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 SparseMatrix< Scalar, ColMajor, StorageIndex >	FactorType

typedef _OrderingType	OrderingType

typedef OrderingType::PermutationType	PermutationType

typedef NumTraits< Scalar >::Real	RealScalar

typedef PermutationType::StorageIndex	StorageIndex

typedef Matrix< StorageIndex, Dynamic, 1 >	VectorIx

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

typedef Matrix< RealScalar, Dynamic, 1 >	VectorRx

typedef Matrix< Scalar, Dynamic, 1 >	VectorSx

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

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

Index	cols () const

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...

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

	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

Index	rows () const

const VectorRx &	scalingS () const

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

Public Member Functions inherited from Eigen::SparseSolverBase< IncompleteCholesky< Scalar, _UpLo, _OrderingType > >
void	_solve_impl (const SparseMatrixBase< Rhs > &b, SparseMatrixBase< Dest > &dest) const

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

	SparseSolverBase ()

	~SparseSolverBase ()

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

Protected Attributes
bool	m_analysisIsOk

bool	m_factorizationIsOk

ComputationInfo	m_info

RealScalar	m_initialShift

FactorType	m_L

PermutationType	m_perm

VectorRx	m_scale

Protected Attributes inherited from Eigen::SparseSolverBase< IncompleteCholesky< Scalar, _UpLo, _OrderingType > >
bool	m_isInitialized

Private Member Functions
void	updateList (Ref< const VectorIx > colPtr, Ref< VectorIx > rowIdx, Ref< VectorSx > vals, const Index &col, const Index &jk, VectorIx &firstElt, VectorList &listCol)

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.

Definition at line 51 of file IncompleteCholesky.h.

Member Typedef Documentation

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

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

protected

Definition at line 54 of file IncompleteCholesky.h.

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

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

Definition at line 61 of file IncompleteCholesky.h.

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

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

Definition at line 58 of file IncompleteCholesky.h.

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

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

Definition at line 59 of file IncompleteCholesky.h.

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

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

Definition at line 57 of file IncompleteCholesky.h.

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

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

Definition at line 60 of file IncompleteCholesky.h.

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

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

Definition at line 64 of file IncompleteCholesky.h.

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

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

Definition at line 65 of file IncompleteCholesky.h.

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

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

Definition at line 63 of file IncompleteCholesky.h.

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

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

Definition at line 62 of file IncompleteCholesky.h.

Member Enumeration Documentation

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

anonymous enum

Enumerator
UpLo

Definition at line 66 of file IncompleteCholesky.h.

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

anonymous enum

Enumerator
ColsAtCompileTime
MaxColsAtCompileTime

Definition at line 67 of file IncompleteCholesky.h.

Constructor & Destructor Documentation

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&)

Definition at line 79 of file IncompleteCholesky.h.

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.

Definition at line 84 of file IncompleteCholesky.h.

Member Function Documentation

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

Definition at line 155 of file IncompleteCholesky.h.

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.

Definition at line 117 of file IncompleteCholesky.h.

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

Definition at line 93 of file IncompleteCholesky.h.

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()

Definition at line 147 of file IncompleteCholesky.h.

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()

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

template<typename _MatrixType >

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

Definition at line 196 of file IncompleteCholesky.h.

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.

Definition at line 104 of file IncompleteCholesky.h.

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

Definition at line 169 of file IncompleteCholesky.h.

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)

Definition at line 175 of file IncompleteCholesky.h.

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

Definition at line 90 of file IncompleteCholesky.h.

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

Definition at line 172 of file IncompleteCholesky.h.

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 $\sigma$ .

Definition at line 112 of file IncompleteCholesky.h.

template<typename Scalar , int _UpLo, typename OrderingType >

void Eigen::IncompleteCholesky< Scalar, _UpLo, OrderingType >::updateList	(	Ref< const VectorIx >	colPtr,
		Ref< VectorIx >	rowIdx,
		Ref< VectorSx >	vals,
		const Index &	col,
		const Index &	jk,
		VectorIx &	firstElt,
		VectorList &	listCol
	)

inlineprivate

Definition at line 379 of file IncompleteCholesky.h.

Member Data Documentation

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

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

protected

Definition at line 181 of file IncompleteCholesky.h.

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

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

protected

Definition at line 182 of file IncompleteCholesky.h.

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

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

protected

Definition at line 183 of file IncompleteCholesky.h.

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

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

protected

Definition at line 180 of file IncompleteCholesky.h.

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

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

protected

Definition at line 178 of file IncompleteCholesky.h.

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

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

protected

Definition at line 184 of file IncompleteCholesky.h.

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

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

protected

Definition at line 179 of file IncompleteCholesky.h.

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

IncompleteCholesky.h

Public Types

Public Member Functions

Protected Types

Protected Attributes

Private Member Functions

Detailed Description

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

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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