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
template<typename Rhs , typename DestScalar , int DestOptions, typename DestIndex >
void	_solve_sparse (const Rhs &b, SparseMatrix< DestScalar, DestOptions, DestIndex > &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.
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

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 76 of file SimplicialCholesky.h.

Member Typedef Documentation

template<typename Derived>

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

Reimplemented in Eigen::SimplicialCholesky< _MatrixType, _UpLo >, Eigen::SimplicialLDLT< _MatrixType, _UpLo >, and Eigen::SimplicialLLT< _MatrixType, _UpLo >.

Definition at line 84 of file SimplicialCholesky.h.

template<typename Derived>

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

Reimplemented in Eigen::SimplicialCholesky< _MatrixType, _UpLo >, Eigen::SimplicialLDLT< _MatrixType, _UpLo >, and Eigen::SimplicialLLT< _MatrixType, _UpLo >.

Definition at line 83 of file SimplicialCholesky.h.

template<typename Derived>

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

Reimplemented in Eigen::SimplicialCholesky< _MatrixType, _UpLo >, Eigen::SimplicialLDLT< _MatrixType, _UpLo >, and Eigen::SimplicialLLT< _MatrixType, _UpLo >.

Definition at line 79 of file SimplicialCholesky.h.

template<typename Derived>

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

Reimplemented in Eigen::SimplicialCholesky< _MatrixType, _UpLo >, Eigen::SimplicialLDLT< _MatrixType, _UpLo >, and Eigen::SimplicialLLT< _MatrixType, _UpLo >.

Definition at line 82 of file SimplicialCholesky.h.

template<typename Derived>

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

Reimplemented in Eigen::SimplicialCholesky< _MatrixType, _UpLo >, Eigen::SimplicialLDLT< _MatrixType, _UpLo >, and Eigen::SimplicialLLT< _MatrixType, _UpLo >.

Definition at line 81 of file SimplicialCholesky.h.

template<typename Derived>

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

Reimplemented in Eigen::SimplicialCholesky< _MatrixType, _UpLo >, Eigen::SimplicialLDLT< _MatrixType, _UpLo >, and Eigen::SimplicialLLT< _MatrixType, _UpLo >.

Definition at line 85 of file SimplicialCholesky.h.

Member Enumeration Documentation

template<typename Derived>

anonymous enum

Enumerator:

UpLo

Definition at line 80 of file SimplicialCholesky.h.

Constructor & Destructor Documentation

template<typename Derived>

Eigen::SimplicialCholeskyBase< Derived >::SimplicialCholeskyBase ( ) [inline]

Default constructor

Definition at line 90 of file SimplicialCholesky.h.

template<typename Derived>

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

Definition at line 94 of file SimplicialCholesky.h.

template<typename Derived>

Eigen::SimplicialCholeskyBase< Derived >::~SimplicialCholeskyBase ( ) [inline]

Definition at line 100 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]`

Reimplemented in Eigen::SimplicialCholesky< _MatrixType, _UpLo >.

Definition at line 192 of file SimplicialCholesky.h.

template<typename Derived>

template<typename Rhs , typename DestScalar , int DestOptions, typename DestIndex >

void Eigen::SimplicialCholeskyBase< Derived >::_solve_sparse	(	const Rhs &	b,
		SparseMatrix< DestScalar, DestOptions, DestIndex > &	dest
	)		const `[inline]`

Definition at line 220 of file SimplicialCholesky.h.

template<typename Derived>

void Eigen::SimplicialCholeskyBase< Derived >::analyzePattern	(	const MatrixType &	a,
		bool	doLDLT
	)		`[inline, protected]`

Definition at line 268 of file SimplicialCholesky.h.

template<typename Derived >

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

Definition at line 697 of file SimplicialCholesky.h.

template<typename Derived>

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

Definition at line 107 of file SimplicialCholesky.h.

template<typename Derived>

template<bool DoLDLT>

void Eigen::SimplicialCholeskyBase< Derived >::compute ( const MatrixType & matrix ) [inline, protected]

Computes the sparse Cholesky decomposition of matrix

Reimplemented in Eigen::SimplicialCholesky< _MatrixType, _UpLo >, Eigen::SimplicialLDLT< _MatrixType, _UpLo >, and Eigen::SimplicialLLT< _MatrixType, _UpLo >.

Definition at line 245 of file SimplicialCholesky.h.

template<typename Derived>

Derived& Eigen::SimplicialCholeskyBase< Derived >::derived ( ) [inline]

Definition at line 104 of file SimplicialCholesky.h.

template<typename Derived>

const Derived& Eigen::SimplicialCholeskyBase< Derived >::derived ( ) const [inline]

Definition at line 105 of file SimplicialCholesky.h.

template<typename Derived>

template<typename Stream >

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

Definition at line 178 of file SimplicialCholesky.h.

template<typename Derived>

template<bool DoLDLT>

void Eigen::SimplicialCholeskyBase< Derived >::factorize ( const MatrixType & a ) [inline, protected]

Reimplemented in Eigen::SimplicialCholesky< _MatrixType, _UpLo >, Eigen::SimplicialLDLT< _MatrixType, _UpLo >, and Eigen::SimplicialLLT< _MatrixType, _UpLo >.

Definition at line 256 of file SimplicialCholesky.h.

template<typename Derived >

template<bool DoLDLT>

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

Definition at line 747 of file SimplicialCholesky.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 115 of file SimplicialCholesky.h.

template<typename Derived >

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

Definition at line 672 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 151 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 156 of file SimplicialCholesky.h.

template<typename Derived>

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

Definition at line 108 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 168 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 127 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]