[20/51] [partial] mahout git commit: (nojira) add native-viennaCL module to codebase. closes apache/mahout#241

[ap...@apache.org]

http://git-wip-us.apache.org/repos/asf/mahout/blob/f7c1f802/native-viennaCL/src/main/cpp/viennacl/linalg/host_based/matrix_operations.hpp
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diff --git a/native-viennaCL/src/main/cpp/viennacl/linalg/host_based/matrix_operations.hpp b/native-viennaCL/src/main/cpp/viennacl/linalg/host_based/matrix_operations.hpp
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+++ b/native-viennaCL/src/main/cpp/viennacl/linalg/host_based/matrix_operations.hpp
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+#ifndef VIENNACL_LINALG_HOST_BASED_MATRIX_OPERATIONS_HPP_
+#define VIENNACL_LINALG_HOST_BASED_MATRIX_OPERATIONS_HPP_
+
+/* =========================================================================
+   Copyright (c) 2010-2016, Institute for Microelectronics,
+                            Institute for Analysis and Scientific Computing,
+                            TU Wien.
+   Portions of this software are copyright by UChicago Argonne, LLC.
+
+                            -----------------
+                  ViennaCL - The Vienna Computing Library
+                            -----------------
+
+   Project Head:    Karl Rupp                   rupp@iue.tuwien.ac.at
+
+   (A list of authors and contributors can be found in the manual)
+
+   License:         MIT (X11), see file LICENSE in the base directory
+============================================================================= */
+
+/** @file  viennacl/linalg/host_based/matrix_operations.hpp
+    @brief Implementations of dense matrix related operations, including matrix-vector products, using a plain single-threaded or OpenMP-enabled execution on CPU.
+*/
+
+#include "viennacl/forwards.h"
+#include "viennacl/scalar.hpp"
+#include "viennacl/vector.hpp"
+#include "viennacl/vector_proxy.hpp"
+#include "viennacl/tools/tools.hpp"
+#include "viennacl/meta/enable_if.hpp"
+#include "viennacl/meta/predicate.hpp"
+#include "viennacl/meta/result_of.hpp"
+#include "viennacl/traits/size.hpp"
+#include "viennacl/traits/start.hpp"
+#include "viennacl/traits/handle.hpp"
+#include "viennacl/traits/stride.hpp"
+#include "viennacl/linalg/detail/op_applier.hpp"
+#include "viennacl/linalg/host_based/common.hpp"
+#include "viennacl/linalg/prod.hpp"
+
+// Minimum Matrix size(size1*size2) for using OpenMP on matrix operations:
+#ifndef VIENNACL_OPENMP_MATRIX_MIN_SIZE
+  #define VIENNACL_OPENMP_MATRIX_MIN_SIZE  5000
+#endif
+
+namespace viennacl
+{
+namespace linalg
+{
+namespace host_based
+{
+
+//
+// Introductory note: By convention, all dimensions are already checked in the dispatcher frontend. No need to double-check again in here!
+//
+
+template<typename DestNumericT, typename SrcNumericT>
+void convert(matrix_base<DestNumericT> & mat1, matrix_base<SrcNumericT> const & mat2)
+{
+  assert(mat1.row_major() == mat2.row_major() && bool("Addition/subtraction on mixed matrix layouts not supported yet!"));
+
+  DestNumericT      * data_A = detail::extract_raw_pointer<DestNumericT>(mat1);
+  SrcNumericT const * data_B = detail::extract_raw_pointer<SrcNumericT>(mat2);
+
+  vcl_size_t A_start1 = viennacl::traits::start1(mat1);
+  vcl_size_t A_start2 = viennacl::traits::start2(mat1);
+  vcl_size_t A_inc1   = viennacl::traits::stride1(mat1);
+  vcl_size_t A_inc2   = viennacl::traits::stride2(mat1);
+  vcl_size_t A_size1  = viennacl::traits::size1(mat1);
+  vcl_size_t A_size2  = viennacl::traits::size2(mat1);
+  vcl_size_t A_internal_size1  = viennacl::traits::internal_size1(mat1);
+  vcl_size_t A_internal_size2  = viennacl::traits::internal_size2(mat1);
+
+  vcl_size_t B_start1 = viennacl::traits::start1(mat2);
+  vcl_size_t B_start2 = viennacl::traits::start2(mat2);
+  vcl_size_t B_inc1   = viennacl::traits::stride1(mat2);
+  vcl_size_t B_inc2   = viennacl::traits::stride2(mat2);
+  vcl_size_t B_internal_size1  = viennacl::traits::internal_size1(mat2);
+  vcl_size_t B_internal_size2  = viennacl::traits::internal_size2(mat2);
+
+  if (mat1.row_major())
+  {
+    detail::matrix_array_wrapper<DestNumericT,      row_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+    detail::matrix_array_wrapper<SrcNumericT const, row_major, false> wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+
+#ifdef VIENNACL_WITH_OPENMP
+    #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+    for (long row = 0; row < static_cast<long>(A_size1); ++row)
+      for (vcl_size_t col = 0; col < A_size2; ++col)
+        wrapper_A(row, col) = static_cast<DestNumericT>(wrapper_B(row, col));
+  }
+  else
+  {
+    detail::matrix_array_wrapper<DestNumericT,      column_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+    detail::matrix_array_wrapper<SrcNumericT const, column_major, false> wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+
+#ifdef VIENNACL_WITH_OPENMP
+    #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+    for (long col = 0; col < static_cast<long>(A_size2); ++col)
+      for (vcl_size_t row = 0; row < A_size1; ++row)
+        wrapper_A(row, col) = static_cast<DestNumericT>(wrapper_B(row, col));
+  }
+}
+
+
+
+template<typename NumericT,
+         typename SizeT, typename DistanceT>
+void trans(const matrix_expression<const matrix_base<NumericT, SizeT, DistanceT>,
+           const matrix_base<NumericT, SizeT, DistanceT>, op_trans> & proxy, matrix_base<NumericT> & temp_trans)
+{
+  typedef NumericT        value_type;
+  const value_type * data_A = detail::extract_raw_pointer<value_type>(proxy.lhs());
+  value_type * data_B       = detail::extract_raw_pointer<value_type>(temp_trans);
+
+  vcl_size_t A_start1         = viennacl::traits::start1(proxy.lhs());
+  vcl_size_t A_start2         = viennacl::traits::start2(proxy.lhs());
+  vcl_size_t A_internal_size1 = viennacl::traits::internal_size1(proxy.lhs());
+  vcl_size_t A_internal_size2 = viennacl::traits::internal_size2(proxy.lhs());
+  vcl_size_t A_inc1           = viennacl::traits::stride1(proxy.lhs());
+  vcl_size_t A_inc2           = viennacl::traits::stride2(proxy.lhs());
+  vcl_size_t A_size1          = viennacl::traits::size1(proxy.lhs());
+  vcl_size_t A_size2          = viennacl::traits::size2(proxy.lhs());
+
+  vcl_size_t B_start1         = viennacl::traits::start1(temp_trans);
+  vcl_size_t B_start2         = viennacl::traits::start2(temp_trans);
+  vcl_size_t B_internal_size1 = viennacl::traits::internal_size1(temp_trans);
+  vcl_size_t B_internal_size2 = viennacl::traits::internal_size2(temp_trans);
+  vcl_size_t B_inc1           = viennacl::traits::stride1(temp_trans);
+  vcl_size_t B_inc2           = viennacl::traits::stride2(temp_trans);
+
+  const vcl_size_t sub_mat_size = 64; //The matrix will be divided into sub-matrices for better storage access.
