/*!
* \file
* \brief QR factorisation test program
* \author Tony Ottosson, Adam Piatyszek and Vasek Smidl
*
* -------------------------------------------------------------------------
*
* 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/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 without Q" << endl;
mat R;
mat A = randn(5, 5);
qr(A, R);
cout << "A = " << round_to_zero(A) << endl;
cout << "norm(A.T()*A - R.T()*R) = " << round_to_zero(norm(A.T()*A - R.T()*R)) << endl
<< endl;
A = randn(4, 2);
qr(A, R);
cout << "A = " << round_to_zero(A) << endl;
cout << "norm(A.T()*A - R.T()*R) = " << round_to_zero(norm(A.T()*A - R.T()*R)) << endl
<< endl;
A = randn(2, 4);
qr(A, R);
cout << "A = " << round_to_zero(A) << endl;
cout << "norm(A.T()*A - R.T()*R) = " << round_to_zero(norm(A.T()*A - R.T()*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 without Q" << endl;
cmat A = randn_c(5, 5);
cmat R, e;
qr(A, R);
e = A.H() * A - R.H() * R;
cout << "A = " << round_to_zero(A) << endl;
cout << "norm(A.H()*A - R.H()*R) = " << round_to_zero(norm(e)) << endl << endl;
A = randn_c(4, 2);
qr(A, R);
e = A.H() * A - R.H() * R;
cout << "A = " << round_to_zero(A) << endl;
cout << "norm(A.H()*A - R.H()*R) = " << round_to_zero(norm(e)) << endl << endl;
A = randn_c(2, 4);
qr(A, R);
e = A.H() * A - R.H() * R;
cout << "A = " << round_to_zero(A) << endl;
cout << "norm(A.H()*A - R.H()*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;
}