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

A direct sparse LDLT Cholesky factorizations without square root. More...

#include <SimplicialCholesky.h>

Public Types
enum	{ UpLo = _UpLo }
typedef _MatrixType	MatrixType
typedef SimplicialCholeskyBase< SimplicialLDLT >	Base
typedef MatrixType::Scalar	Scalar
typedef MatrixType::RealScalar	RealScalar
typedef MatrixType::StorageIndex	StorageIndex
typedef SparseMatrix< Scalar, ColMajor, StorageIndex >	CholMatrixType
typedef Matrix< Scalar, Dynamic, 1 >	VectorType
typedef internal::traits< SimplicialLDLT >	Traits
typedef Traits::MatrixL	MatrixL
typedef Traits::MatrixU	MatrixU

Public Member Functions
	SimplicialLDLT ()
	SimplicialLDLT (const MatrixType &matrix)
const VectorType	vectorD () const
const MatrixL	matrixL () const
const MatrixU	matrixU () const
SimplicialLDLT &	compute (const MatrixType &matrix)
void	analyzePattern (const MatrixType &a)
void	factorize (const MatrixType &a)
Scalar	determinant () const

Detailed Description

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

A direct sparse LDLT Cholesky factorizations without square root.

This class provides a LDL^T Cholesky factorizations without square root 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<>

\implsparsesolverconcept

See also

class SimplicialLLT, class AMDOrdering, class NaturalOrdering

Constructor & Destructor Documentation

SimplicialLDLT() [1/2]

template<typename _MatrixType , int _UpLo, typename _Ordering >

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

inline

Default constructor

SimplicialLDLT() [2/2]

template<typename _MatrixType , int _UpLo, typename _Ordering >

Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::SimplicialLDLT ( 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::SimplicialLDLT< _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 >

SimplicialLDLT& Eigen::SimplicialLDLT< _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::SimplicialLDLT< _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::SimplicialLDLT< _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::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::matrixL ( ) const

inline

Returns

an expression of the factor L

matrixU()

template<typename _MatrixType , int _UpLo, typename _Ordering >

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

inline

Returns

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

vectorD()

template<typename _MatrixType , int _UpLo, typename _Ordering >

const VectorType Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >::vectorD ( ) const

inline

Returns

a vector expression of the diagonal D

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

• SimplicialCholesky.h