+
+  vcl_size_t row_count = A_size1 / sub_mat_size;
+  vcl_size_t col_count = A_size2 / sub_mat_size;
+
+  vcl_size_t row_count_remainder = A_size1 % sub_mat_size;
+  vcl_size_t col_count_remainder = A_size2 % sub_mat_size;
+
+  if (proxy.lhs().row_major())
+  {
+#ifdef VIENNACL_WITH_OPENMP
+    #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+    for(long i = 0; i < static_cast<long>(row_count*col_count); ++i)//This is the main part of the transposition
+    {
+      vcl_size_t row = vcl_size_t(i) / col_count;
+      vcl_size_t col = vcl_size_t(i) % col_count;
+
+      detail::matrix_array_wrapper<value_type const, row_major, false> wrapper_A(data_A, A_start1 + A_inc1 * (row * sub_mat_size)
+                                                                               , A_start2 + A_inc2 * (col * sub_mat_size), A_inc1
+                                                                               , A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type      , row_major, false> wrapper_B(data_B, B_start1 + B_inc1 * (col * sub_mat_size)
+                                                                               , B_start2 + B_inc2 * (row * sub_mat_size), B_inc1
+                                                                               , B_inc2, B_internal_size1, B_internal_size2);
+      for(vcl_size_t j = 0; j < (sub_mat_size); ++j)
+        for(vcl_size_t k = 0; k < (sub_mat_size); ++k)
+          wrapper_B(j, k) = wrapper_A(k, j);
+    }
+    { //This is the transposition of the remainder on the right side of the matrix
+      detail::matrix_array_wrapper<value_type const, row_major, false> wrapper_A(data_A, A_start1
+                                                                               , A_start2 + A_inc2 * (col_count * sub_mat_size), A_inc1
+                                                                               , A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type      , row_major, false> wrapper_B(data_B, B_start1 + B_inc1 * (col_count * sub_mat_size)
+                                                                               , B_start2, B_inc1
+                                                                               , B_inc2, B_internal_size1, B_internal_size2);
+      for(vcl_size_t j = 0; j < col_count_remainder; ++j)
+        for(vcl_size_t k = 0 ; k < A_size1; ++k)
+          wrapper_B(j, k) = wrapper_A(k, j);
+    }
+    { //This is the transposition of the remainder on the bottom side of the matrix
+      detail::matrix_array_wrapper<value_type const, row_major, false> wrapper_A(data_A, A_start1 + A_inc1 * (row_count * sub_mat_size)
+                                                                               , A_start2, A_inc1
+                                                                               , A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type      , row_major, false> wrapper_B(data_B,B_start1
+                                                                               , B_start2  + B_inc2 * (row_count * sub_mat_size), B_inc1
+                                                                               , B_inc2, B_internal_size1, B_internal_size2);
+      for(vcl_size_t j = 0; j < row_count_remainder; ++j)
+        for(vcl_size_t k = 0; k < (A_size2 - col_count_remainder); ++k)
+          wrapper_B(k, j) = wrapper_A(j, k);
+    }
+  }
+  else
+  {
+#ifdef VIENNACL_WITH_OPENMP
+    #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+    for(long i = 0; i < static_cast<long>(row_count*col_count); ++i)//This is the main part of the transposition
+    {
+      vcl_size_t row = vcl_size_t(i) / col_count;
+      vcl_size_t col = vcl_size_t(i) % col_count;
+
+      detail::matrix_array_wrapper<value_type const, column_major, false> wrapper_A(data_A, A_start1 + A_inc1 * (row * sub_mat_size)
+                                                                                  , A_start2 + A_inc2 * (col * sub_mat_size), A_inc1
+                                                                                  , A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type      , column_major, false> wrapper_B(data_B, B_start1 + B_inc1 * (col * sub_mat_size)
+                                                                                  , B_start2 + B_inc2 * (row * sub_mat_size), B_inc1
+                                                                                  , B_inc2, B_internal_size1, B_internal_size2);
+      for(vcl_size_t j = 0; j < (sub_mat_size); ++j)
+        for(vcl_size_t k = 0; k < (sub_mat_size); ++k)
+          wrapper_B(k, j)=wrapper_A(j, k);
+    }
+    { //This is the transposition of the remainder on the right side of the matrix
+      detail::matrix_array_wrapper<value_type const, column_major, false> wrapper_A(data_A, A_start1
+                                                                                  , A_start2 + A_inc2 * (col_count * sub_mat_size), A_inc1
+                                                                                  , A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type      , column_major, false> wrapper_B(data_B,B_start1 + B_inc1 * (col_count * sub_mat_size)
+                                                                                  , B_start2, B_inc1
+                                                                                  , B_inc2, B_internal_size1, B_internal_size2);
+      for(vcl_size_t j = 0; j < col_count_remainder; ++j)
+        for(vcl_size_t k = 0; k < A_size1; ++k)
+          wrapper_B(j, k)=wrapper_A(k, j);
+    }
+    { //This is the transposition of the remainder on the bottom side of the matrix
+      detail::matrix_array_wrapper<value_type const, column_major, false> wrapper_A(data_A, A_start1 + A_inc1 * (row_count * sub_mat_size)
+                                                                                  , A_start2, A_inc1
+                                                                                  , A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type      , column_major, false> wrapper_B(data_B, B_start1
+                                                                                  , B_start2  + B_inc2 * (row_count * sub_mat_size), B_inc1
+                                                                                  , B_inc2, B_internal_size1, B_internal_size2);
+      for(vcl_size_t j = 0; j < row_count_remainder; ++j)
+        for(vcl_size_t k = 0; k < (A_size2 - col_count_remainder); ++k)
+          wrapper_B(k, j)=wrapper_A(j, k);
+    }
+  }
+}
+
+template<typename NumericT, typename ScalarT1>
+void am(matrix_base<NumericT> & mat1,
+        matrix_base<NumericT> const & mat2, ScalarT1 const & alpha, vcl_size_t /*len_alpha*/, bool reciprocal_alpha, bool flip_sign_alpha)
+{
+  assert(mat1.row_major() == mat2.row_major() && bool("Addition/subtraction on mixed matrix layouts not supported yet!"));
+
+  typedef NumericT        value_type;
+
+  value_type       * data_A = detail::extract_raw_pointer<value_type>(mat1);
+  value_type const * data_B = detail::extract_raw_pointer<value_type>(mat2);
+
+  value_type data_alpha = alpha;
+  if (flip_sign_alpha)
+    data_alpha = -data_alpha;
+
+  vcl_size_t A_start1 = viennacl::traits::start1(mat1);
+  vcl_size_t A_start2 = viennacl::traits::start2(mat1);
+  vcl_size_t A_inc1   = viennacl::traits::stride1(mat1);
+  vcl_size_t A_inc2   = viennacl::traits::stride2(mat1);
+  vcl_size_t A_size1  = viennacl::traits::size1(mat1);
+  vcl_size_t A_size2  = viennacl::traits::size2(mat1);
+  vcl_size_t A_internal_size1  = viennacl::traits::internal_size1(mat1);
+  vcl_size_t A_internal_size2  = viennacl::traits::internal_size2(mat1);
+
+  vcl_size_t B_start1 = viennacl::traits::start1(mat2);
+  vcl_size_t B_start2 = viennacl::traits::start2(mat2);
+  vcl_size_t B_inc1   = viennacl::traits::stride1(mat2);
+  vcl_size_t B_inc2   = viennacl::traits::stride2(mat2);
+  vcl_size_t B_internal_size1  = viennacl::traits::internal_size1(mat2);
+  vcl_size_t B_internal_size2  = viennacl::traits::internal_size2(mat2);
+
+  if (mat1.row_major())
+  {
+    detail::matrix_array_wrapper<value_type,       row_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+    detail::matrix_array_wrapper<value_type const, row_major, false> wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+
+    if (reciprocal_alpha)
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long row = 0; row < static_cast<long>(A_size1); ++row)
+        for (vcl_size_t col = 0; col < A_size2; ++col)
+          wrapper_A(row, col) = wrapper_B(row, col) / data_alpha;
+    }
+    else
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long row = 0; row < static_cast<long>(A_size1); ++row)
+        for (vcl_size_t col = 0; col < A_size2; ++col)
+          wrapper_A(row, col) = wrapper_B(row, col) * data_alpha;
+    }
+  }
+  else
+  {
+    detail::matrix_array_wrapper<value_type,       column_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+    detail::matrix_array_wrapper<value_type const, column_major, false> wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+
+    if (reciprocal_alpha)
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long col = 0; col < static_cast<long>(A_size2); ++col)
+        for (vcl_size_t row = 0; row < A_size1; ++row)
+          wrapper_A(row, col) = wrapper_B(row, col) / data_alpha;
+    }
+    else
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long col = 0; col < static_cast<long>(A_size2); ++col)
+        for (vcl_size_t row = 0; row < A_size1; ++row)
