Chris@16: //
Chris@16: //  Copyright (c) 2000-2002
Chris@16: //  Joerg Walter, Mathias Koch
Chris@16: //
Chris@16: //  Distributed under the Boost Software License, Version 1.0. (See
Chris@16: //  accompanying file LICENSE_1_0.txt or copy at
Chris@16: //  http://www.boost.org/LICENSE_1_0.txt)
Chris@16: //
Chris@16: //  The authors gratefully acknowledge the support of
Chris@16: //  GeNeSys mbH & Co. KG in producing this work.
Chris@16: //
Chris@16: 
Chris@16: #ifndef _BOOST_UBLAS_OPERATION_
Chris@16: #define _BOOST_UBLAS_OPERATION_
Chris@16: 
Chris@16: #include <boost/numeric/ublas/matrix_proxy.hpp>
Chris@16: 
Chris@16: /** \file operation.hpp
Chris@16:  *  \brief This file contains some specialized products.
Chris@16:  */
Chris@16: 
Chris@16: // axpy-based products
Chris@16: // Alexei Novakov had a lot of ideas to improve these. Thanks.
Chris@16: // Hendrik Kueck proposed some new kernel. Thanks again.
Chris@16: 
Chris@16: namespace boost { namespace numeric { namespace ublas {
Chris@16: 
Chris@16:     template<class V, class T1, class L1, class IA1, class TA1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     V &
Chris@16:     axpy_prod (const compressed_matrix<T1, L1, 0, IA1, TA1> &e1,
Chris@16:                const vector_expression<E2> &e2,
Chris@16:                V &v, row_major_tag) {
Chris@16:         typedef typename V::size_type size_type;
Chris@16:         typedef typename V::value_type value_type;
Chris@16: 
Chris@16:         for (size_type i = 0; i < e1.filled1 () -1; ++ i) {
Chris@16:             size_type begin = e1.index1_data () [i];
Chris@16:             size_type end = e1.index1_data () [i + 1];
Chris@16:             value_type t (v (i));
Chris@16:             for (size_type j = begin; j < end; ++ j)
Chris@16:                 t += e1.value_data () [j] * e2 () (e1.index2_data () [j]);
Chris@16:             v (i) = t;
Chris@16:         }
Chris@16:         return v;
Chris@16:     }
Chris@16: 
Chris@16:     template<class V, class T1, class L1, class IA1, class TA1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     V &
Chris@16:     axpy_prod (const compressed_matrix<T1, L1, 0, IA1, TA1> &e1,
Chris@16:                const vector_expression<E2> &e2,
Chris@16:                V &v, column_major_tag) {
Chris@16:         typedef typename V::size_type size_type;
Chris@16: 
Chris@16:         for (size_type j = 0; j < e1.filled1 () -1; ++ j) {
Chris@16:             size_type begin = e1.index1_data () [j];
Chris@16:             size_type end = e1.index1_data () [j + 1];
Chris@16:             for (size_type i = begin; i < end; ++ i)
Chris@16:                 v (e1.index2_data () [i]) += e1.value_data () [i] * e2 () (j);
Chris@16:         }
Chris@16:         return v;
Chris@16:     }
Chris@16: 
Chris@16:     // Dispatcher
Chris@16:     template<class V, class T1, class L1, class IA1, class TA1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     V &
Chris@16:     axpy_prod (const compressed_matrix<T1, L1, 0, IA1, TA1> &e1,
Chris@16:                const vector_expression<E2> &e2,
Chris@16:                V &v, bool init = true) {
Chris@16:         typedef typename V::value_type value_type;
Chris@16:         typedef typename L1::orientation_category orientation_category;
Chris@16: 
Chris@16:         if (init)
Chris@16:             v.assign (zero_vector<value_type> (e1.size1 ()));
Chris@16: #if BOOST_UBLAS_TYPE_CHECK
Chris@16:         vector<value_type> cv (v);
Chris@16:         typedef typename type_traits<value_type>::real_type real_type;
Chris@16:         real_type verrorbound (norm_1 (v) + norm_1 (e1) * norm_1 (e2));
Chris@16:         indexing_vector_assign<scalar_plus_assign> (cv, prod (e1, e2));
Chris@16: #endif
Chris@16:         axpy_prod (e1, e2, v, orientation_category ());
Chris@16: #if BOOST_UBLAS_TYPE_CHECK
Chris@16:         BOOST_UBLAS_CHECK (norm_1 (v - cv) <= 2 * std::numeric_limits<real_type>::epsilon () * verrorbound, internal_logic ());
Chris@16: #endif
Chris@16:         return v;
Chris@16:     }
Chris@16:     template<class V, class T1, class L1, class IA1, class TA1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     V
Chris@16:     axpy_prod (const compressed_matrix<T1, L1, 0, IA1, TA1> &e1,
Chris@16:                const vector_expression<E2> &e2) {
Chris@16:         typedef V vector_type;
Chris@16: 
Chris@16:         vector_type v (e1.size1 ());
Chris@16:         return axpy_prod (e1, e2, v, true);
Chris@16:     }
Chris@16: 
Chris@16:     template<class V, class T1, class L1, class IA1, class TA1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     V &
Chris@16:     axpy_prod (const coordinate_matrix<T1, L1, 0, IA1, TA1> &e1,
Chris@16:                const vector_expression<E2> &e2,
Chris@16:                V &v, bool init = true) {
Chris@16:         typedef typename V::size_type size_type;
Chris@16:         typedef typename V::value_type value_type;
Chris@16:         typedef L1 layout_type;
Chris@16: 
Chris@16:         size_type size1 = e1.size1();
