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/*!
* \file
* \brief QR factorisation test program
* \author Tony Ottosson and Adam Piatyszek
*
* -------------------------------------------------------------------------
*
* 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/itstat.h>
using namespace itpp;
using namespace std;
int main()
{
cout << "=================================" << endl;
cout << "Test of QR factorization routines" << endl;
cout << "=================================" << endl;
{
cout << "QR of Real matrix" << endl;
mat Q, R, e;
mat A = randn(5, 5);
qr(A, Q, R);
cout << "A = " << round_to_zero(A) << endl;
cout << "norm(A - Q*R) = " << round_to_zero(norm(A - Q * R)) << endl
<< endl;
// This does not give same sizes as matlab. Why???!!!!!
A = randn(4, 2);
qr(A, Q, R);
cout << "A = " << round_to_zero(A) << endl;
cout << "norm(A - Q*R) = " << round_to_zero(norm(A - Q * R)) << endl
<< endl;
A = randn(2, 4);
qr(A, Q, R);
cout << "A = " << round_to_zero(A) << endl;
cout << "norm(A - Q*R) = " << round_to_zero(norm(A - Q * R)) << endl
<< endl;
}
{
cout << "QR of Real matrix with pivoting" << endl;
mat Q, R, e;
bmat P;
mat A = randn(5, 5);
qr(A, Q, R, P);
e = A*to_mat(P) - Q*R;
cout << "A = " << round_to_zero(A) << endl;
cout << "norm(A*mat(P) - Q*R) = " << round_to_zero(norm(e)) << endl << endl;
// This does not give same sizes as matlab. Why???!!!!!
A = randn(4, 2);
qr(A, Q, R, P);
e = A*to_mat(P) - Q*R;
cout << "A = " << round_to_zero(A) << endl;
cout << "norm(A*mat(P) - Q*R) = " << round_to_zero(norm(e)) << endl << endl;
A = randn(2, 4);
qr(A, Q, R, P);
e = A*to_mat(P) - Q*R;
cout << "A = " << round_to_zero(A) << endl;
cout << "norm(A*mat(P) - Q*R) = " << round_to_zero(norm(e)) << endl << endl;
}
{
cout << "QR of Complex matrix" << endl;
cmat A = randn_c(5, 5);
cmat Q, R, e;
qr(A, Q, R);
e = A - Q*R;
cout << "A = " << round_to_zero(A) << endl;
cout << "norm(A - Q*R) = " << round_to_zero(norm(e)) << endl << endl;
// This does not give same sizes as matlab. Why???!!!!!
A = randn_c(4, 2);
qr(A, Q, R);
e = A - Q*R;
cout << "A = " << round_to_zero(A) << endl;
cout << "norm(A - Q*R) = " << round_to_zero(norm(e)) << endl << endl;
A = randn_c(2, 4);
qr(A, Q, R);
e = A - Q*R;
cout << "A = " << round_to_zero(A) << endl;
cout << "norm(A - Q*R) = " << round_to_zero(norm(e)) << endl << endl;
}
{
cout << "QR of Complex matrix with pivoting" << endl;
cmat A = randn_c(5, 5);
cmat Q, R, e;
bmat P;
qr(A, Q, R, P);
e = A*to_mat(P) - Q*R;
cout << "A = " << round_to_zero(A) << endl;
cout << "norm(A*mat(P) - Q*R) = " << round_to_zero(norm(e)) << endl << endl;
// This does not give same sizes as matlab. Why???!!!!!
A = randn_c(4, 2);
qr(A, Q, R, P);
e = A*to_mat(P) - Q*R;
cout << "A = " << round_to_zero(A) << endl;
cout << "norm(A*mat(P) - Q*R) = " << round_to_zero(norm(e)) << endl << endl;
A = randn_c(2, 4);
qr(A, Q, R, P);
e = A*to_mat(P) - Q*R;
cout << "A = " << round_to_zero(A) << endl;
cout << "norm(A*mat(P) - Q*R) = " << round_to_zero(norm(e)) << endl << endl;
}
return 0;
}
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