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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// 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);
QR<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 Derived>
void doSomeRankPreservingOperations(Eigen::MatrixBase<Derived>& m)
{
typedef typename Derived::RealScalar RealScalar;
for(int a = 0; a < 3*(m.rows()+m.cols()); a++)
{
RealScalar d = Eigen::ei_random<RealScalar>(-1,1);
int i = Eigen::ei_random<int>(0,m.rows()-1); // i is a random row number
int j;
do {
j = Eigen::ei_random<int>(0,m.rows()-1);
} while (i==j); // j is another one (must be different)
m.row(i) += d * m.row(j);
i = Eigen::ei_random<int>(0,m.cols()-1); // i is a random column number
do {
j = Eigen::ei_random<int>(0,m.cols()-1);
} while (i==j); // j is another one (must be different)
m.col(i) += d * m.col(j);
}
}
template<typename MatrixType> void qr_non_invertible()
{
/* this test covers the following files: QR.h */
// NOTE there seems to be a problem with too small sizes -- could easily lie in the doSomeRankPreservingOperations function
int rows = ei_random<int>(20,200), cols = ei_random<int>(20,rows), cols2 = ei_random<int>(20,rows);
int rank = ei_random<int>(1, std::min(rows, cols)-1);
MatrixType m1(rows, cols), m2(cols, cols2), m3(rows, cols2), k(1,1);
m1 = MatrixType::Random(rows,cols);
if(rows <= cols)
for(int i = rank; i < rows; i++) m1.row(i).setZero();
else
for(int i = rank; i < cols; i++) m1.col(i).setZero();
doSomeRankPreservingOperations(m1);
QR<MatrixType> lu(m1);
// typename LU<MatrixType>::KernelResultType m1kernel = lu.kernel();
// typename LU<MatrixType>::ImageResultType m1image = lu.image();
std::cerr << rows << "x" << cols << " " << rank << " " << lu.rank() << "\n";
if (rank != lu.rank())
std::cerr << lu.matrixR().diagonal().transpose() << "\n";
VERIFY(rank == lu.rank());
VERIFY(cols - lu.rank() == lu.dimensionOfKernel());
VERIFY(!lu.isInjective());
VERIFY(!lu.isInvertible());
VERIFY(lu.isSurjective() == (lu.rank() == rows));
// VERIFY((m1 * m1kernel).isMuchSmallerThan(m1));
// VERIFY(m1image.lu().rank() == rank);
// MatrixType sidebyside(m1.rows(), m1.cols() + m1image.cols());
// sidebyside << m1, m1image;
// VERIFY(sidebyside.lu().rank() == rank);
m2 = MatrixType::Random(cols,cols2);
m3 = m1*m2;
m2 = MatrixType::Random(cols,cols2);
lu.solve(m3, &m2);
VERIFY_IS_APPROX(m3, m1*m2);
m3 = MatrixType::Random(rows,cols2);
VERIFY(!lu.solve(m3, &m2));
}
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();
}
QR<MatrixType> lu(m1);
VERIFY(0 == lu.dimensionOfKernel());
VERIFY(size == lu.rank());
VERIFY(lu.isInjective());
VERIFY(lu.isSurjective());
VERIFY(lu.isInvertible());
// VERIFY(lu.image().lu().isInvertible());
m3 = MatrixType::Random(size,size);
lu.solve(m3, &m2);
//std::cerr << m3 - m1*m2 << "\n\n";
VERIFY_IS_APPROX(m3, m1*m2);
// VERIFY_IS_APPROX(m2, lu.inverse()*m3);
m3 = MatrixType::Random(size,size);
VERIFY(lu.solve(m3, &m2));
}
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)) );
}
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST( qr_non_invertible<MatrixXf>() );
// CALL_SUBTEST( qr_non_invertible<MatrixXd>() );
// TODO fix issue with complex
// CALL_SUBTEST( qr_non_invertible<MatrixXcf>() );
// CALL_SUBTEST( qr_non_invertible<MatrixXcd>() );
// 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>() );
}
}
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