring/gemm/run.sh @@ -138,15 +138,15 @@ do done echo "Float:" -cat $PREFIX"s"$bench.out" -echo "" +cat $PREFIX"s""$bench.out" +echo " " echo "Double:" -cat $PREFIX"d"$bench.out" +cat $PREFIX"d""$bench.out" echo "" echo "Complex:" -cat $PREFIX"c"$bench.out" +cat $PREFIX"c""$bench.out" echo "" ./make_plot.sh $PREFIX"s"$bench $bench diff --git a/cmake/FindSuperLU.cmake b/cmake/FindSuperLU.cmake index e4142fe4d..f38146e06 100644 --- a/cmake/FindSuperLU.cmake +++ b/cmake/FindSuperLU.cmake @@ -17,7 +17,10 @@ find_path(SUPERLU_INCLUDES SRC ) -find_library(SUPERLU_LIBRARIES NAMES "superlu_4.3" "superlu_4.2" "superlu_4.1" "superlu_4.0" "superlu_3.1" "superlu_3.0" "superlu" PATHS $ENV{SUPERLUDIR} ${LIB_INSTALL_DIR} PATH_SUFFIXES lib) +find_library(SUPERLU_LIBRARIES + NAMES "superlu_5.2.1" "superlu_5.2" "superlu_5.1.1" "superlu_5.1" "superlu_5.0" "superlu_4.3" "superlu_4.2" "superlu_4.1" "superlu_4.0" "superlu_3.1" "superlu_3.0" "superlu" + PATHS $ENV{SUPERLUDIR} ${LIB_INSTALL_DIR} + PATH_SUFFIXES lib) if(SUPERLU_INCLUDES AND SUPERLU_LIBRARIES) @@ -48,11 +51,25 @@ int main() { }" SUPERLU_HAS_CLEAN_ENUMS) -if(SUPERLU_HAS_CLEAN_ENUMS) +check_cxx_source_compiles(" +typedef int int_t; +#include <supermatrix.h> +#include <slu_util.h> +int main(void) +{ + GlobalLU_t glu; + return 0; +}" +SUPERLU_HAS_GLOBALLU_T) + +if(SUPERLU_HAS_GLOBALLU_T) + # at least 5.0 + set(SUPERLU_VERSION_VAR "5.0") +elseif(SUPERLU_HAS_CLEAN_ENUMS) # at least 4.3 set(SUPERLU_VERSION_VAR "4.3") elseif(SUPERLU_HAS_GLOBAL_MEM_USAGE_T) - # at least 4.3 + # at least 4.0 set(SUPERLU_VERSION_VAR "4.0") else() set(SUPERLU_VERSION_VAR "3.0") diff --git a/doc/CMakeLists.txt b/doc/CMakeLists.txt index 4d01a0424..db413bc65 100644 --- a/doc/CMakeLists.txt +++ b/doc/CMakeLists.txt @@ -78,6 +78,8 @@ add_custom_target( COMMAND ${CMAKE_COMMAND} -E make_directory ${CMAKE_CURRENT_BINARY_DIR}/html/ COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/eigen_navtree_hacks.js ${CMAKE_CURRENT_BINARY_DIR}/html/ COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/Eigen_Silly_Professor_64x64.png ${CMAKE_CURRENT_BINARY_DIR}/html/ + COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/ftv2pnode.png ${CMAKE_CURRENT_BINARY_DIR}/html/ + COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/ftv2node.png ${CMAKE_CURRENT_BINARY_DIR}/html/ COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/AsciiQuickReference.txt ${CMAKE_CURRENT_BINARY_DIR}/html/ WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR} ) @@ -88,6 +90,8 @@ add_custom_target( COMMAND ${CMAKE_COMMAND} -E make_directory ${Eigen_BINARY_DIR}/doc/html/unsupported COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/eigen_navtree_hacks.js ${CMAKE_CURRENT_BINARY_DIR}/html/unsupported/ COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/Eigen_Silly_Professor_64x64.png ${CMAKE_CURRENT_BINARY_DIR}/html/unsupported/ + COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/ftv2pnode.png ${CMAKE_CURRENT_BINARY_DIR}/html/unsupported/ + COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/ftv2node.png ${CMAKE_CURRENT_BINARY_DIR}/html/unsupported/ WORKING_DIRECTORY ${Eigen_BINARY_DIR}/doc ) diff --git a/doc/CoeffwiseMathFunctionsTable.dox b/doc/CoeffwiseMathFunctionsTable.dox index c466c14c8..ac6e0bd31 100644 --- a/doc/CoeffwiseMathFunctionsTable.dox +++ b/doc/CoeffwiseMathFunctionsTable.dox @@ -3,11 +3,11 @@ namespace Eigen { /** \eigenManualPage CoeffwiseMathFunctions Catalog of coefficient-wise math functions -<span style="font-size:300%; color:red; font-weight: 900;">!WORK IN PROGRESS!</span> +<!-- <span style="font-size:300%; color:red; font-weight: 900;">!WORK IN PROGRESS!</span> --> This table presents a catalog of the coefficient-wise math functions supported by %Eigen. In this table, \c a, \c b, refer to Array objects or expressions, and \c m refers to a linear algebra Matrix/Vector object. Standard scalar types are abbreviated as follows: - - \c int: \c ui32 + - \c int: \c i32 - \c float: \c f - \c double: \c d - \c std::complex<float>: \c cf @@ -43,7 +43,35 @@ This also means that, unless specified, if the function \c std::foo is available using <a href="http://en.cppreference.com/w/cpp/numeric/math/fabs">std::abs</a>; \n abs(a[i]); </td> - <td>SSE2, AVX (ui32,f,d)</td> + <td>SSE2, AVX (i32,f,d)</td> +</tr> +<tr> + <td class="code"> + \anchor cwisetable_inverse + a.\link ArrayBase::inverse inverse\endlink(); \n + \link Eigen::inverse inverse\endlink(a); \n + m.\link MatrixBase::cwiseInverse cwiseInverse\endlink(); + </td> + <td>inverse value (\f$ 1/a_i \f$) </td> + <td class="code"> + 1/a[i]; + </td> + <td>All engines (f,d,fc,fd)</td> +</tr> +<tr> + <td class="code"> + \anchor cwisetable_conj + a.\link ArrayBase::conjugate conjugate\endlink(); \n + \link Eigen::conj conj\endlink(a); \n + m.\link MatrixBase::conjugate conjugate(); + </td> + <td><a href="https://en.wikipedia.org/wiki/Complex_conjugate">complex conjugate</a> (\f$ \bar{a_i} \f$),\n + no-op for real </td> + <td class="code"> + using <a href="http://en.cppreference.com/w/cpp/numeric/complex/conj">std::conj</a>; \n + conj(a[i]); + </td> + <td>All engines (fc,fd)</td> </tr> <tr> <th colspan="4">Exponential functions</th> @@ -67,12 +95,12 @@ This also means that, unless specified, if the function \c std::foo is available a.\link ArrayBase::log log\endlink(); \n \link Eigen::log log\endlink(a); </td> - <td>natural (base \f$ e \f$) logarithm (\f$ ln({a_i}) \f$)</td> + <td>natural (base \f$ e \f$) logarithm (\f$ \ln({a_i}) \f$)</td> <td class="code"> using <a href="http://en.cppreference.com/w/cpp/numeric/math/log">std::log</a>; \n log(a[i]); </td> - <td>SSE2, AVX (f,d)</td> + <td>SSE2, AVX (f)</td> </tr> <tr> <td class="code"> @@ -80,23 +108,298 @@ This also means that, unless specified, if the function \c std::foo is available a.\link ArrayBase::log1p log1p\endlink(); \n \link Eigen::log1p log1p\endlink(a); </td> - <td>natural (base \f$ e \f$) logarithm of 1 plus \n the given number (\f$ ln({1+a_i}) \f$)</td> + <td>natural (base \f$ e \f$) logarithm of 1 plus \n the given number (\f$ \ln({1+a_i}) \f$)</td> <td>built-in generic implementation based on \c log,\n plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/log1p">\c std::log1p </a>; \cpp11</td> <td></td> </tr> <tr> + <td class="code"> + \anchor cwisetable_log10 + a.\link ArrayBase::log10 log10\endlink(); \n + \link Eigen::log10 log10\endlink(a); + </td> + <td>base 10 logarithm (\f$ \log_{10}({a_i}) \f$)</td> + <td class="code"> + using <a href="http://en.cppreference.com/w/cpp/numeric/math/log10">std::log10</a>; \n + log10(a[i]); + </td> + <td></td> +</tr> +<tr> <th colspan="4">Power functions</th> </tr> <tr> + <td class="code"> + \anchor cwisetable_pow + a.\link ArrayBase::pow pow\endlink(b); \n + \link Eigen::pow pow\endlink(a,b); + </td> + <td>raises a number to the given power (\f$ a_i ^ {b_i} \f$) \n \c a and \c b can be either an array or scalar.</td> + <td class="code"> + using <a href="http://en.cppreference.com/w/cpp/numeric/math/pow">std::pow</a>; \n + pow(a[i],b[i]);\n + (plus builtin for integer types)</td> + <td></td> +</tr> +<tr> + <td class="code"> + \anchor cwisetable_sqrt + a.\link ArrayBase::sqrt sqrt\endlink(); \n + \link Eigen::sqrt sqrt\endlink(a);\n + m.\link MatrixBase::cwiseSqrt cwiseSqrt\endlink(); + </td> + <td>computes square root (\f$ \sqrt a_i \f$)</td> + <td class="code"> + using <a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt">std::sqrt</a>; \n + sqrt(a[i]);</td> + <td>SSE2, AVX (f,d)</td> +</tr> +<tr> + <td class="code"> + \anchor cwisetable_rsqrt + a.\link ArrayBase::rsqrt rsqrt\endlink(); \n + \link Eigen::rsqrt rsqrt\endlink(a); + </td> + <td><a href="https://en.wikipedia.org/wiki/Fast_inverse_square_root">reciprocal square root</a> (\f$ 1/{\sqrt a_i} \f$)</td> + <td class="code"> + using <a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt">std::sqrt</a>; \n + 1/sqrt(a[i]); \n + </td> + <td>SSE2, AVX, AltiVec, ZVector (f,d)\n + (approx + 1 Newton iteration)</td> +</tr> +<tr> + <td class="code"> + \anchor cwisetable_square + a.\link ArrayBase::square square\endlink(); \n + \link Eigen::square square\endlink(a); + </td> + <td>computes square power (\f$ a_i^2 \f$)</td> + <td class="code"> + a[i]*a[i]</td> + <td>All (i32,f,d,cf,cd)</td> +</tr> +<tr> + <td class="code"> + \anchor cwisetable_cube + a.\link ArrayBase::cube cube\endlink(); \n + \link Eigen::cube cube\endlink(a); + </td> + <td>computes cubic power (\f$ a_i^3 \f$)</td> + <td class="code"> + a[i]*a[i]*a[i]</td> + <td>All (i32,f,d,cf,cd)</td> +</tr> +<tr> + <td class="code"> + \anchor cwisetable_abs2 + a.\link ArrayBase::abs2 abs2\endlink(); \n + \link Eigen::abs2 abs2\endlink(a);\n + m.\link MatrixBase::cwiseAbs2 cwiseAbs2\endlink(); + </td> + <td>computes the squared absolute value (\f$ |a_i|^2 \f$)</td> + <td class="code"> + real: a[i]*a[i] \n + complex: real(a[i])*real(a[i]) \n + + imag(a[i])*imag(a[i])</td> + <td>All (i32,f,d)</td> +</tr> +<tr> <th colspan="4">Trigonometric functions</th> </tr> <tr> + <td class="code"> + \anchor cwisetable_sin + a.\link ArrayBase::sin sin\endlink(); \n + \link Eigen::sin sin\endlink(a); + </td> + <td>computes sine</td> + <td class="code"> + using <a href="http://en.cppreference.com/w/cpp/numeric/math/sin">std::sin</a>; \n + sin(a[i]);</td> + <td>SSE2, AVX (f)</td> +</tr> +<tr> + <td class="code"> + \anchor cwisetable_cos + a.\link ArrayBase::cos cos\endlink(); \n + \link Eigen::cos cos\endlink(a); + </td> + <td>computes cosine</td> + <td class="code"> + using <a href="http://en.cppreference.com/w/cpp/numeric/math/cos">std::cos</a>; \n + cos(a[i]);</td> + <td>SSE2, AVX (f)</td> +</tr> +<tr> + <td class="code"> + \anchor cwisetable_tan + a.\link ArrayBase::tan tan\endlink(); \n + \link Eigen::tan tan\endlink(a); + </td> + <td>computes tangent</td> + <td class="code"> + using <a href="http://en.cppreference.com/w/cpp/numeric/math/tan">std::tan</a>; \n + tan(a[i]);</td> + <td></td> +</tr> +<tr> + <td class="code"> + \anchor cwisetable_asin + a.\link ArrayBase::asin asin\endlink(); \n + \link Eigen::asin asin\endlink(a); + </td> + <td>computes arc sine (\f$ \sin^{-1} a_i \f$)</td> + <td class="code"> + using <a href="http://en.cppreference.com/w/cpp/numeric/math/asin">std::asin</a>; \n + asin(a[i]);</td> + <td></td> +</tr> +<tr> + <td class="code"> + \anchor cwisetable_acos + a.\link ArrayBase::acos acos\endlink(); \n + \link Eigen::acos acos\endlink(a); + </td> + <td>computes arc cosine (\f$ \cos^{-1} a_i \f$)</td> + <td class="code"> + using <a href="http://en.cppreference.com/w/cpp/numeric/math/acos">std::acos</a>; \n + acos(a[i]);</td> + <td></td> +</tr> +<tr> + <td class="code"> + \anchor cwisetable_atan + a.\link ArrayBase::atan tan\endlink(); \n + \link Eigen::atan atan\endlink(a); + </td> + <td>computes arc tangent (\f$ \tan^{-1} a_i \f$)</td> + <td class="code"> + using <a href="http://en.cppreference.com/w/cpp/numeric/math/atan">std::atan</a>; \n + atan(a[i]);</td> + <td></td> +</tr> +<tr> <th colspan="4">Hyperbolic functions</th> </tr> <tr> + <td class="code"> + \anchor cwisetable_sinh + a.\link ArrayBase::sinh sinh\endlink(); \n + \link Eigen::sinh sinh\endlink(a); + </td> + <td>computes hyperbolic sine</td> + <td class="code"> + using <a href="http://en.cppreference.com/w/cpp/numeric/math/sinh">std::sinh</a>; \n + sinh(a[i]);</td> + <td></td> +</tr> +<tr> + <td class="code"> + \anchor cwisetable_cosh + a.\link ArrayBase::cosh cohs\endlink(); \n + \link Eigen::cosh cosh\endlink(a); + </td> + <td>computes hyperbolic cosine</td> + <td class="code"> + using <a href="http://en.cppreference.com/w/cpp/numeric/math/cosh">std::cosh</a>; \n + cosh(a[i]);</td> + <td></td> +</tr> +<tr> + <td class="code"> + \anchor cwisetable_tanh + a.\link ArrayBase::tanh tanh\endlink(); \n + \link Eigen::tanh tanh\endlink(a); + </td> + <td>computes hyperbolic tangent</td> + <td class="code"> + using <a href="http://en.cppreference.com/w/cpp/numeric/math/tanh">std::tanh</a>; \n + tanh(a[i]);</td> + <td></td> +</tr> +<tr> +<th colspan="4">Nearest integer floating point operations</th> +</tr> +<tr> + <td class="code"> + \anchor cwisetable_ceil + a.\link ArrayBase::ceil ceil\endlink(); \n + \link Eigen::ceil ceil\endlink(a); + </td> + <td>nearest integer not less than the given value</td> + <td class="code"> + using <a href="http://en.cppreference.com/w/cpp/numeric/math/ceil">std::ceil</a>; \n + ceil(a[i]);</td> + <td>SSE4,AVX,ZVector (f,d)</td> +</tr> +<tr> + <td class="code"> + \anchor cwisetable_floor + a.\link ArrayBase::floor floor\endlink(); \n + \link Eigen::floor floor\endlink(a); + </td> + <td>nearest integer not greater than the given value</td> + <td class="code"> + using <a href="http://en.cppreference.com/w/cpp/numeric/math/floor">std::floor</a>; \n + floor(a[i]);</td> + <td>SSE4,AVX,ZVector (f,d)</td> +</tr> +<tr> + <td class="code"> + \anchor cwisetable_round + a.\link ArrayBase::round round\endlink(); \n + \link Eigen::round round\endlink(a); + </td> + <td>nearest integer, \n rounding away from zero in halfway cases</td> + <td>built-in generic implementation \n based on \c floor and \c ceil,\n + plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/round">\c std::round </a>; \cpp11</td> + <td>SSE4,AVX,ZVector (f,d)</td> +</tr> +<tr> +<th colspan="4">Floating point manipulation functions</th> +</tr> +<tr> +<th colspan="4">Classification and comparison</th> +</tr> +<tr> + <td class="code"> + \anchor cwisetable_isfinite + a.\link ArrayBase::isfinite isfinite\endlink(); \n + \link Eigen::isfinite isfinite\endlink(a); + </td> + <td>checks if the given number has finite value</td> + <td>built-in generic implementation,\n + plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/isfinite">\c std::isfinite </a>; \cpp11</td> + <td></td> +</tr> +<tr> + <td class="code"> + \anchor cwisetable_isinf + a.\link ArrayBase::isinf isinf\endlink(); \n + \link Eigen::isinf isinf\endlink(a); + </td> + <td>checks if the given number is infinite</td> + <td>built-in generic implementation,\n + plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/isinf">\c std::isinf </a>; \cpp11</td> + <td></td> +</tr> +<tr> + <td class="code"> + \anchor cwisetable_isnan + a.\link ArrayBase::isnan isnan\endlink(); \n + \link Eigen::isnan isnan\endlink(a); + </td> + <td>checks if the given number is not a number</td> + <td>built-in generic implementation,\n + plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/isnan">\c std::isnan </a>; \cpp11</td> + <td></td> +</tr> +<tr> <th colspan="4">Error and gamma functions</th> </tr> +<tr> <td colspan="4"> Require \c #include \c <unsupported/Eigen/SpecialFunctions> </td></tr> <tr> <td class="code"> \anchor cwisetable_erf @@ -124,24 +427,89 @@ This also means that, unless specified, if the function \c std::foo is available <td></td> </tr> <tr> -<th colspan="4">Nearest integer floating point operations</th> + <td class="code"> + \anchor cwisetable_lgamma + a.\link ArrayBase::lgamma lgamma\endlink(); \n + \link Eigen::lgamma lgamma\endlink(a); + </td> + <td>natural logarithm of the gamma function</td> + <td class="code"> + using <a href="http://en.cppreference.com/w/cpp/numeric/math/lgamma">std::lgamma</a>; \cpp11 \n + lgamma(a[i]); + </td> + <td></td> </tr> <tr> -<th colspan="4">Floating point manipulation functions</th> + <td class="code"> + \anchor cwisetable_digamma + a.\link ArrayBase::digamma digamma\endlink(); \n + \link Eigen::digamma digamma\endlink(a); + </td> + <td><a href="https://en.wikipedia.org/wiki/Digamma_function">logarithmic derivative of the gamma function</a></td> + <td> + built-in for float and double + </td> + <td></td> </tr> <tr> -<th colspan="4">Classification and comparison</th> + <td class="code"> + \anchor cwisetable_igamma + \link Eigen::igamma igamma\endlink(a,x); + </td> + <td><a href="https://en.wikipedia.org/wiki/Incomplete_gamma_function">lower incomplete gamma integral</a> + \n \f$ \gamma(a_i,x_i)= \frac{1}{|a_i|} \int_{0}^{x_i}e^{\text{-}t} t^{a_i-1} \mathrm{d} t \f$</td> + <td> + built-in for float and double,\n but requires \cpp11 + </td> + <td></td> +</tr> +<tr> + <td class="code"> + \anchor cwisetable_igammac + \link Eigen::igammac igammac\endlink(a,x); + </td> + <td><a href="https://en.wikipedia.org/wiki/Incomplete_gamma_function">upper incomplete gamma integral</a> + \n \f$ \Gamma(a_i,x_i) = \frac{1}{|a_i|} \int_{x_i}^{\infty}e^{\text{-}t} t^{a_i-1} \mathrm{d} t \f$</td> + <td> + built-in for float and double,\n but requires \cpp11 + </td> + <td></td> +</tr> +<tr> +<th colspan="4">Special functions</th> +</tr> +<tr> <td colspan="4"> Require \c #include \c <unsupported/Eigen/SpecialFunctions> </td></tr> +<tr> + <td class="code"> + \anchor cwisetable_polygamma + \link Eigen::polygamma polygamma\endlink(n,x); + </td> + <td><a href="https://en.wikipedia.org/wiki/Polygamma_function">n-th derivative of digamma at x</a></td> + <td> + built-in generic based on\n <a href="#cwisetable_lgamma">\c lgamma </a>, + <a href="#cwisetable_digamma"> \c digamma </a> + and <a href="#cwisetable_zeta">\c zeta </a>. + </td> + <td></td> </tr> <tr> -<th colspan="4">Miscellaneous</th> + <td class="code"> + \anchor cwisetable_betainc + \link Eigen::betainc betainc\endlink(a,b,x); + </td> + <td><a href="https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function">Incomplete beta function</a></td> + <td> + built-in for float and double,\n but requires \cpp11 + </td> + <td></td> </tr> <tr> <td class="code"> \anchor cwisetable_zeta - a.\link ArrayBase::zeta zeta\endlink(b); \n \link Eigen::zeta zeta\endlink(a,b); </td> - <td><a href="https://en.wikipedia.org/wiki/Hurwitz_zeta_function">Hurwitz zeta function</a> \n \f$ \zeta(a_i,b_i)=\sum_{k=0}^{\infty}(b_i+k)^{\text{-}a_i} \f$</td> + <td><a href="https://en.wikipedia.org/wiki/Hurwitz_zeta_function">Hurwitz zeta function</a> + \n \f$ \zeta(a_i,b_i)=\sum_{k=0}^{\infty}(b_i+k)^{\text{-}a_i} \f$</td> <td> built-in for float and double </td> diff --git a/doc/CustomizingEigen.dox b/doc/CustomizingEigen.dox index 607f86658..1b15c69a4 100644 --- a/doc/CustomizingEigen.dox +++ b/doc/CustomizingEigen.dox @@ -165,8 +165,7 @@ This other example adds support for the \c mpq_class type from <a href="https:// #include <boost/operators.hpp> namespace Eigen { - template<class> struct NumTraits; - template<> struct NumTraits<mpq_class> + template<> struct NumTraits<mpq_class> : GenericNumTraits<mpq_class> { typedef mpq_class Real; typedef mpq_class NonInteger; @@ -174,6 +173,7 @@ namespace Eigen { static inline Real epsilon() { return 0; } static inline Real dummy_precision() { return 0; } + static inline Real digits10() { return 0; } enum { IsInteger = 0, @@ -187,31 +187,25 @@ namespace Eigen { }; namespace internal { - template<> - struct significant_decimals_impl<mpq_class> - { - // Infinite precision when printing - static inline int run() { return 0; } - }; template<> struct scalar_score_coeff_op<mpq_class> { struct result_type : boost::totally_ordered1<result_type> { - std::size_t len; - result_type(int i = 0) : len(i) {} // Eigen uses Score(0) and Score() - result_type(mpq_class const& q) : - len(mpz_size(q.get_num_mpz_t())+ - mpz_size(q.get_den_mpz_t())-1) {} - friend bool operator<(result_type x, result_type y) { - // 0 is the worst possible pivot - if (x.len == 0) return y.len > 0; - if (y.len == 0) return false; - // Prefer a pivot with a small representation - return x.len > y.len; - } - friend bool operator==(result_type x, result_type y) { - // Only used to test if the score is 0 - return x.len == y.len; - } + std::size_t len; + result_type(int i = 0) : len(i) {} // Eigen uses Score(0) and Score() + result_type(mpq_class const& q) : + len(mpz_size(q.get_num_mpz_t())+ + mpz_size(q.get_den_mpz_t())-1) {} + friend bool operator<(result_type x, result_type y) { + // 0 is the worst possible pivot + if (x.len == 0) return y.len > 0; + if (y.len == 0) return false; + // Prefer a pivot with a small representation + return x.len > y.len; + } + friend bool operator==(result_type x, result_type y) { + // Only used to test if the score is 0 + return x.len == y.len; + } }; result_type operator()(mpq_class const& x) const { return x; } }; diff --git a/doc/DenseDecompositionBenchmark.dox b/doc/DenseDecompositionBenchmark.dox new file mode 100644 index 000000000..7be9c70cd --- /dev/null +++ b/doc/DenseDecompositionBenchmark.dox @@ -0,0 +1,42 @@ +namespace Eigen { + +/** \eigenManualPage DenseDecompositionBenchmark Benchmark of dense decompositions + +This page presents a speed comparison of the dense matrix decompositions offered by %Eigen for a wide range of square matrices and overconstrained problems. + +For a more general overview on the features and numerical robustness of linear solvers and decompositions, check this \link TopicLinearAlgebraDecompositions table \endlink. + +This benchmark has been run on a laptop equipped with an Intel core i7 \@ 2,6 GHz, and compiled with clang with \b AVX and \b FMA instruction sets enabled but without multi-threading. +It uses \b single \b precision \b float numbers. For double, you can get a good estimate by multiplying the timings by a factor 2. + +The square matrices are symmetric, and for the overconstrained matrices, the reported timmings include the cost to compute the symmetric covariance matrix \f$ A^T A \f$ for the first four solvers based on Cholesky and LU, as denoted by the \b * symbol (top-right corner part of the table). +Timings are in \b milliseconds, and factors are relative to the LLT decomposition which is the fastest but also the least general and robust. + +<table class="manual"> +<tr><th>solver/size</th> + <th>8x8</th> <th>100x100</th> <th>1000x1000</th> <th>4000x4000</th> <th>10000x8</th> <th>10000x100</th> <th>10000x1000</th> <th>10000x4000</th></tr> +<tr><td>LLT</td><td>0.05</td><td>0.42</td><td>5.83</td><td>374.55</td><td>6.79 <sup><a href="#note_ls">*</a></sup></td><td>30.15 <sup><a href="#note_ls">*</a></sup></td><td>236.34 <sup><a href="#note_ls">*</a></sup></td><td>3847.17 <sup><a href="#note_ls">*</a></sup></td></tr> +<tr class="alt"><td>LDLT</td><td>0.07 (x1.3)</td><td>0.65 (x1.5)</td><td>26.86 (x4.6)</td><td>2361.18 (x6.3)</td><td>6.81 (x1) <sup><a href="#note_ls">*</a></sup></td><td>31.91 (x1.1) <sup><a href="#note_ls">*</a></sup></td><td>252.61 (x1.1) <sup><a href="#note_ls">*</a></sup></td><td>5807.66 (x1.5) <sup><a href="#note_ls">*</a></sup></td></tr> +<tr><td>PartialPivLU</td><td>0.08 (x1.5)</td><td>0.69 (x1.6)</td><td>15.63 (x2.7)</td><td>709.32 (x1.9)</td><td>6.81 (x1) <sup><a href="#note_ls">*</a></sup></td><td>31.32 (x1) <sup><a href="#note_ls">*</a></sup></td><td>241.68 (x1) <sup><a href="#note_ls">*</a></sup></td><td>4270.48 (x1.1) <sup><a href="#note_ls">*</a></sup></td></tr> +<tr class="alt"><td>FullPivLU</td><td>0.1 (x1.9)</td><td>4.48 (x10.6)</td><td>281.33 (x48.2)</td><td>-</td><td>6.83 (x1) <sup><a href="#note_ls">*</a></sup></td><td>32.67 (x1.1) <sup><a href="#note_ls">*</a></sup></td><td>498.25 (x2.1) <sup><a href="#note_ls">*</a></sup></td><td>-</td></tr> +<tr><td>HouseholderQR</td><td>0.19 (x3.5)</td><td>2.18 (x5.2)</td><td>23.42 (x4)</td><td>1337.52 (x3.6)</td><td>34.26 (x5)</td><td>129.01 (x4.3)</td><td>377.37 (x1.6)</td><td>4839.1 (x1.3)</td></tr> +<tr class="alt"><td>ColPivHouseholderQR</td><td>0.23 (x4.3)</td><td>2.23 (x5.3)</td><td>103.34 (x17.7)</td><td>9987.16 (x26.7)</td><td>36.05 (x5.3)</td><td>163.18 (x5.4)</td><td>2354.08 (x10)</td><td>37860.5 (x9.8)</td></tr> +<tr><td>CompleteOrthogonalDecomposition</td><td>0.23 (x4.3)</td><td>2.22 (x5.2)</td><td>99.44 (x17.1)</td><td>10555.3 (x28.2)</td><td>35.75 (x5.3)</td><td>169.39 (x5.6)</td><td>2150.56 (x9.1)</td><td>36981.8 (x9.6)</td></tr> +<tr class="alt"><td>FullPivHouseholderQR</td><td>0.23 (x4.3)</td><td>4.64 (x11)</td><td>289.1 (x49.6)</td><td>-</td><td>69.38 (x10.2)</td><td>446.73 (x14.8)</td><td>4852.12 (x20.5)</td><td>-</td></tr> +<tr><td>JacobiSVD</td><td>1.01 (x18.6)</td><td>71.43 (x168.4)</td><td>-</td><td>-</td><td>113.81 (x16.7)</td><td>1179.66 (x39.1)</td><td>-</td><td>-</td></tr> +<tr class="alt"><td>BDCSVD</td><td>1.07 (x19.7)</td><td>21.83 (x51.5)</td><td>331.77 (x56.9)</td><td>18587.9 (x49.6)</td><td>110.53 (x16.3)</td><td>397.67 (x13.2)</td><td>2975 (x12.6)</td><td>48593.2 (x12.6)</td></tr> +</table> + +<a name="note_ls">\b *: </a> This decomposition do not support direct least-square solving for over-constrained problems, and the reported timing include the cost to form the symmetric covariance matrix \f$ A^T A \f$. + +\b Observations: + + LLT is always the fastest solvers. + + For largely over-constrained problems, the cost of Cholesky/LU decompositions is dominated by the computation of the symmetric covariance matrix. + + For large problem sizes, only the decomposition implementing a cache-friendly blocking strategy scale well. Those include LLT, PartialPivLU, HouseholderQR, and BDCSVD. This explain why for a 4k x 4k matrix, HouseholderQR is faster than LDLT. In the future, LDLT and ColPivHouseholderQR will also implement blocking strategies. + + CompleteOrthogonalDecomposition is based on ColPivHouseholderQR and they thus achieve the same level of performance. + +The above table has been generated by the <a href="https://bitbucket.org/eigen/eigen/raw/default/bench/dense_solvers.cpp">bench/dense_solvers.cpp</a> file, feel-free to hack it to generate a table matching your hardware, compiler, and favorite problem sizes. + +*/ + +} diff --git a/doc/Doxyfile.in b/doc/Doxyfile.in index 0c3673f89..058c88b97 100644 --- a/doc/Doxyfile.in +++ b/doc/Doxyfile.in @@ -216,6 +216,7 @@ ALIASES = "only_for_vectors=This is only for vectors (either row- "lu_module=This is defined in the %LU module. \code #include <Eigen/LU> \endcode" \ "qr_module=This is defined in the %QR module. \code #include <Eigen/QR> \endcode" \ "svd_module=This is defined in the %SVD module. \code #include <Eigen/SVD> \endcode" \ + "specialfunctions_module=This is defined in the \b unsupported SpecialFunctions module. \code #include <Eigen/SpecialFunctions> \endcode" \ "label=\bug" \ "matrixworld=<a href='#matrixonly' style='color:green;text-decoration: none;'>*</a>" \ "arrayworld=<a href='#arrayonly' style='color:blue;text-decoration: none;'>*</a>" \ diff --git a/doc/InplaceDecomposition.dox b/doc/InplaceDecomposition.dox new file mode 100644 index 000000000..cb1c6d413 --- /dev/null +++ b/doc/InplaceDecomposition.dox @@ -0,0 +1,115 @@ +namespace Eigen { + +/** \eigenManualPage InplaceDecomposition Inplace matrix decompositions + +Starting from %Eigen 3.3, the LU, Cholesky, and QR decompositions can operate \em inplace, that is, directly within the given input matrix. +This feature is especially useful when dealing with huge matrices, and or when the available memory is very limited (embedded systems). + +To this end, the respective decomposition class must be instantiated with a Ref<> matrix type, and the decomposition object must be constructed with the input matrix as argument. As an example, let us consider an inplace LU decomposition with partial pivoting. + +Let's start with the basic inclusions, and declaration of a 2x2 matrix \c A: + +<table class="example"> +<tr><th>code</th><th>output</th></tr> +<tr> + <td>\snippet TutorialInplaceLU.cpp init + </td> + <td>\snippet TutorialInplaceLU.out init + </td> +</tr> +</table> + +No surprise here! Then, let's declare our inplace LU object \c lu, and check the content of the matrix \c A: + +<table class="example"> +<tr> + <td>\snippet TutorialInplaceLU.cpp declaration + </td> + <td>\snippet TutorialInplaceLU.out declaration + </td> +</tr> +</table> + +Here, the \c lu object computes and stores the \c L and \c U factors within the memory held by the matrix \c A. +The coefficients of \c A have thus been destroyed during the factorization, and replaced by the L and U factors as one can verify: + +<table class="example"> +<tr> + <td>\snippet TutorialInplaceLU.cpp matrixLU + </td> + <td>\snippet TutorialInplaceLU.out matrixLU + </td> +</tr> +</table> + +Then, one can use the \c lu object as usual, for instance to solve the Ax=b problem: +<table class="example"> +<tr> + <td>\snippet TutorialInplaceLU.cpp solve + </td> + <td>\snippet TutorialInplaceLU.out solve + </td> +</tr> +</table> + +Here, since the content of the original matrix \c A has been lost, we had to declared a new matrix \c A0 to verify the result. + +Since the memory is shared between \c A and \c lu, modifying the matrix \c A will make \c lu invalid. +This can easily be verified by modifying the content of \c A and trying to solve the initial problem again: + +<table class="example"> +<tr> + <td>\snippet TutorialInplaceLU.cpp modifyA + </td> + <td>\snippet TutorialInplaceLU.out modifyA + </td> +</tr> +</table> + +Note that there is no shared pointer under the hood, it is the \b responsibility \b of \b the \b user to keep the input matrix \c A in life as long as \c lu is living. + +If one wants to update the factorization with the modified A, one has to call the compute method as usual: +<table class="example"> +<tr> + <td>\snippet TutorialInplaceLU.cpp recompute + </td> + <td>\snippet TutorialInplaceLU.out recompute + </td> +</tr> +</table> + +Note that calling compute does not change the memory which is referenced by the \c lu object. Therefore, if the compute method is called with another matrix \c A1 different than \c A, then the content of \c A1 won't be modified. This is still the content of \c A that will be used to store the L and U factors of the matrix \c A1. +This can easily be verified as follows: +<table class="example"> +<tr> + <td>\snippet TutorialInplaceLU.cpp recompute_bis0 + </td> + <td>\snippet TutorialInplaceLU.out recompute_bis0 + </td> +</tr> +</table> +The matrix \c A1 is unchanged, and one can thus solve A1*x=b, and directly check the residual without any copy of \c A1: +<table class="example"> +<tr> + <td>\snippet TutorialInplaceLU.cpp recompute_bis1 + </td> + <td>\snippet TutorialInplaceLU.out recompute_bis1 + </td> +</tr> +</table> + + +Here is the list of matrix decompositions supporting this inplace mechanism: + +- class LLT +- class LDLT +- class PartialPivLU +- class FullPivLU +- class HouseholderQR +- class ColPivHouseholderQR +- class FullPivHouseholderQR +- class CompleteOrthogonalDecomposition + +*/ + +}
