This class provides defines a implements basic task and tools which are useful while solving PDEs. More...

#include <PDESolver.hpp>

Inheritance diagram for sgpp::pde::PDESolver:

Public Member Functions
void	coarsenInitialGridSurplus (sgpp::base::DataVector &alpha, double dThreshold)
	Coarsens a grid by taking the grid's coefficients into account. More...

virtual void	constructGrid (sgpp::base::BoundingBox &myBoundingBox, size_t level)=0
	Use this routine the construct a regular grid to solve a PDE. More...

void	deleteGrid ()
	deletes the grid created within that solver More...

void	evaluateCuboid (sgpp::base::DataVector &alpha, sgpp::base::DataVector &FunctionValues, sgpp::base::DataMatrix &EvaluationPoints)
	Evaluates the sparse grid's function given by the stored grid and the alpha coefficients. More...

double	evaluatePoint (sgpp::base::DataVector &evalPoint, sgpp::base::DataVector &alpha)
	Determines the value of the function in the d-dimensional space. More...

std::string	getGrid () const
	gets the a string the describes the grid which is currently used to solve More...

size_t	getNumberDimensions () const
	use this the determine the number of dimensions that are currently used in the solver. More...

size_t	getNumberGridPoints () const
	use this to determine the number of grid points, used to solve the current problem More...

size_t	getNumberInnerGridPoints () const
	use this to determine the number of inner grid points, used to solve the current problem More...

	PDESolver ()
	Std-Constructor of the solver. More...

virtual void	printGrid (sgpp::base::DataVector &alpha, size_t PointesPerDimension, std::string tfilename) const
	This is some kind of debug functionality. More...

virtual void	printGridDomain (sgpp::base::DataVector &alpha, size_t PointesPerDimension, sgpp::base::BoundingBox &GridArea, std::string tfilename) const
	This is some kind of debug functionality. More...

virtual void	printLevelIndexGrid (std::string tfilename) const
	Prints the level,index pairs of the grid for each Gridpoint to a file. More...

virtual void	printSparseGrid (sgpp::base::DataVector &alpha, std::string tfilename, bool bSurplus) const
	Prints the sgpp::base::Grid Points of the Sparse sgpp::base::Grid either with their node basis value or their hierarchical surplus. More...

virtual void	printSparseGridExpTransform (sgpp::base::DataVector &alpha, std::string tfilename, bool bSurplus) const
	Prints the sgpp::base::Grid Points of the Sparse sgpp::base::Grid either with their node basis value or their hierarchical surplus. More...

void	refineInitialGridSurplus (sgpp::base::DataVector &alpha, int numRefinePoints, double dThreshold)
	Refines a grid by taking the grid's coefficients into account. More...

void	refineInitialGridSurplusSubDomain (sgpp::base::DataVector &alpha, int numRefinePoints, double dThreshold, std::vector< double > &norm_mu, std::vector< double > &norm_sigma)
	Refines a grid by taking the grid's coefficients into account. More...

void	refineInitialGridSurplusToMaxLevel (sgpp::base::DataVector &alpha, double dThreshold, sgpp::base::level_t maxLevel)
	Refines a grid by taking the grid's coefficients into account. More...

void	refineInitialGridSurplusToMaxLevelSubDomain (sgpp::base::DataVector &alpha, double dThreshold, sgpp::base::level_t maxLevel, std::vector< double > &norm_mu, std::vector< double > &norm_sigma)
	Refines a grid by taking the grid's coefficients into account. More...

void	setGrid (const std::string &serializedGrid)
	Sets the grid used in this BlackScholes Solver by an given serialized string of the grid. More...

virtual	~PDESolver ()
	Std-Destructor of the solver. More...

Protected Member Functions
virtual void	getGridNormalDistribution (sgpp::base::DataVector &alpha, std::vector< double > &norm_mu, std::vector< double > &norm_sigma)
	This function calculates for every grid point the value of a normal distribution given by norm_mu and norm_sigma. More...

