householder.cpp (6286B)
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@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 static bool even = true; 16 even = !even; 17 /* this test covers the following files: 18 Householder.h 19 */ 20 Index rows = m.rows(); 21 Index cols = m.cols(); 22 23 typedef typename MatrixType::Scalar Scalar; 24 typedef typename NumTraits<Scalar>::Real RealScalar; 25 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; 26 typedef Matrix<Scalar, internal::decrement_size<MatrixType::RowsAtCompileTime>::ret, 1> EssentialVectorType; 27 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType; 28 typedef Matrix<Scalar, Dynamic, MatrixType::ColsAtCompileTime> HBlockMatrixType; 29 typedef Matrix<Scalar, Dynamic, 1> HCoeffsVectorType; 30 31 typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::RowsAtCompileTime> TMatrixType; 32 33 Matrix<Scalar, EIGEN_SIZE_MAX(MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime), 1> _tmp((std::max)(rows,cols)); 34 Scalar* tmp = &_tmp.coeffRef(0,0); 35 36 Scalar beta; 37 RealScalar alpha; 38 EssentialVectorType essential; 39 40 VectorType v1 = VectorType::Random(rows), v2; 41 v2 = v1; 42 v1.makeHouseholder(essential, beta, alpha); 43 v1.applyHouseholderOnTheLeft(essential,beta,tmp); 44 VERIFY_IS_APPROX(v1.norm(), v2.norm()); 45 if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(v1.tail(rows-1).norm(), v1.norm()); 46 v1 = VectorType::Random(rows); 47 v2 = v1; 48 v1.applyHouseholderOnTheLeft(essential,beta,tmp); 49 VERIFY_IS_APPROX(v1.norm(), v2.norm()); 50 51 // reconstruct householder matrix: 52 SquareMatrixType id, H1, H2; 53 id.setIdentity(rows, rows); 54 H1 = H2 = id; 55 VectorType vv(rows); 56 vv << Scalar(1), essential; 57 H1.applyHouseholderOnTheLeft(essential, beta, tmp); 58 H2.applyHouseholderOnTheRight(essential, beta, tmp); 59 VERIFY_IS_APPROX(H1, H2); 60 VERIFY_IS_APPROX(H1, id - beta * vv*vv.adjoint()); 61 62 MatrixType m1(rows, cols), 63 m2(rows, cols); 64 65 v1 = VectorType::Random(rows); 66 if(even) v1.tail(rows-1).setZero(); 67 m1.colwise() = v1; 68 m2 = m1; 69 m1.col(0).makeHouseholder(essential, beta, alpha); 70 m1.applyHouseholderOnTheLeft(essential,beta,tmp); 71 VERIFY_IS_APPROX(m1.norm(), m2.norm()); 72 if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m1.block(1,0,rows-1,cols).norm(), m1.norm()); 73 VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m1(0,0)), numext::real(m1(0,0))); 74 VERIFY_IS_APPROX(numext::real(m1(0,0)), alpha); 75 76 v1 = VectorType::Random(rows); 77 if(even) v1.tail(rows-1).setZero(); 78 SquareMatrixType m3(rows,rows), m4(rows,rows); 79 m3.rowwise() = v1.transpose(); 80 m4 = m3; 81 m3.row(0).makeHouseholder(essential, beta, alpha); 82 m3.applyHouseholderOnTheRight(essential.conjugate(),beta,tmp); 83 VERIFY_IS_APPROX(m3.norm(), m4.norm()); 84 if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m3.block(0,1,rows,rows-1).norm(), m3.norm()); 85 VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m3(0,0)), numext::real(m3(0,0))); 86 VERIFY_IS_APPROX(numext::real(m3(0,0)), alpha); 87 88 // test householder sequence on the left with a shift 89 90 Index shift = internal::random<Index>(0, std::max<Index>(rows-2,0)); 91 Index brows = rows - shift; 92 m1.setRandom(rows, cols); 93 HBlockMatrixType hbm = m1.block(shift,0,brows,cols); 94 HouseholderQR<HBlockMatrixType> qr(hbm); 95 m2 = m1; 96 m2.block(shift,0,brows,cols) = qr.matrixQR(); 97 HCoeffsVectorType hc = qr.hCoeffs().conjugate(); 98 HouseholderSequence<MatrixType, HCoeffsVectorType> hseq(m2, hc); 99 hseq.setLength(hc.size()).setShift(shift); 100 VERIFY(hseq.length() == hc.size()); 101 VERIFY(hseq.shift() == shift); 102 103 MatrixType m5 = m2; 104 m5.block(shift,0,brows,cols).template triangularView<StrictlyLower>().setZero(); 105 VERIFY_IS_APPROX(hseq * m5, m1); // test applying hseq directly 106 m3 = hseq; 107 VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating hseq to a dense matrix, then applying 108 109 SquareMatrixType hseq_mat = hseq; 110 SquareMatrixType hseq_mat_conj = hseq.conjugate(); 111 SquareMatrixType hseq_mat_adj = hseq.adjoint(); 112 SquareMatrixType hseq_mat_trans = hseq.transpose(); 113 SquareMatrixType m6 = SquareMatrixType::Random(rows, rows); 114 VERIFY_IS_APPROX(hseq_mat.adjoint(), hseq_mat_adj); 115 VERIFY_IS_APPROX(hseq_mat.conjugate(), hseq_mat_conj); 116 VERIFY_IS_APPROX(hseq_mat.transpose(), hseq_mat_trans); 117 VERIFY_IS_APPROX(hseq * m6, hseq_mat * m6); 118 VERIFY_IS_APPROX(hseq.adjoint() * m6, hseq_mat_adj * m6); 119 VERIFY_IS_APPROX(hseq.conjugate() * m6, hseq_mat_conj * m6); 120 VERIFY_IS_APPROX(hseq.transpose() * m6, hseq_mat_trans * m6); 121 VERIFY_IS_APPROX(m6 * hseq, m6 * hseq_mat); 122 VERIFY_IS_APPROX(m6 * hseq.adjoint(), m6 * hseq_mat_adj); 123 VERIFY_IS_APPROX(m6 * hseq.conjugate(), m6 * hseq_mat_conj); 124 VERIFY_IS_APPROX(m6 * hseq.transpose(), m6 * hseq_mat_trans); 125 126 // test householder sequence on the right with a shift 127 128 TMatrixType tm2 = m2.transpose(); 129 HouseholderSequence<TMatrixType, HCoeffsVectorType, OnTheRight> rhseq(tm2, hc); 130 rhseq.setLength(hc.size()).setShift(shift); 131 VERIFY_IS_APPROX(rhseq * m5, m1); // test applying rhseq directly 132 m3 = rhseq; 133 VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating rhseq to a dense matrix, then applying 134 } 135 136 EIGEN_DECLARE_TEST(householder) 137 { 138 for(int i = 0; i < g_repeat; i++) { 139 CALL_SUBTEST_1( householder(Matrix<double,2,2>()) ); 140 CALL_SUBTEST_2( householder(Matrix<float,2,3>()) ); 141 CALL_SUBTEST_3( householder(Matrix<double,3,5>()) ); 142 CALL_SUBTEST_4( householder(Matrix<float,4,4>()) ); 143 CALL_SUBTEST_5( householder(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 144 CALL_SUBTEST_6( householder(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 145 CALL_SUBTEST_7( householder(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 146 CALL_SUBTEST_8( householder(Matrix<double,1,1>()) ); 147 } 148 }