A direct sparse LLT Cholesky factorizations. More...

#include <SimplicialCholesky.h>

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

Public Types
enum	{ UpLo = _UpLo }

typedef SimplicialCholeskyBase< SimplicialLLT >	Base

typedef SparseMatrix< Scalar, ColMajor, Index >	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< SimplicialLLT >	Traits

typedef Matrix< Scalar, Dynamic, 1 >	VectorType

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

enum

typedef SparseMatrix< Scalar, ColMajor, StorageIndex >	CholMatrixType

typedef CholMatrixType const *	ConstCholMatrixPtr

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

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

typedef MatrixType::RealScalar	RealScalar

typedef MatrixType::Scalar	Scalar

typedef MatrixType::StorageIndex	StorageIndex

typedef Matrix< StorageIndex, Dynamic, 1 >	VectorI

typedef Matrix< Scalar, Dynamic, 1 >	VectorType

Public Member Functions
void	analyzePattern (const MatrixType &a)

SimplicialLLT &	compute (const MatrixType &matrix)

Scalar	determinant () const

void	factorize (const MatrixType &a)

const MatrixL	matrixL () const

const MatrixU	matrixU () const

	SimplicialLLT ()

	SimplicialLLT (const MatrixType &matrix)

Public Member Functions inherited from Eigen::SimplicialCholeskyBase< SimplicialLLT< _MatrixType, _UpLo, _Ordering > >
void	_solve_impl (const MatrixBase< Rhs > &b, MatrixBase< Dest > &dest) const

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

Index	cols () const

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

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

void	dumpMemory (Stream &s)

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

const PermutationMatrix< Dynamic, Dynamic, StorageIndex > &	permutationP () const

const PermutationMatrix< Dynamic, Dynamic, StorageIndex > &	permutationPinv () const

Index	rows () const

SimplicialLLT< _MatrixType, _UpLo, _Ordering > &	setShift (const RealScalar &offset, const RealScalar &scale=1)

	SimplicialCholeskyBase ()

	SimplicialCholeskyBase (const MatrixType &matrix)

	~SimplicialCholeskyBase ()

Public Member Functions inherited from Eigen::SparseSolverBase< SimplicialLLT< _MatrixType, _UpLo, _Ordering > >
void	_solve_impl (const SparseMatrixBase< Rhs > &b, SparseMatrixBase< Dest > &dest) const

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

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

const Solve< SimplicialLLT< _MatrixType, _UpLo, _Ordering >, Rhs >	solve (const MatrixBase< Rhs > &b) const

const Solve< SimplicialLLT< _MatrixType, _UpLo, _Ordering >, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const

	SparseSolverBase ()

	~SparseSolverBase ()

Additional Inherited Members
Protected Member Functions inherited from Eigen::SimplicialCholeskyBase< SimplicialLLT< _MatrixType, _UpLo, _Ordering > >
void	analyzePattern (const MatrixType &a, bool doLDLT)

void	analyzePattern_preordered (const CholMatrixType &a, bool doLDLT)

void	compute (const MatrixType &matrix)

void	factorize (const MatrixType &a)

void	factorize_preordered (const CholMatrixType &a)

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

Protected Attributes inherited from Eigen::SimplicialCholeskyBase< SimplicialLLT< _MatrixType, _UpLo, _Ordering > >
bool	m_analysisIsOk

VectorType	m_diag

bool	m_factorizationIsOk

ComputationInfo	m_info

CholMatrixType	m_matrix

VectorI	m_nonZerosPerCol

PermutationMatrix< Dynamic, Dynamic, StorageIndex >	m_P

VectorI	m_parent

PermutationMatrix< Dynamic, Dynamic, StorageIndex >	m_Pinv

RealScalar	m_shiftOffset

RealScalar	m_shiftScale

Protected Attributes inherited from Eigen::SparseSolverBase< SimplicialLLT< _MatrixType, _UpLo, _Ordering > >
bool	m_isInitialized

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<>

See also: class SimplicialLDLT, class AMDOrdering, class NaturalOrdering

Definition at line 266 of file SimplicialCholesky.h.