Protected Attributes
bool	bGridConstructed
	stores if the grid was created inside the solver More...

size_t	dim
	the dimension of the grid More...

int	levels
	the number of levels used for an regular grid More...

sgpp::base::BoundingBox *	myBoundingBox
	Stores Pointer to the sgpp::base::Grid's Bounding Box. More...

sgpp::base::Grid *	myGrid
	The Sparse sgpp::base::Grid needed in this classificator. More...

sgpp::base::GridStorage *	myGridStorage
	Stores Pointer to the Girs's Storage. More...

Detailed Description

This class provides defines a implements basic task and tools which are useful while solving PDEs.

E.g. grid construction, simple grid evaluation tools grid printing, initial grid refinement etc.

Constructor & Destructor Documentation

◆ PDESolver()

sgpp::pde::PDESolver::PDESolver ( )

Std-Constructor of the solver.

References bGridConstructed.

◆ ~PDESolver()

sgpp::pde::PDESolver::~PDESolver ( )

virtual

Std-Destructor of the solver.

References bGridConstructed, and myGrid.

Member Function Documentation

◆ coarsenInitialGridSurplus()

void sgpp::pde::PDESolver::coarsenInitialGridSurplus	(	sgpp::base::DataVector &	alpha,
		double	dThreshold
	)

Coarsens a grid by taking the grid's coefficients into account.

This coarsen method coarsens the grid based on the surplus by coarsening grid points with small surpluses first.

Parameters

alpha	a sgpp::base::DataVector containing the grids coefficients
dThreshold	Threshold for a point's surplus for coarsening this point

References bGridConstructed, sgpp::base::GridGenerator::coarsenNFirstOnly(), sgpp::base::Grid::getGenerator(), sgpp::base::GridGenerator::getNumberOfRemovablePoints(), sgpp::base::Grid::getSize(), and myGrid.

◆ constructGrid()

virtual void sgpp::pde::PDESolver::constructGrid	(	sgpp::base::BoundingBox &	myBoundingBox,
		size_t	level
	)

pure virtual

Use this routine the construct a regular grid to solve a PDE.

Parameters

myBoundingBox	reference to a bounding box that describes the grid
level	number of the regular's grid levels

Implemented in sgpp::pde::HeatEquationSolverWithStretching, sgpp::pde::HeatEquationSolver, and sgpp::pde::PoissonEquationSolver.

◆ deleteGrid()

void sgpp::pde::PDESolver::deleteGrid ( )

deletes the grid created within that solver

References bGridConstructed, myBoundingBox, myGrid, and myGridStorage.

◆ evaluateCuboid()

void sgpp::pde::PDESolver::evaluateCuboid	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	FunctionValues,
		sgpp::base::DataMatrix &	EvaluationPoints
	)

Evaluates the sparse grid's function given by the stored grid and the alpha coefficients.

on different points specified in EvaluationPoints and stores the result into FunctionValues.

Parameters

alpha	the sparse grid's coefficients
FunctionValues	sgpp::base::DataVector into the which the result of function's evaluation is stored
EvaluationPoints	sgpp::base::DataMatrix that contains the points at which the sparse grid's function is evaluated

References bGridConstructed, sgpp::op_factory::createOperationMultipleEval(), sgpp::base::DataMatrix::getNrows(), sgpp::base::DataVector::getSize(), and myGrid.

◆ evaluatePoint()

double sgpp::pde::PDESolver::evaluatePoint	(	sgpp::base::DataVector &	evalPoint,
		sgpp::base::DataVector &	alpha
	)

Determines the value of the function in the d-dimensional space.

Parameters

evalPoint	coordinates of the point at which the function should be evaluated
alpha	the ansatzfunctions' coefficients

Returns: price of option for given point

References bGridConstructed, sgpp::op_factory::createOperationEval(), and sgpp::base::OperationEval::eval().

