// // 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