Solve the system of equations with a LL'-decomposed matrix where LL' is created by an iterative, incomplete cholesky factorization on a dense matrix. More...

#include <DBMatDMSDenseIChol.hpp>

Inheritance diagram for sgpp::datadriven::DBMatDMSDenseIChol:

Public Member Functions
	DBMatDMSDenseIChol (const sgpp::datadriven::DensityEstimationConfiguration &densityEstimationConfig, Grid &grid, double lambda, bool doCV)

Public Member Functions inherited from sgpp::datadriven::DBMatDMSChol
void	choleskyDowndate (sgpp::base::DataMatrix &decompMatrix, const sgpp::base::DataVector &downdate, bool do_cv=false) const
	Performe a rank one cholesky downdate. More...

void	choleskyUpdate (sgpp::base::DataMatrix &decompMatrix, const sgpp::base::DataVector &update, bool do_cv=false) const
	Performe a rank one cholesky update. More...

	DBMatDMSChol ()=default
	Default constructor. More...

virtual void	solve (sgpp::base::DataMatrix &decompMatrix, sgpp::base::DataVector &alpha, const sgpp::base::DataVector &b, double lambda_old, double lambda_new) const
	Solves a system of equations. More...

Public Member Functions inherited from sgpp::datadriven::DBMatDecompMatrixSolver
	DBMatDecompMatrixSolver ()

Public Member Functions inherited from sgpp::solver::SGSolver
double	getEpsilon ()
	gets the the epsilon, that is used in the SGSolver More...

size_t	getNumberIterations ()
	function that returns the number of needed solve steps More...

double	getResiduum ()
	function the returns the residuum (current or final), error of the solver More...

void	setEpsilon (double eps)
	resets the epsilon, that is used in the SGSolver More...

void	setMaxIterations (size_t nIterations)
	resets the number of maximum iterations More...

	SGSolver (size_t nMaximumIterations, double epsilon)
	Std-Constructor. More...

virtual	~SGSolver ()
	Std-Destructor. More...

Protected Member Functions
void	choleskyBackwardSolve (const DataMatrix &decompMatrix, const DataVector &y, DataVector &alpha) const override
	Perform backward substitution solving the triangular system $A alpha = y$ with a parallel Jaccobi solver. More...

void	choleskyForwardSolve (const DataMatrix &decompMatrix, const DataVector &b, DataVector &y) const override
	Perform forward substitution solving the triangular system $L y = b$ with a parallel Jaccobi solver. More...

void	choleskyUpdateLambda (DataMatrix &decompMatrix, double lambdaUp) const override
	Update the regularization factor of the decomposition. More...

Additional Inherited Members
Protected Attributes inherited from sgpp::solver::SGSolver
double	myEpsilon
	epsilon needed in the, e.g. final error in the iterative solver, or a timestep More...

size_t	nIterations
	Number of Iterations needed for the solve. More...

size_t	nMaxIterations
	Number of maximum iterations for cg. More...

double	residuum
	residuum More...

Detailed Description

Solve the system of equations with a LL'-decomposed matrix where LL' is created by an iterative, incomplete cholesky factorization on a dense matrix.

Constructor & Destructor Documentation

◆ DBMatDMSDenseIChol()

sgpp::datadriven::DBMatDMSDenseIChol::DBMatDMSDenseIChol	(	const sgpp::datadriven::DensityEstimationConfiguration &	densityEstimationConfig,
		Grid &	grid,
		double	lambda,
		bool	doCV
	)

References sgpp::op_factory::createOperationLTwoDotExplicit(), grid(), lambda, and sgpp::base::DataMatrix::resizeQuadratic().

Member Function Documentation

◆ choleskyBackwardSolve()

void sgpp::datadriven::DBMatDMSDenseIChol::choleskyBackwardSolve	(	const DataMatrix &	decompMatrix,
		const DataVector &	y,
		DataVector &	alpha
	)		const

overrideprotectedvirtual

Perform backward substitution solving the triangular system $A alpha = y$ with a parallel Jaccobi solver.

Parameters

decompMatrix	Triangular matrix
y	right hand side obtained by forward substitution
alpha	the vector of unknowns we solve for

Reimplemented from sgpp::datadriven::DBMatDMSChol.

References sgpp::base::DataVector::get(), sgpp::base::DataMatrix::get(), sgpp::base::DataVector::getSize(), python.statsfileInfo::i, sgpp::datadriven::DensityEstimationConfiguration::iCholSweepsSolver_, python.utils.statsfile2gnuplot::j, sgpp::base::DataVector::set(), sgpp::base::DataVector::setAll(), and python.utils.pca_normalize_dataset::u.

◆ choleskyForwardSolve()

void sgpp::datadriven::DBMatDMSDenseIChol::choleskyForwardSolve	(	const DataMatrix &	decompMatrix,
		const DataVector &	b,
		DataVector &	y
	)		const

overrideprotectedvirtual

Perform forward substitution solving the triangular system $L y = b$ with a parallel Jaccobi solver.

Parameters

decompMatrix	Triangular matrix
b	right hand side of our initial system matrix we solve for
y	the vector of unknowns we solve for

Reimplemented from sgpp::datadriven::DBMatDMSChol.

References sgpp::base::DataVector::get(), sgpp::base::DataMatrix::get(), sgpp::base::DataMatrix::getNrows(), sgpp::base::DataVector::getSize(), python.statsfileInfo::i, sgpp::datadriven::DensityEstimationConfiguration::iCholSweepsSolver_, python.utils.statsfile2gnuplot::j, sgpp::base::DataVector::set(), sgpp::base::DataMatrix::set(), sgpp::base::DataVector::setAll(), analyse_erg::tmp, and python.utils.pca_normalize_dataset::u.

◆ choleskyUpdateLambda()

void sgpp::datadriven::DBMatDMSDenseIChol::choleskyUpdateLambda	(	DataMatrix &	decompMatrix,
		double	lambdaUp
	)		const

overrideprotectedvirtual

Update the regularization factor of the decomposition.

This is a very costly operation as the iterative algorithm will need to recalculate the entire decomposition. However the current solution is used as an initial guess, reducing the required amount of sweeps.

Parameters

decompMatrix
lambdaUp

Reimplemented from sgpp::datadriven::DBMatDMSChol.

References sgpp::datadriven::DBMatOfflineDenseIChol::ichol(), and sgpp::datadriven::DensityEstimationConfiguration::iCholSweepsUpdateLambda_.

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

datadriven/src/sgpp/datadriven/algorithm/DBMatDMSDenseIChol.hpp
datadriven/src/sgpp/datadriven/algorithm/DBMatDMSDenseIChol.cpp

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ DBMatDMSDenseIChol()

Member Function Documentation

◆ choleskyBackwardSolve()

◆ choleskyForwardSolve()

◆ choleskyUpdateLambda()