+          wrapper_A(row, col) = wrapper_B(row, col) * data_alpha;
+    }
+  }
+}
+
+
+template<typename NumericT,
+         typename ScalarT1, typename ScalarT2>
+void ambm(matrix_base<NumericT> & mat1,
+          matrix_base<NumericT> const & mat2, ScalarT1 const & alpha, vcl_size_t /*len_alpha*/, bool reciprocal_alpha, bool flip_sign_alpha,
+          matrix_base<NumericT> const & mat3, ScalarT2 const & beta,  vcl_size_t /*len_beta*/,  bool reciprocal_beta,  bool flip_sign_beta)
+{
+  assert(mat1.row_major() == mat2.row_major() && mat1.row_major() == mat3.row_major() && bool("Addition/subtraction on mixed matrix layouts not supported yet!"));
+
+  typedef NumericT        value_type;
+
+  value_type       * data_A = detail::extract_raw_pointer<value_type>(mat1);
+  value_type const * data_B = detail::extract_raw_pointer<value_type>(mat2);
+  value_type const * data_C = detail::extract_raw_pointer<value_type>(mat3);
+
+  value_type data_alpha = alpha;
+  if (flip_sign_alpha)
+    data_alpha = -data_alpha;
+
+  value_type data_beta = beta;
+  if (flip_sign_beta)
+    data_beta = -data_beta;
+
+  vcl_size_t A_start1 = viennacl::traits::start1(mat1);
+  vcl_size_t A_start2 = viennacl::traits::start2(mat1);
+  vcl_size_t A_inc1   = viennacl::traits::stride1(mat1);
+  vcl_size_t A_inc2   = viennacl::traits::stride2(mat1);
+  vcl_size_t A_size1  = viennacl::traits::size1(mat1);
+  vcl_size_t A_size2  = viennacl::traits::size2(mat1);
+  vcl_size_t A_internal_size1  = viennacl::traits::internal_size1(mat1);
+  vcl_size_t A_internal_size2  = viennacl::traits::internal_size2(mat1);
+
+  vcl_size_t B_start1 = viennacl::traits::start1(mat2);
+  vcl_size_t B_start2 = viennacl::traits::start2(mat2);
+  vcl_size_t B_inc1   = viennacl::traits::stride1(mat2);
+  vcl_size_t B_inc2   = viennacl::traits::stride2(mat2);
+  vcl_size_t B_internal_size1  = viennacl::traits::internal_size1(mat2);
+  vcl_size_t B_internal_size2  = viennacl::traits::internal_size2(mat2);
+
+  vcl_size_t C_start1 = viennacl::traits::start1(mat3);
+  vcl_size_t C_start2 = viennacl::traits::start2(mat3);
+  vcl_size_t C_inc1   = viennacl::traits::stride1(mat3);
+  vcl_size_t C_inc2   = viennacl::traits::stride2(mat3);
+  vcl_size_t C_internal_size1  = viennacl::traits::internal_size1(mat3);
+  vcl_size_t C_internal_size2  = viennacl::traits::internal_size2(mat3);
+
+  if (mat1.row_major())
+  {
+    detail::matrix_array_wrapper<value_type,       row_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+    detail::matrix_array_wrapper<value_type const, row_major, false> wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+    detail::matrix_array_wrapper<value_type const, row_major, false> wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+    if (reciprocal_alpha && reciprocal_beta)
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long row = 0; row < static_cast<long>(A_size1); ++row)
+        for (vcl_size_t col = 0; col < A_size2; ++col)
+          wrapper_A(row, col) = wrapper_B(row, col) / data_alpha + wrapper_C(row, col) / data_beta;
+    }
+    else if (reciprocal_alpha && !reciprocal_beta)
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long row = 0; row < static_cast<long>(A_size1); ++row)
+        for (vcl_size_t col = 0; col < A_size2; ++col)
+          wrapper_A(row, col) = wrapper_B(row, col) / data_alpha + wrapper_C(row, col) * data_beta;
+    }
+    else if (!reciprocal_alpha && reciprocal_beta)
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long row = 0; row < static_cast<long>(A_size1); ++row)
+        for (vcl_size_t col = 0; col < A_size2; ++col)
+          wrapper_A(row, col) = wrapper_B(row, col) * data_alpha + wrapper_C(row, col) / data_beta;
+    }
+    else if (!reciprocal_alpha && !reciprocal_beta)
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long row = 0; row < static_cast<long>(A_size1); ++row)
+        for (vcl_size_t col = 0; col < A_size2; ++col)
+          wrapper_A(row, col) = wrapper_B(row, col) * data_alpha + wrapper_C(row, col) * data_beta;
+    }
+  }
+  else
+  {
+    detail::matrix_array_wrapper<value_type,       column_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+    detail::matrix_array_wrapper<value_type const, column_major, false> wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+    detail::matrix_array_wrapper<value_type const, column_major, false> wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+    if (reciprocal_alpha && reciprocal_beta)
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long col = 0; col < static_cast<long>(A_size2); ++col)
+        for (vcl_size_t row = 0; row < A_size1; ++row)
+          wrapper_A(row, col) = wrapper_B(row, col) / data_alpha + wrapper_C(row, col) / data_beta;
+    }
+    else if (reciprocal_alpha && !reciprocal_beta)
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long col = 0; col < static_cast<long>(A_size2); ++col)
+        for (vcl_size_t row = 0; row < A_size1; ++row)
+          wrapper_A(row, col) = wrapper_B(row, col) / data_alpha + wrapper_C(row, col) * data_beta;
+    }
+    else if (!reciprocal_alpha && reciprocal_beta)
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long col = 0; col < static_cast<long>(A_size2); ++col)
+        for (vcl_size_t row = 0; row < A_size1; ++row)
+          wrapper_A(row, col) = wrapper_B(row, col) * data_alpha + wrapper_C(row, col) / data_beta;
+    }
+    else if (!reciprocal_alpha && !reciprocal_beta)
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long col = 0; col < static_cast<long>(A_size2); ++col)
+        for (vcl_size_t row = 0; row < A_size1; ++row)
+          wrapper_A(row, col) = wrapper_B(row, col) * data_alpha + wrapper_C(row, col) * data_beta;
+    }
+  }
+
+}
+
+
+template<typename NumericT,
+         typename ScalarT1, typename ScalarT2>
+void ambm_m(matrix_base<NumericT> & mat1,
+            matrix_base<NumericT> const & mat2, ScalarT1 const & alpha, vcl_size_t /*len_alpha*/, bool reciprocal_alpha, bool flip_sign_alpha,
+            matrix_base<NumericT> const & mat3, ScalarT2 const & beta,  vcl_size_t /*len_beta*/,  bool reciprocal_beta,  bool flip_sign_beta)
+{
+  assert(mat1.row_major() == mat2.row_major() && mat1.row_major() == mat3.row_major() && bool("Addition/subtraction on mixed matrix layouts not supported yet!"));
+
+  typedef NumericT        value_type;
+
+  value_type       * data_A = detail::extract_raw_pointer<value_type>(mat1);
+  value_type const * data_B = detail::extract_raw_pointer<value_type>(mat2);
+  value_type const * data_C = detail::extract_raw_pointer<value_type>(mat3);
+
+  value_type data_alpha = alpha;
+  if (flip_sign_alpha)
+    data_alpha = -data_alpha;
+
+  value_type data_beta = beta;
+  if (flip_sign_beta)
+    data_beta = -data_beta;
+
+  vcl_size_t A_start1 = viennacl::traits::start1(mat1);
+  vcl_size_t A_start2 = viennacl::traits::start2(mat1);
+  vcl_size_t A_inc1   = viennacl::traits::stride1(mat1);
+  vcl_size_t A_inc2   = viennacl::traits::stride2(mat1);
+  vcl_size_t A_size1  = viennacl::traits::size1(mat1);
+  vcl_size_t A_size2  = viennacl::traits::size2(mat1);
+  vcl_size_t A_internal_size1  = viennacl::traits::internal_size1(mat1);
+  vcl_size_t A_internal_size2  = viennacl::traits::internal_size2(mat1);
+
+  vcl_size_t B_start1 = viennacl::traits::start1(mat2);
+  vcl_size_t B_start2 = viennacl::traits::start2(mat2);
+  vcl_size_t B_inc1   = viennacl::traits::stride1(mat2);
+  vcl_size_t B_inc2   = viennacl::traits::stride2(mat2);
+  vcl_size_t B_internal_size1  = viennacl::traits::internal_size1(mat2);
+  vcl_size_t B_internal_size2  = viennacl::traits::internal_size2(mat2);
+
+  vcl_size_t C_start1 = viennacl::traits::start1(mat3);
+  vcl_size_t C_start2 = viennacl::traits::start2(mat3);
+  vcl_size_t C_inc1   = viennacl::traits::stride1(mat3);
+  vcl_size_t C_inc2   = viennacl::traits::stride2(mat3);
+  vcl_size_t C_internal_size1  = viennacl::traits::internal_size1(mat3);
+  vcl_size_t C_internal_size2  = viennacl::traits::internal_size2(mat3);
+
+  if (mat1.row_major())
+  {
+    detail::matrix_array_wrapper<value_type,       row_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+    detail::matrix_array_wrapper<value_type const, row_major, false> wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+    detail::matrix_array_wrapper<value_type const, row_major, false> wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+    if (reciprocal_alpha && reciprocal_beta)
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long row = 0; row < static_cast<long>(A_size1); ++row)
+        for (vcl_size_t col = 0; col < A_size2; ++col)
+          wrapper_A(row, col) += wrapper_B(row, col) / data_alpha + wrapper_C(row, col) / data_beta;
+    }
+    else if (reciprocal_alpha && !reciprocal_beta)
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long row = 0; row < static_cast<long>(A_size1); ++row)
+        for (vcl_size_t col = 0; col < A_size2; ++col)
+          wrapper_A(row, col) += wrapper_B(row, col) / data_alpha + wrapper_C(row, col) * data_beta;
+    }
+    else if (!reciprocal_alpha && reciprocal_beta)
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long row = 0; row < static_cast<long>(A_size1); ++row)
+        for (vcl_size_t col = 0; col < A_size2; ++col)
+          wrapper_A(row, col) += wrapper_B(row, col) * data_alpha + wrapper_C(row, col) / data_beta;
+    }
+    else if (!reciprocal_alpha && !reciprocal_beta)
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long row = 0; row < static_cast<long>(A_size1); ++row)
+        for (vcl_size_t col = 0; col < A_size2; ++col)
