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/*!
* \file
* \brief Implementation of determinant calculations
* \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/>.
*
* -------------------------------------------------------------------------
*/
#include <itpp/base/algebra/det.h>
#include <itpp/base/algebra/lu.h>
namespace itpp
{
/* Determinant of square matrix.
Calculate determinant of inmatrix (Uses LU-factorisation)
(See Theorem 3.2.1 p. 97 in Golub & van Loan, "Matrix Computations").
det(X) = det(P')*det(L)*det(U) = det(P')*1*prod(diag(U))
*/
double det(const mat &X)
{
it_assert_debug(X.rows() == X.cols(), "det : Only square matrices");
mat L, U;
ivec p;
double s = 1.0;
int i;
lu(X, L, U, p); // calculate LU-factorisation
double temp = U(0, 0);
for (i = 1;i < X.rows();i++) {
temp *= U(i, i);
}
// Calculate det(P'). Equal to (-1)^(no row changes)
for (i = 0; i < p.size(); i++)
if (i != p(i))
s *= -1.0;
return temp*s;
}
/* Determinant of complex square matrix.
Calculate determinant of inmatrix (Uses LU-factorisation)
(See Theorem 3.2.1 p. 97 in Golub & van Loan, "Matrix Computations").
det(X) = det(P')*det(L)*det(U) = det(P')*1*prod(diag(U))
Needs LU-factorization of complex matrices (LAPACK)
*/
std::complex<double> det(const cmat &X)
{
it_assert_debug(X.rows() == X.cols(), "det : Only square matrices");
int i;
cmat L, U;
ivec p;
double s = 1.0;
lu(X, L, U, p); // calculate LU-factorisation
std::complex<double> temp = U(0, 0);
for (i = 1;i < X.rows();i++) {
temp *= U(i, i);
}
// Calculate det(P'). Equal to (-1)^(no row changes)
for (i = 0; i < p.size(); i++)
if (i != p(i))
s *= -1.0;
return temp*s;
}
} // namespace itpp
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