Eigen  3.4.90 (git rev 9589cc4e7fd8e4538bedef80dd36c7738977a8be)
 
Loading...
Searching...
No Matches
Public Member Functions | List of all members
Eigen::IncompleteCholesky< Scalar, UpLo_, OrderingType_ > Class Template Reference

#include <Eigen/src/IterativeLinearSolvers/IncompleteCholesky.h>

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
Scalarthe 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>.

This class follows the sparse solver concept .

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

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, and $ \sigma = 0 $. Otherwise, the factorization is performed on the shifted matrix $ B + \sigma I $ for a shifting factor $ \sigma $. We start with $ \sigma = \sigma_0 - \beta $, where $ \sigma_0 $ is the initial shift value as returned and set by setInitialShift() method. The default value is $\sigma_0 = 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.
 
 IncompleteCholesky ()
 
template<typename MatrixType>
 IncompleteCholesky (const MatrixType &matrix)
 
ComputationInfo info () const
 Reports whether previous computation was successful.
 
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 $.
 
RealScalar shift () const
 
- Public Member Functions inherited from Eigen::SparseSolverBase< Derived >
template<typename Rhs>
const Solve< Derived, Rhs > solve (const MatrixBase< Rhs > &b) const
 
template<typename Rhs>
const Solve< Derived, 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 ( ) 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 ( ) 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

◆ shift()

template<typename Scalar, int UpLo_ = Lower, typename OrderingType_ = AMDOrdering<int>>
RealScalar Eigen::IncompleteCholesky< Scalar, UpLo_, OrderingType_ >::shift ( ) const
inline
Returns
the final shift parameter from the computation
The documentation for this class was generated from the following file: