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-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2009-2010 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_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
-#define EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
-
-namespace Eigen {
-
-template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjLhs, bool ConjRhs>
-struct selfadjoint_rank1_update;
-
-namespace internal {
-
-/**********************************************************************
-* This file implements a general A * B product while
-* evaluating only one triangular part of the product.
-* This is more general version of self adjoint product (C += A A^T)
-* as the level 3 SYRK Blas routine.
-**********************************************************************/
-
-// forward declarations (defined at the end of this file)
-template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo>
-struct tribb_kernel;
-
-/* Optimized matrix-matrix product evaluating only one triangular half */
-template <typename Index,
- typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
- typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs,
- int ResStorageOrder, int UpLo, int Version = Specialized>
-struct general_matrix_matrix_triangular_product;
-
-// as usual if the result is row major => we transpose the product
-template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
- typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int UpLo, int Version>
-struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor,UpLo,Version>
-{
- typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
- static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* lhs, Index lhsStride,
- const RhsScalar* rhs, Index rhsStride, ResScalar* res, Index resStride, const ResScalar& alpha)
- {
- general_matrix_matrix_triangular_product<Index,
- RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs,
- LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs,
- ColMajor, UpLo==Lower?Upper:Lower>
- ::run(size,depth,rhs,rhsStride,lhs,lhsStride,res,resStride,alpha);
- }
-};
-
-template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
- typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int UpLo, int Version>
-struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor,UpLo,Version>
-{
- typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
- static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* _lhs, Index lhsStride,
- const RhsScalar* _rhs, Index rhsStride, ResScalar* _res, Index resStride, const ResScalar& alpha)
- {
- typedef gebp_traits<LhsScalar,RhsScalar> Traits;
-
- typedef const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> LhsMapper;
- typedef const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> RhsMapper;
- typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor> ResMapper;
- LhsMapper lhs(_lhs,lhsStride);
- RhsMapper rhs(_rhs,rhsStride);
- ResMapper res(_res, resStride);
-
- Index kc = depth; // cache block size along the K direction
- Index mc = size; // cache block size along the M direction
- Index nc = size; // cache block size along the N direction
- computeProductBlockingSizes<LhsScalar,RhsScalar>(kc, mc, nc, Index(1));
- // !!! mc must be a multiple of nr:
- if(mc > Traits::nr)
- mc = (mc/Traits::nr)*Traits::nr;
-
- ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, kc*mc, 0);
- ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, kc*size, 0);
-
- gemm_pack_lhs<LhsScalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
- gemm_pack_rhs<RhsScalar, Index, RhsMapper, Traits::nr, RhsStorageOrder> pack_rhs;
- gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp;
- tribb_kernel<LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs, UpLo> sybb;
-
- for(Index k2=0; k2<depth; k2+=kc)
- {
- const Index actual_kc = (std::min)(k2+kc,depth)-k2;
-
- // note that the actual rhs is the transpose/adjoint of mat
- pack_rhs(blockB, rhs.getSubMapper(k2,0), actual_kc, size);
-
- for(Index i2=0; i2<size; i2+=mc)
- {
- const Index actual_mc = (std::min)(i2+mc,size)-i2;
-
- pack_lhs(blockA, lhs.getSubMapper(i2, k2), actual_kc, actual_mc);
-
- // the selected actual_mc * size panel of res is split into three different part:
- // 1 - before the diagonal => processed with gebp or skipped
- // 2 - the actual_mc x actual_mc symmetric block => processed with a special kernel
- // 3 - after the diagonal => processed with gebp or skipped
- if (UpLo==Lower)
- gebp(res.getSubMapper(i2, 0), blockA, blockB, actual_mc, actual_kc,
- (std::min)(size,i2), alpha, -1, -1, 0, 0);
-
-
- sybb(_res+resStride*i2 + i2, resStride, blockA, blockB + actual_kc*i2, actual_mc, actual_kc, alpha);
-
- if (UpLo==Upper)
- {
- Index j2 = i2+actual_mc;
- gebp(res.getSubMapper(i2, j2), blockA, blockB+actual_kc*j2, actual_mc,
- actual_kc, (std::max)(Index(0), size-j2), alpha, -1, -1, 0, 0);
- }
- }
- }
- }
-};
-
-// Optimized packed Block * packed Block product kernel evaluating only one given triangular part
-// This kernel is built on top of the gebp kernel:
-// - the current destination block is processed per panel of actual_mc x BlockSize
-// where BlockSize is set to the minimal value allowing gebp to be as fast as possible
-// - then, as usual, each panel is split into three parts along the diagonal,
-// the sub blocks above and below the diagonal are processed as usual,
-// while the triangular block overlapping the diagonal is evaluated into a
-// small temporary buffer which is then accumulated into the result using a
-// triangular traversal.
-template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo>
-struct tribb_kernel
-{
- typedef gebp_traits<LhsScalar,RhsScalar,ConjLhs,ConjRhs> Traits;
- typedef typename Traits::ResScalar ResScalar;
-
- enum {
- BlockSize = EIGEN_PLAIN_ENUM_MAX(mr,nr)
- };
- void operator()(ResScalar* _res, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index size, Index depth, const ResScalar& alpha)
- {
- typedef blas_data_mapper<ResScalar, Index, ColMajor> ResMapper;
- ResMapper res(_res, resStride);
- gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, mr, nr, ConjLhs, ConjRhs> gebp_kernel;
-
- Matrix<ResScalar,BlockSize,BlockSize,ColMajor> buffer;
-
- // let's process the block per panel of actual_mc x BlockSize,
- // again, each is split into three parts, etc.
