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 Eigen  3.3.9
Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering > Class Template Reference

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 .

class SimplicialLDLT, class AMDOrdering, class NaturalOrdering

Public Member Functions

void analyzePattern (const MatrixType &a)

SimplicialLLTcompute (const MatrixType &matrix)

Scalar determinant () const

void factorize (const MatrixType &a)

const MatrixL matrixL () const

const MatrixU matrixU () const

SimplicialLLT ()

SimplicialLLT (const MatrixType &matrix)

◆ 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

◆ 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.

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.

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^*)

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