merge

15 files changed, 179 insertions, 93 deletions

diff --git a/Eigen/Eigenvalues b/Eigen/Eigenvalues
index ea93eb303..216a6d51d 100644
--- a/Eigen/Eigenvalues
+++ b/Eigen/Eigenvalues
@@ -32,6 +32,7 @@
   * \endcode
   */
 
+#include "src/misc/RealSvd2x2.h"
 #include "src/Eigenvalues/Tridiagonalization.h"
 #include "src/Eigenvalues/RealSchur.h"
 #include "src/Eigenvalues/EigenSolver.h"
diff --git a/Eigen/SVD b/Eigen/SVD
index b353f3f54..565d9c90d 100644
--- a/Eigen/SVD
+++ b/Eigen/SVD
@@ -31,6 +31,7 @@
   * \endcode
   */
 
+#include "src/misc/RealSvd2x2.h"
 #include "src/SVD/UpperBidiagonalization.h"
 #include "src/SVD/SVDBase.h"
 #include "src/SVD/JacobiSVD.h"
diff --git a/Eigen/src/Core/Array.h b/Eigen/src/Core/Array.h
index c0af4aa9d..7c2e0de16 100644
--- a/Eigen/src/Core/Array.h
+++ b/Eigen/src/Core/Array.h
@@ -149,7 +149,7 @@ class Array
 
 #if EIGEN_HAS_RVALUE_REFERENCES
     EIGEN_DEVICE_FUNC
-    Array(Array&& other)
+    Array(Array&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_constructible<Scalar>::value)
       : Base(std::move(other))
     {
       Base::_check_template_params();
@@ -157,7 +157,7 @@ class Array
         Base::_set_noalias(other);
     }
     EIGEN_DEVICE_FUNC
-    Array& operator=(Array&& other)
+    Array& operator=(Array&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_assignable<Scalar>::value)
     {
       other.swap(*this);
       return *this;
diff --git a/Eigen/src/Core/arch/CUDA/PacketMathHalf.h b/Eigen/src/Core/arch/CUDA/PacketMathHalf.h
index 51386506f..959dff886 100644
--- a/Eigen/src/Core/arch/CUDA/PacketMathHalf.h
+++ b/Eigen/src/Core/arch/CUDA/PacketMathHalf.h
@@ -28,6 +28,8 @@ template<> struct packet_traits<Eigen::half> : default_packet_traits
     AlignedOnScalar = 1,
     size=2,
     HasHalfPacket = 0,
+    HasAdd    = 1,
+    HasMul    = 1,
     HasDiv    = 1,
     HasSqrt   = 1,
     HasRsqrt  = 1,
diff --git a/Eigen/src/Core/arch/NEON/Complex.h b/Eigen/src/Core/arch/NEON/Complex.h
index d2d467936..ccc00e5a6 100644
--- a/Eigen/src/Core/arch/NEON/Complex.h
+++ b/Eigen/src/Core/arch/NEON/Complex.h
@@ -14,8 +14,9 @@ namespace Eigen {
 
 namespace internal {
 
-static uint32x4_t p4ui_CONJ_XOR = EIGEN_INIT_NEON_PACKET4(0x00000000, 0x80000000, 0x00000000, 0x80000000);
-static uint32x2_t p2ui_CONJ_XOR = EIGEN_INIT_NEON_PACKET2(0x00000000, 0x80000000);
+const uint32_t  conj_XOR_DATA[] = { 0x00000000, 0x80000000, 0x00000000, 0x80000000 };
+static uint32x4_t p4ui_CONJ_XOR = vld1q_u32( conj_XOR_DATA );
+static uint32x2_t p2ui_CONJ_XOR = vld1_u32( conj_XOR_DATA );
 
