[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
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| 5 | //
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| 6 | // This Source Code Form is subject to the terms of the Mozilla
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| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 9 |
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| 10 | #include "main.h"
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| 11 | #include <Eigen/QR>
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| 12 |
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| 13 | template<typename MatrixType> void householder(const MatrixType& m)
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| 14 | {
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| 15 | typedef typename MatrixType::Index Index;
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| 16 | static bool even = true;
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| 17 | even = !even;
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| 18 | /* this test covers the following files:
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| 19 | Householder.h
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| 20 | */
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| 21 | Index rows = m.rows();
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| 22 | Index cols = m.cols();
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| 23 |
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| 24 | typedef typename MatrixType::Scalar Scalar;
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| 25 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 26 | typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
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| 27 | typedef Matrix<Scalar, internal::decrement_size<MatrixType::RowsAtCompileTime>::ret, 1> EssentialVectorType;
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| 28 | typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
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| 29 | typedef Matrix<Scalar, Dynamic, MatrixType::ColsAtCompileTime> HBlockMatrixType;
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| 30 | typedef Matrix<Scalar, Dynamic, 1> HCoeffsVectorType;
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| 31 |
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| 32 | typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::RowsAtCompileTime> TMatrixType;
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| 33 |
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| 34 | Matrix<Scalar, EIGEN_SIZE_MAX(MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime), 1> _tmp((std::max)(rows,cols));
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| 35 | Scalar* tmp = &_tmp.coeffRef(0,0);
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| 36 |
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| 37 | Scalar beta;
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| 38 | RealScalar alpha;
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| 39 | EssentialVectorType essential;
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| 40 |
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| 41 | VectorType v1 = VectorType::Random(rows), v2;
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| 42 | v2 = v1;
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| 43 | v1.makeHouseholder(essential, beta, alpha);
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| 44 | v1.applyHouseholderOnTheLeft(essential,beta,tmp);
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| 45 | VERIFY_IS_APPROX(v1.norm(), v2.norm());
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| 46 | if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(v1.tail(rows-1).norm(), v1.norm());
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| 47 | v1 = VectorType::Random(rows);
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| 48 | v2 = v1;
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| 49 | v1.applyHouseholderOnTheLeft(essential,beta,tmp);
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| 50 | VERIFY_IS_APPROX(v1.norm(), v2.norm());
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| 51 |
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| 52 | MatrixType m1(rows, cols),
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| 53 | m2(rows, cols);
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| 54 |
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| 55 | v1 = VectorType::Random(rows);
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| 56 | if(even) v1.tail(rows-1).setZero();
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| 57 | m1.colwise() = v1;
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| 58 | m2 = m1;
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| 59 | m1.col(0).makeHouseholder(essential, beta, alpha);
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| 60 | m1.applyHouseholderOnTheLeft(essential,beta,tmp);
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| 61 | VERIFY_IS_APPROX(m1.norm(), m2.norm());
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| 62 | if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m1.block(1,0,rows-1,cols).norm(), m1.norm());
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| 63 | VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m1(0,0)), numext::real(m1(0,0)));
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| 64 | VERIFY_IS_APPROX(numext::real(m1(0,0)), alpha);
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| 65 |
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| 66 | v1 = VectorType::Random(rows);
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| 67 | if(even) v1.tail(rows-1).setZero();
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| 68 | SquareMatrixType m3(rows,rows), m4(rows,rows);
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| 69 | m3.rowwise() = v1.transpose();
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| 70 | m4 = m3;
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| 71 | m3.row(0).makeHouseholder(essential, beta, alpha);
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| 72 | m3.applyHouseholderOnTheRight(essential,beta,tmp);
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| 73 | VERIFY_IS_APPROX(m3.norm(), m4.norm());
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| 74 | if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m3.block(0,1,rows,rows-1).norm(), m3.norm());
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| 75 | VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m3(0,0)), numext::real(m3(0,0)));
