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@@ -1,350 +0,0 @@
-//
-// Copyright (c) 2000-2002
-// Joerg Walter, Mathias Koch
-//
-// 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_LU_
-#define _BOOST_UBLAS_LU_
-
-#include <boost/numeric/ublas/operation.hpp>
-#include <boost/numeric/ublas/vector_proxy.hpp>
-#include <boost/numeric/ublas/matrix_proxy.hpp>
-#include <boost/numeric/ublas/vector.hpp>
-#include <boost/numeric/ublas/triangular.hpp>
-
-// LU factorizations in the spirit of LAPACK and Golub & van Loan
-
-namespace boost { namespace numeric { namespace ublas {
-
- /** \brief
- *
- * \tparam T
- * \tparam A
- */
- template<class T = std::size_t, class A = unbounded_array<T> >
- class permutation_matrix:
- public vector<T, A> {
- public:
- typedef vector<T, A> vector_type;
- typedef typename vector_type::size_type size_type;
-
- // Construction and destruction
- BOOST_UBLAS_INLINE
- explicit
- permutation_matrix (size_type size):
- vector<T, A> (size) {
- for (size_type i = 0; i < size; ++ i)
- (*this) (i) = i;
- }
- BOOST_UBLAS_INLINE
- explicit
- permutation_matrix (const vector_type & init)
- : vector_type(init)
- { }
- BOOST_UBLAS_INLINE
- ~permutation_matrix () {}
-
- // Assignment
- BOOST_UBLAS_INLINE
- permutation_matrix &operator = (const permutation_matrix &m) {
- vector_type::operator = (m);
- return *this;
- }
- };
-
- template<class PM, class MV>
- BOOST_UBLAS_INLINE
- void swap_rows (const PM &pm, MV &mv, vector_tag) {
- typedef typename PM::size_type size_type;
-
- size_type size = pm.size ();
- for (size_type i = 0; i < size; ++ i) {
- if (i != pm (i))
- std::swap (mv (i), mv (pm (i)));
- }
- }
- template<class PM, class MV>
- BOOST_UBLAS_INLINE
- void swap_rows (const PM &pm, MV &mv, matrix_tag) {
- typedef typename PM::size_type size_type;
-
- size_type size = pm.size ();
- for (size_type i = 0; i < size; ++ i) {
- if (i != pm (i))
- row (mv, i).swap (row (mv, pm (i)));
- }
- }
- // Dispatcher
- template<class PM, class MV>
- BOOST_UBLAS_INLINE
- void swap_rows (const PM &pm, MV &mv) {
- swap_rows (pm, mv, typename MV::type_category ());
- }
-
- // LU factorization without pivoting
- template<class M>
- typename M::size_type lu_factorize (M &m) {
-
- typedef typename M::size_type size_type;
- typedef typename M::value_type value_type;
-
-#if BOOST_UBLAS_TYPE_CHECK
- typedef M matrix_type;
- matrix_type cm (m);
-#endif
- size_type singular = 0;
- size_type size1 = m.size1 ();
- size_type size2 = m.size2 ();
- size_type size = (std::min) (size1, size2);
- for (size_type i = 0; i < size; ++ i) {
- matrix_column<M> mci (column (m, i));
- matrix_row<M> mri (row (m, i));
- if (m (i, i) != value_type/*zero*/()) {
- value_type m_inv = value_type (1) / m (i, i);
- project (mci, range (i + 1, size1)) *= m_inv;
- } else if (singular == 0) {
- singular = i + 1;
- }
- project (m, range (i + 1, size1), range (i + 1, size2)).minus_assign (
- outer_prod (project (mci, range (i + 1, size1)),
- project (mri, range (i + 1, size2))));
- }
-#if BOOST_UBLAS_TYPE_CHECK
- BOOST_UBLAS_CHECK (singular != 0 ||
- detail::expression_type_check (prod (triangular_adaptor<matrix_type, unit_lower> (m),
- triangular_adaptor<matrix_type, upper> (m)),
- cm), internal_logic ());
-#endif
- return singular;
- }
-
- // LU factorization with partial pivoting
- template<class M, class PM>
- typename M::size_type lu_factorize (M &m, PM &pm) {
- typedef typename M::size_type size_type;
- typedef typename M::value_type value_type;
-
-#if BOOST_UBLAS_TYPE_CHECK
- typedef M matrix_type;
- matrix_type cm (m);
-#endif
- size_type singular = 0;
- size_type size1 = m.size1 ();
- size_type size2 = m.size2 ();
- size_type size = (std::min) (size1, size2);
- for (size_type i = 0; i < size; ++ i) {
- matrix_column<M> mci (column (m, i));
- matrix_row<M> mri (row (m, i));
- size_type i_norm_inf = i + index_norm_inf (project (mci, range (i, size1)));