+          wrapper_A(row, col) += wrapper_B(row, col) * data_alpha + wrapper_C(row, col) * data_beta;
+    }
+  }
+  else
+  {
+    detail::matrix_array_wrapper<value_type,       column_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+    detail::matrix_array_wrapper<value_type const, column_major, false> wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+    detail::matrix_array_wrapper<value_type const, column_major, false> wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+    if (reciprocal_alpha && reciprocal_beta)
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long col = 0; col < static_cast<long>(A_size2); ++col)
+        for (vcl_size_t row = 0; row < A_size1; ++row)
+          wrapper_A(row, col) += wrapper_B(row, col) / data_alpha + wrapper_C(row, col) / data_beta;
+    }
+    else if (reciprocal_alpha && !reciprocal_beta)
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long col = 0; col < static_cast<long>(A_size2); ++col)
+        for (vcl_size_t row = 0; row < A_size1; ++row)
+          wrapper_A(row, col) += wrapper_B(row, col) / data_alpha + wrapper_C(row, col) * data_beta;
+    }
+    else if (!reciprocal_alpha && reciprocal_beta)
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long col = 0; col < static_cast<long>(A_size2); ++col)
+        for (vcl_size_t row = 0; row < A_size1; ++row)
+          wrapper_A(row, col) += wrapper_B(row, col) * data_alpha + wrapper_C(row, col) / data_beta;
+    }
+    else if (!reciprocal_alpha && !reciprocal_beta)
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long col = 0; col < static_cast<long>(A_size2); ++col)
+        for (vcl_size_t row = 0; row < A_size1; ++row)
+          wrapper_A(row, col) += wrapper_B(row, col) * data_alpha + wrapper_C(row, col) * data_beta;
+    }
+  }
+
+}
+
+
+
+
+template<typename NumericT>
+void matrix_assign(matrix_base<NumericT> & mat, NumericT s, bool clear = false)
+{
+  typedef NumericT        value_type;
+
+  value_type * data_A = detail::extract_raw_pointer<value_type>(mat);
+  value_type    alpha = static_cast<value_type>(s);
+
+  vcl_size_t A_start1 = viennacl::traits::start1(mat);
+  vcl_size_t A_start2 = viennacl::traits::start2(mat);
+  vcl_size_t A_inc1   = viennacl::traits::stride1(mat);
+  vcl_size_t A_inc2   = viennacl::traits::stride2(mat);
+  vcl_size_t A_size1  = clear ? viennacl::traits::internal_size1(mat) : viennacl::traits::size1(mat);
+  vcl_size_t A_size2  = clear ? viennacl::traits::internal_size2(mat) : viennacl::traits::size2(mat);
+  vcl_size_t A_internal_size1  = viennacl::traits::internal_size1(mat);
+  vcl_size_t A_internal_size2  = viennacl::traits::internal_size2(mat);
+
+  if (mat.row_major())
+  {
+    detail::matrix_array_wrapper<value_type, row_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+
+#ifdef VIENNACL_WITH_OPENMP
+    #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+    for (long row = 0; row < static_cast<long>(A_size1); ++row)
+      for (vcl_size_t col = 0; col < A_size2; ++col)
+        wrapper_A(static_cast<vcl_size_t>(row), col) = alpha;
+        //data_A[index_generator_A::mem_index(row * A_inc1 + A_start1, col * A_inc2 + A_start2, A_internal_size1, A_internal_size2)]
+        // = data_B[index_generator_B::mem_index(row * B_inc1 + B_start1, col * B_inc2 + B_start2, B_internal_size1, B_internal_size2)] * alpha;
+  }
+  else
+  {
+    detail::matrix_array_wrapper<value_type, column_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+
+#ifdef VIENNACL_WITH_OPENMP
+    #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+    for (long col = 0; col < static_cast<long>(A_size2); ++col)
+      for (vcl_size_t row = 0; row < A_size1; ++row)
+        wrapper_A(row, static_cast<vcl_size_t>(col)) = alpha;
+        //data_A[index_generator_A::mem_index(row * A_inc1 + A_start1, col * A_inc2 + A_start2, A_internal_size1, A_internal_size2)]
+        // = data_B[index_generator_B::mem_index(row * B_inc1 + B_start1, col * B_inc2 + B_start2, B_internal_size1, B_internal_size2)] * alpha;
+  }
+}
+
+
+
+template<typename NumericT>
+void matrix_diagonal_assign(matrix_base<NumericT> & mat, NumericT s)
+{
+  typedef NumericT        value_type;
+
+  value_type * data_A = detail::extract_raw_pointer<value_type>(mat);
+  value_type    alpha = static_cast<value_type>(s);
+
+  vcl_size_t A_start1 = viennacl::traits::start1(mat);
+  vcl_size_t A_start2 = viennacl::traits::start2(mat);
+  vcl_size_t A_inc1   = viennacl::traits::stride1(mat);
+  vcl_size_t A_inc2   = viennacl::traits::stride2(mat);
+  vcl_size_t A_size1  = viennacl::traits::size1(mat);
+  //vcl_size_t A_size2  = viennacl::traits::size2(mat);
+  vcl_size_t A_internal_size1  = viennacl::traits::internal_size1(mat);
+  vcl_size_t A_internal_size2  = viennacl::traits::internal_size2(mat);
+
+  if (mat.row_major())
+  {
+    detail::matrix_array_wrapper<value_type, row_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+
+#ifdef VIENNACL_WITH_OPENMP
+    #pragma omp parallel for if ((A_size1*A_size1) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+    for (long row = 0; row < static_cast<long>(A_size1); ++row)
+      wrapper_A(row, row) = alpha;
+  }
+  else
+  {
+    detail::matrix_array_wrapper<value_type, column_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+
+#ifdef VIENNACL_WITH_OPENMP
+    #pragma omp parallel for if ((A_size1*A_size1) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+    for (long row = 0; row < static_cast<long>(A_size1); ++row)
+      wrapper_A(row, row) = alpha;
+  }
+}
+
+template<typename NumericT>
+void matrix_diag_from_vector(const vector_base<NumericT> & vec, int k, matrix_base<NumericT> & mat)
+{
+  typedef NumericT        value_type;
+
+  value_type       *data_A   = detail::extract_raw_pointer<value_type>(mat);
+  value_type const *data_vec = detail::extract_raw_pointer<value_type>(vec);
+
+  vcl_size_t A_start1 = viennacl::traits::start1(mat);
+  vcl_size_t A_start2 = viennacl::traits::start2(mat);
+  vcl_size_t A_inc1   = viennacl::traits::stride1(mat);
+  vcl_size_t A_inc2   = viennacl::traits::stride2(mat);
+  //vcl_size_t A_size1  = viennacl::traits::size1(mat);
+  //vcl_size_t A_size2  = viennacl::traits::size2(mat);
+  vcl_size_t A_internal_size1  = viennacl::traits::internal_size1(mat);
+  vcl_size_t A_internal_size2  = viennacl::traits::internal_size2(mat);
+
+  vcl_size_t v_start = viennacl::traits::start(vec);
+  vcl_size_t v_inc   = viennacl::traits::stride(vec);
+  vcl_size_t v_size  = viennacl::traits::size(vec);
+
+  vcl_size_t row_start = 0;
+  vcl_size_t col_start = 0;
+
+  if (k >= 0)
+    col_start = static_cast<vcl_size_t>(k);
+  else
+    row_start = static_cast<vcl_size_t>(-k);
+
+  matrix_assign(mat, NumericT(0));
+
+  if (mat.row_major())
+  {
+    detail::matrix_array_wrapper<value_type, row_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+
+    for (vcl_size_t i = 0; i < v_size; ++i)
+      wrapper_A(row_start + i, col_start + i) = data_vec[v_start + i * v_inc];
+  }
+  else
+  {
+    detail::matrix_array_wrapper<value_type, column_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+
+    for (vcl_size_t i = 0; i < v_size; ++i)
+      wrapper_A(row_start + i, col_start + i) = data_vec[v_start + i * v_inc];
+  }
+}
+
+template<typename NumericT>
+void matrix_diag_to_vector(const matrix_base<NumericT> & mat, int k, vector_base<NumericT> & vec)
+{
+  typedef NumericT        value_type;
+
+  value_type const * data_A   = detail::extract_raw_pointer<value_type>(mat);
+  value_type       * data_vec = detail::extract_raw_pointer<value_type>(vec);
+
+  vcl_size_t A_start1 = viennacl::traits::start1(mat);
+  vcl_size_t A_start2 = viennacl::traits::start2(mat);
+  vcl_size_t A_inc1   = viennacl::traits::stride1(mat);
+  vcl_size_t A_inc2   = viennacl::traits::stride2(mat);
+  //vcl_size_t A_size1  = viennacl::traits::size1(mat);
+  //vcl_size_t A_size2  = viennacl::traits::size2(mat);
+  vcl_size_t A_internal_size1  = viennacl::traits::internal_size1(mat);
+  vcl_size_t A_internal_size2  = viennacl::traits::internal_size2(mat);
+
+  vcl_size_t v_start = viennacl::traits::start(vec);
+  vcl_size_t v_inc   = viennacl::traits::stride(vec);
+  vcl_size_t v_size  = viennacl::traits::size(vec);
+
+  vcl_size_t row_start = 0;
+  vcl_size_t col_start = 0;
+
+  if (k >= 0)
+    col_start = static_cast<vcl_size_t>(k);
+  else
+    row_start = static_cast<vcl_size_t>(-k);
+
+  if (mat.row_major())
+  {
+    detail::matrix_array_wrapper<value_type const, row_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+
+    for (vcl_size_t i = 0; i < v_size; ++i)
+      data_vec[v_start + i * v_inc] = wrapper_A(row_start + i, col_start + i);
+  }
+  else
+  {
+    detail::matrix_array_wrapper<value_type const, column_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+
+    for (vcl_size_t i = 0; i < v_size; ++i)
+      data_vec[v_start + i * v_inc] = wrapper_A(row_start + i, col_start + i);
+  }
+}
+
+template<typename NumericT>
+void matrix_row(const matrix_base<NumericT> & mat, unsigned int i, vector_base<NumericT> & vec)
+{
+  typedef NumericT        value_type;
+
+  value_type const * data_A   = detail::extract_raw_pointer<value_type>(mat);
+  value_type       * data_vec = detail::extract_raw_pointer<value_type>(vec);
+
+  vcl_size_t A_start1 = viennacl::traits::start1(mat);
+  vcl_size_t A_start2 = viennacl::traits::start2(mat);
+  vcl_size_t A_inc1   = viennacl::traits::stride1(mat);
+  vcl_size_t A_inc2   = viennacl::traits::stride2(mat);
+  //vcl_size_t A_size1  = viennacl::traits::size1(mat);
+  //vcl_size_t A_size2  = viennacl::traits::size2(mat);