 //---------- float ----------
 struct Packet2cf
@@ -274,7 +275,8 @@ ptranspose(PacketBlock<Packet2cf,2>& kernel) {
 //---------- double ----------
 #if EIGEN_ARCH_ARM64 && !EIGEN_APPLE_DOUBLE_NEON_BUG
 
-static uint64x2_t p2ul_CONJ_XOR = EIGEN_INIT_NEON_PACKET2(0x0, 0x8000000000000000);
+const uint64_t  p2ul_conj_XOR_DATA[] = { 0x0, 0x8000000000000000 };
+static uint64x2_t p2ul_CONJ_XOR = vld1q_u64( p2ul_conj_XOR_DATA );
 
 struct Packet1cd
 {
diff --git a/Eigen/src/Core/arch/NEON/PacketMath.h b/Eigen/src/Core/arch/NEON/PacketMath.h
index deb2d7e42..e1247696d 100644
--- a/Eigen/src/Core/arch/NEON/PacketMath.h
+++ b/Eigen/src/Core/arch/NEON/PacketMath.h
@@ -49,17 +49,6 @@ typedef uint32x4_t  Packet4ui;
 #define _EIGEN_DECLARE_CONST_Packet4i(NAME,X) \
   const Packet4i p4i_##NAME = pset1<Packet4i>(X)
 
-#if EIGEN_COMP_LLVM && !EIGEN_COMP_CLANG
-  //Special treatment for Apple's llvm-gcc, its NEON packet types are unions
-  #define EIGEN_INIT_NEON_PACKET2(X, Y)       {{X, Y}}
-  #define EIGEN_INIT_NEON_PACKET4(X, Y, Z, W) {{X, Y, Z, W}}
-#else
-  //Default initializer for packets
-  #define EIGEN_INIT_NEON_PACKET2(X, Y)       {X, Y}
-  #define EIGEN_INIT_NEON_PACKET4(X, Y, Z, W) {X, Y, Z, W}
-#endif
-
-
 // arm64 does have the pld instruction. If available, let's trust the __builtin_prefetch built-in function
 // which available on LLVM and GCC (at least)
 #if EIGEN_HAS_BUILTIN(__builtin_prefetch) || EIGEN_COMP_GNUC
@@ -122,12 +111,14 @@ template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int&    from)   {
 
 template<> EIGEN_STRONG_INLINE Packet4f plset<Packet4f>(const float& a)
 {
-  Packet4f countdown = EIGEN_INIT_NEON_PACKET4(0, 1, 2, 3);
+  const float32_t f[] = {0, 1, 2, 3};
+  Packet4f countdown = vld1q_f32(f);
   return vaddq_f32(pset1<Packet4f>(a), countdown);
 }
 template<> EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int& a)
 {
-  Packet4i countdown = EIGEN_INIT_NEON_PACKET4(0, 1, 2, 3);
+  const int32_t i[] = {0, 1, 2, 3};
+  Packet4i countdown = vld1q_s32(i);
   return vaddq_s32(pset1<Packet4i>(a), countdown);
 }
 
@@ -585,7 +576,8 @@ template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double&  from) { r
 