◆ getGrid()

std::string sgpp::pde::PDESolver::getGrid ( ) const

gets the a string the describes the grid which is currently used to solve

Returns: a string containing a serialized grid

References bGridConstructed, myGrid, and sgpp::base::Grid::serialize().

◆ getGridNormalDistribution()

void sgpp::pde::PDESolver::getGridNormalDistribution	(	sgpp::base::DataVector &	alpha,
		std::vector< double > &	norm_mu,
		std::vector< double > &	norm_sigma
	)

protectedvirtual

This function calculates for every grid point the value of a normal distribution given by norm_mu and norm_sigma.

The result is stored dehierarchized in alpha.

Parameters

alpha	contains dehierarchized sparse grid coefficients containing the values of the multi dimensional normal distribution after call
norm_mu	the expected values of the normal distribution for every grid dimension
norm_sigma	the standard deviation of the normal distribution for every grid dimension

References bGridConstructed, dim, sgpp::base::HashGridStorage::getCoordinates(), sgpp::base::StdNormalDistribution::getDensity(), sgpp::base::HashGridStorage::getPoint(), sgpp::base::Grid::getSize(), python.statsfileInfo::i, python.utils.statsfile2gnuplot::j, myGrid, myGridStorage, and analyse_erg::tmp.

Referenced by refineInitialGridSurplusSubDomain(), and refineInitialGridSurplusToMaxLevelSubDomain().

◆ getNumberDimensions()

size_t sgpp::pde::PDESolver::getNumberDimensions ( ) const

use this the determine the number of dimensions that are currently used in the solver.

Returns: returns the number of the grid's dimensions, if the grid isn't constructed, yet it returns 0

References bGridConstructed, sgpp::base::HashGridStorage::getDimension(), and myGridStorage.

◆ getNumberGridPoints()

size_t sgpp::pde::PDESolver::getNumberGridPoints ( ) const

use this to determine the number of grid points, used to solve the current problem

Returns: the number of grid points

References bGridConstructed, sgpp::base::HashGridStorage::getSize(), and myGridStorage.

◆ getNumberInnerGridPoints()

size_t sgpp::pde::PDESolver::getNumberInnerGridPoints ( ) const

use this to determine the number of inner grid points, used to solve the current problem

Returns: the number of inner grid points

References bGridConstructed, sgpp::base::HashGridStorage::getNumberOfInnerPoints(), and myGridStorage.

◆ printGrid()

void sgpp::pde::PDESolver::printGrid	(	sgpp::base::DataVector &	alpha,
		size_t	PointesPerDimension,
		std::string	tfilename
	)		const

virtual

This is some kind of debug functionality.

It writes a file, that can be used with gnuplot the print the grid.

Is only implemented for 1D and 2D grids!

Parameters

alpha	the coefficients of the Sparse Gird's basis functions
PointesPerDimension	the distance between evaluation points
tfilename	absolute path to file into which the grid's evaluation is written

Reimplemented in sgpp::pde::HeatEquationSolverWithStretching.

References myGrid, and sgpp::base::GridPrinter::printGrid().

◆ printGridDomain()

void sgpp::pde::PDESolver::printGridDomain	(	sgpp::base::DataVector &	alpha,
		size_t	PointesPerDimension,
		sgpp::base::BoundingBox &	GridArea,
		std::string	tfilename
	)		const

virtual

This is some kind of debug functionality.

It writes a file, that can be used with gnuplot the print the grid.

Is only implemented for 2D grids!

Parameters

alpha	the coefficients of the Sparse Gird's basis functions
PointesPerDimension	the distance between evaluation points
GridArea	the area in which the function should be plotted
tfilename	absolute path to file into which the grid's evaluation is written

Reimplemented in sgpp::pde::HeatEquationSolverWithStretching.

References myGrid, and sgpp::base::GridPrinter::printGridDomain().

