Modified Incomplete Cholesky with dual threshold. More...

#include <IncompleteCholesky.h>

Inheritance diagram for Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >:

Public Types
enum	{ UpLo = _UpLo }

enum	{ ColsAtCompileTime = Dynamic, MaxColsAtCompileTime = Dynamic }

typedef NumTraits< Scalar >::Real	RealScalar

typedef _OrderingType	OrderingType

typedef OrderingType::PermutationType	PermutationType

typedef PermutationType::StorageIndex	StorageIndex

typedef SparseMatrix< Scalar, ColMajor, StorageIndex >	FactorType

typedef Matrix< Scalar, Dynamic, 1 >	VectorSx

typedef Matrix< RealScalar, Dynamic, 1 >	VectorRx

typedef Matrix< StorageIndex, Dynamic, 1 >	VectorIx

typedef std::vector< std::list< StorageIndex > >	VectorList

Public Member Functions
	IncompleteCholesky ()

template<typename MatrixType >
	IncompleteCholesky (const MatrixType &matrix)

Index	rows () const

Index	cols () const

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

void	setInitialShift (RealScalar shift)
	Set the initial shift parameter $\sigma$ .

template<typename MatrixType >
void	analyzePattern (const MatrixType &mat)
	Computes the fill reducing permutation vector using the sparsity pattern of mat.

template<typename MatrixType >
void	factorize (const MatrixType &mat)
	Performs the numerical factorization of the input matrix mat. More...

template<typename MatrixType >
void	compute (const MatrixType &mat)

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

const FactorType &	matrixL () const

const VectorRx &	scalingS () const

const PermutationType &	permutationP () const

template<typename _MatrixType >
void	factorize (const _MatrixType &mat)

Public Member Functions inherited from Eigen::SparseSolverBase< IncompleteCholesky< Scalar, Lower, AMDOrdering< int > > >
	SparseSolverBase ()

IncompleteCholesky< Scalar, Lower, AMDOrdering< int > > &	derived ()

const IncompleteCholesky< Scalar, Lower, AMDOrdering< int > > &	derived () const

const Solve< IncompleteCholesky< Scalar, Lower, AMDOrdering< int > >, Rhs >	solve (const MatrixBase< Rhs > &b) const

const Solve< IncompleteCholesky< Scalar, Lower, AMDOrdering< int > >, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const

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

Protected Types
typedef SparseSolverBase< IncompleteCholesky< Scalar, _UpLo, _OrderingType > >	Base

Protected Attributes
FactorType	m_L

VectorRx	m_scale

RealScalar	m_initialShift

bool	m_analysisIsOk

bool	m_factorizationIsOk

ComputationInfo	m_info

PermutationType	m_perm

bool	m_isInitialized

Protected Attributes inherited from Eigen::SparseSolverBase< IncompleteCholesky< Scalar, Lower, AMDOrdering< int > > >
bool	m_isInitialized

Detailed Description

template<typename Scalar, int _UpLo = Lower, typename _OrderingType = AMDOrdering<int>>
class Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >

Modified Incomplete Cholesky with dual threshold.

References : C-J. Lin and J. J. Moré, Incomplete Cholesky Factorizations with Limited memory, SIAM J. Sci. Comput. 21(1), pp. 24-45, 1999

Template Parameters

Scalar	the scalar type of the input matrices
_UpLo	The triangular part that will be used for the computations. It can be Lower or Upper. Default is Lower.
_OrderingType	The ordering method to use, either AMDOrdering<> or NaturalOrdering<>. Default is AMDOrdering<int>, unless EIGEN_MPL2_ONLY is defined, in which case the default is NaturalOrdering<int>.

\implsparsesolverconcept

It performs the following incomplete factorization: $S P A P' S \approx L L'$ where L is a lower triangular factor, S is a diagonal scaling matrix, and P is a fill-in reducing permutation as computed by the ordering method.

