1c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This file is part of Eigen, a lightweight C++ template library 2c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// for linear algebra. 3c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 4c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com> 5c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 6c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This Source Code Form is subject to the terms of the Mozilla 7c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Public License v. 2.0. If a copy of the MPL was not distributed 8c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 9c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 10c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include "main.h" 11c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include <Eigen/QR> 12c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 13c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType> void householder(const MatrixType& m) 14c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 15c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename MatrixType::Index Index; 16c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath static bool even = true; 17c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath even = !even; 18c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /* this test covers the following files: 19c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Householder.h 20c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 21c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index rows = m.rows(); 22c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index cols = m.cols(); 23c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 24c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename MatrixType::Scalar Scalar; 25c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename NumTraits<Scalar>::Real RealScalar; 26c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; 27c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar, internal::decrement_size<MatrixType::RowsAtCompileTime>::ret, 1> EssentialVectorType; 28c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType; 29c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar, Dynamic, MatrixType::ColsAtCompileTime> HBlockMatrixType; 30c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar, Dynamic, 1> HCoeffsVectorType; 31c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 32c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::RowsAtCompileTime> TMatrixType; 33c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 34c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix<Scalar, EIGEN_SIZE_MAX(MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime), 1> _tmp((std::max)(rows,cols)); 35c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar* tmp = &_tmp.coeffRef(0,0); 36c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 37c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar beta; 38c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath RealScalar alpha; 39c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath EssentialVectorType essential; 40c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 41c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VectorType v1 = VectorType::Random(rows), v2; 42c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath v2 = v1; 43c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath v1.makeHouseholder(essential, beta, alpha); 44c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath v1.applyHouseholderOnTheLeft(essential,beta,tmp); 45c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(v1.norm(), v2.norm()); 46c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(v1.tail(rows-1).norm(), v1.norm()); 47c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath v1 = VectorType::Random(rows); 48c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath v2 = v1; 49c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath v1.applyHouseholderOnTheLeft(essential,beta,tmp); 50c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(v1.norm(), v2.norm()); 51c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 52c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType m1(rows, cols), 53c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m2(rows, cols); 54c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 55c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath v1 = VectorType::Random(rows); 56c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if(even) v1.tail(rows-1).setZero(); 57c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m1.colwise() = v1; 58c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m2 = m1; 59c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m1.col(0).makeHouseholder(essential, beta, alpha); 60c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m1.applyHouseholderOnTheLeft(essential,beta,tmp); 61c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(m1.norm(), m2.norm()); 62c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m1.block(1,0,rows-1,cols).norm(), m1.norm()); 637faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m1(0,0)), numext::real(m1(0,0))); 647faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez VERIFY_IS_APPROX(numext::real(m1(0,0)), alpha); 65c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 66c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath v1 = VectorType::Random(rows); 67c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if(even) v1.tail(rows-1).setZero(); 68c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath SquareMatrixType m3(rows,rows), m4(rows,rows); 69c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m3.rowwise() = v1.transpose(); 70c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m4 = m3; 71c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m3.row(0).makeHouseholder(essential, beta, alpha); 72c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m3.applyHouseholderOnTheRight(essential,beta,tmp); 73c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(m3.norm(), m4.norm()); 74c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m3.block(0,1,rows,rows-1).norm(), m3.norm()); 757faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m3(0,0)), numext::real(m3(0,0))); 767faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez VERIFY_IS_APPROX(numext::real(m3(0,0)), alpha); 77c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 78c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // test householder sequence on the left with a shift 79c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 80c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index shift = internal::random<Index>(0, std::max<Index>(rows-2,0)); 81c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index brows = rows - shift; 82c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m1.setRandom(rows, cols); 83c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath HBlockMatrixType hbm = m1.block(shift,0,brows,cols); 84c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath HouseholderQR<HBlockMatrixType> qr(hbm); 85c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m2 = m1; 86c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m2.block(shift,0,brows,cols) = qr.matrixQR(); 87c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath HCoeffsVectorType hc = qr.hCoeffs().conjugate(); 88c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath HouseholderSequence<MatrixType, HCoeffsVectorType> hseq(m2, hc); 89c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath hseq.setLength(hc.size()).setShift(shift); 90c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY(hseq.length() == hc.size()); 91c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY(hseq.shift() == shift); 927faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 93c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType m5 = m2; 94c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m5.block(shift,0,brows,cols).template triangularView<StrictlyLower>().setZero(); 95c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(hseq * m5, m1); // test applying hseq directly 96c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m3 = hseq; 97c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating hseq to a dense matrix, then applying 987faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 997faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez SquareMatrixType hseq_mat = hseq; 1007faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez SquareMatrixType hseq_mat_conj = hseq.conjugate(); 1017faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez SquareMatrixType hseq_mat_adj = hseq.adjoint(); 1027faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez SquareMatrixType hseq_mat_trans = hseq.transpose(); 1037faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez SquareMatrixType m6 = SquareMatrixType::Random(rows, rows); 1047faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez VERIFY_IS_APPROX(hseq_mat.adjoint(), hseq_mat_adj); 1057faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez VERIFY_IS_APPROX(hseq_mat.conjugate(), hseq_mat_conj); 1067faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez VERIFY_IS_APPROX(hseq_mat.transpose(), hseq_mat_trans); 1077faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez VERIFY_IS_APPROX(hseq_mat * m6, hseq_mat * m6); 1087faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez VERIFY_IS_APPROX(hseq_mat.adjoint() * m6, hseq_mat_adj * m6); 1097faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez VERIFY_IS_APPROX(hseq_mat.conjugate() * m6, hseq_mat_conj * m6); 1107faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez VERIFY_IS_APPROX(hseq_mat.transpose() * m6, hseq_mat_trans * m6); 1117faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez VERIFY_IS_APPROX(m6 * hseq_mat, m6 * hseq_mat); 1127faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez VERIFY_IS_APPROX(m6 * hseq_mat.adjoint(), m6 * hseq_mat_adj); 1137faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez VERIFY_IS_APPROX(m6 * hseq_mat.conjugate(), m6 * hseq_mat_conj); 1147faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez VERIFY_IS_APPROX(m6 * hseq_mat.transpose(), m6 * hseq_mat_trans); 115c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 116c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // test householder sequence on the right with a shift 117c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 118c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath TMatrixType tm2 = m2.transpose(); 119c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath HouseholderSequence<TMatrixType, HCoeffsVectorType, OnTheRight> rhseq(tm2, hc); 120c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath rhseq.setLength(hc.size()).setShift(shift); 121c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(rhseq * m5, m1); // test applying rhseq directly 122c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m3 = rhseq; 123c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating rhseq to a dense matrix, then applying 124c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 125c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 126c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathvoid test_householder() 127c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 128c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for(int i = 0; i < g_repeat; i++) { 129c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_1( householder(Matrix<double,2,2>()) ); 130c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_2( householder(Matrix<float,2,3>()) ); 131c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_3( householder(Matrix<double,3,5>()) ); 132c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_4( householder(Matrix<float,4,4>()) ); 133c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_5( householder(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 134c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_6( householder(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 135c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_7( householder(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); 136c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_8( householder(Matrix<double,1,1>()) ); 137c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 138c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 139