Eigen::SimplicialCholeskyBase< Derived > Class Template Reference

A direct sparse Cholesky factorizations. More...

#include <SimplicialCholesky.h>

Inheritance diagram for Eigen::SimplicialCholeskyBase< Derived >:

Classes
struct	keep_diag

Public Types
enum	{ UpLo = internal::traits<Derived>::UpLo }
typedef SparseMatrix< Scalar, ColMajor, Index >	CholMatrixType
typedef MatrixType::Index	Index
typedef internal::traits< Derived >::MatrixType	MatrixType
typedef MatrixType::RealScalar	RealScalar
typedef MatrixType::Scalar	Scalar
typedef Matrix< Scalar, Dynamic, 1 >	VectorType

Public Member Functions
template<typename Rhs , typename Dest >
void	_solve (const MatrixBase< Rhs > &b, MatrixBase< Dest > &dest) const
Index	cols () const
Derived &	derived ()
const Derived &	derived () const
template<typename Stream >
void	dumpMemory (Stream &s)
ComputationInfo	info () const
	Reports whether previous computation was successful. More...
const PermutationMatrix< Dynamic, Dynamic, Index > &	permutationP () const
const PermutationMatrix< Dynamic, Dynamic, Index > &	permutationPinv () const
Index	rows () const
Derived &	setShift (const RealScalar &offset, const RealScalar &scale=1)
	SimplicialCholeskyBase ()
	SimplicialCholeskyBase (const MatrixType &matrix)
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
	~SimplicialCholeskyBase ()

Protected Member Functions
void	analyzePattern (const MatrixType &a, bool doLDLT)
void	analyzePattern_preordered (const CholMatrixType &a, bool doLDLT)
template<bool DoLDLT>
void	compute (const MatrixType &matrix)
template<bool DoLDLT>
void	factorize (const MatrixType &a)
template<bool DoLDLT>
void	factorize_preordered (const CholMatrixType &a)
void	ordering (const MatrixType &a, CholMatrixType &ap)

Protected Attributes
bool	m_analysisIsOk
VectorType	m_diag
bool	m_factorizationIsOk
ComputationInfo	m_info
bool	m_isInitialized
CholMatrixType	m_matrix
VectorXi	m_nonZerosPerCol
PermutationMatrix< Dynamic, Dynamic, Index >	m_P
VectorXi	m_parent
PermutationMatrix< Dynamic, Dynamic, Index >	m_Pinv
RealScalar	m_shiftOffset
RealScalar	m_shiftScale

Additional Inherited Members
Private Member Functions inherited from Eigen::internal::noncopyable
	noncopyable ()
	~noncopyable ()

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.

Definition at line 36 of file SimplicialCholesky.h.

Member Typedef Documentation

template<typename Derived>

typedef SparseMatrix<Scalar,ColMajor,Index> Eigen::SimplicialCholeskyBase< Derived >::CholMatrixType

Definition at line 44 of file SimplicialCholesky.h.

template<typename Derived>

typedef MatrixType::Index Eigen::SimplicialCholeskyBase< Derived >::Index

Definition at line 43 of file SimplicialCholesky.h.

template<typename Derived>

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

Definition at line 39 of file SimplicialCholesky.h.

template<typename Derived>

typedef MatrixType::RealScalar Eigen::SimplicialCholeskyBase< Derived >::RealScalar

Definition at line 42 of file SimplicialCholesky.h.

template<typename Derived>

typedef MatrixType::Scalar Eigen::SimplicialCholeskyBase< Derived >::Scalar

Definition at line 41 of file SimplicialCholesky.h.

template<typename Derived>

typedef Matrix<Scalar,Dynamic,1> Eigen::SimplicialCholeskyBase< Derived >::VectorType

Definition at line 45 of file SimplicialCholesky.h.

Member Enumeration Documentation

template<typename Derived>

anonymous enum

Enumerator
UpLo

Definition at line 40 of file SimplicialCholesky.h.

Constructor & Destructor Documentation

template<typename Derived>

Eigen::SimplicialCholeskyBase< Derived >::SimplicialCholeskyBase ( )

inline

Default constructor

Definition at line 50 of file SimplicialCholesky.h.

template<typename Derived>

Eigen::SimplicialCholeskyBase< Derived >::SimplicialCholeskyBase ( const MatrixType &  matrix )

inline

Definition at line 54 of file SimplicialCholesky.h.

template<typename Derived>

Eigen::SimplicialCholeskyBase< Derived >::~SimplicialCholeskyBase ( )

inline

Definition at line 60 of file SimplicialCholesky.h.

