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350 lines
14 KiB
350 lines
14 KiB
// |
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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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