 template<> EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a)
 {
-  Packet2d countdown = EIGEN_INIT_NEON_PACKET2(0, 1);
+  const double countdown_raw[] = {0.0,1.0};
+  const Packet2d countdown = vld1q_f64(countdown_raw);
   return vaddq_f64(pset1<Packet2d>(a), countdown);
 }
 template<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return vaddq_f64(a,b); }
diff --git a/Eigen/src/Core/util/Meta.h b/Eigen/src/Core/util/Meta.h
index efb9961ce..a4a491ff8 100644
--- a/Eigen/src/Core/util/Meta.h
+++ b/Eigen/src/Core/util/Meta.h
@@ -328,6 +328,30 @@ struct result_of<Func(ArgType0,ArgType1)> {
     enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};
     typedef typename binary_result_of_select<Func, ArgType0, ArgType1, FunctorType>::type type;
 };
+
+template<typename Func, typename ArgType0, typename ArgType1, typename ArgType2, int SizeOf=sizeof(has_none)>
+struct ternary_result_of_select {typedef typename internal::remove_all<ArgType0>::type type;};
+
+template<typename Func, typename ArgType0, typename ArgType1, typename ArgType2>
+struct ternary_result_of_select<Func, ArgType0, ArgType1, ArgType2, sizeof(has_std_result_type)>
+{typedef typename Func::result_type type;};
+
+template<typename Func, typename ArgType0, typename ArgType1, typename ArgType2>
+struct ternary_result_of_select<Func, ArgType0, ArgType1, ArgType2, sizeof(has_tr1_result)>
+{typedef typename Func::template result<Func(ArgType0,ArgType1,ArgType2)>::type type;};
+
+template<typename Func, typename ArgType0, typename ArgType1, typename ArgType2>
+struct result_of<Func(ArgType0,ArgType1,ArgType2)> {
+    template<typename T>
+    static has_std_result_type    testFunctor(T const *, typename T::result_type const * = 0);
+    template<typename T>
+    static has_tr1_result         testFunctor(T const *, typename T::template result<T(ArgType0,ArgType1,ArgType2)>::type const * = 0);
+    static has_none               testFunctor(...);
+
+    // note that the following indirection is needed for gcc-3.3
+    enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};
+    typedef typename ternary_result_of_select<Func, ArgType0, ArgType1, ArgType2, FunctorType>::type type;
+};
 #endif
 
 /** \internal In short, it computes int(sqrt(\a Y)) with \a Y an integer.
diff --git a/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h b/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h
index 07a9ccf46..650617ca7 100644
--- a/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h
+++ b/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h
@@ -327,33 +327,22 @@ GeneralizedEigenSolver<MatrixType>::compute(const MatrixType& A, const MatrixTyp
       }
       else
       {
-        // We need to extract the generalized eigenvalues of the pair of a general 2x2 block S and a triangular 2x2 block T
-        // From the eigen decomposition of T = U * E * U^-1,
-        // we can extract the eigenvalues of (U^-1 * S * U) / E
-        // Here, we can take advantage that E = diag(T), and U = [ 1 T_01 ; 0 T_11-T_00], and U^-1 = [1 -T_11/(T_11-T_00) ; 0 1/(T_11-T_00)].
-        // Then taking beta=T_00*T_11*(T_11-T_00), we can avoid any division, and alpha is the eigenvalues of A = (U^-1 * S * U) * diag(T_11,T_00) * (T_11-T_00):
-
-        // T =  [a b ; 0 c]
-        // S =  [e f ; g h]
-        RealScalar a = m_realQZ.matrixT().coeff(i, i), b = m_realQZ.matrixT().coeff(i, i+1), c = m_realQZ.matrixT().coeff(i+1, i+1);
-        RealScalar e = m_matS.coeff(i, i), f = m_matS.coeff(i, i+1), g = m_matS.coeff(i+1, i), h = m_matS.coeff(i+1, i+1);
-        RealScalar d = c-a;
-        RealScalar gb = g*b;
-        Matrix<RealScalar,2,2> A;
-        A <<  (e*d-gb)*c,  ((e*b+f*d-h*b)*d-gb*b)*a,
-              g*c       ,  (gb+h*d)*a;
-
-        // NOTE, we could also compute the SVD of T's block during the QZ factorization so that the respective T block is guaranteed to be diagonal,
-        // and then we could directly apply the formula below (while taking care of scaling S columns by T11,T00):
-
-        Scalar p = Scalar(0.5) * (A.coeff(i, i) - A.coeff(i+1, i+1));
-        Scalar z = sqrt(abs(p * p + A.coeff(i+1, i) * A.coeff(i, i+1)));
-        m_alphas.coeffRef(i)   = ComplexScalar(A.coeff(i+1, i+1) + p, z);
-        m_alphas.coeffRef(i+1) = ComplexScalar(A.coeff(i+1, i+1) + p, -z);
+        // We need to extract the generalized eigenvalues of the pair of a general 2x2 block S and a positive diagonal 2x2 block T
+        // Then taking beta=T_00*T_11, we can avoid any division, and alpha is the eigenvalues of A = (U^-1 * S * U) * diag(T_11,T_00):
 
-        m_betas.coeffRef(i)   =
-        m_betas.coeffRef(i+1) = a*c*d;
+        // T =  [a 0]
+        //      [0 b]
+        RealScalar a = m_realQZ.matrixT().coeff(i, i), b = m_realQZ.matrixT().coeff(i+1, i+1);
+        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));
+        Scalar z = sqrt(abs(p * p + S2.coeff(1,0) * S2.coeff(0,1)));
+        m_alphas.coeffRef(i)   = ComplexScalar(S2.coeff(1,1) + p,  z);
+        m_alphas.coeffRef(i+1) = ComplexScalar(S2.coeff(1,1) + p, -z);
 
+        m_betas.coeffRef(i)   =
+        m_betas.coeffRef(i+1) = a*b;
+        
         i += 2;
       }
     }
diff --git a/Eigen/src/Eigenvalues/RealQZ.h b/Eigen/src/Eigenvalues/RealQZ.h
index a62071d42..b3a910dd9 100644
--- a/Eigen/src/Eigenvalues/RealQZ.h
+++ b/Eigen/src/Eigenvalues/RealQZ.h
@@ -552,7 +552,6 @@ namespace Eigen {
       m_T.coeffRef(l,l-1) = Scalar(0.0);
     }
 
-
   template<typename MatrixType>
     RealQZ<MatrixType>& RealQZ<MatrixType>::compute(const MatrixType& A_in, const MatrixType& B_in, bool computeQZ)
     {
@@ -616,6 +615,37 @@ namespace Eigen {
       }
       // check if we converged before reaching iterations limit
       m_info = (local_iter<m_maxIters) ? Success : NoConvergence;
+
+      // For each non triangular 2x2 diagonal block of S,
+      //    reduce the respective 2x2 diagonal block of T to positive diagonal form using 2x2 SVD.
+      // This step is not mandatory for QZ, but it does help further extraction of eigenvalues/eigenvectors,
+      // and is in par with Lapack/Matlab QZ.
+      if(m_info==Success)
+      {
+        for(Index i=0; i<dim-1; ++i)
+        {
+          if(m_S.coeff(i+1, i) != Scalar(0))
+          {
+            JacobiRotation<Scalar> j_left, j_right;
+            internal::real_2x2_jacobi_svd(m_T, i, i+1, &j_left, &j_right);
+
+            // Apply resulting Jacobi rotations
+            m_S.applyOnTheLeft(i,i+1,j_left);
+            m_S.applyOnTheRight(i,i+1,j_right);
+            m_T.applyOnTheLeft(i,i+1,j_left);
+            m_T.applyOnTheRight(i,i+1,j_right);
+            m_T(i+1,i) = m_T(i,i+1) = Scalar(0);
+
+            if(m_computeQZ) {
+              m_Q.applyOnTheRight(i,i+1,j_left.transpose());
+              m_Z.applyOnTheLeft(i,i+1,j_right.transpose());
+            }
+
+            i++;
+          }
+        }
+      }
+
       return *this;
     } // end compute
 
diff --git a/Eigen/src/Eigenvalues/Tridiagonalization.h b/Eigen/src/Eigenvalues/Tridiagonalization.h
index 2030b5be1..1d102c17b 100644
--- a/Eigen/src/Eigenvalues/Tridiagonalization.h
+++ b/Eigen/src/Eigenvalues/Tridiagonalization.h
@@ -367,10 +367,10 @@ void tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs)
     hCoeffs.tail(n-i-1).noalias() = (matA.bottomRightCorner(remainingSize,remainingSize).template selfadjointView<Lower>()
                                   * (conj(h) * matA.col(i).tail(remainingSize)));
 