Member Function Documentation

template<typename Derived>

template<typename Rhs , typename Dest >

void Eigen::SimplicialCholeskyBase< Derived >::_solve ( const MatrixBase< Rhs > &  b, MatrixBase< Dest > &  dest  ) const

inline

Definition at line 152 of file SimplicialCholesky.h.

template<typename Derived>

void Eigen::SimplicialCholeskyBase< Derived >::analyzePattern ( const MatrixType &  a, bool  doLDLT  )

inlineprotected

Definition at line 207 of file SimplicialCholesky.h.

template<typename Derived >

void Eigen::SimplicialCholeskyBase< Derived >::analyzePattern_preordered ( const CholMatrixType &  a, bool  doLDLT  )

protected

Definition at line 51 of file SimplicialCholesky_impl.h.

template<typename Derived>

Index Eigen::SimplicialCholeskyBase< Derived >::cols ( void  ) const

inline

Definition at line 67 of file SimplicialCholesky.h.

template<typename Derived>

template<bool DoLDLT>

void Eigen::SimplicialCholeskyBase< Derived >::compute ( const MatrixType &  matrix )

inlineprotected

Computes the sparse Cholesky decomposition of matrix

Definition at line 184 of file SimplicialCholesky.h.

template<typename Derived>

Derived& Eigen::SimplicialCholeskyBase< Derived >::derived ( )

inline

Definition at line 64 of file SimplicialCholesky.h.

template<typename Derived>

const Derived& Eigen::SimplicialCholeskyBase< Derived >::derived ( ) const

inline

Definition at line 65 of file SimplicialCholesky.h.

template<typename Derived>

template<typename Stream >

void Eigen::SimplicialCholeskyBase< Derived >::dumpMemory ( Stream &  s )

inline

Definition at line 138 of file SimplicialCholesky.h.

template<typename Derived>

template<bool DoLDLT>

void Eigen::SimplicialCholeskyBase< Derived >::factorize ( const MatrixType &  a )

inlineprotected

Definition at line 195 of file SimplicialCholesky.h.

template<typename Derived >

template<bool DoLDLT>

void Eigen::SimplicialCholeskyBase< Derived >::factorize_preordered ( const CholMatrixType &  a )

protected

Definition at line 101 of file SimplicialCholesky_impl.h.

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.

Definition at line 75 of file SimplicialCholesky.h.

template<typename Derived >

void Eigen::SimplicialCholeskyBase< Derived >::ordering ( const MatrixType &  a, CholMatrixType &  ap  )

protected

Definition at line 611 of file SimplicialCholesky.h.

template<typename Derived>

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

inline

Returns

the permutation P

See also

permutationPinv()

Definition at line 111 of file SimplicialCholesky.h.

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()

Definition at line 116 of file SimplicialCholesky.h.

template<typename Derived>

Index Eigen::SimplicialCholeskyBase< Derived >::rows ( void  ) const

inline

Definition at line 68 of file SimplicialCholesky.h.

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.

Definition at line 128 of file SimplicialCholesky.h.

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 using the current decomposition of A.

See also

compute()

Definition at line 87 of file SimplicialCholesky.h.

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 using the current decomposition of A.

See also

compute()

Definition at line 101 of file SimplicialCholesky.h.

Member Data Documentation

template<typename Derived>

bool Eigen::SimplicialCholeskyBase< Derived >::m_analysisIsOk

protected

Definition at line 230 of file SimplicialCholesky.h.

template<typename Derived>

VectorType Eigen::SimplicialCholeskyBase< Derived >::m_diag

protected

Definition at line 233 of file SimplicialCholesky.h.

template<typename Derived>

bool Eigen::SimplicialCholeskyBase< Derived >::m_factorizationIsOk

protected

Definition at line 229 of file SimplicialCholesky.h.

template<typename Derived>

ComputationInfo Eigen::SimplicialCholeskyBase< Derived >::m_info

mutableprotected

Definition at line 227 of file SimplicialCholesky.h.

template<typename Derived>

bool Eigen::SimplicialCholeskyBase< Derived >::m_isInitialized

protected

Definition at line 228 of file SimplicialCholesky.h.

template<typename Derived>

CholMatrixType Eigen::SimplicialCholeskyBase< Derived >::m_matrix

protected

Definition at line 232 of file SimplicialCholesky.h.

template<typename Derived>

VectorXi Eigen::SimplicialCholeskyBase< Derived >::m_nonZerosPerCol

protected

Definition at line 235 of file SimplicialCholesky.h.

template<typename Derived>

PermutationMatrix<Dynamic,Dynamic,Index> Eigen::SimplicialCholeskyBase< Derived >::m_P

protected

Definition at line 236 of file SimplicialCholesky.h.

template<typename Derived>

VectorXi Eigen::SimplicialCholeskyBase< Derived >::m_parent

protected

Definition at line 234 of file SimplicialCholesky.h.

template<typename Derived>

PermutationMatrix<Dynamic,Dynamic,Index> Eigen::SimplicialCholeskyBase< Derived >::m_Pinv

protected

Definition at line 237 of file SimplicialCholesky.h.

template<typename Derived>

RealScalar Eigen::SimplicialCholeskyBase< Derived >::m_shiftOffset

protected

Definition at line 239 of file SimplicialCholesky.h.

template<typename Derived>

RealScalar Eigen::SimplicialCholeskyBase< Derived >::m_shiftScale

protected

Definition at line 240 of file SimplicialCholesky.h.

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

• SimplicialCholesky.h
• SimplicialCholesky_impl.h