A direct sparse Cholesky factorizations. More...

#include <SimplicialCholesky.h>

Inheritance diagram for Eigen::SimplicialCholeskyBase< Derived >:

Classes
struct	keep_diag
	keeps off-diagonal entries; drops diagonal entries More...

Public Types
enum	{ UpLo = internal::traits<Derived>::UpLo }

typedef internal::traits< Derived >::MatrixType	MatrixType

typedef internal::traits< Derived >::OrderingType	OrderingType

typedef MatrixType::Scalar	Scalar

typedef MatrixType::RealScalar	RealScalar

typedef MatrixType::Index	Index

typedef SparseMatrix< Scalar, ColMajor, Index >	CholMatrixType

typedef Matrix< Scalar, Dynamic, 1 >	VectorType

Public Member Functions
	SimplicialCholeskyBase ()
	Default constructor.

	SimplicialCholeskyBase (const MatrixType &matrix)

Derived &	derived ()

const Derived &	derived () const

Index	cols () const

Index	rows () const

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

template<typename Rhs >
const internal::solve_retval< SimplicialCholeskyBase, Rhs >	solve (const MatrixBase< Rhs > &b) const

template<typename Rhs >
const internal::sparse_solve_retval< SimplicialCholeskyBase, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const

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

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

Derived &	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. More...

template<typename Stream >
void	dumpMemory (Stream &s)

template<typename Rhs , typename Dest >
void	_solve (const MatrixBase< Rhs > &b, MatrixBase< Dest > &dest) const

Protected Member Functions
template<bool DoLDLT>
void	compute (const MatrixType &matrix)
	Computes the sparse Cholesky decomposition of matrix.

template<bool DoLDLT>
void	factorize (const MatrixType &a)

template<bool DoLDLT>
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, CholMatrixType &ap)

Protected Attributes
ComputationInfo	m_info

bool	m_isInitialized

bool	m_factorizationIsOk

bool	m_analysisIsOk

CholMatrixType	m_matrix

VectorType	m_diag

VectorXi	m_parent

VectorXi	m_nonZerosPerCol

PermutationMatrix< Dynamic, Dynamic, Index >	m_P

PermutationMatrix< Dynamic, Dynamic, Index >	m_Pinv

RealScalar	m_shiftOffset

RealScalar	m_shiftScale

Detailed Description

template<typename Derived>
class Eigen::SimplicialCholeskyBase< Derived >

A direct sparse Cholesky factorizations.

These classes provide LL^T and LDL^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.

Member Function Documentation

§ info()

template<typename Derived>

ComputationInfo Eigen::SimplicialCholeskyBase< Derived >::info ( ) const

inline

Reports whether previous computation was successful.

Returns: Success if computation was succesful, NumericalIssue if the matrix.appears to be negative.

§ permutationP()

template<typename Derived>

const PermutationMatrix<Dynamic,Dynamic,Index>& Eigen::SimplicialCholeskyBase< Derived >::permutationP ( ) const

inline

Returns: the permutation P

See also: permutationPinv()

§ permutationPinv()

template<typename Derived>

const PermutationMatrix<Dynamic,Dynamic,Index>& Eigen::SimplicialCholeskyBase< Derived >::permutationPinv ( ) const

inline

Returns: the inverse P^-1 of the permutation P

See also: permutationP()

§ setShift()

template<typename Derived>

Derived& Eigen::SimplicialCholeskyBase< Derived >::setShift	(	const RealScalar &	offset,
		const RealScalar &	scale = `1`
	)

inline

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

During the numerical factorization, the diagonal coefficients are transformed by the following linear model:
d_ii = offset + scale * d_ii

The default is the identity transformation with offset=0, and scale=1.

Returns: a reference to *this.

§ solve() [1/2]

template<typename Derived>

template<typename Rhs >

const internal::solve_retval<SimplicialCholeskyBase, Rhs> Eigen::SimplicialCholeskyBase< Derived >::solve ( const MatrixBase< Rhs > & b ) const

inline

Returns: the solution x of \( A x = b \) using the current decomposition of A.

See also: compute()

§ solve() [2/2]

template<typename Derived>

template<typename Rhs >

const internal::sparse_solve_retval<SimplicialCholeskyBase, Rhs> Eigen::SimplicialCholeskyBase< Derived >::solve ( const SparseMatrixBase< Rhs > & b ) const

inline

Returns: the solution x of \( A x = b \) using the current decomposition of A.

See also: compute()

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

vendor/eigen/Eigen/src/SparseCholesky/SimplicialCholesky.h
vendor/eigen/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h

Classes

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

template<typename Derived> class Eigen::SimplicialCholeskyBase< Derived >

Member Function Documentation

§ info()

§ permutationP()

§ permutationPinv()

§ setShift()

§ solve() [1/2]

§ solve() [2/2]

template<typename Derived>
class Eigen::SimplicialCholeskyBase< Derived >