-    hCoeffs.tail(n-i-1) += (conj(h)*Scalar(-0.5)*(hCoeffs.tail(remainingSize).dot(matA.col(i).tail(remainingSize)))) * matA.col(i).tail(n-i-1);
+    hCoeffs.tail(n-i-1) += (conj(h)*RealScalar(-0.5)*(hCoeffs.tail(remainingSize).dot(matA.col(i).tail(remainingSize)))) * matA.col(i).tail(n-i-1);
 
     matA.bottomRightCorner(remainingSize, remainingSize).template selfadjointView<Lower>()
-      .rankUpdate(matA.col(i).tail(remainingSize), hCoeffs.tail(remainingSize), -1);
+      .rankUpdate(matA.col(i).tail(remainingSize), hCoeffs.tail(remainingSize), Scalar(-1));
 
     matA.col(i).coeffRef(i+1) = beta;
     hCoeffs.coeffRef(i) = h;
diff --git a/Eigen/src/Geometry/Transform.h b/Eigen/src/Geometry/Transform.h
index 4fc876bcf..073f4dcd1 100644
--- a/Eigen/src/Geometry/Transform.h
+++ b/Eigen/src/Geometry/Transform.h
@@ -1367,7 +1367,7 @@ struct transform_right_product_impl< TransformType, MatrixType, 2, 1> // rhs is
     EIGEN_STATIC_ASSERT(OtherRows==Dim, YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES);
 
     Matrix<typename ResultType::Scalar, Dim+1, 1> rhs;
-    rhs << other,1;
+    rhs.template head<Dim>() = other; rhs[Dim] = typename ResultType::Scalar(1);
     Matrix<typename ResultType::Scalar, WorkingRows, 1> res(T.matrix() * rhs);
     return res.template head<Dim>();
   }
diff --git a/Eigen/src/PardisoSupport/PardisoSupport.h b/Eigen/src/PardisoSupport/PardisoSupport.h
index 80d914f25..091c3970e 100644
--- a/Eigen/src/PardisoSupport/PardisoSupport.h
+++ b/Eigen/src/PardisoSupport/PardisoSupport.h
@@ -183,7 +183,7 @@ class PardisoImpl : public SparseSolverBase<Derived>
     {
       if(m_isInitialized) // Factorization ran at least once
       {
-        internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, -1, m_size,0, 0, 0, m_perm.data(), 0,
+        internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, -1, internal::convert_index<StorageIndex>(m_size),0, 0, 0, m_perm.data(), 0,
                                                           m_iparm.data(), m_msglvl, NULL, NULL);
         m_isInitialized = false;
       }
@@ -194,11 +194,11 @@ class PardisoImpl : public SparseSolverBase<Derived>
       m_type = type;
       bool symmetric = std::abs(m_type) < 10;
       m_iparm[0] = 1;   // No solver default
-      m_iparm[1] = 3;   // use Metis for the ordering
-      m_iparm[2] = 1;   // Numbers of processors, value of OMP_NUM_THREADS
+      m_iparm[1] = 2;   // use Metis for the ordering
+      m_iparm[2] = 0;   // Reserved. Set to zero. (??Numbers of processors, value of OMP_NUM_THREADS??)
       m_iparm[3] = 0;   // No iterative-direct algorithm
       m_iparm[4] = 0;   // No user fill-in reducing permutation
-      m_iparm[5] = 0;   // Write solution into x
+      m_iparm[5] = 0;   // Write solution into x, b is left unchanged
       m_iparm[6] = 0;   // Not in use
       m_iparm[7] = 2;   // Max numbers of iterative refinement steps
       m_iparm[8] = 0;   // Not in use
@@ -219,7 +219,8 @@ class PardisoImpl : public SparseSolverBase<Derived>
       m_iparm[26] = 0;  // No matrix checker
       m_iparm[27] = (sizeof(RealScalar) == 4) ? 1 : 0;
       m_iparm[34] = 1;  // C indexing
-      m_iparm[59] = 1;  // Automatic switch between In-Core and Out-of-Core modes
+      m_iparm[36] = 0;  // CSR
+      m_iparm[59] = 0;  // 0 - In-Core ; 1 - Automatic switch between In-Core and Out-of-Core modes ; 2 - Out-of-Core
       
