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/*!
* \file
* \brief Schur decomposition test program
* \author Adam Piatyszek
*
* -------------------------------------------------------------------------
*
* 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()
{
int size = 5;
double thres = 1e-13;
cout << "==========================================" << endl;
cout << " Test of Schur decomposition routines " << endl;
cout << "==========================================" << endl;
{
cout << "Real matrix" << endl;
mat A = randn(size, size);
mat T, U;
schur(A, U, T);
cout << "A = " << round_to_zero(A) << endl;
cout << "norm(A - U*T*U^T) = "
<< round_to_zero(norm(A - (U * T * transpose(U))), thres) << endl;
cout << "norm(I - U*U^T) = "
<< round_to_zero(norm(eye(size) - (U * transpose(U))), thres) << endl;
double temp_sum = 0;
for (int i = 2; i < size; i++)
for (int j = 0; j < i - 1; j++)
temp_sum += sqr(T(i, j));
cout << "norm(lower triangular part of T) = "
<< round_to_zero(sqrt(temp_sum), thres) << endl;
}
{
cout << endl << "Complex matrix" << endl;
cmat A = randn_c(size, size);
cmat T, U;
schur(A, U, T);
cout << "A = " << round_to_zero(A) << endl;
cout << "norm(A - U*T*U^H) = "
<< round_to_zero(norm(A - (U * T * hermitian_transpose(U))), thres)
<< endl;
cout << "norm(I - U*U^H) = "
<< round_to_zero(norm(eye(size) - (U * hermitian_transpose(U))), thres)
<< endl;
double temp_sum = 0;
for (int i = 1; i < size; i++)
for (int j = 0; j < i; j++)
temp_sum += sqr(T(i, j));
cout << "norm(lower triangular part of T) = "
<< round_to_zero(sqrt(temp_sum), thres) << endl;
}
return 0;
}
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