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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_SPARSECHOLESKY_H
#define EIGEN_SPARSECHOLESKY_H
enum {
CholFull = 0x0, // full is the default
CholPartial = 0x1,
CholUseEigen = 0x0, // Eigen's impl is the default
CholUseTaucs = 0x2,
CholUseCholmod = 0x4,
};
/** \ingroup Sparse_Module
*
* \class SparseCholesky
*
* \brief Standard Cholesky decomposition of a matrix and associated features
*
* \param MatrixType the type of the matrix of which we are computing the Cholesky decomposition
*
* \sa class Cholesky, class CholeskyWithoutSquareRoot
*/
template<typename MatrixType> class SparseCholesky
{
private:
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
typedef SparseMatrix<Scalar,Lower> CholMatrixType;
enum {
PacketSize = ei_packet_traits<Scalar>::size,
AlignmentMask = int(PacketSize)-1
};
public:
SparseCholesky(const MatrixType& matrix, int flags = 0)
: m_matrix(matrix.rows(), matrix.cols()), m_flags(flags)
{
compute(matrix);
}
inline const CholMatrixType& matrixL(void) const { return m_matrix; }
/** \returns true if the matrix is positive definite */
inline bool isPositiveDefinite(void) const { return m_isPositiveDefinite; }
// TODO impl the solver
// template<typename Derived>
// typename Derived::Eval solve(const MatrixBase<Derived> &b) const;
void compute(const MatrixType& matrix);
protected:
void computeUsingEigen(const MatrixType& matrix);
void computeUsingTaucs(const MatrixType& matrix);
void computeUsingCholmod(const MatrixType& matrix);
protected:
/** \internal
* Used to compute and store L
* The strict upper part is not used and even not initialized.
*/
CholMatrixType m_matrix;
int m_flags;
bool m_isPositiveDefinite;
};
/** Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of \a matrix
*/
template<typename MatrixType>
void SparseCholesky<MatrixType>::compute(const MatrixType& a)
{
if (m_flags&CholUseTaucs)
computeUsingTaucs(a);
else if (m_flags&CholUseCholmod)
computeUsingCholmod(a);
else
computeUsingEigen(a);
}
template<typename MatrixType>
void SparseCholesky<MatrixType>::computeUsingEigen(const MatrixType& a)
{
assert(a.rows()==a.cols());
const int size = a.rows();
m_matrix.resize(size, size);
const RealScalar eps = ei_sqrt(precision<Scalar>());
// allocate a temporary vector for accumulations
AmbiVector<Scalar> tempVector(size);
// TODO estimate the number of nnz
m_matrix.startFill(a.nonZeros()*2);
for (int j = 0; j < size; ++j)
{
// std::cout << j << "\n";
Scalar x = ei_real(a.coeff(j,j));
int endSize = size-j-1;
// TODO estimate the number of non zero entries
// float ratioLhs = float(lhs.nonZeros())/float(lhs.rows()*lhs.cols());
// float avgNnzPerRhsColumn = float(rhs.nonZeros())/float(cols);
// float ratioRes = std::min(ratioLhs * avgNnzPerRhsColumn, 1.f);
// let's do a more accurate determination of the nnz ratio for the current column j of res
//float ratioColRes = std::min(ratioLhs * rhs.innerNonZeros(j), 1.f);
// FIXME find a nice way to get the number of nonzeros of a sub matrix (here an inner vector)
// float ratioColRes = ratioRes;
// if (ratioColRes>0.1)
// tempVector.init(IsSparse);
tempVector.init(IsDense);
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 MatrixType::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 remaing 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); it; ++it)
{
m_matrix.fill(it.index(), j) = it.value() * y;
}
}
m_matrix.endFill();
}
#endif // EIGEN_BASICSPARSECHOLESKY_H
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