       memset(m_pt, 0, sizeof(m_pt));
     }
@@ -246,7 +247,7 @@ class PardisoImpl : public SparseSolverBase<Derived>
     mutable SparseMatrixType m_matrix;
     mutable ComputationInfo m_info;
     bool m_analysisIsOk, m_factorizationIsOk;
-    Index m_type, m_msglvl;
+    StorageIndex m_type, m_msglvl;
     mutable void *m_pt[64];
     mutable ParameterType m_iparm;
     mutable IntColVectorType m_perm;
@@ -265,10 +266,9 @@ Derived& PardisoImpl<Derived>::compute(const MatrixType& a)
   derived().getMatrix(a);
   
   Index error;
-  error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 12, m_size,
+  error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 12, internal::convert_index<StorageIndex>(m_size),
                                                             m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
                                                             m_perm.data(), 0, m_iparm.data(), m_msglvl, NULL, NULL);
-
   manageErrorCode(error);
   m_analysisIsOk = true;
   m_factorizationIsOk = true;
@@ -287,7 +287,7 @@ Derived& PardisoImpl<Derived>::analyzePattern(const MatrixType& a)
   derived().getMatrix(a);
   
   Index error;
-  error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 11, m_size,
+  error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 11, internal::convert_index<StorageIndex>(m_size),
                                                             m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
                                                             m_perm.data(), 0, m_iparm.data(), m_msglvl, NULL, NULL);
   
@@ -306,8 +306,8 @@ Derived& PardisoImpl<Derived>::factorize(const MatrixType& a)
   
   derived().getMatrix(a);
 
-  Index error;  
-  error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 22, m_size,
+  Index error;
+  error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 22, internal::convert_index<StorageIndex>(m_size),
                                                             m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
                                                             m_perm.data(), 0, m_iparm.data(), m_msglvl, NULL, NULL);
   
@@ -354,9 +354,9 @@ void PardisoImpl<Derived>::_solve_impl(const MatrixBase<BDerived> &b, MatrixBase
   }
   
   Index error;
-  error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 33, m_size,
+  error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 33, internal::convert_index<StorageIndex>(m_size),
                                                             m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
-                                                            m_perm.data(), nrhs, m_iparm.data(), m_msglvl,
+                                                            m_perm.data(), internal::convert_index<StorageIndex>(nrhs), m_iparm.data(), m_msglvl,
                                                             rhs_ptr, x.derived().data());
 
