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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.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()
{
typedef typename MatrixType::Index Index;
Index rows = internal::random<Index>(2,200), cols = internal::random<Index>(2,200), cols2 = internal::random<Index>(2,200);
Index rank = internal::random<Index>(1, std::min(rows, cols)-1);
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
MatrixType m1;
createRandomPIMatrixOfRank(rank,rows,cols,m1);
ColPivHouseholderQR<MatrixType> qr(m1);
VERIFY(rank == qr.rank());
VERIFY(cols - qr.rank() == qr.dimensionOfKernel());
VERIFY(!qr.isInjective());
VERIFY(!qr.isInvertible());
VERIFY(!qr.isSurjective());
MatrixQType q = qr.householderQ();
VERIFY_IS_UNITARY(q);
MatrixType r = qr.matrixQR().template triangularView<Upper>();
MatrixType c = q * r * qr.colsPermutation().inverse();
VERIFY_IS_APPROX(m1, c);
MatrixType m2 = MatrixType::Random(cols,cols2);
MatrixType m3 = m1*m2;
m2 = MatrixType::Random(cols,cols2);
m2 = qr.solve(m3);
VERIFY_IS_APPROX(m3, m1*m2);
}
template<typename MatrixType, int Cols2> void qr_fixedsize()
{
enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
typedef typename MatrixType::Scalar Scalar;
int rank = internal::random<int>(1, std::min(int(Rows), int(Cols))-1);
Matrix<Scalar,Rows,Cols> m1;
createRandomPIMatrixOfRank(rank,Rows,Cols,m1);
ColPivHouseholderQR<Matrix<Scalar,Rows,Cols> > qr(m1);
VERIFY(rank == qr.rank());
VERIFY(Cols - qr.rank() == qr.dimensionOfKernel());
VERIFY(qr.isInjective() == (rank == Rows));
VERIFY(qr.isSurjective() == (rank == Cols));
VERIFY(qr.isInvertible() == (qr.isInjective() && qr.isSurjective()));
Matrix<Scalar,Rows,Cols> r = qr.matrixQR().template triangularView<Upper>();
Matrix<Scalar,Rows,Cols> c = qr.householderQ() * r * qr.colsPermutation().inverse();
VERIFY_IS_APPROX(m1, c);
Matrix<Scalar,Cols,Cols2> m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
Matrix<Scalar,Rows,Cols2> m3 = m1*m2;
m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
m2 = qr.solve(m3);
VERIFY_IS_APPROX(m3, m1*m2);
}
template<typename MatrixType> void qr_invertible()
{
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
typedef typename MatrixType::Scalar Scalar;
int size = internal::random<int>(10,50);
MatrixType m1(size, size), m2(size, size), m3(size, size);
m1 = MatrixType::Random(size,size);
if (internal::is_same<RealScalar,float>::value)
{
// let's build a matrix more stable to inverse
MatrixType a = MatrixType::Random(size,size*2);
m1 += a * a.adjoint();
}
ColPivHouseholderQR<MatrixType> qr(m1);
m3 = MatrixType::Random(size,size);
m2 = qr.solve(m3);
//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) = internal::random<Scalar>();
RealScalar absdet = internal::abs(m1.diagonal().prod());
m3 = qr.householderQ(); // get a unitary
m1 = m3 * m1 * m3;
qr.compute(m1);
VERIFY_IS_APPROX(absdet, qr.absDeterminant());
VERIFY_IS_APPROX(internal::log(absdet), qr.logAbsDeterminant());
}
template<typename MatrixType> void qr_verify_assert()
{
MatrixType tmp;
ColPivHouseholderQR<MatrixType> qr;
VERIFY_RAISES_ASSERT(qr.matrixQR())
VERIFY_RAISES_ASSERT(qr.solve(tmp))
VERIFY_RAISES_ASSERT(qr.householderQ())
VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())
VERIFY_RAISES_ASSERT(qr.isInjective())
VERIFY_RAISES_ASSERT(qr.isSurjective())
VERIFY_RAISES_ASSERT(qr.isInvertible())
VERIFY_RAISES_ASSERT(qr.inverse())
VERIFY_RAISES_ASSERT(qr.absDeterminant())
VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
}
void test_qr_colpivoting()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( qr<MatrixXf>() );
CALL_SUBTEST_2( qr<MatrixXd>() );
CALL_SUBTEST_3( qr<MatrixXcd>() );
CALL_SUBTEST_4(( qr_fixedsize<Matrix<float,3,5>, 4 >() ));
CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,6,2>, 3 >() ));
CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,1,1>, 1 >() ));
}
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
CALL_SUBTEST_2( qr_invertible<MatrixXd>() );
CALL_SUBTEST_6( qr_invertible<MatrixXcf>() );
CALL_SUBTEST_3( qr_invertible<MatrixXcd>() );
}
CALL_SUBTEST_7(qr_verify_assert<Matrix3f>());
CALL_SUBTEST_8(qr_verify_assert<Matrix3d>());
CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
CALL_SUBTEST_2(qr_verify_assert<MatrixXd>());
CALL_SUBTEST_6(qr_verify_assert<MatrixXcf>());
CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>());
// Test problem size constructors
CALL_SUBTEST_9(ColPivHouseholderQR<MatrixXf>(10, 20));
}
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