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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Alexey Korepanov <kaikaikai@yandex.ru>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, 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.
//
// Eigen 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 Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#include "main.h"
#include <limits>
#include <Eigen/Eigenvalues>
template<typename MatrixType> void real_qz(const MatrixType& m)
{
/* this test covers the following files:
RealQZ.h
*/
typedef typename MatrixType::Index Index;
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType;
typedef typename std::complex<typename NumTraits<typename MatrixType::Scalar>::Real> Complex;
Index dim = m.cols();
MatrixType A = MatrixType::Random(dim,dim),
B = MatrixType::Random(dim,dim);
RealQZ<MatrixType> qz(A,B);
VERIFY_IS_EQUAL(qz.info(), Success);
// check for zeros
bool all_zeros = true;
for (Index i=0; i<A.cols(); i++)
for (Index j=0; j<i; j++) {
if (internal::abs(qz.matrixT()(i,j))!=Scalar(0.0))
all_zeros = false;
if (j<i-1 && internal::abs(qz.matrixS()(i,j))!=Scalar(0.0))
all_zeros = false;
if (j==i-1 && j>0 && internal::abs(qz.matrixS()(i,j))!=Scalar(0.0) && internal::abs(qz.matrixS()(i-1,j-1))!=Scalar(0.0))
all_zeros = false;
}
VERIFY_IS_EQUAL(all_zeros, true);
VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixS()*qz.matrixZ(), A);
VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixT()*qz.matrixZ(), B);
VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixQ().adjoint(), MatrixType::Identity(dim,dim));
VERIFY_IS_APPROX(qz.matrixZ()*qz.matrixZ().adjoint(), MatrixType::Identity(dim,dim));
}
void test_real_qz()
{
int s;
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( real_qz(Matrix4f()) );
s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
CALL_SUBTEST_2( real_qz(MatrixXd(s,s)) );
// some trivial but implementation-wise tricky cases
CALL_SUBTEST_2( real_qz(MatrixXd(1,1)) );
CALL_SUBTEST_2( real_qz(MatrixXd(2,2)) );
CALL_SUBTEST_3( real_qz(Matrix<double,1,1>()) );
CALL_SUBTEST_4( real_qz(Matrix2d()) );
}
EIGEN_UNUSED_VARIABLE(s)
}
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