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//
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// Copyright (c) 2000-2002
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// Joerg Walter, Mathias Koch
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//
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// Permission to use, copy, modify, distribute and sell this software
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// and its documentation for any purpose is hereby granted without fee,
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// provided that the above copyright notice appear in all copies and
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// that both that copyright notice and this permission notice appear
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// in supporting documentation. The authors make no representations
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// about the suitability of this software for any purpose.
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// It is provided "as is" without express or implied warranty.
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//
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// The authors gratefully acknowledge the support of
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// GeNeSys mbH & Co. KG in producing this work.
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//
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#ifndef _BOOST_UBLAS_BLAS_
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#define _BOOST_UBLAS_BLAS_
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#include <boost/numeric/ublas/traits.hpp>
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namespace boost { namespace numeric { namespace ublas {
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namespace blas_1 {
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/** \namespace boost::numeric::ublas::blas_1
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\brief wrapper functions for level 1 blas
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*/
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/** \brief 1-Norm: \f$\sum_i |x_i|\f$
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\ingroup blas1
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*/
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template<class V>
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typename type_traits<typename V::value_type>::real_type
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asum (const V &v) {
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return norm_1 (v);
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}
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/** \brief 2-Norm: \f$\sum_i |x_i|^2\f$
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\ingroup blas1
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*/
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template<class V>
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typename type_traits<typename V::value_type>::real_type
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nrm2 (const V &v) {
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return norm_2 (v);
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}
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/** \brief element with larges absolute value: \f$\max_i |x_i|\f$
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\ingroup blas1
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*/
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template<class V>
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typename type_traits<typename V::value_type>::real_type
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amax (const V &v) {
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return norm_inf (v);
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}
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/** \brief inner product of vectors \a v1 and \a v2
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\ingroup blas1
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*/
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template<class V1, class V2>
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typename promote_traits<typename V1::value_type, typename V2::value_type>::promote_type
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dot (const V1 &v1, const V2 &v2) {
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return inner_prod (v1, v2);
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}
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/** \brief copy vector \a v2 to \a v1
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\ingroup blas1
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*/
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template<class V1, class V2>
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V1 &
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copy (V1 &v1, const V2 &v2) {
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return v1.assign (v2);
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}
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/** \brief swap vectors \a v1 and \a v2
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\ingroup blas1
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*/
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template<class V1, class V2>
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void swap (V1 &v1, V2 &v2) {
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v1.swap (v2);
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}
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/** \brief scale vector \a v with scalar \a t
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\ingroup blas1
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*/
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template<class V, class T>
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V &
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scal (V &v, const T &t) {
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return v *= t;
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}
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/** \brief compute \a v1 = \a v1 + \a t * \a v2
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\ingroup blas1
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*/
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template<class V1, class T, class V2>
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V1 &
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axpy (V1 &v1, const T &t, const V2 &v2) {
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return v1.plus_assign (t * v2);
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}
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/** \brief apply plane rotation
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\ingroup blas1
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*/
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template<class T1, class V1, class T2, class V2>
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void
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rot (const T1 &t1, V1 &v1, const T2 &t2, V2 &v2) {
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typedef typename promote_traits<typename V1::value_type, typename V2::value_type>::promote_type promote_type;
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vector<promote_type> vt (t1 * v1 + t2 * v2);
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v2.assign (- t2 * v1 + t1 * v2);
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v1.assign (vt);
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}
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}
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namespace blas_2 {
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/** \namespace boost::numeric::ublas::blas_2
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\brief wrapper functions for level 2 blas
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*/
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/** \brief multiply vector \a v with triangular matrix \a m
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\ingroup blas2
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\todo: check that matrix is really triangular
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*/
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template<class V, class M>
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V &
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tmv (V &v, const M &m) {
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return v = prod (m, v);
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}
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/** \brief solve \a m \a x = \a v in place, \a m is triangular matrix
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\ingroup blas2
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*/
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template<class V, class M, class C>
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V &
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tsv (V &v, const M &m, C) {
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return v = solve (m, v, C ());
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}
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/** \brief compute \a v1 = \a t1 * \a v1 + \a t2 * (\a m * \a v2)
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\ingroup blas2
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*/
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template<class V1, class T1, class T2, class M, class V2>
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V1 &
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gmv (V1 &v1, const T1 &t1, const T2 &t2, const M &m, const V2 &v2) {
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return v1 = t1 * v1 + t2 * prod (m, v2);
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}
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/** \brief rank 1 update: \a m = \a m + \a t * (\a v1 * \a v2<sup>T</sup>)
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\ingroup blas2
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*/
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template<class M, class T, class V1, class V2>
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M &
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gr (M &m, const T &t, const V1 &v1, const V2 &v2) {
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#ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG
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return m += t * outer_prod (v1, v2);
