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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;
typedef typename MV::value_type value_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;
typedef typename MV::value_type value_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 M matrix_type;
typedef typename M::size_type size_type;
typedef typename M::value_type value_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);
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 M matrix_type;
typedef typename M::size_type size_type;
typedef typename M::value_type value_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);
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) {
typedef const M const_matrix_type;
typedef vector<typename E::value_type> vector_type;
#if BOOST_UBLAS_TYPE_CHECK
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) {
typedef const M const_matrix_type;
typedef matrix<typename E::value_type> matrix_type;
#if BOOST_UBLAS_TYPE_CHECK
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) {
typedef const M const_matrix_type;
typedef vector<typename E::value_type> vector_type;
#if BOOST_UBLAS_TYPE_CHECK
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) {
typedef const M const_matrix_type;
typedef matrix<typename E::value_type> matrix_type;
#if BOOST_UBLAS_TYPE_CHECK
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
|