Member Typedef Documentation

◆ Base

template<typename _MatrixType, int _UpLo, typename _Ordering>

typedef SimplicialCholeskyBase<SimplicialLLT> Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::Base

Definition at line 335 of file SimplicialCholesky.h.

◆ CholMatrixType

template<typename _MatrixType, int _UpLo, typename _Ordering>

typedef SparseMatrix<Scalar,ColMajor,Index> Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::CholMatrixType

Definition at line 339 of file SimplicialCholesky.h.

◆ MatrixL

template<typename _MatrixType, int _UpLo, typename _Ordering>

typedef Traits::MatrixL Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::MatrixL

Definition at line 342 of file SimplicialCholesky.h.

◆ MatrixType

template<typename _MatrixType, int _UpLo, typename _Ordering>

typedef _MatrixType Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::MatrixType

Definition at line 333 of file SimplicialCholesky.h.

◆ MatrixU

template<typename _MatrixType, int _UpLo, typename _Ordering>

typedef Traits::MatrixU Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::MatrixU

Definition at line 343 of file SimplicialCholesky.h.

◆ RealScalar

template<typename _MatrixType, int _UpLo, typename _Ordering>

typedef MatrixType::RealScalar Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::RealScalar

Definition at line 337 of file SimplicialCholesky.h.

◆ Scalar

template<typename _MatrixType, int _UpLo, typename _Ordering>

typedef MatrixType::Scalar Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::Scalar

Definition at line 336 of file SimplicialCholesky.h.

◆ StorageIndex

template<typename _MatrixType, int _UpLo, typename _Ordering>

typedef MatrixType::StorageIndex Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::StorageIndex

Definition at line 338 of file SimplicialCholesky.h.

◆ Traits

template<typename _MatrixType, int _UpLo, typename _Ordering>

typedef internal::traits<SimplicialLLT> Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::Traits

Definition at line 341 of file SimplicialCholesky.h.

◆ VectorType

template<typename _MatrixType, int _UpLo, typename _Ordering>

typedef Matrix<Scalar,Dynamic,1> Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::VectorType

Definition at line 340 of file SimplicialCholesky.h.

Member Enumeration Documentation

◆ anonymous enum

template<typename _MatrixType, int _UpLo, typename _Ordering>

anonymous enum

Enumerator
UpLo

Definition at line 334 of file SimplicialCholesky.h.

Constructor & Destructor Documentation

◆ SimplicialLLT() [1/2]

template<typename _MatrixType, int _UpLo, typename _Ordering>

Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >::SimplicialLLT ( )

inline

Default constructor

Definition at line 346 of file SimplicialCholesky.h.

◆ 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

Definition at line 348 of file SimplicialCholesky.h.

Member Function Documentation

◆ 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.

See also: factorize()

Definition at line 376 of file SimplicialCholesky.h.

◆ 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

Definition at line 364 of file SimplicialCholesky.h.

◆ 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

Definition at line 393 of file SimplicialCholesky.h.

◆ 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.

See also: analyzePattern()

Definition at line 387 of file SimplicialCholesky.h.

◆ 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

Definition at line 352 of file SimplicialCholesky.h.

◆ 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^*)

Definition at line 358 of file SimplicialCholesky.h.

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

SimplicialCholesky.h

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

template<typename _MatrixType, int _UpLo, typename _Ordering> class Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >

Member Typedef Documentation

◆ Base

◆ CholMatrixType

◆ MatrixL

◆ MatrixType

◆ MatrixU

◆ RealScalar

◆ Scalar

◆ StorageIndex

◆ Traits

◆ VectorType

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ SimplicialLLT() [1/2]

◆ SimplicialLLT() [2/2]

Member Function Documentation

◆ analyzePattern()

◆ compute()

◆ determinant()

◆ factorize()

◆ matrixL()

◆ matrixU()

template<typename _MatrixType, int _UpLo, typename _Ordering>
class Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering >