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