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

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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 >:

List of all members.

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)

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Constructor & Destructor Documentation

template<typename _MatrixType , int _UpLo, typename _Ordering >

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

(

)

[inline]

Default constructor

template<typename _MatrixType , int _UpLo, typename _Ordering >

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

(

const MatrixType &

matrix

)

[inline, explicit]

Constructs and performs the LLT factorization of matrix

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Member Function Documentation

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()

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

Reimplemented from Eigen::SimplicialCholeskyBase< SimplicialLLT< _MatrixType, _UpLo, _Ordering > >.

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

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()

Reimplemented from Eigen::SimplicialCholeskyBase< SimplicialLLT< _MatrixType, _UpLo, _Ordering > >.

template<typename _MatrixType , int _UpLo, typename _Ordering >

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

(

)

const [inline]

Returns:

an expression of the factor L

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:

• SimplicialCholesky.h