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

#include <SimplicialCholesky.h>

Inheritance diagram for Eigen::SimplicialLDLT< _MatrixType, _UpLo, _Ordering >:

Public Types
enum	{ UpLo = _UpLo }

typedef _MatrixType	MatrixType

typedef SimplicialCholeskyBase< SimplicialLDLT >	Base

typedef MatrixType::Scalar	Scalar

typedef MatrixType::RealScalar	RealScalar

typedef MatrixType::StorageIndex	StorageIndex

typedef SparseMatrix< Scalar, ColMajor, StorageIndex >	CholMatrixType

typedef Matrix< Scalar, Dynamic, 1 >	VectorType

typedef internal::traits< SimplicialLDLT >	Traits

typedef Traits::MatrixL	MatrixL

typedef Traits::MatrixU	MatrixU

Public Types inherited from Eigen::SimplicialCholeskyBase< SimplicialLDLT< _MatrixType, _UpLo, _Ordering > >
enum

enum

typedef internal::traits< SimplicialLDLT< _MatrixType, _UpLo, _Ordering > >::MatrixType	MatrixType

typedef internal::traits< SimplicialLDLT< _MatrixType, _UpLo, _Ordering > >::OrderingType	OrderingType

typedef MatrixType::Scalar	Scalar

typedef MatrixType::RealScalar	RealScalar

typedef MatrixType::StorageIndex	StorageIndex

typedef SparseMatrix< Scalar, ColMajor, StorageIndex >	CholMatrixType

typedef CholMatrixType const *	ConstCholMatrixPtr

typedef Matrix< Scalar, Dynamic, 1 >	VectorType

typedef Matrix< StorageIndex, Dynamic, 1 >	VectorI

Public Member Functions
	SimplicialLDLT ()
	Default constructor.

	SimplicialLDLT (const MatrixType &matrix)
	Constructs and performs the LLT factorization of matrix.

const VectorType	vectorD () const

const MatrixL	matrixL () const

const MatrixU	matrixU () const

SimplicialLDLT &	compute (const MatrixType &matrix)
	Computes the sparse Cholesky decomposition of matrix.

void	analyzePattern (const MatrixType &a)
	Performs a symbolic decomposition on the sparcity of matrix.

void	factorize (const MatrixType &a)
	Performs a numeric decomposition of matrix.

Scalar	determinant () const

Public Member Functions inherited from Eigen::SimplicialCholeskyBase< SimplicialLDLT< _MatrixType, _UpLo, _Ordering > >
	SimplicialCholeskyBase ()
	Default constructor.

	SimplicialCholeskyBase (const MatrixType &matrix)

SimplicialLDLT< _MatrixType, _UpLo, _Ordering > &	derived ()

const SimplicialLDLT< _MatrixType, _UpLo, _Ordering > &	derived () const

SimplicialLDLT< _MatrixType, _UpLo, _Ordering > &	derived ()

const SimplicialLDLT< _MatrixType, _UpLo, _Ordering > &	derived () const

Index	cols () const

Index	rows () const

ComputationInfo	info () const
	Reports whether previous computation was successful.

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)
	Sets the shift parameters that will be used to adjust the diagonal coefficients during the numerical factorization.

void	dumpMemory (Stream &s)

void	_solve_impl (const MatrixBase< Rhs > &b, MatrixBase< Dest > &dest) const

void	_solve_impl (const SparseMatrixBase< Rhs > &b, SparseMatrixBase< Dest > &dest) const

Public Member Functions inherited from Eigen::SparseSolverBase< Derived >
	SparseSolverBase ()
	Default constructor.

Derived &	derived ()

const Derived &	derived () const

template<typename Rhs >
const Solve< Derived, Rhs >	solve (const MatrixBase< Rhs > &b) const

template<typename Rhs >
const Solve< Derived, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const

template<typename Rhs , typename Dest >
void	_solve_impl (const SparseMatrixBase< Rhs > &b, SparseMatrixBase< Dest > &dest) const

Additional Inherited Members
Protected Member Functions inherited from Eigen::SimplicialCholeskyBase< SimplicialLDLT< _MatrixType, _UpLo, _Ordering > >
void	compute (const MatrixType &matrix)
	Computes the sparse Cholesky decomposition of matrix.

void	factorize (const MatrixType &a)

void	factorize_preordered (const CholMatrixType &a)

void	analyzePattern (const MatrixType &a, bool doLDLT)

void	analyzePattern_preordered (const CholMatrixType &a, bool doLDLT)

void	ordering (const MatrixType &a, ConstCholMatrixPtr &pmat, CholMatrixType &ap)

Protected Attributes inherited from Eigen::SimplicialCholeskyBase< SimplicialLDLT< _MatrixType, _UpLo, _Ordering > >
ComputationInfo	m_info

bool	m_factorizationIsOk

bool	m_analysisIsOk

CholMatrixType	m_matrix

VectorType	m_diag

VectorI	m_parent

VectorI	m_nonZerosPerCol

PermutationMatrix< Dynamic, Dynamic, StorageIndex >	m_P

PermutationMatrix< Dynamic, Dynamic, StorageIndex >	m_Pinv

RealScalar	m_shiftOffset

RealScalar	m_shiftScale

Protected Attributes inherited from Eigen::SparseSolverBase< Derived >
bool	m_isInitialized

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<>

\implsparsesolverconcept

See also: class SimplicialLLT, class AMDOrdering, class NaturalOrdering

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()

◆ 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

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

External/Eigen/src/SparseCholesky/SimplicialCholesky.h

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ analyzePattern()

◆ determinant()

◆ factorize()

◆ matrixL()

◆ matrixU()

◆ vectorD()