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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_SPARSELLT_H
#define EIGEN_SPARSELLT_H
/** \ingroup Sparse_Module
*
* \class SparseLLT
*
* \brief LLT Cholesky decomposition of a sparse matrix and associated features
*
* \param MatrixType the type of the matrix of which we are computing the LLT Cholesky decomposition
*
* \sa class LLT, class LDLT
*/
template<typename MatrixType, int Backend = DefaultBackend>
class SparseLLT
{
protected:
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
typedef SparseMatrix<Scalar,LowerTriangular> CholMatrixType;
enum {
SupernodalFactorIsDirty = 0x10000,
MatrixLIsDirty = 0x20000
};
public:
/** Creates a dummy LLT factorization object with flags \a flags. */
SparseLLT(int flags = 0)
: m_flags(flags), m_status(0)
{
m_precision = RealScalar(0.1) * Eigen::precision<RealScalar>();
}
/** Creates a LLT object and compute the respective factorization of \a matrix using
* flags \a flags. */
SparseLLT(const MatrixType& matrix, int flags = 0)
: m_matrix(matrix.rows(), matrix.cols()), m_flags(flags), m_status(0)
{
m_precision = RealScalar(0.1) * Eigen::precision<RealScalar>();
compute(matrix);
}
/** Sets the relative threshold value used to prune zero coefficients during the decomposition.
*
* Setting a value greater than zero speeds up computation, and yields to an imcomplete
* factorization with fewer non zero coefficients. Such approximate factors are especially
* useful to initialize an iterative solver.
*
* \warning if precision is greater that zero, the LLT factorization is not guaranteed to succeed
* even if the matrix is positive definite.
*
* Note that the exact meaning of this parameter might depends on the actual
* backend. Moreover, not all backends support this feature.
*
* \sa precision() */
void setPrecision(RealScalar v) { m_precision = v; }
/** \returns the current precision.
*
* \sa setPrecision() */
RealScalar precision() const { return m_precision; }
/** Sets the flags. Possible values are:
* - CompleteFactorization
* - IncompleteFactorization
* - MemoryEfficient (hint to use the memory most efficient method offered by the backend)
* - SupernodalMultifrontal (implies a complete factorization if supported by the backend,
* overloads the MemoryEfficient flags)
* - SupernodalLeftLooking (implies a complete factorization if supported by the backend,
* overloads the MemoryEfficient flags)
*
* \sa flags() */
void setFlags(int f) { m_flags = f; }
/** \returns the current flags */
int flags() const { return m_flags; }
/** Computes/re-computes the LLT factorization */
void compute(const MatrixType& matrix);
/** \returns the lower triangular matrix L */
inline const CholMatrixType& matrixL(void) const { return m_matrix; }
template<typename Derived>
bool solveInPlace(MatrixBase<Derived> &b) const;
/** \returns true if the factorization succeeded */
inline bool succeeded(void) const { return m_succeeded; }
protected:
CholMatrixType m_matrix;
RealScalar m_precision;
int m_flags;
mutable int m_status;
bool m_succeeded;
};
/** Computes / recomputes the LLT decomposition of matrix \a a
* using the default algorithm.
*/
template<typename MatrixType, int Backend>
void SparseLLT<MatrixType,Backend>::compute(const MatrixType& a)
{
assert(a.rows()==a.cols());
const int size = a.rows();
m_matrix.resize(size, size);
// allocate a temporary vector for accumulations
AmbiVector<Scalar> tempVector(size);
RealScalar density = a.nonZeros()/RealScalar(size*size);
// TODO estimate the number of non zeros
m_matrix.startFill(a.nonZeros()*2);
for (int j = 0; j < size; ++j)
{
Scalar x = ei_real(a.coeff(j,j));
// TODO better estimate of the density !
tempVector.init(density>0.001? IsDense : IsSparse);
tempVector.setBounds(j+1,size);
tempVector.setZero();
// init with current matrix a
{
typename MatrixType::InnerIterator it(a,j);
++it; // skip diagonal element
for (; it; ++it)
tempVector.coeffRef(it.index()) = it.value();
}
for (int k=0; k<j+1; ++k)
{
typename CholMatrixType::InnerIterator it(m_matrix, k);
while (it && it.index()<j)
++it;
if (it && it.index()==j)
{
Scalar y = it.value();
x -= ei_abs2(y);
++it; // skip j-th element, and process remaining column coefficients
tempVector.restart();
for (; it; ++it)
{
tempVector.coeffRef(it.index()) -= it.value() * y;
}
}
}
// copy the temporary vector to the respective m_matrix.col()
// while scaling the result by 1/real(x)
RealScalar rx = ei_sqrt(ei_real(x));
m_matrix.fill(j,j) = rx;
Scalar y = Scalar(1)/rx;
for (typename AmbiVector<Scalar>::Iterator it(tempVector, m_precision*rx); it; ++it)
{
m_matrix.fill(it.index(), j) = it.value() * y;
}
}
m_matrix.endFill();
}
/** Computes b = L^-T L^-1 b */
template<typename MatrixType, int Backend>
template<typename Derived>
bool SparseLLT<MatrixType, Backend>::solveInPlace(MatrixBase<Derived> &b) const
{
const int size = m_matrix.rows();
ei_assert(size==b.rows());
m_matrix.solveTriangularInPlace(b);
// FIXME should be .adjoint() but it fails to compile...
m_matrix.transpose().solveTriangularInPlace(b);
return true;
}
#endif // EIGEN_SPARSELLT_H
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