boost/numeric/ublas/blas.hpp
// Copyright (c) 2000-2011 Joerg Walter, Mathias Koch, David Bellot // // Distributed under the Boost Software License, Version 1.0. (See // accompanying file LICENSE_1_0.txt or copy at // http://www.boost.org/LICENSE_1_0.txt) // // The authors gratefully acknowledge the support of // GeNeSys mbH & Co. KG in producing this work. #ifndef _BOOST_UBLAS_BLAS_ #define _BOOST_UBLAS_BLAS_ #include <boost/numeric/ublas/traits.hpp> namespace boost { namespace numeric { namespace ublas { /** Interface and implementation of BLAS level 1 * This includes functions which perform \b vector-vector operations. * More information about BLAS can be found at * <a href="http://en.wikipedia.org/wiki/BLAS">http://en.wikipedia.org/wiki/BLAS</a> */ namespace blas_1 { /** 1-Norm: \f$\sum_i |x_i|\f$ (also called \f$\mathcal{L}_1\f$ or Manhattan norm) * * \param v a vector or vector expression * \return the 1-Norm with type of the vector's type * * \tparam V type of the vector (not needed by default) */ template<class V> typename type_traits<typename V::value_type>::real_type asum (const V &v) { return norm_1 (v); } /** 2-Norm: \f$\sum_i |x_i|^2\f$ (also called \f$\mathcal{L}_2\f$ or Euclidean norm) * * \param v a vector or vector expression * \return the 2-Norm with type of the vector's type * * \tparam V type of the vector (not needed by default) */ template<class V> typename type_traits<typename V::value_type>::real_type nrm2 (const V &v) { return norm_2 (v); } /** Infinite-norm: \f$\max_i |x_i|\f$ (also called \f$\mathcal{L}_\infty\f$ norm) * * \param v a vector or vector expression * \return the Infinite-Norm with type of the vector's type * * \tparam V type of the vector (not needed by default) */ template<class V> typename type_traits<typename V::value_type>::real_type amax (const V &v) { return norm_inf (v); } /** Inner product of vectors \f$v_1\f$ and \f$v_2\f$ * * \param v1 first vector of the inner product * \param v2 second vector of the inner product * \return the inner product of the type of the most generic type of the 2 vectors * * \tparam V1 type of first vector (not needed by default) * \tparam V2 type of second vector (not needed by default) */ template<class V1, class V2> typename promote_traits<typename V1::value_type, typename V2::value_type>::promote_type dot (const V1 &v1, const V2 &v2) { return inner_prod (v1, v2); } /** Copy vector \f$v_2\f$ to \f$v_1\f$ * * \param v1 target vector * \param v2 source vector * \return a reference to the target vector * * \tparam V1 type of first vector (not needed by default) * \tparam V2 type of second vector (not needed by default) */ template<class V1, class V2> V1 & copy (V1 &v1, const V2 &v2) { return v1.assign (v2); } /** Swap vectors \f$v_1\f$ and \f$v_2\f$ * * \param v1 first vector * \param v2 second vector * * \tparam V1 type of first vector (not needed by default) * \tparam V2 type of second vector (not needed by default) */ template<class V1, class V2> void swap (V1 &v1, V2 &v2) { v1.swap (v2); } /** scale vector \f$v\f$ with scalar \f$t\f$ * * \param v vector to be scaled * \param t the scalar * \return \c t*v * * \tparam V type of the vector (not needed by default) * \tparam T type of the scalar (not needed by default) */ template<class V, class T> V & scal (V &v, const T &t) { return v *= t; } /** Compute \f$v_1= v_1 + t.v_2\f$ * * \param v1 target and first vector * \param t the scalar * \param v2 second vector * \return a reference to the first and target vector * * \tparam V1 type of the first vector (not needed by default) * \tparam T type of the scalar (not needed by default) * \tparam V2 type of the second vector (not needed by default) */ template<class V1, class T, class V2> V1 & axpy (V1 &v1, const T &t, const V2 &v2) { return v1.plus_assign (t * v2); } /** Performs