+  vcl_size_t A_internal_size1  = viennacl::traits::internal_size1(mat);
+  vcl_size_t A_internal_size2  = viennacl::traits::internal_size2(mat);
+
+  vcl_size_t v_start = viennacl::traits::start(vec);
+  vcl_size_t v_inc   = viennacl::traits::stride(vec);
+  vcl_size_t v_size  = viennacl::traits::size(vec);
+
+  if (mat.row_major())
+  {
+    detail::matrix_array_wrapper<value_type const, row_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+
+    for (vcl_size_t j = 0; j < v_size; ++j)
+      data_vec[v_start + j * v_inc] = wrapper_A(static_cast<vcl_size_t>(i), j);
+  }
+  else
+  {
+    detail::matrix_array_wrapper<value_type const, column_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+
+    for (vcl_size_t j = 0; j < v_size; ++j)
+      data_vec[v_start + j * v_inc] = wrapper_A(static_cast<vcl_size_t>(i), j);
+  }
+}
+
+template<typename NumericT>
+void matrix_column(const matrix_base<NumericT> & mat, unsigned int j, vector_base<NumericT> & vec)
+{
+  typedef NumericT        value_type;
+
+  value_type const * data_A   = detail::extract_raw_pointer<value_type>(mat);
+  value_type       * data_vec = detail::extract_raw_pointer<value_type>(vec);
+
+  vcl_size_t A_start1 = viennacl::traits::start1(mat);
+  vcl_size_t A_start2 = viennacl::traits::start2(mat);
+  vcl_size_t A_inc1   = viennacl::traits::stride1(mat);
+  vcl_size_t A_inc2   = viennacl::traits::stride2(mat);
+  //vcl_size_t A_size1  = viennacl::traits::size1(mat);
+  //vcl_size_t A_size2  = viennacl::traits::size2(mat);
+  vcl_size_t A_internal_size1  = viennacl::traits::internal_size1(mat);
+  vcl_size_t A_internal_size2  = viennacl::traits::internal_size2(mat);
+
+  vcl_size_t v_start = viennacl::traits::start(vec);
+  vcl_size_t v_inc   = viennacl::traits::stride(vec);
+  vcl_size_t v_size  = viennacl::traits::size(vec);
+
+  if (mat.row_major())
+  {
+    detail::matrix_array_wrapper<value_type const, row_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+
+    for (vcl_size_t i = 0; i < v_size; ++i)
+      data_vec[v_start + i * v_inc] = wrapper_A(i, static_cast<vcl_size_t>(j));
+  }
+  else
+  {
+    detail::matrix_array_wrapper<value_type const, column_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+
+    for (vcl_size_t i = 0; i < v_size; ++i)
+      data_vec[v_start + i * v_inc] = wrapper_A(i, static_cast<vcl_size_t>(j));
+  }
+}
+
+//
+///////////////////////// Element-wise operation //////////////////////////////////
+//
+
+// Binary operations A = B .* C and A = B ./ C
+
+/** @brief Implementation of the element-wise operations A = B .* C and A = B ./ C    (using MATLAB syntax)
+*
+* @param A      The result matrix (or -range, or -slice)
+* @param proxy  The proxy object holding B, C, and the operation
+*/
+template<typename NumericT, typename OpT>
+void element_op(matrix_base<NumericT> & A,
+                matrix_expression<const matrix_base<NumericT>, const matrix_base<NumericT>, op_element_binary<OpT> > const & proxy)
+{
+  assert(A.row_major() == proxy.lhs().row_major() && A.row_major() == proxy.rhs().row_major() && bool("Element-wise operations on mixed matrix layouts not supported yet!"));
+
+  typedef NumericT        value_type;
+  typedef viennacl::linalg::detail::op_applier<op_element_binary<OpT> >    OpFunctor;
+
+  value_type       * data_A = detail::extract_raw_pointer<value_type>(A);
+  value_type const * data_B = detail::extract_raw_pointer<value_type>(proxy.lhs());
+  value_type const * data_C = detail::extract_raw_pointer<value_type>(proxy.rhs());
+
+  vcl_size_t A_start1 = viennacl::traits::start1(A);
+  vcl_size_t A_start2 = viennacl::traits::start2(A);
+  vcl_size_t A_inc1   = viennacl::traits::stride1(A);
+  vcl_size_t A_inc2   = viennacl::traits::stride2(A);
+  vcl_size_t A_size1  = viennacl::traits::size1(A);
+  vcl_size_t A_size2  = viennacl::traits::size2(A);
+  vcl_size_t A_internal_size1  = viennacl::traits::internal_size1(A);
+  vcl_size_t A_internal_size2  = viennacl::traits::internal_size2(A);
+
+  vcl_size_t B_start1 = viennacl::traits::start1(proxy.lhs());
+  vcl_size_t B_start2 = viennacl::traits::start2(proxy.lhs());
+  vcl_size_t B_inc1   = viennacl::traits::stride1(proxy.lhs());
+  vcl_size_t B_inc2   = viennacl::traits::stride2(proxy.lhs());
+  vcl_size_t B_internal_size1  = viennacl::traits::internal_size1(proxy.lhs());
+  vcl_size_t B_internal_size2  = viennacl::traits::internal_size2(proxy.lhs());
+
+  vcl_size_t C_start1 = viennacl::traits::start1(proxy.rhs());
+  vcl_size_t C_start2 = viennacl::traits::start2(proxy.rhs());
+  vcl_size_t C_inc1   = viennacl::traits::stride1(proxy.rhs());
+  vcl_size_t C_inc2   = viennacl::traits::stride2(proxy.rhs());
+  vcl_size_t C_internal_size1  = viennacl::traits::internal_size1(proxy.rhs());
+  vcl_size_t C_internal_size2  = viennacl::traits::internal_size2(proxy.rhs());
+
+  if (A.row_major())
+  {
+    detail::matrix_array_wrapper<value_type,       row_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+    detail::matrix_array_wrapper<value_type const, row_major, false> wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+    detail::matrix_array_wrapper<value_type const, row_major, false> wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+#ifdef VIENNACL_WITH_OPENMP
+    #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+    for (long row = 0; row < static_cast<long>(A_size1); ++row)
+      for (vcl_size_t col = 0; col < A_size2; ++col)
+        OpFunctor::apply(wrapper_A(row, col), wrapper_B(row, col), wrapper_C(row, col));
+        //data_A[index_generator_A::mem_index(row * A_inc1 + A_start1, col * A_inc2 + A_start2, A_internal_size1, A_internal_size2)]
+        // =   data_B[index_generator_B::mem_index(row * B_inc1 + B_start1, col * B_inc2 + B_start2, B_internal_size1, B_internal_size2)] * alpha
+        //   + data_C[index_generator_C::mem_index(row * C_inc1 + C_start1, col * C_inc2 + C_start2, C_internal_size1, C_internal_size2)] * beta;
+  }
+  else
+  {
+    detail::matrix_array_wrapper<value_type,       column_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+    detail::matrix_array_wrapper<value_type const, column_major, false> wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+    detail::matrix_array_wrapper<value_type const, column_major, false> wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+#ifdef VIENNACL_WITH_OPENMP
+    #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+    for (long col = 0; col < static_cast<long>(A_size2); ++col)
+      for (vcl_size_t row = 0; row < A_size1; ++row)
+        OpFunctor::apply(wrapper_A(row, col), wrapper_B(row, col), wrapper_C(row, col));
+
+        //data_A[index_generator_A::mem_index(row * A_inc1 + A_start1, col * A_inc2 + A_start2, A_internal_size1, A_internal_size2)]
+        // =   data_B[index_generator_B::mem_index(row * B_inc1 + B_start1, col * B_inc2 + B_start2, B_internal_size1, B_internal_size2)] * alpha
+        //   + data_C[index_generator_C::mem_index(row * C_inc1 + C_start1, col * C_inc2 + C_start2, C_internal_size1, C_internal_size2)] * beta;
+  }
+}
+
+// Unary operations
+
+// A = op(B)
+template<typename NumericT, typename OpT>
+void element_op(matrix_base<NumericT> & A,
+                matrix_expression<const matrix_base<NumericT>, const matrix_base<NumericT>, op_element_unary<OpT> > const & proxy)
+{
+  assert(A.row_major() == proxy.lhs().row_major() && A.row_major() == proxy.rhs().row_major() && bool("Element-wise operations on mixed matrix layouts not supported yet!"));
+
+  typedef NumericT        value_type;
+  typedef viennacl::linalg::detail::op_applier<op_element_unary<OpT> >    OpFunctor;
+
+  value_type       * data_A = detail::extract_raw_pointer<value_type>(A);
+  value_type const * data_B = detail::extract_raw_pointer<value_type>(proxy.lhs());
+
+  vcl_size_t A_start1 = viennacl::traits::start1(A);
+  vcl_size_t A_start2 = viennacl::traits::start2(A);
+  vcl_size_t A_inc1   = viennacl::traits::stride1(A);
+  vcl_size_t A_inc2   = viennacl::traits::stride2(A);
+  vcl_size_t A_size1  = viennacl::traits::size1(A);
+  vcl_size_t A_size2  = viennacl::traits::size2(A);
+  vcl_size_t A_internal_size1  = viennacl::traits::internal_size1(A);
+  vcl_size_t A_internal_size2  = viennacl::traits::internal_size2(A);
+
+  vcl_size_t B_start1 = viennacl::traits::start1(proxy.lhs());
+  vcl_size_t B_start2 = viennacl::traits::start2(proxy.lhs());
+  vcl_size_t B_inc1   = viennacl::traits::stride1(proxy.lhs());
+  vcl_size_t B_inc2   = viennacl::traits::stride2(proxy.lhs());
+  vcl_size_t B_internal_size1  = viennacl::traits::internal_size1(proxy.lhs());
+  vcl_size_t B_internal_size2  = viennacl::traits::internal_size2(proxy.lhs());
+
+  if (A.row_major())
+  {
+    detail::matrix_array_wrapper<value_type,       row_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+    detail::matrix_array_wrapper<value_type const, row_major, false> wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+
+#ifdef VIENNACL_WITH_OPENMP
+    #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+    for (long row = 0; row < static_cast<long>(A_size1); ++row)
+      for (vcl_size_t col = 0; col < A_size2; ++col)
+        OpFunctor::apply(wrapper_A(row, col), wrapper_B(row, col));
+  }
+  else
+  {
+    detail::matrix_array_wrapper<value_type,       column_major, false> wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+    detail::matrix_array_wrapper<value_type const, column_major, false> wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+
+#ifdef VIENNACL_WITH_OPENMP
+    #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+    for (long col = 0; col < static_cast<long>(A_size2); ++col)