- BOOST_UBLAS_CHECK (i_norm_inf < size1, external_logic ());
- if (m (i_norm_inf, i) != value_type/*zero*/()) {
- if (i_norm_inf != i) {
- pm (i) = i_norm_inf;
- row (m, i_norm_inf).swap (mri);
- } else {
- BOOST_UBLAS_CHECK (pm (i) == i_norm_inf, external_logic ());
- }
- value_type m_inv = value_type (1) / m (i, i);
- project (mci, range (i + 1, size1)) *= m_inv;
- } else if (singular == 0) {
- singular = i + 1;
- }
- project (m, range (i + 1, size1), range (i + 1, size2)).minus_assign (
- outer_prod (project (mci, range (i + 1, size1)),
- project (mri, range (i + 1, size2))));
- }
-#if BOOST_UBLAS_TYPE_CHECK
- swap_rows (pm, cm);
- BOOST_UBLAS_CHECK (singular != 0 ||
- detail::expression_type_check (prod (triangular_adaptor<matrix_type, unit_lower> (m),
- triangular_adaptor<matrix_type, upper> (m)), cm), internal_logic ());
-#endif
- return singular;
- }
-
- template<class M, class PM>
- typename M::size_type axpy_lu_factorize (M &m, PM &pm) {
- typedef M matrix_type;
- typedef typename M::size_type size_type;
- typedef typename M::value_type value_type;
- typedef vector<value_type> vector_type;
-
-#if BOOST_UBLAS_TYPE_CHECK
- matrix_type cm (m);
-#endif
- size_type singular = 0;
- size_type size1 = m.size1 ();
- size_type size2 = m.size2 ();
- size_type size = (std::min) (size1, size2);
-#ifndef BOOST_UBLAS_LU_WITH_INPLACE_SOLVE
- matrix_type mr (m);
- mr.assign (zero_matrix<value_type> (size1, size2));
- vector_type v (size1);
- for (size_type i = 0; i < size; ++ i) {
- matrix_range<matrix_type> lrr (project (mr, range (0, i), range (0, i)));
- vector_range<matrix_column<matrix_type> > urr (project (column (mr, i), range (0, i)));
- urr.assign (solve (lrr, project (column (m, i), range (0, i)), unit_lower_tag ()));
- project (v, range (i, size1)).assign (
- project (column (m, i), range (i, size1)) -
- axpy_prod<vector_type> (project (mr, range (i, size1), range (0, i)), urr));
- size_type i_norm_inf = i + index_norm_inf (project (v, range (i, size1)));
- BOOST_UBLAS_CHECK (i_norm_inf < size1, external_logic ());
- if (v (i_norm_inf) != value_type/*zero*/()) {
- if (i_norm_inf != i) {
- pm (i) = i_norm_inf;
- std::swap (v (i_norm_inf), v (i));
- project (row (m, i_norm_inf), range (i + 1, size2)).swap (project (row (m, i), range (i + 1, size2)));
- } else {
- BOOST_UBLAS_CHECK (pm (i) == i_norm_inf, external_logic ());
- }
- project (column (mr, i), range (i + 1, size1)).assign (
- project (v, range (i + 1, size1)) / v (i));
- if (i_norm_inf != i) {
- project (row (mr, i_norm_inf), range (0, i)).swap (project (row (mr, i), range (0, i)));
- }
- } else if (singular == 0) {
- singular = i + 1;
- }
- mr (i, i) = v (i);
- }
- m.assign (mr);
-#else
- matrix_type lr (m);
- matrix_type ur (m);
- lr.assign (identity_matrix<value_type> (size1, size2));
- ur.assign (zero_matrix<value_type> (size1, size2));
- vector_type v (size1);
- for (size_type i = 0; i < size; ++ i) {
- matrix_range<matrix_type> lrr (project (lr, range (0, i), range (0, i)));
- vector_range<matrix_column<matrix_type> > urr (project (column (ur, i), range (0, i)));
- urr.assign (project (column (m, i), range (0, i)));
- inplace_solve (lrr, urr, unit_lower_tag ());
- project (v, range (i, size1)).assign (
- project (column (m, i), range (i, size1)) -
- axpy_prod<vector_type> (project (lr, range (i, size1), range (0, i)), urr));
- size_type i_norm_inf = i + index_norm_inf (project (v, range (i, size1)));
- BOOST_UBLAS_CHECK (i_norm_inf < size1, external_logic ());
- if (v (i_norm_inf) != value_type/*zero*/()) {
- if (i_norm_inf != i) {
- pm (i) = i_norm_inf;
- std::swap (v (i_norm_inf), v (i));
- project (row (m, i_norm_inf), range (i + 1, size2)).swap (project (row (m, i), range (i + 1, size2)));
- } else {
- BOOST_UBLAS_CHECK (pm (i) == i_norm_inf, external_logic ());
- }
- project (column (lr, i), range (i + 1, size1)).assign (