rotation of points in the plane and assign the result to the first vector * * Each point is defined as a pair \c v1(i) and \c v2(i), being respectively * the \f$x\f$ and \f$y\f$ coordinates. The parameters \c t1 and \t2 are respectively * the cosine and sine of the angle of the rotation. * Results are not returned but directly written into \c v1. * * \param t1 cosine of the rotation * \param v1 vector of \f$x\f$ values * \param t2 sine of the rotation * \param v2 vector of \f$y\f$ values * * \tparam T1 type of the cosine value (not needed by default) * \tparam V1 type of the \f$x\f$ vector (not needed by default) * \tparam T2 type of the sine value (not needed by default) * \tparam V2 type of the \f$y\f$ vector (not needed by default) */ template<class T1, class V1, class T2, class V2> void rot (const T1 &t1, V1 &v1, const T2 &t2, V2 &v2) { typedef typename promote_traits<typename V1::value_type, typename V2::value_type>::promote_type promote_type; vector<promote_type> vt (t1 * v1 + t2 * v2); v2.assign (- t2 * v1 + t1 * v2); v1.assign (vt); } } /** \brief Interface and implementation of BLAS level 2 * This includes functions which perform \b matrix-vector operations. * More information about BLAS can be found at * <a href="http://en.wikipedia.org/wiki/BLAS">http://en.wikipedia.org/wiki/BLAS</a> */ namespace blas_2 { /** \brief multiply vector \c v with triangular matrix \c m * * \param v a vector * \param m a triangular matrix * \return the result of the product * * \tparam V type of the vector (not needed by default) * \tparam M type of the matrix (not needed by default) */ template<class V, class M> V & tmv (V &v, const M &m) { return v = prod (m, v); } /** \brief solve \f$m.x = v\f$ in place, where \c m is a triangular matrix * * \param v a vector * \param m a matrix * \param C (this parameter is not needed) * \return a result vector from the above operation * * \tparam V type of the vector (not needed by default) * \tparam M type of the matrix (not needed by default) * \tparam C n/a */ template<class V, class M, class C> V & tsv (V &v, const M &m, C) { return v = solve (m, v, C ()); } /** \brief compute \f$ v_1 = t_1.v_1 + t_2.(m.v_2)\f$, a general matrix-vector product * * \param v1 a vector * \param t1 a scalar * \param t2 another scalar * \param m a matrix * \param v2 another vector * \return the vector \c v1 with the result from the above operation * * \tparam V1 type of first vector (not needed by default) * \tparam T1 type of first scalar (not needed by default) * \tparam T2 type of second scalar (not needed by default) * \tparam M type of matrix (not needed by default) * \tparam V2 type of second vector (not needed by default) */ template<class V1, class T1, class T2, class M, class V2> V1 & gmv (V1 &v1, const T1 &t1, const T2 &t2, const M &m, const V2 &v2) { return v1 = t1 * v1 + t2 * prod (m, v2); } /** \brief Rank 1 update: \f$ m = m + t.(v_1.v_2^T)\f$ * * \param m a matrix * \param t a scalar * \param v1 a vector * \param v2 another vector * \return a matrix with the result from the above operation * * \tparam M type of matrix (not needed by default) * \tparam T type of scalar (not needed by default) * \tparam V1 type of first vector (not needed by default) * \tparam V2type of second vector (not needed by default) */ template<class M, class T, class V1, class V2> M & gr (M &m, const T &t, const V1 &v1, const V2 &v2) { #ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG return m += t * outer_prod (v1, v2); #else return m = m + t * outer_prod (v1, v2); #endif } /** \brief symmetric rank 1 update: \f$m = m + t.