Chris@16:         size_type size2 = e1.size2();
Chris@16: 
Chris@16:         if (init) {
Chris@16:             noalias(v) = zero_vector<value_type>(size1);
Chris@16:         }
Chris@16: 
Chris@16:         for (size_type i = 0; i < e1.nnz(); ++i) {
Chris@16:             size_type row_index = layout_type::index_M( e1.index1_data () [i], e1.index2_data () [i] );
Chris@16:             size_type col_index = layout_type::index_m( e1.index1_data () [i], e1.index2_data () [i] );
Chris@16:             v( row_index ) += e1.value_data () [i] * e2 () (col_index);
Chris@16:         }
Chris@16:         return v;
Chris@16:     }
Chris@16: 
Chris@16:     template<class V, class E1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     V &
Chris@16:     axpy_prod (const matrix_expression<E1> &e1,
Chris@16:                const vector_expression<E2> &e2,
Chris@16:                V &v, packed_random_access_iterator_tag, row_major_tag) {
Chris@16:         typedef const E1 expression1_type;
Chris@16:         typedef typename V::size_type size_type;
Chris@16: 
Chris@16:         typename expression1_type::const_iterator1 it1 (e1 ().begin1 ());
Chris@16:         typename expression1_type::const_iterator1 it1_end (e1 ().end1 ());
Chris@16:         while (it1 != it1_end) {
Chris@16:             size_type index1 (it1.index1 ());
Chris@16: #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
Chris@16:             typename expression1_type::const_iterator2 it2 (it1.begin ());
Chris@16:             typename expression1_type::const_iterator2 it2_end (it1.end ());
Chris@16: #else
Chris@16:             typename expression1_type::const_iterator2 it2 (boost::numeric::ublas::begin (it1, iterator1_tag ()));
Chris@16:             typename expression1_type::const_iterator2 it2_end (boost::numeric::ublas::end (it1, iterator1_tag ()));
Chris@16: #endif
Chris@16:             while (it2 != it2_end) {
Chris@16:                 v (index1) += *it2 * e2 () (it2.index2 ());
Chris@16:                 ++ it2;
Chris@16:             }
Chris@16:             ++ it1;
Chris@16:         }
Chris@16:         return v;
Chris@16:     }
Chris@16: 
Chris@16:     template<class V, class E1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     V &
Chris@16:     axpy_prod (const matrix_expression<E1> &e1,
Chris@16:                const vector_expression<E2> &e2,
Chris@16:                V &v, packed_random_access_iterator_tag, column_major_tag) {
Chris@16:         typedef const E1 expression1_type;
Chris@16:         typedef typename V::size_type size_type;
Chris@16: 
Chris@16:         typename expression1_type::const_iterator2 it2 (e1 ().begin2 ());
Chris@16:         typename expression1_type::const_iterator2 it2_end (e1 ().end2 ());
Chris@16:         while (it2 != it2_end) {
Chris@16:             size_type index2 (it2.index2 ());
Chris@16: #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
Chris@16:             typename expression1_type::const_iterator1 it1 (it2.begin ());
Chris@16:             typename expression1_type::const_iterator1 it1_end (it2.end ());
Chris@16: #else
Chris@16:             typename expression1_type::const_iterator1 it1 (boost::numeric::ublas::begin (it2, iterator2_tag ()));
Chris@16:             typename expression1_type::const_iterator1 it1_end (boost::numeric::ublas::end (it2, iterator2_tag ()));
Chris@16: #endif
Chris@16:             while (it1 != it1_end) {
Chris@16:                 v (it1.index1 ()) += *it1 * e2 () (index2);
Chris@16:                 ++ it1;
Chris@16:             }
Chris@16:             ++ it2;
Chris@16:         }
Chris@16:         return v;
Chris@16:     }
Chris@16: 
Chris@16:     template<class V, class E1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     V &
Chris@16:     axpy_prod (const matrix_expression<E1> &e1,
Chris@16:                const vector_expression<E2> &e2,
Chris@16:                V &v, sparse_bidirectional_iterator_tag) {
Chris@16:         typedef const E2 expression2_type;
Chris@16: 
Chris@16:         typename expression2_type::const_iterator it (e2 ().begin ());
Chris@16:         typename expression2_type::const_iterator it_end (e2 ().end ());
Chris@16:         while (it != it_end) {
Chris@16:             v.plus_assign (column (e1 (), it.index ()) * *it);
Chris@16:             ++ it;
Chris@16:         }
Chris@16:         return v;
Chris@16:     }
Chris@16: 
Chris@16:     // Dispatcher
Chris@16:     template<class V, class E1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     V &
Chris@16:     axpy_prod (const matrix_expression<E1> &e1,
Chris@16:                const vector_expression<E2> &e2,
Chris@16:                V &v, packed_random_access_iterator_tag) {
Chris@16:         typedef typename E1::orientation_category orientation_category;
Chris@16:         return axpy_prod (e1, e2, v, packed_random_access_iterator_tag (), orientation_category ());
Chris@16:     }
Chris@16: 
Chris@16: 
Chris@16:   /** \brief computes <tt>v += A x</tt> or <tt>v = A x</tt> in an
Chris@16:           optimized fashion.
