eigen/test/qr.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
//
// 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(const MatrixType& m)
{
  /* this test covers the following files: QR.h */
  int rows = m.rows();
  int cols = m.cols();

  typedef typename MatrixType::Scalar Scalar;
  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> SquareMatrixType;
  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;

  MatrixType a = MatrixType::Random(rows,cols);
  QR<MatrixType> qrOfA(a);
  VERIFY_IS_APPROX(a, qrOfA.matrixQ() * qrOfA.matrixR());
  VERIFY_IS_NOT_APPROX(a+MatrixType::Identity(rows, cols), qrOfA.matrixQ() * qrOfA.matrixR());

  SquareMatrixType b = a.adjoint() * a;

  // check tridiagonalization
  Tridiagonalization<SquareMatrixType> tridiag(b);
  VERIFY_IS_APPROX(b, tridiag.matrixQ() * tridiag.matrixT() * tridiag.matrixQ().adjoint());

  // check hessenberg decomposition
  HessenbergDecomposition<SquareMatrixType> hess(b);
  VERIFY_IS_APPROX(b, hess.matrixQ() * hess.matrixH() * hess.matrixQ().adjoint());
  VERIFY_IS_APPROX(tridiag.matrixT(), hess.matrixH());
  b = SquareMatrixType::Random(cols,cols);
  hess.compute(b);
  VERIFY_IS_APPROX(b, hess.matrixQ() * hess.matrixH() * hess.matrixQ().adjoint());
}

template<typename Derived>
void doSomeRankPreservingOperations(Eigen::MatrixBase<Derived>& m)
{
  typedef typename Derived::RealScalar RealScalar;
  for(int a = 0; a < 3*(m.rows()+m.cols()); a++)
  {
    RealScalar d = Eigen::ei_random<RealScalar>(-1,1);
    int i = Eigen::ei_random<int>(0,m.rows()-1); // i is a random row number
    int j;
    do {
      j = Eigen::ei_random<int>(0,m.rows()-1);
    } while (i==j); // j is another one (must be different)
    m.row(i) += d * m.row(j);

    i = Eigen::ei_random<int>(0,m.cols()-1); // i is a random column number
    do {
      j = Eigen::ei_random<int>(0,m.cols()-1);
    } while (i==j); // j is another one (must be different)
    m.col(i) += d * m.col(j);
  }
}

template<typename MatrixType> void qr_non_invertible()
{
  /* this test covers the following files: QR.h */
  // NOTE there seems to be a problem with too small sizes -- could easily lie in the doSomeRankPreservingOperations function
  int rows = ei_random<int>(20,200), cols = ei_random<int>(20,rows), cols2 = ei_random<int>(20,rows);
  int rank = ei_random<int>(1, std::min(rows, cols)-1);

  MatrixType m1(rows, cols), m2(cols, cols2), m3(rows, cols2), k(1,1);
  m1 = MatrixType::Random(rows,cols);
  if(rows <= cols)
    for(int i = rank; i < rows; i++) m1.row(i).setZero();
  else
    for(int i = rank; i < cols; i++) m1.col(i).setZero();
  doSomeRankPreservingOperations(m1);

  QR<MatrixType> lu(m1);
//   typename LU<MatrixType>::KernelResultType m1kernel = lu.kernel();
//   typename LU<MatrixType>::ImageResultType m1image = lu.image();
  std::cerr << rows << "x" << cols << "   " << rank << " " << lu.rank() << "\n";
  if (rank != lu.rank())
    std::cerr << lu.matrixR().diagonal().transpose() << "\n";
  VERIFY(rank == lu.rank());
  VERIFY(cols - lu.rank() == lu.dimensionOfKernel());
  VERIFY(!lu.isInjective());
  VERIFY(!lu.isInvertible());
  VERIFY(lu.isSurjective() == (lu.rank() == rows));
//   VERIFY((m1 * m1kernel).isMuchSmallerThan(m1));
//   VERIFY(m1image.lu().rank() == rank);
//   MatrixType sidebyside(m1.rows(), m1.cols() + m1image.cols());
//   sidebyside << m1, m1image;
//   VERIFY(sidebyside.lu().rank() == rank);
  m2 = MatrixType::Random(cols,cols2);
  m3 = m1*m2;
  m2 = MatrixType::Random(cols,cols2);
  lu.solve(m3, &m2);
  VERIFY_IS_APPROX(m3, m1*m2);
  m3 = MatrixType::Random(rows,cols2);
  VERIFY(!lu.solve(m3, &m2));
}

template<typename MatrixType> void qr_invertible()
{
  /* this test covers the following files: QR.h */
  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
  int size = ei_random<int>(10,200);

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

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

  QR<MatrixType> lu(m1);
  VERIFY(0 == lu.dimensionOfKernel());
  VERIFY(size == lu.rank());
  VERIFY(lu.isInjective());
  VERIFY(lu.isSurjective());
  VERIFY(lu.isInvertible());
//   VERIFY(lu.image().lu().isInvertible());
  m3 = MatrixType::Random(size,size);
  lu.solve(m3, &m2);
  //std::cerr << m3 - m1*m2 << "\n\n";
  VERIFY_IS_APPROX(m3, m1*m2);
//   VERIFY_IS_APPROX(m2, lu.inverse()*m3);
  m3 = MatrixType::Random(size,size);
  VERIFY(lu.solve(m3, &m2));
}

void test_qr()
{
  for(int i = 0; i < 1; i++) {
//     CALL_SUBTEST( qr(Matrix2f()) );
//     CALL_SUBTEST( qr(Matrix4d()) );
//     CALL_SUBTEST( qr(MatrixXf(12,8)) );
//     CALL_SUBTEST( qr(MatrixXcd(5,5)) );
//     CALL_SUBTEST( qr(MatrixXcd(7,3)) );
    CALL_SUBTEST( qr(MatrixXf(47,47)) );
  }

  for(int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST( qr_non_invertible<MatrixXf>() );
    CALL_SUBTEST( qr_non_invertible<MatrixXd>() );
    // TODO fix issue with complex
//     CALL_SUBTEST( qr_non_invertible<MatrixXcf>() );
//     CALL_SUBTEST( qr_non_invertible<MatrixXcd>() );
    CALL_SUBTEST( qr_invertible<MatrixXf>() );
    CALL_SUBTEST( qr_invertible<MatrixXd>() );
    // TODO fix issue with complex
//     CALL_SUBTEST( qr_invertible<MatrixXcf>() );
//     CALL_SUBTEST( qr_invertible<MatrixXcd>() );
  }
}