boost/numeric/ublas/operation.hpp
// // Copyright (c) 2000-2002 // Joerg Walter, Mathias Koch // // Distributed under the Boost Software License, Version 1.0. (See // accompanying file LICENSE_1_0.txt or copy at // http://www.boost.org/LICENSE_1_0.txt) // // The authors gratefully acknowledge the support of // GeNeSys mbH & Co. KG in producing this work. // #ifndef _BOOST_UBLAS_OPERATION_ #define _BOOST_UBLAS_OPERATION_ #include <boost/numeric/ublas/matrix_proxy.hpp> /** \file operation.hpp * \brief This file contains some specialized products. */ // axpy-based products // Alexei Novakov had a lot of ideas to improve these. Thanks. // Hendrik Kueck proposed some new kernel. Thanks again. namespace boost { namespace numeric { namespace ublas { template<class V, class T1, class L1, class IA1, class TA1, class E2> BOOST_UBLAS_INLINE V & axpy_prod (const compressed_matrix<T1, L1, 0, IA1, TA1> &e1, const vector_expression<E2> &e2, V &v, row_major_tag) { typedef typename V::size_type size_type; typedef typename V::value_type value_type; for (size_type i = 0; i < e1.filled1 () -1; ++ i) { size_type begin = e1.index1_data () [i]; size_type end = e1.index1_data () [i + 1]; value_type t (v (i)); for (size_type j = begin; j < end; ++ j) t += e1.value_data () [j] * e2 () (e1.index2_data () [j]); v (i) = t; } return v; } template<class V, class T1, class L1, class IA1, class TA1, class E2> BOOST_UBLAS_INLINE V & axpy_prod (const compressed_matrix<T1, L1, 0, IA1, TA1> &e1, const vector_expression<E2> &e2, V &v, column_major_tag) { typedef typename V::size_type size_type; for (size_type j = 0; j < e1.filled1 () -1; ++ j) { size_type begin = e1.index1_data () [j]; size_type end = e1.index1_data () [j + 1]; for (size_type i = begin; i < end; ++ i) v (e1.index2_data () [i]) += e1.value_data () [i] * e2 () (j); } return v; } // Dispatcher template<class V, class T1, class L1, class IA1, class TA1, class E2> BOOST_UBLAS_INLINE V & axpy_prod (const compressed_matrix<T1, L1, 0, IA1, TA1> &e1, const vector_expression<E2> &e2, V &v, bool init = true) { typedef typename V::value_type value_type; typedef typename L1::orientation_category orientation_category; if (init) v.assign (zero_vector<value_type> (e1.size1 ())); #if BOOST_UBLAS_TYPE_CHECK vector<value_type> cv (v); typedef typename type_traits<value_type>::real_type real_type; real_type verrorbound (norm_1 (v) + norm_1 (e1) * norm_1 (e2)); indexing_vector_assign<scalar_plus_assign> (cv, prod (e1, e2)); #endif axpy_prod (e1, e2, v, orientation_category ()); #if BOOST_UBLAS_TYPE_CHECK BOOST_UBLAS_CHECK (norm_1 (v - cv) <= 2 * std::numeric_limits<real_type>::epsilon () * verrorbound, internal_logic ()); #endif return v; } template<class V, class T1, class L1, class IA1, class TA1, class E2> BOOST_UBLAS_INLINE V axpy_prod (const compressed_matrix<T1, L1, 0, IA1, TA1> &e1, const vector_expression<E2> &e2) { typedef V vector_type; vector_type v (e1.size1 ()); return axpy_prod (e1, e2, v, true); } template<class V, class T1, class L1, class IA1, class TA1, class E2> BOOST_UBLAS_INLINE V & axpy_prod (const coordinate_matrix<T1, L1, 0, IA1, TA1> &e1, const vector_expression<E2> &e2, V &v, bool init = true) { typedef typename V::size_type size_type; typedef typename V::value_type value_type; typedef L1 layout_type; size_type size1 = e1.size1(); size_type size2 = e1.size2(); if (init) { noalias(v) = zero_vector<value_type>(size1); } for (size_type i = 0; i < e1.nnz(); ++i) { size_type row_index = layout_type::index_M( e1.index1_data () [i], e1.index2_data () [i] ); size_type col_index = layout_type::index_m( e1.index1_data () [i], e1.index2_data () [i] ); v( row_index ) += e1.value_data () [i] * e2 () (col_index); } return v; } template<class V, class E1, class