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/*!
* \file
* \brief Implementation of LU factorisation functions.
* \author Tony Ottosson
*
* -------------------------------------------------------------------------
*
* Copyright (C) 1995-2010 (see AUTHORS file for a list of contributors)
*
* This file is part of IT++ - a C++ library of mathematical, signal
* processing, speech processing, and communications classes and functions.
*
* IT++ is free software: you can redistribute it and/or modify it under the
* terms of the GNU General Public License as published by the Free Software
* Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* IT++ is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
* details.
*
* You should have received a copy of the GNU General Public License along
* with IT++. If not, see <http://www.gnu.org/licenses/>.
*
* -------------------------------------------------------------------------
*/
#ifndef _MSC_VER
# include <itpp/config.h>
#else
# include <itpp/config_msvc.h>
#endif
#if defined(HAVE_LAPACK)
# include <itpp/base/algebra/lapack.h>
#endif
#include <itpp/base/algebra/lu.h>
#include <itpp/base/specmat.h>
namespace itpp
{
#if defined(HAVE_LAPACK)
bool lu(const mat &X, mat &L, mat &U, ivec &p)
{
it_assert_debug(X.rows() == X.cols(), "lu: matrix is not quadratic");
//int m, n, lda, info;
//m = n = lda = X.rows();
int m = X.rows(), info;
mat A(X);
L.set_size(m, m, false);
U.set_size(m, m, false);
p.set_size(m, false);
dgetrf_(&m, &m, A._data(), &m, p._data(), &info);
for (int i = 0; i < m; i++) {
for (int j = i; j < m; j++) {
if (i == j) { // diagonal
L(i, j) = 1;
U(i, j) = A(i, j);
}
else { // upper and lower triangular parts
L(i, j) = U(j, i) = 0;
L(j, i) = A(j, i);
U(i, j) = A(i, j);
}
}
}
p = p - 1; // Fortran counts from 1
return (info == 0);
}
// Slower than not using LAPACK when matrix size smaller than approx 20.
bool lu(const cmat &X, cmat &L, cmat &U, ivec &p)
{
it_assert_debug(X.rows() == X.cols(), "lu: matrix is not quadratic");
//int m, n, lda, info;
//m = n = lda = X.rows();
int m = X.rows(), info;
cmat A(X);
L.set_size(m, m, false);
U.set_size(m, m, false);
p.set_size(m, false);
zgetrf_(&m, &m, A._data(), &m, p._data(), &info);
for (int i = 0; i < m; i++) {
for (int j = i; j < m; j++) {
if (i == j) { // diagonal
L(i, j) = 1;
U(i, j) = A(i, j);
}
else { // upper and lower triangular parts
L(i, j) = U(j, i) = 0;
L(j, i) = A(j, i);
U(i, j) = A(i, j);
}
}
}
p = p - 1; // Fortran counts from 1
return (info == 0);
}
#else
bool lu(const mat &X, mat &L, mat &U, ivec &p)
{
it_error("LAPACK library is needed to use lu() function");
return false;
}
bool lu(const cmat &X, cmat &L, cmat &U, ivec &p)
{
it_error("LAPACK library is needed to use lu() function");
return false;
}
#endif // HAVE_LAPACK
void interchange_permutations(vec &b, const ivec &p)
{
it_assert(b.size() == p.size(), "interchange_permutations(): dimension mismatch");
double temp;
for (int k = 0; k < b.size(); k++) {
temp = b(k);
b(k) = b(p(k));
b(p(k)) = temp;
}
}
bmat permutation_matrix(const ivec &p)
{
it_assert(p.size() > 0, "permutation_matrix(): vector must have nonzero size");
int n = p.size(), k;
bmat P, identity;
bvec row_k, row_pk;
identity = eye_b(n);
for (k = n - 1; k >= 0; k--) {
// swap rows k and p(k) in identity
row_k = identity.get_row(k);
row_pk = identity.get_row(p(k));
identity.set_row(k, row_pk);
identity.set_row(p(k), row_k);
if (k == n - 1) {
P = identity;
}
else {
P *= identity;
}
// swap back
identity.set_row(k, row_k);
identity.set_row(p(k), row_pk);
}
return P;
}
} // namespace itpp