◆ printLevelIndexGrid()

void sgpp::pde::PDESolver::printLevelIndexGrid ( std::string tfilename ) const

virtual

Prints the level,index pairs of the grid for each Gridpoint to a file.

Parameters

tfilename relative path to file into which the grid's evaluation is written

References myGrid, and sgpp::base::GridPrinter::printLevelIndexGrid().

◆ printSparseGrid()

void sgpp::pde::PDESolver::printSparseGrid	(	sgpp::base::DataVector &	alpha,
		std::string	tfilename,
		bool	bSurplus
	)		const

virtual

Prints the sgpp::base::Grid Points of the Sparse sgpp::base::Grid either with their node basis value or their hierarchical surplus.

This function is available for all dimensions

Parameters

alpha	the coefficients of the grid's ansatzfunctions
tfilename	absoulte path to the file the grid is written into
bSurplus	specifies whether the surplus (true) or the node basis value (false) is written

Reimplemented in sgpp::pde::HeatEquationSolverWithStretching.

References myGrid, and sgpp::base::GridPrinter::printSparseGrid().

◆ printSparseGridExpTransform()

void sgpp::pde::PDESolver::printSparseGridExpTransform	(	sgpp::base::DataVector &	alpha,
		std::string	tfilename,
		bool	bSurplus
	)		const

virtual

Prints the sgpp::base::Grid Points of the Sparse sgpp::base::Grid either with their node basis value or their hierarchical surplus.

This function is available for all dimensions.

The coordinates of the grid points are pushed the exp function. So log transformed grids can be plotted in cartesion coordinates.

Parameters

alpha	the coefficients of the grid's ansatzfunctions
tfilename	absoulte path to the file the grid is written into
bSurplus	specifies whether the surplus (true) or the node basis value (false) is written

Reimplemented in sgpp::pde::HeatEquationSolverWithStretching.

References myGrid, and sgpp::base::GridPrinter::printSparseGridExpTransform().

◆ refineInitialGridSurplus()

void sgpp::pde::PDESolver::refineInitialGridSurplus	(	sgpp::base::DataVector &	alpha,
		int	numRefinePoints,
		double	dThreshold
	)

Refines a grid by taking the grid's coefficients into account.

This refinement method refines the grid based on the surplus by refining grid points with big surpluses first. The number of grid points to refine may be specified by the numRefinePoints parameter.

Parameters

alpha	a sgpp::base::DataVector containing the grids coefficients
numRefinePoints	the number of grid points that should be refined; if this smaller than zero -> all refineable points will be refined
dThreshold	Threshold for a point's surplus for refining this point

References bGridConstructed, sgpp::base::Grid::getGenerator(), sgpp::base::GridGenerator::getNumberOfRefinablePoints(), sgpp::base::HashGridStorage::getSize(), myGrid, myGridStorage, and sgpp::base::GridGenerator::refine().

◆ refineInitialGridSurplusSubDomain()

void sgpp::pde::PDESolver::refineInitialGridSurplusSubDomain	(	sgpp::base::DataVector &	alpha,
		int	numRefinePoints,
		double	dThreshold,
		std::vector< double > &	norm_mu,
		std::vector< double > &	norm_sigma
	)

Refines a grid by taking the grid's coefficients into account.

This refinement method refines the grid based on the surplus by refining grid points with big surpluses first. The number of grid points to refine may be specified by the numRefinePoints parameter.

This functions refines the grid only in subdomain specified by a multi-dimensional normal distribution. The normal distribution is given by the parameters norm_mu and norm_sigma which are d-dimensional vectors.

Parameters

alpha	a sgpp::base::DataVector containing the grids coefficients
numRefinePoints	the number of grid points that should be refined; if this smaller than zero -> all refineable points will be refined
dThreshold	Threshold for a point's surplus for refining this point
norm_mu	the expected values of the normal distribution for every grid dimension
norm_sigma	the standard deviation of the normal distribution for every grid dimension

References bGridConstructed, sgpp::base::Grid::getGenerator(), getGridNormalDistribution(), sgpp::base::GridGenerator::getNumberOfRefinablePoints(), sgpp::base::HashGridStorage::getSize(), sgpp::base::DataVector::getSize(), myGrid, myGridStorage, and sgpp::base::GridGenerator::refine().