   manageErrorCode(error);
@@ -371,6 +371,9 @@ void PardisoImpl<Derived>::_solve_impl(const MatrixBase<BDerived> &b, MatrixBase
   * using the Intel MKL PARDISO library. The sparse matrix A must be squared and invertible.
   * The vectors or matrices X and B can be either dense or sparse.
   *
+  * By default, it runs in in-core mode. To enable PARDISO's out-of-core feature, set:
+  * \code solver.pardisoParameterArray()[59] = 1; \endcode
+  *
   * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
   *
   * \implsparsesolverconcept
@@ -421,6 +424,9 @@ class PardisoLU : public PardisoImpl< PardisoLU<MatrixType> >
   * using the Intel MKL PARDISO library. The sparse matrix A must be selfajoint and positive definite.
   * The vectors or matrices X and B can be either dense or sparse.
   *
+  * By default, it runs in in-core mode. To enable PARDISO's out-of-core feature, set:
+  * \code solver.pardisoParameterArray()[59] = 1; \endcode
+  *
   * \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
   * \tparam UpLo can be any bitwise combination of Upper, Lower. The default is Upper, meaning only the upper triangular part has to be used.
   *         Upper|Lower can be used to tell both triangular parts can be used as input.
@@ -480,6 +486,9 @@ class PardisoLLT : public PardisoImpl< PardisoLLT<MatrixType,_UpLo> >
   * For complex matrices, A can also be symmetric only, see the \a Options template parameter.
   * The vectors or matrices X and B can be either dense or sparse.
   *
+  * By default, it runs in in-core mode. To enable PARDISO's out-of-core feature, set:
+  * \code solver.pardisoParameterArray()[59] = 1; \endcode
+  *
   * \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
   * \tparam Options can be any bitwise combination of Upper, Lower, and Symmetric. The default is Upper, meaning only the upper triangular part has to be used.
   *         Symmetric can be used for symmetric, non-selfadjoint complex matrices, the default being to assume a selfadjoint matrix.
diff --git a/Eigen/src/SVD/JacobiSVD.h b/Eigen/src/SVD/JacobiSVD.h
index 1940c8294..b83fd7a4d 100644
--- a/Eigen/src/SVD/JacobiSVD.h
+++ b/Eigen/src/SVD/JacobiSVD.h
@@ -419,38 +419,6 @@ struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, true>
   }
 };
 
