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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>
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// 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()
{
int rows = ei_random<int>(20,200), cols = ei_random<int>(20,200), cols2 = ei_random<int>(20,200);
int rank = ei_random<int>(1, std::min(rows, cols)-1);
typedef typename MatrixType::Scalar Scalar;
typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> SquareMatrixType;
typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
MatrixType m1;
createRandomMatrixOfRank(rank,rows,cols,m1);
ColPivotingHouseholderQR<MatrixType> qr(m1);
VERIFY_IS_APPROX(rank, qr.rank());
VERIFY(cols - qr.rank() == qr.dimensionOfKernel());
VERIFY(!qr.isInjective());
VERIFY(!qr.isInvertible());
VERIFY(!qr.isSurjective());
MatrixType r = qr.matrixQR();
// FIXME need better way to construct trapezoid
for(int i = 0; i < rows; i++) for(int j = 0; j < cols; j++) if(i>j) r(i,j) = Scalar(0);
MatrixType b = qr.matrixQ() * r;
MatrixType c = MatrixType::Zero(rows,cols);
for(int i = 0; i < cols; ++i) c.col(qr.colsPermutation().coeff(i)) = b.col(i);
VERIFY_IS_APPROX(m1, c);
MatrixType m2 = MatrixType::Random(cols,cols2);
MatrixType m3 = m1*m2;
m2 = MatrixType::Random(cols,cols2);
VERIFY(qr.solve(m3, &m2));
VERIFY_IS_APPROX(m3, m1*m2);
m3 = MatrixType::Random(rows,cols2);
VERIFY(!qr.solve(m3, &m2));
}
template<typename MatrixType> void qr_invertible()
{
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
typedef typename MatrixType::Scalar Scalar;
int size = ei_random<int>(10,50);
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();
}
ColPivotingHouseholderQR<MatrixType> qr(m1);
m3 = MatrixType::Random(size,size);
qr.solve(m3, &m2);
VERIFY_IS_APPROX(m3, m1*m2);
// now construct a matrix with prescribed determinant
m1.setZero();
for(int i = 0; i < size; i++) m1(i,i) = ei_random<Scalar>();
RealScalar absdet = ei_abs(m1.diagonal().prod());
m3 = qr.matrixQ(); // get a unitary
m1 = m3 * m1 * m3;
qr.compute(m1);
VERIFY_IS_APPROX(absdet, qr.absDeterminant());
VERIFY_IS_APPROX(ei_log(absdet), qr.logAbsDeterminant());
}
template<typename MatrixType> void qr_verify_assert()
{
MatrixType tmp;
ColPivotingHouseholderQR<MatrixType> qr;
VERIFY_RAISES_ASSERT(qr.matrixQR())
VERIFY_RAISES_ASSERT(qr.solve(tmp,&tmp))
VERIFY_RAISES_ASSERT(qr.matrixQ())
VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())
VERIFY_RAISES_ASSERT(qr.isInjective())
VERIFY_RAISES_ASSERT(qr.isSurjective())
VERIFY_RAISES_ASSERT(qr.isInvertible())
VERIFY_RAISES_ASSERT(qr.computeInverse(&tmp))
VERIFY_RAISES_ASSERT(qr.inverse())
VERIFY_RAISES_ASSERT(qr.absDeterminant())
VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
}
void test_qr_colpivoting()
{
for(int i = 0; i < 1; i++) {
CALL_SUBTEST( qr<MatrixXf>() );
CALL_SUBTEST( qr<MatrixXd>() );
CALL_SUBTEST( qr<MatrixXcd>() );
}
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST( qr_invertible<MatrixXf>() );
CALL_SUBTEST( qr_invertible<MatrixXd>() );
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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