◆ refineInitialGridSurplusToMaxLevel()

void sgpp::pde::PDESolver::refineInitialGridSurplusToMaxLevel	(	sgpp::base::DataVector &	alpha,
		double	dThreshold,
		sgpp::base::level_t	maxLevel
	)

Refines a grid by taking the grid's coefficients into account.

This refinement method refines the grid based on the surplus by refining grid points with big surpluses first. The grid is refined to max. Level!

Parameters

alpha	a sgpp::base::DataVector containing the grids coefficients
dThreshold	Threshold for a point's surplus for refining this point
maxLevel	maxLevel of refinement

References bGridConstructed, sgpp::base::Grid::getGenerator(), sgpp::base::GridGenerator::getNumberOfRefinablePointsToMaxLevel(), sgpp::base::HashGridStorage::getSize(), myGrid, myGridStorage, and sgpp::base::GridGenerator::refineMaxLevel().

◆ refineInitialGridSurplusToMaxLevelSubDomain()

void sgpp::pde::PDESolver::refineInitialGridSurplusToMaxLevelSubDomain	(	sgpp::base::DataVector &	alpha,
		double	dThreshold,
		sgpp::base::level_t	maxLevel,
		std::vector< double > &	norm_mu,
		std::vector< double > &	norm_sigma
	)

Refines a grid by taking the grid's coefficients into account.

This refinement method refines the grid based on the surplus by refining grid points with big surpluses first. The grid is refined to max. Level!

This functions refines the grid only in subdomain specified by a multi-dimensional normal distribution. The normal distribution is given by the parameters norm_mu and norm_sigma which are d-dimensional vectors.

Parameters

alpha	a sgpp::base::DataVector containing the grids coefficients
dThreshold	Threshold for a point's surplus for refining this point
maxLevel	maxLevel of refinement
norm_mu	the expected values of the normal distribution for every grid dimension
norm_sigma	the standard deviation of the normal distribution for every grid dimension

References bGridConstructed, sgpp::base::Grid::getGenerator(), getGridNormalDistribution(), sgpp::base::GridGenerator::getNumberOfRefinablePointsToMaxLevel(), sgpp::base::HashGridStorage::getSize(), sgpp::base::DataVector::getSize(), myGrid, myGridStorage, and sgpp::base::GridGenerator::refineMaxLevel().

◆ setGrid()

void sgpp::pde::PDESolver::setGrid ( const std::string & serializedGrid )

Sets the grid used in this BlackScholes Solver by an given serialized string of the grid.

Parameters

serializedGrid a string that describes the grid that should be used in this solver

References bGridConstructed, dim, sgpp::base::Grid::getBoundingBox(), sgpp::base::Grid::getDimension(), sgpp::base::Grid::getStorage(), levels, myBoundingBox, myGrid, myGridStorage, and sgpp::base::Grid::unserialize().

Member Data Documentation

◆ bGridConstructed

bool sgpp::pde::PDESolver::bGridConstructed

protected

stores if the grid was created inside the solver

◆ dim

size_t sgpp::pde::PDESolver::dim

protected

the dimension of the grid

Referenced by sgpp::pde::PoissonEquationSolver::constructGrid(), sgpp::pde::HeatEquationSolver::constructGrid(), sgpp::pde::HeatEquationSolverWithStretching::constructGrid(), python.uq.dists.KDEDist.KDEDist::cov(), python.uq.dists.NatafDist.NatafDist::getDim(), getGridNormalDistribution(), sgpp::pde::PoissonEquationSolver::initGridWithExpHeat(), sgpp::pde::PoissonEquationSolver::initGridWithExpHeatFullDomain(), sgpp::pde::PoissonEquationSolver::initGridWithSmoothHeat(), sgpp::pde::HeatEquationSolver::initGridWithSmoothHeat(), sgpp::pde::HeatEquationSolverWithStretching::initGridWithSmoothHeat(), sgpp::pde::PoissonEquationSolver::initGridWithSmoothHeatFullDomain(), python.uq.dists.KDEDist.KDEDist::rvs(), python.uq.dists.NatafDist.NatafDist::rvs(), and setGrid().