Chris@16: 
Chris@16:           \param e1 the matrix expression \c A
Chris@16:           \param e2 the vector expression \c x
Chris@16:           \param v  the result vector \c v
Chris@16:           \param init a boolean parameter
Chris@16: 
Chris@16:           <tt>axpy_prod(A, x, v, init)</tt> implements the well known
Chris@16:           axpy-product.  Setting \a init to \c true is equivalent to call
Chris@16:           <tt>v.clear()</tt> before <tt>axpy_prod</tt>. Currently \a init
Chris@16:           defaults to \c true, but this may change in the future.
Chris@16: 
Chris@16:           Up to now there are some specialisation for compressed
Chris@16:           matrices that give a large speed up compared to prod.
Chris@16:           
Chris@16:           \ingroup blas2
Chris@16: 
Chris@16:           \internal
Chris@16:           
Chris@16:           template parameters:
Chris@16:           \param V type of the result vector \c v
Chris@16:           \param E1 type of a matrix expression \c A
Chris@16:           \param E2 type of a vector expression \c x
Chris@16:   */
Chris@16:     template<class V, class E1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     V &
Chris@16:     axpy_prod (const matrix_expression<E1> &e1,
Chris@16:                const vector_expression<E2> &e2,
Chris@16:                V &v, bool init = true) {
Chris@16:         typedef typename V::value_type value_type;
Chris@16:         typedef typename E2::const_iterator::iterator_category iterator_category;
Chris@16: 
Chris@16:         if (init)
Chris@16:             v.assign (zero_vector<value_type> (e1 ().size1 ()));
Chris@16: #if BOOST_UBLAS_TYPE_CHECK
Chris@16:         vector<value_type> cv (v);
Chris@16:         typedef typename type_traits<value_type>::real_type real_type;
Chris@16:         real_type verrorbound (norm_1 (v) + norm_1 (e1) * norm_1 (e2));
Chris@16:         indexing_vector_assign<scalar_plus_assign> (cv, prod (e1, e2));
Chris@16: #endif
Chris@16:         axpy_prod (e1, e2, v, iterator_category ());
Chris@16: #if BOOST_UBLAS_TYPE_CHECK
Chris@16:         BOOST_UBLAS_CHECK (norm_1 (v - cv) <= 2 * std::numeric_limits<real_type>::epsilon () * verrorbound, internal_logic ());
Chris@16: #endif
Chris@16:         return v;
Chris@16:     }
Chris@16:     template<class V, class E1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     V
Chris@16:     axpy_prod (const matrix_expression<E1> &e1,
Chris@16:                const vector_expression<E2> &e2) {
Chris@16:         typedef V vector_type;
Chris@16: 
Chris@16:         vector_type v (e1 ().size1 ());
Chris@16:         return axpy_prod (e1, e2, v, true);
Chris@16:     }
Chris@16: 
Chris@16:     template<class V, class E1, class T2, class IA2, class TA2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     V &
Chris@16:     axpy_prod (const vector_expression<E1> &e1,
Chris@16:                const compressed_matrix<T2, column_major, 0, IA2, TA2> &e2,
Chris@16:                V &v, column_major_tag) {
Chris@16:         typedef typename V::size_type size_type;
Chris@16:         typedef typename V::value_type value_type;
Chris@16: 
Chris@16:         for (size_type j = 0; j < e2.filled1 () -1; ++ j) {
Chris@16:             size_type begin = e2.index1_data () [j];
Chris@16:             size_type end = e2.index1_data () [j + 1];
Chris@16:             value_type t (v (j));
Chris@16:             for (size_type i = begin; i < end; ++ i)
Chris@16:                 t += e2.value_data () [i] * e1 () (e2.index2_data () [i]);
Chris@16:             v (j) = t;
Chris@16:         }
Chris@16:         return v;
Chris@16:     }
Chris@16: 
Chris@16:     template<class V, class E1, class T2, class IA2, class TA2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     V &
Chris@16:     axpy_prod (const vector_expression<E1> &e1,
Chris@16:                const compressed_matrix<T2, row_major, 0, IA2, TA2> &e2,
Chris@16:                V &v, row_major_tag) {
Chris@16:         typedef typename V::size_type size_type;
Chris@16: 
Chris@16:         for (size_type i = 0; i < e2.filled1 () -1; ++ i) {
Chris@16:             size_type begin = e2.index1_data () [i];
Chris@16:             size_type end = e2.index1_data () [i + 1];
Chris@16:             for (size_type j = begin; j < end; ++ j)
Chris@16:                 v (e2.index2_data () [j]) += e2.value_data () [j] * e1 () (i);
Chris@16:         }
Chris@16:         return v;
Chris@16:     }
Chris@16: 
Chris@16:     // Dispatcher
Chris@16:     template<class V, class E1, class T2, class L2, class IA2, class TA2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     V &
Chris@16:     axpy_prod (const vector_expression<E1> &e1,
Chris@16:                const compressed_matrix<T2, L2, 0, IA2, TA2> &e2,
Chris@16:                V &v, bool init = true) {
Chris@16:         typedef typename V::value_type value_type;
Chris@16:         typedef typename L2::orientation_category orientation_category;
Chris@16: 
Chris@16:         if (init)
Chris@16:             v.assign (zero_vector<value_type> (e2.size2 ()));
Chris@16: #if BOOST_UBLAS_TYPE_CHECK
Chris@16:         vector<value_type> cv (v);
Chris@16:         typedef typename type_traits<value_type>::real_type real_type;
Chris@16:         real_type verrorbound (norm_1 (v) + norm_1 (e1) * norm_1 (e2));