(v.v^T)\f$ * * \param m a matrix * \param t a scalar * \param v a vector * \return a matrix with the result from the above operation * * \tparam M type of matrix (not needed by default) * \tparam T type of scalar (not needed by default) * \tparam V type of vector (not needed by default) */ template<class M, class T, class V> M & sr (M &m, const T &t, const V &v) { #ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG return m += t * outer_prod (v, v); #else return m = m + t * outer_prod (v, v); #endif } /** \brief hermitian rank 1 update: \f$m = m + t.(v.v^H)\f$ * * \param m a matrix * \param t a scalar * \param v a vector * \return a matrix with the result from the above operation * * \tparam M type of matrix (not needed by default) * \tparam T type of scalar (not needed by default) * \tparam V type of vector (not needed by default) */ template<class M, class T, class V> M & hr (M &m, const T &t, const V &v) { #ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG return m += t * outer_prod (v, conj (v)); #else return m = m + t * outer_prod (v, conj (v)); #endif } /** \brief symmetric rank 2 update: \f$ m=m+ t.(v_1.v_2^T + v_2.v_1^T)\f$ * * \param m a matrix * \param t a scalar * \param v1 a vector * \param v2 another vector * \return a matrix with the result from the above operation * * \tparam M type of matrix (not needed by default) * \tparam T type of scalar (not needed by default) * \tparam V1 type of first vector (not needed by default) * \tparam V2type of second vector (not needed by default) */ template<class M, class T, class V1, class V2> M & sr2 (M &m, const T &t, const V1 &v1, const V2 &v2) { #ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG return m += t * (outer_prod (v1, v2) + outer_prod (v2, v1)); #else return m = m + t * (outer_prod (v1, v2) + outer_prod (v2, v1)); #endif } /** \brief hermitian rank 2 update: \f$m=m+t.(v_1.v_2^H) + v_2.(t.v_1)^H)\f$ * * \param m a matrix * \param t a scalar * \param v1 a vector * \param v2 another vector * \return a matrix with the result from the above operation * * \tparam M type of matrix (not needed by default) * \tparam T type of scalar (not needed by default) * \tparam V1 type of first vector (not needed by default) * \tparam V2type of second vector (not needed by default) */ template<class M, class T, class V1, class V2> M & hr2 (M &m, const T &t, const V1 &v1, const V2 &v2) { #ifndef BOOST_UBLAS_SIMPLE_ET_DEBUG return m += t * outer_prod (v1, conj (v2)) + type_traits<T>::conj (t) * outer_prod (v2, conj (v1)); #else return m = m + t * outer_prod (v1, conj (v2)) + type_traits<T>::conj (t) * outer_prod (v2, conj (v1)); #endif } } /** \brief Interface and implementation of BLAS level 3 * This includes functions which perform \b matrix-matrix operations. * More information about BLAS can be found at * <a href="http://en.wikipedia.org/wiki/BLAS">http://en.wikipedia.org/wiki/BLAS</a> */ namespace blas_3 { /** \brief triangular matrix multiplication \f$m_1=t.m_2.m_3\f$ where \f$m_2\f$ and \f$m_3\f$ are triangular * * \param m1 a matrix for storing result * \param t a scalar * \param m2 a triangular matrix * \param m3 a triangular matrix * \return the matrix \c m1 * * \tparam M1 type of the result matrix (not needed by default) * \tparam T type of the scalar (not needed by default) * \tparam M2 type of the first triangular matrix (not needed by default) * \tparam M3 type of the second triangular matrix (not needed by default) * */ template<class M1, class T, class M2, class M3> M1 & tmm (M1 &m1, const T &t, const M2 &m2, const M3 &m3) { return m1 = t * prod (m2, m3); } /** \brief triangular solve \f$ m_2.x = t.m_1\f$ in place, \f$m_2\f$ is a triangular matrix * * \param m1 a matrix * \param t a scalar * \param m2 a triangular matrix * \param C (not used) * \return the \f$m_1\f$ matrix * * \tparam M1 type of the first matrix (not needed by default) * \tparam T type of the scalar (not needed by default) * \tparam M2 type of the triangular matrix (not needed by default) * \tparam C (n/a) */ template<class M1, class T, class M2, class C> M1 & tsm (M1 &m1, const T &t, const M2 &m2, C) { return m1 = solve (m2, t * m1, C ()); } /** \brief general matrix multiplication \f$m_1=t_1.m_1 + t_2.m_2.m_3\f$ * * \param m1 first matrix * \param t1 first scalar * \param t2 second scalar * \param m2 second matrix * \param m3 third matrix * \return the matrix \c m1 * * \tparam M1 type of the first matrix (not needed by default) * \tparam T1 type of the first scalar (not needed by default) * \tparam T2 type of the second scalar (not needed by default) * \tparam M2 type of the second matrix (not needed by default) * \tparam M3 type of the third matrix (not needed by default) */ template<class M1, class T1, class T2, class M2, class M3> M1 & gmm (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2, const M3 &m3) { return m1 = t1 * m1 + t2 * prod (m2, m3); } /** \brief symmetric rank \a k update: \f$m_1=t.m_1+t_2.(m_2.m_2^T)\f$ * * \param m1 first matrix * \param t1 first scalar * \param t2 second scalar * \param m2 second matrix * \return matrix \c m1 * * \tparam M1 type of the first matrix (not needed by default) * \tparam T1 type of the first scalar (not needed by default) * \tparam T2 type of the second scalar (not needed by default) * \tparam M2 type of the second matrix (not needed by default) * \todo use opb_prod() */ template<class M1, class T1, class T2, class M2> M1 & srk (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2) { return m1 = t1 * m1 + t2 * prod (m2, trans (m2)); } /** \brief hermitian rank \a k update: \f$m_1=t.m_1+t_2.(m_2.m2^H)\f$ * * \param m1 first matrix * \param t1 first scalar * \param t2 second scalar * \param m2 second matrix * \return matrix \c m1 * * \tparam M1 type of the first matrix (not needed by default) * \tparam T1 type of the first scalar (not needed by default) * \tparam T2 type of the second scalar (not needed by default) * \tparam M2 type of the second matrix (not needed by default) * \todo use opb_prod() */ template<class M1, class T1, class T2, class M2> M1 & hrk (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2) { return m1 = t1 * m1 + t2 * prod (m2, herm (m2)); } /** \brief generalized symmetric rank \a k update: \f$m_1=t_1.m_1+t_2.(m_2.m3^T)+t_2.(m_3.m2^T)\f$ * * \param m1 first matrix * \param t1 first scalar * \param t2 second scalar * \param m2 second matrix * \param m3 third matrix * \return matrix \c m1 * * \tparam M1 type of the first matrix (not needed by default) * \tparam T1 type of the first scalar (not needed by default) * \tparam T2 type of the second scalar (not needed by default) * \tparam M2 type of the second matrix (not needed by default) * \tparam M3 type of the third matrix (not needed by default) * \todo use opb_prod() */ template<class M1, class T1, class T2, class M2, class M3> M1 & sr2k (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2, const M3 &m3) { return m1 = t1 * m1 + t2 * (prod (m2, trans (m3)) + prod (m3, trans (m2))); } /** \brief generalized hermitian rank \a k update: * \f$m_1=t_1.m_1+t_2.(m_2.m_3^H)+(m_3.(t_2.m_2)^H)\f$ * * \param m1 first matrix * \param t1 first scalar * \param t2 second scalar * \param m2 second matrix * \param m3 third matrix * \return matrix \c m1 * * \tparam M1 type of the first matrix (not needed by default) * \tparam T1 type of the first scalar (not needed by default) * \tparam T2 type of the second scalar (not needed by default) * \tparam M2 type of the second matrix (not needed by default) * \tparam M3 type of the third matrix (not needed by default) * \todo use opb_prod() */ template<class M1, class T1, class T2, class M2, class M3> M1 & hr2k (M1 &m1, const T1 &t1, const T2 &t2, const M2 &m2, const M3 &m3) { return m1 = t1 * m1 + t2 * prod (m2, herm (m3)) + type_traits<T2>::conj (t2) * prod (m3, herm (m2)); } } }}} #endif