\ No newline at end of file diff --git a/doc/Manual.dox b/doc/Manual.dox index 8940b0070..db73e1199 100644 --- a/doc/Manual.dox +++ b/doc/Manual.dox @@ -10,6 +10,7 @@ namespace Eigen { - \subpage TopicAssertions - \subpage TopicCustomizingEigen - \subpage TopicMultiThreading + - \subpage TopicUsingBlasLapack - \subpage TopicUsingIntelMKL - \subpage TopicCUDA - \subpage TopicPitfalls @@ -106,6 +107,10 @@ namespace Eigen { \ingroup DenseLinearSolvers_chapter */ /** \addtogroup LeastSquares \ingroup DenseLinearSolvers_chapter */ +/** \addtogroup InplaceDecomposition + \ingroup DenseLinearSolvers_chapter */ +/** \addtogroup DenseDecompositionBenchmark + \ingroup DenseLinearSolvers_chapter */ /** \addtogroup DenseLinearSolvers_Reference \ingroup DenseLinearSolvers_chapter */ diff --git a/doc/MatrixfreeSolverExample.dox b/doc/MatrixfreeSolverExample.dox index 000cb0bbe..3efa292b5 100644 --- a/doc/MatrixfreeSolverExample.dox +++ b/doc/MatrixfreeSolverExample.dox @@ -6,12 +6,12 @@ namespace Eigen { \eigenManualPage MatrixfreeSolverExample Matrix-free solvers Iterative solvers such as ConjugateGradient and BiCGSTAB can be used in a matrix free context. To this end, user must provide a wrapper class inheriting EigenBase<> and implementing the following methods: - - Index rows() and Index cols(): returns number of rows and columns respectively - - operator* with and %Eigen dense column vector (its actual implementation goes in a specialization of the internal::generic_product_impl class) + - \c Index \c rows() and \c Index \c cols(): returns number of rows and columns respectively + - \c operator* with your type and an %Eigen dense column vector (its actual implementation goes in a specialization of the internal::generic_product_impl class) -Eigen::internal::traits<> must also be specialized for the wrapper type. +\c Eigen::internal::traits<> must also be specialized for the wrapper type. -Here is a complete example wrapping a Eigen::SparseMatrix: +Here is a complete example wrapping an Eigen::SparseMatrix: \include matrixfree_cg.cpp Output: \verbinclude matrixfree_cg.out diff --git a/doc/SparseLinearSystems.dox b/doc/SparseLinearSystems.dox index ee4f53a4e..fc33b93e7 100644 --- a/doc/SparseLinearSystems.dox +++ b/doc/SparseLinearSystems.dox @@ -76,6 +76,9 @@ They are summarized in the following tables: <tr><td>SPQR</td><td>\link SPQRSupport_Module SPQRSupport \endlink </td> <td> QR factorization </td> <td> Any, rectangular</td><td>fill-in reducing, multithreaded, fast dense algebra</td> <td> requires the <a href="http://www.suitesparse.com">SuiteSparse</a> package, \b GPL </td><td>recommended for linear least-squares problems, has a rank-revealing feature</tr> +<tr><td>PardisoLLT \n PardisoLDLT \n PardisoLU</td><td>\link PardisoSupport_Module PardisoSupport \endlink</td><td>Direct LLt, LDLt, LU factorizations</td><td>SPD \n SPD \n Square</td><td>Fill-in reducing, Leverage fast dense algebra, Multithreading</td> + <td>Requires the <a href="http://eigen.tuxfamily.org/Counter/redirect_to_mkl.php">Intel MKL</a> package, \b Proprietary </td> + <td>optimized for tough problems patterns, see also \link TopicUsingIntelMKL using MKL with Eigen \endlink</td></tr> </table> Here \c SPD means symmetric positive definite. diff --git a/doc/TopicLinearAlgebraDecompositions.dox b/doc/TopicLinearAlgebraDecompositions.dox index 5bcff2c96..491470627 100644 --- a/doc/TopicLinearAlgebraDecompositions.dox +++ b/doc/TopicLinearAlgebraDecompositions.dox @@ -4,6 +4,7 @@ namespace Eigen { This page presents a catalogue of the dense matrix decompositions offered by Eigen. For an introduction on linear solvers and decompositions, check this \link TutorialLinearAlgebra page \endlink. +To get an overview of the true relative speed of the different decomposition, check this \link DenseDecompositionBenchmark benchmark \endlink. \section TopicLinAlgBigTable Catalogue of decompositions offered by Eigen @@ -256,6 +257,7 @@ For an introduction on linear solvers and decompositions, check this \link Tutor <dd></dd> </dl> + */ } diff --git a/doc/UsingBlasLapackBackends.dox b/doc/UsingBlasLapackBackends.dox new file mode 100644 index 000000000..caa597122 --- /dev/null +++ b/doc/UsingBlasLapackBackends.dox @@ -0,0 +1,133 @@ +/* + Copyright (c) 2011, Intel Corporation. All rights reserved. + Copyright (C) 2011-2016 Gael Guennebaud <gael.guennebaud@inria.fr> + + Redistribution and use in source and binary forms, with or without modification, + are permitted provided that the following conditions are met: + + * Redistributions of source code must retain the above copyright notice, this + list of conditions and the following disclaimer. + * Redistributions in binary form must reproduce the above copyright notice, + this list of conditions and the following disclaimer in the documentation + and/or other materials provided with the distribution. + * Neither the name of Intel Corporation nor the names of its contributors may + be used to endorse or promote products derived from this software without + specific prior written permission. + + THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND + ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED + WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE + DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR + ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES + (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; + LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON + ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS + SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + + ******************************************************************************** + * Content : Documentation on the use of BLAS/LAPACK libraries through Eigen + ******************************************************************************** +*/ + +namespace Eigen { + +/** \page TopicUsingBlasLapack Using BLAS/LAPACK from %Eigen + + +Since %Eigen version 3.3 and later, any F77 compatible BLAS or LAPACK libraries can be used as backends for dense matrix products and dense matrix decompositions. +For instance, one can use <a href="http://eigen.tuxfamily.org/Counter/redirect_to_mkl.php">Intel® MKL</a>, Apple's Accelerate framework on OSX, <a href="http://www.openblas.net/">OpenBLAS</a>, <a href="http://www.netlib.org/lapack">Netlib LAPACK</a>, etc. + +Do not miss this \link TopicUsingIntelMKL page \endlink for further discussions on the specific use of Intel® MKL (also includes VML, PARDISO, etc.) + +In order to use an external BLAS and/or LAPACK library, you must link you own application to the respective libraries and their dependencies. +For LAPACK, you must also link to the standard <a href="http://www.netlib.org/lapack/lapacke.html">Lapacke</a> library, which is used as a convenient think layer between %Eigen's C++ code and LAPACK F77 interface. Then you must activate their usage by defining one or multiple of the following macros (\b before including any %Eigen's header): + +\note For Mac users, in order to use the lapack version shipped with the Accelerate framework, you also need the lapacke library. +Using <a href="https://www.macports.org/">MacPorts</a>, this is as easy as: +\code +sudo port install lapack +\endcode +and then use the following link flags: \c -framework \c Accelerate \c /opt/local/lib/lapack/liblapacke.dylib + +<table class="manual"> +<tr><td>\c EIGEN_USE_BLAS </td><td>Enables the use of external BLAS level 2 and 3 routines (compatible with any F77 BLAS interface)</td></tr> +<tr class="alt"><td>\c EIGEN_USE_LAPACKE </td><td>Enables the use of external Lapack routines via the <a href="http://www.netlib.org/lapack/lapacke.html">Lapacke</a> C interface to Lapack (compatible with any F77 LAPACK interface)</td></tr> +<tr><td>\c EIGEN_USE_LAPACKE_STRICT </td><td>Same as \c EIGEN_USE_LAPACKE but algorithms of lower numerical robustness are disabled. \n This currently concerns only JacobiSVD which otherwise would be replaced by \c gesvd that is less robust than Jacobi rotations.</td></tr> +</table> + +When doing so, a number of %Eigen's algorithms are silently substituted with calls to BLAS or LAPACK routines. +These substitutions apply only for \b Dynamic \b or \b large enough objects with one of the following four standard scalar types: \c float, \c double, \c complex<float>, and \c complex<double>. +Operations on other scalar types or mixing reals and complexes will continue to use the built-in algorithms. + +The breadth of %Eigen functionality that can be substituted is listed in the table below. +<table class="manual"> +<tr><th>Functional domain</th><th>Code example</th><th>BLAS/LAPACK routines</th></tr> +<tr><td>Matrix-matrix operations \n \c EIGEN_USE_BLAS </td><td>\code +m1*m2.transpose(); +m1.selfadjointView<Lower>()*m2; +m1*m2.triangularView<Upper>(); +m1.selfadjointView<Lower>().rankUpdate(m2,1.0); +\endcode</td><td>\code +?gemm +?symm/?hemm +?trmm +dsyrk/ssyrk +\endcode</td></tr> +<tr class="alt"><td>Matrix-vector operations \n \c EIGEN_USE_BLAS </td><td>\code +m1.adjoint()*b; +m1.selfadjointView<Lower>()*b; +m1.triangularView<Upper>()*b; +\endcode</td><td>\code +?gemv +?symv/?hemv +?trmv +\endcode</td></tr> +<tr><td>LU decomposition \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code +v1 = m1.lu().solve(v2); +\endcode</td><td>\code +?getrf +\endcode</td></tr> +<tr class="alt"><td>Cholesky decomposition \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code +v1 = m2.selfadjointView<Upper>().llt().solve(v2); +\endcode</td><td>\code +?potrf +\endcode</td></tr> +<tr><td>QR decomposition \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code +m1.householderQr(); +m1.colPivHouseholderQr(); +\endcode</td><td>\code +?geqrf +?geqp3 +\endcode</td></tr> +<tr class="alt"><td>Singular value decomposition \n \c EIGEN_USE_LAPACKE </td><td>\code +JacobiSVD<MatrixXd> svd; +svd.compute(m1, ComputeThinV); +\endcode</td><td>\code +?gesvd +\endcode</td></tr> +<tr><td>Eigen-value decompositions \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code +EigenSolver<MatrixXd> es(m1); +ComplexEigenSolver<MatrixXcd> ces(m1); +SelfAdjointEigenSolver<MatrixXd> saes(m1+m1.transpose()); +GeneralizedSelfAdjointEigenSolver<MatrixXd> + gsaes(m1+m1.transpose(),m2+m2.transpose()); +\endcode</td><td>\code +?gees +?gees +?syev/?heev +?syev/?heev, +?potrf +\endcode</td></tr> +<tr class="alt"><td>Schur decomposition \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code +RealSchur<MatrixXd> schurR(m1); +ComplexSchur<MatrixXcd> schurC(m1); +\endcode</td><td>\code +?gees +\endcode</td></tr> +</table> +In the examples, m1 and m2 are dense matrices and v1 and v2 are dense vectors. + +*/ + +} diff --git a/doc/UsingIntelMKL.dox b/doc/UsingIntelMKL.dox index dbe559e53..a1a3a18f2 100644 --- a/doc/UsingIntelMKL.dox +++ b/doc/UsingIntelMKL.dox @@ -32,107 +32,45 @@ namespace Eigen { -/** \page TopicUsingIntelMKL Using Intel® Math Kernel Library from Eigen +/** \page TopicUsingIntelMKL Using Intel® MKL from %Eigen -\section TopicUsingIntelMKL_Intro Eigen and Intel® Math Kernel Library (Intel® MKL) +<!-- \section TopicUsingIntelMKL_Intro Eigen and Intel® Math Kernel Library (Intel® MKL) --> + +Since %Eigen version 3.1 and later, users can benefit from built-in Intel® Math Kernel Library (MKL) optimizations with an installed copy of Intel MKL 10.3 (or later). -Since Eigen version 3.1 and later, users can benefit from built-in Intel MKL optimizations with an installed copy of Intel MKL 10.3 (or later). <a href="http://eigen.tuxfamily.org/Counter/redirect_to_mkl.php"> Intel MKL </a> provides highly optimized multi-threaded mathematical routines for x86-compatible architectures. Intel MKL is available on Linux, Mac and Windows for both Intel64 and IA32 architectures. \note Intel® MKL is a proprietary software and it is the responsibility of users to buy or register for community (free) Intel MKL licenses for their products. Moreover, the license of the user product has to allow linking to proprietary software that excludes any unmodified versions of the GPL. -Using Intel MKL through Eigen is easy: --# define the \c EIGEN_USE_MKL_ALL macro before including any Eigen's header +Using Intel MKL through %Eigen is easy: +-# define the \c EIGEN_USE_MKL_ALL macro before including any %Eigen's header -# link your program to MKL libraries (see the <a href="http://software.intel.com/en-us/articles/intel-mkl-link-line-advisor/">MKL linking advisor</a>) -# on a 64bits system, you must use the LP64 interface (not the ILP64 one) -When doing so, a number of Eigen's algorithms are silently substituted with calls to Intel MKL routines. +When doing so, a number of %Eigen's algorithms are silently substituted with calls to Intel MKL routines. These substitutions apply only for \b Dynamic \b or \b large enough objects with one of the following four standard scalar types: \c float, \c double, \c complex<float>, and \c complex<double>. Operations on other scalar types or mixing reals and complexes will continue to use the built-in algorithms. In addition you can choose which parts will be substituted by defining one or multiple of the following macros: <table class="manual"> -<tr><td>\c EIGEN_USE_BLAS </td><td>Enables the use of external BLAS level 2 and 3 routines (compatible with any F77 BLAS interface, not only Intel MKL)</td></tr> -<tr class="alt"><td>\c EIGEN_USE_LAPACKE </td><td>Enables the use of external Lapack routines via the <a href="http://www.netlib.org/lapack/lapacke.html">Intel Lapacke</a> C interface to Lapack (currently works with Intel MKL only)</td></tr> -<tr><td>\c EIGEN_USE_LAPACKE_STRICT </td><td>Same as \c EIGEN_USE_LAPACKE but algorithm of lower robustness are disabled. This currently concerns only JacobiSVD which otherwise would be replaced by \c gesvd that is less robust than Jacobi rotations.</td></tr> +<tr><td>\c EIGEN_USE_BLAS </td><td>Enables the use of external BLAS level 2 and 3 routines</td></tr> +<tr class="alt"><td>\c EIGEN_USE_LAPACKE </td><td>Enables the use of external Lapack routines via the <a href="http://www.netlib.org/lapack/lapacke.html">Lapacke</a> C interface to Lapack</td></tr> +<tr><td>\c EIGEN_USE_LAPACKE_STRICT </td><td>Same as \c EIGEN_USE_LAPACKE but algorithm of lower robustness are disabled. \n This currently concerns only JacobiSVD which otherwise would be replaced by \c gesvd that is less robust than Jacobi rotations.</td></tr> <tr class="alt"><td>\c EIGEN_USE_MKL_VML </td><td>Enables the use of Intel VML (vector operations)</td></tr> <tr><td>\c EIGEN_USE_MKL_ALL </td><td>Defines \c EIGEN_USE_BLAS, \c EIGEN_USE_LAPACKE, and \c EIGEN_USE_MKL_VML </td></tr> </table> -Finally, the PARDISO sparse solver shipped with Intel MKL can be used through the \ref PardisoLU, \ref PardisoLLT and \ref PardisoLDLT classes of the \ref PardisoSupport_Module. - +Note that the BLAS and LAPACKE backends can be enabled for any F77 compatible BLAS and LAPACK libraries. See this \link TopicUsingBlasLapack page \endlink for the details. -\section TopicUsingIntelMKL_SupportedFeatures List of supported features +Finally, the PARDISO sparse solver shipped with Intel MKL can be used through the \ref PardisoLU, \ref PardisoLLT and \ref PardisoLDLT classes of the \ref PardisoSupport_Module. -The breadth of Eigen functionality covered by Intel MKL is listed in the table below. +The following table summarizes the list of functions covered by \c EIGEN_USE_MKL_VML: <table class="manual"> -<tr><th>Functional domain</th><th>Code example</th><th>MKL routines</th></tr> -<tr><td>Matrix-matrix operations \n \c EIGEN_USE_BLAS </td><td>\code -m1*m2.transpose(); -m1.selfadjointView<Lower>()*m2; -m1*m2.triangularView<Upper>(); -m1.selfadjointView<Lower>().rankUpdate(m2,1.0); -\endcode</td><td>\code -?gemm -?symm/?hemm -?trmm -dsyrk/ssyrk -\endcode</td></tr> -<tr class="alt"><td>Matrix-vector operations \n \c EIGEN_USE_BLAS </td><td>\code -m1.adjoint()*b; -m1.selfadjointView<Lower>()*b; -m1.triangularView<Upper>()*b; -\endcode</td><td>\code -?gemv -?symv/?hemv -?trmv -\endcode</td></tr> -<tr><td>LU decomposition \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code -v1 = m1.lu().solve(v2); -\endcode</td><td>\code -?getrf -\endcode</td></tr> -<tr class="alt"><td>Cholesky decomposition \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code -v1 = m2.selfadjointView<Upper>().llt().solve(v2); -\endcode</td><td>\code -?potrf -\endcode</td></tr> -<tr><td>QR decomposition \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code -m1.householderQr(); -m1.colPivHouseholderQr(); -\endcode</td><td>\code -?geqrf -?geqp3 -\endcode</td></tr> -<tr class="alt"><td>Singular value decomposition \n \c EIGEN_USE_LAPACKE </td><td>\code -JacobiSVD<MatrixXd> svd; -svd.compute(m1, ComputeThinV); -\endcode</td><td>\code -?gesvd -\endcode</td></tr> -<tr><td>Eigen-value decompositions \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code -EigenSolver<MatrixXd> es(m1); -ComplexEigenSolver<MatrixXcd> ces(m1); -SelfAdjointEigenSolver<MatrixXd> saes(m1+m1.transpose()); -GeneralizedSelfAdjointEigenSolver<MatrixXd> - gsaes(m1+m1.transpose(),m2+m2.transpose()); -\endcode</td><td>\code -?gees -?gees -?syev/?heev -?syev/?heev, -?potrf -\endcode</td></tr> -<tr class="alt"><td>Schur decomposition \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code -RealSchur<MatrixXd> schurR(m1); -ComplexSchur<MatrixXcd> schurC(m1); -\endcode</td><td>\code -?gees -\endcode</td></tr> -<tr><td>Vector Math \n \c EIGEN_USE_MKL_VML </td><td>\code +<tr><th>Code example</th><th>MKL routines</th></tr> +<tr><td>\code v2=v1.array().sin(); v2=v1.array().asin(); v2=v1.array().cos(); @@ -156,7 +94,7 @@ v?Sqr v?Powx \endcode</td></tr> </table> -In the examples, m1 and m2 are dense matrices and v1 and v2 are dense vectors. +In the examples, v1 and v2 are dense vectors. \section TopicUsingIntelMKL_Links Links diff --git a/doc/examples/Cwise_erf.cpp b/doc/examples/Cwise_erf.cpp new file mode 100644 index 000000000..e7cd2c1c0 --- /dev/null +++ b/doc/examples/Cwise_erf.cpp @@ -0,0 +1,9 @@ +#include <Eigen/Core> +#include <unsupported/Eigen/SpecialFunctions> +#include <iostream> +using namespace Eigen; +int main() +{ + Array4d v(-0.5,2,0,-7); + std::cout << v.erf() << std::endl; +} diff --git a/doc/examples/Cwise_erfc.cpp b/doc/examples/Cwise_erfc.cpp new file mode 100644 index 000000000..d8bb04c30 --- /dev/null +++ b/doc/examples/Cwise_erfc.cpp @@ -0,0 +1,9 @@ +#include <Eigen/Core> +#include <unsupported/Eigen/SpecialFunctions> +#include <iostream> +using namespace Eigen; +int main() +{ + Array4d v(-0.5,2,0,-7); + std::cout << v.erfc() << std::endl; +} diff --git a/doc/examples/Cwise_lgamma.cpp b/doc/examples/Cwise_lgamma.cpp new file mode 100644 index 000000000..f1c4f503e --- /dev/null +++ b/doc/examples/Cwise_lgamma.cpp @@ -0,0 +1,9 @@ +#include <Eigen/Core> +#include <unsupported/Eigen/SpecialFunctions> +#include <iostream> +using namespace Eigen; +int main() +{ + Array4d v(0.5,10,0,-1); + std::cout << v.lgamma() << std::endl; +}
\ No newline at end of file diff --git a/doc/examples/TutorialInplaceLU.cpp b/doc/examples/TutorialInplaceLU.cpp new file mode 100644 index 000000000..cb9c59b60 --- /dev/null +++ b/doc/examples/TutorialInplaceLU.cpp @@ -0,0 +1,61 @@ +#include <iostream> +struct init { + init() { std::cout << "[" << "init" << "]" << std::endl; } +}; +init init_obj; +// [init] +#include <iostream> +#include <Eigen/Dense> + +using namespace std; +using namespace Eigen; + +int main() +{ + MatrixXd A(2,2); + A << 2, -1, 1, 3; + cout << "Here is the input matrix A before decomposition:\n" << A << endl; +cout << "[init]" << endl; + +cout << "[declaration]" << endl; + PartialPivLU<Ref<MatrixXd> > lu(A); + cout << "Here is the input matrix A after decomposition:\n" << A << endl; +cout << "[declaration]" << endl; + +cout << "[matrixLU]" << endl; + cout << "Here is the matrix storing the L and U factors:\n" << lu.matrixLU() << endl; +cout << "[matrixLU]" << endl; + +cout << "[solve]" << endl; + MatrixXd A0(2,2); A0 << 2, -1, 1, 3; + VectorXd b(2); b << 1, 2; + VectorXd x = lu.solve(b); + cout << "Residual: " << (A0 * x - b).norm() << endl; +cout << "[solve]" << endl; + +cout << "[modifyA]" << endl; + A << 3, 4, -2, 1; + x = lu.solve(b); + cout << "Residual: " << (A0 * x - b).norm() << endl; +cout << "[modifyA]" << endl; + +cout << "[recompute]" << endl; + A0 = A; // save A + lu.compute(A); + x = lu.solve(b); + cout << "Residual: " << (A0 * x - b).norm() << endl; +cout << "[recompute]" << endl; + +cout << "[recompute_bis0]" << endl; + MatrixXd A1(2,2); + A1 << 5,-2,3,4; + lu.compute(A1); + cout << "Here is the input matrix A1 after decomposition:\n" << A1 << endl; +cout << "[recompute_bis0]" << endl; + +cout << "[recompute_bis1]" << endl; + x = lu.solve(b); + cout << "Residual: " << (A1 * x - b).norm() << endl; +cout << "[recompute_bis1]" << endl; + +} diff --git a/doc/ftv2node.png b/doc/ftv2node.png Binary files differnew file mode 100644 index 000000000..63c605bb4 --- /dev/null +++ b/doc/ftv2node.png diff --git a/doc/ftv2pnode.png b/doc/ftv2pnode.png Binary files differnew file mode 100644 index 000000000..c6ee22f93 --- /dev/null +++ b/doc/ftv2pnode.png diff --git a/doc/snippets/Cwise_erf.cpp b/doc/snippets/Cwise_erf.cpp deleted file mode 100644 index 7f51c1b6a..000000000 --- a/doc/snippets/Cwise_erf.cpp +++ /dev/null @@ -1,2 +0,0 @@ -Array4d v(-0.5,2,0,-7); -cout << v.erf() << endl; diff --git a/doc/snippets/Cwise_erfc.cpp b/doc/snippets/Cwise_erfc.cpp deleted file mode 100644 index f0453d4b1..000000000 --- a/doc/snippets/Cwise_erfc.cpp +++ /dev/null @@ -1,2 +0,0 @@ -Array4d v(-0.5,2,0,-7); -cout << v.erfc() << endl; diff --git a/doc/snippets/Cwise_lgamma.cpp b/doc/snippets/Cwise_lgamma.cpp deleted file mode 100644 index cbc69b989..000000000 --- a/doc/snippets/Cwise_lgamma.cpp +++ /dev/null @@ -1,2 +0,0 @@ -Array4d v(0.5,10,0,-1); -cout << v.lgamma() << endl;