◆ levels

int sgpp::pde::PDESolver::levels

protected

the number of levels used for an regular grid

Referenced by sgpp::pde::PoissonEquationSolver::constructGrid(), sgpp::pde::HeatEquationSolver::constructGrid(), sgpp::pde::HeatEquationSolverWithStretching::constructGrid(), and setGrid().

◆ myBoundingBox

sgpp::base::BoundingBox* sgpp::pde::PDESolver::myBoundingBox

protected

Stores Pointer to the sgpp::base::Grid's Bounding Box.

Referenced by sgpp::pde::PoissonEquationSolver::constructGrid(), sgpp::pde::HeatEquationSolver::constructGrid(), deleteGrid(), sgpp::pde::PoissonEquationSolver::initGridWithExpHeat(), sgpp::pde::PoissonEquationSolver::initGridWithSmoothHeat(), and setGrid().

◆ myGrid

sgpp::base::Grid* sgpp::pde::PDESolver::myGrid

protected

The Sparse sgpp::base::Grid needed in this classificator.

◆ myGridStorage

sgpp::base::GridStorage* sgpp::pde::PDESolver::myGridStorage

protected

Stores Pointer to the Girs's Storage.

Referenced by sgpp::pde::PoissonEquationSolver::constructGrid(), sgpp::pde::HeatEquationSolver::constructGrid(), sgpp::pde::HeatEquationSolverWithStretching::constructGrid(), deleteGrid(), getGridNormalDistribution(), getNumberDimensions(), getNumberGridPoints(), getNumberInnerGridPoints(), sgpp::pde::PoissonEquationSolver::initGridWithExpHeat(), sgpp::pde::PoissonEquationSolver::initGridWithExpHeatFullDomain(), sgpp::pde::PoissonEquationSolver::initGridWithSmoothHeat(), sgpp::pde::HeatEquationSolver::initGridWithSmoothHeat(), sgpp::pde::HeatEquationSolverWithStretching::initGridWithSmoothHeat(), sgpp::pde::PoissonEquationSolver::initGridWithSmoothHeatFullDomain(), refineInitialGridSurplus(), refineInitialGridSurplusSubDomain(), refineInitialGridSurplusToMaxLevel(), refineInitialGridSurplusToMaxLevelSubDomain(), and setGrid().

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

pde/src/sgpp/pde/application/PDESolver.hpp
pde/src/sgpp/pde/application/PDESolver.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ PDESolver()

◆ ~PDESolver()

Member Function Documentation

◆ coarsenInitialGridSurplus()

◆ constructGrid()

◆ deleteGrid()

◆ evaluateCuboid()

◆ evaluatePoint()

◆ getGrid()

◆ getGridNormalDistribution()

◆ getNumberDimensions()

◆ getNumberGridPoints()

◆ getNumberInnerGridPoints()

◆ printGrid()

◆ printGridDomain()

◆ printLevelIndexGrid()

◆ printSparseGrid()

◆ printSparseGridExpTransform()

◆ refineInitialGridSurplus()

◆ refineInitialGridSurplusSubDomain()

◆ refineInitialGridSurplusToMaxLevel()

◆ refineInitialGridSurplusToMaxLevelSubDomain()

◆ setGrid()

Member Data Documentation

◆ bGridConstructed

◆ dim

◆ levels

◆ myBoundingBox

◆ myGrid

◆ myGridStorage