LDLT.h

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// 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/>.

#ifndef EIGEN_LDLT_H
#define EIGEN_LDLT_H

template<typename MatrixType> class LDLT
{
  public:

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

    LDLT(const MatrixType& matrix)
      : m_matrix(matrix.rows(), matrix.cols())
    {
      compute(matrix);
    }

    inline Part<MatrixType, UnitLowerTriangular> matrixL(void) const { return m_matrix; }

    inline DiagonalCoeffs<MatrixType> vectorD(void) const { return m_matrix.diagonal(); }

    inline bool isPositiveDefinite(void) const { return m_isPositiveDefinite; }

    template<typename RhsDerived, typename ResultType>
    bool solve(const MatrixBase<RhsDerived> &b, ResultType *result) const;

    template<typename Derived>
    bool solveInPlace(MatrixBase<Derived> &bAndX) const;

    void compute(const MatrixType& matrix);

  protected:
    MatrixType m_matrix;

    bool m_isPositiveDefinite;
};

template<typename MatrixType>
void LDLT<MatrixType>::compute(const MatrixType& a)
{
  assert(a.rows()==a.cols());
  const int size = a.rows();
  m_matrix.resize(size, size);
  m_isPositiveDefinite = true; // always true. This decomposition is not rank-revealing anyway.

  if (size<=1)
  {
    m_matrix = a;
    return;
  }

  // Let's preallocate a temporay vector to evaluate the matrix-vector product into it.
  // Unlike the standard LLT decomposition, here we cannot evaluate it to the destination
  // matrix because it a sub-row which is not compatible suitable for efficient packet evaluation.
  // (at least if we assume the matrix is col-major)
  Matrix<Scalar,MatrixType::RowsAtCompileTime,1> _temporary(size);

  // Note that, in this algorithm the rows of the strict upper part of m_matrix is used to store
  // column vector, thus the strange .conjugate() and .transpose()...

  m_matrix.row(0) = a.row(0).conjugate();
  m_matrix.col(0).end(size-1) = m_matrix.row(0).end(size-1) / m_matrix.coeff(0,0);
  for (int j = 1; j < size; ++j)
  {
    RealScalar tmp = ei_real(a.coeff(j,j) - (m_matrix.row(j).start(j) * m_matrix.col(j).start(j).conjugate()).coeff(0,0));
    m_matrix.coeffRef(j,j) = tmp;

    int endSize = size-j-1;
    if (endSize>0)
    {
      _temporary.end(endSize) = ( m_matrix.block(j+1,0, endSize, j)
                                  * m_matrix.col(j).start(j).conjugate() ).lazy();

      m_matrix.row(j).end(endSize) = a.row(j).end(endSize).conjugate()
                                   - _temporary.end(endSize).transpose();

      if(tmp != RealScalar(0))
        m_matrix.col(j).end(endSize) = m_matrix.row(j).end(endSize) / tmp;
    }
  }
}

template<typename MatrixType>
template<typename RhsDerived, typename ResultType>
bool LDLT<MatrixType>
::solve(const MatrixBase<RhsDerived> &b, ResultType *result) const
{
  const int size = m_matrix.rows();
  ei_assert(size==b.rows() && "LLT::solve(): invalid number of rows of the right hand side matrix b");
  *result = b;
  return solveInPlace(*result);
}

template<typename MatrixType>
template<typename Derived>
bool LDLT<MatrixType>::solveInPlace(MatrixBase<Derived> &bAndX) const
{
  const int size = m_matrix.rows();
  ei_assert(size==bAndX.rows());
  if (!m_isPositiveDefinite)
    return false;
  matrixL().solveTriangularInPlace(bAndX);
  bAndX = (m_matrix.cwise().inverse().template part<Diagonal>() * bAndX).lazy();
  m_matrix.adjoint().template part<UnitUpperTriangular>().solveTriangularInPlace(bAndX);
  return true;
}

template<typename Derived>
inline const LDLT<typename MatrixBase<Derived>::PlainMatrixType>
MatrixBase<Derived>::ldlt() const
{
  return LDLT<PlainMatrixType>(derived());
}

#endif // EIGEN_LDLT_H

---

vcglib
Author(s): Christian Bersch
autogenerated on Fri Jan 11 09:17:26 2013