Shifting strategy: Let $ B = S P A P' S $ be the scaled matrix on which the factorization is carried out, and $\beta$ be the minimum value of the diagonal. If $\beta > 0$ then, the factorization is directly performed on the matrix B. Otherwise, the factorization is performed on the shifted matrix $B + (\sigma+|\beta| I$ where $\sigma$ is the initial shift value as returned and set by setInitialShift() method. The default value is $\sigma = 10^{-3}$ . If the factorization fails, then the shift in doubled until it succeed or a maximum of ten attempts. If it still fails, as returned by the info() method, then you can either increase the initial shift, or better use another preconditioning technique.

Constructor & Destructor Documentation

◆ IncompleteCholesky() [1/2]

template<typename Scalar , int _UpLo = Lower, typename _OrderingType = AMDOrdering<int>>

Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::IncompleteCholesky ( )

inline

Default constructor leaving the object in a partly non-initialized stage.

You must call compute() or the pair analyzePattern()/factorize() to make it valid.

See also: IncompleteCholesky(const MatrixType&)

◆ IncompleteCholesky() [2/2]

template<typename Scalar , int _UpLo = Lower, typename _OrderingType = AMDOrdering<int>>

template<typename MatrixType >

Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::IncompleteCholesky ( const MatrixType & matrix )

inline

Constructor computing the incomplete factorization for the given matrix matrix.

Member Function Documentation

◆ cols()

template<typename Scalar , int _UpLo = Lower, typename _OrderingType = AMDOrdering<int>>

Index Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::cols ( void ) const

inline

Returns: number of columns of the factored matrix

◆ compute()

template<typename Scalar , int _UpLo = Lower, typename _OrderingType = AMDOrdering<int>>

template<typename MatrixType >

void Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::compute ( const MatrixType & mat )

inline

Computes or re-computes the incomplete Cholesky factorization of the input matrix mat

It is a shortcut for a sequential call to the analyzePattern() and factorize() methods.

See also: analyzePattern(), factorize()

◆ factorize()

template<typename Scalar , int _UpLo = Lower, typename _OrderingType = AMDOrdering<int>>

template<typename MatrixType >

void Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::factorize ( const MatrixType & mat )

Performs the numerical factorization of the input matrix mat.

The method analyzePattern() or compute() must have been called beforehand with a matrix having the same pattern.

See also: compute(), analyzePattern()

◆ info()

template<typename Scalar , int _UpLo = Lower, typename _OrderingType = AMDOrdering<int>>

ComputationInfo Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::info ( ) const

inline

Reports whether previous computation was successful.

It triggers an assertion if *this has not been initialized through the respective constructor, or a call to compute() or analyzePattern().

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

◆ matrixL()

template<typename Scalar , int _UpLo = Lower, typename _OrderingType = AMDOrdering<int>>

const FactorType& Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::matrixL ( ) const

inline

Returns: the sparse lower triangular factor L

◆ permutationP()

template<typename Scalar , int _UpLo = Lower, typename _OrderingType = AMDOrdering<int>>

const PermutationType& Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::permutationP ( ) const

inline

Returns: the fill-in reducing permutation P (can be empty for a natural ordering)

◆ rows()

template<typename Scalar , int _UpLo = Lower, typename _OrderingType = AMDOrdering<int>>

Index Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::rows ( void ) const

inline

Returns: number of rows of the factored matrix

◆ scalingS()

template<typename Scalar , int _UpLo = Lower, typename _OrderingType = AMDOrdering<int>>

const VectorRx& Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::scalingS ( ) const

inline

Returns: a vector representing the scaling factor S

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

IncompleteCholesky.h

Public Types

Public Member Functions

Protected Types

Protected Attributes

Detailed Description

template<typename Scalar, int _UpLo = Lower, typename _OrderingType = AMDOrdering<int>> class Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >

Constructor & Destructor Documentation

◆ IncompleteCholesky() [1/2]

◆ IncompleteCholesky() [2/2]

Member Function Documentation

◆ cols()

◆ compute()

◆ factorize()

◆ info()

◆ matrixL()

◆ permutationP()

◆ rows()

◆ scalingS()

template<typename Scalar, int _UpLo = Lower, typename _OrderingType = AMDOrdering<int>>
class Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >