1c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This file is part of Eigen, a lightweight C++ template library 2c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// for linear algebra. 3c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 4c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr> 5c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com> 6c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 7c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This Source Code Form is subject to the terms of the Mozilla 8c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Public License v. 2.0. If a copy of the MPL was not distributed 9c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 10c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 11c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include "main.h" 12c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include <Eigen/QR> 13c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 14c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType> void qr() 15c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 16c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename MatrixType::Index Index; 17c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 18c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index rows = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE), cols = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE), cols2 = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE); 19c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1); 20c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 21c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename MatrixType::Scalar Scalar; 22c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType; 23c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType m1; 24c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath createRandomPIMatrixOfRank(rank,rows,cols,m1); 25c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ColPivHouseholderQR<MatrixType> qr(m1); 26c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY(rank == qr.rank()); 27c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY(cols - qr.rank() == qr.dimensionOfKernel()); 28c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY(!qr.isInjective()); 29c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY(!qr.isInvertible()); 30c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY(!qr.isSurjective()); 31c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 32c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixQType q = qr.householderQ(); 33c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_UNITARY(q); 34c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 35c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType r = qr.matrixQR().template triangularView<Upper>(); 36c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType c = q * r * qr.colsPermutation().inverse(); 37c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(m1, c); 38c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 39c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType m2 = MatrixType::Random(cols,cols2); 40c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType m3 = m1*m2; 41c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m2 = MatrixType::Random(cols,cols2); 42c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m2 = qr.solve(m3); 43c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(m3, m1*m2); 44c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 45c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 46c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType, int Cols2> void qr_fixedsize() 47c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 48c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime }; 49c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename MatrixType::Scalar Scalar; 50c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath int rank = internal::random<int>(1, (std::min)(int(Rows), int(Cols))-1); 51c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix<Scalar,Rows,Cols> m1; 52c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath createRandomPIMatrixOfRank(rank,Rows,Cols,m1); 53c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ColPivHouseholderQR<Matrix<Scalar,Rows,Cols> > qr(m1); 54c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY(rank == qr.rank()); 55c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY(Cols - qr.rank() == qr.dimensionOfKernel()); 56c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY(qr.isInjective() == (rank == Rows)); 57c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY(qr.isSurjective() == (rank == Cols)); 58c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY(qr.isInvertible() == (qr.isInjective() && qr.isSurjective())); 59c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 60c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix<Scalar,Rows,Cols> r = qr.matrixQR().template triangularView<Upper>(); 61c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix<Scalar,Rows,Cols> c = qr.householderQ() * r * qr.colsPermutation().inverse(); 62c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(m1, c); 63c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 64c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix<Scalar,Cols,Cols2> m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2); 65c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix<Scalar,Rows,Cols2> m3 = m1*m2; 66c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2); 67c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m2 = qr.solve(m3); 68c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(m3, m1*m2); 69c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 70c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 71c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType> void qr_invertible() 72c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 737faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez using std::log; 747faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez using std::abs; 75c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar; 76c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename MatrixType::Scalar Scalar; 77c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 78c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath int size = internal::random<int>(10,50); 79c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 80c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType m1(size, size), m2(size, size), m3(size, size); 81c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m1 = MatrixType::Random(size,size); 82c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 83c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (internal::is_same<RealScalar,float>::value) 84c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 85c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // let's build a matrix more stable to inverse 86c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType a = MatrixType::Random(size,size*2); 87c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m1 += a * a.adjoint(); 88c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 89c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 90c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ColPivHouseholderQR<MatrixType> qr(m1); 91c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m3 = MatrixType::Random(size,size); 92c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m2 = qr.solve(m3); 93c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath //VERIFY_IS_APPROX(m3, m1*m2); 94c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 95c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // now construct a matrix with prescribed determinant 96c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m1.setZero(); 97c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>(); 987faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez RealScalar absdet = abs(m1.diagonal().prod()); 99c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m3 = qr.householderQ(); // get a unitary 100c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m1 = m3 * m1 * m3; 101c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath qr.compute(m1); 102c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(absdet, qr.absDeterminant()); 1037faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant()); 104c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 105c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 106c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType> void qr_verify_assert() 107c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 108c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType tmp; 109c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 110c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ColPivHouseholderQR<MatrixType> qr; 111c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(qr.matrixQR()) 112c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(qr.solve(tmp)) 113c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(qr.householderQ()) 114c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(qr.dimensionOfKernel()) 115c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(qr.isInjective()) 116c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(qr.isSurjective()) 117c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(qr.isInvertible()) 118c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(qr.inverse()) 119c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(qr.absDeterminant()) 120c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(qr.logAbsDeterminant()) 121c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 122c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 123c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathvoid test_qr_colpivoting() 124c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 125c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for(int i = 0; i < g_repeat; i++) { 126c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_1( qr<MatrixXf>() ); 127c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_2( qr<MatrixXd>() ); 128c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_3( qr<MatrixXcd>() ); 129c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_4(( qr_fixedsize<Matrix<float,3,5>, 4 >() )); 130c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,6,2>, 3 >() )); 131c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,1,1>, 1 >() )); 132c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 133c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 134c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for(int i = 0; i < g_repeat; i++) { 135c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_1( qr_invertible<MatrixXf>() ); 136c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_2( qr_invertible<MatrixXd>() ); 137c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_6( qr_invertible<MatrixXcf>() ); 138c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_3( qr_invertible<MatrixXcd>() ); 139c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 140c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 141c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_7(qr_verify_assert<Matrix3f>()); 142c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_8(qr_verify_assert<Matrix3d>()); 143c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_1(qr_verify_assert<MatrixXf>()); 144c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_2(qr_verify_assert<MatrixXd>()); 145c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_6(qr_verify_assert<MatrixXcf>()); 146c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>()); 147c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 148c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Test problem size constructors 149c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_9(ColPivHouseholderQR<MatrixXf>(10, 20)); 150c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 151