sgpp::datadriven::DBMatDMSChol Class Reference

Class to solve the system of equations with a LL'-decomposed matrix. More...

#include <DBMatDMSChol.hpp>

Inheritance diagram for sgpp::datadriven::DBMatDMSChol:

Public Member Functions
void	choleskyDowndate (sgpp::base::DataMatrix &decompMatrix, const sgpp::base::DataVector &downdate, bool do_cv=false) const
	Performe a rank one cholesky downdate.
void	choleskyUpdate (sgpp::base::DataMatrix &decompMatrix, const sgpp::base::DataVector &update, bool do_cv=false) const
	Performe a rank one cholesky update.
	DBMatDMSChol ()=default
	Default constructor.
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.
void	solveParallel (DataMatrixDistributed &decompMatrix, DataVectorDistributed &x, double lambda_old, double lambda_new) const
	Parallel (distributed) version of solve.
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
size_t	getNumberIterations ()
	function that returns the number of needed solve steps
double	getResiduum ()
	function the returns the residuum (current or final), error of the solver
void	setEpsilon (double eps)
	resets the epsilon, that is used in the SGSolver
void	setMaxIterations (size_t nIterations)
	resets the number of maximum iterations
	SGSolver (size_t nMaximumIterations, double epsilon)
	Std-Constructor.
virtual	~SGSolver ()
	Std-Destructor.

Protected Member Functions
virtual void	choleskyBackwardSolve (const sgpp::base::DataMatrix &decompMatrix, const sgpp::base::DataVector &y, sgpp::base::DataVector &alpha) const
	Perform Backward substitution solving the triangular system $A alpha = y$.
virtual void	choleskyForwardSolve (const sgpp::base::DataMatrix &decompMatrix, const sgpp::base::DataVector &b, sgpp::base::DataVector &y) const
	Perform forward substitution solving the triangular system $L y = b$.
virtual void	choleskyUpdateLambda (sgpp::base::DataMatrix &decompMatrix, double lambdaUpdate) const
	Update the decomposition if the regularization parameter changes.

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
size_t	nIterations
	Number of Iterations needed for the solve.
size_t	nMaxIterations
	Number of maximum iterations for cg.
double	residuum
	residuum

Detailed Description

Class to solve the system of equations with a LL'-decomposed matrix.

Constructor & Destructor Documentation

DBMatDMSChol()

sgpp::datadriven::DBMatDMSChol::DBMatDMSChol ( )

default

Default constructor.

Member Function Documentation

choleskyBackwardSolve()

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

protectedvirtual

Perform Backward substitution solving the triangular system $A alpha = y$.

Parameters

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

Reimplemented in sgpp::datadriven::DBMatDMSDenseIChol.

References alpha, sgpp::base::DataMatrix::get(), and sgpp::base::DataMatrix::getNcols().

Referenced by solve().

choleskyDowndate()

void sgpp::datadriven::DBMatDMSChol::choleskyDowndate	(	sgpp::base::DataMatrix &	decompMatrix,
		const sgpp::base::DataVector &	downdate,
		bool	do_cv = false
	)		const

Performe a rank one cholesky downdate.

Parameters

decompMatrix	the LL' lower triangular cholesky factor
downdate	the vector representing the rank one matrix (xx')
do_cv	indicating if updates are used for cross valdiation (using special structure of update vectors to save runtime)

References sgpp::base::DataMatrix::getNrows(), sgpp::base::DataMatrix::getPointer(), sgpp::base::DataVector::getPointer(), sgpp::base::DataVector::getSize(), and m.

Referenced by choleskyUpdateLambda().

choleskyForwardSolve()

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

protectedvirtual

Perform forward substitution solving the triangular system $L y = b$.

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 in sgpp::datadriven::DBMatDMSDenseIChol.

References sgpp::base::DataMatrix::get(), and sgpp::base::DataMatrix::getNcols().

Referenced by solve().

choleskyUpdate()

void sgpp::datadriven::DBMatDMSChol::choleskyUpdate	(	sgpp::base::DataMatrix &	decompMatrix,
		const sgpp::base::DataVector &	update,
		bool	do_cv = false
	)		const

Performe a rank one cholesky update.

Parameters

decompMatrix	the LL' lower triangular cholesky factor
update	the vector representing the rank one matrix (xx')
do_cv	indicating if updates are used for cross valdiation (using special structure of update vectors to save runtime)

References sgpp::base::DataMatrix::getNrows(), sgpp::base::DataMatrix::getPointer(), sgpp::base::DataVector::getPointer(), sgpp::base::DataVector::getSize(), and m.

Referenced by sgpp::datadriven::DBMatOfflineChol::choleskyModification(), and choleskyUpdateLambda().

choleskyUpdateLambda()

void sgpp::datadriven::DBMatDMSChol::choleskyUpdateLambda ( sgpp::base::DataMatrix &  decompMatrix, double  lambdaUpdate  ) const

protectedvirtual

Update the decomposition if the regularization parameter changes.

This may be more expensive then recalculating the decomposition.

Parameters

decompMatrix	decomposed matrix to be modified
lambdaUpdate	the value by which the regularization parameter modifies the diagonal.

Reimplemented in sgpp::datadriven::DBMatDMSDenseIChol.

References choleskyDowndate(), choleskyUpdate(), sgpp::base::DataMatrix::getNcols(), sgpp::base::DataVector::set(), and sgpp::base::DataVector::setAll().

Referenced by solve(), and solveParallel().

solve()

void sgpp::datadriven::DBMatDMSChol::solve ( sgpp::base::DataMatrix &  decompMatrix, sgpp::base::DataVector &  alpha, const sgpp::base::DataVector &  b, double  lambda_old, double  lambda_new  ) const

virtual

Solves a system of equations.

Parameters

decompMatrix	the LL' lower triangular cholesky factor
alpha	the vector of unknowns (the result is stored there)
b	the right hand vector of the equation system
lambda_old	the current regularization paramter
lambda_new	the new regularization paramter (e.g. if cross-validation is applied)

References alpha, choleskyBackwardSolve(), choleskyForwardSolve(), choleskyUpdateLambda(), and sgpp::base::DataMatrix::getNcols().

Referenced by sgpp::datadriven::DBMatOnlineDEChol::solveSLE().

solveParallel()

void sgpp::datadriven::DBMatDMSChol::solveParallel	(	DataMatrixDistributed &	decompMatrix,
		DataVectorDistributed &	x,
		double	lambda_old,
		double	lambda_new
	)		const

Parallel (distributed) version of solve.

Parameters

decompMatrix	the LL' lower triangular cholesky factor
x	input: the right hand vector of the equation system, output: the vector of unknowns (the result is stored there)
lambda_old	the current regularization paramter
lambda_new	the new regularization paramter (e.g. if cross-validation is applied)

References choleskyUpdateLambda(), sgpp::datadriven::DataMatrixDistributed::distribute(), sgpp::datadriven::DataMatrixDistributed::getProcessGrid(), sgpp::datadriven::DataMatrixDistributed::solveCholesky(), and sgpp::datadriven::DataMatrixDistributed::toLocalDataMatrix().

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

• datadriven/src/sgpp/datadriven/algorithm/DBMatDMSChol.hpp
• datadriven/src/sgpp/datadriven/algorithm/DBMatDMSChol.cpp