| // | |
| // 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 const E2 expression2_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 const E2 expression2_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 E1 expression1_type; | |
| typedef const E2 expression2_type; | |
| typedef typename V::size_type size_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 E1 expression1_type; | |
| 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 E1 expression1_type; | |
| 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; | |
| typedef const E2 expression2_type; | |
| typedef typename V::size_type size_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 M matrix_type; | |
| typedef const E1 expression1_type; | |
| typedef const E2 expression2_type; | |
| 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 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 M matrix_type; | |
| typedef TRI triangular_restriction; | |
| typedef const E1 expression1_type; | |
| typedef const E2 expression2_type; | |
| 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 | |
| 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 M matrix_type; | |
| typedef const E1 expression1_type; | |
| typedef const E2 expression2_type; | |
| 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 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 M matrix_type; | |
| typedef TRI triangular_restriction; | |
| typedef const E1 expression1_type; | |
| typedef const E2 expression2_type; | |
| 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 | |
| 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 M matrix_type; | |
| typedef const E1 expression1_type; | |
| typedef const E2 expression2_type; | |
| 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 M matrix_type; | |
| typedef const E1 expression1_type; | |
| typedef const E2 expression2_type; | |
| 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 |