eigen/test/cholesky.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/>.

#define EIGEN_NO_ASSERTION_CHECKING
#include "main.h"
#include <Eigen/Cholesky>
#include <Eigen/QR>

#ifdef HAS_GSL
#include "gsl_helper.h"
#endif

template<typename MatrixType> void cholesky(const MatrixType& m)
{
  /* this test covers the following files:
     LLT.h LDLT.h
  */
  int rows = m.rows();
  int cols = m.cols();

  typedef typename MatrixType::Scalar Scalar;
  typedef typename NumTraits<Scalar>::Real RealScalar;
  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;

  MatrixType a0 = MatrixType::Random(rows,cols);
  VectorType vecB = VectorType::Random(rows), vecX(rows);
  MatrixType matB = MatrixType::Random(rows,cols), matX(rows,cols);
  SquareMatrixType symm =  a0 * a0.adjoint();
  // let's make sure the matrix is not singular or near singular
  MatrixType a1 = MatrixType::Random(rows,cols);
  symm += a1 * a1.adjoint();

  // to test if really Cholesky only uses the upper triangular part, uncomment the following
  // FIXME: currently that fails !!
  //symm.template part<StrictlyLowerTriangular>().setZero();

  #ifdef HAS_GSL
  if (ei_is_same_type<RealScalar,double>::ret)
  {
    typedef GslTraits<Scalar> Gsl;
    typename Gsl::Matrix gMatA=0, gSymm=0;
    typename Gsl::Vector gVecB=0, gVecX=0;
    convert<MatrixType>(symm, gSymm);
    convert<MatrixType>(symm, gMatA);
    convert<VectorType>(vecB, gVecB);
    convert<VectorType>(vecB, gVecX);
    Gsl::cholesky(gMatA);
    Gsl::cholesky_solve(gMatA, gVecB, gVecX);
    VectorType vecX(rows), _vecX, _vecB;
    convert(gVecX, _vecX);
    symm.llt().solve(vecB, &vecX);
    Gsl::prod(gSymm, gVecX, gVecB);
    convert(gVecB, _vecB);
    // test gsl itself !
    VERIFY_IS_APPROX(vecB, _vecB);
    VERIFY_IS_APPROX(vecX, _vecX);

    Gsl::free(gMatA);
    Gsl::free(gSymm);
    Gsl::free(gVecB);
    Gsl::free(gVecX);
  }
  #endif

  {
    LLT<SquareMatrixType> chol(symm);
    VERIFY(chol.isPositiveDefinite());
    VERIFY_IS_APPROX(symm, chol.matrixL() * chol.matrixL().adjoint());
    chol.solve(vecB, &vecX);
    VERIFY_IS_APPROX(symm * vecX, vecB);
    chol.solve(matB, &matX);
    VERIFY_IS_APPROX(symm * matX, matB);
  }

  int sign = ei_random<int>()%2 ? 1 : -1;

  if(sign == -1)
  {
    symm = -symm; // test a negative matrix
  }

  {
    LDLT<SquareMatrixType> ldlt(symm);
    VERIFY(ldlt.isInvertible());
    if(sign == 1)
    {
      VERIFY(ldlt.isPositive());
      VERIFY(ldlt.isPositiveDefinite());
    }
    if(sign == -1)
    {
      VERIFY(ldlt.isNegative());
      VERIFY(ldlt.isNegativeDefinite());
    }

    // TODO(keir): This doesn't make sense now that LDLT pivots.
    //VERIFY_IS_APPROX(symm, ldlt.matrixL() * ldlt.vectorD().asDiagonal() * ldlt.matrixL().adjoint());
    ldlt.solve(vecB, &vecX);
    VERIFY_IS_APPROX(symm * vecX, vecB);
    ldlt.solve(matB, &matX);
    VERIFY_IS_APPROX(symm * matX, matB);
  }

  // test isPositiveDefinite on non definite matrix
  if (rows>4)
  {
    SquareMatrixType symm =  a0.block(0,0,rows,cols-4) * a0.block(0,0,rows,cols-4).adjoint();
    LLT<SquareMatrixType> chol(symm);
    VERIFY(!chol.isPositiveDefinite());
    LDLT<SquareMatrixType> cholnosqrt(symm);
    VERIFY(!cholnosqrt.isPositiveDefinite());
  }
}

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 ldlt_rank()
{
  // NOTE there seems to be a problem with too small sizes -- could easily lie in the doSomeRankPreservingOperations function
  int rows = ei_random<int>(50,200);
  int rank = ei_random<int>(40, rows-1);


  // generate a random positive matrix a of given rank
  MatrixType m = MatrixType::Random(rows,rows);
  QR<MatrixType> qr(m);
  typedef typename MatrixType::Scalar Scalar;
  typedef typename NumTraits<Scalar>::Real RealScalar;
  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> DiagVectorType;
  DiagVectorType d(rows);
  d.setZero();
  for(int i = 0; i < rank; i++) d(i)=RealScalar(1);
  MatrixType a = qr.matrixQ() * d.asDiagonal() * qr.matrixQ().adjoint();

  LDLT<MatrixType> ldlt(a);

  VERIFY( ei_abs(ldlt.rank() - rank) <= rank / 20 ); // yes, LDLT::rank is a bit inaccurate...
}


void test_cholesky()
{
  for(int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST( cholesky(Matrix<double,1,1>()) );
    CALL_SUBTEST( cholesky(Matrix2d()) );
    CALL_SUBTEST( cholesky(Matrix3f()) );
    CALL_SUBTEST( cholesky(Matrix4d()) );
    CALL_SUBTEST( cholesky(MatrixXcd(7,7)) );
    CALL_SUBTEST( cholesky(MatrixXd(17,17)) );
    CALL_SUBTEST( cholesky(MatrixXf(200,200)) );
  }
  for(int i = 0; i < g_repeat/3; i++) {
    CALL_SUBTEST( ldlt_rank<MatrixXd>() );
    CALL_SUBTEST( ldlt_rank<MatrixXf>() );
    CALL_SUBTEST( ldlt_rank<MatrixXcd>() );
  }
}