qr_colpivoting.cpp

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2009 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 qr()
{
  typedef typename MatrixType::Index Index;

  Index rows = internal::random<Index>(2,200), cols = internal::random<Index>(2,200), cols2 = internal::random<Index>(2,200);
  Index rank = internal::random<Index>(1, std::min(rows, cols)-1);

  typedef typename MatrixType::Scalar Scalar;
  typedef typename MatrixType::RealScalar RealScalar;
  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
  MatrixType m1;
  createRandomPIMatrixOfRank(rank,rows,cols,m1);
  ColPivHouseholderQR<MatrixType> qr(m1);
  VERIFY(rank == qr.rank());
  VERIFY(cols - qr.rank() == qr.dimensionOfKernel());
  VERIFY(!qr.isInjective());
  VERIFY(!qr.isInvertible());
  VERIFY(!qr.isSurjective());

  MatrixQType q = qr.householderQ();
  VERIFY_IS_UNITARY(q);

  MatrixType r = qr.matrixQR().template triangularView<Upper>();
  MatrixType c = q * r * qr.colsPermutation().inverse();
  VERIFY_IS_APPROX(m1, c);

  MatrixType m2 = MatrixType::Random(cols,cols2);
  MatrixType m3 = m1*m2;
  m2 = MatrixType::Random(cols,cols2);
  m2 = qr.solve(m3);
  VERIFY_IS_APPROX(m3, m1*m2);
}

template<typename MatrixType, int Cols2> void qr_fixedsize()
{
  enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
  typedef typename MatrixType::Scalar Scalar;
  int rank = internal::random<int>(1, std::min(int(Rows), int(Cols))-1);
  Matrix<Scalar,Rows,Cols> m1;
  createRandomPIMatrixOfRank(rank,Rows,Cols,m1);
  ColPivHouseholderQR<Matrix<Scalar,Rows,Cols> > qr(m1);
  VERIFY(rank == qr.rank());
  VERIFY(Cols - qr.rank() == qr.dimensionOfKernel());
  VERIFY(qr.isInjective() == (rank == Rows));
  VERIFY(qr.isSurjective() == (rank == Cols));
  VERIFY(qr.isInvertible() == (qr.isInjective() && qr.isSurjective()));

  Matrix<Scalar,Rows,Cols> r = qr.matrixQR().template triangularView<Upper>();
  Matrix<Scalar,Rows,Cols> c = qr.householderQ() * r * qr.colsPermutation().inverse();
  VERIFY_IS_APPROX(m1, c);

  Matrix<Scalar,Cols,Cols2> m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
  Matrix<Scalar,Rows,Cols2> m3 = m1*m2;
  m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);
  m2 = qr.solve(m3);
  VERIFY_IS_APPROX(m3, m1*m2);
}

template<typename MatrixType> void qr_invertible()
{
  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
  typedef typename MatrixType::Scalar Scalar;

  int size = internal::random<int>(10,50);

  MatrixType m1(size, size), m2(size, size), m3(size, size);
  m1 = MatrixType::Random(size,size);

  if (internal::is_same<RealScalar,float>::value)
  {
    // let's build a matrix more stable to inverse
    MatrixType a = MatrixType::Random(size,size*2);
    m1 += a * a.adjoint();
  }

  ColPivHouseholderQR<MatrixType> qr(m1);
  m3 = MatrixType::Random(size,size);
  m2 = qr.solve(m3);
  //VERIFY_IS_APPROX(m3, m1*m2);

  // now construct a matrix with prescribed determinant
  m1.setZero();
  for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
  RealScalar absdet = internal::abs(m1.diagonal().prod());
  m3 = qr.householderQ(); // get a unitary
  m1 = m3 * m1 * m3;
  qr.compute(m1);
  VERIFY_IS_APPROX(absdet, qr.absDeterminant());
  VERIFY_IS_APPROX(internal::log(absdet), qr.logAbsDeterminant());
}

template<typename MatrixType> void qr_verify_assert()
{
  MatrixType tmp;

  ColPivHouseholderQR<MatrixType> qr;
  VERIFY_RAISES_ASSERT(qr.matrixQR())
  VERIFY_RAISES_ASSERT(qr.solve(tmp))
  VERIFY_RAISES_ASSERT(qr.householderQ())
  VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())
  VERIFY_RAISES_ASSERT(qr.isInjective())
  VERIFY_RAISES_ASSERT(qr.isSurjective())
  VERIFY_RAISES_ASSERT(qr.isInvertible())
  VERIFY_RAISES_ASSERT(qr.inverse())
  VERIFY_RAISES_ASSERT(qr.absDeterminant())
  VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
}

void test_qr_colpivoting()
{
  for(int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_1( qr<MatrixXf>() );
    CALL_SUBTEST_2( qr<MatrixXd>() );
    CALL_SUBTEST_3( qr<MatrixXcd>() );
    CALL_SUBTEST_4(( qr_fixedsize<Matrix<float,3,5>, 4 >() ));
    CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,6,2>, 3 >() ));
    CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,1,1>, 1 >() ));
  }

  for(int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
    CALL_SUBTEST_2( qr_invertible<MatrixXd>() );
    CALL_SUBTEST_6( qr_invertible<MatrixXcf>() );
    CALL_SUBTEST_3( qr_invertible<MatrixXcd>() );
  }

  CALL_SUBTEST_7(qr_verify_assert<Matrix3f>());
  CALL_SUBTEST_8(qr_verify_assert<Matrix3d>());
  CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
  CALL_SUBTEST_2(qr_verify_assert<MatrixXd>());
  CALL_SUBTEST_6(qr_verify_assert<MatrixXcf>());
  CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>());

  // Test problem size constructors
  CALL_SUBTEST_9(ColPivHouseholderQR<MatrixXf>(10, 20));
}