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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>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#include "main.h"
#include <Eigen/QR>
template<typename MatrixType> void householder(const MatrixType& m)
{
typedef typename MatrixType::Index Index;
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::ColsAtCompileTime> RightSquareMatrixType;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, Dynamic> VBlockMatrixType;
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());
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(internal::imag(m1(0,0)), internal::real(m1(0,0)));
VERIFY_IS_APPROX(internal::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,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(internal::imag(m3(0,0)), internal::real(m3(0,0)));
VERIFY_IS_APPROX(internal::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, false, hc.size(), 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
// test householder sequence on the right with a shift
TMatrixType tm2 = m2.transpose();
HouseholderSequence<TMatrixType, HCoeffsVectorType, OnTheRight> rhseq(tm2, hc, false, hc.size(), 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
}
void 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(10,12)) );
CALL_SUBTEST_6( householder(MatrixXcf(16,17)) );
CALL_SUBTEST_7( householder(MatrixXf(25,7)) );
CALL_SUBTEST_8( householder(Matrix<double,1,1>()) );
}
}
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