E2> BOOST_UBLAS_INLINE V & axpy_prod (const matrix_expression<E1> &e1, const vector_expression<E2> &e2, V &v, packed_random_access_iterator_tag, row_major_tag) { typedef const E1 expression1_type; typedef typename V::size_type size_type; typename expression1_type::const_iterator1 it1 (e1 ().begin1 ()); typename expression1_type::const_iterator1 it1_end (e1 ().end1 ()); while (it1 != it1_end) { size_type index1 (it1.index1 ()); #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION typename expression1_type::const_iterator2 it2 (it1.begin ()); typename expression1_type::const_iterator2 it2_end (it1.end ()); #else typename expression1_type::const_iterator2 it2 (boost::numeric::ublas::begin (it1, iterator1_tag ())); typename expression1_type::const_iterator2 it2_end (boost::numeric::ublas::end (it1, iterator1_tag ())); #endif while (it2 != it2_end) { v (index1) += *it2 * e2 () (it2.index2 ()); ++ it2; } ++ it1; } return v; } template<class V, class E1, class E2> BOOST_UBLAS_INLINE V & axpy_prod (const matrix_expression<E1> &e1, const vector_expression<E2> &e2, V &v, packed_random_access_iterator_tag, column_major_tag) { typedef const E1 expression1_type; typedef typename V::size_type size_type; typename expression1_type::const_iterator2 it2 (e1 ().begin2 ()); typename expression1_type::const_iterator2 it2_end (e1 ().end2 ()); while (it2 != it2_end) { size_type index2 (it2.index2 ()); #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION typename expression1_type::const_iterator1 it1 (it2.begin ()); typename expression1_type::const_iterator1 it1_end (it2.end ()); #else typename expression1_type::const_iterator1 it1 (boost::numeric::ublas::begin (it2, iterator2_tag ())); typename expression1_type::const_iterator1 it1_end (boost::numeric::ublas::end (it2, iterator2_tag ())); #endif while (it1 != it1_end) { v (it1.index1 ()) += *it1 * e2 () (index2); ++ it1; } ++ it2; } return v; } template<class V, class E1, class E2> BOOST_UBLAS_INLINE V & axpy_prod (const matrix_expression<E1> &e1, const vector_expression<E2> &e2, V &v, sparse_bidirectional_iterator_tag) { typedef const E2 expression2_type; typename expression2_type::const_iterator it (e2 ().begin ()); typename expression2_type::const_iterator it_end (e2 ().end ()); while (it != it_end) { v.plus_assign (column (e1 (), it.index ()) * *it); ++ it; } return v; } // Dispatcher template<class V, class E1, class E2> BOOST_UBLAS_INLINE V & axpy_prod (const matrix_expression<E1> &e1, const vector_expression<E2> &e2, V &v, packed_random_access_iterator_tag) { typedef typename E1::orientation_category orientation_category; return axpy_prod (e1, e2, v, packed_random_access_iterator_tag (), orientation_category ()); } /** \brief computes <tt>v += A x</tt> or <tt>v = A x</tt> in an optimized fashion. \param e1 the matrix expression \c A \param e2 the vector expression \c x \param v the result vector \c v \param init a boolean parameter <tt>axpy_prod(A, x, v, init)</tt> implements the well known axpy-product. Setting \a init to \c true is equivalent to call <tt>v.clear()</tt> before <tt>axpy_prod</tt>. Currently \a init defaults to \c true, but this may change in the future. Up to now there are some specialisation for compressed matrices that give a large speed up compared to prod. \ingroup blas2 \internal template parameters: \param V type of the result vector \c v \param E1 type of a matrix expression \c A \param E2 type of a vector expression \c x */ template<class V, class E1, class E2> BOOST_UBLAS_INLINE V & axpy_prod (const matrix_expression<E1> &e1, const vector_expression<E2> &e2, V &v, bool init = true) { typedef typename V::value_type value_type; typedef typename E2::const_iterator::iterator_category iterator_category; if (init) v.assign (zero_vector<value_type> (e1 ().size1 ())); #if BOOST_UBLAS_TYPE_CHECK vector<value_type> cv (v); typedef typename type_traits<value_type>::real_type real_type; real_type verrorbound (norm_1 (v) + norm_1 (e1) * norm_1 (e2)); indexing_vector_assign<scalar_plus_assign> (cv, prod (e1, e2)); #endif axpy_prod (e1, e2, v, iterator_category ()); #if BOOST_UBLAS_TYPE_CHECK BOOST_UBLAS_CHECK (norm_1 (v - cv) <= 2 * std::numeric_limits<real_type>::epsilon () * verrorbound, internal_logic ()); #endif return v; } template<class V, class E1, class E2> BOOST_UBLAS_INLINE V axpy_prod (const matrix_expression<E1> &e1, const vector_expression<E2> &e2) { typedef V vector_type; vector_type v (e1 ().size1 ()); return axpy_prod (e1, e2, v, true); } template<class V, class E1, class T2, class IA2, class TA2> BOOST_UBLAS_INLINE V & axpy_prod (const vector_expression<E1> &e1, const compressed_matrix<T2, column_major, 0, IA2, TA2> &e2, V &v, column_major_tag) { typedef typename V::size_type size_type; typedef typename V::value_type value_type; for (size_type j = 0; j < e2.filled1 () -1; ++ j) { size_type begin = e2.index1_data () [j]; size_type end = e2.index1_data () [j + 1]; value_type t (v (j)); for (size_type i = begin; i < end; ++ i) t += e2.value_data () [i] * e1 () (e2.index2_data () [i]); v (j) = t; } return v; } template<class V, class E1, class T2, class IA2, class TA2> BOOST_UBLAS_INLINE V & axpy_prod (const vector_expression<E1> &e1, const compressed_matrix<T2, row_major, 0, IA2, TA2> &e2, V &v, row_major_tag) { typedef typename V::size_type size_type; for (size_type i = 0; i < e2.filled1 () -1; ++ i) { size_type begin = e2.index1_data () [i]; size_type end = e2.index1_data () [i + 1]; for (size_type j = begin; j < end; ++ j) v (e2.index2_data () [j]) += e2.value_data () [j] * e1 () (i); } return v; } // Dispatcher template<class V, class E1, class T2, class L2, class IA2, class TA2> BOOST_UBLAS_INLINE V & axpy_prod (const vector_expression<E1> &e1, const compressed_matrix<T2, L2, 0, IA2, TA2> &e2, V &v, bool init = true) { typedef typename V::value_type value_type; typedef typename L2::orientation_category orientation_category; if (init) v.assign (zero_vector<value_type> (e2.size2 ())); #if BOOST_UBLAS_TYPE_CHECK vector<value_type> cv (v); typedef typename type_traits<value_type>::real_type real_type; real_type verrorbound (norm_1 (v) + norm_1 (e1) * norm_1 (e2)); indexing_vector_assign<scalar_plus_assign> (cv, prod (e1, e2)); #endif axpy_prod (e1, e2, v, orientation_category ()); #if BOOST_UBLAS_TYPE_CHECK BOOST_UBLAS_CHECK (norm_1 (v - cv) <= 2 * std::numeric_limits<real_type>::epsilon () * verrorbound, internal_logic ()); #endif return v; } template<class V, class E1, class T2, class L2, class IA2, class TA2> BOOST_UBLAS_INLINE V axpy_prod (const vector_expression<E1> &e1, const compressed_matrix<T2, L2, 0, IA2, TA2> &e2) { typedef V vector_type; vector_type v (e2.size2 ()); return axpy_prod (e1, e2, v, true); } template<class V, class E1, class E2> BOOST_UBLAS_INLINE V & axpy_prod (const vector_expression<E1> &e1, const matrix_expression<E2> &e2, V &v, packed_random_access_iterator_tag, column_major_tag) { typedef const E2 expression2_type; typedef typename V::size_type size_type; typename expression2_type::const_iterator2 it2 (e2 ().begin2 ()); typename expression2_type::const_iterator2 it2_end (e2 ().end2 ()); while (it2 != it2_end) { size_type index2 (it2.index2 ()); #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION typename expression2_type::const_iterator1 it1 (it2.begin ()); typename expression2_type::const_iterator1 it1_end (it2.end ()); #else typename expression2_type::const_iterator1 it1 (boost::numeric::ublas::begin (it2, iterator2_tag ())); typename expression2_type::const_iterator1 