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| 76 | VERIFY_IS_APPROX(numext::real(m3(0,0)), alpha);
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| 77 |
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| 78 | // test householder sequence on the left with a shift
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| 79 |
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| 80 | Index shift = internal::random<Index>(0, std::max<Index>(rows-2,0));
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| 81 | Index brows = rows - shift;
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| 82 | m1.setRandom(rows, cols);
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| 83 | HBlockMatrixType hbm = m1.block(shift,0,brows,cols);
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| 84 | HouseholderQR<HBlockMatrixType> qr(hbm);
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| 85 | m2 = m1;
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| 86 | m2.block(shift,0,brows,cols) = qr.matrixQR();
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| 87 | HCoeffsVectorType hc = qr.hCoeffs().conjugate();
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| 88 | HouseholderSequence<MatrixType, HCoeffsVectorType> hseq(m2, hc);
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| 89 | hseq.setLength(hc.size()).setShift(shift);
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| 90 | VERIFY(hseq.length() == hc.size());
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| 91 | VERIFY(hseq.shift() == shift);
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| 92 |
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| 93 | MatrixType m5 = m2;
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| 94 | m5.block(shift,0,brows,cols).template triangularView<StrictlyLower>().setZero();
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| 95 | VERIFY_IS_APPROX(hseq * m5, m1); // test applying hseq directly
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| 96 | m3 = hseq;
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| 97 | VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating hseq to a dense matrix, then applying
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| 98 |
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| 99 | SquareMatrixType hseq_mat = hseq;
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| 100 | SquareMatrixType hseq_mat_conj = hseq.conjugate();
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| 101 | SquareMatrixType hseq_mat_adj = hseq.adjoint();
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| 102 | SquareMatrixType hseq_mat_trans = hseq.transpose();
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| 103 | SquareMatrixType m6 = SquareMatrixType::Random(rows, rows);
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| 104 | VERIFY_IS_APPROX(hseq_mat.adjoint(), hseq_mat_adj);
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| 105 | VERIFY_IS_APPROX(hseq_mat.conjugate(), hseq_mat_conj);
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| 106 | VERIFY_IS_APPROX(hseq_mat.transpose(), hseq_mat_trans);
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| 107 | VERIFY_IS_APPROX(hseq_mat * m6, hseq_mat * m6);
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| 108 | VERIFY_IS_APPROX(hseq_mat.adjoint() * m6, hseq_mat_adj * m6);
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| 109 | VERIFY_IS_APPROX(hseq_mat.conjugate() * m6, hseq_mat_conj * m6);
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| 110 | VERIFY_IS_APPROX(hseq_mat.transpose() * m6, hseq_mat_trans * m6);
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| 111 | VERIFY_IS_APPROX(m6 * hseq_mat, m6 * hseq_mat);
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| 112 | VERIFY_IS_APPROX(m6 * hseq_mat.adjoint(), m6 * hseq_mat_adj);
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| 113 | VERIFY_IS_APPROX(m6 * hseq_mat.conjugate(), m6 * hseq_mat_conj);
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| 114 | VERIFY_IS_APPROX(m6 * hseq_mat.transpose(), m6 * hseq_mat_trans);
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| 115 |
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| 116 | // test householder sequence on the right with a shift
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| 117 |
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| 118 | TMatrixType tm2 = m2.transpose();
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| 119 | HouseholderSequence<TMatrixType, HCoeffsVectorType, OnTheRight> rhseq(tm2, hc);
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| 120 | rhseq.setLength(hc.size()).setShift(shift);
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| 121 | VERIFY_IS_APPROX(rhseq * m5, m1); // test applying rhseq directly
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| 122 | m3 = rhseq;
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| 123 | VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating rhseq to a dense matrix, then applying
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| 124 | }
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| 125 |
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| 126 | void test_householder()
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| 127 | {
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| 128 | for(int i = 0; i < g_repeat; i++) {
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| 129 | CALL_SUBTEST_1( householder(Matrix<double,2,2>()) );
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| 130 | CALL_SUBTEST_2( householder(Matrix<float,2,3>()) );
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| 131 | CALL_SUBTEST_3( householder(Matrix<double,3,5>()) );
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| 132 | CALL_SUBTEST_4( householder(Matrix<float,4,4>()) );
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| 133 | CALL_SUBTEST_5( householder(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
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| 134 | CALL_SUBTEST_6( householder(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
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| 135 | CALL_SUBTEST_7( householder(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
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| 136 | CALL_SUBTEST_8( householder(Matrix<double,1,1>()) );
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| 137 | }
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| 138 | }
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