\ No newline at end of file diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt index 9d49f1e97..926b284e6 100644 --- a/test/CMakeLists.txt +++ b/test/CMakeLists.txt @@ -258,6 +258,9 @@ ei_add_test(rvalue_types) ei_add_test(dense_storage) ei_add_test(ctorleak) ei_add_test(mpl2only) +ei_add_test(inplace_decomposition) +ei_add_test(half_float) +ei_add_test(array_of_string) add_executable(bug1213 bug1213.cpp bug1213_main.cpp) @@ -326,6 +329,16 @@ if(EIGEN_TEST_EIGEN2) message(WARNING "The Eigen2 test suite has been removed") endif() +# boost MP unit test +find_package(Boost) +if(Boost_FOUND) + include_directories(${Boost_INCLUDE_DIRS}) + ei_add_test(boostmultiprec "" "${Boost_LIBRARIES}") + ei_add_property(EIGEN_TESTED_BACKENDS "Boost.Multiprecision, ") +else() + ei_add_property(EIGEN_MISSING_BACKENDS "Boost.Multiprecision, ") +endif() + # CUDA unit tests option(EIGEN_TEST_CUDA "Enable CUDA support in unit tests" OFF) diff --git a/test/array.cpp b/test/array.cpp index 7e41e9e20..15c3266a9 100644 --- a/test/array.cpp +++ b/test/array.cpp @@ -117,7 +117,7 @@ template<typename ArrayType> void array(const ArrayType& m) VERIFY_IS_APPROX((2*m1).pow(exponents), 4*m1.square()); VERIFY_IS_APPROX(Eigen::pow(m1,2*exponents), m1.square().square()); VERIFY_IS_APPROX(m1.pow(2*exponents), m1.square().square()); - VERIFY_IS_APPROX(pow(m1(0,0), exponents), ArrayType::Constant(rows,cols,m1(0,0)*m1(0,0))); + VERIFY_IS_APPROX(Eigen::pow(m1(0,0), exponents), ArrayType::Constant(rows,cols,m1(0,0)*m1(0,0))); // Check possible conflicts with 1D ctor typedef Array<Scalar, Dynamic, 1> OneDArrayType; @@ -234,12 +234,7 @@ template<typename ArrayType> void array_real(const ArrayType& m) VERIFY_IS_APPROX(m1.sinh(), sinh(m1)); VERIFY_IS_APPROX(m1.cosh(), cosh(m1)); VERIFY_IS_APPROX(m1.tanh(), tanh(m1)); -#if EIGEN_HAS_C99_MATH - VERIFY_IS_APPROX(m1.lgamma(), lgamma(m1)); - VERIFY_IS_APPROX(m1.digamma(), digamma(m1)); - VERIFY_IS_APPROX(m1.erf(), erf(m1)); - VERIFY_IS_APPROX(m1.erfc(), erfc(m1)); -#endif // EIGEN_HAS_C99_MATH + VERIFY_IS_APPROX(m1.arg(), arg(m1)); VERIFY_IS_APPROX(m1.round(), round(m1)); VERIFY_IS_APPROX(m1.floor(), floor(m1)); @@ -260,6 +255,7 @@ template<typename ArrayType> void array_real(const ArrayType& m) m3 = m1.abs(); VERIFY_IS_APPROX(m3.sqrt(), sqrt(abs(m1))); VERIFY_IS_APPROX(m3.rsqrt(), Scalar(1)/sqrt(abs(m1))); + VERIFY_IS_APPROX(rsqrt(m3), Scalar(1)/sqrt(abs(m1))); VERIFY_IS_APPROX(m3.log(), log(m3)); VERIFY_IS_APPROX(m3.log1p(), log1p(m3)); VERIFY_IS_APPROX(m3.log10(), log10(m3)); @@ -313,88 +309,6 @@ template<typename ArrayType> void array_real(const ArrayType& m) m1 += ArrayType::Constant(rows,cols,Scalar(tiny)); VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse()); - - -#if EIGEN_HAS_C99_MATH - // check special functions (comparing against numpy implementation) - if (!NumTraits<Scalar>::IsComplex) - { - - { - // Test various propreties of igamma & igammac. These are normalized - // gamma integrals where - // igammac(a, x) = Gamma(a, x) / Gamma(a) - // igamma(a, x) = gamma(a, x) / Gamma(a) - // where Gamma and gamma are considered the standard unnormalized - // upper and lower incomplete gamma functions, respectively. - ArrayType a = m1.abs() + 2; - ArrayType x = m2.abs() + 2; - ArrayType zero = ArrayType::Zero(rows, cols); - ArrayType one = ArrayType::Constant(rows, cols, Scalar(1.0)); - ArrayType a_m1 = a - one; - ArrayType Gamma_a_x = Eigen::igammac(a, x) * a.lgamma().exp(); - ArrayType Gamma_a_m1_x = Eigen::igammac(a_m1, x) * a_m1.lgamma().exp(); - ArrayType gamma_a_x = Eigen::igamma(a, x) * a.lgamma().exp(); - ArrayType gamma_a_m1_x = Eigen::igamma(a_m1, x) * a_m1.lgamma().exp(); - - // Gamma(a, 0) == Gamma(a) - VERIFY_IS_APPROX(Eigen::igammac(a, zero), one); - - // Gamma(a, x) + gamma(a, x) == Gamma(a) - VERIFY_IS_APPROX(Gamma_a_x + gamma_a_x, a.lgamma().exp()); - - // Gamma(a, x) == (a - 1) * Gamma(a-1, x) + x^(a-1) * exp(-x) - VERIFY_IS_APPROX(Gamma_a_x, (a - 1) * Gamma_a_m1_x + x.pow(a-1) * (-x).exp()); - - // gamma(a, x) == (a - 1) * gamma(a-1, x) - x^(a-1) * exp(-x) - VERIFY_IS_APPROX(gamma_a_x, (a - 1) * gamma_a_m1_x - x.pow(a-1) * (-x).exp()); - } - - // Check exact values of igamma and igammac against a third party calculation. - Scalar a_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)}; - Scalar x_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)}; - - // location i*6+j corresponds to a_s[i], x_s[j]. - Scalar nan = std::numeric_limits<Scalar>::quiet_NaN(); - Scalar igamma_s[][6] = {{0.0, nan, nan, nan, nan, nan}, - {0.0, 0.6321205588285578, 0.7768698398515702, - 0.9816843611112658, 9.999500016666262e-05, 1.0}, - {0.0, 0.4275932955291202, 0.608374823728911, - 0.9539882943107686, 7.522076445089201e-07, 1.0}, - {0.0, 0.01898815687615381, 0.06564245437845008, - 0.5665298796332909, 4.166333347221828e-18, 1.0}, - {0.0, 0.9999780593618628, 0.9999899967080838, - 0.9999996219837988, 0.9991370418689945, 1.0}, - {0.0, 0.0, 0.0, 0.0, 0.0, 0.5042041932513908}}; - Scalar igammac_s[][6] = {{nan, nan, nan, nan, nan, nan}, - {1.0, 0.36787944117144233, 0.22313016014842982, - 0.018315638888734182, 0.9999000049998333, 0.0}, - {1.0, 0.5724067044708798, 0.3916251762710878, - 0.04601170568923136, 0.9999992477923555, 0.0}, - {1.0, 0.9810118431238462, 0.9343575456215499, - 0.4334701203667089, 1.0, 0.0}, - {1.0, 2.1940638138146658e-05, 1.0003291916285e-05, - 3.7801620118431334e-07, 0.0008629581310054535, - 0.0}, - {1.0, 1.0, 1.0, 1.0, 1.0, 0.49579580674813944}}; - for (int i = 0; i < 6; ++i) { - for (int j = 0; j < 6; ++j) { - if ((std::isnan)(igamma_s[i][j])) { - VERIFY((std::isnan)(numext::igamma(a_s[i], x_s[j]))); - } else { - VERIFY_IS_APPROX(numext::igamma(a_s[i], x_s[j]), igamma_s[i][j]); - } - - if ((std::isnan)(igammac_s[i][j])) { - VERIFY((std::isnan)(numext::igammac(a_s[i], x_s[j]))); - } else { - VERIFY_IS_APPROX(numext::igammac(a_s[i], x_s[j]), igammac_s[i][j]); - } - } - } - } -#endif // EIGEN_HAS_C99_MATH - // check inplace transpose m3 = m1; m3.transposeInPlace(); @@ -537,242 +451,8 @@ template<typename ArrayType> void min_max(const ArrayType& m) } -template<typename X, typename Y> -void verify_component_wise(const X& x, const Y& y) -{ - for(Index i=0; i<x.size(); ++i) - { - if((numext::isfinite)(y(i))) - VERIFY_IS_APPROX( x(i), y(i) ); - else if((numext::isnan)(y(i))) - VERIFY((numext::isnan)(x(i))); - else - VERIFY_IS_EQUAL( x(i), y(i) ); - } -} - -// check special functions (comparing against numpy implementation) -template<typename ArrayType> void array_special_functions() -{ - using std::abs; - using std::sqrt; - typedef typename ArrayType::Scalar Scalar; - typedef typename NumTraits<Scalar>::Real RealScalar; - - Scalar plusinf = std::numeric_limits<Scalar>::infinity(); - Scalar nan = std::numeric_limits<Scalar>::quiet_NaN(); - - // Check the zeta function against scipy.special.zeta - { - ArrayType x(7), q(7), res(7), ref(7); - x << 1.5, 4, 10.5, 10000.5, 3, 1, 0.9; - q << 2, 1.5, 3, 1.0001, -2.5, 1.2345, 1.2345; - ref << 1.61237534869, 0.234848505667, 1.03086757337e-5, 0.367879440865, 0.054102025820864097, plusinf, nan; - CALL_SUBTEST( verify_component_wise(ref, ref); ); - CALL_SUBTEST( res = x.zeta(q); verify_component_wise(res, ref); ); - CALL_SUBTEST( res = zeta(x,q); verify_component_wise(res, ref); ); - } - - // digamma - { - ArrayType x(7), res(7), ref(7); - x << 1, 1.5, 4, -10.5, 10000.5, 0, -1; - ref << -0.5772156649015329, 0.03648997397857645, 1.2561176684318, 2.398239129535781, 9.210340372392849, plusinf, plusinf; - CALL_SUBTEST( verify_component_wise(ref, ref); ); - - CALL_SUBTEST( res = x.digamma(); verify_component_wise(res, ref); ); - CALL_SUBTEST( res = digamma(x); verify_component_wise(res, ref); ); - } - - -#if EIGEN_HAS_C99_MATH - { - ArrayType n(11), x(11), res(11), ref(11); - n << 1, 1, 1, 1.5, 17, 31, 28, 8, 42, 147, 170; - x << 2, 3, 25.5, 1.5, 4.7, 11.8, 17.7, 30.2, 15.8, 54.1, 64; - ref << 0.644934066848, 0.394934066848, 0.0399946696496, nan, 293.334565435, 0.445487887616, -2.47810300902e-07, -8.29668781082e-09, -0.434562276666, 0.567742190178, -0.0108615497927; - CALL_SUBTEST( verify_component_wise(ref, ref); ); - - if(sizeof(RealScalar)>=8) { // double - // Reason for commented line: http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1232 - // CALL_SUBTEST( res = x.polygamma(n); verify_component_wise(res, ref); ); - CALL_SUBTEST( res = polygamma(n,x); verify_component_wise(res, ref); ); - } - else { - // CALL_SUBTEST( res = x.polygamma(n); verify_component_wise(res.head(8), ref.head(8)); ); - CALL_SUBTEST( res = polygamma(n,x); verify_component_wise(res.head(8), ref.head(8)); ); - } - } -#endif - -#if EIGEN_HAS_C99_MATH - { - // Inputs and ground truth generated with scipy via: - // a = np.logspace(-3, 3, 5) - 1e-3 - // b = np.logspace(-3, 3, 5) - 1e-3 - // x = np.linspace(-0.1, 1.1, 5) - // (full_a, full_b, full_x) = np.vectorize(lambda a, b, x: (a, b, x))(*np.ix_(a, b, x)) - // full_a = full_a.flatten().tolist() # same for full_b, full_x - // v = scipy.special.betainc(full_a, full_b, full_x).flatten().tolist() - // - // Note in Eigen, we call betainc with arguments in the order (x, a, b). - ArrayType a(125); - ArrayType b(125); - ArrayType x(125); - ArrayType v(125); - ArrayType res(125); - - a << 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, - 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, - 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, - 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, - 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, - 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, - 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, - 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, - 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, - 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, - 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, - 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, - 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, - 31.62177660168379, 31.62177660168379, 31.62177660168379, - 31.62177660168379, 31.62177660168379, 31.62177660168379, - 31.62177660168379, 31.62177660168379, 31.62177660168379, - 31.62177660168379, 31.62177660168379, 31.62177660168379, - 31.62177660168379, 31.62177660168379, 31.62177660168379, - 31.62177660168379, 31.62177660168379, 31.62177660168379, - 31.62177660168379, 31.62177660168379, 31.62177660168379, - 31.62177660168379, 31.62177660168379, 31.62177660168379, - 31.62177660168379, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, - 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, - 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, - 999.999, 999.999, 999.999; - - b << 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379, 0.03062277660168379, - 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.999, - 0.999, 0.999, 0.999, 0.999, 31.62177660168379, 31.62177660168379, - 31.62177660168379, 31.62177660168379, 31.62177660168379, 999.999, - 999.999, 999.999, 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, - 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, - 0.03062277660168379, 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, - 0.999, 31.62177660168379, 31.62177660168379, 31.62177660168379, - 31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999, - 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379, - 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, - 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, - 31.62177660168379, 31.62177660168379, 31.62177660168379, - 31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999, - 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379, - 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, - 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, - 31.62177660168379, 31.62177660168379, 31.62177660168379, - 31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999, - 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379, - 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, - 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, - 31.62177660168379, 31.62177660168379, 31.62177660168379, - 31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999, - 999.999, 999.999; - - x << -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, - 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, - 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, - 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, - -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, - 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, - 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, - 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, - 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, - 0.8, 1.1; - - v << nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, - nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, - nan, nan, nan, 0.47972119876364683, 0.5, 0.5202788012363533, nan, nan, - 0.9518683957740043, 0.9789663010413743, 0.9931729188073435, nan, nan, - 0.999995949033062, 0.9999999999993698, 0.9999999999999999, nan, nan, - 0.9999999999999999, 0.9999999999999999, 0.9999999999999999, nan, nan, - nan, nan, nan, nan, nan, 0.006827081192655869, 0.0210336989586256, - 0.04813160422599567, nan, nan, 0.20014344256217678, 0.5000000000000001, - 0.7998565574378232, nan, nan, 0.9991401428435834, 0.999999999698403, - 0.9999999999999999, nan, nan, 0.9999999999999999, 0.9999999999999999, - 0.9999999999999999, nan, nan, nan, nan, nan, nan, nan, - 1.0646600232370887e-25, 6.301722877826246e-13, 4.050966937974938e-06, - nan, nan, 7.864342668429763e-23, 3.015969667594166e-10, - 0.0008598571564165444, nan, nan, 6.031987710123844e-08, - 0.5000000000000007, 0.9999999396801229, nan, nan, 0.9999999999999999, - 0.9999999999999999, 0.9999999999999999, nan, nan, nan, nan, nan, nan, - nan, 0.0, 7.029920380986636e-306, 2.2450728208591345e-101, nan, nan, - 0.0, 9.275871147869727e-302, 1.2232913026152827e-97, nan, nan, 0.0, - 3.0891393081932924e-252, 2.9303043666183996e-60, nan, nan, - 2.248913486879199e-196, 0.5000000000004947, 0.9999999999999999, nan; - - CALL_SUBTEST(res = betainc(a, b, x); - verify_component_wise(res, v);); - } - - // Test various properties of betainc - { - ArrayType m1 = ArrayType::Random(32); - ArrayType m2 = ArrayType::Random(32); - ArrayType m3 = ArrayType::Random(32); - ArrayType one = ArrayType::Constant(32, Scalar(1.0)); - const Scalar eps = std::numeric_limits<Scalar>::epsilon(); - ArrayType a = (m1 * 4.0).exp(); - ArrayType b = (m2 * 4.0).exp(); - ArrayType x = m3.abs(); - - // betainc(a, 1, x) == x**a - CALL_SUBTEST( - ArrayType test = betainc(a, one, x); - ArrayType expected = x.pow(a); - verify_component_wise(test, expected);); - - // betainc(1, b, x) == 1 - (1 - x)**b - CALL_SUBTEST( - ArrayType test = betainc(one, b, x); - ArrayType expected = one - (one - x).pow(b); - verify_component_wise(test, expected);); - - // betainc(a, b, x) == 1 - betainc(b, a, 1-x) - CALL_SUBTEST( - ArrayType test = betainc(a, b, x) + betainc(b, a, one - x); - ArrayType expected = one; - verify_component_wise(test, expected);); - - // betainc(a+1, b, x) = betainc(a, b, x) - x**a * (1 - x)**b / (a * beta(a, b)) - CALL_SUBTEST( - ArrayType num = x.pow(a) * (one - x).pow(b); - ArrayType denom = a * (a.lgamma() + b.lgamma() - (a + b).lgamma()).exp(); - // Add eps to rhs and lhs so that component-wise test doesn't result in - // nans when both outputs are zeros. - ArrayType expected = betainc(a, b, x) - num / denom + eps; - ArrayType test = betainc(a + one, b, x) + eps; - if (sizeof(Scalar) >= 8) { // double - verify_component_wise(test, expected); - } else { - // Reason for limited test: http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1232 - verify_component_wise(test.head(8), expected.head(8)); - }); - - // betainc(a, b+1, x) = betainc(a, b, x) + x**a * (1 - x)**b / (b * beta(a, b)) - CALL_SUBTEST( - // Add eps to rhs and lhs so that component-wise test doesn't result in - // nans when both outputs are zeros. - ArrayType num = x.pow(a) * (one - x).pow(b); - ArrayType denom = b * (a.lgamma() + b.lgamma() - (a + b).lgamma()).exp(); - ArrayType expected = betainc(a, b, x) + num / denom + eps; - ArrayType test = betainc(a, b + one, x) + eps; - verify_component_wise(test, expected);); - } -#endif -} - void test_array() { -#ifndef EIGEN_HAS_C99_MATH - std::cerr << "WARNING: testing of special math functions disabled" << std::endl; -#endif - for(int i = 0; i < g_repeat; i++) { CALL_SUBTEST_1( array(Array<float, 1, 1>()) ); CALL_SUBTEST_2( array(Array22f()) ); @@ -812,7 +492,4 @@ void test_array() VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Xpr>::type, ArrayBase<Xpr> >::value)); - - CALL_SUBTEST_7(array_special_functions<ArrayXf>()); - CALL_SUBTEST_7(array_special_functions<ArrayXd>()); } diff --git a/test/array_of_string.cpp b/test/array_of_string.cpp new file mode 100644 index 000000000..e23b7c59e --- /dev/null +++ b/test/array_of_string.cpp @@ -0,0 +1,32 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" + +void test_array_of_string() +{ + typedef Array<std::string,1,Dynamic> ArrayXs; + ArrayXs a1(3), a2(3), a3(3), a3ref(3); + a1 << "one", "two", "three"; + a2 << "1", "2", "3"; + a3ref << "one (1)", "two (2)", "three (3)"; + std::stringstream s1; + s1 << a1; + VERIFY_IS_EQUAL(s1.str(), std::string(" one two three")); + a3 = a1 + std::string(" (") + a2 + std::string(")"); + VERIFY((a3==a3ref).all()); + + a3 = a1; + a3 += std::string(" (") + a2 + std::string(")"); + VERIFY((a3==a3ref).all()); + + a1.swap(a3); + VERIFY((a1==a3ref).all()); + VERIFY((a3!=a3ref).all()); +} diff --git a/test/array_reverse.cpp b/test/array_reverse.cpp index a5c0d37f9..c9d9f90c3 100644 --- a/test/array_reverse.cpp +++ b/test/array_reverse.cpp @@ -117,13 +117,11 @@ template<typename MatrixType> void reverse(const MatrixType& m) m2.colwise().reverseInPlace(); VERIFY_IS_APPROX(m2,m1.colwise().reverse().eval()); - /* m1.colwise().reverse()(r, c) = x; VERIFY_IS_APPROX(x, m1(rows - 1 - r, c)); m1.rowwise().reverse()(r, c) = x; VERIFY_IS_APPROX(x, m1(r, cols - 1 - c)); - */ } void test_array_reverse() diff --git a/test/boostmultiprec.cpp b/test/boostmultiprec.cpp new file mode 100644 index 000000000..e06e9bdaf --- /dev/null +++ b/test/boostmultiprec.cpp @@ -0,0 +1,201 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include <sstream> + +#ifdef EIGEN_TEST_MAX_SIZE +#undef EIGEN_TEST_MAX_SIZE +#endif + +#define EIGEN_TEST_MAX_SIZE 50 + +#ifdef EIGEN_TEST_PART_1 +#include "cholesky.cpp" +#endif + +#ifdef EIGEN_TEST_PART_2 +#include "lu.cpp" +#endif + +#ifdef EIGEN_TEST_PART_3 +#include "qr.cpp" +#endif + +#ifdef EIGEN_TEST_PART_4 +#include "qr_colpivoting.cpp" +#endif + +#ifdef EIGEN_TEST_PART_5 +#include "qr_fullpivoting.cpp" +#endif + +#ifdef EIGEN_TEST_PART_6 +#include "eigensolver_selfadjoint.cpp" +#endif + +#ifdef EIGEN_TEST_PART_7 +#include "eigensolver_generic.cpp" +#endif + +#ifdef EIGEN_TEST_PART_8 +#include "eigensolver_generalized_real.cpp" +#endif + +#ifdef EIGEN_TEST_PART_9 +#include "jacobisvd.cpp" +#endif + +#ifdef EIGEN_TEST_PART_10 +#include "bdcsvd.cpp" +#endif + +#include <Eigen/Dense> + +#undef min +#undef max +#undef isnan +#undef isinf +#undef isfinite + +#include <boost/multiprecision/cpp_dec_float.hpp> +#include <boost/multiprecision/number.hpp> +#include <boost/math/special_functions.hpp> +#include <boost/math/complex.hpp> + +namespace mp = boost::multiprecision; +typedef mp::number<mp::cpp_dec_float<100>, mp::et_on> Real; + +namespace Eigen { + template<> struct NumTraits<Real> : GenericNumTraits<Real> { + static inline Real dummy_precision() { return 1e-50; } + }; + + template<typename T1,typename T2,typename T3,typename T4,typename T5> + struct NumTraits<boost::multiprecision::detail::expression<T1,T2,T3,T4,T5> > : NumTraits<Real> {}; + + template<> + Real test_precision<Real>() { return 1e-50; } + + // needed in C++93 mode where number does not support explicit cast. + namespace internal { + template<typename NewType> + struct cast_impl<Real,NewType> { + static inline NewType run(const Real& x) { + return x.template convert_to<NewType>(); + } + }; + + template<> + struct cast_impl<Real,std::complex<Real> > { + static inline std::complex<Real> run(const Real& x) { + return std::complex<Real>(x); + } + }; + } +} + +namespace boost { +namespace multiprecision { + // to make ADL works as expected: + using boost::math::isfinite; + using boost::math::isnan; + using boost::math::isinf; + using boost::math::copysign; + using boost::math::hypot; + + // The following is needed for std::complex<Real>: + Real fabs(const Real& a) { return abs EIGEN_NOT_A_MACRO (a); } + Real fmax(const Real& a, const Real& b) { using std::max; return max(a,b); } + + // some specialization for the unit tests: + inline bool test_isMuchSmallerThan(const Real& a, const Real& b) { + return internal::isMuchSmallerThan(a, b, test_precision<Real>()); + } + + inline bool test_isApprox(const Real& a, const Real& b) { + return internal::isApprox(a, b, test_precision<Real>()); + } + + inline bool test_isApproxOrLessThan(const Real& a, const Real& b) { + return internal::isApproxOrLessThan(a, b, test_precision<Real>()); + } + + Real get_test_precision(const Real&) { + return test_precision<Real>(); + } + + Real test_relative_error(const Real &a, const Real &b) { + using Eigen::numext::abs2; + return sqrt(abs2<Real>(a-b)/Eigen::numext::mini<Real>(abs2(a),abs2(b))); + } +} +} + +namespace Eigen { + +} + +void test_boostmultiprec() +{ + typedef Matrix<Real,Dynamic,Dynamic> Mat; + typedef Matrix<std::complex<Real>,Dynamic,Dynamic> MatC; + + std::cout << "NumTraits<Real>::epsilon() = " << NumTraits<Real>::epsilon() << std::endl; + std::cout << "NumTraits<Real>::dummy_precision() = " << NumTraits<Real>::dummy_precision() << std::endl; + std::cout << "NumTraits<Real>::lowest() = " << NumTraits<Real>::lowest() << std::endl; + std::cout << "NumTraits<Real>::highest() = " << NumTraits<Real>::highest() << std::endl; + std::cout << "NumTraits<Real>::digits10() = " << NumTraits<Real>::digits10() << std::endl; + + // chekc stream output + { + Mat A(10,10); + A.setRandom(); + std::stringstream ss; + ss << A; + } + { + MatC A(10,10); + A.setRandom(); + std::stringstream ss; + ss << A; + } + + for(int i = 0; i < g_repeat; i++) { + int s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE); + + CALL_SUBTEST_1( cholesky(Mat(s,s)) ); + + CALL_SUBTEST_2( lu_non_invertible<Mat>() ); + CALL_SUBTEST_2( lu_invertible<Mat>() ); + CALL_SUBTEST_2( lu_non_invertible<MatC>() ); + CALL_SUBTEST_2( lu_invertible<MatC>() ); + + CALL_SUBTEST_3( qr(Mat(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_3( qr_invertible<Mat>() ); + + CALL_SUBTEST_4( qr<Mat>() ); + CALL_SUBTEST_4( cod<Mat>() ); + CALL_SUBTEST_4( qr_invertible<Mat>() ); + + CALL_SUBTEST_5( qr<Mat>() ); + CALL_SUBTEST_5( qr_invertible<Mat>() ); + + CALL_SUBTEST_6( selfadjointeigensolver(Mat(s,s)) ); + + CALL_SUBTEST_7( eigensolver(Mat(s,s)) ); + + CALL_SUBTEST_8( generalized_eigensolver_real(Mat(s,s)) ); + + TEST_SET_BUT_UNUSED_VARIABLE(s) + } + + CALL_SUBTEST_9(( jacobisvd(Mat(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2))) )); + CALL_SUBTEST_10(( bdcsvd(Mat(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2))) )); +} + diff --git a/test/cholesky.cpp b/test/cholesky.cpp index b7abc230b..12efd2d60 100644 --- a/test/cholesky.cpp +++ b/test/cholesky.cpp @@ -243,11 +243,13 @@ template<typename MatrixType> void cholesky(const MatrixType& m) // check matrices with a wide spectrum if(rows>=3) { + using std::pow; + using std::sqrt; RealScalar s = (std::min)(16,std::numeric_limits<RealScalar>::max_exponent10/8); Matrix<Scalar,Dynamic,Dynamic> a = Matrix<Scalar,Dynamic,Dynamic>::Random(rows,rows); Matrix<RealScalar,Dynamic,1> d = Matrix<RealScalar,Dynamic,1>::Random(rows); for(Index k=0; k<rows; ++k) - d(k) = d(k)*std::pow(RealScalar(10),internal::random<RealScalar>(-s,s)); + d(k) = d(k)*pow(RealScalar(10),internal::random<RealScalar>(-s,s)); SquareMatrixType A = a * d.asDiagonal() * a.adjoint(); // Make sure a solution exists: vecX.setRandom(); @@ -263,7 +265,7 @@ template<typename MatrixType> void cholesky(const MatrixType& m) } else { - RealScalar large_tol = std::sqrt(test_precision<RealScalar>()); + RealScalar large_tol = sqrt(test_precision<RealScalar>()); VERIFY((A * vecX).isApprox(vecB, large_tol)); ++g_test_level; diff --git a/test/eigensolver_generic.cpp b/test/eigensolver_generic.cpp index 566546310..e18fbf687 100644 --- a/test/eigensolver_generic.cpp +++ b/test/eigensolver_generic.cpp @@ -127,16 +127,29 @@ void test_eigensolver_generic() } ); - // regression test for bug 793 #ifdef EIGEN_TEST_PART_2 { - MatrixXd a(3,3); - a << 0, 0, 1, - 1, 1, 1, - 1, 1e+200, 1; - Eigen::EigenSolver<MatrixXd> eig(a); - VERIFY_IS_APPROX(a * eig.pseudoEigenvectors(), eig.pseudoEigenvectors() * eig.pseudoEigenvalueMatrix()); - VERIFY_IS_APPROX(a * eig.eigenvectors(), eig.eigenvectors() * eig.eigenvalues().asDiagonal()); + // regression test for bug 793 + MatrixXd a(3,3); + a << 0, 0, 1, + 1, 1, 1, + 1, 1e+200, 1; + Eigen::EigenSolver<MatrixXd> eig(a); + double scale = 1e-200; // scale to avoid overflow during the comparisons + VERIFY_IS_APPROX(a * eig.pseudoEigenvectors()*scale, eig.pseudoEigenvectors() * eig.pseudoEigenvalueMatrix()*scale); + VERIFY_IS_APPROX(a * eig.eigenvectors()*scale, eig.eigenvectors() * eig.eigenvalues().asDiagonal()*scale); + } + { + // check a case where all eigenvalues are null. + MatrixXd a(2,2); + a << 1, 1, + -1, -1; + Eigen::EigenSolver<MatrixXd> eig(a); + VERIFY_IS_APPROX(eig.pseudoEigenvectors().squaredNorm(), 2.); + VERIFY_IS_APPROX((a * eig.pseudoEigenvectors()).norm()+1., 1.); + VERIFY_IS_APPROX((eig.pseudoEigenvectors() * eig.pseudoEigenvalueMatrix()).norm()+1., 1.); + VERIFY_IS_APPROX((a * eig.eigenvectors()).norm()+1., 1.); + VERIFY_IS_APPROX((eig.eigenvectors() * eig.eigenvalues().asDiagonal()).norm()+1., 1.); } #endif diff --git a/test/eigensolver_selfadjoint.cpp b/test/eigensolver_selfadjoint.cpp index cd0ae5c2f..4ed126116 100644 --- a/test/eigensolver_selfadjoint.cpp +++ b/test/eigensolver_selfadjoint.cpp @@ -19,12 +19,22 @@ template<typename MatrixType> void selfadjointeigensolver_essential_check(const { typedef typename MatrixType::Scalar Scalar; typedef typename NumTraits<Scalar>::Real RealScalar; - RealScalar eival_eps = (std::min)(test_precision<RealScalar>(), NumTraits<Scalar>::dummy_precision()*20000); + RealScalar eival_eps = numext::mini<RealScalar>(test_precision<RealScalar>(), NumTraits<Scalar>::dummy_precision()*20000); SelfAdjointEigenSolver<MatrixType> eiSymm(m); VERIFY_IS_EQUAL(eiSymm.info(), Success); - VERIFY_IS_APPROX(m.template selfadjointView<Lower>() * eiSymm.eigenvectors(), - eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal()); + + RealScalar scaling = m.cwiseAbs().maxCoeff(); + + if(scaling<(std::numeric_limits<RealScalar>::min)()) + { + VERIFY(eiSymm.eigenvalues().cwiseAbs().maxCoeff() <= (std::numeric_limits<RealScalar>::min)()); + } + else + { + VERIFY_IS_APPROX((m.template selfadjointView<Lower>() * eiSymm.eigenvectors())/scaling, + (eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal())/scaling); + } VERIFY_IS_APPROX(m.template selfadjointView<Lower>().eigenvalues(), eiSymm.eigenvalues()); VERIFY_IS_UNITARY(eiSymm.eigenvectors()); @@ -33,7 +43,6 @@ template<typename MatrixType> void selfadjointeigensolver_essential_check(const SelfAdjointEigenSolver<MatrixType> eiDirect; eiDirect.computeDirect(m); VERIFY_IS_EQUAL(eiDirect.info(), Success); - VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiDirect.eigenvalues()); if(! eiSymm.eigenvalues().isApprox(eiDirect.eigenvalues(), eival_eps) ) { std::cerr << "reference eigenvalues: " << eiSymm.eigenvalues().transpose() << "\n" @@ -41,10 +50,18 @@ template<typename MatrixType> void selfadjointeigensolver_essential_check(const << "diff: " << (eiSymm.eigenvalues()-eiDirect.eigenvalues()).transpose() << "\n" << "error (eps): " << (eiSymm.eigenvalues()-eiDirect.eigenvalues()).norm() / eiSymm.eigenvalues().norm() << " (" << eival_eps << ")\n"; } - VERIFY(eiSymm.eigenvalues().isApprox(eiDirect.eigenvalues(), eival_eps)); - VERIFY_IS_APPROX(m.template selfadjointView<Lower>() * eiDirect.eigenvectors(), - eiDirect.eigenvectors() * eiDirect.eigenvalues().asDiagonal()); - VERIFY_IS_APPROX(m.template selfadjointView<Lower>().eigenvalues(), eiDirect.eigenvalues()); + if(scaling<(std::numeric_limits<RealScalar>::min)()) + { + VERIFY(eiDirect.eigenvalues().cwiseAbs().maxCoeff() <= (std::numeric_limits<RealScalar>::min)()); + } + else + { + VERIFY_IS_APPROX(eiSymm.eigenvalues()/scaling, eiDirect.eigenvalues()/scaling); + VERIFY_IS_APPROX((m.template selfadjointView<Lower>() * eiDirect.eigenvectors())/scaling, + (eiDirect.eigenvectors() * eiDirect.eigenvalues().asDiagonal())/scaling); + VERIFY_IS_APPROX(m.template selfadjointView<Lower>().eigenvalues()/scaling, eiDirect.eigenvalues()/scaling); + } + VERIFY_IS_UNITARY(eiDirect.eigenvectors()); } } diff --git a/test/geo_alignedbox.cpp b/test/geo_alignedbox.cpp index ba3378aab..d2339a651 100644 --- a/test/geo_alignedbox.cpp +++ b/test/geo_alignedbox.cpp @@ -49,7 +49,7 @@ template<typename BoxType> void alignedbox(const BoxType& _box) b0.extend(p1); VERIFY(b0.contains(p0*s1+(Scalar(1)-s1)*p1)); VERIFY(b0.contains(b0.center())); - VERIFY(b0.center()==(p0+p1)/Scalar(2)); + VERIFY_IS_APPROX(b0.center(),(p0+p1)/Scalar(2)); (b2 = b0).extend(b1); VERIFY(b2.contains(b0)); diff --git a/test/half_float.cpp b/test/half_float.cpp new file mode 100644 index 000000000..289e4f662 --- /dev/null +++ b/test/half_float.cpp @@ -0,0 +1,242 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include <sstream> + +#include "main.h" + +#include <Eigen/src/Core/arch/CUDA/Half.h> + +using Eigen::half; + +void test_conversion() +{ + using Eigen::half_impl::__half; + + // Conversion from float. + VERIFY_IS_EQUAL(half(1.0f).x, 0x3c00); + VERIFY_IS_EQUAL(half(0.5f).x, 0x3800); + VERIFY_IS_EQUAL(half(0.33333f).x, 0x3555); + VERIFY_IS_EQUAL(half(0.0f).x, 0x0000); + VERIFY_IS_EQUAL(half(-0.0f).x, 0x8000); + VERIFY_IS_EQUAL(half(65504.0f).x, 0x7bff); + VERIFY_IS_EQUAL(half(65536.0f).x, 0x7c00); // Becomes infinity. + + // Denormals. + VERIFY_IS_EQUAL(half(-5.96046e-08f).x, 0x8001); + VERIFY_IS_EQUAL(half(5.96046e-08f).x, 0x0001); + VERIFY_IS_EQUAL(half(1.19209e-07f).x, 0x0002); + + // Verify round-to-nearest-even behavior. + float val1 = float(half(__half(0x3c00))); + float val2 = float(half(__half(0x3c01))); + float val3 = float(half(__half(0x3c02))); + VERIFY_IS_EQUAL(half(0.5f * (val1 + val2)).x, 0x3c00); + VERIFY_IS_EQUAL(half(0.5f * (val2 + val3)).x, 0x3c02); + + // Conversion from int. + VERIFY_IS_EQUAL(half(-1).x, 0xbc00); + VERIFY_IS_EQUAL(half(0).x, 0x0000); + VERIFY_IS_EQUAL(half(1).x, 0x3c00); + VERIFY_IS_EQUAL(half(2).x, 0x4000); + VERIFY_IS_EQUAL(half(3).x, 0x4200); + + // Conversion from bool. + VERIFY_IS_EQUAL(half(false).x, 0x0000); + VERIFY_IS_EQUAL(half(true).x, 0x3c00); + + // Conversion to float. + VERIFY_IS_EQUAL(float(half(__half(0x0000))), 0.0f); + VERIFY_IS_EQUAL(float(half(__half(0x3c00))), 1.0f); + + // Denormals. + VERIFY_IS_APPROX(float(half(__half(0x8001))), -5.96046e-08f); + VERIFY_IS_APPROX(float(half(__half(0x0001))), 5.96046e-08f); + VERIFY_IS_APPROX(float(half(__half(0x0002))), 1.19209e-07f); + + // NaNs and infinities. + VERIFY(!