- project (v, range (i + 1, size1)) / v (i));
- if (i_norm_inf != i) {
- project (row (lr, i_norm_inf), range (0, i)).swap (project (row (lr, i), range (0, i)));
- }
- } else if (singular == 0) {
- singular = i + 1;
- }
- ur (i, i) = v (i);
- }
- m.assign (triangular_adaptor<matrix_type, strict_lower> (lr) +
- triangular_adaptor<matrix_type, upper> (ur));
-#endif
-#if BOOST_UBLAS_TYPE_CHECK
- swap_rows (pm, cm);
- BOOST_UBLAS_CHECK (singular != 0 ||
- detail::expression_type_check (prod (triangular_adaptor<matrix_type, unit_lower> (m),
- triangular_adaptor<matrix_type, upper> (m)), cm), internal_logic ());
-#endif
- return singular;
- }
-
- // LU substitution
- template<class M, class E>
- void lu_substitute (const M &m, vector_expression<E> &e) {
-#if BOOST_UBLAS_TYPE_CHECK
- typedef const M const_matrix_type;
- typedef vector<typename E::value_type> vector_type;
-
- vector_type cv1 (e);
-#endif
- inplace_solve (m, e, unit_lower_tag ());
-#if BOOST_UBLAS_TYPE_CHECK
- BOOST_UBLAS_CHECK (detail::expression_type_check (prod (triangular_adaptor<const_matrix_type, unit_lower> (m), e), cv1), internal_logic ());
- vector_type cv2 (e);
-#endif
- inplace_solve (m, e, upper_tag ());
-#if BOOST_UBLAS_TYPE_CHECK
- BOOST_UBLAS_CHECK (detail::expression_type_check (prod (triangular_adaptor<const_matrix_type, upper> (m), e), cv2), internal_logic ());
-#endif
- }
- template<class M, class E>
- void lu_substitute (const M &m, matrix_expression<E> &e) {
-#if BOOST_UBLAS_TYPE_CHECK
- typedef const M const_matrix_type;
- typedef matrix<typename E::value_type> matrix_type;
-
- matrix_type cm1 (e);
-#endif
- inplace_solve (m, e, unit_lower_tag ());
-#if BOOST_UBLAS_TYPE_CHECK
- BOOST_UBLAS_CHECK (detail::expression_type_check (prod (triangular_adaptor<const_matrix_type, unit_lower> (m), e), cm1), internal_logic ());
- matrix_type cm2 (e);
-#endif
- inplace_solve (m, e, upper_tag ());
-#if BOOST_UBLAS_TYPE_CHECK
- BOOST_UBLAS_CHECK (detail::expression_type_check (prod (triangular_adaptor<const_matrix_type, upper> (m), e), cm2), internal_logic ());
-#endif
- }
- template<class M, class PMT, class PMA, class MV>
- void lu_substitute (const M &m, const permutation_matrix<PMT, PMA> &pm, MV &mv) {
- swap_rows (pm, mv);
- lu_substitute (m, mv);
- }
- template<class E, class M>
- void lu_substitute (vector_expression<E> &e, const M &m) {
-#if BOOST_UBLAS_TYPE_CHECK
- typedef const M const_matrix_type;
- typedef vector<typename E::value_type> vector_type;
-
- vector_type cv1 (e);
-#endif
- inplace_solve (e, m, upper_tag ());
-#if BOOST_UBLAS_TYPE_CHECK
- BOOST_UBLAS_CHECK (detail::expression_type_check (prod (e, triangular_adaptor<const_matrix_type, upper> (m)), cv1), internal_logic ());
- vector_type cv2 (e);
-#endif
- inplace_solve (e, m, unit_lower_tag ());
-#if BOOST_UBLAS_TYPE_CHECK
- BOOST_UBLAS_CHECK (detail::expression_type_check (prod (e, triangular_adaptor<const_matrix_type, unit_lower> (m)), cv2), internal_logic ());
-#endif
- }
- template<class E, class M>
- void lu_substitute (matrix_expression<E> &e, const M &m) {
-#if BOOST_UBLAS_TYPE_CHECK
- typedef const M const_matrix_type;
- typedef matrix<typename E::value_type> matrix_type;
-
- matrix_type cm1 (e);
-#endif
- inplace_solve (e, m, upper_tag ());
-#if BOOST_UBLAS_TYPE_CHECK
- BOOST_UBLAS_CHECK (detail::expression_type_check (prod (e, triangular_adaptor<const_matrix_type, upper> (m)), cm1), internal_logic ());
- matrix_type cm2 (e);
-#endif
- inplace_solve (e, m, unit_lower_tag ());
-#if BOOST_UBLAS_TYPE_CHECK
- BOOST_UBLAS_CHECK (detail::expression_type_check (prod (e, triangular_adaptor<const_matrix_type, unit_lower> (m)), cm2), internal_logic ());
-#endif
- }
- template<class MV, class M, class PMT, class PMA>
- void lu_substitute (MV &mv, const M &m, const permutation_matrix<PMT, PMA> &pm) {
- swap_rows (pm, mv);
- lu_substitute (mv, m);
- }
-
-}}}
-
-#endif