Chris@16:         indexing_vector_assign<scalar_plus_assign> (cv, prod (e1, e2));
Chris@16: #endif
Chris@16:         axpy_prod (e1, e2, v, orientation_category ());
Chris@16: #if BOOST_UBLAS_TYPE_CHECK
Chris@16:         BOOST_UBLAS_CHECK (norm_1 (v - cv) <= 2 * std::numeric_limits<real_type>::epsilon () * verrorbound, internal_logic ());
Chris@16: #endif
Chris@16:         return v;
Chris@16:     }
Chris@16:     template<class V, class E1, class T2, class L2, class IA2, class TA2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     V
Chris@16:     axpy_prod (const vector_expression<E1> &e1,
Chris@16:                const compressed_matrix<T2, L2, 0, IA2, TA2> &e2) {
Chris@16:         typedef V vector_type;
Chris@16: 
Chris@16:         vector_type v (e2.size2 ());
Chris@16:         return axpy_prod (e1, e2, v, true);
Chris@16:     }
Chris@16: 
Chris@16:     template<class V, class E1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     V &
Chris@16:     axpy_prod (const vector_expression<E1> &e1,
Chris@16:                const matrix_expression<E2> &e2,
Chris@16:                V &v, packed_random_access_iterator_tag, column_major_tag) {
Chris@16:         typedef const E2 expression2_type;
Chris@16:         typedef typename V::size_type size_type;
Chris@16: 
Chris@16:         typename expression2_type::const_iterator2 it2 (e2 ().begin2 ());
Chris@16:         typename expression2_type::const_iterator2 it2_end (e2 ().end2 ());
Chris@16:         while (it2 != it2_end) {
Chris@16:             size_type index2 (it2.index2 ());
Chris@16: #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
Chris@16:             typename expression2_type::const_iterator1 it1 (it2.begin ());
Chris@16:             typename expression2_type::const_iterator1 it1_end (it2.end ());
Chris@16: #else
Chris@16:             typename expression2_type::const_iterator1 it1 (boost::numeric::ublas::begin (it2, iterator2_tag ()));
Chris@16:             typename expression2_type::const_iterator1 it1_end (boost::numeric::ublas::end (it2, iterator2_tag ()));
Chris@16: #endif
Chris@16:             while (it1 != it1_end) {
Chris@16:                 v (index2) += *it1 * e1 () (it1.index1 ());
Chris@16:                 ++ it1;
Chris@16:             }
Chris@16:             ++ it2;
Chris@16:         }
Chris@16:         return v;
Chris@16:     }
Chris@16: 
Chris@16:     template<class V, class E1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     V &
Chris@16:     axpy_prod (const vector_expression<E1> &e1,
Chris@16:                const matrix_expression<E2> &e2,
Chris@16:                V &v, packed_random_access_iterator_tag, row_major_tag) {
Chris@16:         typedef const E2 expression2_type;
Chris@16:         typedef typename V::size_type size_type;
Chris@16: 
Chris@16:         typename expression2_type::const_iterator1 it1 (e2 ().begin1 ());
Chris@16:         typename expression2_type::const_iterator1 it1_end (e2 ().end1 ());
Chris@16:         while (it1 != it1_end) {
Chris@16:             size_type index1 (it1.index1 ());
Chris@16: #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
Chris@16:             typename expression2_type::const_iterator2 it2 (it1.begin ());
Chris@16:             typename expression2_type::const_iterator2 it2_end (it1.end ());
Chris@16: #else
Chris@16:             typename expression2_type::const_iterator2 it2 (boost::numeric::ublas::begin (it1, iterator1_tag ()));
Chris@16:             typename expression2_type::const_iterator2 it2_end (boost::numeric::ublas::end (it1, iterator1_tag ()));
Chris@16: #endif
Chris@16:             while (it2 != it2_end) {
Chris@16:                 v (it2.index2 ()) += *it2 * e1 () (index1);
Chris@16:                 ++ it2;
Chris@16:             }
Chris@16:             ++ it1;
Chris@16:         }
Chris@16:         return v;
Chris@16:     }
Chris@16: 
Chris@16:     template<class V, class E1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     V &
Chris@16:     axpy_prod (const vector_expression<E1> &e1,
Chris@16:                const matrix_expression<E2> &e2,
Chris@16:                V &v, sparse_bidirectional_iterator_tag) {
Chris@16:         typedef const E1 expression1_type;
Chris@16: 
Chris@16:         typename expression1_type::const_iterator it (e1 ().begin ());
Chris@16:         typename expression1_type::const_iterator it_end (e1 ().end ());
Chris@16:         while (it != it_end) {
Chris@16:             v.plus_assign (*it * row (e2 (), it.index ()));
Chris@16:             ++ it;
Chris@16:         }
Chris@16:         return v;
Chris@16:     }
Chris@16: 
Chris@16:     // Dispatcher
Chris@16:     template<class V, class E1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     V &
Chris@16:     axpy_prod (const vector_expression<E1> &e1,
Chris@16:                const matrix_expression<E2> &e2,
Chris@16:                V &v, packed_random_access_iterator_tag) {
Chris@16:         typedef typename E2::orientation_category orientation_category;
Chris@16:         return axpy_prod (e1, e2, v, packed_random_access_iterator_tag (), orientation_category ());
Chris@16:     }
Chris@16: 
Chris@16: 
Chris@16:   /** \brief computes <tt>v += A<sup>T</sup> x</tt> or <tt>v = A<sup>T</sup> x</tt> in an
Chris@16:           optimized fashion.
