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 typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar; 58 typedef typename MatrixType::Scalar Scalar; 59 60 int size = internal::random<int>(10,50); 61 62 MatrixType m1(size, size), m2(size, size), m3(size, size); 63 m1 = MatrixType::Random(size,size); 64 65 if (internal::is_same<RealScalar,float>::value) 66 { 67 // let's build a matrix more stable to inverse 68 MatrixType a = MatrixType::Random(size,size*2); 69 m1 += a * a.adjoint(); 70 } 71 72 HouseholderQR<MatrixType> qr(m1); 73 m3 = MatrixType::Random(size,size); 74 m2 = qr.solve(m3); 75 VERIFY_IS_APPROX(m3, m1*m2); 76 77 // now construct a matrix with prescribed determinant 78 m1.setZero(); 79 for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>(); 80 RealScalar absdet = abs(m1.diagonal().prod()); 81 m3 = qr.householderQ(); // get a unitary 82 m1 = m3 * m1 * m3; 83 qr.compute(m1); 84 VERIFY_IS_APPROX(absdet, qr.absDeterminant()); 85 VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant()); 86 } 87 88 template<typename MatrixType> void qr_verify_assert() 89 { 90 MatrixType tmp; 91 92 HouseholderQR<MatrixType> qr; 93 VERIFY_RAISES_ASSERT(qr.matrixQR()) 94 VERIFY_RAISES_ASSERT(qr.solve(tmp)) 95 VERIFY_RAISES_ASSERT(qr.householderQ()) 96 VERIFY_RAISES_ASSERT(qr.absDeterminant()) 97 VERIFY_RAISES_ASSERT(qr.logAbsDeterminant()) 98 } 99 100 void test_qr() 101 { 102 for(int i = 0; i < g_repeat; i++) { 103 CALL_SUBTEST_1( qr(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 104 CALL_SUBTEST_2( qr(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2),internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) ); 105 CALL_SUBTEST_3(( qr_fixedsize<Matrix<float,3,4>, 2 >() )); 106 CALL_SUBTEST_4(( qr_fixedsize<Matrix<double,6,2>, 4 >() )); 107 CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,2,5>, 7 >() )); 108 CALL_SUBTEST_11( qr(Matrix<float,1,1>()) ); 109 } 110 111 for(int i = 0; i < g_repeat; i++) { 112 CALL_SUBTEST_1( qr_invertible<MatrixXf>() ); 113 CALL_SUBTEST_6( qr_invertible<MatrixXd>() ); 114 CALL_SUBTEST_7( qr_invertible<MatrixXcf>() ); 115 CALL_SUBTEST_8( qr_invertible<MatrixXcd>() ); 116 } 117 118 CALL_SUBTEST_9(qr_verify_assert<Matrix3f>()); 119 CALL_SUBTEST_10(qr_verify_assert<Matrix3d>()); 120 CALL_SUBTEST_1(qr_verify_assert<MatrixXf>()); 121 CALL_SUBTEST_6(qr_verify_assert<MatrixXd>()); 122 CALL_SUBTEST_7(qr_verify_assert<MatrixXcf>()); 123 CALL_SUBTEST_8(qr_verify_assert<MatrixXcd>()); 124 125 // Test problem size constructors 126 CALL_SUBTEST_12(HouseholderQR<MatrixXf>(10, 20)); 127 } 128
