cla3p::PardisoLDLt< T_Matrix > Class Template Reference

The indefinite Cholesky (LDL') linear solver for sparse matrices. More...

Inheritance diagram for cla3p::PardisoLDLt< T_Matrix >:

Public Member Functions
	PardisoLDLt ()
	The default constructor.
	~PardisoLDLt ()=default
	Destroys the solver.
void	setScaling (bool flg)
	Scaling vectors.
void	setMatching (bool flg)
	Improved accuracy using symmetric weighted matching.
void	setPivoting (pardiso::pivot_t pivot)
	Pivoting strategy.
void	setPivotingPerturbation (int_t p)
	Small/zero pivot handling.
int_t	inertiaPositive () const
	Inertia: number of positive eigenvalues.
int_t	inertiaNegative () const
	Inertia: number of negative eigenvalues.
Public Member Functions inherited from cla3p::PardisoBase< T_Matrix >
void	clear ()
	Clears the solver internal data.
void	clearNumeric ()
	Clears the solver numeric factor data.
void	analysis (const T_Matrix &mat)
	Performs matrix analysis & symbolic decomposition.
void	decompose (const T_Matrix &mat)
	Performs matrix decomposition.
void	solve (const dns::XxMatrix< T_Scalar > &rhs, dns::XxMatrix< T_Scalar > &sol)
	Performs matrix solution.
void	solve (const dns::XxVector< T_Scalar > &rhs, dns::XxVector< T_Scalar > &sol)
	Performs vector solution.
void	setVerbose (bool flg)
	Message level information.
const prm::PiMatrix &	fillReducingOrdering () const
	Gets the calculated fill-reducing permutation matrix.
int_t	iterativeRefinementSteps () const
	Iterative refinement steps performed.
int_t	perturbedPivots () const
	Number of perturbed pivots.
int_t	peakAnalysisMemory () const
	Peak memory on symbolic factorization.
int_t	permanentAnalysisMemory () const
	Permanent memory on symbolic factorization.
int_t	factorMemory () const
	Size of factors/Peak memory on numerical factorization and solution.
Public Member Functions inherited from cla3p::pardiso::GlobalParams
void	setMatrixChecker (bool flg)
	Forces Pardiso to check input matrix.
Public Member Functions inherited from cla3p::pardiso::AnalysisParams
void	setFillReducer (pardiso::reorder_t reorderMethod)
	Sets the fill reducing ordering method.
void	setFillReducer (const prm::PiMatrix &permMatrix)
	Sets a custom fill-reducing permutation.
Public Member Functions inherited from cla3p::pardiso::SolveParams
void	setMaxIterativeRefinements (int_t numIters)
	Sets maximum number of iterative refinement steps.

Detailed Description

template<typename T_Matrix>
class cla3p::PardisoLDLt< T_Matrix >

The indefinite Cholesky (LDL') linear solver for sparse matrices.

Examples

ex07c_solving_sparse_linear_systems_ldlt.cpp.

Constructor & Destructor Documentation

PardisoLDLt()

template<typename T_Matrix>

cla3p::PardisoLDLt< T_Matrix >::PardisoLDLt ( )

inline

The default constructor.

Constructs an empty solver object.

~PardisoLDLt()

template<typename T_Matrix>

cla3p::PardisoLDLt< T_Matrix >::~PardisoLDLt ( )

default

Destroys the solver.

Clears all internal data and destroys the solver.

Member Function Documentation

setScaling()

template<typename T_Matrix>

void cla3p::PardisoLDLt< T_Matrix >::setScaling ( bool flg )

inline

Scaling vectors.

Parameters

[in]

flg

Enables/disables scaling.

Pardiso uses a maximum weight matching algorithm to permute large elements on the diagonal and to scale so that the diagonal elements are equal to 1 and the absolute values of the off-diagonal entries are less than or equal to 1. The scaling can also be used for symmetric indefinite matrices when the symmetric weighted matchings are applied. Use scaling and matching for highly indefinite symmetric matrices, for example, from interior point optimizations or saddle point problems.

Set before analysis. Default value is false.

setMatching()

template<typename T_Matrix>

void cla3p::PardisoLDLt< T_Matrix >::setMatching ( bool flg )

inline

Improved accuracy using symmetric weighted matching.

Parameters

[in]

flg

Enables/disables matching.

Pardiso can use a maximum weighted matching algorithm to permute large elements close the diagonal. This strategy adds an additional level of reliability to the factorization methods and complements the alternative of using more complete pivoting techniques during the numerical factorization. Use scaling and matching for highly indefinite symmetric matrices, for example, from interior point optimizations or saddle point problems.

Set before analysis. Default value is false.

setPivoting()

template<typename T_Matrix>

void cla3p::PardisoLDLt< T_Matrix >::setPivoting ( pardiso::pivot_t pivot )

inline

Pivoting strategy.

Parameters

[in]

pivot

The pivoting strategy modifier.

Selects pivoting strategy for symmetric indefinite matrices.

• 1x1 Diagonal
• 1x1 and 2x2 Bunch-Kaufman (default)

Set before decomposition.

setPivotingPerturbation()

template<typename T_Matrix>

void cla3p::PardisoLDLt< T_Matrix >::setPivotingPerturbation ( int_t p )

inline

Small/zero pivot handling.

Parameters

[in]

p

Negative power in the perturbation calculation formula.

This parameter instructs Pardiso how to handle small pivots or zero pivots. Small pivots are perturbed with eps = 10^-p. For more details, refer to the Pardiso manual (iparm[9]).

Set before decomposition. Default value is 8.

inertiaPositive()

template<typename T_Matrix>

int_t cla3p::PardisoLDLt< T_Matrix >::inertiaPositive ( ) const

inline

Inertia: number of positive eigenvalues.

Returns

The number of positive eigenvalues.

Pardiso reports the number of positive eigenvalues for symmetric indefinite matrices.

Available after decomposition.

inertiaNegative()

template<typename T_Matrix>

int_t cla3p::PardisoLDLt< T_Matrix >::inertiaNegative ( ) const

inline

Inertia: number of negative eigenvalues.

Returns

The number of negative eigenvalues.

Pardiso reports the number of negative eigenvalues for symmetric indefinite matrices.

Available after decomposition.