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 // 6 // This Source Code Form is subject to the terms of the Mozilla 7 // Public License v. 2.0. If a copy of the MPL was not distributed 8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 9 10 #include "main.h" 11 #include <Eigen/QR> 12 13 template<typename MatrixType> void qr(const MatrixType& m) 14 { 15 typedef typename MatrixType::Index Index; 16 17 Index rows = m.rows(); 18 Index cols = m.cols(); 19 20 typedef typename MatrixType::Scalar Scalar; 21 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType; 22 23 MatrixType a = MatrixType::Random(rows,cols); 24 HouseholderQR<MatrixType> qrOfA(a); 25 26 MatrixQType q = qrOfA.householderQ(); 27 VERIFY_IS_UNITARY(q); 28 29 MatrixType r = qrOfA.matrixQR().template triangularView<Upper>(); 30 VERIFY_IS_APPROX(a, qrOfA.householderQ() * r); 31 } 32 33 template<typename MatrixType, int Cols2> void qr_fixedsize() 34 { 35 enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime }; 36 typedef typename MatrixType::Scalar Scalar; 37 Matrix<Scalar,Rows,Cols> m1 = Matrix<Scalar,Rows,Cols>::Random(); 38 HouseholderQR<Matrix<Scalar,Rows,Cols> > qr(m1); 39 40 Matrix<Scalar,Rows,Cols> r = qr.matrixQR(); 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 VERIFY_IS_APPROX(m1, qr.householderQ() * r); 45 46 Matrix<Scalar,Cols,Cols2> m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2); 47 Matrix<Scalar,Rows,Cols2> m3 = m1*m2; 48 m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2); 49 m2 = qr.solve(m3); 50 VERIFY_IS_APPROX(m3, m1*m2); 51 } 52 53 template<typename MatrixType> void qr_invertible() 54 { 55 using std::log; 56 using std::abs; 57 using std::pow; 58 using std::max; 59 typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar; 60 typedef typename MatrixType::Scalar Scalar; 61 62 int size = internal::random<int>(10,50); 63 64 MatrixType m1(size, size), m2(size, size), m3(size, size); 65 m1 = MatrixType::Random(size,size); 66 67 if (internal::is_same<RealScalar,float>::value) 68 { 69 // let's build a matrix more stable to inverse 70 MatrixType a = MatrixType::Random(size,size*4); 71 m1 += a * a.adjoint(); 72 } 73 74 HouseholderQR<MatrixType> qr(m1); 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.householderQ(); // get a unitary 84 m1 = m3 * m1 * m3; 85 qr.compute(m1); 86 VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant()); 87 // This test is tricky if the determinant becomes too small. 88 // Since we generate random numbers with magnitude rrange [0,1], the average determinant is 0.5^size 89 VERIFY_IS_MUCH_SMALLER_THAN( abs(absdet-qr.absDeterminant()), numext::maxi(RealScalar(pow(0.5,size)),numext::maxi<RealScalar>(abs(absdet),abs(qr.absDeterminant()))) ); 90 91 } 92 93 template<typename MatrixType> void qr_verify_assert() 94 { 95 MatrixType tmp; 96 97 HouseholderQR<MatrixType> qr; 98 VERIFY_RAISES_ASSERT(qr.matrixQR()) 99 VERIFY_RAISES_ASSERT(qr.solve(tmp)) 100 VERIFY_RAISES_ASSERT(qr.householderQ()) 101 VERIFY_RAISES_ASSERT(qr.absDeterminant()) 102 VERIFY_RAISES_ASSERT(qr.logAbsDeterminant()) 103 } 104 105 void test_qr() 106 { 107 for(int i = 0; i < g_repeat; i++) { 108 CALL_SUBTEST_1( qr(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 109 CALL_SUBTEST_2( qr(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2),internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) ); 110 CALL_SUBTEST_3(( qr_fixedsize<Matrix<float,3,4>, 2 >() )); 111 CALL_SUBTEST_4(( qr_fixedsize<Matrix<double,6,2>, 4 >() )); 112 CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,2,5>, 7 >() )); 113 CALL_SUBTEST_11( qr(Matrix<float,1,1>()) ); 114 } 115 116 for(int i = 0; i < g_repeat; i++) { 117 CALL_SUBTEST_1( qr_invertible<MatrixXf>() ); 118 CALL_SUBTEST_6( qr_invertible<MatrixXd>() ); 119 CALL_SUBTEST_7( qr_invertible<MatrixXcf>() ); 120 CALL_SUBTEST_8( qr_invertible<MatrixXcd>() ); 121 } 122 123 CALL_SUBTEST_9(qr_verify_assert<Matrix3f>()); 124 CALL_SUBTEST_10(qr_verify_assert<Matrix3d>()); 125 CALL_SUBTEST_1(qr_verify_assert<MatrixXf>()); 126 CALL_SUBTEST_6(qr_verify_assert<MatrixXd>()); 127 CALL_SUBTEST_7(qr_verify_assert<MatrixXcf>()); 128 CALL_SUBTEST_8(qr_verify_assert<MatrixXcd>()); 129 130 // Test problem size constructors 131 CALL_SUBTEST_12(HouseholderQR<MatrixXf>(10, 20)); 132 } 133
