149 lines
6.1 KiB
C++
149 lines
6.1 KiB
C++
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include "main.h"
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#include <Eigen/QR>
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template<typename MatrixType> void householder(const MatrixType& m)
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{
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static bool even = true;
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even = !even;
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/* this test covers the following files:
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Householder.h
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*/
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Index rows = m.rows();
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Index cols = m.cols();
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typedef typename MatrixType::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
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typedef Matrix<Scalar, internal::decrement_size<MatrixType::RowsAtCompileTime>::ret, 1> EssentialVectorType;
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typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
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typedef Matrix<Scalar, Dynamic, MatrixType::ColsAtCompileTime> HBlockMatrixType;
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typedef Matrix<Scalar, Dynamic, 1> HCoeffsVectorType;
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typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::RowsAtCompileTime> TMatrixType;
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Matrix<Scalar, EIGEN_SIZE_MAX(MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime), 1> _tmp((std::max)(rows,cols));
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Scalar* tmp = &_tmp.coeffRef(0,0);
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Scalar beta;
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RealScalar alpha;
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EssentialVectorType essential;
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VectorType v1 = VectorType::Random(rows), v2;
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v2 = v1;
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v1.makeHouseholder(essential, beta, alpha);
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v1.applyHouseholderOnTheLeft(essential,beta,tmp);
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VERIFY_IS_APPROX(v1.norm(), v2.norm());
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if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(v1.tail(rows-1).norm(), v1.norm());
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v1 = VectorType::Random(rows);
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v2 = v1;
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v1.applyHouseholderOnTheLeft(essential,beta,tmp);
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VERIFY_IS_APPROX(v1.norm(), v2.norm());
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// reconstruct householder matrix:
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SquareMatrixType id, H1, H2;
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id.setIdentity(rows, rows);
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H1 = H2 = id;
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VectorType vv(rows);
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vv << Scalar(1), essential;
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H1.applyHouseholderOnTheLeft(essential, beta, tmp);
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H2.applyHouseholderOnTheRight(essential, beta, tmp);
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VERIFY_IS_APPROX(H1, H2);
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VERIFY_IS_APPROX(H1, id - beta * vv*vv.adjoint());
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MatrixType m1(rows, cols),
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m2(rows, cols);
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v1 = VectorType::Random(rows);
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if(even) v1.tail(rows-1).setZero();
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m1.colwise() = v1;
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m2 = m1;
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m1.col(0).makeHouseholder(essential, beta, alpha);
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m1.applyHouseholderOnTheLeft(essential,beta,tmp);
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VERIFY_IS_APPROX(m1.norm(), m2.norm());
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if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m1.block(1,0,rows-1,cols).norm(), m1.norm());
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VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m1(0,0)), numext::real(m1(0,0)));
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VERIFY_IS_APPROX(numext::real(m1(0,0)), alpha);
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v1 = VectorType::Random(rows);
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if(even) v1.tail(rows-1).setZero();
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SquareMatrixType m3(rows,rows), m4(rows,rows);
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m3.rowwise() = v1.transpose();
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m4 = m3;
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m3.row(0).makeHouseholder(essential, beta, alpha);
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m3.applyHouseholderOnTheRight(essential.conjugate(),beta,tmp);
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VERIFY_IS_APPROX(m3.norm(), m4.norm());
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if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m3.block(0,1,rows,rows-1).norm(), m3.norm());
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VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m3(0,0)), numext::real(m3(0,0)));
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VERIFY_IS_APPROX(numext::real(m3(0,0)), alpha);
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// test householder sequence on the left with a shift
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Index shift = internal::random<Index>(0, std::max<Index>(rows-2,0));
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Index brows = rows - shift;
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m1.setRandom(rows, cols);
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HBlockMatrixType hbm = m1.block(shift,0,brows,cols);
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HouseholderQR<HBlockMatrixType> qr(hbm);
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m2 = m1;
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m2.block(shift,0,brows,cols) = qr.matrixQR();
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HCoeffsVectorType hc = qr.hCoeffs().conjugate();
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HouseholderSequence<MatrixType, HCoeffsVectorType> hseq(m2, hc);
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hseq.setLength(hc.size()).setShift(shift);
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VERIFY(hseq.length() == hc.size());
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VERIFY(hseq.shift() == shift);
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MatrixType m5 = m2;
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m5.block(shift,0,brows,cols).template triangularView<StrictlyLower>().setZero();
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VERIFY_IS_APPROX(hseq * m5, m1); // test applying hseq directly
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m3 = hseq;
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VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating hseq to a dense matrix, then applying
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SquareMatrixType hseq_mat = hseq;
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SquareMatrixType hseq_mat_conj = hseq.conjugate();
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SquareMatrixType hseq_mat_adj = hseq.adjoint();
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SquareMatrixType hseq_mat_trans = hseq.transpose();
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SquareMatrixType m6 = SquareMatrixType::Random(rows, rows);
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VERIFY_IS_APPROX(hseq_mat.adjoint(), hseq_mat_adj);
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VERIFY_IS_APPROX(hseq_mat.conjugate(), hseq_mat_conj);
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VERIFY_IS_APPROX(hseq_mat.transpose(), hseq_mat_trans);
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VERIFY_IS_APPROX(hseq * m6, hseq_mat * m6);
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VERIFY_IS_APPROX(hseq.adjoint() * m6, hseq_mat_adj * m6);
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VERIFY_IS_APPROX(hseq.conjugate() * m6, hseq_mat_conj * m6);
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VERIFY_IS_APPROX(hseq.transpose() * m6, hseq_mat_trans * m6);
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VERIFY_IS_APPROX(m6 * hseq, m6 * hseq_mat);
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VERIFY_IS_APPROX(m6 * hseq.adjoint(), m6 * hseq_mat_adj);
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VERIFY_IS_APPROX(m6 * hseq.conjugate(), m6 * hseq_mat_conj);
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VERIFY_IS_APPROX(m6 * hseq.transpose(), m6 * hseq_mat_trans);
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// test householder sequence on the right with a shift
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TMatrixType tm2 = m2.transpose();
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HouseholderSequence<TMatrixType, HCoeffsVectorType, OnTheRight> rhseq(tm2, hc);
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rhseq.setLength(hc.size()).setShift(shift);
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VERIFY_IS_APPROX(rhseq * m5, m1); // test applying rhseq directly
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m3 = rhseq;
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VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating rhseq to a dense matrix, then applying
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}
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EIGEN_DECLARE_TEST(householder)
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{
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for(int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST_1( householder(Matrix<double,2,2>()) );
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CALL_SUBTEST_2( householder(Matrix<float,2,3>()) );
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CALL_SUBTEST_3( householder(Matrix<double,3,5>()) );
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CALL_SUBTEST_4( householder(Matrix<float,4,4>()) );
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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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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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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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CALL_SUBTEST_8( householder(Matrix<double,1,1>()) );
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}
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}
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