Eigen::SimplicialLDLT< MatrixType_, UpLo_, Ordering_ > Class Template Reference

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<>

This class follows the sparse solver concept .

See also

class SimplicialLLT, class AMDOrdering, class NaturalOrdering

Inheritance diagram for Eigen::SimplicialLDLT< MatrixType_, UpLo_, Ordering_ >:

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

Additional Inherited Members
Protected Member Functions inherited from Eigen::SimplicialCholeskyBase< SimplicialLDLT< MatrixType_, UpLo_, Ordering_ > >
void	compute (const MatrixType &matrix)

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