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351 lines
14 KiB
351 lines
14 KiB
5 years ago
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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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// Distributed under the Boost Software License, Version 1.0. (See
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// accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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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_LU_
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#define _BOOST_UBLAS_LU_
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#include <boost/numeric/ublas/operation.hpp>
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#include <boost/numeric/ublas/vector_proxy.hpp>
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#include <boost/numeric/ublas/matrix_proxy.hpp>
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#include <boost/numeric/ublas/vector.hpp>
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#include <boost/numeric/ublas/triangular.hpp>
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// LU factorizations in the spirit of LAPACK and Golub & van Loan
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namespace boost { namespace numeric { namespace ublas {
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/** \brief
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*
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* \tparam T
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* \tparam A
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*/
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template<class T = std::size_t, class A = unbounded_array<T> >
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class permutation_matrix:
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public vector<T, A> {
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public:
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typedef vector<T, A> vector_type;
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typedef typename vector_type::size_type size_type;
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// Construction and destruction
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BOOST_UBLAS_INLINE
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explicit
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permutation_matrix (size_type size):
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vector<T, A> (size) {
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for (size_type i = 0; i < size; ++ i)
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(*this) (i) = i;
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}
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BOOST_UBLAS_INLINE
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explicit
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permutation_matrix (const vector_type & init)
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: vector_type(init)
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{ }
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BOOST_UBLAS_INLINE
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~permutation_matrix () {}
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// Assignment
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BOOST_UBLAS_INLINE
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permutation_matrix &operator = (const permutation_matrix &m) {
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vector_type::operator = (m);
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return *this;
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}
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};
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template<class PM, class MV>
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BOOST_UBLAS_INLINE
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void swap_rows (const PM &pm, MV &mv, vector_tag) {
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typedef typename PM::size_type size_type;
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size_type size = pm.size ();
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for (size_type i = 0; i < size; ++ i) {
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if (i != pm (i))
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std::swap (mv (i), mv (pm (i)));
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}
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}
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template<class PM, class MV>
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BOOST_UBLAS_INLINE
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void swap_rows (const PM &pm, MV &mv, matrix_tag) {
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typedef typename PM::size_type size_type;
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size_type size = pm.size ();
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for (size_type i = 0; i < size; ++ i) {
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if (i != pm (i))
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row (mv, i).swap (row (mv, pm (i)));
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}
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}
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// Dispatcher
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template<class PM, class MV>
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BOOST_UBLAS_INLINE
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void swap_rows (const PM &pm, MV &mv) {
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swap_rows (pm, mv, typename MV::type_category ());
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}
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// LU factorization without pivoting
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template<class M>
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typename M::size_type lu_factorize (M &m) {
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typedef typename M::size_type size_type;
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typedef typename M::value_type value_type;
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#if BOOST_UBLAS_TYPE_CHECK
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typedef M matrix_type;
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matrix_type cm (m);
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#endif
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size_type singular = 0;
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size_type size1 = m.size1 ();
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size_type size2 = m.size2 ();
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size_type size = (std::min) (size1, size2);
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for (size_type i = 0; i < size; ++ i) {
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matrix_column<M> mci (column (m, i));
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matrix_row<M> mri (row (m, i));
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if (m (i, i) != value_type/*zero*/()) {
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value_type m_inv = value_type (1) / m (i, i);
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project (mci, range (i + 1, size1)) *= m_inv;
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} else if (singular == 0) {
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singular = i + 1;
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}
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project (m, range (i + 1, size1), range (i + 1, size2)).minus_assign (
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outer_prod (project (mci, range (i + 1, size1)),
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project (mri, range (i + 1, size2))));
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}
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#if BOOST_UBLAS_TYPE_CHECK
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BOOST_UBLAS_CHECK (singular != 0 ||
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detail::expression_type_check (prod (triangular_adaptor<matrix_type, unit_lower> (m),
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triangular_adaptor<matrix_type, upper> (m)),
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cm), internal_logic ());
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#endif
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return singular;
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}
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// LU factorization with partial pivoting
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template<class M, class PM>
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typename M::size_type lu_factorize (M &m, PM &pm) {
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typedef typename M::size_type size_type;
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typedef typename M::value_type value_type;
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#if BOOST_UBLAS_TYPE_CHECK
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typedef M matrix_type;
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matrix_type cm (m);
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#endif
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size_type singular = 0;
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size_type size1 = m.size1 ();
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size_type size2 = m.size2 ();
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size_type size = (std::min) (size1, size2);
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for (size_type i = 0; i < size; ++ i) {
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matrix_column<M> mci (column (m, i));
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matrix_row<M> mri (row (m, i));
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size_type i_norm_inf = i + index_norm_inf (project (mci, range (i, size1)));
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BOOST_UBLAS_CHECK (i_norm_inf < size1, external_logic ());
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if (m (i_norm_inf, i) != value_type/*zero*/()) {
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if (i_norm_inf != i) {
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pm (i) = i_norm_inf;
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row (m, i_norm_inf).swap (mri);
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} else {
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BOOST_UBLAS_CHECK (pm (i) == i_norm_inf, external_logic ());
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}
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value_type m_inv = value_type (1) / m (i, i);
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project (mci, range (i + 1, size1)) *= m_inv;
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} else if (singular == 0) {
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singular = i + 1;
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}
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project (m, range (i + 1, size1), range (i + 1, size2)).minus_assign (
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outer_prod (project (mci, range (i + 1, size1)),
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project (mri, range (i + 1, size2))));
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}
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#if BOOST_UBLAS_TYPE_CHECK
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swap_rows (pm, cm);
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BOOST_UBLAS_CHECK (singular != 0 ||
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detail::expression_type_check (prod (triangular_adaptor<matrix_type, unit_lower> (m),
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triangular_adaptor<matrix_type, upper> (m)), cm), internal_logic ());
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#endif
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return singular;
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}
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template<class M, class PM>
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typename M::size_type axpy_lu_factorize (M &m, PM &pm) {
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typedef M matrix_type;
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typedef typename M::size_type size_type;
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typedef typename M::value_type value_type;
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typedef vector<value_type> vector_type;
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#if BOOST_UBLAS_TYPE_CHECK
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matrix_type cm (m);
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#endif
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size_type singular = 0;
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size_type size1 = m.size1 ();
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size_type size2 = m.size2 ();
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size_type size = (std::min) (size1, size2);
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#ifndef BOOST_UBLAS_LU_WITH_INPLACE_SOLVE
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matrix_type mr (m);
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mr.assign (zero_matrix<value_type> (size1, size2));
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vector_type v (size1);
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for (size_type i = 0; i < size; ++ i) {
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matrix_range<matrix_type> lrr (project (mr, range (0, i), range (0, i)));
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vector_range<matrix_column<matrix_type> > urr (project (column (mr, i), range (0, i)));
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urr.assign (solve (lrr, project (column (m, i), range (0, i)), unit_lower_tag ()));
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project (v, range (i, size1)).assign (
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project (column (m, i), range (i, size1)) -
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axpy_prod<vector_type> (project (mr, range (i, size1), range (0, i)), urr));
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size_type i_norm_inf = i + index_norm_inf (project (v, range (i, size1)));
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BOOST_UBLAS_CHECK (i_norm_inf < size1, external_logic ());
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if (v (i_norm_inf) != value_type/*zero*/()) {
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if (i_norm_inf != i) {
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pm (i) = i_norm_inf;
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std::swap (v (i_norm_inf), v (i));
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project (row (m, i_norm_inf), range (i + 1, size2)).swap (project (row (m, i), range (i + 1, size2)));
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} else {
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BOOST_UBLAS_CHECK (pm (i) == i_norm_inf, external_logic ());
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}
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project (column (mr, i), range (i + 1, size1)).assign (
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project (v, range (i + 1, size1)) / v (i));
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if (i_norm_inf != i) {
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project (row (mr, i_norm_inf), range (0, i)).swap (project (row (mr, i), range (0, i)));
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}
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} else if (singular == 0) {
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singular = i + 1;
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}
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mr (i, i) = v (i);
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}
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m.assign (mr);
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#else
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matrix_type lr (m);
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matrix_type ur (m);
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lr.assign (identity_matrix<value_type> (size1, size2));
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ur.assign (zero_matrix<value_type> (size1, size2));
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vector_type v (size1);
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for (size_type i = 0; i < size; ++ i) {
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matrix_range<matrix_type> lrr (project (lr, range (0, i), range (0, i)));
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vector_range<matrix_column<matrix_type> > urr (project (column (ur, i), range (0, i)));
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urr.assign (project (column (m, i), range (0, i)));
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inplace_solve (lrr, urr, unit_lower_tag ());
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project (v, range (i, size1)).assign (
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project (column (m, i), range (i, size1)) -
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axpy_prod<vector_type> (project (lr, range (i, size1), range (0, i)), urr));
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size_type i_norm_inf = i + index_norm_inf (project (v, range (i, size1)));
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BOOST_UBLAS_CHECK (i_norm_inf < size1, external_logic ());
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if (v (i_norm_inf) != value_type/*zero*/()) {
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if (i_norm_inf != i) {
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pm (i) = i_norm_inf;
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std::swap (v (i_norm_inf), v (i));
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project (row (m, i_norm_inf), range (i + 1, size2)).swap (project (row (m, i), range (i + 1, size2)));
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} else {
