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::ColsAtCompileTime> RightSquareMatrixType; 33 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, Dynamic> VBlockMatrixType; 34 typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::RowsAtCompileTime> TMatrixType; 35 36 Matrix<Scalar, EIGEN_SIZE_MAX(MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime), 1> _tmp((std::max)(rows,cols)); 37 Scalar* tmp = &_tmp.coeffRef(0,0); 38 39 Scalar beta; 40 RealScalar alpha; 41 EssentialVectorType essential; 42 43 VectorType v1 = VectorType::Random(rows), v2; 44 v2 = v1; 45 v1.makeHouseholder(essential, beta, alpha); 46 v1.applyHouseholderOnTheLeft(essential,beta,tmp); 47 VERIFY_IS_APPROX(v1.norm(), v2.norm()); 48 if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(v1.tail(rows-1).norm(), v1.norm()); 49 v1 = VectorType::Random(rows); 50 v2 = v1; 51 v1.applyHouseholderOnTheLeft(essential,beta,tmp); 52 VERIFY_IS_APPROX(v1.norm(), v2.norm()); 53 54 MatrixType m1(rows, cols), 55 m2(rows, cols); 56 57 v1 = VectorType::Random(rows); 58 if(even) v1.tail(rows-1).setZero(); 59 m1.colwise() = v1; 60 m2 = m1; 61 m1.col(0).makeHouseholder(essential, beta, alpha); 62 m1.applyHouseholderOnTheLeft(essential,beta,tmp); 63 VERIFY_IS_APPROX(m1.norm(), m2.norm()); 64 if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m1.block(1,0,rows-1,cols).norm(), m1.norm()); 65 VERIFY_IS_MUCH_SMALLER_THAN(internal::imag(m1(0,0)), internal::real(m1(0,0))); 66 VERIFY_IS_APPROX(internal::real(m1(0,0)), alpha); 67 68 v1 = VectorType::Random(rows); 69 if(even) v1.tail(rows-1).setZero(); 70 SquareMatrixType m3(rows,rows), m4(rows,rows); 71 m3.rowwise() = v1.transpose(); 72 m4 = m3; 73 m3.row(0).makeHouseholder(essential, beta, alpha); 74 m3.applyHouseholderOnTheRight(essential,beta,tmp); 75 VERIFY_IS_APPROX(m3.norm(), m4.norm()); 76 if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m3.block(0,1,rows,rows-1).norm(), m3.norm()); 77 VERIFY_IS_MUCH_SMALLER_THAN(internal::imag(m3(0,0)), internal::real(m3(0,0))); 78 VERIFY_IS_APPROX(internal::real(m3(0,0)), alpha); 79 80 // test householder sequence on the left with a shift 81 82 Index shift = internal::random<Index>(0, std::max<Index>(rows-2,0)); 83 Index brows = rows - shift; 84 m1.setRandom(rows, cols); 85 HBlockMatrixType hbm = m1.block(shift,0,brows,cols); 86 HouseholderQR<HBlockMatrixType> qr(hbm); 87 m2 = m1; 88 m2.block(shift,0,brows,cols) = qr.matrixQR(); 89 HCoeffsVectorType hc = qr.hCoeffs().conjugate(); 90 HouseholderSequence<MatrixType, HCoeffsVectorType> hseq(m2, hc); 91 hseq.setLength(hc.size()).setShift(shift); 92 VERIFY(hseq.length() == hc.size()); 93 VERIFY(hseq.shift() == shift); 94 95 MatrixType m5 = m2; 96 m5.block(shift,0,brows,cols).template triangularView<StrictlyLower>().setZero(); 97 VERIFY_IS_APPROX(hseq * m5, m1); // test applying hseq directly 98 m3 = hseq; 99 VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating hseq to a dense matrix, then applying 100 101 // test householder sequence on the right with a shift 102 103 TMatrixType tm2 = m2.transpose(); 104 HouseholderSequence<TMatrixType, HCoeffsVectorType, OnTheRight> rhseq(tm2, hc); 105 rhseq.setLength(hc.size()).setShift(shift); 106 VERIFY_IS_APPROX(rhseq * m5, m1); // test applying rhseq directly 107 m3 = rhseq; 108 VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating rhseq to a dense matrix, then applying 109 } 110 111 void test_householder() 112 { 113 for(int i = 0; i < g_repeat; i++) { 114 CALL_SUBTEST_1( householder(Matrix<double,2,2>()) ); 115 CALL_SUBTEST_2( householder(Matrix<float,2,3>()) ); 116 CALL_SUBTEST_3( householder(Matrix<double,3,5>()) ); 117 CALL_SUBTEST_4( householder(Matrix<float,4,4>()) ); 118 CALL_SUBTEST_5( householder(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 119 CALL_SUBTEST_6( householder(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 120 CALL_SUBTEST_7( householder(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 121 CALL_SUBTEST_8( householder(Matrix<double,1,1>()) ); 122 } 123 } 124