(numext::isinf)(float(half(65504.0f)))); // Largest finite number. + VERIFY(!(numext::isnan)(float(half(0.0f)))); + VERIFY((numext::isinf)(float(half(__half(0xfc00))))); + VERIFY((numext::isnan)(float(half(__half(0xfc01))))); + VERIFY((numext::isinf)(float(half(__half(0x7c00))))); + VERIFY((numext::isnan)(float(half(__half(0x7c01))))); + +#if !EIGEN_COMP_MSVC + // Visual Studio errors out on divisions by 0 + VERIFY((numext::isnan)(float(half(0.0 / 0.0)))); + VERIFY((numext::isinf)(float(half(1.0 / 0.0)))); + VERIFY((numext::isinf)(float(half(-1.0 / 0.0)))); +#endif + + // Exactly same checks as above, just directly on the half representation. + VERIFY(!(numext::isinf)(half(__half(0x7bff)))); + VERIFY(!(numext::isnan)(half(__half(0x0000)))); + VERIFY((numext::isinf)(half(__half(0xfc00)))); + VERIFY((numext::isnan)(half(__half(0xfc01)))); + VERIFY((numext::isinf)(half(__half(0x7c00)))); + VERIFY((numext::isnan)(half(__half(0x7c01)))); + +#if !EIGEN_COMP_MSVC + // Visual Studio errors out on divisions by 0 + VERIFY((numext::isnan)(half(0.0 / 0.0))); + VERIFY((numext::isinf)(half(1.0 / 0.0))); + VERIFY((numext::isinf)(half(-1.0 / 0.0))); +#endif +} + +void test_numtraits() +{ + std::cout << "epsilon = " << NumTraits<half>::epsilon() << std::endl; + std::cout << "highest = " << NumTraits<half>::highest() << std::endl; + std::cout << "lowest = " << NumTraits<half>::lowest() << std::endl; + std::cout << "inifinty = " << NumTraits<half>::infinity() << std::endl; + std::cout << "nan = " << NumTraits<half>::quiet_NaN() << std::endl; + +} + +void test_arithmetic() +{ + VERIFY_IS_EQUAL(float(half(2) + half(2)), 4); + VERIFY_IS_EQUAL(float(half(2) + half(-2)), 0); + VERIFY_IS_APPROX(float(half(0.33333f) + half(0.66667f)), 1.0f); + VERIFY_IS_EQUAL(float(half(2.0f) * half(-5.5f)), -11.0f); + VERIFY_IS_APPROX(float(half(1.0f) / half(3.0f)), 0.33333f); + VERIFY_IS_EQUAL(float(-half(4096.0f)), -4096.0f); + VERIFY_IS_EQUAL(float(-half(-4096.0f)), 4096.0f); +} + +void test_comparison() +{ + VERIFY(half(1.0f) > half(0.5f)); + VERIFY(half(0.5f) < half(1.0f)); + VERIFY(!(half(1.0f) < half(0.5f))); + VERIFY(!(half(0.5f) > half(1.0f))); + + VERIFY(!(half(4.0f) > half(4.0f))); + VERIFY(!(half(4.0f) < half(4.0f))); + + VERIFY(!(half(0.0f) < half(-0.0f))); + VERIFY(!(half(-0.0f) < half(0.0f))); + VERIFY(!(half(0.0f) > half(-0.0f))); + VERIFY(!(half(-0.0f) > half(0.0f))); + + VERIFY(half(0.2f) > half(-1.0f)); + VERIFY(half(-1.0f) < half(0.2f)); + VERIFY(half(-16.0f) < half(-15.0f)); + + VERIFY(half(1.0f) == half(1.0f)); + VERIFY(half(1.0f) != half(2.0f)); + + // Comparisons with NaNs and infinities. +#if !EIGEN_COMP_MSVC + // Visual Studio errors out on divisions by 0 + VERIFY(!(half(0.0 / 0.0) == half(0.0 / 0.0))); + VERIFY(half(0.0 / 0.0) != half(0.0 / 0.0)); + + VERIFY(!(half(1.0) == half(0.0 / 0.0))); + VERIFY(!(half(1.0) < half(0.0 / 0.0))); + VERIFY(!(half(1.0) > half(0.0 / 0.0))); + VERIFY(half(1.0) != half(0.0 / 0.0)); + + VERIFY(half(1.0) < half(1.0 / 0.0)); + VERIFY(half(1.0) > half(-1.0 / 0.0)); +#endif +} + +void test_basic_functions() +{ + VERIFY_IS_EQUAL(float(numext::abs(half(3.5f))), 3.5f); + VERIFY_IS_EQUAL(float(abs(half(3.5f))), 3.5f); + VERIFY_IS_EQUAL(float(numext::abs(half(-3.5f))), 3.5f); + VERIFY_IS_EQUAL(float(abs(half(-3.5f))), 3.5f); + + VERIFY_IS_EQUAL(float(numext::floor(half(3.5f))), 3.0f); + VERIFY_IS_EQUAL(float(floor(half(3.5f))), 3.0f); + VERIFY_IS_EQUAL(float(numext::floor(half(-3.5f))), -4.0f); + VERIFY_IS_EQUAL(float(floor(half(-3.5f))), -4.0f); + + VERIFY_IS_EQUAL(float(numext::ceil(half(3.5f))), 4.0f); + VERIFY_IS_EQUAL(float(ceil(half(3.5f))), 4.0f); + VERIFY_IS_EQUAL(float(numext::ceil(half(-3.5f))), -3.0f); + VERIFY_IS_EQUAL(float(ceil(half(-3.5f))), -3.0f); + + VERIFY_IS_APPROX(float(numext::sqrt(half(0.0f))), 0.0f); + VERIFY_IS_APPROX(float(sqrt(half(0.0f))), 0.0f); + VERIFY_IS_APPROX(float(numext::sqrt(half(4.0f))), 2.0f); + VERIFY_IS_APPROX(float(sqrt(half(4.0f))), 2.0f); + + VERIFY_IS_APPROX(float(numext::pow(half(0.0f), half(1.0f))), 0.0f); + VERIFY_IS_APPROX(float(pow(half(0.0f), half(1.0f))), 0.0f); + VERIFY_IS_APPROX(float(numext::pow(half(2.0f), half(2.0f))), 4.0f); + VERIFY_IS_APPROX(float(pow(half(2.0f), half(2.0f))), 4.0f); + + VERIFY_IS_EQUAL(float(numext::exp(half(0.0f))), 1.0f); + VERIFY_IS_EQUAL(float(exp(half(0.0f))), 1.0f); + VERIFY_IS_APPROX(float(numext::exp(half(EIGEN_PI))), 20.f + float(EIGEN_PI)); + VERIFY_IS_APPROX(float(exp(half(EIGEN_PI))), 20.f + float(EIGEN_PI)); + + VERIFY_IS_EQUAL(float(numext::log(half(1.0f))), 0.0f); + VERIFY_IS_EQUAL(float(log(half(1.0f))), 0.0f); + VERIFY_IS_APPROX(float(numext::log(half(10.0f))), 2.30273f); + VERIFY_IS_APPROX(float(log(half(10.0f))), 2.30273f); +} + +void test_trigonometric_functions() +{ + VERIFY_IS_APPROX(numext::cos(half(0.0f)), half(cosf(0.0f))); + VERIFY_IS_APPROX(cos(half(0.0f)), half(cosf(0.0f))); + VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI)), half(cosf(EIGEN_PI))); + //VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI/2)), half(cosf(EIGEN_PI/2))); + //VERIFY_IS_APPROX(numext::cos(half(3*EIGEN_PI/2)), half(cosf(3*EIGEN_PI/2))); + VERIFY_IS_APPROX(numext::cos(half(3.5f)), half(cosf(3.5f))); + + VERIFY_IS_APPROX(numext::sin(half(0.0f)), half(sinf(0.0f))); + VERIFY_IS_APPROX(sin(half(0.0f)), half(sinf(0.0f))); + // VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI)), half(sinf(EIGEN_PI))); + VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI/2)), half(sinf(EIGEN_PI/2))); + VERIFY_IS_APPROX(numext::sin(half(3*EIGEN_PI/2)), half(sinf(3*EIGEN_PI/2))); + VERIFY_IS_APPROX(numext::sin(half(3.5f)), half(sinf(3.5f))); + + VERIFY_IS_APPROX(numext::tan(half(0.0f)), half(tanf(0.0f))); + VERIFY_IS_APPROX(tan(half(0.0f)), half(tanf(0.0f))); + // VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI)), half(tanf(EIGEN_PI))); + // VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI/2)), half(tanf(EIGEN_PI/2))); + //VERIFY_IS_APPROX(numext::tan(half(3*EIGEN_PI/2)), half(tanf(3*EIGEN_PI/2))); + VERIFY_IS_APPROX(numext::tan(half(3.5f)), half(tanf(3.5f))); +} + +void test_array() +{ + typedef Array<half,1,Dynamic> ArrayXh; + Index size = internal::random<Index>(1,10); + Index i = internal::random<Index>(0,size-1); + ArrayXh a1 = ArrayXh::Random(size), a2 = ArrayXh::Random(size); + VERIFY_IS_APPROX( a1+a1, half(2)*a1 ); + VERIFY( (a1.abs() >= half(0)).all() ); + VERIFY_IS_APPROX( (a1*a1).sqrt(), a1.abs() ); + + VERIFY( ((a1.min)(a2) <= (a1.max)(a2)).all() ); + a1(i) = half(-10.); + VERIFY_IS_EQUAL( a1.minCoeff(), half(-10.) ); + a1(i) = half(10.); + VERIFY_IS_EQUAL( a1.maxCoeff(), half(10.) ); + + std::stringstream ss; + ss << a1; +} + +void test_half_float() +{ + CALL_SUBTEST(test_conversion()); + CALL_SUBTEST(test_numtraits()); + CALL_SUBTEST(test_arithmetic()); + CALL_SUBTEST(test_comparison()); + CALL_SUBTEST(test_basic_functions()); + CALL_SUBTEST(test_trigonometric_functions()); + CALL_SUBTEST(test_array()); +} diff --git a/test/inplace_decomposition.cpp b/test/inplace_decomposition.cpp new file mode 100644 index 000000000..92d0d91b6 --- /dev/null +++ b/test/inplace_decomposition.cpp @@ -0,0 +1,110 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include <Eigen/LU> +#include <Eigen/Cholesky> +#include <Eigen/QR> + +// This file test inplace decomposition through Ref<>, as supported by Cholesky, LU, and QR decompositions. + +template<typename DecType,typename MatrixType> void inplace(bool square = false, bool SPD = false) +{ + typedef typename MatrixType::Scalar Scalar; + typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> RhsType; + typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> ResType; + + Index rows = MatrixType::RowsAtCompileTime==Dynamic ? internal::random<Index>(2,EIGEN_TEST_MAX_SIZE/2) : Index(MatrixType::RowsAtCompileTime); + Index cols = MatrixType::ColsAtCompileTime==Dynamic ? (square?rows:internal::random<Index>(2,rows)) : Index(MatrixType::ColsAtCompileTime); + + MatrixType A = MatrixType::Random(rows,cols); + RhsType b = RhsType::Random(rows); + ResType x(cols); + + if(SPD) + { + assert(square); + A.topRows(cols) = A.topRows(cols).adjoint() * A.topRows(cols); + A.diagonal().array() += 1e-3; + } + + MatrixType A0 = A; + MatrixType A1 = A; + + DecType dec(A); + + // Check that the content of A has been modified + VERIFY_IS_NOT_APPROX( A, A0 ); + + // Check that the decomposition is correct: + if(rows==cols) + { + VERIFY_IS_APPROX( A0 * (x = dec.solve(b)), b ); + } + else + { + VERIFY_IS_APPROX( A0.transpose() * A0 * (x = dec.solve(b)), A0.transpose() * b ); + } + + // Check that modifying A breaks the current dec: + A.setRandom(); + if(rows==cols) + { + VERIFY_IS_NOT_APPROX( A0 * (x = dec.solve(b)), b ); + } + else + { + VERIFY_IS_NOT_APPROX( A0.transpose() * A0 * (x = dec.solve(b)), A0.transpose() * b ); + } + + // Check that calling compute(A1) does not modify A1: + A = A0; + dec.compute(A1); + VERIFY_IS_EQUAL(A0,A1); + VERIFY_IS_NOT_APPROX( A, A0 ); + if(rows==cols) + { + VERIFY_IS_APPROX( A0 * (x = dec.solve(b)), b ); + } + else + { + VERIFY_IS_APPROX( A0.transpose() * A0 * (x = dec.solve(b)), A0.transpose() * b ); + } +} + + +void test_inplace_decomposition() +{ + EIGEN_UNUSED typedef Matrix<double,4,3> Matrix43d; + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1(( inplace<LLT<Ref<MatrixXd> >, MatrixXd>(true,true) )); + CALL_SUBTEST_1(( inplace<LLT<Ref<Matrix4d> >, Matrix4d>(true,true) )); + + CALL_SUBTEST_2(( inplace<LDLT<Ref<MatrixXd> >, MatrixXd>(true,true) )); + CALL_SUBTEST_2(( inplace<LDLT<Ref<Matrix4d> >, Matrix4d>(true,true) )); + + CALL_SUBTEST_3(( inplace<PartialPivLU<Ref<MatrixXd> >, MatrixXd>(true,false) )); + CALL_SUBTEST_3(( inplace<PartialPivLU<Ref<Matrix4d> >, Matrix4d>(true,false) )); + + CALL_SUBTEST_4(( inplace<FullPivLU<Ref<MatrixXd> >, MatrixXd>(true,false) )); + CALL_SUBTEST_4(( inplace<FullPivLU<Ref<Matrix4d> >, Matrix4d>(true,false) )); + + CALL_SUBTEST_5(( inplace<HouseholderQR<Ref<MatrixXd> >, MatrixXd>(false,false) )); + CALL_SUBTEST_5(( inplace<HouseholderQR<Ref<Matrix43d> >, Matrix43d>(false,false) )); + + CALL_SUBTEST_6(( inplace<ColPivHouseholderQR<Ref<MatrixXd> >, MatrixXd>(false,false) )); + CALL_SUBTEST_6(( inplace<ColPivHouseholderQR<Ref<Matrix43d> >, Matrix43d>(false,false) )); + + CALL_SUBTEST_7(( inplace<FullPivHouseholderQR<Ref<MatrixXd> >, MatrixXd>(false,false) )); + CALL_SUBTEST_7(( inplace<FullPivHouseholderQR<Ref<Matrix43d> >, Matrix43d>(false,false) )); + + CALL_SUBTEST_8(( inplace<CompleteOrthogonalDecomposition<Ref<MatrixXd> >, MatrixXd>(false,false) )); + CALL_SUBTEST_8(( inplace<CompleteOrthogonalDecomposition<Ref<Matrix43d> >, Matrix43d>(false,false) )); + } +} diff --git a/test/main.h b/test/main.h index bda6d38c6..74ff96a23 100644 --- a/test/main.h +++ b/test/main.h @@ -452,20 +452,20 @@ T test_relative_error(const AngleAxis<T> &a, const AngleAxis<T> &b) } template<typename Type1, typename Type2> -inline bool test_isApprox(const Type1& a, const Type2& b) +inline bool test_isApprox(const Type1& a, const Type2& b, typename Type1::Scalar* = 0) // Enabled for Eigen's type only { return a.isApprox(b, test_precision<typename Type1::Scalar>()); } // get_test_precision is a small wrapper to test_precision allowing to return the scalar precision for either scalars or expressions template<typename T> -typename NumTraits<typename T::Scalar>::Real get_test_precision(const typename T::Scalar* = 0) +typename NumTraits<typename T::Scalar>::Real get_test_precision(const T&, const typename T::Scalar* = 0) { return test_precision<typename NumTraits<typename T::Scalar>::Real>(); } template<typename T> -typename NumTraits<T>::Real get_test_precision(typename internal::enable_if<internal::is_arithmetic<typename NumTraits<T>::Real>::value, T>::type* = 0) +typename NumTraits<T>::Real get_test_precision(const T&,typename internal::enable_if<internal::is_arithmetic<typename NumTraits<T>::Real>::value, T>::type* = 0) { return test_precision<typename NumTraits<T>::Real>(); } @@ -477,7 +477,7 @@ inline bool verifyIsApprox(const Type1& a, const Type2& b) bool ret = test_isApprox(a,b); if(!ret) { - std::cerr << "Difference too large wrt tolerance " << get_test_precision<Type1>() << ", relative error is: " << test_relative_error(a,b) << std::endl; + std::cerr << "Difference too large wrt tolerance " << get_test_precision(a) << ", relative error is: " << test_relative_error(a,b) << std::endl; } return ret; } diff --git a/test/mixingtypes.cpp b/test/mixingtypes.cpp index 57ef85c32..ad9c2c652 100644 --- a/test/mixingtypes.cpp +++ b/test/mixingtypes.cpp @@ -63,9 +63,16 @@ template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType) complex<float> scf = internal::random<complex<float> >(); complex<double> scd = internal::random<complex<double> >(); - mf+mf; + float epsf = std::sqrt(std::numeric_limits<float> ::min EIGEN_EMPTY ()); + double epsd = std::sqrt(std::numeric_limits<double>::min EIGEN_EMPTY ()); + + while(std::abs(sf )<epsf) sf = internal::random<float>(); + while(std::abs(sd )<epsd) sf = internal::random<double>(); + while(std::abs(scf)<epsf) scf = internal::random<CF>(); + while(std::abs(scd)<epsd) scd = internal::random<CD>(); + // VERIFY_RAISES_ASSERT(mf+md); // does not even compile #ifdef EIGEN_DONT_VECTORIZE @@ -103,12 +110,12 @@ template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType) VERIFY_MIX_SCALAR(scd - vd.array() , scd - vd.template cast<complex<double> >().array()); // check scalar powers - VERIFY_MIX_SCALAR( pow(vcf.array(), sf), pow(vcf.array(), complex<float>(sf)) ); - VERIFY_MIX_SCALAR( vcf.array().pow(sf) , pow(vcf.array(), complex<float>(sf)) ); - VERIFY_MIX_SCALAR( pow(sd, vcd.array()), pow(complex<double>(sd), vcd.array()) ); - VERIFY_MIX_SCALAR( pow(vf.array(), scf), pow(vf.template cast<complex<float> >().array(), scf) ); - VERIFY_MIX_SCALAR( vf.array().pow(scf) , pow(vf.template cast<complex<float> >().array(), scf) ); - VERIFY_MIX_SCALAR( pow(scd, vd.array()), pow(scd, vd.template cast<complex<double> >().array()) ); + VERIFY_MIX_SCALAR( pow(vcf.array(), sf), Eigen::pow(vcf.array(), complex<float>(sf)) ); + VERIFY_MIX_SCALAR( vcf.array().pow(sf) , Eigen::pow(vcf.array(), complex<float>(sf)) ); + VERIFY_MIX_SCALAR( pow(sd, vcd.array()), Eigen::pow(complex<double>(sd), vcd.array()) ); + VERIFY_MIX_SCALAR( Eigen::pow(vf.array(), scf), Eigen::pow(vf.template cast<complex<float> >().array(), scf) ); + VERIFY_MIX_SCALAR( vf.array().pow(scf) , Eigen::pow(vf.template cast<complex<float> >().array(), scf) ); + VERIFY_MIX_SCALAR( Eigen::pow(scd, vd.array()), Eigen::pow(scd, vd.template cast<complex<double> >().array()) ); // check dot product vf.dot(vf); @@ -222,7 +229,6 @@ template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType) Mat_cd((scd * md.template cast<CD>().eval() * mcd).template triangularView<Upper>())); - VERIFY_IS_APPROX( md.array() * mcd.array(), md.template cast<CD>().eval().array() * mcd.array() ); VERIFY_IS_APPROX( mcd.array() * md.array(), mcd.array() * md.template cast<CD>().eval().array() ); @@ -232,14 +238,23 @@ template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType) VERIFY_IS_APPROX( md.array() - mcd.array(), md.template cast<CD>().eval().array() - mcd.array() ); VERIFY_IS_APPROX( mcd.array() - md.array(), mcd.array() - md.template cast<CD>().eval().array() ); - VERIFY_IS_APPROX( md.array() / mcd.array(), md.template cast<CD>().eval().array() / mcd.array() ); - VERIFY_IS_APPROX( mcd.array() / md.array(), mcd.array() / md.template cast<CD>().eval().array() ); + if(mcd.array().abs().minCoeff()>epsd) + { + VERIFY_IS_APPROX( md.array() / mcd.array(), md.template cast<CD>().eval().array() / mcd.array() ); + } + if(md.array().abs().minCoeff()>epsd) + { + VERIFY_IS_APPROX( mcd.array() / md.array(), mcd.array() / md.template cast<CD>().eval().array() ); + } - VERIFY_IS_APPROX( md.array().pow(mcd.array()), md.template cast<CD>().eval().array().pow(mcd.array()) ); - VERIFY_IS_APPROX( mcd.array().pow(md.array()), mcd.array().pow(md.template cast<CD>().eval().array()) ); + if(md.array().abs().minCoeff()>epsd || mcd.array().abs().minCoeff()>epsd) + { + VERIFY_IS_APPROX( md.array().pow(mcd.array()), md.template cast<CD>().eval().array().pow(mcd.array()) ); + VERIFY_IS_APPROX( mcd.array().pow(md.array()), mcd.array().pow(md.template cast<CD>().eval().array()) ); - VERIFY_IS_APPROX( pow(md.array(),mcd.array()), md.template cast<CD>().eval().array().pow(mcd.array()) ); - VERIFY_IS_APPROX( pow(mcd.array(),md.array()), mcd.array().pow(md.template cast<CD>().eval().array()) ); + VERIFY_IS_APPROX( pow(md.array(),mcd.array()), md.template cast<CD>().eval().array().pow(mcd.array()) ); + VERIFY_IS_APPROX( pow(mcd.array(),md.array()), mcd.array().pow(md.template cast<CD>().eval().array()) ); + } rcd = mcd; VERIFY_IS_APPROX( rcd = md, md.template cast<CD>().eval() ); @@ -250,7 +265,10 @@ template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType) rcd = mcd; VERIFY_IS_APPROX( rcd.array() *= md.array(), mcd.array() * md.template cast<CD>().eval().array() ); rcd = mcd; - VERIFY_IS_APPROX( rcd.array() /= md.array(), mcd.array() / md.template cast<CD>().eval().array() ); + if(md.array().abs().minCoeff()>epsd) + { + VERIFY_IS_APPROX( rcd.array() /= md.array(), mcd.array() / md.template cast<CD>().eval().array() ); + } rcd = mcd; VERIFY_IS_APPROX( rcd.noalias() += md + mcd*md, mcd + (md.template cast<CD>().eval()) + mcd*(md.template cast<CD>().eval())); diff --git a/test/packetmath.cpp b/test/packetmath.cpp index d560d005c..ea1786be2 100644 --- a/test/packetmath.cpp +++ b/test/packetmath.cpp @@ -9,6 +9,7 @@ // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. #include "main.h" +#include "unsupported/Eigen/SpecialFunctions" #if defined __GNUC__ && __GNUC__>=6 #pragma GCC diagnostic ignored "-Wignored-attributes" diff --git a/test/product_small.cpp b/test/product_small.cpp index c35db6f65..3e8dab01e 100644 --- a/test/product_small.cpp +++ b/test/product_small.cpp @@ -177,6 +177,38 @@ void test_lazy_l3() CALL_SUBTEST(( test_lazy_all_layout<T,4,-1,-1>(4,cols,depth) )); } +template<typename T,int N,int M,int K> +void test_linear_but_not_vectorizable() +{ + // Check tricky cases for which the result of the product is a vector and thus must exhibit the LinearBit flag, + // but is not vectorizable along the linear dimension. + Index n = N==Dynamic ? internal::random<Index>(1,32) : N; + Index m = M==Dynamic ? internal::random<Index>(1,32) : M; + Index k = K==Dynamic ? internal::random<Index>(1,32) : K; + + { + Matrix<T,N,M+1> A; A.setRandom(n,m+1); + Matrix<T,M*2,K> B; B.setRandom(m*2,k); + Matrix<T,1,K> C; + Matrix<T,1,K> R; + + C.noalias() = A.template topLeftCorner<1,M>() * (B.template topRows<M>()+B.template bottomRows<M>()); + R.noalias() = A.template topLeftCorner<1,M>() * (B.template topRows<M>()+B.template bottomRows<M>()).eval(); + VERIFY_IS_APPROX(C,R); + } + + { + Matrix<T,M+1,N,RowMajor> A; A.setRandom(m+1,n); + Matrix<T,K,M*2,RowMajor> B; B.setRandom(k,m*2); + Matrix<T,K,1> C; + Matrix<T,K,1> R; + + C.noalias() = (B.template leftCols<M>()+B.template rightCols<M>()) * A.template topLeftCorner<M,1>(); + R.noalias() = (B.template leftCols<M>()+B.template rightCols<M>()).eval() * A.template topLeftCorner<M,1>(); + VERIFY_IS_APPROX(C,R); + } +} + void test_product_small() { for(int i = 0; i < g_repeat; i++) { @@ -202,6 +234,10 @@ void test_product_small() CALL_SUBTEST_41( test_lazy_l1<std::complex<double> >() ); CALL_SUBTEST_42( test_lazy_l2<std::complex<double> >() ); CALL_SUBTEST_43( test_lazy_l3<std::complex<double> >() ); + + CALL_SUBTEST_7(( test_linear_but_not_vectorizable<float,2,1,Dynamic>() )); + CALL_SUBTEST_7(( test_linear_but_not_vectorizable<float,3,1,Dynamic>() )); + CALL_SUBTEST_7(( test_linear_but_not_vectorizable<float,2,1,16>() )); } #ifdef EIGEN_TEST_PART_6 diff --git a/test/qr.cpp b/test/qr.cpp index 98738777f..dfcc1e8f9 100644 --- a/test/qr.cpp +++ b/test/qr.cpp @@ -86,7 +86,7 @@ template<typename MatrixType> void qr_invertible() VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant()); // This test is tricky if the determinant becomes too small. // Since we generate random numbers with magnitude rrange [0,1], the average determinant is 0.5^size - VERIFY_IS_MUCH_SMALLER_THAN( abs(absdet-qr.absDeterminant()), (max)(RealScalar(pow(0.5,size)),(max)(abs(absdet),abs(qr.absDeterminant()))) ); + VERIFY_IS_MUCH_SMALLER_THAN( abs(absdet-qr.absDeterminant()), numext::maxi(RealScalar(pow(0.5,size)),numext::maxi<RealScalar>(abs(absdet),abs(qr.absDeterminant()))) ); } diff --git a/test/qr_colpivoting.cpp b/test/qr_colpivoting.cpp index 38de635a7..057bb014c 100644 --- a/test/qr_colpivoting.cpp +++ b/test/qr_colpivoting.cpp @@ -93,6 +93,7 @@ void cod_fixedsize() { template<typename MatrixType> void qr() { + using std::sqrt; typedef typename MatrixType::Index Index; Index rows = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE), cols = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE), cols2 = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE); @@ -120,14 +121,14 @@ template<typename MatrixType> void qr() // Verify that the absolute value of the diagonal elements in R are // non-increasing until they reach the singularity threshold. RealScalar threshold = - std::sqrt(RealScalar(rows)) * (std::abs)(r(0, 0)) * NumTraits<Scalar>::epsilon(); + sqrt(RealScalar(rows)) * numext::abs(r(0, 0)) * NumTraits<Scalar>::epsilon(); for (Index i = 0; i < (std::min)(rows, cols) - 1; ++i) { - RealScalar x = (std::abs)(r(i, i)); - RealScalar y = (std::abs)(r(i + 1, i + 1)); + RealScalar x = numext::abs(r(i, i)); + RealScalar y = numext::abs(r(i + 1, i + 1)); if (x < threshold && y < threshold) continue; if (!test_isApproxOrLessThan(y, x)) { for (Index j = 0; j < (std::min)(rows, cols); ++j) { - std::cout << "i = " << j << ", |r_ii| = " << (std::abs)(r(j, j)) << std::endl; + std::cout << "i = " << j << ", |r_ii| = " << numext::abs(r(j, j)) << std::endl; } std::cout << "Failure at i=" << i << ", rank=" << rank << ", threshold=" << threshold << std::endl; @@ -144,6 +145,8 @@ template<typename MatrixType> void qr() template<typename MatrixType, int Cols2> void qr_fixedsize() { + using std::sqrt; + using std::abs; enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime }; typedef typename MatrixType::Scalar Scalar; typedef typename MatrixType::RealScalar RealScalar; @@ -169,14 +172,14 @@ template<typename MatrixType, int Cols2> void qr_fixedsize() // Verify that the absolute value of the diagonal elements in R are // non-increasing until they reache the singularity threshold. RealScalar threshold = - std::sqrt(RealScalar(Rows)) * (std::abs)(r(0, 0)) * NumTraits<Scalar>::epsilon(); + sqrt(RealScalar(Rows)) * (std::abs)(r(0, 0)) * NumTraits<Scalar>::epsilon(); for (Index i = 0; i < (std::min)(int(Rows), int(Cols)) - 1; ++i) { - RealScalar x = (std::abs)(r(i, i)); - RealScalar y = (std::abs)(r(i + 1, i + 1)); + RealScalar x = numext::abs(r(i, i)); + RealScalar y = numext::abs(r(i + 1, i + 1)); if (x < threshold && y < threshold) continue; if (!test_isApproxOrLessThan(y, x)) { for (Index j = 0; j < (std::min)(int(Rows), int(Cols)); ++j) { - std::cout << "i = " << j << ", |r_ii| = " << (std::abs)(r(j, j)) << std::endl; + std::cout << "i = " << j << ", |r_ii| = " << numext::abs(r(j, j)) << std::endl; } std::cout << "Failure at i=" << i << ", rank=" << rank << ", threshold=" << threshold << std::endl; @@ -194,6 +197,8 @@ template<typename MatrixType, int Cols2> void qr_fixedsize() // page 3 for more detail. template<typename MatrixType> void qr_kahan_matrix() { + using std::sqrt; + using std::abs; typedef typename MatrixType::Index Index; typedef typename MatrixType::Scalar Scalar; typedef typename MatrixType::RealScalar RealScalar; @@ -215,14 +220,14 @@ template<typename MatrixType> void qr_kahan_matrix() MatrixType r = qr.matrixQR().template triangularView<Upper>(); RealScalar threshold = - std::sqrt(RealScalar(rows)) * (std::abs)(r(0, 0)) * NumTraits<Scalar>::epsilon(); + std::sqrt(RealScalar(rows)) * numext::abs(r(0, 0)) * NumTraits<Scalar>::epsilon(); for (Index i = 0; i < (std::min)(rows, cols) - 1; ++i) { - RealScalar x = (std::abs)(r(i, i)); - RealScalar y = (std::abs)(r(i + 1, i + 1)); + RealScalar x = numext::abs(r(i, i)); + RealScalar y = numext::abs(r(i + 1, i + 1)); if (x < threshold && y < threshold) continue; if (!test_isApproxOrLessThan(y, x)) { for (Index j = 0; j < (std::min)(rows, cols); ++j) { - std::cout << "i = " << j << ", |r_ii| = " << (std::abs)(r(j, j)) << std::endl; + std::cout << "i = " << j << ", |r_ii| = " << numext::abs(r(j, j)) << std::endl; } std::cout << "Failure at i=" << i << ", rank=" << qr.rank() << ", threshold=" << threshold << std::endl; diff --git a/test/qr_fullpivoting.cpp b/test/qr_fullpivoting.cpp index d82e123d0..05a705887 100644 --- a/test/qr_fullpivoting.cpp +++ b/test/qr_fullpivoting.cpp @@ -15,8 +15,12 @@ template<typename MatrixType> void qr() { typedef typename MatrixType::Index Index; - Index rows = internal::random<Index>(20,200), cols = internal::random<int>(20,200), cols2 = internal::random<int>(20,200); - Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1); + Index max_size = EIGEN_TEST_MAX_SIZE; + Index min_size = numext::maxi(1,EIGEN_TEST_MAX_SIZE/10); + Index rows = internal::random<Index>(min_size,max_size), + cols = internal::random<Index>(min_size,max_size), + cols2 = internal::random<Index>(min_size,max_size), + rank = internal::random<Index>(1, (std::min)(rows, cols)-1); typedef typename MatrixType::Scalar Scalar; typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType; @@ -59,7 +63,9 @@ template<typename MatrixType> void qr_invertible() typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar; typedef typename MatrixType::Scalar Scalar; - int size = internal::random<int>(10,50); + Index max_size = numext::mini(50,EIGEN_TEST_MAX_SIZE); + Index min_size = numext::maxi(1,EIGEN_TEST_MAX_SIZE/10); + Index size = internal::random<Index>(min_size,max_size); MatrixType m1(size, size), m2(size, size), m3(size, size); m1 = MatrixType::Random(size,size); diff --git a/test/schur_real.cpp b/test/schur_real.cpp index cfe4570d4..4aede87df 100644 --- a/test/schur_real.cpp +++ b/test/schur_real.cpp @@ -82,7 +82,7 @@ template<typename MatrixType> void schur(int size = MatrixType::ColsAtCompileTim Atriangular.template triangularView<StrictlyLower>().setZero(); rs3.setMaxIterations(1).compute(Atriangular); // triangular matrices do not need any iterations VERIFY_IS_EQUAL(rs3.info(), Success); - VERIFY_IS_EQUAL(rs3.matrixT(), Atriangular); + VERIFY_IS_APPROX(rs3.matrixT(), Atriangular); // approx because of scaling... VERIFY_IS_EQUAL(rs3.matrixU(), MatrixType::Identity(size, size)); // Test computation of only T, not U diff --git a/test/sparse_basic.cpp b/test/sparse_basic.cpp index 77523bab5..10309b3a9 100644 --- a/test/sparse_basic.cpp +++ b/test/sparse_basic.cpp @@ -317,6 +317,17 @@ template<typename SparseMatrixType> void sparse_basic(const SparseMatrixType& re VERIFY_IS_APPROX(mapMat2+mapMat3, refMat2+refMat3); VERIFY_IS_APPROX(mapMat2+mapMat3, refMat2+refMat3); } + + Index i = internal::random<Index>(0,rows-1); + Index j = internal::random<Index>(0,cols-1); + m2.coeffRef(i,j) = 123; + if(internal::random<bool>()) + m2.makeCompressed(); + Map<SparseMatrixType> mapMat2(rows, cols, m2.nonZeros(), m2.outerIndexPtr(), m2.innerIndexPtr(), m2.valuePtr(), m2.innerNonZeroPtr()); + VERIFY_IS_EQUAL(m2.coeff(i,j),Scalar(123)); + VERIFY_IS_EQUAL(mapMat2.coeff(i,j),Scalar(123)); + mapMat2.coeffRef(i,j) = -123; + VERIFY_IS_EQUAL(m2.coeff(i,j),Scalar(-123)); } // test