Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering > Class Template Reference

#include <Eigen/src/SparseCholesky/SimplicialCholesky.h>

Detailed Description

template<typename _MatrixType, int _UpLo, typename _Ordering>
class Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >

A direct sparse LLT Cholesky factorizations.

This class provides a LL^T Cholesky factorizations of sparse matrices that are selfadjoint and positive definite. The factorization allows for solving A.X = B where X and B can be either dense or sparse.

In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization such that the factorized matrix is P A P^-1.

Template Parameters

_MatrixType	the type of the sparse matrix A, it must be a SparseMatrix<>
_UpLo	the triangular part that will be used for the computations. It can be Lower or Upper. Default is Lower.
_Ordering	The ordering method to use, either AMDOrdering<> or NaturalOrdering<>. Default is AMDOrdering<>

This class follows the sparse solver concept .

See also

class SimplicialLDLT, class AMDOrdering, class NaturalOrdering

Inheritance diagram for Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >:

Public Member Functions
void	analyzePattern (const MatrixType &a)
SimplicialLLT &	compute (const MatrixType &matrix)
Scalar	determinant () const
void	factorize (const MatrixType &a)
const MatrixL	matrixL () const
const MatrixU	matrixU () const
	SimplicialLLT ()
	SimplicialLLT (const MatrixType &matrix)
Public Member Functions inherited from Eigen::SimplicialCholeskyBase< SimplicialLLT< _MatrixType, _UpLo, _Ordering > >
ComputationInfo	info () const
	Reports whether previous computation was successful.
const PermutationMatrix< Dynamic, Dynamic, StorageIndex > &	permutationP () const
const PermutationMatrix< Dynamic, Dynamic, StorageIndex > &	permutationPinv () const
SimplicialLLT< _MatrixType, _UpLo, _Ordering > &	setShift (const RealScalar &offset, const RealScalar &scale=1)
	SimplicialCholeskyBase ()
Public Member Functions inherited from Eigen::SparseSolverBase< SimplicialLLT< _MatrixType, _UpLo, _Ordering > >
const Solve< SimplicialLLT< _MatrixType, _UpLo, _Ordering >, Rhs >	solve (const MatrixBase< Rhs > &b) const
const Solve< SimplicialLLT< _MatrixType, _UpLo, _Ordering >, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const
	SparseSolverBase ()

Additional Inherited Members
Protected Member Functions inherited from Eigen::SimplicialCholeskyBase< SimplicialLLT< _MatrixType, _UpLo, _Ordering > >
void	compute (const MatrixType &matrix)

Constructor & Destructor Documentation

SimplicialLLT() [1/2]

template<typename _MatrixType, int _UpLo, typename _Ordering>

Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::SimplicialLLT ( )

inline

Default constructor

SimplicialLLT() [2/2]

template<typename _MatrixType, int _UpLo, typename _Ordering>

Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::SimplicialLLT ( const MatrixType & matrix )

inlineexplicit

Constructs and performs the LLT factorization of matrix

Member Function Documentation

analyzePattern()

template<typename _MatrixType, int _UpLo, typename _Ordering>

void Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::analyzePattern ( const MatrixType & a )

inline

Performs a symbolic decomposition on the sparcity of matrix.

This function is particularly useful when solving for several problems having the same structure.

See also

factorize()

compute()

template<typename _MatrixType, int _UpLo, typename _Ordering>

SimplicialLLT & Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::compute ( const MatrixType & matrix )

inline

Computes the sparse Cholesky decomposition of matrix

determinant()

template<typename _MatrixType, int _UpLo, typename _Ordering>

Scalar Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::determinant ( ) const

inline

Returns

the determinant of the underlying matrix from the current factorization

factorize()

template<typename _MatrixType, int _UpLo, typename _Ordering>

void Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::factorize ( const MatrixType & a )

inline

Performs a numeric decomposition of matrix

The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.

See also

analyzePattern()

matrixL()

template<typename _MatrixType, int _UpLo, typename _Ordering>

const MatrixL Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::matrixL ( ) const

inline

Returns

an expression of the factor L

matrixU()

template<typename _MatrixType, int _UpLo, typename _Ordering>

const MatrixU Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::matrixU ( ) const

inline

Returns

an expression of the factor U (= L^*)

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The documentation for this class was generated from the following file:

• /builds/libeigen/eigen/Eigen/src/SparseCholesky/SimplicialCholesky.h