Eigen::IncompleteCholesky< Scalar, UpLo_, OrderingType_ > Class Template Reference

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>.

This class follows the sparse solver concept .

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.

Inheritance diagram for Eigen::IncompleteCholesky< Scalar, UpLo_, OrderingType_ >:

Public Member Functions
template<typename MatrixType >
void	analyzePattern (const MatrixType &mat)
	Computes the fill reducing permutation vector using the sparsity pattern of mat.
EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT
template<typename MatrixType >
void	compute (const MatrixType &mat)
template<typename MatrixType >
void	factorize (const MatrixType &mat)
	Performs the numerical factorization of the input matrix mat. More...
	IncompleteCholesky ()
template<typename MatrixType >
	IncompleteCholesky (const MatrixType &matrix)
ComputationInfo	info () const
	Reports whether previous computation was successful. More...
const FactorType &	matrixL () const
const PermutationType &	permutationP () const
EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT
const VectorRx &	scalingS () const
void	setInitialShift (RealScalar shift)
	Set the initial shift parameter \( \sigma \).
Public Member Functions inherited from Eigen::SparseSolverBase< IncompleteCholesky< Scalar, Lower, AMDOrdering< int > > >
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
	SparseSolverBase ()

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>>

EIGEN_CONSTEXPR 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>>

EIGEN_CONSTEXPR 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:

• IncompleteCholesky.h