triangularView diff --git a/test/sparse_solver.h b/test/sparse_solver.h index b67653496..fd6199f3e 100644 --- a/test/sparse_solver.h +++ b/test/sparse_solver.h @@ -11,6 +11,33 @@ #include <Eigen/SparseCore> #include <sstream> +template<typename Solver, typename Rhs, typename Guess,typename Result> +void solve_with_guess(IterativeSolverBase<Solver>& solver, const MatrixBase<Rhs>& b, const Guess& g, Result &x) { + if(internal::random<bool>()) + { + // With a temporary through evaluator<SolveWithGuess> + x = solver.derived().solveWithGuess(b,g) + Result::Zero(x.rows(), x.cols()); + } + else + { + // direct evaluation within x through Assignment<Result,SolveWithGuess> + x = solver.derived().solveWithGuess(b.derived(),g); + } +} + +template<typename Solver, typename Rhs, typename Guess,typename Result> +void solve_with_guess(SparseSolverBase<Solver>& solver, const MatrixBase<Rhs>& b, const Guess& , Result& x) { + if(internal::random<bool>()) + x = solver.derived().solve(b) + Result::Zero(x.rows(), x.cols()); + else + x = solver.derived().solve(b); +} + +template<typename Solver, typename Rhs, typename Guess,typename Result> +void solve_with_guess(SparseSolverBase<Solver>& solver, const SparseMatrixBase<Rhs>& b, const Guess& , Result& x) { + x = solver.derived().solve(b); +} + template<typename Solver, typename Rhs, typename DenseMat, typename DenseRhs> void check_sparse_solving(Solver& solver, const typename Solver::MatrixType& A, const Rhs& b, const DenseMat& dA, const DenseRhs& db) { @@ -37,6 +64,12 @@ void check_sparse_solving(Solver& solver, const typename Solver::MatrixType& A, } VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!"); VERIFY(x.isApprox(refX,test_precision<Scalar>())); + + x.setZero(); + solve_with_guess(solver, b, x, x); + VERIFY(solver.info() == Success && "solving failed when using analyzePattern/factorize API"); + VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!"); + VERIFY(x.isApprox(refX,test_precision<Scalar>())); x.setZero(); // test the analyze/factorize API diff --git a/test/svd_common.h b/test/svd_common.h index 3588eefaa..605d5dfef 100644 --- a/test/svd_common.h +++ b/test/svd_common.h @@ -42,9 +42,14 @@ void svd_check_full(const MatrixType& m, const SvdType& svd) MatrixUType u = svd.matrixU(); MatrixVType v = svd.matrixV(); RealScalar scaling = m.cwiseAbs().maxCoeff(); - if(scaling<=(std::numeric_limits<RealScalar>::min)()) - scaling = RealScalar(1); - VERIFY_IS_APPROX(m/scaling, u * (sigma/scaling) * v.adjoint()); + if(scaling<(std::numeric_limits<RealScalar>::min)()) + { + VERIFY(sigma.cwiseAbs().maxCoeff() <= (std::numeric_limits<RealScalar>::min)()); + } + else + { + VERIFY_IS_APPROX(m/scaling, u * (sigma/scaling) * v.adjoint()); + } VERIFY_IS_UNITARY(u); VERIFY_IS_UNITARY(v); } @@ -336,7 +341,7 @@ void svd_underoverflow() M << value_set(id(0)), value_set(id(1)), value_set(id(2)), value_set(id(3)); svd.compute(M,ComputeFullU|ComputeFullV); CALL_SUBTEST( svd_check_full(M,svd) ); - + id(k)++; if(id(k)>=value_set.size()) { @@ -344,7 +349,7 @@ void svd_underoverflow() id.head(k).setZero(); k=0; } - + } while((id<int(value_set.size())).all()); #if defined __INTEL_COMPILER diff --git a/test/svd_fill.h b/test/svd_fill.h index 500954d47..a705fa011 100644 --- a/test/svd_fill.h +++ b/test/svd_fill.h @@ -10,6 +10,7 @@ template<typename MatrixType> void svd_fill_random(MatrixType &m, int Option = 0) { + using std::pow; typedef typename MatrixType::Scalar Scalar; typedef typename MatrixType::RealScalar RealScalar; typedef typename MatrixType::Index Index; @@ -18,7 +19,7 @@ void svd_fill_random(MatrixType &m, int Option = 0) s = internal::random<RealScalar>(1,s); Matrix<RealScalar,Dynamic,1> d = Matrix<RealScalar,Dynamic,1>::Random(diagSize); for(Index k=0; k<diagSize; ++k) - d(k) = d(k)*std::pow(RealScalar(10),internal::random<RealScalar>(-s,s)); + d(k) = d(k)*pow(RealScalar(10),internal::random<RealScalar>(-s,s)); bool dup = internal::random<int>(0,10) < 3; bool unit_uv = internal::random<int>(0,10) < (dup?7:3); // if we duplicate some diagonal entries, then increase the chance to preserve them using unitary U and V factors @@ -53,8 +54,8 @@ void svd_fill_random(MatrixType &m, int Option = 0) VT.setRandom(); } - Matrix<Scalar,Dynamic,1> samples(7); - samples << 0, 5.60844e-313, -5.60844e-313, 4.94e-324, -4.94e-324, -RealScalar(1)/NumTraits<RealScalar>::highest(), RealScalar(1)/NumTraits<RealScalar>::highest(); + Matrix<Scalar,Dynamic,1> samples(9); + samples << 0, 5.60844e-313, -5.60844e-313, 4.94e-324, -4.94e-324, -RealScalar(1)/NumTraits<RealScalar>::highest(), RealScalar(1)/NumTraits<RealScalar>::highest(), (std::numeric_limits<RealScalar>::min)(), pow((std::numeric_limits<RealScalar>::min)(),0.8); if(Option==Symmetric) { diff --git a/test/vectorization_logic.cpp b/test/vectorization_logic.cpp index b7c2df64b..83c1439ad 100644 --- a/test/vectorization_logic.cpp +++ b/test/vectorization_logic.cpp @@ -195,8 +195,7 @@ struct vectorization_logic VERIFY(test_assign(Matrix11(),Matrix<Scalar,17,17>().template block<PacketSize,PacketSize>(2,3)+Matrix<Scalar,17,17>().template block<PacketSize,PacketSize>(8,4), - (EIGEN_UNALIGNED_VECTORIZE) ? InnerVectorizedTraversal : DefaultTraversal, - (EIGEN_UNALIGNED_VECTORIZE || PacketSize<=4) ? CompleteUnrolling : InnerUnrolling )); + (EIGEN_UNALIGNED_VECTORIZE) ? InnerVectorizedTraversal : DefaultTraversal, CompleteUnrolling|InnerUnrolling)); VERIFY(test_assign(Vector1(),Matrix11()*Vector1(), InnerVectorizedTraversal,CompleteUnrolling)); @@ -234,7 +233,7 @@ struct vectorization_logic VERIFY((test_assign< Map<Matrix<Scalar,EIGEN_PLAIN_ENUM_MAX(2,PacketSize),EIGEN_PLAIN_ENUM_MAX(2,PacketSize)>, AlignedMax, InnerStride<3*PacketSize> >, Matrix<Scalar,EIGEN_PLAIN_ENUM_MAX(2,PacketSize),EIGEN_PLAIN_ENUM_MAX(2,PacketSize)> - >(DefaultTraversal,CompleteUnrolling))); + >(DefaultTraversal,PacketSize>=8?InnerUnrolling:CompleteUnrolling))); VERIFY((test_assign(Matrix11(), Matrix<Scalar,PacketSize,EIGEN_PLAIN_ENUM_MIN(2,PacketSize)>()*Matrix<Scalar,EIGEN_PLAIN_ENUM_MIN(2,PacketSize),PacketSize>(), InnerVectorizedTraversal, CompleteUnrolling))); @@ -371,7 +370,7 @@ struct vectorization_logic_half >(DefaultTraversal,CompleteUnrolling))); VERIFY((test_assign(Matrix57(), Matrix<Scalar,5*PacketSize,3>()*Matrix<Scalar,3,7>(), - InnerVectorizedTraversal, CompleteUnrolling))); + InnerVectorizedTraversal, InnerUnrolling|CompleteUnrolling))); #endif } }; diff --git a/unsupported/Eigen/CMakeLists.txt b/unsupported/Eigen/CMakeLists.txt index 6d0cf4f9d..7478b6b0d 100644 --- a/unsupported/Eigen/CMakeLists.txt +++ b/unsupported/Eigen/CMakeLists.txt @@ -17,6 +17,7 @@ set(Eigen_HEADERS Polynomials Skyline SparseExtra + SpecialFunctions Splines ) diff --git a/unsupported/Eigen/CXX11/Tensor b/unsupported/Eigen/CXX11/Tensor index 79bac2f67..f7b94cee1 100644 --- a/unsupported/Eigen/CXX11/Tensor +++ b/unsupported/Eigen/CXX11/Tensor @@ -15,6 +15,7 @@ #include <Eigen/src/Core/util/DisableStupidWarnings.h> +#include "../SpecialFunctions" #include "src/util/CXX11Meta.h" #include "src/util/MaxSizeVector.h" diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h b/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h index 142778df8..19d2b50b5 100644 --- a/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h +++ b/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h @@ -817,8 +817,8 @@ class TensorBase<Derived, ReadOnlyAccessors> EIGEN_STRONG_INLINE const Derived& derived() const { return *static_cast<const Derived*>(this); } }; -template<typename Derived> -class TensorBase<Derived, WriteAccessors> : public TensorBase<Derived, ReadOnlyAccessors> { +template<typename Derived, int AccessLevel = internal::accessors_level<Derived>::value> +class TensorBase : public TensorBase<Derived, ReadOnlyAccessors> { public: typedef internal::traits<Derived> DerivedTraits; typedef typename DerivedTraits::Scalar Scalar; @@ -828,7 +828,7 @@ class TensorBase<Derived, WriteAccessors> : public TensorBase<Derived, ReadOnlyA template <typename Scalar, int NumIndices, int Options, typename IndexType> friend class Tensor; template <typename Scalar, typename Dimensions, int Option, typename IndexTypes> friend class TensorFixedSize; - template <typename OtherDerived, int AccessLevel> friend class TensorBase; + template <typename OtherDerived, int OtherAccessLevel> friend class TensorBase; EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& setZero() { diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorContractionCuda.h b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionCuda.h index 886474986..d65dbb40f 100644 --- a/unsupported/Eigen/CXX11/src/Tensor/TensorContractionCuda.h +++ b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionCuda.h @@ -461,8 +461,8 @@ EigenContractionKernelInternal(const LhsMapper lhs, const RhsMapper rhs, #undef writeResultShmem #undef writeRow - const int max_i_write = (min)((int)((m_size - base_m - threadIdx.y + 7) / 8), 8); - const int max_j_write = (min)((int)((n_size - base_n - threadIdx.z + 7) / 8), 8); + const int max_i_write = numext::mini((int)((m_size - base_m - threadIdx.y + 7) / 8), 8); + const int max_j_write = numext::mini((int)((n_size - base_n - threadIdx.z + 7) / 8), 8); if (threadIdx.x < max_i_write) { if (max_j_write == 8) { diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorContractionMapper.h b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionMapper.h index b27e1a1b4..9b2cb3ff6 100644 --- a/unsupported/Eigen/CXX11/src/Tensor/TensorContractionMapper.h +++ b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionMapper.h @@ -130,19 +130,19 @@ class SimpleTensorContractionMapper { } Index contract_val = left ? col : row; - for (int i = static_cast<int>(array_size<contract_t>::value) - 1; i > 0; i--) { - const Index idx = contract_val / m_k_strides[i]; - linidx += idx * m_contract_strides[i]; - contract_val -= idx * m_k_strides[i]; - } - if(array_size<contract_t>::value > 0) { - if (side == Rhs && inner_dim_contiguous) { - eigen_assert(m_contract_strides[0] == 1); - linidx += contract_val; - } else { - linidx += contract_val * m_contract_strides[0]; - } + for (int i = static_cast<int>(array_size<contract_t>::value) - 1; i > 0; i--) { + const Index idx = contract_val / m_k_strides[i]; + linidx += idx * m_contract_strides[i]; + contract_val -= idx * m_k_strides[i]; + } + + if (side == Rhs && inner_dim_contiguous) { + eigen_assert(m_contract_strides[0] == 1); + linidx += contract_val; + } else { + linidx += contract_val * m_contract_strides[0]; + } } return linidx; @@ -153,15 +153,15 @@ class SimpleTensorContractionMapper { const bool left = (side == Lhs); Index nocontract_val[2] = {left ? row : col, left ? row + distance : col}; Index linidx[2] = {0, 0}; - for (int i = static_cast<int>(array_size<nocontract_t>::value) - 1; i > 0; i--) { - const Index idx0 = nocontract_val[0] / m_ij_strides[i]; - const Index idx1 = nocontract_val[1] / m_ij_strides[i]; - linidx[0] += idx0 * m_nocontract_strides[i]; - linidx[1] += idx1 * m_nocontract_strides[i]; - nocontract_val[0] -= idx0 * m_ij_strides[i]; - nocontract_val[1] -= idx1 * m_ij_strides[i]; - } if (array_size<typename Tensor::Dimensions>::value > array_size<contract_t>::value) { + for (int i = static_cast<int>(array_size<nocontract_t>::value) - 1; i > 0; i--) { + const Index idx0 = nocontract_val[0] / m_ij_strides[i]; + const Index idx1 = nocontract_val[1] / m_ij_strides[i]; + linidx[0] += idx0 * m_nocontract_strides[i]; + linidx[1] += idx1 * m_nocontract_strides[i]; + nocontract_val[0] -= idx0 * m_ij_strides[i]; + nocontract_val[1] -= idx1 * m_ij_strides[i]; + } if (side == Lhs && inner_dim_contiguous) { eigen_assert(m_nocontract_strides[0] == 1); linidx[0] += nocontract_val[0]; @@ -173,22 +173,24 @@ class SimpleTensorContractionMapper { } Index contract_val[2] = {left ? col : row, left ? col : row + distance}; - for (int i = static_cast<int>(array_size<contract_t>::value) - 1; i > 0; i--) { - const Index idx0 = contract_val[0] / m_k_strides[i]; - const Index idx1 = contract_val[1] / m_k_strides[i]; - linidx[0] += idx0 * m_contract_strides[i]; - linidx[1] += idx1 * m_contract_strides[i]; - contract_val[0] -= idx0 * m_k_strides[i]; - contract_val[1] -= idx1 * m_k_strides[i]; - } + if (array_size<contract_t>::value> 0) { + for (int i = static_cast<int>(array_size<contract_t>::value) - 1; i > 0; i--) { + const Index idx0 = contract_val[0] / m_k_strides[i]; + const Index idx1 = contract_val[1] / m_k_strides[i]; + linidx[0] += idx0 * m_contract_strides[i]; + linidx[1] += idx1 * m_contract_strides[i]; + contract_val[0] -= idx0 * m_k_strides[i]; + contract_val[1] -= idx1 * m_k_strides[i]; + } - if (side == Rhs && inner_dim_contiguous) { - eigen_assert(m_contract_strides[0] == 1); - linidx[0] += contract_val[0]; - linidx[1] += contract_val[1]; - } else { - linidx[0] += contract_val[0] * m_contract_strides[0]; - linidx[1] += contract_val[1] * m_contract_strides[0]; + if (side == Rhs && inner_dim_contiguous) { + eigen_assert(m_contract_strides[0] == 1); + linidx[0] += contract_val[0]; + linidx[1] += contract_val[1]; + } else { + linidx[0] += contract_val[0] * m_contract_strides[0]; + linidx[1] += contract_val[1] * m_contract_strides[0]; + } } return IndexPair<Index>(linidx[0], linidx[1]); } @@ -200,7 +202,7 @@ class SimpleTensorContractionMapper { return (Alignment == Aligned) && (side == Lhs) && inner_dim_contiguous ? 0 : size; } EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Index stride() const { - return ((side == Lhs) && inner_dim_contiguous) ? m_contract_strides[0] : 1; + return ((side == Lhs) && inner_dim_contiguous && array_size<contract_t>::value > 0) ? m_contract_strides[0] : 1; } protected: diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h index 34270730b..069680a11 100644 --- a/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h +++ b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h @@ -151,9 +151,7 @@ struct ThreadPoolDevice { template <class Function, class... Args> EIGEN_STRONG_INLINE Notification* enqueue(Function&& f, Args&&... args) const { Notification* n = new Notification(); - std::function<void()> func = - std::bind(&FunctionWrapperWithNotification<Function, Args...>::run, n, f, args...); - pool_->Schedule(func); + pool_->Schedule(std::bind(&FunctionWrapperWithNotification<Function, Args...>::run, n, f, args...)); return n; } @@ -161,15 +159,13 @@ struct ThreadPoolDevice { EIGEN_STRONG_INLINE void enqueue_with_barrier(Barrier* b, Function&& f, Args&&... args) const { - std::function<void()> func = std::bind( - &FunctionWrapperWithBarrier<Function, Args...>::run, b, f, args...); - pool_->Schedule(func); + pool_->Schedule(std::bind( + &FunctionWrapperWithBarrier<Function, Args...>::run, b, f, args...)); } template <class Function, class... Args> EIGEN_STRONG_INLINE void enqueueNoNotification(Function&& f, Args&&... args) const { - std::function<void()> func = std::bind(f, args...); - pool_->Schedule(func); + pool_->Schedule(std::bind(f, args...)); } // Returns a logical thread index between 0 and pool_->NumThreads() - 1 if diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorEvalTo.h b/unsupported/Eigen/CXX11/src/Tensor/TensorEvalTo.h index 26b1f65a8..a08dfa7c3 100644 --- a/unsupported/Eigen/CXX11/src/Tensor/TensorEvalTo.h +++ b/unsupported/Eigen/CXX11/src/Tensor/TensorEvalTo.h @@ -94,7 +94,7 @@ struct TensorEvaluator<const TensorEvalToOp<ArgType>, Device> static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size; enum { - IsAligned = true, + IsAligned = TensorEvaluator<ArgType, Device>::IsAligned, PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess, Layout = TensorEvaluator<ArgType, Device>::Layout, CoordAccess = false, // to be implemented diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorEvaluator.h b/unsupported/Eigen/CXX11/src/Tensor/TensorEvaluator.h index a48cb1daa..c2a327bf0 100644 --- a/unsupported/Eigen/CXX11/src/Tensor/TensorEvaluator.h +++ b/unsupported/Eigen/CXX11/src/Tensor/TensorEvaluator.h @@ -131,7 +131,7 @@ double loadConstant(const double* address) { } template <> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Eigen::half loadConstant(const Eigen::half* address) { - return Eigen::half(internal::raw_uint16_to_half(__ldg(&address->x))); + return Eigen::half(half_impl::raw_uint16_to_half(__ldg(&address->x))); } #endif } diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorExecutor.h b/unsupported/Eigen/CXX11/src/Tensor/TensorExecutor.h index ad5c97b57..a116bf17f 100644 --- a/unsupported/Eigen/CXX11/src/Tensor/TensorExecutor.h +++ b/unsupported/Eigen/CXX11/src/Tensor/TensorExecutor.h @@ -159,7 +159,6 @@ class TensorExecutor<Expression, ThreadPoolDevice, Vectorizable> { #else size_t num_threads = device.numThreads(); if (num_threads > 1) { - cost = evaluator.costPerCoeff(Vectorizable) num_threads = TensorCostModel<ThreadPoolDevice>::numThreads( size, evaluator.costPerCoeff(Vectorizable), num_threads); } diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorFFT.h b/unsupported/Eigen/CXX11/src/Tensor/TensorFFT.h index ece2ed91b..08eb5595a 100644 --- a/unsupported/Eigen/CXX11/src/Tensor/TensorFFT.h +++ b/unsupported/Eigen/CXX11/src/Tensor/TensorFFT.h @@ -329,7 +329,7 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D for (Index i = 0; i < n; ++i) { if(FFTDir == FFT_FORWARD) { - a[i] = data[i] * std::conj(pos_j_base_powered[i]); + a[i] = data[i] * numext::conj(pos_j_base_powered[i]); } else { a[i] = data[i] * pos_j_base_powered[i]; @@ -344,7 +344,7 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D b[i] = pos_j_base_powered[i]; } else { - b[i] = std::conj(pos_j_base_powered[i]); + b[i] = numext::conj(pos_j_base_powered[i]); } } for (Index i = n; i < m - n; ++i) { @@ -355,7 +355,7 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D b[i] = pos_j_base_powered[m-i]; } else { - b[i] = std::conj(pos_j_base_powered[m-i]); + b[i] = numext::conj(pos_j_base_powered[m-i]); } } @@ -379,7 +379,7 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D for (Index i = 0; i < n; ++i) { if(FFTDir == FFT_FORWARD) { - data[i] = a[i] * std::conj(pos_j_base_powered[i]); + data[i] = a[i] * numext::conj(pos_j_base_powered[i]); } else { data[i] = a[i] * pos_j_base_powered[i]; diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorForwardDeclarations.h b/unsupported/Eigen/CXX11/src/Tensor/TensorForwardDeclarations.h index f35275ffb..490ddd8bd 100644 --- a/unsupported/Eigen/CXX11/src/Tensor/TensorForwardDeclarations.h +++ b/unsupported/Eigen/CXX11/src/Tensor/TensorForwardDeclarations.h @@ -16,7 +16,7 @@ template<typename Scalar_, int NumIndices_, int Options_ = 0, typename IndexType template<typename Scalar_, typename Dimensions, int Options_ = 0, typename IndexType = DenseIndex> class TensorFixedSize; template<typename PlainObjectType, int Options_ = Unaligned> class TensorMap; template<typename PlainObjectType> class TensorRef; -template<typename Derived, int AccessLevel = internal::accessors_level<Derived>::value> class TensorBase; +template<typename Derived, int AccessLevel> class TensorBase; template<typename NullaryOp, typename PlainObjectType> class TensorCwiseNullaryOp; template<typename UnaryOp, typename XprType> class TensorCwiseUnaryOp; diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorIO.h b/unsupported/Eigen/CXX11/src/Tensor/TensorIO.h index f3a3a1b88..a901c5dd4 100644 --- a/unsupported/Eigen/CXX11/src/Tensor/TensorIO.h +++ b/unsupported/Eigen/CXX11/src/Tensor/TensorIO.h @@ -13,11 +13,6 @@ namespace Eigen { namespace internal { -template<> -struct significant_decimals_impl<std::string> - : significant_decimals_default_impl<std::string, true> -{}; - // Print the tensor as a 2d matrix template <typename Tensor, int Rank> diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorIntDiv.h b/unsupported/Eigen/CXX11/src/Tensor/TensorIntDiv.h index 33c6c1b0f..ede3939c2 100644 --- a/unsupported/Eigen/CXX11/src/Tensor/TensorIntDiv.h +++ b/unsupported/Eigen/CXX11/src/Tensor/TensorIntDiv.h @@ -29,25 +29,47 @@ namespace Eigen { namespace internal { namespace { + // Note: result is undefined if val == 0 template <typename T> - EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE int count_leading_zeros(const T val) + EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE + typename internal::enable_if<sizeof(T)==4,int>::type count_leading_zeros(const T val) { #ifdef __CUDA_ARCH__ - return (sizeof(T) == 8) ? __clzll(val) : __clz(val); + return __clz(val); #elif EIGEN_COMP_MSVC - unsigned long index; - if (sizeof(T) == 8) { - _BitScanReverse64(&index, val); - } else { - _BitScanReverse(&index, val); - } - return (sizeof(T) == 8) ? 63 - index : 31 - index; + unsigned long index; + _BitScanReverse(&index, val); + return 31 - index; +#else + EIGEN_STATIC_ASSERT(sizeof(unsigned long long) == 8, YOU_MADE_A_PROGRAMMING_MISTAKE); + return __builtin_clz(static_cast<uint32_t>(val)); +#endif + } + + template <typename T> + EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE + typename internal::enable_if<sizeof(T)==8,int>::type count_leading_zeros(const T val) + { +#ifdef __CUDA_ARCH__ + return __clzll(val); +#elif EIGEN_COMP_MSVC && EIGEN_ARCH_x86_64 + unsigned long index; + _BitScanReverse64(&index, val); + return 63 - index; +#elif EIGEN_COMP_MSVC + // MSVC's _BitScanReverse64 is not available for 32bits builds. + unsigned int lo = (unsigned int)(val&0xffffffff); + unsigned int hi = (unsigned int)((val>>32)&0xffffffff); + int n; + if(hi==0) + n = 32 + count_leading_zeros<unsigned int>(lo); + else + n = count_leading_zeros<unsigned int>(hi); + return n; #else EIGEN_STATIC_ASSERT(sizeof(unsigned long long) == 8, YOU_MADE_A_PROGRAMMING_MISTAKE); - return (sizeof(T) == 8) ? - __builtin_clzll(static_cast<uint64_t>(val)) : - __builtin_clz(static_cast<uint32_t>(val)); + return __builtin_clzll(static_cast<uint64_t>(val)); #endif } @@ -98,7 +120,9 @@ namespace { return static_cast<uint64_t>((static_cast<__uint128_t>(1) << (64+log_div)) / static_cast<__uint128_t>(divider) - (static_cast<__uint128_t>(1) << 64) + 1); #else const uint64_t shift = 1ULL << log_div; - TensorUInt128<uint64_t, uint64_t> result = (TensorUInt128<uint64_t, static_val<0> >(shift, 0) / TensorUInt128<static_val<0>, uint64_t>(divider) - TensorUInt128<static_val<1>, static_val<0> >(1, 0) + TensorUInt128<static_val<0>, static_val<1> >(1)); + TensorUInt128<uint64_t, uint64_t> result = TensorUInt128<uint64_t, static_val<0> >(shift, 0) / TensorUInt128<static_val<0>, uint64_t>(divider) + - TensorUInt128<static_val<1>, static_val<0> >(1, 0) + + TensorUInt128<static_val<0>, static_val<1> >(1); return static_cast<uint64_t>(result); #endif } diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorReduction.h b/unsupported/Eigen/CXX11/src/Tensor/TensorReduction.h index 04ba45a8f..0e1576954 100644 --- a/unsupported/Eigen/CXX11/src/Tensor/TensorReduction.h +++ b/unsupported/Eigen/CXX11/src/Tensor/TensorReduction.h @@ -264,7 +264,7 @@ struct FullReducer<Self, Op, ThreadPoolDevice, Vectorizable> { const Index numblocks = blocksize > 0 ? num_coeffs / blocksize : 0; eigen_assert(num_coeffs >= numblocks * blocksize); - Barrier barrier(numblocks); + Barrier barrier(internal::convert_index<unsigned int>(numblocks)); MaxSizeVector<typename Self::CoeffReturnType> shards(numblocks, reducer.initialize()); for (Index i = 0; i < numblocks; ++i) { device.enqueue_with_barrier(&barrier, &FullReducerShard<Self, Op, Vectorizable>::run, @@ -492,7 +492,7 @@ struct TensorEvaluator<const TensorReductionOp<Op, Dims, ArgType>, Device> } // Attempt to use an optimized reduction. - else if (RunningOnGPU && data && (m_device.majorDeviceVersion() >= 3)) { + else if (RunningOnGPU && (m_device.majorDeviceVersion() >= 3)) { bool reducing_inner_dims = true; for (int i = 0; i < NumReducedDims; ++i) { if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) { @@ -505,8 +505,12 @@ struct TensorEvaluator<const TensorReductionOp<Op, Dims, ArgType>, Device> (reducing_inner_dims || ReducingInnerMostDims)) { const Index num_values_to_reduce = internal::array_prod(m_reducedDims); const Index num_coeffs_to_preserve = internal::array_prod(m_dimensions); + if (!data && num_coeffs_to_preserve < 1024 && num_values_to_reduce > num_coeffs_to_preserve) { + data = static_cast<CoeffReturnType*>(m_device.allocate(sizeof(CoeffReturnType) * num_coeffs_to_preserve)); + m_result = data; + } Op reducer(m_reducer); - return internal::InnerReducer<Self, Op, Device>::run(*this, reducer, m_device, data, num_values_to_reduce, num_coeffs_to_preserve); + return internal::InnerReducer<Self, Op, Device>::run(*this, reducer, m_device, data, num_values_to_reduce, num_coeffs_to_preserve) || (m_result != NULL); } bool preserving_inner_dims = true; @@ -521,8 +525,12 @@ struct TensorEvaluator<const TensorReductionOp<Op, Dims, ArgType>, Device> preserving_inner_dims) { const Index num_values_to_reduce = internal::array_prod(m_reducedDims); const Index num_coeffs_to_preserve = internal::array_prod(m_dimensions); + if (!data && num_coeffs_to_preserve < 1024 && num_values_to_reduce > num_coeffs_to_preserve) { + data = static_cast<CoeffReturnType*>(m_device.allocate(sizeof(CoeffReturnType) * num_coeffs_to_preserve)); + m_result = data; + } Op reducer(m_reducer); - return internal::OuterReducer<Self, Op, Device>::run(*this, reducer, m_device, data, num_values_to_reduce, num_coeffs_to_preserve); + return internal::OuterReducer<Self, Op, Device>::run(*this, reducer, m_device, data, num_values_to_reduce, num_coeffs_to_preserve) || (m_result != NULL); } } return true; @@ -537,8 +545,8 @@ struct TensorEvaluator<const TensorReductionOp<Op, Dims, ArgType>, Device> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const { - if (RunningFullReduction && m_result) { - return *m_result; + if ((RunningFullReduction || RunningOnGPU) && m_result) { + return *(m_result + index); } Op reducer(m_reducer); if (ReducingInnerMostDims || RunningFullReduction) { @@ -558,7 +566,11 @@ struct TensorEvaluator<const TensorReductionOp<Op, Dims, ArgType>, Device> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const { EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE) - eigen_assert(index + PacketSize - 1 < internal::array_prod(dimensions())); + eigen_assert(index + PacketSize - 1 < Index(internal::array_prod(dimensions()))); + + if (RunningOnGPU && m_result) { + return internal::pload<PacketReturnType>(m_result + index); + } EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize]; if (ReducingInnerMostDims) { diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorReductionCuda.h b/unsupported/Eigen/CXX11/src/Tensor/TensorReductionCuda.h index d3894e625..5e512490c 100644 --- a/unsupported/Eigen/CXX11/src/Tensor/TensorReductionCuda.h +++ b/unsupported/Eigen/CXX11/src/Tensor/TensorReductionCuda.h @@ -336,11 +336,9 @@ struct FullReducer<Self, Op, GpuDevice, Vectorizable> { static const bool HasOptimizedImplementation = !Op::IsStateful && (internal::is_same<typename Self::CoeffReturnType, float>::value || (internal::is_same<typename Self::CoeffReturnType, Eigen::half>::value && reducer_traits<Op, GpuDevice>::PacketAccess)); -#elif __CUDA_ARCH__ >= 300 +#else static const bool HasOptimizedImplementation = !Op::IsStateful && internal::is_same<typename Self::CoeffReturnType, float>::value; -#else - static const bool HasOptimizedImplementation = false; #endif template <typename OutputType> @@ -619,11 +617,9 @@ struct InnerReducer<Self, Op, GpuDevice> { static const bool HasOptimizedImplementation = !Op::IsStateful && (internal::is_same<typename Self::CoeffReturnType, float>::value || (internal::is_same<typename Self::CoeffReturnType, Eigen::half>::value && reducer_traits<Op, GpuDevice>::PacketAccess)); -#elif __CUDA_ARCH__ >= 300 +#else static const bool HasOptimizedImplementation = !Op::IsStateful && internal::is_same<typename Self::CoeffReturnType, float>::value; -#else - static const bool HasOptimizedImplementation = false; #endif template <typename OutputType> @@ -678,12 +674,8 @@ struct OuterReducer<Self, Op, GpuDevice> { // Unfortunately nvidia doesn't support well exotic types such as complex, // so reduce the scope of the optimized version of the code to the simple case // of floats. -#if __CUDA_ARCH__ >= 300 static const bool HasOptimizedImplementation = !Op::IsStateful && internal::is_same<typename Self::CoeffReturnType, float>::value; -#else - static const bool HasOptimizedImplementation = false; -#endif template <typename Device, typename OutputType> static EIGEN_DEVICE_FUNC bool run(const Self&, Op&, const Device&, OutputType*, typename Self::Index, typename Self::Index) { diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h b/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h index a61b14ded..8501466ce 100644 --- a/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h +++ b/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h @@ -94,7 +94,7 @@ struct TensorEvaluator<const TensorScanOp<Op, ArgType>, Device> { enum { IsAligned = false, - PacketAccess = (internal::packet_traits<Scalar>::size > 1), + PacketAccess = (internal::unpacket_traits<PacketReturnType>::size > 1), BlockAccess = false, Layout = TensorEvaluator<ArgType, Device>::Layout, CoordAccess = false, diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorUInt128.h b/unsupported/Eigen/CXX11/src/Tensor/TensorUInt128.h index bdcd70fd9..3523e7c94 100644 --- a/unsupported/Eigen/CXX11/src/Tensor/TensorUInt128.h +++ b/unsupported/Eigen/CXX11/src/Tensor/TensorUInt128.h @@ -20,6 +20,7 @@ struct static_val { EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE operator uint64_t() const { return n; } EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static_val() { } + template <typename T> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static_val(const T& v) { eigen_assert(v == n); @@ -53,7 +54,7 @@ struct TensorUInt128 template<typename T> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE explicit TensorUInt128(const T& x) : high(0), low(x) { - eigen_assert((static_cast<typename conditional<sizeof(T) == 8, uint64_t, uint32_t>::type>(x) <= static_cast<typename conditional<sizeof(LOW) == 8, uint64_t, uint32_t>::type>(NumTraits<LOW>::highest()))); + eigen_assert((static_cast<typename conditional<sizeof(T) == 8, uint64_t, uint32_t>::type>(x) <= NumTraits<uint64_t>::highest())); eigen_assert(x >= 0); } diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/ThreadEnvironment.h b/unsupported/Eigen/CXX11/src/ThreadPool/ThreadEnvironment.h index d2204ad5b..399f95cc1 100644 --- a/unsupported/Eigen/CXX11/src/ThreadPool/ThreadEnvironment.h +++ b/unsupported/Eigen/CXX11/src/ThreadPool/ThreadEnvironment.h @@ -21,14 +21,14 @@ struct StlThreadEnvironment { // destructor must join the thread. class EnvThread { public: - EnvThread(std::function<void()> f) : thr_(f) {} + EnvThread(std::function<void()> f) : thr_(std::move(f)) {} ~EnvThread() { thr_.join(); } private: std::thread thr_; }; - EnvThread* CreateThread(std::function<void()> f) { return new EnvThread(f); } + EnvThread* CreateThread(std::function<void()> f) { return new EnvThread(std::move(f)); } Task CreateTask(std::function<void()> f) { return Task{std::move(f)}; } void ExecuteTask(const Task& t) { t.f(); } }; diff --git a/unsupported/Eigen/MPRealSupport b/unsupported/Eigen/MPRealSupport index 89036886b..7f0b70c63 100644 --- a/unsupported/Eigen/MPRealSupport +++ b/unsupported/Eigen/MPRealSupport @@ -67,27 +67,32 @@ int main() IsSigned = 1, IsComplex = 0, RequireInitialization = 1, - ReadCost = 10, - AddCost = 10, - MulCost = 40 + ReadCost = HugeCost, + AddCost = HugeCost, + MulCost = HugeCost }; typedef mpfr::mpreal Real; typedef mpfr::mpreal NonInteger; - inline static Real highest (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::maxval(Precision); } - inline static Real lowest (long Precision = mpfr::mpreal::get_default_prec()) { return -mpfr::maxval(Precision); } + static inline Real highest (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::maxval(Precision); } + static inline Real lowest (long Precision = mpfr::mpreal::get_default_prec()) { return -mpfr::maxval(Precision); } // Constants - inline static Real Pi (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_pi(Precision); } - inline static Real Euler (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_euler(Precision); } - inline static Real Log2 (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_log2(Precision); } - inline static Real Catalan (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_catalan(Precision); } + static inline Real Pi (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_pi(Precision); } + static inline Real Euler (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_euler(Precision); } + static inline Real Log2 (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_log2(Precision); } + static inline Real Catalan (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_catalan(Precision); } - inline static Real epsilon (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::machine_epsilon(Precision); } - inline static Real epsilon (const Real& x) { return mpfr::machine_epsilon(x); } + static inline Real epsilon (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::machine_epsilon(Precision); } + static inline Real epsilon (const Real& x) { return mpfr::machine_epsilon(x); } - inline static Real dummy_precision() +#ifdef MPREAL_HAVE_DYNAMIC_STD_NUMERIC_LIMITS + static inline int digits10 (long Precision = mpfr::mpreal::get_default_prec()) { return std::numeric_limits<Real>::digits10(Precision); } + static inline int digits10 (const Real& x) { return std::numeric_limits<Real>::digits10(x); } +#endif + + static inline Real dummy_precision() { mpfr_prec_t weak_prec = ((mpfr::mpreal::get_default_prec()-1) * 90) / 100; return mpfr::machine_epsilon(weak_prec); diff --git a/unsupported/Eigen/SpecialFunctions b/unsupported/Eigen/SpecialFunctions new file mode 100644 index 000000000..7c7493c56 --- /dev/null +++ b/unsupported/Eigen/SpecialFunctions @@ -0,0 +1,61 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2016 Gael Guennebaud <g.gael@free.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SPECIALFUNCTIONS_MODULE +#define EIGEN_SPECIALFUNCTIONS_MODULE + +#include "../../Eigen/Core" + +#include "../../Eigen/src/Core/util/DisableStupidWarnings.h" + +namespace Eigen { + +/** + * \defgroup SpecialFunctions_Module Special math functions module + * + * This module features additional coefficient-wise math functions available + * within the numext:: namespace for the scalar version, and as method and/or free + * functions of Array. Those include: + * + * - erf + * - erfc + * - lgamma + * - igamma + * - igammac + * - digamma + * - polygamma + * - zeta + * - betainc + * + * \code + * #include <unsupported/Eigen/SpecialFunctions> + * \endcode + */ +//@{ + +} + +#include "src/SpecialFunctions/SpecialFunctionsImpl.h" +#include "src/SpecialFunctions/SpecialFunctionsPacketMath.h" +#include "src/SpecialFunctions/SpecialFunctionsHalf.h" +#include "src/SpecialFunctions/SpecialFunctionsFunctors.h" +#include "src/SpecialFunctions/SpecialFunctionsArrayAPI.h" + +#if defined EIGEN_VECTORIZE_CUDA + #include "src/SpecialFunctions/arch/CUDA/CudaSpecialFunctions.h" +#endif + +namespace Eigen { +//@} +} + + +#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_SPECIALFUNCTIONS_MODULE diff --git a/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h index 76bf2d96c..50fedf6ac 100755 --- a/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h +++ b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h @@ -497,31 +497,15 @@ struct make_coherent_impl<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, } // end namespace internal -template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols, typename BinOp> -struct ScalarBinaryOpTraits<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>,A_Scalar,BinOp> -{ - enum { Defined = 1 }; - typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> ReturnType; -}; - -template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols, typename BinOp> -struct ScalarBinaryOpTraits<A_Scalar, Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>, BinOp> -{ - enum { Defined = 1 }; - typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> ReturnType; -}; - template<typename DerType, typename BinOp> struct ScalarBinaryOpTraits<AutoDiffScalar<DerType>,typename DerType::Scalar,BinOp> { - enum { Defined = 1 }; typedef AutoDiffScalar<DerType> ReturnType; }; template<typename DerType, typename BinOp> struct ScalarBinaryOpTraits<typename DerType::Scalar,AutoDiffScalar<DerType>, BinOp> { - enum { Defined = 1 }; typedef AutoDiffScalar<DerType> ReturnType; }; @@ -578,6 +562,15 @@ inline AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::Plain typedef AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> ADS; return (x > y ? ADS(x) : ADS(y)); } +template<typename DerType> +inline AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> (min)(const AutoDiffScalar<DerType>& x, const AutoDiffScalar<DerType>& y) { + return (x.value() < y.value() ? x : y); +} +template<typename DerType> +inline AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> (max)(const AutoDiffScalar<DerType>& x, const AutoDiffScalar<DerType>& y) { + return (x.value() >= y.value() ? x : y); +} + EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(abs, using std::abs; @@ -617,7 +610,8 @@ EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(typename internal::remove_all<DerType>::t pow(const Eigen::AutoDiffScalar<DerType> &x, const typename internal::traits<typename internal::remove_all<DerType>::type>::Scalar &y) { using namespace Eigen; - return Eigen::MakeAutoDiffScalar(std::pow(x.value(),y), x.derivatives() * (y * std::pow(x.value(),y-1))); + using std::pow; + return Eigen::MakeAutoDiffScalar(pow(x.value(),y), x.derivatives() * (y * pow(x.value(),y-1))); } @@ -672,13 +666,14 @@ EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(cosh, #undef EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY template<typename DerType> struct NumTraits<AutoDiffScalar<DerType> > - : NumTraits< typename NumTraits<typename DerType::Scalar>::Real > + : NumTraits< typename NumTraits<typename internal::remove_all<DerType>::type::Scalar>::Real > { - typedef AutoDiffScalar<Matrix<typename NumTraits<typename DerType::Scalar>::Real,DerType::RowsAtCompileTime,DerType::ColsAtCompileTime, - 0, DerType::MaxRowsAtCompileTime, DerType::MaxColsAtCompileTime> > Real; + typedef typename internal::remove_all<DerType>::type DerTypeCleaned; + typedef AutoDiffScalar<Matrix<typename NumTraits<typename DerTypeCleaned::Scalar>::Real,DerTypeCleaned::RowsAtCompileTime,DerTypeCleaned::ColsAtCompileTime, + 0, DerTypeCleaned::MaxRowsAtCompileTime, DerTypeCleaned::MaxColsAtCompileTime> > Real; typedef AutoDiffScalar<DerType> NonInteger; typedef AutoDiffScalar<DerType> Nested; - typedef typename NumTraits<typename DerType::Scalar>::Literal Literal; + typedef typename NumTraits<typename DerTypeCleaned::Scalar>::Literal Literal; enum{ RequireInitialization = 1 }; diff --git a/unsupported/Eigen/src/CMakeLists.txt b/unsupported/Eigen/src/CMakeLists.txt index a7e8c7553..f42946793 100644 --- a/unsupported/Eigen/src/CMakeLists.txt +++ b/unsupported/Eigen/src/CMakeLists.txt @@ -11,5 +11,6 @@ ADD_SUBDIRECTORY(NumericalDiff) ADD_SUBDIRECTORY(Polynomials) ADD_SUBDIRECTORY(Skyline) ADD_SUBDIRECTORY(SparseExtra) +ADD_SUBDIRECTORY(SpecialFunctions) ADD_SUBDIRECTORY(KroneckerProduct) ADD_SUBDIRECTORY(Splines) diff --git a/unsupported/Eigen/src/SpecialFunctions/CMakeLists.txt b/unsupported/Eigen/src/SpecialFunctions/CMakeLists.txt new file mode 100644 index 000000000..25df9439d --- /dev/null +++ b/unsupported/Eigen/src/SpecialFunctions/CMakeLists.txt @@ -0,0 +1,11 @@ +FILE(GLOB Eigen_SpecialFunctions_SRCS "*.h") +INSTALL(FILES + ${Eigen_SpecialFunctions_SRCS} + DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/src/SpecialFunctions COMPONENT Devel + ) + +FILE(GLOB Eigen_SpecialFunctions_arch_CUDA_SRCS "arch/CUDA/*.h") +INSTALL(FILES + ${Eigen_SpecialFunctions_arch_CUDA_SRCS} + DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/src/SpecialFunctions/arch/CUDA COMPONENT Devel + )
\ No newline at end of file diff --git a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsArrayAPI.h b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsArrayAPI.h new file mode 100644 index 000000000..ed415db99 --- /dev/null +++ b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsArrayAPI.h @@ -0,0 +1,124 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + + +#ifndef EIGEN_SPECIALFUNCTIONS_ARRAYAPI_H +#define EIGEN_SPECIALFUNCTIONS_ARRAYAPI_H + +namespace Eigen { + +/** \cpp11 \returns an expression of the coefficient-wise igamma(\a a, \a x) to the given arrays. + * + * This function computes the coefficient-wise incomplete gamma function. + * + * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types, + * or float/double in non c++11 mode, the user has to provide implementations of igammac(T,T) for any scalar + * type T to be supported. + * + * \sa Eigen::igammac(), Eigen::lgamma() + */ +template<typename Derived,typename ExponentDerived> +inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived, const ExponentDerived> +igamma(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x) +{ + return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived, const ExponentDerived>( + a.derived(), + x.derived() + ); +} + +/** \cpp11 \returns an expression of the coefficient-wise igammac(\a a, \a x) to the given arrays. + * + * This function computes the coefficient-wise complementary incomplete gamma function. + * + * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types, + * or float/double in non c++11 mode, the user has to provide implementations of igammac(T,T) for any scalar + * type T to be supported. + * + * \sa Eigen::igamma(), Eigen::lgamma() + */ +template<typename Derived,typename ExponentDerived> +inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived, const ExponentDerived> +igammac(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x) +{ + return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived, const ExponentDerived>( + a.derived(), + x.derived() + ); +} + +/** \cpp11 \returns an expression of the coefficient-wise polygamma(\a n, \a x) to the given arrays. + * + * It returns the \a n -th derivative of the digamma(psi) evaluated at \c x. + * + * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types, + * or float/double in non c++11 mode, the user has to provide implementations of polygamma(T,T) for any scalar + * type T to be supported. + * + * \sa Eigen::digamma() + */ +// * \warning Be careful with the order of the parameters: x.polygamma(n) is equivalent to polygamma(n,x) +// * \sa ArrayBase::polygamma() +template<typename DerivedN,typename DerivedX> +inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_polygamma_op<typename DerivedX::Scalar>, const DerivedN, const DerivedX> +polygamma(const Eigen::ArrayBase<DerivedN>& n, const Eigen::ArrayBase<DerivedX>& x) +{ + return Eigen::CwiseBinaryOp<Eigen::internal::scalar_polygamma_op<typename DerivedX::Scalar>, const DerivedN, const DerivedX>( + n.derived(), + x.derived() + ); +} + +/** \cpp11 \returns an expression of the coefficient-wise betainc(\a x, \a a, \a b) to the given arrays. + * + * This function computes the regularized incomplete beta function (integral). + * + * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types, + * or float/double in non c++11 mode, the user has to provide implementations of betainc(T,T,T) for any scalar + * type T to be supported. + * + * \sa Eigen::betainc(), Eigen::lgamma() + */ +template<typename ArgADerived, typename ArgBDerived, typename ArgXDerived> +inline const Eigen::CwiseTernaryOp<Eigen::internal::scalar_betainc_op<typename ArgXDerived::Scalar>, const ArgADerived, const ArgBDerived, const ArgXDerived> +betainc(const Eigen::ArrayBase<ArgADerived>& a, const Eigen::ArrayBase<ArgBDerived>& b, const Eigen::ArrayBase<ArgXDerived>& x) +{ + return Eigen::CwiseTernaryOp<Eigen::internal::scalar_betainc_op<typename ArgXDerived::Scalar>, const ArgADerived, const ArgBDerived, const ArgXDerived>( + a.derived(), + b.derived(), + x.derived() + ); +} + + +/** \returns an expression of the coefficient-wise zeta(\a x, \a q) to the given arrays. + * + * It returns the Riemann zeta function of two arguments \a x and \a q: + * + * \param x is the exposent, it must be > 1 + * \param q is the shift, it must be > 0 + * + * \note This function supports only float and double scalar types. To support other scalar types, the user has + * to provide implementations of zeta(T,T) for any scalar type T to be supported. + * + * \sa ArrayBase::zeta() + */ +template<typename DerivedX,typename DerivedQ> +inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_zeta_op<typename DerivedX::Scalar>, const DerivedX, const DerivedQ> +zeta(const Eigen::ArrayBase<DerivedX>& x, const Eigen::ArrayBase<DerivedQ>& q) +{ + return Eigen::CwiseBinaryOp<Eigen::internal::scalar_zeta_op<typename DerivedX::Scalar>, const DerivedX, const DerivedQ>( + x.derived(), + q.derived() + ); +} + +} // end namespace Eigen + +#endif // EIGEN_SPECIALFUNCTIONS_ARRAYAPI_H diff --git a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsFunctors.h b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsFunctors.h new file mode 100644 index 000000000..d8f2363be --- /dev/null +++ b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsFunctors.h @@ -0,0 +1,236 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2016 Eugene Brevdo <ebrevdo@gmail.com> +// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SPECIALFUNCTIONS_FUNCTORS_H +#define EIGEN_SPECIALFUNCTIONS_FUNCTORS_H + +namespace Eigen { + +namespace internal { + + +/** \internal + * \brief Template functor to compute the incomplete gamma function igamma(a, x) + * + * \sa class CwiseBinaryOp, Cwise::igamma + */ +template<typename Scalar> struct scalar_igamma_op : binary_op_base<Scalar,Scalar> +{ + EIGEN_EMPTY_STRUCT_CTOR(scalar_igamma_op) + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& x) const { + using numext::igamma; return igamma(a, x); + } + template<typename Packet> + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const { + return internal::pigamma(a, x); + } +}; +template<typename Scalar> +struct functor_traits<scalar_igamma_op<Scalar> > { + enum { + // Guesstimate + Cost = 20 * NumTraits<Scalar>::MulCost + 10 * NumTraits<Scalar>::AddCost, + PacketAccess = packet_traits<Scalar>::HasIGamma + }; +}; + + +/** \internal + * \brief Template functor to compute the complementary incomplete gamma function igammac(a, x) + * + * \sa class CwiseBinaryOp, Cwise::igammac + */ +template<typename Scalar> struct scalar_igammac_op : binary_op_base<Scalar,Scalar> +{ + EIGEN_EMPTY_STRUCT_CTOR(scalar_igammac_op) + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& x) const { + using numext::igammac; return igammac(a, x); + } + template<typename Packet> + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const + { + return internal::pigammac(a, x); + } +}; +template<typename Scalar> +struct functor_traits<scalar_igammac_op<Scalar> > { + enum { + // Guesstimate + Cost = 20 * NumTraits<Scalar>::MulCost + 10 * NumTraits<Scalar>::AddCost, + PacketAccess = packet_traits<Scalar>::HasIGammac + }; +}; + + +/** \internal + * \brief Template functor to compute the incomplete beta integral betainc(a, b, x) + * + */ +template<typename Scalar> struct scalar_betainc_op { + EIGEN_EMPTY_STRUCT_CTOR(scalar_betainc_op) + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& x, const Scalar& a, const Scalar& b) const { + using numext::betainc; return betainc(x, a, b); + } + template<typename Packet> + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& x, const Packet& a, const Packet& b) const + { + return internal::pbetainc(x, a, b); + } +}; +template<typename Scalar> +struct functor_traits<scalar_betainc_op<Scalar> > { + enum { + // Guesstimate + Cost = 400 * NumTraits<Scalar>::MulCost + 400 * NumTraits<Scalar>::AddCost, + PacketAccess = packet_traits<Scalar>::HasBetaInc + }; +}; + + +/** \internal + * \brief Template functor to compute the natural log of the absolute + * value of Gamma of a scalar + * \sa class CwiseUnaryOp, Cwise::lgamma() + */ +template<typename Scalar> struct scalar_lgamma_op { + EIGEN_EMPTY_STRUCT_CTOR(scalar_lgamma_op) + EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { + using numext::lgamma; return lgamma(a); + } + typedef typename packet_traits<Scalar>::type Packet; + EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::plgamma(a); } +}; +template<typename Scalar> +struct functor_traits<scalar_lgamma_op<Scalar> > +{ + enum { + // Guesstimate + Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost, + PacketAccess = packet_traits<Scalar>::HasLGamma + }; +}; + +/** \internal + * \brief Template functor to compute psi, the derivative of lgamma of a scalar. + * \sa class CwiseUnaryOp, Cwise::digamma() + */ +template<typename Scalar> struct scalar_digamma_op { + EIGEN_EMPTY_STRUCT_CTOR(scalar_digamma_op) + EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { + using numext::digamma; return digamma(a); + } + typedef typename packet_traits<Scalar>::type Packet; + EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pdigamma(a); } +}; +template<typename Scalar> +struct functor_traits<scalar_digamma_op<Scalar> > +{ + enum { + // Guesstimate + Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost, + PacketAccess = packet_traits<Scalar>::HasDiGamma + }; +}; + +/** \internal + * \brief Template functor to compute the Riemann Zeta function of two arguments. + * \sa class CwiseUnaryOp, Cwise::zeta() + */ +template<typename Scalar> struct scalar_zeta_op { + EIGEN_EMPTY_STRUCT_CTOR(scalar_zeta_op) + EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& x, const Scalar& q) const { + using numext::zeta; return zeta(x, q); + } + typedef typename packet_traits<Scalar>::type Packet; + EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& x, const Packet& q) const { return internal::pzeta(x, q); } +}; +template<typename Scalar> +struct functor_traits<scalar_zeta_op<Scalar> > +{ + enum { + // Guesstimate + Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost, + PacketAccess = packet_traits<Scalar>::HasZeta + }; +}; + +/** \internal + * \brief Template functor to compute the polygamma function. + * \sa class CwiseUnaryOp, Cwise::polygamma() + */ +template<typename Scalar> struct scalar_polygamma_op { + EIGEN_EMPTY_STRUCT_CTOR(scalar_polygamma_op) + EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& n, const Scalar& x) const { + using numext::polygamma; return polygamma(n, x); + } + typedef typename packet_traits<Scalar>::type Packet; + EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& n, const Packet& x) const { return internal::ppolygamma(n, x); } +}; +template<typename Scalar> +struct functor_traits<scalar_polygamma_op<Scalar> > +{ + enum { + // Guesstimate + Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost, + PacketAccess = packet_traits<Scalar>::HasPolygamma + }; +}; + +/** \internal + * \brief Template functor to compute the Gauss error function of a + * scalar + * \sa class CwiseUnaryOp, Cwise::erf() + */ +template<typename Scalar> struct scalar_erf_op { + EIGEN_EMPTY_STRUCT_CTOR(scalar_erf_op) + EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { + using numext::erf; return erf(a); + } + typedef typename packet_traits<Scalar>::type Packet; + EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::perf(a); } +}; +template<typename Scalar> +struct functor_traits<scalar_erf_op<Scalar> > +{ + enum { + // Guesstimate + Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost, + PacketAccess = packet_traits<Scalar>::HasErf + }; +}; + +/** \internal + * \brief Template functor to compute the Complementary Error Function + * of a scalar + * \sa class CwiseUnaryOp, Cwise::erfc() + */ +template<typename Scalar> struct scalar_erfc_op { + EIGEN_EMPTY_STRUCT_CTOR(scalar_erfc_op) + EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { + using numext::erfc; return erfc(a); + } + typedef typename packet_traits<Scalar>::type Packet; + EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::perfc(a); } +}; +template<typename Scalar> +struct functor_traits<scalar_erfc_op<Scalar> > +{ + enum { + // Guesstimate + Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost, + PacketAccess = packet_traits<Scalar>::HasErfc + }; +}; + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_SPECIALFUNCTIONS_FUNCTORS_H diff --git a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsHalf.h b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsHalf.h new file mode 100644 index 000000000..553bcda6a --- /dev/null +++ b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsHalf.h @@ -0,0 +1,47 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SPECIALFUNCTIONS_HALF_H +#define EIGEN_SPECIALFUNCTIONS_HALF_H + +namespace Eigen { +namespace numext { + +#if EIGEN_HAS_C99_MATH +template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half lgamma(const Eigen::half& a) { + return Eigen::half(Eigen::numext::lgamma(static_cast<float>(a))); +} +template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half digamma(const Eigen::half& a) { + return Eigen::half(Eigen::numext::digamma(static_cast<float>(a))); +} +template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half zeta(const Eigen::half& x, const Eigen::half& q) { + return Eigen::half(Eigen::numext::zeta(static_cast<float>(x), static_cast<float>(q))); +} +template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half polygamma(const Eigen::half& n, const Eigen::half& x) { + return Eigen::half(Eigen::numext::polygamma(static_cast<float>(n), static_cast<float>(x))); +} +template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half erf(const Eigen::half& a) { + return Eigen::half(Eigen::numext::erf(static_cast<float>(a))); +} +template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half erfc(const Eigen::half& a) { + return Eigen::half(Eigen::numext::erfc(static_cast<float>(a))); +} +template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half igamma(const Eigen::half& a, const Eigen::half& x) { + return Eigen::half(Eigen::numext::igamma(static_cast<float>(a), static_cast<float>(x))); +} +template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half igammac(const Eigen::half& a, const Eigen::half& x) { + return Eigen::half(Eigen::numext::igammac(static_cast<float>(a), static_cast<float>(x))); +} +template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half betainc(const Eigen::half& a, const Eigen::half& b, const Eigen::half& x) { + return Eigen::half(Eigen::numext::betainc(static_cast<float>(a), static_cast<float>(b), static_cast<float>(x))); +} +#endif + +} // end namespace numext +} // end namespace Eigen + +#endif // EIGEN_SPECIALFUNCTIONS_HALF_H diff --git a/Eigen/src/Core/SpecialFunctions.h b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsImpl.h index a657cb854..52619fc0c 100644 --- a/Eigen/src/Core/SpecialFunctions.h +++ b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsImpl.h @@ -1382,7 +1382,7 @@ struct betainc_helper<double> { */ t = lgamma_impl<double>::run(a + b) - lgamma_impl<double>::run(a) - lgamma_impl<double>::run(b) + u + numext::log(s); - return s = exp(t); + return s = numext::exp(t); } }; diff --git a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsPacketMath.h