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BOOST_UBLAS_CHECK (pm (i) == i_norm_inf, external_logic ());
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}
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project (column (lr, i), range (i + 1, size1)).assign (
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project (v, range (i + 1, size1)) / v (i));
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if (i_norm_inf != i) {
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project (row (lr, i_norm_inf), range (0, i)).swap (project (row (lr, i), range (0, i)));
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}
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} else if (singular == 0) {
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singular = i + 1;
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}
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ur (i, i) = v (i);
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}
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m.assign (triangular_adaptor<matrix_type, strict_lower> (lr) +
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triangular_adaptor<matrix_type, upper> (ur));
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#endif
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#if BOOST_UBLAS_TYPE_CHECK
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swap_rows (pm, cm);
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BOOST_UBLAS_CHECK (singular != 0 ||
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detail::expression_type_check (prod (triangular_adaptor<matrix_type, unit_lower> (m),
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triangular_adaptor<matrix_type, upper> (m)), cm), internal_logic ());
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#endif
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return singular;
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}
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// LU substitution
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template<class M, class E>
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void lu_substitute (const M &m, vector_expression<E> &e) {
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#if BOOST_UBLAS_TYPE_CHECK
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typedef const M const_matrix_type;
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typedef vector<typename E::value_type> vector_type;
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vector_type cv1 (e);
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#endif
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inplace_solve (m, e, unit_lower_tag ());
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#if BOOST_UBLAS_TYPE_CHECK
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BOOST_UBLAS_CHECK (detail::expression_type_check (prod (triangular_adaptor<const_matrix_type, unit_lower> (m), e), cv1), internal_logic ());
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vector_type cv2 (e);
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#endif
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inplace_solve (m, e, upper_tag ());
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#if BOOST_UBLAS_TYPE_CHECK
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BOOST_UBLAS_CHECK (detail::expression_type_check (prod (triangular_adaptor<const_matrix_type, upper> (m), e), cv2), internal_logic ());
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#endif
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}
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template<class M, class E>
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void lu_substitute (const M &m, matrix_expression<E> &e) {
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#if BOOST_UBLAS_TYPE_CHECK
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typedef const M const_matrix_type;
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typedef matrix<typename E::value_type> matrix_type;
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matrix_type cm1 (e);
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#endif
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inplace_solve (m, e, unit_lower_tag ());
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#if BOOST_UBLAS_TYPE_CHECK
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BOOST_UBLAS_CHECK (detail::expression_type_check (prod (triangular_adaptor<const_matrix_type, unit_lower> (m), e), cm1), internal_logic ());
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matrix_type cm2 (e);
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#endif
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inplace_solve (m, e, upper_tag ());
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#if BOOST_UBLAS_TYPE_CHECK
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BOOST_UBLAS_CHECK (detail::expression_type_check (prod (triangular_adaptor<const_matrix_type, upper> (m), e), cm2), internal_logic ());
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#endif
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}
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template<class M, class PMT, class PMA, class MV>
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void lu_substitute (const M &m, const permutation_matrix<PMT, PMA> &pm, MV &mv) {
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swap_rows (pm, mv);
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lu_substitute (m, mv);
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}
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template<class E, class M>
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void lu_substitute (vector_expression<E> &e, const M &m) {
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#if BOOST_UBLAS_TYPE_CHECK
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typedef const M const_matrix_type;
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typedef vector<typename E::value_type> vector_type;
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vector_type cv1 (e);
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#endif
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inplace_solve (e, m, upper_tag ());
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#if BOOST_UBLAS_TYPE_CHECK
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BOOST_UBLAS_CHECK (detail::expression_type_check (prod (e, triangular_adaptor<const_matrix_type, upper> (m)), cv1), internal_logic ());
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vector_type cv2 (e);
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#endif
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inplace_solve (e, m, unit_lower_tag ());
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#if BOOST_UBLAS_TYPE_CHECK
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BOOST_UBLAS_CHECK (detail::expression_type_check (prod (e, triangular_adaptor<const_matrix_type, unit_lower> (m)), cv2), internal_logic ());
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#endif
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}
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template<class E, class M>
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void lu_substitute (matrix_expression<E> &e, const M &m) {
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#if BOOST_UBLAS_TYPE_CHECK
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typedef const M const_matrix_type;
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typedef matrix<typename E::value_type> matrix_type;
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matrix_type cm1 (e);
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#endif
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inplace_solve (e, m, upper_tag ());
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#if BOOST_UBLAS_TYPE_CHECK
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BOOST_UBLAS_CHECK (detail::expression_type_check (prod (e, triangular_adaptor<const_matrix_type, upper> (m)), cm1), internal_logic ());
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matrix_type cm2 (e);
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#endif
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inplace_solve (e, m, unit_lower_tag ());
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#if BOOST_UBLAS_TYPE_CHECK
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BOOST_UBLAS_CHECK (detail::expression_type_check (prod (e, triangular_adaptor<const_matrix_type, unit_lower> (m)), cm2), internal_logic ());
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#endif
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}
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template<class MV, class M, class PMT, class PMA>
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void lu_substitute (MV &mv, const M &m, const permutation_matrix<PMT, PMA> &pm) {
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swap_rows (pm, mv);
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lu_substitute (mv, m);
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}
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}}}
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#endif
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