// 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 = ei_random<Index>(2,200), cols = ei_random<Index>(2,200), cols2 = ei_random<Index>(2,200); Index rank = ei_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 = ei_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 = 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(); } 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) = ei_random<Scalar>(); RealScalar absdet = ei_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(ei_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)); }