+      for (vcl_size_t row = 0; row < A_size1; ++row)
+        OpFunctor::apply(wrapper_A(row, col), wrapper_B(row, col));
+  }
+}
+
+
+
+//
+/////////////////////////   matrix-vector products /////////////////////////////////
+//
+
+// A * x
+
+/** @brief Carries out matrix-vector multiplication
+*
+* Implementation of the convenience expression result = prod(mat, vec);
+*
+* @param mat    The matrix
+* @param trans  Flag whether mat is to be transposed
+* @param vec    The vector
+* @param result The result vector
+*/
+template<typename NumericT>
+void prod_impl(const matrix_base<NumericT> & mat, bool trans,
+               const vector_base<NumericT> & vec,
+                     vector_base<NumericT> & result)
+{
+  typedef NumericT        value_type;
+
+  value_type const * data_A = detail::extract_raw_pointer<value_type>(mat);
+  value_type const * data_x = detail::extract_raw_pointer<value_type>(vec);
+  value_type       * data_result = detail::extract_raw_pointer<value_type>(result);
+
+  vcl_size_t A_start1 = viennacl::traits::start1(mat);
+  vcl_size_t A_start2 = viennacl::traits::start2(mat);
+  vcl_size_t A_inc1   = viennacl::traits::stride1(mat);
+  vcl_size_t A_inc2   = viennacl::traits::stride2(mat);
+  vcl_size_t A_size1  = viennacl::traits::size1(mat);
+  vcl_size_t A_size2  = viennacl::traits::size2(mat);
+  vcl_size_t A_internal_size1  = viennacl::traits::internal_size1(mat);
+  vcl_size_t A_internal_size2  = viennacl::traits::internal_size2(mat);
+
+  vcl_size_t start1 = viennacl::traits::start(vec);
+  vcl_size_t inc1   = viennacl::traits::stride(vec);
+
+  vcl_size_t start2 = viennacl::traits::start(result);
+  vcl_size_t inc2   = viennacl::traits::stride(result);
+
+  if (mat.row_major())
+  {
+    if (trans)
+    {
+      vcl_size_t thread_count = 1;
+#ifdef VIENNACL_WITH_OPENMP
+      if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+        thread_count = omp_get_max_threads();
+#endif
+      std::vector<value_type> temp_array(A_size2*thread_count, 0);
+      detail::vector_array_wrapper<value_type> wrapper_res(data_result, start2, inc2);
+
+      for (vcl_size_t col = 0; col < A_size2; ++col)
+        wrapper_res(col) = 0;
+
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      {
+        vcl_size_t id = 0;
+#ifdef VIENNACL_WITH_OPENMP
+        if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+          id = omp_get_thread_num();
+ #endif
+        vcl_size_t begin = (A_size1 * id) / thread_count;
+        vcl_size_t end   = (A_size1 * (id + 1)) / thread_count;
+
+        detail::matrix_array_wrapper<value_type const, row_major, false> wrapper_mat(data_A, A_start1 + A_inc1 * begin, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+        detail::vector_array_wrapper<value_type const> wrapper_vec(data_x, start1 + inc1 * begin, inc1);
+
+        for (vcl_size_t row = 0; row < (end - begin); ++row)  //run through matrix sequentially
+        {
+          value_type temp = wrapper_vec(row);
+          for (vcl_size_t col = 0; col < A_size2; ++col)
+            temp_array[A_size2 * id + col] += wrapper_mat(row , col) * temp;
+        }
+      }
+      for (vcl_size_t id = 0; id < thread_count; ++id)
+        for (vcl_size_t col = 0; col < A_size2; ++col)
+          wrapper_res(col) += temp_array[A_size2 * id + col];
+    }
+
+    else
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long row = 0; row < static_cast<long>(A_size1); ++row)
+      {
+        value_type temp = 0;
+        for (vcl_size_t col = 0; col < A_size2; ++col)
+          temp += data_A[viennacl::row_major::mem_index(static_cast<vcl_size_t>(row) * A_inc1 + A_start1, col * A_inc2 + A_start2, A_internal_size1, A_internal_size2)] * data_x[col * inc1 + start1];
+
+        data_result[static_cast<vcl_size_t>(row) * inc2 + start2] = temp;
+      }
+    }
+  }
+  else
+  {
+    if (!trans)
+    {
+      vcl_size_t thread_count = 1;
+#ifdef VIENNACL_WITH_OPENMP
+      if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+        thread_count = omp_get_max_threads();
+#endif
+      std::vector<value_type> temp_array(A_size1*thread_count, 0);
+      detail::vector_array_wrapper<value_type> wrapper_res(data_result, start2, inc2);
+
+      for (vcl_size_t row = 0; row < A_size1; ++row)
+        wrapper_res(row) = 0;
+
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      {
+        vcl_size_t id = 0;
+#ifdef VIENNACL_WITH_OPENMP
+        if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+          id = omp_get_thread_num();
+ #endif
+        vcl_size_t begin = (A_size2 * id) / thread_count;
+        vcl_size_t end   = (A_size2 * (id + 1)) / thread_count;
+
+        detail::matrix_array_wrapper<value_type const, column_major, false> wrapper_mat(data_A, A_start1, A_start2 + A_inc2 * begin, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+        detail::vector_array_wrapper<value_type const> wrapper_vec(data_x, start1 + inc1 * begin, inc1);
+
+        for (vcl_size_t col = 0; col < (end - begin); ++col)  //run through matrix sequentially
+        {
+          value_type temp = wrapper_vec(col);
+          for (vcl_size_t row = 0; row < A_size1; ++row)
+            temp_array[A_size1 * id + row] += wrapper_mat(row , col) * temp;
+        }
+      }
+      for (vcl_size_t id = 0; id < thread_count; ++id)
+        for (vcl_size_t row = 0; row < A_size1; ++row)
+          wrapper_res(row) += temp_array[A_size1 * id + row];
+    }
+    else
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long row = 0; row < static_cast<long>(A_size2); ++row)
+      {
+        value_type temp = 0;
+        for (vcl_size_t col = 0; col < A_size1; ++col)
+          temp += data_A[viennacl::column_major::mem_index(col * A_inc1 + A_start1, static_cast<vcl_size_t>(row) * A_inc2 + A_start2, A_internal_size1, A_internal_size2)] * data_x[col * inc1 + start1];
+
+        data_result[static_cast<vcl_size_t>(row) * inc2 + start2] = temp;
+      }
+    }
+  }
+}
+
+
+
+//
+/////////////////////////   matrix-matrix products /////////////////////////////////
+//
+
+namespace detail
+{
+  template<typename MatrixAccT1, typename MatrixAccT2, typename MatrixAccT3, typename NumericT>
+  void prod(MatrixAccT1 & A, MatrixAccT2 & B, MatrixAccT3 & C,
+            vcl_size_t C_size1, vcl_size_t C_size2, vcl_size_t A_size2,
+            NumericT alpha, NumericT beta)
+  {
+    if (C_size1 == 0 || C_size2 == 0 || A_size2 == 0)
+      return;
+
+    static const vcl_size_t blocksize = 64;
+
+    vcl_size_t num_blocks_C1 = (C_size1 - 1) / blocksize + 1;
+    vcl_size_t num_blocks_C2 = (C_size2 - 1) / blocksize + 1;
+    vcl_size_t num_blocks_A2 = (A_size2 - 1) / blocksize + 1;
+
+    //
+    // outer loop pair: Run over all blocks with indices (block_idx_i, block_idx_j) of the result matrix C:
+    //
+#ifdef VIENNACL_WITH_OPENMP
+    #pragma omp parallel for if ((C_size1*C_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+    for (long block_idx_i2=0; block_idx_i2<static_cast<long>(num_blocks_C1); ++block_idx_i2)
+    {
+      // thread-local auxiliary buffers
+      std::vector<NumericT> buffer_A(blocksize * blocksize); // row-major
+      std::vector<NumericT> buffer_B(blocksize * blocksize); // column-major
+      std::vector<NumericT> buffer_C(blocksize * blocksize); // row-major
+
+      vcl_size_t block_idx_i = static_cast<vcl_size_t>(block_idx_i2);
+      for (vcl_size_t block_idx_j=0; block_idx_j<num_blocks_C2; ++block_idx_j)
+      {
+        // Reset block matrix:
+        std::fill(buffer_C.begin(), buffer_C.end(), NumericT(0));
+
+        vcl_size_t offset_i = block_idx_i*blocksize;
+        vcl_size_t offset_j = block_idx_j*blocksize;
+
+        //  C(block_idx_i, block_idx_i) += A(block_idx_i, block_idx_k) * B(block_idx_k, block_idx_j)
+        for (vcl_size_t block_idx_k=0; block_idx_k<num_blocks_A2; ++block_idx_k)
+        {
+          // flush buffers:
+          std::fill(buffer_A.begin(), buffer_A.end(), NumericT(0));
+          std::fill(buffer_B.begin(), buffer_B.end(), NumericT(0));
+
+          vcl_size_t offset_k = block_idx_k*blocksize;
+
+          // load current data:
+          for (vcl_size_t i = offset_i; i < std::min(offset_i + blocksize, C_size1); ++i)
+            for (vcl_size_t k = offset_k; k < std::min(offset_k + blocksize, A_size2); ++k)
+              buffer_A[(i - offset_i) * blocksize + (k - offset_k)] = A(i, k);
+
+          for (vcl_size_t j = offset_j; j < std::min(offset_j + blocksize, C_size2); ++j)
+            for (vcl_size_t k = offset_k; k < std::min(offset_k + blocksize, A_size2); ++k)
+              buffer_B[(k - offset_k) + (j - offset_j) * blocksize] = B(k, j);
+
+          // multiply (this is the hot spot in terms of flops)
+          for (vcl_size_t i = 0; i < blocksize; ++i)
+          {
+            NumericT const * ptrA = &(buffer_A[i*blocksize]);
+            for (vcl_size_t j = 0; j < blocksize; ++j)
+            {
+              NumericT const * ptrB = &(buffer_B[j*blocksize]);
+
+              NumericT temp = NumericT(0);
+              for (vcl_size_t k = 0; k < blocksize; ++k)
+                temp += ptrA[k] * ptrB[k];  // buffer_A[i*blocksize + k] * buffer_B[k + j*blocksize];
+
+              buffer_C[i*blocksize + j] += temp;
+            }
+          }
+        }
+
+        // write result:
+        if (beta > 0 || beta < 0)
+        {
+          for (vcl_size_t i = offset_i; i < std::min(offset_i + blocksize, C_size1); ++i)
+            for (vcl_size_t j = offset_j; j < std::min(offset_j + blocksize, C_size2); ++j)
