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/*!
* \file
* \brief Implementation of determinant calculations
* \author Tony Ottosson
*
* -------------------------------------------------------------------------
*
* IT++ - C++ library of mathematical, signal processing, speech processing,
* and communications classes and functions
*
* Copyright (C) 1995-2008 (see AUTHORS file for a list of contributors)
*
* This program 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 2 of the License, or
* (at your option) any later version.
*
* This program 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 this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
*
* -------------------------------------------------------------------------
*/
#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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