Chris@16: 
Chris@16:           \param e1 the vector expression \c x
Chris@16:           \param e2 the matrix expression \c A
Chris@16:           \param v  the result vector \c v
Chris@16:           \param init a boolean parameter
Chris@16: 
Chris@16:           <tt>axpy_prod(x, A, v, init)</tt> implements the well known
Chris@16:           axpy-product.  Setting \a init to \c true is equivalent to call
Chris@16:           <tt>v.clear()</tt> before <tt>axpy_prod</tt>. Currently \a init
Chris@16:           defaults to \c true, but this may change in the future.
Chris@16: 
Chris@16:           Up to now there are some specialisation for compressed
Chris@16:           matrices that give a large speed up compared to prod.
Chris@16:           
Chris@16:           \ingroup blas2
Chris@16: 
Chris@16:           \internal
Chris@16:           
Chris@16:           template parameters:
Chris@16:           \param V type of the result vector \c v
Chris@16:           \param E1 type of a vector expression \c x
Chris@16:           \param E2 type of a matrix expression \c A
Chris@16:   */
Chris@16:     template<class V, class E1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     V &
Chris@16:     axpy_prod (const vector_expression<E1> &e1,
Chris@16:                const matrix_expression<E2> &e2,
Chris@16:                V &v, bool init = true) {
Chris@16:         typedef typename V::value_type value_type;
Chris@16:         typedef typename E1::const_iterator::iterator_category iterator_category;
Chris@16: 
Chris@16:         if (init)
Chris@16:             v.assign (zero_vector<value_type> (e2 ().size2 ()));
Chris@16: #if BOOST_UBLAS_TYPE_CHECK
Chris@16:         vector<value_type> cv (v);
Chris@16:         typedef typename type_traits<value_type>::real_type real_type;
Chris@16:         real_type verrorbound (norm_1 (v) + norm_1 (e1) * norm_1 (e2));
Chris@16:         indexing_vector_assign<scalar_plus_assign> (cv, prod (e1, e2));
Chris@16: #endif
Chris@16:         axpy_prod (e1, e2, v, iterator_category ());
Chris@16: #if BOOST_UBLAS_TYPE_CHECK
Chris@16:         BOOST_UBLAS_CHECK (norm_1 (v - cv) <= 2 * std::numeric_limits<real_type>::epsilon () * verrorbound, internal_logic ());
Chris@16: #endif
Chris@16:         return v;
Chris@16:     }
Chris@16:     template<class V, class E1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     V
Chris@16:     axpy_prod (const vector_expression<E1> &e1,
Chris@16:                const matrix_expression<E2> &e2) {
Chris@16:         typedef V vector_type;
Chris@16: 
Chris@16:         vector_type v (e2 ().size2 ());
Chris@16:         return axpy_prod (e1, e2, v, true);
Chris@16:     }
Chris@16: 
Chris@16:     template<class M, class E1, class E2, class TRI>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     M &
Chris@16:     axpy_prod (const matrix_expression<E1> &e1,
Chris@16:                const matrix_expression<E2> &e2,
Chris@16:                M &m, TRI,
Chris@16:                dense_proxy_tag, row_major_tag) {
Chris@101: 
Chris@16:         typedef typename M::size_type size_type;
Chris@16: 
Chris@16: #if BOOST_UBLAS_TYPE_CHECK
Chris@101:         typedef typename M::value_type value_type;
Chris@16:         matrix<value_type, row_major> cm (m);
Chris@16:         typedef typename type_traits<value_type>::real_type real_type;
Chris@16:         real_type merrorbound (norm_1 (m) + norm_1 (e1) * norm_1 (e2));
Chris@16:         indexing_matrix_assign<scalar_plus_assign> (cm, prod (e1, e2), row_major_tag ());
Chris@16: #endif
Chris@16:         size_type size1 (e1 ().size1 ());
Chris@16:         size_type size2 (e1 ().size2 ());
Chris@16:         for (size_type i = 0; i < size1; ++ i)
Chris@16:             for (size_type j = 0; j < size2; ++ j)
Chris@16:                 row (m, i).plus_assign (e1 () (i, j) * row (e2 (), j));
Chris@16: #if BOOST_UBLAS_TYPE_CHECK
Chris@16:         BOOST_UBLAS_CHECK (norm_1 (m - cm) <= 2 * std::numeric_limits<real_type>::epsilon () * merrorbound, internal_logic ());
Chris@16: #endif
Chris@16:         return m;
Chris@16:     }
Chris@16:     template<class M, class E1, class E2, class TRI>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     M &
Chris@16:     axpy_prod (const matrix_expression<E1> &e1,
Chris@16:                const matrix_expression<E2> &e2,
Chris@16:                M &m, TRI,
Chris@16:                sparse_proxy_tag, row_major_tag) {
Chris@101: 
Chris@16:         typedef TRI triangular_restriction;
Chris@16:         typedef const E1 expression1_type;
Chris@16:         typedef const E2 expression2_type;
Chris@16: 
Chris@16: #if BOOST_UBLAS_TYPE_CHECK
Chris@101:         typedef typename M::value_type value_type;
Chris@16:         matrix<value_type, row_major> cm (m);
Chris@16:         typedef typename type_traits<value_type>::real_type real_type;
Chris@16:         real_type merrorbound (norm_1 (m) + norm_1 (e1) * norm_1 (e2));
Chris@16:         indexing_matrix_assign<scalar_plus_assign> (cm, prod (e1, e2), row_major_tag ());