- for (Index j=0; j<size; j+=BlockSize)
- {
- Index actualBlockSize = std::min<Index>(BlockSize,size - j);
- const RhsScalar* actual_b = blockB+j*depth;
-
- if(UpLo==Upper)
- gebp_kernel(res.getSubMapper(0, j), blockA, actual_b, j, depth, actualBlockSize, alpha,
- -1, -1, 0, 0);
-
- // selfadjoint micro block
- {
- Index i = j;
- buffer.setZero();
- // 1 - apply the kernel on the temporary buffer
- gebp_kernel(ResMapper(buffer.data(), BlockSize), blockA+depth*i, actual_b, actualBlockSize, depth, actualBlockSize, alpha,
- -1, -1, 0, 0);
- // 2 - triangular accumulation
- for(Index j1=0; j1<actualBlockSize; ++j1)
- {
- ResScalar* r = &res(i, j + j1);
- for(Index i1=UpLo==Lower ? j1 : 0;
- UpLo==Lower ? i1<actualBlockSize : i1<=j1; ++i1)
- r[i1] += buffer(i1,j1);
- }
- }
-
- if(UpLo==Lower)
- {
- Index i = j+actualBlockSize;
- gebp_kernel(res.getSubMapper(i, j), blockA+depth*i, actual_b, size-i,
- depth, actualBlockSize, alpha, -1, -1, 0, 0);
- }
- }
- }
-};
-
-} // end namespace internal
-
-// high level API
-
-template<typename MatrixType, typename ProductType, int UpLo, bool IsOuterProduct>
-struct general_product_to_triangular_selector;
-
-
-template<typename MatrixType, typename ProductType, int UpLo>
-struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,true>
-{
- static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha)
- {
- typedef typename MatrixType::Scalar Scalar;
- typedef typename MatrixType::Index Index;
-
- typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs;
- typedef internal::blas_traits<Lhs> LhsBlasTraits;
- typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs;
- typedef typename internal::remove_all<ActualLhs>::type _ActualLhs;
- typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
-
- typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs;
- typedef internal::blas_traits<Rhs> RhsBlasTraits;
- typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs;
- typedef typename internal::remove_all<ActualRhs>::type _ActualRhs;
- typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
-
- Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived());
-
- enum {
- StorageOrder = (internal::traits<MatrixType>::Flags&RowMajorBit) ? RowMajor : ColMajor,
- UseLhsDirectly = _ActualLhs::InnerStrideAtCompileTime==1,
- UseRhsDirectly = _ActualRhs::InnerStrideAtCompileTime==1
- };
-
- internal::gemv_static_vector_if<Scalar,Lhs::SizeAtCompileTime,Lhs::MaxSizeAtCompileTime,!UseLhsDirectly> static_lhs;
- ei_declare_aligned_stack_constructed_variable(Scalar, actualLhsPtr, actualLhs.size(),
- (UseLhsDirectly ? const_cast<Scalar*>(actualLhs.data()) : static_lhs.data()));
- if(!UseLhsDirectly) Map<typename _ActualLhs::PlainObject>(actualLhsPtr, actualLhs.size()) = actualLhs;
-
- internal::gemv_static_vector_if<Scalar,Rhs::SizeAtCompileTime,Rhs::MaxSizeAtCompileTime,!UseRhsDirectly> static_rhs;
- ei_declare_aligned_stack_constructed_variable(Scalar, actualRhsPtr, actualRhs.size(),
- (UseRhsDirectly ? const_cast<Scalar*>(actualRhs.data()) : static_rhs.data()));
- if(!UseRhsDirectly) Map<typename _ActualRhs::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
-
-
- selfadjoint_rank1_update<Scalar,Index,StorageOrder,UpLo,
- LhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex,
- RhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex>
- ::run(actualLhs.size(), mat.data(), mat.outerStride(), actualLhsPtr, actualRhsPtr, actualAlpha);
- }
-};
-
-template<typename MatrixType, typename ProductType, int UpLo>
-struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,false>
-{
- static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha)
- {
- typedef typename MatrixType::Index Index;
-
- typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs;
- typedef internal::blas_traits<Lhs> LhsBlasTraits;
- typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs;
- typedef typename internal::remove_all<ActualLhs>::type _ActualLhs;
- typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
-
- typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs;
- typedef internal::blas_traits<Rhs> RhsBlasTraits;
- typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs;
- typedef typename internal::remove_all<ActualRhs>::type _ActualRhs;
- typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
-
- typename ProductType::Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived());
-
- internal::general_matrix_matrix_triangular_product<Index,
- typename Lhs::Scalar, _ActualLhs::Flags&RowMajorBit ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
- typename Rhs::Scalar, _ActualRhs::Flags&RowMajorBit ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
- MatrixType::Flags&RowMajorBit ? RowMajor : ColMajor, UpLo>
- ::run(mat.cols(), actualLhs.cols(),
- &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &actualRhs.coeffRef(0,0), actualRhs.outerStride(),
- mat.data(), mat.outerStride(), actualAlpha);
- }
-};
-
-template<typename MatrixType, unsigned int UpLo>
-template<typename ProductDerived, typename _Lhs, typename _Rhs>
-TriangularView<MatrixType,UpLo>& TriangularView<MatrixType,UpLo>::assignProduct(const ProductBase<ProductDerived, _Lhs,_Rhs>& prod, const Scalar& alpha)
-{
- eigen_assert(m_matrix.rows() == prod.rows() && m_matrix.cols() == prod.cols());
-
- general_product_to_triangular_selector<MatrixType, ProductDerived, UpLo, (_Lhs::ColsAtCompileTime==1) || (_Rhs::RowsAtCompileTime==1)>::run(m_matrix.const_cast_derived(), prod.derived(), alpha);
-
- return *this;
-}
-
-} // end namespace Eigen
-
-#endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H