diff -r 000000000000 -r bde4ae8d615e os/ossrv/ossrv_pub/boost_apis/boost/numeric/ublas/operation.hpp
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/os/ossrv/ossrv_pub/boost_apis/boost/numeric/ublas/operation.hpp	Fri Jun 15 03:10:57 2012 +0200
@@ -0,0 +1,855 @@
+//
+//  Copyright (c) 2000-2002
+//  Joerg Walter, Mathias Koch
+//
+//  Permission to use, copy, modify, distribute and sell this software
+//  and its documentation for any purpose is hereby granted without fee,
+//  provided that the above copyright notice appear in all copies and
+//  that both that copyright notice and this permission notice appear
+//  in supporting documentation.  The authors make no representations
+//  about the suitability of this software for any purpose.
+//  It is provided "as is" without express or implied warranty.
+//
+//  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 IA1, class TA1, class E2>
+    BOOST_UBLAS_INLINE
+    V &
+    axpy_prod (const compressed_matrix<T1, row_major, 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 IA1, class TA1, class E2>
+    BOOST_UBLAS_INLINE
+    V &
+    axpy_prod (const compressed_matrix<T1, column_major, 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::element1( e1.index1_data () [i], size1, e1.index2_data () [i], size2 );
+            size_type col_index = layout_type::element2( e1.index1_data () [i], size1, e1.index2_data () [i], size2 );
+            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::functor_type ().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