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#else
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return m = m + t * outer_prod (v1, v2);
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#endif
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}
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/** \brief symmetric rank 1 update: \a m = \a m + \a t * (\a v * \a v<sup>T</sup>)
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\ingroup blas2
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*/
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template<class M, class T, class V>
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M &
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sr (M &m, const T &t, const V &v) {
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#ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG
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return m += t * outer_prod (v, v);
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#else
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return m = m + t * outer_prod (v, v);
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#endif
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}
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/** \brief hermitian rank 1 update: \a m = \a m + \a t * (\a v * \a v<sup>H</sup>)
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\ingroup blas2
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*/
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template<class M, class T, class V>
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M &
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hr (M &m, const T &t, const V &v) {
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#ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG
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return m += t * outer_prod (v, conj (v));
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#else
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return m = m + t * outer_prod (v, conj (v));
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#endif
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}
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/** \brief symmetric rank 2 update: \a m = \a m + \a t *
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(\a v1 * \a v2<sup>T</sup> + \a v2 * \a v1<sup>T</sup>)
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\ingroup blas2
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*/
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template<class M, class T, class V1, class V2>
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M &
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sr2 (M &m, const T &t, const V1 &v1, const V2 &v2) {
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#ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG
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return m += t * (outer_prod (v1, v2) + outer_prod (v2, v1));
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#else
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return m = m + t * (outer_prod (v1, v2) + outer_prod (v2, v1));
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#endif
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}
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/** \brief hermitian rank 2 update: \a m = \a m +
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\a t * (\a v1 * \a v2<sup>H</sup>)
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+ \a v2 * (\a t * \a v1)<sup>H</sup>)
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\ingroup blas2
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*/
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template<class M, class T, class V1, class V2>
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M &
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hr2 (M &m, const T &t, const V1 &v1, const V2 &v2) {
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#ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG
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return m += t * outer_prod (v1, conj (v2)) + type_traits<T>::conj (t) * outer_prod (v2, conj (v1));
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#else
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return m = m + t * outer_prod (v1, conj (v2)) + type_traits<T>::conj (t) * outer_prod (v2, conj (v1));
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#endif
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}
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}
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namespace blas_3 {
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/** \namespace boost::numeric::ublas::blas_3
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\brief wrapper functions for level 3 blas
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*/
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/** \brief triangular matrix multiplication
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\ingroup blas3
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*/
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template<class M1, class T, class M2, class M3>
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M1 &
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tmm (M1 &m1, const T &t, const M2 &m2, const M3 &m3) {
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return m1 = t * prod (m2, m3);
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}
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/** \brief triangular solve \a m2 * \a x = \a t * \a m1 in place,
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\a m2 is a triangular matrix
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\ingroup blas3
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*/
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template<class M1, class T, class M2, class C>
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M1 &
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tsm (M1 &m1, const T &t, const M2 &m2, C) {
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return m1 = solve (m2, t * m1, C ());
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}
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/** \brief general matrix multiplication
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\ingroup blas3
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*/
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template<class M1, class T1, class T2, class M2, class M3>
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M1 &
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gmm (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2, const M3 &m3) {
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return m1 = t1 * m1 + t2 * prod (m2, m3);
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}
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/** \brief symmetric rank k update: \a m1 = \a t * \a m1 +
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\a t2 * (\a m2 * \a m2<sup>T</sup>)
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\ingroup blas3
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\todo use opb_prod()
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*/
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template<class M1, class T1, class T2, class M2>
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M1 &
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srk (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2) {
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return m1 = t1 * m1 + t2 * prod (m2, trans (m2));
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}
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/** \brief hermitian rank k update: \a m1 = \a t * \a m1 +
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\a t2 * (\a m2 * \a m2<sup>H</sup>)
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\ingroup blas3
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\todo use opb_prod()
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*/
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template<class M1, class T1, class T2, class M2>
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M1 &
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hrk (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2) {
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return m1 = t1 * m1 + t2 * prod (m2, herm (m2));
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}
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/** \brief generalized symmetric rank k update:
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\a m1 = \a t1 * \a m1 + \a t2 * (\a m2 * \a m3<sup>T</sup>)
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+ \a t2 * (\a m3 * \a m2<sup>T</sup>)
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\ingroup blas3
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\todo use opb_prod()
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*/
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template<class M1, class T1, class T2, class M2, class M3>
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M1 &
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sr2k (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2, const M3 &m3) {
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return m1 = t1 * m1 + t2 * (prod (m2, trans (m3)) + prod (m3, trans (m2)));
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}
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/** \brief generalized hermitian rank k update:
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\a m1 = \a t1 * \a m1 + \a t2 * (\a m2 * \a m3<sup>H</sup>)
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+ (\a m3 * (\a t2 * \a m2)<sup>H</sup>)
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\ingroup blas3
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\todo use opb_prod()
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*/
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template<class M1, class T1, class T2, class M2, class M3>
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M1 &
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hr2k (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2, const M3 &m3) {
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return m1 = t1 * m1 + t2 * prod (m2, herm (m3)) + type_traits<T2>::conj (t2) * prod (m3, herm (m2));
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}
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}
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}}}
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#endif
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