b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsPacketMath.h new file mode 100644 index 000000000..46d60d323 --- /dev/null +++ b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsPacketMath.h @@ -0,0 +1,58 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SPECIALFUNCTIONS_PACKETMATH_H +#define EIGEN_SPECIALFUNCTIONS_PACKETMATH_H + +namespace Eigen { + +namespace internal { + +/** \internal \returns the ln(|gamma(\a a)|) (coeff-wise) */ +template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet plgamma(const Packet& a) { using numext::lgamma; return lgamma(a); } + +/** \internal \returns the derivative of lgamma, psi(\a a) (coeff-wise) */ +template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet pdigamma(const Packet& a) { using numext::digamma; return digamma(a); } + +/** \internal \returns the zeta function of two arguments (coeff-wise) */ +template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet pzeta(const Packet& x, const Packet& q) { using numext::zeta; return zeta(x, q); } + +/** \internal \returns the polygamma function (coeff-wise) */ +template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet ppolygamma(const Packet& n, const Packet& x) { using numext::polygamma; return polygamma(n, x); } + +/** \internal \returns the erf(\a a) (coeff-wise) */ +template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet perf(const Packet& a) { using numext::erf; return erf(a); } + +/** \internal \returns the erfc(\a a) (coeff-wise) */ +template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet perfc(const Packet& a) { using numext::erfc; return erfc(a); } + +/** \internal \returns the incomplete gamma function igamma(\a a, \a x) */ +template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +Packet pigamma(const Packet& a, const Packet& x) { using numext::igamma; return igamma(a, x); } + +/** \internal \returns the complementary incomplete gamma function igammac(\a a, \a x) */ +template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +Packet pigammac(const Packet& a, const Packet& x) { using numext::igammac; return igammac(a, x); } + +/** \internal \returns the complementary incomplete gamma function betainc(\a a, \a b, \a x) */ +template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +Packet pbetainc(const Packet& a, const Packet& b,const Packet& x) { using numext::betainc; return betainc(a, b, x); } + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_SPECIALFUNCTIONS_PACKETMATH_H + diff --git a/unsupported/Eigen/src/SpecialFunctions/arch/CUDA/CudaSpecialFunctions.h b/unsupported/Eigen/src/SpecialFunctions/arch/CUDA/CudaSpecialFunctions.h new file mode 100644 index 000000000..0ef440495 --- /dev/null +++ b/unsupported/Eigen/src/SpecialFunctions/arch/CUDA/CudaSpecialFunctions.h @@ -0,0 +1,165 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_CUDA_SPECIALFUNCTIONS_H +#define EIGEN_CUDA_SPECIALFUNCTIONS_H + +namespace Eigen { + +namespace internal { + +// Make sure this is only available when targeting a GPU: we don't want to +// introduce conflicts between these packet_traits definitions and the ones +// we'll use on the host side (SSE, AVX, ...) +#if defined(__CUDACC__) && defined(EIGEN_USE_GPU) + +template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +float4 plgamma<float4>(const float4& a) +{ + return make_float4(lgammaf(a.x), lgammaf(a.y), lgammaf(a.z), lgammaf(a.w)); +} + +template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +double2 plgamma<double2>(const double2& a) +{ + using numext::lgamma; + return make_double2(lgamma(a.x), lgamma(a.y)); +} + +template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +float4 pdigamma<float4>(const float4& a) +{ + using numext::digamma; + return make_float4(digamma(a.x), digamma(a.y), digamma(a.z), digamma(a.w)); +} + +template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +double2 pdigamma<double2>(const double2& a) +{ + using numext::digamma; + return make_double2(digamma(a.x), digamma(a.y)); +} + +template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +float4 pzeta<float4>(const float4& x, const float4& q) +{ + using numext::zeta; + return make_float4(zeta(x.x, q.x), zeta(x.y, q.y), zeta(x.z, q.z), zeta(x.w, q.w)); +} + +template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +double2 pzeta<double2>(const double2& x, const double2& q) +{ + using numext::zeta; + return make_double2(zeta(x.x, q.x), zeta(x.y, q.y)); +} + +template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +float4 ppolygamma<float4>(const float4& n, const float4& x) +{ + using numext::polygamma; + return make_float4(polygamma(n.x, x.x), polygamma(n.y, x.y), polygamma(n.z, x.z), polygamma(n.w, x.w)); +} + +template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +double2 ppolygamma<double2>(const double2& n, const double2& x) +{ + using numext::polygamma; + return make_double2(polygamma(n.x, x.x), polygamma(n.y, x.y)); +} + +template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +float4 perf<float4>(const float4& a) +{ + return make_float4(erff(a.x), erff(a.y), erff(a.z), erff(a.w)); +} + +template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +double2 perf<double2>(const double2& a) +{ + using numext::erf; + return make_double2(erf(a.x), erf(a.y)); +} + +template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +float4 perfc<float4>(const float4& a) +{ + using std::erfcf; + return make_float4(erfcf(a.x), erfcf(a.y), erfcf(a.z), erfcf(a.w)); +} + +template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +double2 perfc<double2>(const double2& a) +{ + using numext::erfc; + return make_double2(erfc(a.x), erfc(a.y)); +} + + +template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +float4 pigamma<float4>(const float4& a, const float4& x) +{ + using numext::igamma; + return make_float4( + igamma(a.x, x.x), + igamma(a.y, x.y), + igamma(a.z, x.z), + igamma(a.w, x.w)); +} + +template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +double2 pigamma<double2>(const double2& a, const double2& x) +{ + using numext::igamma; + return make_double2(igamma(a.x, x.x), igamma(a.y, x.y)); +} + +template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +float4 pigammac<float4>(const float4& a, const float4& x) +{ + using numext::igammac; + return make_float4( + igammac(a.x, x.x), + igammac(a.y, x.y), + igammac(a.z, x.z), + igammac(a.w, x.w)); +} + +template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +double2 pigammac<double2>(const double2& a, const double2& x) +{ + using numext::igammac; + return make_double2(igammac(a.x, x.x), igammac(a.y, x.y)); +} + +template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +float4 pbetainc<float4>(const float4& a, const float4& b, const float4& x) +{ + using numext::betainc; + return make_float4( + betainc(a.x, b.x, x.x), + betainc(a.y, b.y, x.y), + betainc(a.z, b.z, x.z), + betainc(a.w, b.w, x.w)); +} + +template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +double2 pbetainc<double2>(const double2& a, const double2& b, const double2& x) +{ + using numext::betainc; + return make_double2(betainc(a.x, b.x, x.x), betainc(a.y, b.y, x.y)); +} + +#endif + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_CUDA_SPECIALFUNCTIONS_H diff --git a/unsupported/Eigen/src/Splines/Spline.h b/unsupported/Eigen/src/Splines/Spline.h index ddcddfc9a..627f6e482 100644 --- a/unsupported/Eigen/src/Splines/Spline.h +++ b/unsupported/Eigen/src/Splines/Spline.h @@ -94,7 +94,7 @@ namespace Eigen const KnotVectorType& knots() const { return m_knots; } /** - * \brief Returns the knots of the underlying spline. + * \brief Returns the ctrls of the underlying spline. **/ const ControlPointVectorType& ctrls() const { return m_ctrls; } diff --git a/unsupported/test/CMakeLists.txt b/unsupported/test/CMakeLists.txt index c9a70d7a7..b29b694e7 100644 --- a/unsupported/test/CMakeLists.txt +++ b/unsupported/test/CMakeLists.txt @@ -109,6 +109,7 @@ ei_add_test(gmres) ei_add_test(minres) ei_add_test(levenberg_marquardt) ei_add_test(kronecker_product) +ei_add_test(special_functions) # TODO: The following test names are prefixed with the cxx11 string, since historically # the tests depended on c++11. This isn't the case anymore so we ought to rename them. @@ -116,7 +117,6 @@ ei_add_test(kronecker_product) # when using visual studio. We should make the check more strict to enable the tests for # newer versions of MSVC. if (NOT CMAKE_CXX_COMPILER_ID STREQUAL "MSVC") -ei_add_test(cxx11_float16) ei_add_test(cxx11_tensor_dimension) ei_add_test(cxx11_tensor_map) ei_add_test(cxx11_tensor_assign) @@ -142,6 +142,9 @@ if(EIGEN_TEST_CXX11) # older compiler that don't support cxx11. set(CMAKE_CXX_STANDARD 11) + # Todo: remove the c++11 bits from this test to make it work with older compilers. + ei_add_test(cxx11_float16) + ei_add_test(cxx11_eventcount "-pthread" "${CMAKE_THREAD_LIBS_INIT}") ei_add_test(cxx11_runqueue "-pthread" "${CMAKE_THREAD_LIBS_INIT}") ei_add_test(cxx11_non_blocking_thread_pool "-pthread" "${CMAKE_THREAD_LIBS_INIT}") @@ -191,10 +194,12 @@ if(CUDA_FOUND AND EIGEN_TEST_CUDA) # Make sure to compile without the -pedantic, -Wundef, -Wnon-virtual-dtor # and -fno-check-new flags since they trigger thousands of compilation warnings # in the CUDA runtime + # Also remove -ansi that is incompatible with std=c++11. string(REPLACE "-pedantic" "" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}") string(REPLACE "-Wundef" "" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}") string(REPLACE "-Wnon-virtual-dtor" "" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}") string(REPLACE "-fno-check-new" "" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}") + string(REPLACE "-ansi" "" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}") message(STATUS "Flags used to compile cuda code: " ${CMAKE_CXX_FLAGS}) @@ -210,7 +215,14 @@ if(CUDA_FOUND AND EIGEN_TEST_CUDA) set(EIGEN_CUDA_RELAXED_CONSTEXPR "--relaxed-constexpr") endif() - set(CUDA_NVCC_FLAGS "-std=c++11 ${EIGEN_CUDA_RELAXED_CONSTEXPR} -arch compute_${EIGEN_CUDA_COMPUTE_ARCH} -Xcudafe \"--display_error_number\"") + if( (NOT EIGEN_TEST_CXX11) OR (CMAKE_VERSION VERSION_LESS 3.3)) + set(EIGEN_CUDA_CXX11_FLAG "-std=c++11") + else() + # otherwise the flag has already been added because of the above set(CMAKE_CXX_STANDARD 11) + set(EIGEN_CUDA_CXX11_FLAG "") + endif() + + set(CUDA_NVCC_FLAGS "${EIGEN_CUDA_CXX11_FLAG} ${EIGEN_CUDA_RELAXED_CONSTEXPR} -arch compute_${EIGEN_CUDA_COMPUTE_ARCH} -Xcudafe \"--display_error_number\" ${CUDA_NVCC_FLAGS}") cuda_include_directories("${CMAKE_CURRENT_BINARY_DIR}" "${CUDA_TOOLKIT_ROOT_DIR}/include") set(EIGEN_ADD_TEST_FILENAME_EXTENSION "cu") diff --git a/unsupported/test/FFTW.cpp b/unsupported/test/FFTW.cpp index 1dd6dc97d..8b7528fb7 100644 --- a/unsupported/test/FFTW.cpp +++ b/unsupported/test/FFTW.cpp @@ -18,11 +18,11 @@ using namespace Eigen; template < typename T> -complex<long double> promote(complex<T> x) { return complex<long double>(x.real(),x.imag()); } +complex<long double> promote(complex<T> x) { return complex<long double>((long double)x.real(),(long double)x.imag()); } -complex<long double> promote(float x) { return complex<long double>( x); } -complex<long double> promote(double x) { return complex<long double>( x); } -complex<long double> promote(long double x) { return complex<long double>( x); } +complex<long double> promote(float x) { return complex<long double>((long double)x); } +complex<long double> promote(double x) { return complex<long double>((long double)x); } +complex<long double> promote(long double x) { return complex<long double>((long double)x); } template <typename VT1,typename VT2> @@ -33,7 +33,7 @@ complex<long double> promote(long double x) { return complex<long double>( x); long double pi = acos((long double)-1 ); for (size_t k0=0;k0<(size_t)fftbuf.size();++k0) { complex<long double> acc = 0; - long double phinc = -2.*k0* pi / timebuf.size(); + long double phinc = (long double)(-2.)*k0* pi / timebuf.size(); for (size_t k1=0;k1<(size_t)timebuf.size();++k1) { acc += promote( timebuf[k1] ) * exp( complex<long double>(0,k1*phinc) ); } @@ -54,8 +54,8 @@ complex<long double> promote(long double x) { return complex<long double>( x); long double difpower=0; size_t n = (min)( buf1.size(),buf2.size() ); for (size_t k=0;k<n;++k) { - totalpower += (numext::abs2( buf1[k] ) + numext::abs2(buf2[k]) )/2; - difpower += numext::abs2(buf1[k] - buf2[k]); + totalpower += (long double)((numext::abs2( buf1[k] ) + numext::abs2(buf2[k]) )/2); + difpower += (long double)(numext::abs2(buf1[k] - buf2[k])); } return sqrt(difpower/totalpower); } @@ -93,19 +93,19 @@ void test_scalar_generic(int nfft) fft.SetFlag(fft.HalfSpectrum ); fft.fwd( freqBuf,tbuf); VERIFY((size_t)freqBuf.size() == (size_t)( (nfft>>1)+1) ); - VERIFY( fft_rmse(freqBuf,tbuf) < test_precision<T>() );// gross check + VERIFY( T(fft_rmse(freqBuf,tbuf)) < test_precision<T>() );// gross check fft.ClearFlag(fft.HalfSpectrum ); fft.fwd( freqBuf,tbuf); VERIFY( (size_t)freqBuf.size() == (size_t)nfft); - VERIFY( fft_rmse(freqBuf,tbuf) < test_precision<T>() );// gross check + VERIFY( T(fft_rmse(freqBuf,tbuf)) < test_precision<T>() );// gross check if (nfft&1) return; // odd FFTs get the wrong size inverse FFT ScalarVector tbuf2; fft.inv( tbuf2 , freqBuf); - VERIFY( dif_rmse(tbuf,tbuf2) < test_precision<T>() );// gross check + VERIFY( T(dif_rmse(tbuf,tbuf2)) < test_precision<T>() );// gross check // verify that the Unscaled flag takes effect @@ -121,12 +121,12 @@ void test_scalar_generic(int nfft) //for (size_t i=0;i<(size_t) tbuf.size();++i) // cout << "freqBuf=" << freqBuf[i] << " in2=" << tbuf3[i] << " - in=" << tbuf[i] << " => " << (tbuf3[i] - tbuf[i] ) << endl; - VERIFY( dif_rmse(tbuf,tbuf3) < test_precision<T>() );// gross check + VERIFY( T(dif_rmse(tbuf,tbuf3)) < test_precision<T>() );// gross check // verify that ClearFlag works fft.ClearFlag(fft.Unscaled); fft.inv( tbuf2 , freqBuf); - VERIFY( dif_rmse(tbuf,tbuf2) < test_precision<T>() );// gross check + VERIFY( T(dif_rmse(tbuf,tbuf2)) < test_precision<T>() );// gross check } template <typename T> @@ -152,10 +152,10 @@ void test_complex_generic(int nfft) inbuf[k]= Complex( (T)(rand()/(double)RAND_MAX - .5), (T)(rand()/(double)RAND_MAX - .5) ); fft.fwd( outbuf , inbuf); - VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>() );// gross check + VERIFY( T(fft_rmse(outbuf,inbuf)) < test_precision<T>() );// gross check fft.inv( buf3 , outbuf); - VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check + VERIFY( T(dif_rmse(inbuf,buf3)) < test_precision<T>() );// gross check // verify that the Unscaled flag takes effect ComplexVector buf4; @@ -163,12 +163,12 @@ void test_complex_generic(int nfft) fft.inv( buf4 , outbuf); for (int k=0;k<nfft;++k) buf4[k] *= T(1./nfft); - VERIFY( dif_rmse(inbuf,buf4) < test_precision<T>() );// gross check + VERIFY( T(dif_rmse(inbuf,buf4)) < test_precision<T>() );// gross check // verify that ClearFlag works fft.ClearFlag(fft.Unscaled); fft.inv( buf3 , outbuf); - VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check + VERIFY( T(dif_rmse(inbuf,buf3)) < test_precision<T>() );// gross check } template <typename T> diff --git a/unsupported/test/autodiff.cpp b/unsupported/test/autodiff.cpp index b59fd1c43..2da6dd8f3 100644 --- a/unsupported/test/autodiff.cpp +++ b/unsupported/test/autodiff.cpp @@ -205,6 +205,10 @@ void test_autodiff_hessian() VERIFY_IS_APPROX(y.value().derivatives()(1), s4*std::cos(s1*s3+s2*s4)); VERIFY_IS_APPROX(y.derivatives()(0).derivatives(), -std::sin(s1*s3+s2*s4)*Vector2d(s3*s3,s4*s3)); VERIFY_IS_APPROX(y.derivatives()(1).derivatives(), -std::sin(s1*s3+s2*s4)*Vector2d(s3*s4,s4*s4)); + + ADD z = x(0)*x(1); + VERIFY_IS_APPROX(z.derivatives()(0).derivatives(), Vector2d(0,1)); + VERIFY_IS_APPROX(z.derivatives()(1).derivatives(), Vector2d(1,0)); } double bug_1222() { @@ -234,6 +238,32 @@ double bug_1223() { return t.value() + t2.value(); } +// regression test for some compilation issues with specializations of ScalarBinaryOpTraits +void bug_1260() { + Matrix4d A; + Vector4d v; + A*v; +} + +// check a compilation issue with numext::max +double bug_1261() { + typedef AutoDiffScalar<Matrix2d> AD; + typedef Matrix<AD,2,1> VectorAD; + + VectorAD v; + const AD maxVal = v.maxCoeff(); + const AD minVal = v.minCoeff(); + return maxVal.value() + minVal.value(); +} + +double bug_1264() { + typedef AutoDiffScalar<Vector2d> AD; + const AD s; + const Matrix<AD, 3, 1> v1; + const Matrix<AD, 3, 1> v2 = (s + 3.0) * v1; + return v2(0).value(); +} + void test_autodiff() { for(int i = 0; i < g_repeat; i++) { @@ -245,5 +275,7 @@ void test_autodiff() bug_1222(); bug_1223(); + bug_1260(); + bug_1261(); } diff --git a/unsupported/test/cxx11_float16.cpp b/unsupported/test/cxx11_float16.cpp index e39a7f83c..f646c9750 100644 --- a/unsupported/test/cxx11_float16.cpp +++ b/unsupported/test/cxx11_float16.cpp @@ -8,194 +8,177 @@ #define EIGEN_TEST_NO_LONGDOUBLE #define EIGEN_TEST_NO_COMPLEX #define EIGEN_TEST_FUNC cxx11_float16 +#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int +#define EIGEN_USE_GPU + +// Make sure it's possible to forward declare Eigen::half +//namespace Eigen { +//struct half; +//} #include "main.h" #include <Eigen/src/Core/arch/CUDA/Half.h> -using Eigen::half; - void test_conversion() { // Conversion from float. - VERIFY_IS_EQUAL(half(1.0f).x, 0x3c00); - VERIFY_IS_EQUAL(half(0.5f).x, 0x3800); - VERIFY_IS_EQUAL(half(0.33333f).x, 0x3555); - VERIFY_IS_EQUAL(half(0.0f).x, 0x0000); - VERIFY_IS_EQUAL(half(-0.0f).x, 0x8000); - VERIFY_IS_EQUAL(half(65504.0f).x, 0x7bff); - VERIFY_IS_EQUAL(half(65536.0f).x, 0x7c00); // Becomes infinity. + VERIFY_IS_EQUAL(Eigen::half(1.0f).x, 0x3c00); + VERIFY_IS_EQUAL(Eigen::half(0.5f).x, 0x3800); + VERIFY_IS_EQUAL(Eigen::half(0.33333f).x, 0x3555); + VERIFY_IS_EQUAL(Eigen::half(0.0f).x, 0x0000); + VERIFY_IS_EQUAL(Eigen::half(-0.0f).x, 0x8000); + VERIFY_IS_EQUAL(Eigen::half(65504.0f).x, 0x7bff); + VERIFY_IS_EQUAL(Eigen::half(65536.0f).x, 0x7c00); // Becomes infinity. // Denormals. - VERIFY_IS_EQUAL(half(-5.96046e-08f).x, 0x8001); - VERIFY_IS_EQUAL(half(5.96046e-08f).x, 0x0001); - VERIFY_IS_EQUAL(half(1.19209e-07f).x, 0x0002); + VERIFY_IS_EQUAL(Eigen::half(-5.96046e-08f).x, 0x8001); + VERIFY_IS_EQUAL(Eigen::half(5.96046e-08f).x, 0x0001); + VERIFY_IS_EQUAL(Eigen::half(1.19209e-07f).x, 0x0002); // Verify round-to-nearest-even behavior. - float val1 = float(half(__half(0x3c00))); - float val2 = float(half(__half(0x3c01))); - float val3 = float(half(__half(0x3c02))); - VERIFY_IS_EQUAL(half(0.5f * (val1 + val2)).x, 0x3c00); - VERIFY_IS_EQUAL(half(0.5f * (val2 + val3)).x, 0x3c02); + float val1 = float(Eigen::half(half_impl::__half{0x3c00})); + float val2 = float(Eigen::half(half_impl::__half{0x3c01})); + float val3 = float(Eigen::half(half_impl::__half{0x3c02})); + VERIFY_IS_EQUAL(Eigen::half(0.5f * (val1 + val2)).x, 0x3c00); + VERIFY_IS_EQUAL(Eigen::half(0.5f * (val2 + val3)).x, 0x3c02); // Conversion from int. - VERIFY_IS_EQUAL(half(-1).x, 0xbc00); - VERIFY_IS_EQUAL(half(0).x, 0x0000); - VERIFY_IS_EQUAL(half(1).x, 0x3c00); - VERIFY_IS_EQUAL(half(2).x, 0x4000); - VERIFY_IS_EQUAL(half(3).x, 0x4200); + VERIFY_IS_EQUAL(Eigen::half(-1).x, 0xbc00); + VERIFY_IS_EQUAL(Eigen::half(0).x, 0x0000); + VERIFY_IS_EQUAL(Eigen::half(1).x, 0x3c00); + VERIFY_IS_EQUAL(Eigen::half(2).x, 0x4000); + VERIFY_IS_EQUAL(Eigen::half(3).x, 0x4200); // Conversion from bool. - VERIFY_IS_EQUAL(half(false).x, 0x0000); - VERIFY_IS_EQUAL(half(true).x, 0x3c00); + VERIFY_IS_EQUAL(Eigen::half(false).x, 0x0000); + VERIFY_IS_EQUAL(Eigen::half(true).x, 0x3c00); // Conversion to float. - VERIFY_IS_EQUAL(float(half(__half(0x0000))), 0.0f); - VERIFY_IS_EQUAL(float(half(__half(0x3c00))), 1.0f); + VERIFY_IS_EQUAL(float(Eigen::half(half_impl::__half{0x0000})), 0.0f); + VERIFY_IS_EQUAL(float(Eigen::half(half_impl::__half{0x3c00})), 1.0f); // Denormals. - VERIFY_IS_APPROX(float(half(__half(0x8001))), -5.96046e-08f); - VERIFY_IS_APPROX(float(half(__half(0x0001))), 5.96046e-08f); - VERIFY_IS_APPROX(float(half(__half(0x0002))), 1.19209e-07f); + VERIFY_IS_APPROX(float(Eigen::half(half_impl::__half{0x8001})), -5.96046e-08f); + VERIFY_IS_APPROX(float(Eigen::half(half_impl::__half{0x0001})), 5.96046e-08f); + VERIFY_IS_APPROX(float(Eigen::half(half_impl::__half{0x0002})), 1.19209e-07f); // NaNs and infinities. - VERIFY(!(numext::isinf)(float(half(65504.0f)))); // Largest finite number. - VERIFY(!(numext::isnan)(float(half(0.0f)))); - VERIFY((numext::isinf)(float(half(__half(0xfc00))))); - VERIFY((numext::isnan)(float(half(__half(0xfc01))))); - VERIFY((numext::isinf)(float(half(__half(0x7c00))))); - VERIFY((numext::isnan)(float(half(__half(0x7c01))))); - -#if !EIGEN_COMP_MSVC - // Visual Studio errors out on divisions by 0 - VERIFY((numext::isnan)(float(half(0.0 / 0.0)))); - VERIFY((numext::isinf)(float(half(1.0 / 0.0)))); - VERIFY((numext::isinf)(float(half(-1.0 / 0.0)))); -#endif + VERIFY(!(isinf)(float(Eigen::half(65504.0f)))); // Largest finite number. + VERIFY(!(isnan)(float(Eigen::half(0.0f)))); + VERIFY((isinf)(float(Eigen::half(half_impl::__half{0xfc00})))); + VERIFY((isnan)(float(Eigen::half(half_impl::__half{0xfc01})))); + VERIFY((isinf)(float(Eigen::half(half_impl::__half{0x7c00})))); + VERIFY((isnan)(float(Eigen::half(half_impl::__half{0x7c01})))); + VERIFY((isnan)(float(Eigen::half(0.0 / 0.0)))); + VERIFY((isinf)(float(Eigen::half(1.0 / 0.0)))); + VERIFY((isinf)(float(Eigen::half(-1.0 / 0.0)))); // Exactly same checks as above, just directly on the half representation. - VERIFY(!(numext::isinf)(half(__half(0x7bff)))); - VERIFY(!(numext::isnan)(half(__half(0x0000)))); - VERIFY((numext::isinf)(half(__half(0xfc00)))); - VERIFY((numext::isnan)(half(__half(0xfc01)))); - VERIFY((numext::isinf)(half(__half(0x7c00)))); - VERIFY((numext::isnan)(half(__half(0x7c01)))); - -#if !EIGEN_COMP_MSVC - // Visual Studio errors out on divisions by 0 - VERIFY((numext::isnan)(half(0.0 / 0.0))); - VERIFY((numext::isinf)(half(1.0 / 0.0))); - VERIFY((numext::isinf)(half(-1.0 / 0.0))); -#endif -} - -void test_numtraits() -{ - std::cout << "expsilin = " << NumTraits<half>::epsilon() << std::endl; - std::cout << "highest = " << NumTraits<half>::highest() << std::endl; - std::cout << "lowest = " << NumTraits<half>::lowest() << std::endl; - std::cout << "inifinty = " << NumTraits<half>::infinity() << std::endl; - std::cout << "nan = " << NumTraits<half>::quiet_NaN() << std::endl; - + VERIFY(!(numext::isinf)(Eigen::half(half_impl::__half{0x7bff}))); + VERIFY(!(numext::isnan)(Eigen::half(half_impl::__half{0x0000}))); + VERIFY((numext::isinf)(Eigen::half(half_impl::__half{0xfc00}))); + VERIFY((numext::isnan)(Eigen::half(half_impl::__half{0xfc01}))); + VERIFY((numext::isinf)(Eigen::half(half_impl::__half{0x7c00}))); + VERIFY((numext::isnan)(Eigen::half(half_impl::__half{0x7c01}))); + VERIFY((numext::isnan)(Eigen::half(0.0 / 0.0))); + VERIFY((numext::isinf)(Eigen::half(1.0 / 0.0))); + VERIFY((numext::isinf)(Eigen::half(-1.0 / 0.0))); } void test_arithmetic() { - VERIFY_IS_EQUAL(float(half(2) + half(2)), 4); - VERIFY_IS_EQUAL(float(half(2) + half(-2)), 0); - VERIFY_IS_APPROX(float(half(0.33333f) + half(0.66667f)), 1.0f); - VERIFY_IS_EQUAL(float(half(2.0f) * half(-5.5f)), -11.0f); - VERIFY_IS_APPROX(float(half(1.0f) / half(3.0f)), 0.33333f); - VERIFY_IS_EQUAL(float(-half(4096.0f)), -4096.0f); - VERIFY_IS_EQUAL(float(-half(-4096.0f)), 4096.0f); + VERIFY_IS_EQUAL(float(Eigen::half(2) + Eigen::half(2)), 4); + VERIFY_IS_EQUAL(float(Eigen::half(2) + Eigen::half(-2)), 0); + VERIFY_IS_APPROX(float(Eigen::half(0.33333f) + Eigen::half(0.66667f)), 1.0f); + VERIFY_IS_EQUAL(float(Eigen::half(2.0f) * Eigen::half(-5.5f)), -11.0f); + VERIFY_IS_APPROX(float(Eigen::half(1.0f) / Eigen::half(3.0f)), 0.33333f); + VERIFY_IS_EQUAL(float(-Eigen::half(4096.0f)), -4096.0f); + VERIFY_IS_EQUAL(float(-Eigen::half(-4096.0f)), 4096.0f); } void test_comparison() { - VERIFY(half(1.0f) > half(0.5f)); - VERIFY(half(0.5f) < half(1.0f)); - VERIFY(!(half(1.0f) < half(0.5f))); - VERIFY(!(half(0.5f) > half(1.0f))); + VERIFY(Eigen::half(1.0f) > Eigen::half(0.5f)); + VERIFY(Eigen::half(0.5f) < Eigen::half(1.0f)); + VERIFY(!(Eigen::half(1.0f) < Eigen::half(0.5f))); + VERIFY(!(Eigen::half(0.5f) > Eigen::half(1.0f))); - VERIFY(!(half(4.0f) > half(4.0f))); - VERIFY(!(half(4.0f) < half(4.0f))); + VERIFY(!(Eigen::half(4.0f) > Eigen::half(4.0f))); + VERIFY(!(Eigen::half(4.0f) < Eigen::half(4.0f))); - VERIFY(!(half(0.0f) < half(-0.0f))); - VERIFY(!(half(-0.0f) < half(0.0f))); - VERIFY(!(half(0.0f) > half(-0.0f))); - VERIFY(!(half(-0.0f) > half(0.0f))); + VERIFY(!(Eigen::half(0.0f) < Eigen::half(-0.0f))); + VERIFY(!(Eigen::half(-0.0f) < Eigen::half(0.0f))); + VERIFY(!(Eigen::half(0.0f) > Eigen::half(-0.0f))); + VERIFY(!(Eigen::half(-0.0f) > Eigen::half(0.0f))); - VERIFY(half(0.2f) > half(-1.0f)); - VERIFY(half(-1.0f) < half(0.2f)); - VERIFY(half(-16.0f) < half(-15.0f)); + VERIFY(Eigen::half(0.2f) > Eigen::half(-1.0f)); + VERIFY(Eigen::half(-1.0f) < Eigen::half(0.2f)); + VERIFY(Eigen::half(-16.0f) < Eigen::half(-15.0f)); - VERIFY(half(1.0f) == half(1.0f)); - VERIFY(half(1.0f) != half(2.0f)); + VERIFY(Eigen::half(1.0f) == Eigen::half(1.0f)); + VERIFY(Eigen::half(1.0f) != Eigen::half(2.0f)); // Comparisons with NaNs and infinities. -#if !EIGEN_COMP_MSVC - // Visual Studio errors out on divisions by 0 - VERIFY(!(half(0.0 / 0.0) == half(0.0 / 0.0))); - VERIFY(half(0.0 / 0.0) != half(0.0 / 0.0)); - - VERIFY(!(half(1.0) == half(0.0 / 0.0))); - VERIFY(!(half(1.0) < half(0.0 / 0.0))); - VERIFY(!(half(1.0) > half(0.0 / 0.0))); - VERIFY(half(1.0) != half(0.0 / 0.0)); - - VERIFY(half(1.0) < half(1.0 / 0.0)); - VERIFY(half(1.0) > half(-1.0 / 0.0)); -#endif + VERIFY(!(Eigen::half(0.0 / 0.0) == Eigen::half(0.0 / 0.0))); + VERIFY(!(Eigen::half(0.0 / 0.0) != Eigen::half(0.0 / 0.0))); + + VERIFY(!(Eigen::half(1.0) == Eigen::half(0.0 / 0.0))); + VERIFY(!(Eigen::half(1.0) < Eigen::half(0.0 / 0.0))); + VERIFY(!(Eigen::half(1.0) > Eigen::half(0.0 / 0.0))); + VERIFY(!