Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType > Class Template Reference

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 ()
	Default constructor leaving the object in a partly non-initialized stage. More...
template<typename MatrixType >
	IncompleteCholesky (const MatrixType &matrix)
	Constructor computing the incomplete factorization for the given matrix 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)
	Computes or re-computes the incomplete Cholesky factorization of the input matrix mat. More...
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, _UpLo, _OrderingType > >
	SparseSolverBase ()
	Default constructor.
IncompleteCholesky< Scalar, _UpLo, _OrderingType > &	derived ()
const IncompleteCholesky< Scalar, _UpLo, _OrderingType > &	derived () const
const Solve< IncompleteCholesky< Scalar, _UpLo, _OrderingType >, Rhs >	solve (const MatrixBase< Rhs > &b) const
const Solve< IncompleteCholesky< Scalar, _UpLo, _OrderingType >, 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
Protected Attributes inherited from Eigen::SparseSolverBase< IncompleteCholesky< Scalar, _UpLo, _OrderingType > >
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>.

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()

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&)

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

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

• third-party-libs/eigen3/Eigen/src/IterativeLinearSolvers/IncompleteCholesky.h