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)

EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT

EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT

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

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.

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< Derived >
	SparseSolverBase ()

	~SparseSolverBase ()

Derived &	derived ()

const Derived &	derived () const

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

template<typename Rhs , typename Dest >
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< Derived >
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.

Member Typedef Documentation

◆ Base

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

typedef SparseSolverBase<IncompleteCholesky<Scalar,_UpLo,_OrderingType> > Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::Base

protected

◆ FactorType

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

typedef SparseMatrix<Scalar,ColMajor,StorageIndex> Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::FactorType

◆ OrderingType

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

typedef _OrderingType Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::OrderingType

◆ PermutationType

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

typedef OrderingType::PermutationType Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::PermutationType

◆ RealScalar

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

typedef NumTraits<Scalar>::Real Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::RealScalar

◆ StorageIndex

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

typedef PermutationType::StorageIndex Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::StorageIndex

◆ VectorIx

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

typedef Matrix<StorageIndex,Dynamic, 1> Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::VectorIx

◆ VectorList

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

typedef std::vector<std::list<StorageIndex> > Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::VectorList

◆ VectorRx

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

typedef Matrix<RealScalar,Dynamic,1> Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::VectorRx

◆ VectorSx

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

typedef Matrix<Scalar,Dynamic,1> Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::VectorSx

Member Enumeration Documentation

◆ anonymous enum

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

anonymous enum

Enumerator
UpLo

◆ anonymous enum

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

anonymous enum

Enumerator
ColsAtCompileTime
MaxColsAtCompileTime

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

◆ _solve_impl()

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

template<typename Rhs , typename Dest >

void Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::_solve_impl	(	const Rhs &	b,
		Dest &	x
	)		const

inline

◆ analyzePattern()

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

template<typename MatrixType >

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

inline

Computes the fill reducing permutation vector using the sparsity pattern of mat.

◆ 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() [1/2]

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

template<typename _MatrixType >

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

◆ factorize() [2/2]

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

◆ setInitialShift()

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

void Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::setInitialShift ( RealScalar shift )

inline

Set the initial shift parameter $\sigma$ .

Member Data Documentation

◆ m_analysisIsOk

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

bool Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::m_analysisIsOk

protected

◆ m_factorizationIsOk

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

bool Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::m_factorizationIsOk

protected

◆ m_info

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

ComputationInfo Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::m_info

protected

◆ m_initialShift

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

RealScalar Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::m_initialShift

protected

◆ m_isInitialized

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

bool Eigen::SparseSolverBase< Derived >::m_isInitialized

mutableprotected

◆ m_L

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

FactorType Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::m_L

protected

◆ m_perm

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

PermutationType Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::m_perm

protected

◆ m_scale

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

VectorRx Eigen::IncompleteCholesky< Scalar, _UpLo, _OrderingType >::m_scale

protected

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

core/util/algorithms/eigen-3.4.0/Eigen/src/IterativeLinearSolvers/IncompleteCholesky.h

Public Types

Public Member Functions

Protected Types

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ Base

◆ FactorType

◆ OrderingType

◆ PermutationType

◆ RealScalar

◆ StorageIndex

◆ VectorIx

◆ VectorList

◆ VectorRx

◆ VectorSx

Member Enumeration Documentation

◆ anonymous enum

◆ anonymous enum

Constructor & Destructor Documentation

◆ IncompleteCholesky() [1/2]

◆ IncompleteCholesky() [2/2]

Member Function Documentation

◆ _solve_impl()

◆ analyzePattern()

◆ cols()

◆ compute()

◆ factorize() [1/2]

◆ factorize() [2/2]

◆ info()

◆ matrixL()

◆ permutationP()

◆ rows()

◆ scalingS()

◆ setInitialShift()

Member Data Documentation

◆ m_analysisIsOk

◆ m_factorizationIsOk

◆ m_info

◆ m_initialShift

◆ m_isInitialized

◆ m_L

◆ m_perm

◆ m_scale