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 max_size = EIGEN_TEST_MAX_SIZE; 19 Index min_size = numext::maxi(1,EIGEN_TEST_MAX_SIZE/10); 20 Index rows = internal::random<Index>(min_size,max_size), 21 cols = internal::random<Index>(min_size,max_size), 22 cols2 = internal::random<Index>(min_size,max_size), 23 rank = internal::random<Index>(1, (std::min)(rows, cols)-1); 24 25 typedef typename MatrixType::Scalar Scalar; 26 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType; 27 MatrixType m1; 28 createRandomPIMatrixOfRank(rank,rows,cols,m1); 29 FullPivHouseholderQR<MatrixType> qr(m1); 30 VERIFY_IS_EQUAL(rank, qr.rank()); 31 VERIFY_IS_EQUAL(cols - qr.rank(), qr.dimensionOfKernel()); 32 VERIFY(!qr.isInjective()); 33 VERIFY(!qr.isInvertible()); 34 VERIFY(!qr.isSurjective()); 35 36 MatrixType r = qr.matrixQR(); 37 38 MatrixQType q = qr.matrixQ(); 39 VERIFY_IS_UNITARY(q); 40 41 // FIXME need better way to construct trapezoid 42 for(int i = 0; i < rows; i++) for(int j = 0; j < cols; j++) if(i>j) r(i,j) = Scalar(0); 43 44 MatrixType c = qr.matrixQ() * r * qr.colsPermutation().inverse(); 45 46 VERIFY_IS_APPROX(m1, c); 47 48 // stress the ReturnByValue mechanism 49 MatrixType tmp; 50 VERIFY_IS_APPROX(tmp.noalias() = qr.matrixQ() * r, (qr.matrixQ() * r).eval()); 51 52 MatrixType m2 = MatrixType::Random(cols,cols2); 53 MatrixType m3 = m1*m2; 54 m2 = MatrixType::Random(cols,cols2); 55 m2 = qr.solve(m3); 56 VERIFY_IS_APPROX(m3, m1*m2); 57 58 { 59 Index size = rows; 60 do { 61 m1 = MatrixType::Random(size,size); 62 qr.compute(m1); 63 } while(!qr.isInvertible()); 64 MatrixType m1_inv = qr.inverse(); 65 m3 = m1 * MatrixType::Random(size,cols2); 66 m2 = qr.solve(m3); 67 VERIFY_IS_APPROX(m2, m1_inv*m3); 68 } 69 } 70 71 template<typename MatrixType> void qr_invertible() 72 { 73 using std::log; 74 using std::abs; 75 typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar; 76 typedef typename MatrixType::Scalar Scalar; 77 78 Index max_size = numext::mini(50,EIGEN_TEST_MAX_SIZE); 79 Index min_size = numext::maxi(1,EIGEN_TEST_MAX_SIZE/10); 80 Index size = internal::random<Index>(min_size,max_size); 81 82 MatrixType m1(size, size), m2(size, size), m3(size, size); 83 m1 = MatrixType::Random(size,size); 84 85 if (internal::is_same<RealScalar,float>::value) 86 { 87 // let's build a matrix more stable to inverse 88 MatrixType a = MatrixType::Random(size,size*2); 89 m1 += a * a.adjoint(); 90 } 91 92 FullPivHouseholderQR<MatrixType> qr(m1); 93 VERIFY(qr.isInjective()); 94 VERIFY(qr.isInvertible()); 95 VERIFY(qr.isSurjective()); 96 97 m3 = MatrixType::Random(size,size); 98 m2 = qr.solve(m3); 99 VERIFY_IS_APPROX(m3, m1*m2); 100 101 // now construct a matrix with prescribed determinant 102 m1.setZero(); 103 for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>(); 104 RealScalar absdet = abs(m1.diagonal().prod()); 105 m3 = qr.matrixQ(); // get a unitary 106 m1 = m3 * m1 * m3; 107 qr.compute(m1); 108 VERIFY_IS_APPROX(absdet, qr.absDeterminant()); 109 VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant()); 110 } 111 112 template<typename MatrixType> void qr_verify_assert() 113 { 114 MatrixType tmp; 115 116 FullPivHouseholderQR<MatrixType> qr; 117 VERIFY_RAISES_ASSERT(qr.matrixQR()) 118 VERIFY_RAISES_ASSERT(qr.solve(tmp)) 119 VERIFY_RAISES_ASSERT(qr.matrixQ()) 120 VERIFY_RAISES_ASSERT(qr.dimensionOfKernel()) 121 VERIFY_RAISES_ASSERT(qr.isInjective()) 122 VERIFY_RAISES_ASSERT(qr.isSurjective()) 123 VERIFY_RAISES_ASSERT(qr.isInvertible()) 124 VERIFY_RAISES_ASSERT(qr.inverse()) 125 VERIFY_RAISES_ASSERT(qr.absDeterminant()) 126 VERIFY_RAISES_ASSERT(qr.logAbsDeterminant()) 127 } 128 129 void test_qr_fullpivoting() 130 { 131 for(int i = 0; i < 1; i++) { 132 // FIXME : very weird bug here 133 // CALL_SUBTEST(qr(Matrix2f()) ); 134 CALL_SUBTEST_1( qr<MatrixXf>() ); 135 CALL_SUBTEST_2( qr<MatrixXd>() ); 136 CALL_SUBTEST_3( qr<MatrixXcd>() ); 137 } 138 139 for(int i = 0; i < g_repeat; i++) { 140 CALL_SUBTEST_1( qr_invertible<MatrixXf>() ); 141 CALL_SUBTEST_2( qr_invertible<MatrixXd>() ); 142 CALL_SUBTEST_4( qr_invertible<MatrixXcf>() ); 143 CALL_SUBTEST_3( qr_invertible<MatrixXcd>() ); 144 } 145 146 CALL_SUBTEST_5(qr_verify_assert<Matrix3f>()); 147 CALL_SUBTEST_6(qr_verify_assert<Matrix3d>()); 148 CALL_SUBTEST_1(qr_verify_assert<MatrixXf>()); 149 CALL_SUBTEST_2(qr_verify_assert<MatrixXd>()); 150 CALL_SUBTEST_4(qr_verify_assert<MatrixXcf>()); 151 CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>()); 152 153 // Test problem size constructors 154 CALL_SUBTEST_7(FullPivHouseholderQR<MatrixXf>(10, 20)); 155 CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(10,20))); 156 CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(Matrix<float,10,20>::Random()))); 157 CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(20,10))); 158 CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(Matrix<float,20,10>::Random()))); 159 } 160