+              C(i,j) = beta * C(i,j) + alpha * buffer_C[(i - offset_i) * blocksize + (j - offset_j)];
+        }
+        else
+        {
+          for (vcl_size_t i = offset_i; i < std::min(offset_i + blocksize, C_size1); ++i)
+            for (vcl_size_t j = offset_j; j < std::min(offset_j + blocksize, C_size2); ++j)
+              C(i,j) =                 alpha * buffer_C[(i - offset_i) * blocksize + (j - offset_j)];
+        }
+
+      } // for block j
+    } // for block i
+
+  } // prod()
+
+} // namespace detail
+
+/** @brief Carries out matrix-matrix multiplication
+*
+* Implementation of C = prod(A, B);
+*
+*/
+template<typename NumericT, typename ScalarT1, typename ScalarT2 >
+void prod_impl(const matrix_base<NumericT> & A, bool trans_A,
+               const matrix_base<NumericT> & B, bool trans_B,
+                     matrix_base<NumericT> & C,
+               ScalarT1 alpha,
+               ScalarT2 beta)
+{
+  typedef NumericT        value_type;
+
+  value_type const * data_A = detail::extract_raw_pointer<value_type>(A);
+  value_type const * data_B = detail::extract_raw_pointer<value_type>(B);
+  value_type       * data_C = detail::extract_raw_pointer<value_type>(C);
+
+  vcl_size_t A_start1 = viennacl::traits::start1(A);
+  vcl_size_t A_start2 = viennacl::traits::start2(A);
+  vcl_size_t A_inc1   = viennacl::traits::stride1(A);
+  vcl_size_t A_inc2   = viennacl::traits::stride2(A);
+  vcl_size_t A_size1  = viennacl::traits::size1(A);
+  vcl_size_t A_size2  = viennacl::traits::size2(A);
+  vcl_size_t A_internal_size1  = viennacl::traits::internal_size1(A);
+  vcl_size_t A_internal_size2  = viennacl::traits::internal_size2(A);
+
+  vcl_size_t B_start1 = viennacl::traits::start1(B);
+  vcl_size_t B_start2 = viennacl::traits::start2(B);
+  vcl_size_t B_inc1   = viennacl::traits::stride1(B);
+  vcl_size_t B_inc2   = viennacl::traits::stride2(B);
+  vcl_size_t B_internal_size1  = viennacl::traits::internal_size1(B);
+  vcl_size_t B_internal_size2  = viennacl::traits::internal_size2(B);
+
+  vcl_size_t C_start1 = viennacl::traits::start1(C);
+  vcl_size_t C_start2 = viennacl::traits::start2(C);
+  vcl_size_t C_inc1   = viennacl::traits::stride1(C);
+  vcl_size_t C_inc2   = viennacl::traits::stride2(C);
+  vcl_size_t C_size1  = viennacl::traits::size1(C);
+  vcl_size_t C_size2  = viennacl::traits::size2(C);
+  vcl_size_t C_internal_size1  = viennacl::traits::internal_size1(C);
+  vcl_size_t C_internal_size2  = viennacl::traits::internal_size2(C);
+
+  if (!trans_A && !trans_B)
+  {
+    if (A.row_major() && B.row_major() && C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, row_major, false>   wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, row_major, false>   wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       row_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size2, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (A.row_major() && B.row_major() && !C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, row_major, false>   wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, row_major, false>   wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       column_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size2, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (A.row_major() && !B.row_major() && C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, row_major, false>   wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, column_major, false>   wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       row_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size2, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (A.row_major() && !B.row_major() && !C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, row_major, false>   wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, column_major, false>   wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       column_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size2, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (!A.row_major() && B.row_major() && C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, column_major, false>   wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, row_major, false>   wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       row_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size2, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (!A.row_major() && B.row_major() && !C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, column_major, false>   wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, row_major, false>   wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       column_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size2, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (!A.row_major() && !B.row_major() && C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, column_major, false>   wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, column_major, false>   wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       row_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size2, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else
+    {
+      detail::matrix_array_wrapper<value_type const, column_major, false>   wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, column_major, false>   wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       column_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size2, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+  }
+  else if (!trans_A && trans_B)
+  {
+    if (A.row_major() && B.row_major() && C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, row_major, false>   wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, row_major, true>    wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       row_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size2, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (A.row_major() && B.row_major() && !C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, row_major, false>   wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, row_major, true>    wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       column_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size2, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (A.row_major() && !B.row_major() && C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, row_major, false>   wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, column_major, true>    wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       row_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size2, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (A.row_major() && !B.row_major() && !C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, row_major, false>   wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, column_major, true>    wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       column_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size2, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (!A.row_major() && B.row_major() && C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, column_major, false>   wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, row_major, true>    wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       row_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size2, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (!A.row_major() && B.row_major() && !C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, column_major, false>   wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, row_major, true>    wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       column_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size2, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (!A.row_major() && !B.row_major() && C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, column_major, false>   wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, column_major, true>    wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       row_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size2, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else
+    {
+      detail::matrix_array_wrapper<value_type const, column_major, false>   wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, column_major, true>    wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       column_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size2, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+  }
+  else if (trans_A && !trans_B)
+  {
