1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud (at) inria.fr> 5 // Copyright (C) 2009 Benoit Jacob <jacob.benoit.1 (at) gmail.com> 6 // 7 // This Source Code Form is subject to the terms of the Mozilla 8 // Public License v. 2.0. If a copy of the MPL was not distributed 9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 10 11 #include "main.h" 12 #include <Eigen/QR> 13 14 template<typename MatrixType> void qr() 15 { 16 typedef typename MatrixType::Index Index; 17 18 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); 19 Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1); 20 21 typedef typename MatrixType::Scalar Scalar; 22 typedef typename MatrixType::RealScalar RealScalar; 23 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType; 24 typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType; 25 MatrixType m1; 26 createRandomPIMatrixOfRank(rank,rows,cols,m1); 27 ColPivHouseholderQR<MatrixType> qr(m1); 28 VERIFY(rank == qr.rank()); 29 VERIFY(cols - qr.rank() == qr.dimensionOfKernel()); 30 VERIFY(!qr.isInjective()); 31 VERIFY(!qr.isInvertible()); 32 VERIFY(!qr.isSurjective()); 33 34 MatrixQType q = qr.householderQ(); 35 VERIFY_IS_UNITARY(q); 36 37 MatrixType r = qr.matrixQR().template triangularView<Upper>(); 38 MatrixType c = q * r * qr.colsPermutation().inverse(); 39 VERIFY_IS_APPROX(m1, c); 40 41 MatrixType m2 = MatrixType::Random(cols,cols2); 42 MatrixType m3 = m1*m2; 43 m2 = MatrixType::Random(cols,cols2); 44 m2 = qr.solve(m3); 45 VERIFY_IS_APPROX(m3, m1*m2); 46 } 47 48 template<typename MatrixType, int Cols2> void qr_fixedsize() 49 { 50 enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime }; 51 typedef typename MatrixType::Scalar Scalar; 52 int rank = internal::random<int>(1, (std::min)(int(Rows), int(Cols))-1); 53 Matrix<Scalar,Rows,Cols> m1; 54 createRandomPIMatrixOfRank(rank,Rows,Cols,m1); 55 ColPivHouseholderQR<Matrix<Scalar,Rows,Cols> > qr(m1); 56 VERIFY(rank == qr.rank()); 57 VERIFY(Cols - qr.rank() == qr.dimensionOfKernel()); 58 VERIFY(qr.isInjective() == (rank == Rows)); 59 VERIFY(qr.isSurjective() == (rank == Cols)); 60 VERIFY(qr.isInvertible() == (qr.isInjective() && qr.isSurjective())); 61 62 Matrix<Scalar,Rows,Cols> r = qr.matrixQR().template triangularView<Upper>(); 63 Matrix<Scalar,Rows,Cols> c = qr.householderQ() * r * qr.colsPermutation().inverse(); 64 VERIFY_IS_APPROX(m1, c); 65 66 Matrix<Scalar,Cols,Cols2> m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2); 67 Matrix<Scalar,Rows,Cols2> m3 = m1*m2; 68 m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2); 69 m2 = qr.solve(m3); 70 VERIFY_IS_APPROX(m3, m1*m2); 71 } 72 73 template<typename MatrixType> void qr_invertible() 74 { 75 typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar; 76 typedef typename MatrixType::Scalar Scalar; 77 78 int size = internal::random<int>(10,50); 79 80 MatrixType m1(size, size), m2(size, size), m3(size, size); 81 m1 = MatrixType::Random(size,size); 82 83 if (internal::is_same<RealScalar,float>::value) 84 { 85 // let's build a matrix more stable to inverse 86 MatrixType a = MatrixType::Random(size,size*2); 87 m1 += a * a.adjoint(); 88 } 89 90 ColPivHouseholderQR<MatrixType> qr(m1); 91 m3 = MatrixType::Random(size,size); 92 m2 = qr.solve(m3); 93 //VERIFY_IS_APPROX(m3, m1*m2); 94 95 // now construct a matrix with prescribed determinant 96 m1.setZero(); 97 for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>(); 98 RealScalar absdet = internal::abs(m1.diagonal().prod()); 99 m3 = qr.householderQ(); // get a unitary 100 m1 = m3 * m1 * m3; 101 qr.compute(m1); 102 VERIFY_IS_APPROX(absdet, qr.absDeterminant()); 103 VERIFY_IS_APPROX(internal::log(absdet), qr.logAbsDeterminant()); 104 } 105 106 template<typename MatrixType> void qr_verify_assert() 107 { 108 MatrixType tmp; 109 110 ColPivHouseholderQR<MatrixType> qr; 111 VERIFY_RAISES_ASSERT(qr.matrixQR()) 112 VERIFY_RAISES_ASSERT(qr.solve(tmp)) 113 VERIFY_RAISES_ASSERT(qr.householderQ()) 114 VERIFY_RAISES_ASSERT(qr.dimensionOfKernel()) 115 VERIFY_RAISES_ASSERT(qr.isInjective()) 116 VERIFY_RAISES_ASSERT(qr.isSurjective()) 117 VERIFY_RAISES_ASSERT(qr.isInvertible()) 118 VERIFY_RAISES_ASSERT(qr.inverse()) 119 VERIFY_RAISES_ASSERT(qr.absDeterminant()) 120 VERIFY_RAISES_ASSERT(qr.logAbsDeterminant()) 121 } 122 123 void test_qr_colpivoting() 124 { 125 for(int i = 0; i < g_repeat; i++) { 126 CALL_SUBTEST_1( qr<MatrixXf>() ); 127 CALL_SUBTEST_2( qr<MatrixXd>() ); 128 CALL_SUBTEST_3( qr<MatrixXcd>() ); 129 CALL_SUBTEST_4(( qr_fixedsize<Matrix<float,3,5>, 4 >() )); 130 CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,6,2>, 3 >() )); 131 CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,1,1>, 1 >() )); 132 } 133 134 for(int i = 0; i < g_repeat; i++) { 135 CALL_SUBTEST_1( qr_invertible<MatrixXf>() ); 136 CALL_SUBTEST_2( qr_invertible<MatrixXd>() ); 137 CALL_SUBTEST_6( qr_invertible<MatrixXcf>() ); 138 CALL_SUBTEST_3( qr_invertible<MatrixXcd>() ); 139 } 140 141 CALL_SUBTEST_7(qr_verify_assert<Matrix3f>()); 142 CALL_SUBTEST_8(qr_verify_assert<Matrix3d>()); 143 CALL_SUBTEST_1(qr_verify_assert<MatrixXf>()); 144 CALL_SUBTEST_2(qr_verify_assert<MatrixXd>()); 145 CALL_SUBTEST_6(qr_verify_assert<MatrixXcf>()); 146 CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>()); 147 148 // Test problem size constructors 149 CALL_SUBTEST_9(ColPivHouseholderQR<MatrixXf>(10, 20)); 150 } 151
