Eigen::SimplicialLDLT Class Reference

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

#include <SimplicialCholesky.h>

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

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

Detailed Description

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

Definition at line 275 of file SimplicialCholesky.h.

Member Typedef Documentation

Base

typedef SimplicialCholeskyBase<SimplicialLDLT> Eigen::SimplicialLDLT::Base

Definition at line 434 of file SimplicialCholesky.h.

CholMatrixType

typedef SparseMatrix<Scalar,ColMajor,StorageIndex> Eigen::SimplicialLDLT::CholMatrixType

Definition at line 438 of file SimplicialCholesky.h.

MatrixL

typedef Traits::MatrixL Eigen::SimplicialLDLT::MatrixL

Definition at line 441 of file SimplicialCholesky.h.

MatrixType

typedef _MatrixType Eigen::SimplicialLDLT::MatrixType

Definition at line 432 of file SimplicialCholesky.h.

MatrixU

typedef Traits::MatrixU Eigen::SimplicialLDLT::MatrixU

Definition at line 442 of file SimplicialCholesky.h.

RealScalar

typedef MatrixType::RealScalar Eigen::SimplicialLDLT::RealScalar

Definition at line 436 of file SimplicialCholesky.h.

Scalar

typedef MatrixType::Scalar Eigen::SimplicialLDLT::Scalar

Definition at line 435 of file SimplicialCholesky.h.

StorageIndex

typedef MatrixType::StorageIndex Eigen::SimplicialLDLT::StorageIndex

Definition at line 437 of file SimplicialCholesky.h.

Traits

typedef internal::traits<SimplicialLDLT> Eigen::SimplicialLDLT::Traits

Definition at line 440 of file SimplicialCholesky.h.

VectorType

typedef Matrix<Scalar,Dynamic,1> Eigen::SimplicialLDLT::VectorType

Definition at line 439 of file SimplicialCholesky.h.

Member Enumeration Documentation

anonymous enum

anonymous enum

Enumerator
UpLo

Definition at line 433 of file SimplicialCholesky.h.

Constructor & Destructor Documentation

SimplicialLDLT() [1/2]

Eigen::SimplicialLDLT::SimplicialLDLT ( )

inline

Default constructor

Definition at line 445 of file SimplicialCholesky.h.

SimplicialLDLT() [2/2]

Eigen::SimplicialLDLT::SimplicialLDLT ( const MatrixType &  matrix )

inlineexplicit

Constructs and performs the LLT factorization of matrix

Definition at line 448 of file SimplicialCholesky.h.

Member Function Documentation

analyzePattern()

void Eigen::SimplicialLDLT::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()

Definition at line 481 of file SimplicialCholesky.h.

compute()

SimplicialLDLT& Eigen::SimplicialLDLT::compute ( const MatrixType &  matrix )

inline

Computes the sparse Cholesky decomposition of matrix

Definition at line 469 of file SimplicialCholesky.h.

determinant()

Scalar Eigen::SimplicialLDLT::determinant ( ) const

inline

Returns

the determinant of the underlying matrix from the current factorization

Definition at line 498 of file SimplicialCholesky.h.

factorize()

void Eigen::SimplicialLDLT::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()

Definition at line 492 of file SimplicialCholesky.h.

matrixL()

const MatrixL Eigen::SimplicialLDLT::matrixL ( ) const

inline

Returns

an expression of the factor L

Definition at line 457 of file SimplicialCholesky.h.

matrixU()

const MatrixU Eigen::SimplicialLDLT::matrixU ( ) const

inline

Returns

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

Definition at line 463 of file SimplicialCholesky.h.

vectorD()

const VectorType Eigen::SimplicialLDLT::vectorD ( ) const

inline

Returns

a vector expression of the diagonal D

Definition at line 452 of file SimplicialCholesky.h.

---

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

• SimplicialCholesky.h