Squashed 'third_party/boostorg/ublas/' content from commit e8607b3
Change-Id: Ia06afd642157a24e17fa9ddea28fb8601810b78e
git-subtree-dir: third_party/boostorg/ublas
git-subtree-split: e8607b3eea238e590eca93bfe498c21f470155c1
diff --git a/include/boost/numeric/ublas/lu.hpp b/include/boost/numeric/ublas/lu.hpp
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+//
+// 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