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>
//
// 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);
  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

  // 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
}

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>()) );
  }
}