-template<typename MatrixType, typename RealScalar, typename Index>
-void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
-                         JacobiRotation<RealScalar> *j_left,
-                         JacobiRotation<RealScalar> *j_right)
-{
-  using std::sqrt;
-  using std::abs;
-  Matrix<RealScalar,2,2> m;
-  m << numext::real(matrix.coeff(p,p)), numext::real(matrix.coeff(p,q)),
-       numext::real(matrix.coeff(q,p)), numext::real(matrix.coeff(q,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))
-  {
-    rot1.s() = RealScalar(0);
-    rot1.c() = RealScalar(1);
-  }
-  else
-  {
-    // If d!=0, then t/d cannot overflow because the magnitude of the
-    // entries forming d are not too small compared to the ones forming t.
-    RealScalar u = t / d;
-    RealScalar tmp = sqrt(RealScalar(1) + numext::abs2(u));
-    rot1.s() = RealScalar(1) / tmp;
-    rot1.c() = u / tmp;
-  }
-  m.applyOnTheLeft(0,1,rot1);
-  j_right->makeJacobi(m,0,1);
-  *j_left = rot1 * j_right->transpose();
-}
-
 template<typename _MatrixType, int QRPreconditioner> 
 struct traits<JacobiSVD<_MatrixType,QRPreconditioner> >
 {
diff --git a/Eigen/src/misc/RealSvd2x2.h b/Eigen/src/misc/RealSvd2x2.h
new file mode 100644
index 000000000..cdd7777d2
--- /dev/null
+++ b/Eigen/src/misc/RealSvd2x2.h
@@ -0,0 +1,54 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2013-2016 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_REALSVD2X2_H
+#define EIGEN_REALSVD2X2_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename MatrixType, typename RealScalar, typename Index>
+void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
+                         JacobiRotation<RealScalar> *j_left,
+                         JacobiRotation<RealScalar> *j_right)
+{
+  using std::sqrt;
+  using std::abs;
+  Matrix<RealScalar,2,2> m;
+  m << numext::real(matrix.coeff(p,p)), numext::real(matrix.coeff(p,q)),
+       numext::real(matrix.coeff(q,p)), numext::real(matrix.coeff(q,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))
+  {
+    rot1.s() = RealScalar(0);
+    rot1.c() = RealScalar(1);
+  }
+  else
+  {
+    // If d!=0, then t/d cannot overflow because the magnitude of the
+    // entries forming d are not too small compared to the ones forming t.
+    RealScalar u = t / d;
+    RealScalar tmp = sqrt(RealScalar(1) + numext::abs2(u));
+    rot1.s() = RealScalar(1) / tmp;
+    rot1.c() = u / tmp;
+  }
+  m.applyOnTheLeft(0,1,rot1);
+  j_right->makeJacobi(m,0,1);
+  *j_left = rot1 * j_right->transpose();
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_REALSVD2X2_H
\ No newline at end of file
diff --git a/Eigen/src/plugins/ArrayCwiseUnaryOps.h b/Eigen/src/plugins/ArrayCwiseUnaryOps.h
index 4a6361d8a..9e42bb540 100644
--- a/Eigen/src/plugins/ArrayCwiseUnaryOps.h
+++ b/Eigen/src/plugins/ArrayCwiseUnaryOps.h
@@ -247,6 +247,7 @@ tan() const
   *
   * \sa tan(), asin(), acos()
   */
+EIGEN_DEVICE_FUNC
 inline const AtanReturnType
 atan() const
 {
@@ -288,6 +289,7 @@ asin() const
   *
   * \sa tan(), sinh(), cosh()
   */
+EIGEN_DEVICE_FUNC
 inline const TanhReturnType
 tanh() const
 {
@@ -301,6 +303,7 @@ tanh() const
   *
   * \sa sin(), tanh(), cosh()
   */
+EIGEN_DEVICE_FUNC
 inline const SinhReturnType
 sinh() const
 {
@@ -314,6 +317,7 @@ sinh() const
   *
   * \sa tan(), sinh(), cosh()
   */
+EIGEN_DEVICE_FUNC
 inline const CoshReturnType
 cosh() const
 {
@@ -331,6 +335,7 @@ cosh() const
   *
   * \sa digamma()
   */
+EIGEN_DEVICE_FUNC
 inline const LgammaReturnType
 lgamma() const
 {
@@ -345,6 +350,7 @@ lgamma() const
   *
   * \sa Eigen::digamma(), Eigen::polygamma(), lgamma()
   */
+EIGEN_DEVICE_FUNC
 inline const DigammaReturnType
 digamma() const
 {
@@ -363,6 +369,7 @@ digamma() const
   *
   * \sa erfc()
   */
+EIGEN_DEVICE_FUNC
 inline const ErfReturnType
 erf() const
 {
@@ -381,6 +388,7 @@ erf() const
   *
   * \sa erf()
   */
+EIGEN_DEVICE_FUNC
 inline const ErfcReturnType
 erfc() const
 {
@@ -436,6 +444,7 @@ cube() const
   *
   * \sa ceil(), floor()
   */
+EIGEN_DEVICE_FUNC
 inline const RoundReturnType
 round() const
 {
@@ -449,6 +458,7 @@ round() const
   *
   * \sa ceil(), round()
   */
+EIGEN_DEVICE_FUNC
 inline const FloorReturnType
 floor() const
 {
@@ -462,6 +472,7 @@ floor() const
   *
   * \sa floor(), round()
   */
+EIGEN_DEVICE_FUNC
 inline const CeilReturnType
 ceil() const
 {
@@ -475,6 +486,7 @@ ceil() const
   *
   * \sa isfinite(), isinf()
   */
+EIGEN_DEVICE_FUNC
 inline const IsNaNReturnType
 isNaN() const
 {
@@ -488,6 +500,7 @@ isNaN() const
   *
   * \sa isnan(), isfinite()
   */
+EIGEN_DEVICE_FUNC
 inline const IsInfReturnType
 isInf() const
 {
@@ -501,6 +514,7 @@ isInf() const
   *
   * \sa isnan(), isinf()
   */
+EIGEN_DEVICE_FUNC
 inline const IsFiniteReturnType
 isFinite() const
 {