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
RealScalar	absDeterminant () const
void	analyzePattern (const MatrixType &a)
SimplicialLLT &	compute (const MatrixType &matrix)
Scalar	determinant () const
void	factorize (const MatrixType &a)
RealScalar	logAbsDeterminant () const
const MatrixL	matrixL () const
const MatrixU	matrixU () const
Scalar	signDeterminant () 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 DiagonalScalar &offset, const DiagonalScalar &scale=1)
	SimplicialCholeskyBase ()
Public Member Functions inherited from Eigen::SparseSolverBase< SimplicialLLT< MatrixType_, UpLo_, Ordering_ > >
Solve< SimplicialLLT< MatrixType_, UpLo_, Ordering_ >, Rhs >	solve (const MatrixBase< Rhs > &b) const
Solve< SimplicialLLT< MatrixType_, UpLo_, Ordering_ >, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const
	SparseSolverBase ()=default

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

absDeterminant()

template<typename MatrixType_, int UpLo_, typename Ordering_>

RealScalar Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >::absDeterminant ( ) const

inline

Returns

the absolute value of the determinant of the underlying matrix from the current factorization

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 sparsity 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 have the same sparsity as the matrix on which the symbolic decomposition has been performed.

See also

analyzePattern()

logAbsDeterminant()

template<typename MatrixType_, int UpLo_, typename Ordering_>

RealScalar Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >::logAbsDeterminant ( ) const

inline

Returns

the natural log of the absolute value of the determinant of the underlying matrix from the current factorization.

Unlike determinant(), this stays finite for the large factorizations where a determinant overflows or underflows.

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^*)

signDeterminant()

template<typename MatrixType_, int UpLo_, typename Ordering_>

Scalar Eigen::SimplicialLLT< MatrixType_, UpLo_, Ordering_ >::signDeterminant ( ) const

inline

Returns

the sign of the determinant of the underlying matrix, which is 1 since that matrix is positive definite.

This method is provided for compatibility with the other decompositions, thus enabling generic code.

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

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