it1_end (boost::numeric::ublas::end (it2, iterator2_tag ())); #endif while (it1 != it1_end) { v (index2) += *it1 * e1 () (it1.index1 ()); ++ it1; } ++ it2; } return v; } template<class V, class E1, class E2> BOOST_UBLAS_INLINE V & axpy_prod (const vector_expression<E1> &e1, const matrix_expression<E2> &e2, V &v, packed_random_access_iterator_tag, row_major_tag) { typedef const E2 expression2_type; typedef typename V::size_type size_type; typename expression2_type::const_iterator1 it1 (e2 ().begin1 ()); typename expression2_type::const_iterator1 it1_end (e2 ().end1 ()); while (it1 != it1_end) { size_type index1 (it1.index1 ()); #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION typename expression2_type::const_iterator2 it2 (it1.begin ()); typename expression2_type::const_iterator2 it2_end (it1.end ()); #else typename expression2_type::const_iterator2 it2 (boost::numeric::ublas::begin (it1, iterator1_tag ())); typename expression2_type::const_iterator2 it2_end (boost::numeric::ublas::end (it1, iterator1_tag ())); #endif while (it2 != it2_end) { v (it2.index2 ()) += *it2 * e1 () (index1); ++ it2; } ++ it1; } return v; } template<class V, class E1, class E2> BOOST_UBLAS_INLINE V & axpy_prod (const vector_expression<E1> &e1, const matrix_expression<E2> &e2, V &v, sparse_bidirectional_iterator_tag) { typedef const E1 expression1_type; typename expression1_type::const_iterator it (e1 ().begin ()); typename expression1_type::const_iterator it_end (e1 ().end ()); while (it != it_end) { v.plus_assign (*it * row (e2 (), it.index ())); ++ it; } return v; } // Dispatcher template<class V, class E1, class E2> BOOST_UBLAS_INLINE V & axpy_prod (const vector_expression<E1> &e1, const matrix_expression<E2> &e2, V &v, packed_random_access_iterator_tag) { typedef typename E2::orientation_category orientation_category; return axpy_prod (e1, e2, v, packed_random_access_iterator_tag (), orientation_category ()); } /** \brief computes <tt>v += A<sup>T</sup> x</tt> or <tt>v = A<sup>T</sup> x</tt> in an optimized fashion. \param e1 the vector expression \c x \param e2 the matrix expression \c A \param v the result vector \c v \param init a boolean parameter <tt>axpy_prod(x, A, v, init)</tt> implements the well known axpy-product. Setting \a init to \c true is equivalent to call <tt>v.clear()</tt> before <tt>axpy_prod</tt>. Currently \a init defaults to \c true, but this may change in the future. Up to now there are some specialisation for compressed matrices that give a large speed up compared to prod. \ingroup blas2 \internal template parameters: \param V type of the result vector \c v \param E1 type of a vector expression \c x \param E2 type of a matrix expression \c A */ template<class V, class E1, class E2> BOOST_UBLAS_INLINE V & axpy_prod (const vector_expression<E1> &e1, const matrix_expression<E2> &e2, V &v, bool init = true) { typedef typename V::value_type value_type; typedef typename E1::const_iterator::iterator_category iterator_category; if (init) v.assign (zero_vector<value_type> (e2 ().size2 ())); #if BOOST_UBLAS_TYPE_CHECK vector<value_type> cv (v); typedef typename type_traits<value_type>::real_type real_type; real_type verrorbound (norm_1 (v) + norm_1 (e1) * norm_1 (e2)); indexing_vector_assign<scalar_plus_assign> (cv, prod (e1, e2)); #endif axpy_prod (e1, e2, v, iterator_category ()); #if BOOST_UBLAS_TYPE_CHECK BOOST_UBLAS_CHECK (norm_1 (v - cv) <= 2 * std::numeric_limits<real_type>::epsilon () * verrorbound, internal_logic ()); #endif return v; } template<class V, class E1, class E2> BOOST_UBLAS_INLINE V axpy_prod (const vector_expression<E1> &e1, const matrix_expression<E2> &e2) { typedef V vector_type; vector_type v (e2 ().size2 ()); return axpy_prod (e1, e2, v, true); } template<class