+    if (A.row_major() && B.row_major() && C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, row_major, true>    wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, row_major, false>   wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       row_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size1, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (A.row_major() && B.row_major() && !C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, row_major, true>    wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, row_major, false>   wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       column_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size1, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (A.row_major() && !B.row_major() && C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, row_major, true>    wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, column_major, false>   wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       row_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size1, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (A.row_major() && !B.row_major() && !C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, row_major, true>    wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, column_major, false>   wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       column_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size1, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (!A.row_major() && B.row_major() && C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, column_major, true>    wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, row_major, false>   wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       row_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size1, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (!A.row_major() && B.row_major() && !C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, column_major, true>    wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, row_major, false>   wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       column_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size1, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (!A.row_major() && !B.row_major() && C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, column_major, true>    wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, column_major, false>   wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       row_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size1, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else
+    {
+      detail::matrix_array_wrapper<value_type const, column_major, true>    wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, column_major, false>   wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       column_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size1, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+  }
+  else if (trans_A && trans_B)
+  {
+    if (A.row_major() && B.row_major() && C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, row_major, true>    wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, row_major, true>    wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       row_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size1, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (A.row_major() && B.row_major() && !C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const,    row_major, true>    wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const,    row_major, true>    wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       column_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size1, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (A.row_major() && !B.row_major() && C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const,    row_major, true>    wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, column_major, true>    wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,          row_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size1, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (A.row_major() && !B.row_major() && !C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const,    row_major, true>    wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, column_major, true>    wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       column_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size1, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (!A.row_major() && B.row_major() && C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, column_major, true>    wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const,    row_major, true>    wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,          row_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size1, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (!A.row_major() && B.row_major() && !C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, column_major, true>    wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const,    row_major, true>    wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       column_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size1, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else if (!A.row_major() && !B.row_major() && C.row_major())
+    {
+      detail::matrix_array_wrapper<value_type const, column_major, true>    wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, column_major, true>    wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,          row_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size1, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+    else
+    {
+      detail::matrix_array_wrapper<value_type const, column_major, true>    wrapper_A(data_A, A_start1, A_start2, A_inc1, A_inc2, A_internal_size1, A_internal_size2);
+      detail::matrix_array_wrapper<value_type const, column_major, true>    wrapper_B(data_B, B_start1, B_start2, B_inc1, B_inc2, B_internal_size1, B_internal_size2);
+      detail::matrix_array_wrapper<value_type,       column_major, false>   wrapper_C(data_C, C_start1, C_start2, C_inc1, C_inc2, C_internal_size1, C_internal_size2);
+
+      detail::prod(wrapper_A, wrapper_B, wrapper_C, C_size1, C_size2, A_size1, static_cast<value_type>(alpha), static_cast<value_type>(beta));
+    }
+  }
+}
+
+
+
+
+//
+/////////////////////////   miscellaneous operations /////////////////////////////////
+//
+
+
+/** @brief The implementation of the operation mat += alpha * vec1 * vec2^T, i.e. a scaled rank 1 update
+*
+* Implementation of the convenience expression result += alpha * outer_prod(vec1, vec2);
+*
+* @param mat1    The matrix to be updated
+* @param alpha            The scaling factor (either a viennacl::scalar<>, float, or double)
+* @param reciprocal_alpha Use 1/alpha instead of alpha
+* @param flip_sign_alpha  Use -alpha instead of alpha
+* @param vec1    The first vector
+* @param vec2    The second vector
+*/
+template<typename NumericT, typename ScalarT>
+void scaled_rank_1_update(matrix_base<NumericT> & mat1,
+                          ScalarT const & alpha, vcl_size_t /*len_alpha*/, bool reciprocal_alpha, bool flip_sign_alpha,
+                          const vector_base<NumericT> & vec1,
+                          const vector_base<NumericT> & vec2)
+{
+  typedef NumericT        value_type;
+
+  value_type       * data_A  = detail::extract_raw_pointer<value_type>(mat1);
+  value_type const * data_v1 = detail::extract_raw_pointer<value_type>(vec1);
+  value_type const * data_v2 = detail::extract_raw_pointer<value_type>(vec2);
+
+  vcl_size_t A_start1 = viennacl::traits::start1(mat1);
+  vcl_size_t A_start2 = viennacl::traits::start2(mat1);
+  vcl_size_t A_inc1   = viennacl::traits::stride1(mat1);
+  vcl_size_t A_inc2   = viennacl::traits::stride2(mat1);
+  vcl_size_t A_size1  = viennacl::traits::size1(mat1);
+  vcl_size_t A_size2  = viennacl::traits::size2(mat1);
+  vcl_size_t A_internal_size1  = viennacl::traits::internal_size1(mat1);
+  vcl_size_t A_internal_size2  = viennacl::traits::internal_size2(mat1);
+
+  vcl_size_t start1 = viennacl::traits::start(vec1);
+  vcl_size_t inc1   = viennacl::traits::stride(vec1);
+
+  vcl_size_t start2 = viennacl::traits::start(vec2);
+  vcl_size_t inc2   = viennacl::traits::stride(vec2);
+
+  value_type data_alpha = alpha;
+  if (flip_sign_alpha)
+    data_alpha = -data_alpha;
+
+  if (mat1.row_major())
+  {
+    if(reciprocal_alpha)
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long row = 0; row < static_cast<long>(A_size1); ++row)
+      {
+        value_type value_v1 = data_v1[static_cast<vcl_size_t>(row) * inc1 + start1] / data_alpha;
+        for (vcl_size_t col = 0; col < A_size2; ++col)
+          data_A[viennacl::row_major::mem_index(static_cast<vcl_size_t>(row) * A_inc1 + A_start1, col * A_inc2 + A_start2, A_internal_size1, A_internal_size2)] += value_v1 * data_v2[col * inc2 + start2];
+      }
+    }
+    else
+    {
+#ifdef VIENNACL_WITH_OPENMP
+      #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+      for (long row = 0; row < static_cast<long>(A_size1); ++row)
+      {
+        value_type value_v1 = data_v1[static_cast<vcl_size_t>(row) * inc1 + start1] * data_alpha;
+        for (vcl_size_t col = 0; col < A_size2; ++col)
+          data_A[viennacl::row_major::mem_index(static_cast<vcl_size_t>(row) * A_inc1 + A_start1, col * A_inc2 + A_start2, A_internal_size1, A_internal_size2)] += value_v1 * data_v2[col * inc2 + start2];
+      }
+    }
+  }
+  else
+  {
+      if(reciprocal_alpha)
+      {
+#ifdef VIENNACL_WITH_OPENMP
+        #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+        for (long col = 0; col < static_cast<long>(A_size2); ++col)  //run through matrix sequentially
+        {
+          value_type value_v2 = data_v2[static_cast<vcl_size_t>(col) * inc2 + start2] / data_alpha;
+          for (vcl_size_t row = 0; row < A_size1; ++row)
+            data_A[viennacl::column_major::mem_index(row * A_inc1 + A_start1, static_cast<vcl_size_t>(col) * A_inc2 + A_start2, A_internal_size1, A_internal_size2)] += data_v1[row * inc1 + start1] * value_v2;
+        }
+      }
+      else
+      {
+#ifdef VIENNACL_WITH_OPENMP
+        #pragma omp parallel for if ((A_size1*A_size2) > VIENNACL_OPENMP_MATRIX_MIN_SIZE)
+#endif
+        for (long col = 0; col < static_cast<long>(A_size2); ++col)  //run through matrix sequentially
+        {
+          value_type value_v2 = data_v2[static_cast<vcl_size_t>(col) * inc2 + start2] * data_alpha;
+          for (vcl_size_t row = 0; row < A_size1; ++row)
+            data_A[viennacl::column_major::mem_index(row * A_inc1 + A_start1, static_cast<vcl_size_t>(col) * A_inc2 + A_start2, A_intern

<TRUNCATED>