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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
//
// 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 <Eigen/QR>
template<typename MatrixType> void qr(const MatrixType& m)
{
/* this test covers the following files: QR.h */
int rows = m.rows();
int cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> SquareMatrixType;
typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
MatrixType a = MatrixType::Random(rows,cols);
HouseholderQR<MatrixType> qrOfA(a);
VERIFY_IS_APPROX(a, qrOfA.matrixQ() * qrOfA.matrixR());
VERIFY_IS_NOT_APPROX(a+MatrixType::Identity(rows, cols), qrOfA.matrixQ() * qrOfA.matrixR());
SquareMatrixType b = a.adjoint() * a;
// check tridiagonalization
Tridiagonalization<SquareMatrixType> tridiag(b);
VERIFY_IS_APPROX(b, tridiag.matrixQ() * tridiag.matrixT() * tridiag.matrixQ().adjoint());
// check hessenberg decomposition
HessenbergDecomposition<SquareMatrixType> hess(b);
VERIFY_IS_APPROX(b, hess.matrixQ() * hess.matrixH() * hess.matrixQ().adjoint());
VERIFY_IS_APPROX(tridiag.matrixT(), hess.matrixH());
b = SquareMatrixType::Random(cols,cols);
hess.compute(b);
VERIFY_IS_APPROX(b, hess.matrixQ() * hess.matrixH() * hess.matrixQ().adjoint());
}
template<typename MatrixType> void qr_invertible()
{
/* this test covers the following files: QR.h */
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
int size = ei_random<int>(10,200);
MatrixType m1(size, size), m2(size, size), m3(size, size);
m1 = MatrixType::Random(size,size);
if (ei_is_same_type<RealScalar,float>::ret)
{
// let's build a matrix more stable to inverse
MatrixType a = MatrixType::Random(size,size*2);
m1 += a * a.adjoint();
}
HouseholderQR<MatrixType> qr(m1);
m3 = MatrixType::Random(size,size);
qr.solve(m3, &m2);
//std::cerr << m3 - m1*m2 << "\n\n";
VERIFY_IS_APPROX(m3, m1*m2);
}
template<typename MatrixType> void qr_verify_assert()
{
MatrixType tmp;
HouseholderQR<MatrixType> qr;
VERIFY_RAISES_ASSERT(qr.matrixR())
VERIFY_RAISES_ASSERT(qr.solve(tmp,&tmp))
VERIFY_RAISES_ASSERT(qr.matrixQ())
}
void test_qr()
{
for(int i = 0; i < 1; i++) {
// CALL_SUBTEST( qr(Matrix2f()) );
// CALL_SUBTEST( qr(Matrix4d()) );
// CALL_SUBTEST( qr(MatrixXf(12,8)) );
// CALL_SUBTEST( qr(MatrixXcd(5,5)) );
// CALL_SUBTEST( qr(MatrixXcd(7,3)) );
CALL_SUBTEST( qr(MatrixXf(47,47)) );
}
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST( qr_invertible<MatrixXf>() );
CALL_SUBTEST( qr_invertible<MatrixXd>() );
// TODO fix issue with complex
// CALL_SUBTEST( qr_invertible<MatrixXcf>() );
// CALL_SUBTEST( qr_invertible<MatrixXcd>() );
}
CALL_SUBTEST(qr_verify_assert<Matrix3f>());
CALL_SUBTEST(qr_verify_assert<Matrix3d>());
CALL_SUBTEST(qr_verify_assert<MatrixXf>());
CALL_SUBTEST(qr_verify_assert<MatrixXd>());
CALL_SUBTEST(qr_verify_assert<MatrixXcf>());
CALL_SUBTEST(qr_verify_assert<MatrixXcd>());
}
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