M, class E1, class E2, class TRI> BOOST_UBLAS_INLINE M & axpy_prod (const matrix_expression<E1> &e1, const matrix_expression<E2> &e2, M &m, TRI, dense_proxy_tag, row_major_tag) { typedef typename M::size_type size_type; #if BOOST_UBLAS_TYPE_CHECK typedef typename M::value_type value_type; matrix<value_type, row_major> cm (m); typedef typename type_traits<value_type>::real_type real_type; real_type merrorbound (norm_1 (m) + norm_1 (e1) * norm_1 (e2)); indexing_matrix_assign<scalar_plus_assign> (cm, prod (e1, e2), row_major_tag ()); #endif size_type size1 (e1 ().size1 ()); size_type size2 (e1 ().size2 ()); for (size_type i = 0; i < size1; ++ i) for (size_type j = 0; j < size2; ++ j) row (m, i).plus_assign (e1 () (i, j) * row (e2 (), j)); #if BOOST_UBLAS_TYPE_CHECK BOOST_UBLAS_CHECK (norm_1 (m - cm) <= 2 * std::numeric_limits<real_type>::epsilon () * merrorbound, internal_logic ()); #endif return m; } template<class M, class E1, class E2, class TRI> BOOST_UBLAS_INLINE M & axpy_prod (const matrix_expression<E1> &e1, const matrix_expression<E2> &e2, M &m, TRI, sparse_proxy_tag, row_major_tag) { typedef TRI triangular_restriction; typedef const E1 expression1_type; typedef const E2 expression2_type; #if BOOST_UBLAS_TYPE_CHECK typedef typename M::value_type value_type; matrix<value_type, row_major> cm (m); typedef typename type_traits<value_type>::real_type real_type; real_type merrorbound (norm_1 (m) + norm_1 (e1) * norm_1 (e2)); indexing_matrix_assign<scalar_plus_assign> (cm, prod (e1, e2), row_major_tag ()); #endif typename expression1_type::const_iterator1 it1 (e1 ().begin1 ()); typename expression1_type::const_iterator1 it1_end (e1 ().end1 ()); while (it1 != it1_end) { #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION typename expression1_type::const_iterator2 it2 (it1.begin ()); typename expression1_type::const_iterator2 it2_end (it1.end ()); #else typename expression1_type::const_iterator2 it2 (boost::numeric::ublas::begin (it1, iterator1_tag ())); typename expression1_type::const_iterator2 it2_end (boost::numeric::ublas::end (it1, iterator1_tag ())); #endif while (it2 != it2_end) { // row (m, it1.index1 ()).plus_assign (*it2 * row (e2 (), it2.index2 ())); matrix_row<expression2_type> mr (e2 (), it2.index2 ()); typename matrix_row<expression2_type>::const_iterator itr (mr.begin ()); typename matrix_row<expression2_type>::const_iterator itr_end (mr.end ()); while (itr != itr_end) { if (triangular_restriction::other (it1.index1 (), itr.index ())) m (it1.index1 (), itr.index ()) += *it2 * *itr; ++ itr; } ++ it2; } ++ it1; } #if BOOST_UBLAS_TYPE_CHECK BOOST_UBLAS_CHECK (norm_1 (m - cm) <= 2 * std::numeric_limits<real_type>::epsilon () * merrorbound, internal_logic ()); #endif return m; } template<class M, class E1, class E2, class TRI> BOOST_UBLAS_INLINE M & axpy_prod (const matrix_expression<E1> &e1, const matrix_expression<E2> &e2, M &m, TRI, dense_proxy_tag, column_major_tag) { typedef typename M::size_type size_type; #if BOOST_UBLAS_TYPE_CHECK typedef typename M::value_type value_type; matrix<value_type, column_major> cm (m); typedef typename type_traits<value_type>::real_type real_type; real_type merrorbound (norm_1 (m) + norm_1 (e1) * norm_1 (e2)); indexing_matrix_assign<scalar_plus_assign> (cm, prod (e1, e2), column_major_tag ()); #endif size_type size1 (e2 ().size1 ()); size_type size2 (e2 ().size2 ()); for (size_type j = 0; j < size2; ++ j) for (size_type i = 0; i < size1; ++ i) column (m, j).plus_assign (e2 () (i, j) * column (e1 (), i)); #if BOOST_UBLAS_TYPE_CHECK BOOST_UBLAS_CHECK (norm_1 (m - cm) <= 2 * std::numeric_limits<real_type>::epsilon () * merrorbound, internal_logic ()); #endif return m; } template<class M, class E1, class E2, class TRI> BOOST_UBLAS_INLINE M & axpy_prod (const matrix_expression<E1> &e1, const matrix_expression<E2> &e2, M &m, TRI, sparse_proxy_tag, column_major_tag) { typedef TRI triangular_restriction; typedef const E1 expression1_type; typedef const E2 expression2_type; #if BOOST_UBLAS_TYPE_CHECK typedef typename M::value_type value_type; matrix<value_type, column_major> cm (m); typedef typename type_traits<value_type>::real_type real_type; real_type merrorbound (norm_1 (m) + norm_1 (e1) * norm_1 (e2)); indexing_matrix_assign<scalar_plus_assign> (cm, prod (e1, e2), column_major_tag ()); #endif typename expression2_type::const_iterator2 it2 (e2 ().begin2 ()); typename expression2_type::const_iterator2 it2_end (e2 ().end2 ()); while (it2 != it2_end) { #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION typename expression2_type::const_iterator1 it1 (it2.begin ()); typename expression2_type::const_iterator1 it1_end (it2.end ()); #else typename expression2_type::const_iterator1 it1 (boost::numeric::ublas::begin (it2, iterator2_tag ())); typename expression2_type::const_iterator1 it1_end (boost::numeric::ublas::end (it2, iterator2_tag ())); #endif while (it1 != it1_end) { // column (m, it2.index2 ()).plus_assign (*it1 * column (e1 (), it1.index1 ())); matrix_column<expression1_type> mc (e1 (), it1.index1 ()); typename matrix_column<expression1_type>::const_iterator itc (mc.begin ()); typename matrix_column<expression1_type>::const_iterator itc_end (mc.end ()); while (itc != itc_end) { if(triangular_restriction::other (itc.index (), it2.index2 ())) m (itc.index (), it2.index2 ()) += *it1 * *itc; ++ itc; } ++ it1; } ++ it2; } #if BOOST_UBLAS_TYPE_CHECK BOOST_UBLAS_CHECK (norm_1 (m - cm) <= 2 * std::numeric_limits<real_type>::epsilon () * merrorbound, internal_logic ()); #endif return m; } // Dispatcher template<class M, class E1, class E2, class TRI> BOOST_UBLAS_INLINE M & axpy_prod (const matrix_expression<E1> &e1, const matrix_expression<E2> &e2, M &m, TRI, bool init = true) { typedef typename M::value_type value_type; typedef typename M::storage_category storage_category; typedef typename M::orientation_category orientation_category; typedef TRI triangular_restriction; if (init) m.assign (zero_matrix<value_type> (e1 ().size1 (), e2 ().size2 ())); return axpy_prod (e1, e2, m, triangular_restriction (), storage_category (), orientation_category ()); } template<class M, class E1, class E2, class TRI> BOOST_UBLAS_INLINE M axpy_prod (const matrix_expression<E1> &e1, const matrix_expression<E2> &e2, TRI) { typedef M matrix_type; typedef TRI triangular_restriction; matrix_type m (e1 ().size1 (), e2 ().size2 ()); return axpy_prod (e1, e2, m, triangular_restriction (), true); } /** \brief computes <tt>M += A X</tt> or <tt>M = A X</tt> in an optimized fashion. \param e1 the matrix expression \c A \param e2 the matrix expression \c X \param m the result matrix \c M \param init a boolean parameter <tt>axpy_prod(A, X, M, init)</tt> implements the well known axpy-product. Setting \a init to \c true is equivalent to call <tt>M.clear()</tt> before <tt>axpy_prod</tt>. Currently \a init defaults to \c true, but this may change in the future. Up to now there are no specialisations. \ingroup blas3 \internal template parameters: \param M type of the result matrix \c M \param E1 type of a matrix expression \c A \param E2 type of a matrix expression \c X */ template<class M, class E1, class E2> BOOST_UBLAS_INLINE M & axpy_prod (const matrix_expression<E1> &e1, const matrix_expression<E2> &e2, M &m, bool init = true) { typedef typename M::value_type value_type; typedef typename M::storage_category storage_category; typedef typename M::orientation_category orientation_category; if (init) m.assign (zero_matrix<value_type> (e1 ().size1 (), e2 ().size2 ())); return axpy_prod (e1, e2, m, full (), storage_category (), orientation_category ()); } template<class M, class E1, class E2> BOOST_UBLAS_INLINE M axpy_prod (const matrix_expression<E1> &e1, const matrix_expression<E2> &e2) { typedef M matrix_type; matrix_type m (e1 ().size1 (), e2 ().size2 ()); return axpy_prod (e1, e2, m, full (), true); } template<class M, class E1, class E2> BOOST_UBLAS_INLINE M & opb_prod (const matrix_expression<E1> &e1, const matrix_expression<E2> &e2, M &m, dense_proxy_tag, row_major_tag) { typedef typename M::size_type size_type; typedef typename M::value_type value_type; #if BOOST_UBLAS_TYPE_CHECK matrix<value_type, row_major> cm (m); typedef typename type_traits<value_type>::real_type real_type; real_type merrorbound (norm_1 (m) + norm_1 (e1) * norm_1 (e2)); indexing_matrix_assign<scalar_plus_assign> (cm, prod (e1, e2), row_major_tag ()); #endif size_type size (BOOST_UBLAS_SAME (e1 ().size2 (), e2 ().size1 ())); for (size_type k = 0; k < size; ++ k) { vector<value_type> ce1 (column (e1 (), k)); vector<value_type> re2 (row (e2 (), k)); m.plus_assign (outer_prod (ce1, re2)); } #if BOOST_UBLAS_TYPE_CHECK BOOST_UBLAS_CHECK (norm_1 (m - cm) <= 2 * std::numeric_limits<real_type>::epsilon () * merrorbound, internal_logic ()); #endif return m; } template<class M, class E1, class E2> BOOST_UBLAS_INLINE M & opb_prod (const matrix_expression<E1> &e1, const matrix_expression<E2> &e2, M &m, dense_proxy_tag, column_major_tag) { typedef typename M::size_type size_type; typedef typename M::value_type value_type; #if BOOST_UBLAS_TYPE_CHECK matrix<value_type, column_major> cm (m); typedef typename type_traits<value_type>::real_type real_type; real_type merrorbound (norm_1 (m) + norm_1 (e1) * norm_1 (e2)); indexing_matrix_assign<scalar_plus_assign> (cm, prod (e1, e2), column_major_tag ()); #endif size_type size (BOOST_UBLAS_SAME (e1 ().size2 (), e2 ().size1 ())); for (size_type k = 0; k < size; ++ k) { vector<value_type> ce1 (column (e1 (), k)); vector<value_type> re2 (row (e2 (), k)); m.plus_assign (outer_prod (ce1, re2)); } #if BOOST_UBLAS_TYPE_CHECK BOOST_UBLAS_CHECK (norm_1 (m - cm) <= 2 * std::numeric_limits<real_type>::epsilon () * merrorbound, internal_logic ()); #endif return m; } // Dispatcher /** \brief computes <tt>M += A X</tt> or <tt>M = A X</tt> in an optimized fashion. \param e1 the matrix expression \c A \param e2 the matrix expression \c X \param m the result matrix \c M \param init a boolean parameter <tt>opb_prod(A, X, M, init)</tt> implements the well known axpy-product. Setting \a init to \c true is equivalent to call <tt>M.clear()</tt> before <tt>opb_prod</tt>. Currently \a init defaults to \c true, but this may change in the future. This function may give a speedup if \c A has less columns than rows, because the product is computed as a sum of outer products. \ingroup blas3 \internal template parameters: \param M type of the result matrix \c M \param E1 type of a matrix expression \c A \param E2 type of a matrix expression \c X */ template<class M, class E1, class E2> BOOST_UBLAS_INLINE M & opb_prod (const matrix_expression<E1> &e1, const matrix_expression<E2> &e2, M &m, bool init = true) { typedef typename M::value_type value_type; typedef typename M::storage_category storage_category; typedef typename M::orientation_category orientation_category; if (init) m.assign (zero_matrix<value_type> (e1 ().size1 (), e2 ().size2 ())); return opb_prod (e1, e2, m, storage_category (), orientation_category ()); } template<class M, class E1, class E2> BOOST_UBLAS_INLINE M opb_prod (const matrix_expression<E1> &e1, const matrix_expression<E2> &e2) { typedef M matrix_type; matrix_type m (e1 ().size1 (), e2 ().size2 ()); return opb_prod (e1, e2, m, true); } }}} #endif