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dlma/eigen-3.4.0/test/householder.cpp
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householder.cpp
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#include "main.h"
#include <Eigen/QR>
template<typename MatrixType> void householder(const MatrixType& m)
{
static bool even = true;
even = !even;
/* this test covers the following files:
Householder.h
*/
Index rows = m.rows();
Index cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
typedef Matrix<Scalar, internal::decrement_size<MatrixType::RowsAtCompileTime>::ret, 1> EssentialVectorType;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
typedef Matrix<Scalar, Dynamic, MatrixType::ColsAtCompileTime> HBlockMatrixType;
typedef Matrix<Scalar, Dynamic, 1> HCoeffsVectorType;
typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::RowsAtCompileTime> TMatrixType;
Matrix<Scalar, EIGEN_SIZE_MAX(MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime), 1> _tmp((std::max)(rows,cols));
Scalar* tmp = &_tmp.coeffRef(0,0);
Scalar beta;
RealScalar alpha;
EssentialVectorType essential;
VectorType v1 = VectorType::Random(rows), v2;
v2 = v1;
v1.makeHouseholder(essential, beta, alpha);
v1.applyHouseholderOnTheLeft(essential,beta,tmp);
VERIFY_IS_APPROX(v1.norm(), v2.norm());
if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(v1.tail(rows-1).norm(), v1.norm());
v1 = VectorType::Random(rows);
v2 = v1;
v1.applyHouseholderOnTheLeft(essential,beta,tmp);
VERIFY_IS_APPROX(v1.norm(), v2.norm());
// reconstruct householder matrix:
SquareMatrixType id, H1, H2;
id.setIdentity(rows, rows);
H1 = H2 = id;
VectorType vv(rows);
vv << Scalar(1), essential;
H1.applyHouseholderOnTheLeft(essential, beta, tmp);
H2.applyHouseholderOnTheRight(essential, beta, tmp);
VERIFY_IS_APPROX(H1, H2);
VERIFY_IS_APPROX(H1, id - beta * vv*vv.adjoint());
MatrixType m1(rows, cols),
m2(rows, cols);
v1 = VectorType::Random(rows);
if(even) v1.tail(rows-1).setZero();
m1.colwise() = v1;
m2 = m1;
m1.col(0).makeHouseholder(essential, beta, alpha);
m1.applyHouseholderOnTheLeft(essential,beta,tmp);
VERIFY_IS_APPROX(m1.norm(), m2.norm());
if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m1.block(1,0,rows-1,cols).norm(), m1.norm());
VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m1(0,0)), numext::real(m1(0,0)));
VERIFY_IS_APPROX(numext::real(m1(0,0)), alpha);
v1 = VectorType::Random(rows);
if(even) v1.tail(rows-1).setZero();
SquareMatrixType m3(rows,rows), m4(rows,rows);
m3.rowwise() = v1.transpose();
m4 = m3;
m3.row(0).makeHouseholder(essential, beta, alpha);
m3.applyHouseholderOnTheRight(essential.conjugate(),beta,tmp);
VERIFY_IS_APPROX(m3.norm(), m4.norm());
if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m3.block(0,1,rows,rows-1).norm(), m3.norm());
VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m3(0,0)), numext::real(m3(0,0)));
VERIFY_IS_APPROX(numext::real(m3(0,0)), alpha);
// test householder sequence on the left with a shift
Index shift = internal::random<Index>(0, std::max<Index>(rows-2,0));
Index brows = rows - shift;
m1.setRandom(rows, cols);
HBlockMatrixType hbm = m1.block(shift,0,brows,cols);
HouseholderQR<HBlockMatrixType> qr(hbm);
m2 = m1;
m2.block(shift,0,brows,cols) = qr.matrixQR();
HCoeffsVectorType hc = qr.hCoeffs().conjugate();
HouseholderSequence<MatrixType, HCoeffsVectorType> hseq(m2, hc);
hseq.setLength(hc.size()).setShift(shift);
VERIFY(hseq.length() == hc.size());
VERIFY(hseq.shift() == shift);
MatrixType m5 = m2;
m5.block(shift,0,brows,cols).template triangularView<StrictlyLower>().setZero();
VERIFY_IS_APPROX(hseq * m5, m1); // test applying hseq directly
m3 = hseq;
VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating hseq to a dense matrix, then applying
SquareMatrixType hseq_mat = hseq;
SquareMatrixType hseq_mat_conj = hseq.conjugate();
SquareMatrixType hseq_mat_adj = hseq.adjoint();
SquareMatrixType hseq_mat_trans = hseq.transpose();
SquareMatrixType m6 = SquareMatrixType::Random(rows, rows);
VERIFY_IS_APPROX(hseq_mat.adjoint(), hseq_mat_adj);
VERIFY_IS_APPROX(hseq_mat.conjugate(), hseq_mat_conj);
VERIFY_IS_APPROX(hseq_mat.transpose(), hseq_mat_trans);
VERIFY_IS_APPROX(hseq * m6, hseq_mat * m6);
VERIFY_IS_APPROX(hseq.adjoint() * m6, hseq_mat_adj * m6);
VERIFY_IS_APPROX(hseq.conjugate() * m6, hseq_mat_conj * m6);
VERIFY_IS_APPROX(hseq.transpose() * m6, hseq_mat_trans * m6);
VERIFY_IS_APPROX(m6 * hseq, m6 * hseq_mat);
VERIFY_IS_APPROX(m6 * hseq.adjoint(), m6 * hseq_mat_adj);
VERIFY_IS_APPROX(m6 * hseq.conjugate(), m6 * hseq_mat_conj);
VERIFY_IS_APPROX(m6 * hseq.transpose(), m6 * hseq_mat_trans);
// test householder sequence on the right with a shift
TMatrixType tm2 = m2.transpose();
HouseholderSequence<TMatrixType, HCoeffsVectorType, OnTheRight> rhseq(tm2, hc);
rhseq.setLength(hc.size()).setShift(shift);
VERIFY_IS_APPROX(rhseq * m5, m1); // test applying rhseq directly
m3 = rhseq;
VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating rhseq to a dense matrix, then applying
}
EIGEN_DECLARE_TEST(householder)
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( householder(Matrix<double,2,2>()) );
CALL_SUBTEST_2( householder(Matrix<float,2,3>()) );
CALL_SUBTEST_3( householder(Matrix<double,3,5>()) );
CALL_SUBTEST_4( householder(Matrix<float,4,4>()) );
CALL_SUBTEST_5( householder(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_6( householder(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_7( householder(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_8( householder(Matrix<double,1,1>()) );
}
}
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