1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1 (at) gmail.com> 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 householder(const MatrixType& m) 14 { 15 typedef typename MatrixType::Index Index; 16 static bool even = true; 17 even = !even; 18 /* this test covers the following files: 19 Householder.h 20 */ 21 Index rows = m.rows(); 22 Index cols = m.cols(); 23 24 typedef typename MatrixType::Scalar Scalar; 25 typedef typename NumTraits<Scalar>::Real RealScalar; 26 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; 27 typedef Matrix<Scalar, internal::decrement_size<MatrixType::RowsAtCompileTime>::ret, 1> EssentialVectorType; 28 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType; 29 typedef Matrix<Scalar, Dynamic, MatrixType::ColsAtCompileTime> HBlockMatrixType; 30 typedef Matrix<Scalar, Dynamic, 1> HCoeffsVectorType; 31 32 typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::RowsAtCompileTime> TMatrixType; 33 34 Matrix<Scalar, EIGEN_SIZE_MAX(MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime), 1> _tmp((std::max)(rows,cols)); 35 Scalar* tmp = &_tmp.coeffRef(0,0); 36 37 Scalar beta; 38 RealScalar alpha; 39 EssentialVectorType essential; 40 41 VectorType v1 = VectorType::Random(rows), v2; 42 v2 = v1; 43 v1.makeHouseholder(essential, beta, alpha); 44 v1.applyHouseholderOnTheLeft(essential,beta,tmp); 45 VERIFY_IS_APPROX(v1.norm(), v2.norm()); 46 if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(v1.tail(rows-1).norm(), v1.norm()); 47 v1 = VectorType::Random(rows); 48 v2 = v1; 49 v1.applyHouseholderOnTheLeft(essential,beta,tmp); 50 VERIFY_IS_APPROX(v1.norm(), v2.norm()); 51 52 MatrixType m1(rows, cols), 53 m2(rows, cols); 54 55 v1 = VectorType::Random(rows); 56 if(even) v1.tail(rows-1).setZero(); 57 m1.colwise() = v1; 58 m2 = m1; 59 m1.col(0).makeHouseholder(essential, beta, alpha); 60 m1.applyHouseholderOnTheLeft(essential,beta,tmp); 61 VERIFY_IS_APPROX(m1.norm(), m2.norm()); 62 if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m1.block(1,0,rows-1,cols).norm(), m1.norm()); 63 VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m1(0,0)), numext::real(m1(0,0))); 64 VERIFY_IS_APPROX(numext::real(m1(0,0)), alpha); 65 66 v1 = VectorType::Random(rows); 67 if(even) v1.tail(rows-1).setZero(); 68 SquareMatrixType m3(rows,rows), m4(rows,rows); 69 m3.rowwise() = v1.transpose(); 70 m4 = m3; 71 m3.row(0).makeHouseholder(essential, beta, alpha); 72 m3.applyHouseholderOnTheRight(essential,beta,tmp); 73 VERIFY_IS_APPROX(m3.norm(), m4.norm()); 74 if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m3.block(0,1,rows,rows-1).norm(), m3.norm()); 75 VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m3(0,0)), numext::real(m3(0,0))); 76 VERIFY_IS_APPROX(numext::real(m3(0,0)), alpha); 77 78 // test householder sequence on the left with a shift 79 80 Index shift = internal::random<Index>(0, std::max<Index>(rows-2,0)); 81 Index brows = rows - shift; 82 m1.setRandom(rows, cols); 83 HBlockMatrixType hbm = m1.block(shift,0,brows,cols); 84 HouseholderQR<HBlockMatrixType> qr(hbm); 85 m2 = m1; 86 m2.block(shift,0,brows,cols) = qr.matrixQR(); 87 HCoeffsVectorType hc = qr.hCoeffs().conjugate(); 88 HouseholderSequence<MatrixType, HCoeffsVectorType> hseq(m2, hc); 89 hseq.setLength(hc.size()).setShift(shift); 90 VERIFY(hseq.length() == hc.size()); 91 VERIFY(hseq.shift() == shift); 92 93 MatrixType m5 = m2; 94 m5.block(shift,0,brows,cols).template triangularView<StrictlyLower>().setZero(); 95 VERIFY_IS_APPROX(hseq * m5, m1); // test applying hseq directly 96 m3 = hseq; 97 VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating hseq to a dense matrix, then applying 98 99 SquareMatrixType hseq_mat = hseq; 100 SquareMatrixType hseq_mat_conj = hseq.conjugate(); 101 SquareMatrixType hseq_mat_adj = hseq.adjoint(); 102 SquareMatrixType hseq_mat_trans = hseq.transpose(); 103 SquareMatrixType m6 = SquareMatrixType::Random(rows, rows); 104 VERIFY_IS_APPROX(hseq_mat.adjoint(), hseq_mat_adj); 105 VERIFY_IS_APPROX(hseq_mat.conjugate(), hseq_mat_conj); 106 VERIFY_IS_APPROX(hseq_mat.transpose(), hseq_mat_trans); 107 VERIFY_IS_APPROX(hseq_mat * m6, hseq_mat * m6); 108 VERIFY_IS_APPROX(hseq_mat.adjoint() * m6, hseq_mat_adj * m6); 109 VERIFY_IS_APPROX(hseq_mat.conjugate() * m6, hseq_mat_conj * m6); 110 VERIFY_IS_APPROX(hseq_mat.transpose() * m6, hseq_mat_trans * m6); 111 VERIFY_IS_APPROX(m6 * hseq_mat, m6 * hseq_mat); 112 VERIFY_IS_APPROX(m6 * hseq_mat.adjoint(), m6 * hseq_mat_adj); 113 VERIFY_IS_APPROX(m6 * hseq_mat.conjugate(), m6 * hseq_mat_conj); 114 VERIFY_IS_APPROX(m6 * hseq_mat.transpose(), m6 * hseq_mat_trans); 115 116 // test householder sequence on the right with a shift 117 118 TMatrixType tm2 = m2.transpose(); 119 HouseholderSequence<TMatrixType, HCoeffsVectorType, OnTheRight> rhseq(tm2, hc); 120 rhseq.setLength(hc.size()).setShift(shift); 121 VERIFY_IS_APPROX(rhseq * m5, m1); // test applying rhseq directly 122 m3 = rhseq; 123 VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating rhseq to a dense matrix, then applying 124 } 125 126 void test_householder() 127 { 128 for(int i = 0; i < g_repeat; i++) { 129 CALL_SUBTEST_1( householder(Matrix<double,2,2>()) ); 130 CALL_SUBTEST_2( householder(Matrix<float,2,3>()) ); 131 CALL_SUBTEST_3( householder(Matrix<double,3,5>()) ); 132 CALL_SUBTEST_4( householder(Matrix<float,4,4>()) ); 133 CALL_SUBTEST_5( householder(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 134 CALL_SUBTEST_6( householder(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 135 CALL_SUBTEST_7( householder(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 136 CALL_SUBTEST_8( householder(Matrix<double,1,1>()) ); 137 } 138 } 139