(Eigen::half(1.0) != Eigen::half(0.0 / 0.0))); + + VERIFY(Eigen::half(1.0) < Eigen::half(1.0 / 0.0)); + VERIFY(Eigen::half(1.0) > Eigen::half(-1.0 / 0.0)); } + void test_basic_functions() { - VERIFY_IS_EQUAL(float(numext::abs(half(3.5f))), 3.5f); - VERIFY_IS_EQUAL(float(numext::abs(half(-3.5f))), 3.5f); + VERIFY_IS_EQUAL(float(numext::abs(Eigen::half(3.5f))), 3.5f); + VERIFY_IS_EQUAL(float(numext::abs(Eigen::half(-3.5f))), 3.5f); - VERIFY_IS_EQUAL(float(numext::floor(half(3.5f))), 3.0f); - VERIFY_IS_EQUAL(float(numext::floor(half(-3.5f))), -4.0f); + VERIFY_IS_EQUAL(float(numext::floor(Eigen::half(3.5f))), 3.0f); + VERIFY_IS_EQUAL(float(numext::floor(Eigen::half(-3.5f))), -4.0f); - VERIFY_IS_EQUAL(float(numext::ceil(half(3.5f))), 4.0f); - VERIFY_IS_EQUAL(float(numext::ceil(half(-3.5f))), -3.0f); + VERIFY_IS_EQUAL(float(numext::ceil(Eigen::half(3.5f))), 4.0f); + VERIFY_IS_EQUAL(float(numext::ceil(Eigen::half(-3.5f))), -3.0f); - VERIFY_IS_APPROX(float(numext::sqrt(half(0.0f))), 0.0f); - VERIFY_IS_APPROX(float(numext::sqrt(half(4.0f))), 2.0f); + VERIFY_IS_APPROX(float(numext::sqrt(Eigen::half(0.0f))), 0.0f); + VERIFY_IS_APPROX(float(numext::sqrt(Eigen::half(4.0f))), 2.0f); - VERIFY_IS_APPROX(float(numext::pow(half(0.0f), half(1.0f))), 0.0f); - VERIFY_IS_APPROX(float(numext::pow(half(2.0f), half(2.0f))), 4.0f); + VERIFY_IS_APPROX(float(numext::pow(Eigen::half(0.0f), Eigen::half(1.0f))), 0.0f); + VERIFY_IS_APPROX(float(numext::pow(Eigen::half(2.0f), Eigen::half(2.0f))), 4.0f); - VERIFY_IS_EQUAL(float(numext::exp(half(0.0f))), 1.0f); - VERIFY_IS_APPROX(float(numext::exp(half(EIGEN_PI))), float(20.0 + EIGEN_PI)); + VERIFY_IS_EQUAL(float(numext::exp(Eigen::half(0.0f))), 1.0f); + VERIFY_IS_APPROX(float(numext::exp(Eigen::half(EIGEN_PI))), float(20.0 + EIGEN_PI)); - VERIFY_IS_EQUAL(float(numext::log(half(1.0f))), 0.0f); - VERIFY_IS_APPROX(float(numext::log(half(10.0f))), 2.30273f); + VERIFY_IS_EQUAL(float(numext::log(Eigen::half(1.0f))), 0.0f); + VERIFY_IS_APPROX(float(numext::log(Eigen::half(10.0f))), 2.30273f); } void test_trigonometric_functions() { - VERIFY_IS_APPROX(numext::cos(half(0.0f)), half(cosf(0.0f))); - VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI)), half(cosf(EIGEN_PI))); - //VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI/2)), half(cosf(EIGEN_PI/2))); - //VERIFY_IS_APPROX(numext::cos(half(3*EIGEN_PI/2)), half(cosf(3*EIGEN_PI/2))); - VERIFY_IS_APPROX(numext::cos(half(3.5f)), half(cosf(3.5f))); - - VERIFY_IS_APPROX(numext::sin(half(0.0f)), half(sinf(0.0f))); - // VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI)), half(sinf(EIGEN_PI))); - VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI/2)), half(sinf(EIGEN_PI/2))); - VERIFY_IS_APPROX(numext::sin(half(3*EIGEN_PI/2)), half(sinf(3*EIGEN_PI/2))); - VERIFY_IS_APPROX(numext::sin(half(3.5f)), half(sinf(3.5f))); - - VERIFY_IS_APPROX(numext::tan(half(0.0f)), half(tanf(0.0f))); - // VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI)), half(tanf(EIGEN_PI))); - // VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI/2)), half(tanf(EIGEN_PI/2))); - //VERIFY_IS_APPROX(numext::tan(half(3*EIGEN_PI/2)), half(tanf(3*EIGEN_PI/2))); - VERIFY_IS_APPROX(numext::tan(half(3.5f)), half(tanf(3.5f))); + VERIFY_IS_APPROX(numext::cos(Eigen::half(0.0f)), Eigen::half(cosf(0.0f))); + VERIFY_IS_APPROX(numext::cos(Eigen::half(EIGEN_PI)), Eigen::half(cosf(EIGEN_PI))); + VERIFY_IS_APPROX_OR_LESS_THAN(numext::cos(Eigen::half(EIGEN_PI/2)), NumTraits<Eigen::half>::epsilon() * Eigen::half(5)); + VERIFY_IS_APPROX_OR_LESS_THAN(numext::cos(Eigen::half(3*EIGEN_PI/2)), NumTraits<Eigen::half>::epsilon() * Eigen::half(5)); + VERIFY_IS_APPROX(numext::cos(Eigen::half(3.5f)), Eigen::half(cosf(3.5f))); + + VERIFY_IS_APPROX(numext::sin(Eigen::half(0.0f)), Eigen::half(sinf(0.0f))); + VERIFY_IS_APPROX_OR_LESS_THAN(numext::sin(Eigen::half(EIGEN_PI)), NumTraits<Eigen::half>::epsilon() * Eigen::half(10)); + + VERIFY_IS_APPROX(numext::sin(Eigen::half(EIGEN_PI/2)), Eigen::half(sinf(EIGEN_PI/2))); + VERIFY_IS_APPROX(numext::sin(Eigen::half(3*EIGEN_PI/2)), Eigen::half(sinf(3*EIGEN_PI/2))); + VERIFY_IS_APPROX(numext::sin(Eigen::half(3.5f)), Eigen::half(sinf(3.5f))); + + VERIFY_IS_APPROX(numext::tan(Eigen::half(0.0f)), Eigen::half(tanf(0.0f))); + VERIFY_IS_APPROX_OR_LESS_THAN(numext::tan(Eigen::half(EIGEN_PI)), NumTraits<Eigen::half>::epsilon() * Eigen::half(10)); + VERIFY_IS_APPROX(numext::tan(Eigen::half(3.5f)), Eigen::half(tanf(3.5f))); } void test_cxx11_float16() { CALL_SUBTEST(test_conversion()); - CALL_SUBTEST(test_numtraits()); CALL_SUBTEST(test_arithmetic()); CALL_SUBTEST(test_comparison()); CALL_SUBTEST(test_basic_functions()); diff --git a/unsupported/test/cxx11_tensor_dimension.cpp b/unsupported/test/cxx11_tensor_dimension.cpp index 0bccc3396..16f168ed4 100644 --- a/unsupported/test/cxx11_tensor_dimension.cpp +++ b/unsupported/test/cxx11_tensor_dimension.cpp @@ -21,7 +21,7 @@ static void test_dynamic_size() VERIFY_IS_EQUAL((int)Eigen::internal::array_get<0>(dimensions), 2); VERIFY_IS_EQUAL((int)Eigen::internal::array_get<1>(dimensions), 3); VERIFY_IS_EQUAL((int)Eigen::internal::array_get<2>(dimensions), 7); - VERIFY_IS_EQUAL(dimensions.TotalSize(), 2*3*7); + VERIFY_IS_EQUAL((int)dimensions.TotalSize(), 2*3*7); VERIFY_IS_EQUAL((int)dimensions[0], 2); VERIFY_IS_EQUAL((int)dimensions[1], 3); VERIFY_IS_EQUAL((int)dimensions[2], 7); @@ -34,12 +34,12 @@ static void test_fixed_size() VERIFY_IS_EQUAL((int)Eigen::internal::array_get<0>(dimensions), 2); VERIFY_IS_EQUAL((int)Eigen::internal::array_get<1>(dimensions), 3); VERIFY_IS_EQUAL((int)Eigen::internal::array_get<2>(dimensions), 7); - VERIFY_IS_EQUAL(dimensions.TotalSize(), 2*3*7); + VERIFY_IS_EQUAL((int)dimensions.TotalSize(), 2*3*7); } static void test_match() { - Eigen::DSizes<int, 3> dyn(2,3,7); + Eigen::DSizes<unsigned int, 3> dyn((unsigned int)2,(unsigned int)3,(unsigned int)7); Eigen::Sizes<2,3,7> stat; VERIFY_IS_EQUAL(Eigen::dimensions_match(dyn, stat), true); @@ -51,13 +51,13 @@ static void test_match() static void test_rank_zero() { Eigen::Sizes<> scalar; - VERIFY_IS_EQUAL(scalar.TotalSize(), 1); - VERIFY_IS_EQUAL(scalar.rank(), 0); - VERIFY_IS_EQUAL(internal::array_prod(scalar), 1); + VERIFY_IS_EQUAL((int)scalar.TotalSize(), 1); + VERIFY_IS_EQUAL((int)scalar.rank(), 0); + VERIFY_IS_EQUAL((int)internal::array_prod(scalar), 1); Eigen::DSizes<ptrdiff_t, 0> dscalar; - VERIFY_IS_EQUAL(dscalar.TotalSize(), 1); - VERIFY_IS_EQUAL(dscalar.rank(), 0u); + VERIFY_IS_EQUAL((int)dscalar.TotalSize(), 1); + VERIFY_IS_EQUAL((int)dscalar.rank(), 0); } void test_cxx11_tensor_dimension() diff --git a/unsupported/test/cxx11_tensor_morphing.cpp b/unsupported/test/cxx11_tensor_morphing.cpp index c575d3fdc..f7de43110 100644 --- a/unsupported/test/cxx11_tensor_morphing.cpp +++ b/unsupported/test/cxx11_tensor_morphing.cpp @@ -13,6 +13,7 @@ using Eigen::Tensor; +template<typename> static void test_simple_reshape() { Tensor<float, 5> tensor1(2,3,1,7,1); @@ -40,7 +41,7 @@ static void test_simple_reshape() } } - +template<typename> static void test_reshape_in_expr() { MatrixXf m1(2,3*5*7*11); MatrixXf m2(3*5*7*11,13); @@ -65,7 +66,7 @@ static void test_reshape_in_expr() { } } - +template<typename> static void test_reshape_as_lvalue() { Tensor<float, 3> tensor(2,3,7); @@ -114,6 +115,7 @@ static void test_simple_slice() } } +template<typename=void> static void test_const_slice() { const float b[1] = {42}; @@ -459,25 +461,25 @@ static void test_composition() void test_cxx11_tensor_morphing() { - CALL_SUBTEST(test_simple_reshape()); - CALL_SUBTEST(test_reshape_in_expr()); - CALL_SUBTEST(test_reshape_as_lvalue()); - - CALL_SUBTEST(test_simple_slice<ColMajor>()); - CALL_SUBTEST(test_simple_slice<RowMajor>()); - CALL_SUBTEST(test_const_slice()); - CALL_SUBTEST(test_slice_in_expr<ColMajor>()); - CALL_SUBTEST(test_slice_in_expr<RowMajor>()); - CALL_SUBTEST(test_slice_as_lvalue<ColMajor>()); - CALL_SUBTEST(test_slice_as_lvalue<RowMajor>()); - CALL_SUBTEST(test_slice_raw_data<ColMajor>()); - CALL_SUBTEST(test_slice_raw_data<RowMajor>()); - - CALL_SUBTEST(test_strided_slice_write<ColMajor>()); - CALL_SUBTEST(test_strided_slice<ColMajor>()); - CALL_SUBTEST(test_strided_slice_write<RowMajor>()); - CALL_SUBTEST(test_strided_slice<RowMajor>()); - - CALL_SUBTEST(test_composition<ColMajor>()); - CALL_SUBTEST(test_composition<RowMajor>()); + CALL_SUBTEST_1(test_simple_reshape<void>()); + CALL_SUBTEST_1(test_reshape_in_expr<void>()); + CALL_SUBTEST_1(test_reshape_as_lvalue<void>()); + + CALL_SUBTEST_1(test_simple_slice<ColMajor>()); + CALL_SUBTEST_1(test_simple_slice<RowMajor>()); + CALL_SUBTEST_1(test_const_slice()); + CALL_SUBTEST_2(test_slice_in_expr<ColMajor>()); + CALL_SUBTEST_3(test_slice_in_expr<RowMajor>()); + CALL_SUBTEST_4(test_slice_as_lvalue<ColMajor>()); + CALL_SUBTEST_4(test_slice_as_lvalue<RowMajor>()); + CALL_SUBTEST_5(test_slice_raw_data<ColMajor>()); + CALL_SUBTEST_5(test_slice_raw_data<RowMajor>()); + + CALL_SUBTEST_6(test_strided_slice_write<ColMajor>()); + CALL_SUBTEST_6(test_strided_slice<ColMajor>()); + CALL_SUBTEST_6(test_strided_slice_write<RowMajor>()); + CALL_SUBTEST_6(test_strided_slice<RowMajor>()); + + CALL_SUBTEST_7(test_composition<ColMajor>()); + CALL_SUBTEST_7(test_composition<RowMajor>()); } diff --git a/unsupported/test/cxx11_tensor_of_float16_cuda.cu b/unsupported/test/cxx11_tensor_of_float16_cuda.cu index 34e9f54a0..b6df5a4d2 100644 --- a/unsupported/test/cxx11_tensor_of_float16_cuda.cu +++ b/unsupported/test/cxx11_tensor_of_float16_cuda.cu @@ -21,6 +21,7 @@ using Eigen::Tensor; #ifdef EIGEN_HAS_CUDA_FP16 +template<typename> void test_cuda_conversion() { Eigen::CudaStreamDevice stream; Eigen::GpuDevice gpu_device(&stream); @@ -55,7 +56,7 @@ void test_cuda_conversion() { gpu_device.deallocate(d_conv); } - +template<typename> void test_cuda_unary() { Eigen::CudaStreamDevice stream; Eigen::GpuDevice gpu_device(&stream); @@ -92,7 +93,7 @@ void test_cuda_unary() { gpu_device.deallocate(d_res_float); } - +template<typename> void test_cuda_elementwise() { Eigen::CudaStreamDevice stream; Eigen::GpuDevice gpu_device(&stream); @@ -134,6 +135,7 @@ void test_cuda_elementwise() { gpu_device.deallocate(d_res_float); } +template<typename> void test_cuda_trancendental() { Eigen::CudaStreamDevice stream; Eigen::GpuDevice gpu_device(&stream); @@ -186,7 +188,10 @@ void test_cuda_trancendental() { } for (int i = 0; i < num_elem; ++i) { std::cout << "Checking elemwise log " << i << " input = " << input2(i) << " full = " << full_prec2(i) << " half = " << half_prec2(i) << std::endl; - VERIFY_IS_APPROX(full_prec2(i), half_prec2(i)); + if(std::abs(input2(i)-1.f)<0.05f) // log lacks accurary nearby 1 + VERIFY_IS_APPROX(full_prec2(i)+Eigen::half(0.1f), half_prec2(i)+Eigen::half(0.1f)); + else + VERIFY_IS_APPROX(full_prec2(i), half_prec2(i)); } gpu_device.deallocate(d_float1); gpu_device.deallocate(d_float2); @@ -196,7 +201,7 @@ void test_cuda_trancendental() { gpu_device.deallocate(d_res2_float); } - +template<typename> void test_cuda_contractions() { Eigen::CudaStreamDevice stream; Eigen::GpuDevice gpu_device(&stream); @@ -247,7 +252,7 @@ void test_cuda_contractions() { gpu_device.deallocate(d_res_float); } - +template<typename> void test_cuda_reductions(int size1, int size2, int redux) { std::cout << "Reducing " << size1 << " by " << size2 @@ -296,17 +301,19 @@ void test_cuda_reductions(int size1, int size2, int redux) { gpu_device.deallocate(d_res_float); } +template<typename> void test_cuda_reductions() { - test_cuda_reductions(13, 13, 0); - test_cuda_reductions(13, 13, 1); + test_cuda_reductions<void>(13, 13, 0); + test_cuda_reductions<void>(13, 13, 1); - test_cuda_reductions(35, 36, 0); - test_cuda_reductions(35, 36, 1); + test_cuda_reductions<void>(35, 36, 0); + test_cuda_reductions<void>(35, 36, 1); - test_cuda_reductions(36, 35, 0); - test_cuda_reductions(36, 35, 1); + test_cuda_reductions<void>(36, 35, 0); + test_cuda_reductions<void>(36, 35, 1); } +template<typename> void test_cuda_full_reductions() { Eigen::CudaStreamDevice stream; Eigen::GpuDevice gpu_device(&stream); @@ -355,7 +362,7 @@ void test_cuda_full_reductions() { gpu_device.deallocate(d_res_float); } - +template<typename> void test_cuda_forced_evals() { Eigen::CudaStreamDevice stream; @@ -409,14 +416,14 @@ void test_cuda_forced_evals() { void test_cxx11_tensor_of_float16_cuda() { #ifdef EIGEN_HAS_CUDA_FP16 - CALL_SUBTEST_1(test_cuda_conversion()); - CALL_SUBTEST_1(test_cuda_unary()); - CALL_SUBTEST_1(test_cuda_elementwise()); - CALL_SUBTEST_1(test_cuda_trancendental()); - CALL_SUBTEST_2(test_cuda_contractions()); - CALL_SUBTEST_3(test_cuda_reductions()); - CALL_SUBTEST_4(test_cuda_full_reductions()); - CALL_SUBTEST_5(test_cuda_forced_evals()); + CALL_SUBTEST_1(test_cuda_conversion<void>()); + CALL_SUBTEST_1(test_cuda_unary<void>()); + CALL_SUBTEST_1(test_cuda_elementwise<void>()); + CALL_SUBTEST_1(test_cuda_trancendental<void>()); + CALL_SUBTEST_2(test_cuda_contractions<void>()); + CALL_SUBTEST_3(test_cuda_reductions<void>()); + CALL_SUBTEST_4(test_cuda_full_reductions<void>()); + CALL_SUBTEST_5(test_cuda_forced_evals<void>()); #else std::cout << "Half floats are not supported by this version of cuda: skipping the test" << std::endl; #endif diff --git a/unsupported/test/cxx11_tensor_reduction.cpp b/unsupported/test/cxx11_tensor_reduction.cpp index ca483257b..1490ec3da 100644 --- a/unsupported/test/cxx11_tensor_reduction.cpp +++ b/unsupported/test/cxx11_tensor_reduction.cpp @@ -239,6 +239,33 @@ static void test_simple_reductions() { } } + +template <int DataLayout> +static void test_reductions_in_expr() { + Tensor<float, 4, DataLayout> tensor(2, 3, 5, 7); + tensor.setRandom(); + array<ptrdiff_t, 2> reduction_axis2; + reduction_axis2[0] = 1; + reduction_axis2[1] = 3; + + Tensor<float, 2, DataLayout> result(2, 5); + result = result.constant(1.0f) - tensor.sum(reduction_axis2); + VERIFY_IS_EQUAL(result.dimension(0), 2); + VERIFY_IS_EQUAL(result.dimension(1), 5); + for (int i = 0; i < 2; ++i) { + for (int j = 0; j < 5; ++j) { + float sum = 0.0f; + for (int k = 0; k < 3; ++k) { + for (int l = 0; l < 7; ++l) { + sum += tensor(i, k, j, l); + } + } + VERIFY_IS_APPROX(result(i, j), 1.0f - sum); + } + } +} + + template <int DataLayout> static void test_full_reductions() { Tensor<float, 2, DataLayout> tensor(2, 3); @@ -462,6 +489,8 @@ void test_cxx11_tensor_reduction() { CALL_SUBTEST(test_trivial_reductions<RowMajor>()); CALL_SUBTEST(test_simple_reductions<ColMajor>()); CALL_SUBTEST(test_simple_reductions<RowMajor>()); + CALL_SUBTEST(test_reductions_in_expr<ColMajor>()); + CALL_SUBTEST(test_reductions_in_expr<RowMajor>()); CALL_SUBTEST(test_full_reductions<ColMajor>()); CALL_SUBTEST(test_full_reductions<RowMajor>()); CALL_SUBTEST(test_user_defined_reductions<ColMajor>()); diff --git a/unsupported/test/mpreal_support.cpp b/unsupported/test/mpreal_support.cpp index 1aa9e786a..ffa5691eb 100644 --- a/unsupported/test/mpreal_support.cpp +++ b/unsupported/test/mpreal_support.cpp @@ -17,6 +17,7 @@ void test_mpreal_support() std::cerr << "dummy_precision = " << NumTraits<mpreal>::dummy_precision() << "\n"; std::cerr << "highest = " << NumTraits<mpreal>::highest() << "\n"; std::cerr << "lowest = " << NumTraits<mpreal>::lowest() << "\n"; + std::cerr << "digits10 = " << NumTraits<mpreal>::digits10() << "\n"; for(int i = 0; i < g_repeat; i++) { int s = Eigen::internal::random<int>(1,100); diff --git a/unsupported/test/special_functions.cpp b/unsupported/test/special_functions.cpp new file mode 100644 index 000000000..057fb3e92 --- /dev/null +++ b/unsupported/test/special_functions.cpp @@ -0,0 +1,345 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include "../Eigen/SpecialFunctions" + +template<typename X, typename Y> +void verify_component_wise(const X& x, const Y& y) +{ + for(Index i=0; i<x.size(); ++i) + { + if((numext::isfinite)(y(i))) + VERIFY_IS_APPROX( x(i), y(i) ); + else if((numext::isnan)(y(i))) + VERIFY((numext::isnan)(x(i))); + else + VERIFY_IS_EQUAL( x(i), y(i) ); + } +} + +template<typename ArrayType> void array_special_functions() +{ + using std::abs; + using std::sqrt; + typedef typename ArrayType::Scalar Scalar; + typedef typename NumTraits<Scalar>::Real RealScalar; + + Scalar plusinf = std::numeric_limits<Scalar>::infinity(); + Scalar nan = std::numeric_limits<Scalar>::quiet_NaN(); + + Index rows = internal::random<Index>(1,30); + Index cols = 1; + + // API + { + ArrayType m1 = ArrayType::Random(rows,cols); +#if EIGEN_HAS_C99_MATH + VERIFY_IS_APPROX(m1.lgamma(), lgamma(m1)); + VERIFY_IS_APPROX(m1.digamma(), digamma(m1)); + VERIFY_IS_APPROX(m1.erf(), erf(m1)); + VERIFY_IS_APPROX(m1.erfc(), erfc(m1)); +#endif // EIGEN_HAS_C99_MATH + } + + +#if EIGEN_HAS_C99_MATH + // check special functions (comparing against numpy implementation) + if (!NumTraits<Scalar>::IsComplex) + { + + { + ArrayType m1 = ArrayType::Random(rows,cols); + ArrayType m2 = ArrayType::Random(rows,cols); + + // Test various propreties of igamma & igammac. These are normalized + // gamma integrals where + // igammac(a, x) = Gamma(a, x) / Gamma(a) + // igamma(a, x) = gamma(a, x) / Gamma(a) + // where Gamma and gamma are considered the standard unnormalized + // upper and lower incomplete gamma functions, respectively. + ArrayType a = m1.abs() + 2; + ArrayType x = m2.abs() + 2; + ArrayType zero = ArrayType::Zero(rows, cols); + ArrayType one = ArrayType::Constant(rows, cols, Scalar(1.0)); + ArrayType a_m1 = a - one; + ArrayType Gamma_a_x = Eigen::igammac(a, x) * a.lgamma().exp(); + ArrayType Gamma_a_m1_x = Eigen::igammac(a_m1, x) * a_m1.lgamma().exp(); + ArrayType gamma_a_x = Eigen::igamma(a, x) * a.lgamma().exp(); + ArrayType gamma_a_m1_x = Eigen::igamma(a_m1, x) * a_m1.lgamma().exp(); + + // Gamma(a, 0) == Gamma(a) + VERIFY_IS_APPROX(Eigen::igammac(a, zero), one); + + // Gamma(a, x) + gamma(a, x) == Gamma(a) + VERIFY_IS_APPROX(Gamma_a_x + gamma_a_x, a.lgamma().exp()); + + // Gamma(a, x) == (a - 1) * Gamma(a-1, x) + x^(a-1) * exp(-x) + VERIFY_IS_APPROX(Gamma_a_x, (a - 1) * Gamma_a_m1_x + x.pow(a-1) * (-x).exp()); + + // gamma(a, x) == (a - 1) * gamma(a-1, x) - x^(a-1) * exp(-x) + VERIFY_IS_APPROX(gamma_a_x, (a - 1) * gamma_a_m1_x - x.pow(a-1) * (-x).exp()); + } + + { + // Check exact values of igamma and igammac against a third party calculation. + Scalar a_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)}; + Scalar x_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)}; + + // location i*6+j corresponds to a_s[i], x_s[j]. + Scalar igamma_s[][6] = {{0.0, nan, nan, nan, nan, nan}, + {0.0, 0.6321205588285578, 0.7768698398515702, + 0.9816843611112658, 9.999500016666262e-05, 1.0}, + {0.0, 0.4275932955291202, 0.608374823728911, + 0.9539882943107686, 7.522076445089201e-07, 1.0}, + {0.0, 0.01898815687615381, 0.06564245437845008, + 0.5665298796332909, 4.166333347221828e-18, 1.0}, + {0.0, 0.9999780593618628, 0.9999899967080838, + 0.9999996219837988, 0.9991370418689945, 1.0}, + {0.0, 0.0, 0.0, 0.0, 0.0, 0.5042041932513908}}; + Scalar igammac_s[][6] = {{nan, nan, nan, nan, nan, nan}, + {1.0, 0.36787944117144233, 0.22313016014842982, + 0.018315638888734182, 0.9999000049998333, 0.0}, + {1.0, 0.5724067044708798, 0.3916251762710878, + 0.04601170568923136, 0.9999992477923555, 0.0}, + {1.0, 0.9810118431238462, 0.9343575456215499, + 0.4334701203667089, 1.0, 0.0}, + {1.0, 2.1940638138146658e-05, 1.0003291916285e-05, + 3.7801620118431334e-07, 0.0008629581310054535, + 0.0}, + {1.0, 1.0, 1.0, 1.0, 1.0, 0.49579580674813944}}; + for (int i = 0; i < 6; ++i) { + for (int j = 0; j < 6; ++j) { + if ((std::isnan)(igamma_s[i][j])) { + VERIFY((std::isnan)(numext::igamma(a_s[i], x_s[j]))); + } else { + VERIFY_IS_APPROX(numext::igamma(a_s[i], x_s[j]), igamma_s[i][j]); + } + + if ((std::isnan)(igammac_s[i][j])) { + VERIFY((std::isnan)(numext::igammac(a_s[i], x_s[j]))); + } else { + VERIFY_IS_APPROX(numext::igammac(a_s[i], x_s[j]), igammac_s[i][j]); + } + } + } + } + } +#endif // EIGEN_HAS_C99_MATH + + // Check the zeta function against scipy.special.zeta + { + ArrayType x(7), q(7), res(7), ref(7); + x << 1.5, 4, 10.5, 10000.5, 3, 1, 0.9; + q << 2, 1.5, 3, 1.0001, -2.5, 1.2345, 1.2345; + ref << 1.61237534869, 0.234848505667, 1.03086757337e-5, 0.367879440865, 0.054102025820864097, plusinf, nan; + CALL_SUBTEST( verify_component_wise(ref, ref); ); + CALL_SUBTEST( res = x.zeta(q); verify_component_wise(res, ref); ); + CALL_SUBTEST( res = zeta(x,q); verify_component_wise(res, ref); ); + } + + // digamma + { + ArrayType x(7), res(7), ref(7); + x << 1, 1.5, 4, -10.5, 10000.5, 0, -1; + ref << -0.5772156649015329, 0.03648997397857645, 1.2561176684318, 2.398239129535781, 9.210340372392849, plusinf, plusinf; + CALL_SUBTEST( verify_component_wise(ref, ref); ); + + CALL_SUBTEST( res = x.digamma(); verify_component_wise(res, ref); ); + CALL_SUBTEST( res = digamma(x); verify_component_wise(res, ref); ); + } + + +#if EIGEN_HAS_C99_MATH + { + ArrayType n(11), x(11), res(11), ref(11); + n << 1, 1, 1, 1.5, 17, 31, 28, 8, 42, 147, 170; + x << 2, 3, 25.5, 1.5, 4.7, 11.8, 17.7, 30.2, 15.8, 54.1, 64; + ref << 0.644934066848, 0.394934066848, 0.0399946696496, nan, 293.334565435, 0.445487887616, -2.47810300902e-07, -8.29668781082e-09, -0.434562276666, 0.567742190178, -0.0108615497927; + CALL_SUBTEST( verify_component_wise(ref, ref); ); + + if(sizeof(RealScalar)>=8) { // double + // Reason for commented line: http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1232 + // CALL_SUBTEST( res = x.polygamma(n); verify_component_wise(res, ref); ); + CALL_SUBTEST( res = polygamma(n,x); verify_component_wise(res, ref); ); + } + else { + // CALL_SUBTEST( res = x.polygamma(n); verify_component_wise(res.head(8), ref.head(8)); ); + CALL_SUBTEST( res = polygamma(n,x); verify_component_wise(res.head(8), ref.head(8)); ); + } + } +#endif + +#if EIGEN_HAS_C99_MATH + { + // Inputs and ground truth generated with scipy via: + // a = np.logspace(-3, 3, 5) - 1e-3 + // b = np.logspace(-3, 3, 5) - 1e-3 + // x = np.linspace(-0.1, 1.1, 5) + // (full_a, full_b, full_x) = np.vectorize(lambda a, b, x: (a, b, x))(*np.ix_(a, b, x)) + // full_a = full_a.flatten().tolist() # same for full_b, full_x + // v = scipy.special.betainc(full_a, full_b, full_x).flatten().tolist() + // + // Note in Eigen, we call betainc with arguments in the order (x, a, b). + ArrayType a(125); + ArrayType b(125); + ArrayType x(125); + ArrayType v(125); + ArrayType res(125); + + a << 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, + 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, + 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, + 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, + 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, + 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, + 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, + 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, + 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, + 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, + 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, + 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, + 31.62177660168379, 31.62177660168379, 31.62177660168379, + 31.62177660168379, 31.62177660168379, 31.62177660168379, + 31.62177660168379, 31.62177660168379, 31.62177660168379, + 31.62177660168379, 31.62177660168379, 31.62177660168379, + 31.62177660168379, 31.62177660168379, 31.62177660168379, + 31.62177660168379, 31.62177660168379, 31.62177660168379, + 31.62177660168379, 31.62177660168379, 31.62177660168379, + 31.62177660168379, 31.62177660168379, 31.62177660168379, + 31.62177660168379, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, + 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, + 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, + 999.999, 999.999, 999.999; + + b << 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379, 0.03062277660168379, + 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.999, + 0.999, 0.999, 0.999, 0.999, 31.62177660168379, 31.62177660168379, + 31.62177660168379, 31.62177660168379, 31.62177660168379, 999.999, + 999.999, 999.999, 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, + 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, + 0.03062277660168379, 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, + 0.999, 31.62177660168379, 31.62177660168379, 31.62177660168379, + 31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999, + 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379, + 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, + 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, + 31.62177660168379, 31.62177660168379, 31.62177660168379, + 31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999, + 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379, + 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, + 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, + 31.62177660168379, 31.62177660168379, 31.62177660168379, + 31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999, + 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379, + 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, + 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, + 31.62177660168379, 31.62177660168379, 31.62177660168379, + 31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999, + 999.999, 999.999; + + x << -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, + 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, + 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, + 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, + -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, + 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, + 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, + 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, + 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, + 0.8, 1.1; + + v << nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, + nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, + nan, nan, nan, 0.47972119876364683, 0.5, 0.5202788012363533, nan, nan, + 0.9518683957740043, 0.9789663010413743, 0.9931729188073435, nan, nan, + 0.999995949033062, 0.9999999999993698, 0.9999999999999999, nan, nan, + 0.9999999999999999, 0.9999999999999999, 0.9999999999999999, nan, nan, + nan, nan, nan, nan, nan, 0.006827081192655869, 0.0210336989586256, + 0.04813160422599567, nan, nan, 0.20014344256217678, 0.5000000000000001, + 0.7998565574378232, nan, nan, 0.9991401428435834, 0.999999999698403, + 0.9999999999999999, nan, nan, 0.9999999999999999, 0.9999999999999999, + 0.9999999999999999, nan, nan, nan, nan, nan, nan, nan, + 1.0646600232370887e-25, 6.301722877826246e-13, 4.050966937974938e-06, + nan, nan, 7.864342668429763e-23, 3.015969667594166e-10, + 0.0008598571564165444, nan, nan, 6.031987710123844e-08, + 0.5000000000000007, 0.9999999396801229, nan, nan, 0.9999999999999999, + 0.9999999999999999, 0.9999999999999999, nan, nan, nan, nan, nan, nan, + nan, 0.0, 7.029920380986636e-306, 2.2450728208591345e-101, nan, nan, + 0.0, 9.275871147869727e-302, 1.2232913026152827e-97, nan, nan, 0.0, + 3.0891393081932924e-252, 2.9303043666183996e-60, nan, nan, + 2.248913486879199e-196, 0.5000000000004947, 0.9999999999999999, nan; + + CALL_SUBTEST(res = betainc(a, b, x); + verify_component_wise(res, v);); + } + + // Test various properties of betainc + { + ArrayType m1 = ArrayType::Random(32); + ArrayType m2 = ArrayType::Random(32); + ArrayType m3 = ArrayType::Random(32); + ArrayType one = ArrayType::Constant(32, Scalar(1.0)); + const Scalar eps = std::numeric_limits<Scalar>::epsilon(); + ArrayType a = (m1 * 4.0).exp(); + ArrayType b = (m2 * 4.0).exp(); + ArrayType x = m3.abs(); + + // betainc(a, 1, x) == x**a + CALL_SUBTEST( + ArrayType test = betainc(a, one, x); + ArrayType expected = x.pow(a); + verify_component_wise(test, expected);); + + // betainc(1, b, x) == 1 - (1 - x)**b + CALL_SUBTEST( + ArrayType test = betainc(one, b, x); + ArrayType expected = one - (one - x).pow(b); + verify_component_wise(test, expected);); + + // betainc(a, b, x) == 1 - betainc(b, a, 1-x) + CALL_SUBTEST( + ArrayType test = betainc(a, b, x) + betainc(b, a, one - x); + ArrayType expected = one; + verify_component_wise(test, expected);); + + // betainc(a+1, b, x) = betainc(a, b, x) - x**a * (1 - x)**b / (a * beta(a, b)) + CALL_SUBTEST( + ArrayType num = x.pow(a) * (one - x).pow(b); + ArrayType denom = a * (a.lgamma() + b.lgamma() - (a + b).lgamma()).exp(); + // Add eps to rhs and lhs so that component-wise test doesn't result in + // nans when both outputs are zeros. + ArrayType expected = betainc(a, b, x) - num / denom + eps; + ArrayType test = betainc(a + one, b, x) + eps; + if (sizeof(Scalar) >= 8) { // double + verify_component_wise(test, expected); + } else { + // Reason for limited test: http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1232 + verify_component_wise(test.head(8), expected.head(8)); + }); + + // betainc(a, b+1, x) = betainc(a, b, x) + x**a * (1 - x)**b / (b * beta(a, b)) + CALL_SUBTEST( + // Add eps to rhs and lhs so that component-wise test doesn't result in + // nans when both outputs are zeros. + ArrayType num = x.pow(a) * (one - x).pow(b); + ArrayType denom = b * (a.lgamma() + b.lgamma() - (a + b).lgamma()).exp(); + ArrayType expected = betainc(a, b, x) + num / denom + eps; + ArrayType test = betainc(a, b + one, x) + eps; + verify_component_wise(test, expected);); + } +#endif +} + +void test_special_functions() +{ + CALL_SUBTEST_1(array_special_functions<ArrayXf>()); + CALL_SUBTEST_2(array_special_functions<ArrayXd>()); +} |