Chris@16: #endif
Chris@16:         typename expression1_type::const_iterator1 it1 (e1 ().begin1 ());
Chris@16:         typename expression1_type::const_iterator1 it1_end (e1 ().end1 ());
Chris@16:         while (it1 != it1_end) {
Chris@16: #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
Chris@16:             typename expression1_type::const_iterator2 it2 (it1.begin ());
Chris@16:             typename expression1_type::const_iterator2 it2_end (it1.end ());
Chris@16: #else
Chris@16:             typename expression1_type::const_iterator2 it2 (boost::numeric::ublas::begin (it1, iterator1_tag ()));
Chris@16:             typename expression1_type::const_iterator2 it2_end (boost::numeric::ublas::end (it1, iterator1_tag ()));
Chris@16: #endif
Chris@16:             while (it2 != it2_end) {
Chris@16:                 // row (m, it1.index1 ()).plus_assign (*it2 * row (e2 (), it2.index2 ()));
Chris@16:                 matrix_row<expression2_type> mr (e2 (), it2.index2 ());
Chris@16:                 typename matrix_row<expression2_type>::const_iterator itr (mr.begin ());
Chris@16:                 typename matrix_row<expression2_type>::const_iterator itr_end (mr.end ());
Chris@16:                 while (itr != itr_end) {
Chris@16:                     if (triangular_restriction::other (it1.index1 (), itr.index ()))
Chris@16:                         m (it1.index1 (), itr.index ()) += *it2 * *itr;
Chris@16:                     ++ itr;
Chris@16:                 }
Chris@16:                 ++ it2;
Chris@16:             }
Chris@16:             ++ it1;
Chris@16:         }
Chris@16: #if BOOST_UBLAS_TYPE_CHECK
Chris@16:         BOOST_UBLAS_CHECK (norm_1 (m - cm) <= 2 * std::numeric_limits<real_type>::epsilon () * merrorbound, internal_logic ());
Chris@16: #endif
Chris@16:         return m;
Chris@16:     }
Chris@16: 
Chris@16:     template<class M, class E1, class E2, class TRI>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     M &
Chris@16:     axpy_prod (const matrix_expression<E1> &e1,
Chris@16:                const matrix_expression<E2> &e2,
Chris@16:                M &m, TRI,
Chris@16:                dense_proxy_tag, column_major_tag) {
Chris@16:         typedef typename M::size_type size_type;
Chris@16: 
Chris@16: #if BOOST_UBLAS_TYPE_CHECK
Chris@101:         typedef typename M::value_type value_type;
Chris@16:         matrix<value_type, column_major> cm (m);
Chris@16:         typedef typename type_traits<value_type>::real_type real_type;
Chris@16:         real_type merrorbound (norm_1 (m) + norm_1 (e1) * norm_1 (e2));
Chris@16:         indexing_matrix_assign<scalar_plus_assign> (cm, prod (e1, e2), column_major_tag ());
Chris@16: #endif
Chris@16:         size_type size1 (e2 ().size1 ());
Chris@16:         size_type size2 (e2 ().size2 ());
Chris@16:         for (size_type j = 0; j < size2; ++ j)
Chris@16:             for (size_type i = 0; i < size1; ++ i)
Chris@16:                 column (m, j).plus_assign (e2 () (i, j) * column (e1 (), i));
Chris@16: #if BOOST_UBLAS_TYPE_CHECK
Chris@16:         BOOST_UBLAS_CHECK (norm_1 (m - cm) <= 2 * std::numeric_limits<real_type>::epsilon () * merrorbound, internal_logic ());
Chris@16: #endif
Chris@16:         return m;
Chris@16:     }
Chris@16:     template<class M, class E1, class E2, class TRI>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     M &
Chris@16:     axpy_prod (const matrix_expression<E1> &e1,
Chris@16:                const matrix_expression<E2> &e2,
Chris@16:                M &m, TRI,
Chris@16:                sparse_proxy_tag, column_major_tag) {
Chris@16:         typedef TRI triangular_restriction;
Chris@16:         typedef const E1 expression1_type;
Chris@16:         typedef const E2 expression2_type;
Chris@101: 
Chris@16: 
Chris@16: #if BOOST_UBLAS_TYPE_CHECK
Chris@101:         typedef typename M::value_type value_type;
Chris@16:         matrix<value_type, column_major> cm (m);
Chris@16:         typedef typename type_traits<value_type>::real_type real_type;
Chris@16:         real_type merrorbound (norm_1 (m) + norm_1 (e1) * norm_1 (e2));
Chris@16:         indexing_matrix_assign<scalar_plus_assign> (cm, prod (e1, e2), column_major_tag ());
Chris@16: #endif
Chris@16:         typename expression2_type::const_iterator2 it2 (e2 ().begin2 ());
Chris@16:         typename expression2_type::const_iterator2 it2_end (e2 ().end2 ());
Chris@16:         while (it2 != it2_end) {
Chris@16: #ifndef BOOST_UBLAS_NO_NESTED_CLASS_RELATION
Chris@16:             typename expression2_type::const_iterator1 it1 (it2.begin ());
Chris@16:             typename expression2_type::const_iterator1 it1_end (it2.end ());
Chris@16: #else
Chris@16:             typename expression2_type::const_iterator1 it1 (boost::numeric::ublas::begin (it2, iterator2_tag ()));
Chris@16:             typename expression2_type::const_iterator1 it1_end (boost::numeric::ublas::end (it2, iterator2_tag ()));
Chris@16: #endif
Chris@16:             while (it1 != it1_end) {
