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>(20,200), cols = internal::random<int>(20,200), cols2 = internal::random<int>(20,200); 19 Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1); 20 21 typedef typename MatrixType::Scalar Scalar; 22 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType; 23 MatrixType m1; 24 createRandomPIMatrixOfRank(rank,rows,cols,m1); 25 FullPivHouseholderQR<MatrixType> qr(m1); 26 VERIFY(rank == qr.rank()); 27 VERIFY(cols - qr.rank() == qr.dimensionOfKernel()); 28 VERIFY(!qr.isInjective()); 29 VERIFY(!qr.isInvertible()); 30 VERIFY(!qr.isSurjective()); 31 32 MatrixType r = qr.matrixQR(); 33 34 MatrixQType q = qr.matrixQ(); 35 VERIFY_IS_UNITARY(q); 36 37 // FIXME need better way to construct trapezoid 38 for(int i = 0; i < rows; i++) for(int j = 0; j < cols; j++) if(i>j) r(i,j) = Scalar(0); 39 40 MatrixType c = qr.matrixQ() * r * qr.colsPermutation().inverse(); 41 42 VERIFY_IS_APPROX(m1, c); 43 44 MatrixType m2 = MatrixType::Random(cols,cols2); 45 MatrixType m3 = m1*m2; 46 m2 = MatrixType::Random(cols,cols2); 47 m2 = qr.solve(m3); 48 VERIFY_IS_APPROX(m3, m1*m2); 49 } 50 51 template<typename MatrixType> void qr_invertible() 52 { 53 using std::log; 54 using std::abs; 55 typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar; 56 typedef typename MatrixType::Scalar Scalar; 57 58 int size = internal::random<int>(10,50); 59 60 MatrixType m1(size, size), m2(size, size), m3(size, size); 61 m1 = MatrixType::Random(size,size); 62 63 if (internal::is_same<RealScalar,float>::value) 64 { 65 // let's build a matrix more stable to inverse 66 MatrixType a = MatrixType::Random(size,size*2); 67 m1 += a * a.adjoint(); 68 } 69 70 FullPivHouseholderQR<MatrixType> qr(m1); 71 VERIFY(qr.isInjective()); 72 VERIFY(qr.isInvertible()); 73 VERIFY(qr.isSurjective()); 74 75 m3 = MatrixType::Random(size,size); 76 m2 = qr.solve(m3); 77 VERIFY_IS_APPROX(m3, m1*m2); 78 79 // now construct a matrix with prescribed determinant 80 m1.setZero(); 81 for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>(); 82 RealScalar absdet = abs(m1.diagonal().prod()); 83 m3 = qr.matrixQ(); // get a unitary 84 m1 = m3 * m1 * m3; 85 qr.compute(m1); 86 VERIFY_IS_APPROX(absdet, qr.absDeterminant()); 87 VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant()); 88 } 89 90 template<typename MatrixType> void qr_verify_assert() 91 { 92 MatrixType tmp; 93 94 FullPivHouseholderQR<MatrixType> qr; 95 VERIFY_RAISES_ASSERT(qr.matrixQR()) 96 VERIFY_RAISES_ASSERT(qr.solve(tmp)) 97 VERIFY_RAISES_ASSERT(qr.matrixQ()) 98 VERIFY_RAISES_ASSERT(qr.dimensionOfKernel()) 99 VERIFY_RAISES_ASSERT(qr.isInjective()) 100 VERIFY_RAISES_ASSERT(qr.isSurjective()) 101 VERIFY_RAISES_ASSERT(qr.isInvertible()) 102 VERIFY_RAISES_ASSERT(qr.inverse()) 103 VERIFY_RAISES_ASSERT(qr.absDeterminant()) 104 VERIFY_RAISES_ASSERT(qr.logAbsDeterminant()) 105 } 106 107 void test_qr_fullpivoting() 108 { 109 for(int i = 0; i < 1; i++) { 110 // FIXME : very weird bug here 111 // CALL_SUBTEST(qr(Matrix2f()) ); 112 CALL_SUBTEST_1( qr<MatrixXf>() ); 113 CALL_SUBTEST_2( qr<MatrixXd>() ); 114 CALL_SUBTEST_3( qr<MatrixXcd>() ); 115 } 116 117 for(int i = 0; i < g_repeat; i++) { 118 CALL_SUBTEST_1( qr_invertible<MatrixXf>() ); 119 CALL_SUBTEST_2( qr_invertible<MatrixXd>() ); 120 CALL_SUBTEST_4( qr_invertible<MatrixXcf>() ); 121 CALL_SUBTEST_3( qr_invertible<MatrixXcd>() ); 122 } 123 124 CALL_SUBTEST_5(qr_verify_assert<Matrix3f>()); 125 CALL_SUBTEST_6(qr_verify_assert<Matrix3d>()); 126 CALL_SUBTEST_1(qr_verify_assert<MatrixXf>()); 127 CALL_SUBTEST_2(qr_verify_assert<MatrixXd>()); 128 CALL_SUBTEST_4(qr_verify_assert<MatrixXcf>()); 129 CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>()); 130 131 // Test problem size constructors 132 CALL_SUBTEST_7(FullPivHouseholderQR<MatrixXf>(10, 20)); 133 CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(10,20))); 134 CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(Matrix<float,10,20>::Random()))); 135 CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(20,10))); 136 CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(Matrix<float,20,10>::Random()))); 137 } 138