Chris@16:                 // column (m, it2.index2 ()).plus_assign (*it1 * column (e1 (), it1.index1 ()));
Chris@16:                 matrix_column<expression1_type> mc (e1 (), it1.index1 ());
Chris@16:                 typename matrix_column<expression1_type>::const_iterator itc (mc.begin ());
Chris@16:                 typename matrix_column<expression1_type>::const_iterator itc_end (mc.end ());
Chris@16:                 while (itc != itc_end) {
Chris@16:                     if(triangular_restriction::other (itc.index (), it2.index2 ()))
Chris@16:                        m (itc.index (), it2.index2 ()) += *it1 * *itc;
Chris@16:                     ++ itc;
Chris@16:                 }
Chris@16:                 ++ it1;
Chris@16:             }
Chris@16:             ++ it2;
Chris@16:         }
Chris@16: #if BOOST_UBLAS_TYPE_CHECK
Chris@16:         BOOST_UBLAS_CHECK (norm_1 (m - cm) <= 2 * std::numeric_limits<real_type>::epsilon () * merrorbound, internal_logic ());
Chris@16: #endif
Chris@16:         return m;
Chris@16:     }
Chris@16: 
Chris@16:     // Dispatcher
Chris@16:     template<class M, class E1, class E2, class TRI>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     M &
Chris@16:     axpy_prod (const matrix_expression<E1> &e1,
Chris@16:                const matrix_expression<E2> &e2,
Chris@16:                M &m, TRI, bool init = true) {
Chris@16:         typedef typename M::value_type value_type;
Chris@16:         typedef typename M::storage_category storage_category;
Chris@16:         typedef typename M::orientation_category orientation_category;
Chris@16:         typedef TRI triangular_restriction;
Chris@16: 
Chris@16:         if (init)
Chris@16:             m.assign (zero_matrix<value_type> (e1 ().size1 (), e2 ().size2 ()));
Chris@16:         return axpy_prod (e1, e2, m, triangular_restriction (), storage_category (), orientation_category ());
Chris@16:     }
Chris@16:     template<class M, class E1, class E2, class TRI>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     M
Chris@16:     axpy_prod (const matrix_expression<E1> &e1,
Chris@16:                const matrix_expression<E2> &e2,
Chris@16:                TRI) {
Chris@16:         typedef M matrix_type;
Chris@16:         typedef TRI triangular_restriction;
Chris@16: 
Chris@16:         matrix_type m (e1 ().size1 (), e2 ().size2 ());
Chris@16:         return axpy_prod (e1, e2, m, triangular_restriction (), true);
Chris@16:     }
Chris@16: 
Chris@16:   /** \brief computes <tt>M += A X</tt> or <tt>M = A X</tt> in an
Chris@16:           optimized fashion.
Chris@16: 
Chris@16:           \param e1 the matrix expression \c A
Chris@16:           \param e2 the matrix expression \c X
Chris@16:           \param m  the result matrix \c M
Chris@16:           \param init a boolean parameter
Chris@16: 
Chris@16:           <tt>axpy_prod(A, X, M, init)</tt> implements the well known
Chris@16:           axpy-product.  Setting \a init to \c true is equivalent to call
Chris@16:           <tt>M.clear()</tt> before <tt>axpy_prod</tt>. Currently \a init
Chris@16:           defaults to \c true, but this may change in the future.
Chris@16: 
Chris@16:           Up to now there are no specialisations.
Chris@16:           
Chris@16:           \ingroup blas3
Chris@16: 
Chris@16:           \internal
Chris@16:           
Chris@16:           template parameters:
Chris@16:           \param M type of the result matrix \c M
Chris@16:           \param E1 type of a matrix expression \c A
Chris@16:           \param E2 type of a matrix expression \c X
Chris@16:   */
Chris@16:     template<class M, class E1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     M &
Chris@16:     axpy_prod (const matrix_expression<E1> &e1,
Chris@16:                const matrix_expression<E2> &e2,
Chris@16:                M &m, bool init = true) {
Chris@16:         typedef typename M::value_type value_type;
Chris@16:         typedef typename M::storage_category storage_category;
Chris@16:         typedef typename M::orientation_category orientation_category;
Chris@16: 
Chris@16:         if (init)
Chris@16:             m.assign (zero_matrix<value_type> (e1 ().size1 (), e2 ().size2 ()));
Chris@16:         return axpy_prod (e1, e2, m, full (), storage_category (), orientation_category ());
Chris@16:     }
Chris@16:     template<class M, class E1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     M
Chris@16:     axpy_prod (const matrix_expression<E1> &e1,
Chris@16:                const matrix_expression<E2> &e2) {
Chris@16:         typedef M matrix_type;
Chris@16: 
Chris@16:         matrix_type m (e1 ().size1 (), e2 ().size2 ());
Chris@16:         return axpy_prod (e1, e2, m, full (), true);
Chris@16:     }
Chris@16: 
Chris@16: 
Chris@16:     template<class M, class E1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     M &
Chris@16:     opb_prod (const matrix_expression<E1> &e1,
Chris@16:               const matrix_expression<E2> &e2,
Chris@16:               M &m,
Chris@16:               dense_proxy_tag, row_major_tag) {
Chris@16:         typedef typename M::size_type size_type;
Chris@16:         typedef typename M::value_type value_type;
Chris@16: 
Chris@16: #if BOOST_UBLAS_TYPE_CHECK
Chris@16:         matrix<value_type, row_major> cm (m);
Chris@16:         typedef typename type_traits<value_type>::real_type real_type;
Chris@16:         real_type merrorbound (norm_1 (m) + norm_1 (e1) * norm_1 (e2));
Chris@16:         indexing_matrix_assign<scalar_plus_assign> (cm, prod (e1, e2), row_major_tag ());
Chris@16: #endif
Chris@16:         size_type size (BOOST_UBLAS_SAME (e1 ().size2 (), e2 ().size1 ()));
Chris@16:         for (size_type k = 0; k < size; ++ k) {
Chris@16:             vector<value_type> ce1 (column (e1 (), k));
Chris@16:             vector<value_type> re2 (row (e2 (), k));
Chris@16:             m.plus_assign (outer_prod (ce1, re2));
Chris@16:         }
Chris@16: #if BOOST_UBLAS_TYPE_CHECK
Chris@16:         BOOST_UBLAS_CHECK (norm_1 (m - cm) <= 2 * std::numeric_limits<real_type>::epsilon () * merrorbound, internal_logic ());
Chris@16: #endif
Chris@16:         return m;
Chris@16:     }
Chris@16: 
Chris@16:     template<class M, class E1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     M &
Chris@16:     opb_prod (const matrix_expression<E1> &e1,
Chris@16:               const matrix_expression<E2> &e2,
Chris@16:               M &m,
Chris@16:               dense_proxy_tag, column_major_tag) {
Chris@16:         typedef typename M::size_type size_type;
Chris@16:         typedef typename M::value_type value_type;
Chris@16: 
Chris@16: #if BOOST_UBLAS_TYPE_CHECK
Chris@16:         matrix<value_type, column_major> cm (m);
Chris@16:         typedef typename type_traits<value_type>::real_type real_type;
Chris@16:         real_type merrorbound (norm_1 (m) + norm_1 (e1) * norm_1 (e2));
Chris@16:         indexing_matrix_assign<scalar_plus_assign> (cm, prod (e1, e2), column_major_tag ());
Chris@16: #endif
Chris@16:         size_type size (BOOST_UBLAS_SAME (e1 ().size2 (), e2 ().size1 ()));
Chris@16:         for (size_type k = 0; k < size; ++ k) {
Chris@16:             vector<value_type> ce1 (column (e1 (), k));
Chris@16:             vector<value_type> re2 (row (e2 (), k));
Chris@16:             m.plus_assign (outer_prod (ce1, re2));
Chris@16:         }
Chris@16: #if BOOST_UBLAS_TYPE_CHECK
Chris@16:         BOOST_UBLAS_CHECK (norm_1 (m - cm) <= 2 * std::numeric_limits<real_type>::epsilon () * merrorbound, internal_logic ());
Chris@16: #endif
Chris@16:         return m;
Chris@16:     }
Chris@16: 
Chris@16:     // Dispatcher
Chris@16: 
Chris@16:   /** \brief computes <tt>M += A X</tt> or <tt>M = A X</tt> in an
Chris@16:           optimized fashion.
Chris@16: 
Chris@16:           \param e1 the matrix expression \c A
Chris@16:           \param e2 the matrix expression \c X
Chris@16:           \param m  the result matrix \c M
Chris@16:           \param init a boolean parameter
Chris@16: 
Chris@16:           <tt>opb_prod(A, X, M, init)</tt> implements the well known
Chris@16:           axpy-product. Setting \a init to \c true is equivalent to call
Chris@16:           <tt>M.clear()</tt> before <tt>opb_prod</tt>. Currently \a init
Chris@16:           defaults to \c true, but this may change in the future.
Chris@16: 
Chris@16:           This function may give a speedup if \c A has less columns than
Chris@16:           rows, because the product is computed as a sum of outer
Chris@16:           products.
Chris@16:           
Chris@16:           \ingroup blas3
Chris@16: 
Chris@16:           \internal
Chris@16:           
Chris@16:           template parameters:
Chris@16:           \param M type of the result matrix \c M
Chris@16:           \param E1 type of a matrix expression \c A
Chris@16:           \param E2 type of a matrix expression \c X
Chris@16:   */
Chris@16:     template<class M, class E1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     M &
Chris@16:     opb_prod (const matrix_expression<E1> &e1,
Chris@16:               const matrix_expression<E2> &e2,
Chris@16:               M &m, bool init = true) {
Chris@16:         typedef typename M::value_type value_type;
Chris@16:         typedef typename M::storage_category storage_category;
Chris@16:         typedef typename M::orientation_category orientation_category;
Chris@16: 
Chris@16:         if (init)
Chris@16:             m.assign (zero_matrix<value_type> (e1 ().size1 (), e2 ().size2 ()));
Chris@16:         return opb_prod (e1, e2, m, storage_category (), orientation_category ());
Chris@16:     }
Chris@16:     template<class M, class E1, class E2>
Chris@16:     BOOST_UBLAS_INLINE
Chris@16:     M
Chris@16:     opb_prod (const matrix_expression<E1> &e1,
Chris@16:               const matrix_expression<E2> &e2) {
Chris@16:         typedef M matrix_type;
Chris@16: 
Chris@16:         matrix_type m (e1 ().size1 (), e2 ().size2 ());
Chris@16:         return opb_prod (e1, e2, m, true);
Chris@16:     }
Chris@16: 
Chris@16: }}}
Chris@16: 
Chris@16: #endif