stores a sparse grid not a knot B-spline interpolant in the framework of a respsonse surface More...

#include <SplineResponseSurface.hpp>

Inheritance diagram for sgpp::optimization::SplineResponseSurface:

Public Member Functions
double	eval (sgpp::base::DataVector v) override
	evaluates this response surface

double	evalGradient (sgpp::base::DataVector v, sgpp::base::DataVector &gradient) override
	evaluates the response surface and its gradient

sgpp::base::DataVector	getCoefficients ()

std::shared_ptr< sgpp::base::Grid >	getGrid ()

double	getIntegral ()
	return the integral of the response surface

sgpp::base::DataVector	getLowerBounds ()

double	getMean (sgpp::base::DistributionsVector pdfs, size_t quadOrder)
	return the mean of the response surface w.r.t.

size_t	getSize ()

sgpp::base::DataVector	getUpperBounds ()

sgpp::base::DataVector	getVariance (sgpp::base::DistributionsVector pdfs, size_t quadOrder)
	return the variance of the response surface w.r.t.

void	nextSurplusAdaptiveGrid (size_t refinementsNum, bool verbose=false)
	refines the grid surplus adaptive but does not recalculate interpolation coefficients

sgpp::base::DataVector	optimize ()
	calculates the minimimum with gradient descent

void	refineSurplusAdaptive (size_t refinementsNum, bool verbose=false)
	refines the grid surplus adaptive and recalculates the interpoaltion coefficients

void	regular (size_t level)
	creates a regular sparse grid interpolant

void	regularByPoints (size_t numPoints, bool verbose=false)
	creates a regular grid of the lowest level with more grid points than specified

void	ritterNovak (size_t maxNumGridPoints, double gamma, size_t initialLevel=3, bool verbose=false)
	creates an adaptive grid based on Ritter-Novak this is favourable for optimization

	SplineResponseSurface (std::shared_ptr< sgpp::base::Grid > grid, sgpp::base::DataVector coefficients, sgpp::base::DataVector lb, sgpp::base::DataVector ub, size_t degree=3)
	Constructor.

	SplineResponseSurface (std::shared_ptr< sgpp::base::ScalarFunction > objectiveFunc, sgpp::base::DataVector lb, sgpp::base::DataVector ub, sgpp::base::GridType gridType, size_t degree=3, size_t boundaryLevel=1)
	Constructor.

	SplineResponseSurface (std::shared_ptr< sgpp::base::ScalarFunction > objectiveFunc, std::shared_ptr< sgpp::base::Grid > grid, sgpp::base::DataVector lb, sgpp::base::DataVector ub, size_t degree=3)
	Constructor.

void	surplusAdaptive (size_t maxNumGridPoints, size_t initialLevel, size_t refinementsNum=3, bool verbose=false)
	creates a surplus adaptive sparse grid interpolant

	~SplineResponseSurface () override
	Destructor.

Public Member Functions inherited from sgpp::optimization::ResponseSurface
double	l2Error (std::shared_ptr< sgpp::base::ScalarFunction > objectiveFunc, size_t numMCPoints=1000)
	Calculates the l2 error between interpolant and objective function.

sgpp::base::DataVector	nrmsError (std::shared_ptr< sgpp::base::ScalarFunction > objectiveFunc, size_t numMCPoints=1000)
	Calculates the normalized root mean square error between interpolant and objective function in random points.

sgpp::base::DataVector	nrmsErrorFromTestData (const std::string &fileName, size_t numMCPoints, size_t numDim)
	Calculates the normalized root mean square error between interpolant and objective function from a precalculated set of test points and according values (this set is usually generated by ResponseSurface::precalculateErrorTestData)

void	precalculateErrorTestData (std::shared_ptr< sgpp::base::ScalarFunction > objectiveFunc, size_t numMCPoints, const std::string &fileName)
	Evaluates the objective function in random points and stores these points with the according evaluation value The stored set of test data can then later be used to calculate and compare the approximation error.

	ResponseSurface (size_t numDim)
	Constructor.

virtual	~ResponseSurface ()
	Destructor.

Additional Inherited Members
Protected Member Functions inherited from sgpp::optimization::ResponseSurface
double	domainVolume ()
	calculates the volume of the tensor product domain given by lb and ub

void	transformPoint (sgpp::base::DataVector &v, sgpp::base::DataVector lBounds, sgpp::base::DataVector uBounds, sgpp::base::DataVector newlBounds, sgpp::base::DataVector newuBounds)
	transforms a point in hyper-rectangle [lBounds,rBounds] to the hyper-rectangle [newlBounds,newuBounds]

Protected Attributes inherited from sgpp::optimization::ResponseSurface
std::shared_ptr< sgpp::base::ScalarFunction >	interpolant

std::shared_ptr< sgpp::base::ScalarFunctionGradient >	interpolantGradient

sgpp::base::DataVector	lb

size_t	numDim

sgpp::base::DataVector	ub

Detailed Description

stores a sparse grid not a knot B-spline interpolant in the framework of a respsonse surface

Constructor & Destructor Documentation

◆ SplineResponseSurface() [1/3]

sgpp::optimization::SplineResponseSurface::SplineResponseSurface	(	std::shared_ptr< sgpp::base::ScalarFunction >	objectiveFunc,
		sgpp::base::DataVector	lb,
		sgpp::base::DataVector	ub,
		sgpp::base::GridType	gridType,
		size_t	degree = `3`,
		size_t	boundaryLevel = `1`
	)

inline

Constructor.

Parameters

objectiveFunc	objective Function
lb	lower bounds
ub	upper bounds
gridType	type of the interpolants grid/basis
degree	degree of the interpolants basis
boundaryLevel	boundary level

Note: Currently boundaryLevel is only available for gridType nakBsplineBoundary

References sgpp::base::Bspline, sgpp::base::BsplineBoundary, sgpp::base::BsplineClenshawCurtis, sgpp::base::FundamentalSpline, sgpp::optimization::ResponseSurface::lb, sgpp::base::ModBspline, sgpp::base::ModFundamentalSpline, sgpp::base::ModNakBspline, sgpp::base::ModPoly, sgpp::base::ModWeaklyFundamentalNakSpline, sgpp::base::NakBspline, sgpp::base::NakBsplineBoundary, sgpp::base::NakBsplineExtended, sgpp::base::NakPBspline, sgpp::optimization::ResponseSurface::numDim, sgpp::base::PolyBoundary, sgpp::optimization::ResponseSurface::ub, and sgpp::base::WeaklyFundamentalNakSplineBoundary.

◆ SplineResponseSurface() [2/3]

sgpp::optimization::SplineResponseSurface::SplineResponseSurface	(	std::shared_ptr< sgpp::base::ScalarFunction >	objectiveFunc,
		std::shared_ptr< sgpp::base::Grid >	grid,
		sgpp::base::DataVector	lb,
		sgpp::base::DataVector	ub,
		size_t	degree = `3`
	)

inline

Constructor.

Parameters

objectiveFunc	objective Function
grid	grid
lb	lower bounds
ub	upper bounds
degree	degree of the interpolants basis

References sgpp::base::Bspline, sgpp::base::BsplineBoundary, sgpp::base::BsplineClenshawCurtis, sgpp::base::FundamentalSpline, sgpp::optimization::ResponseSurface::interpolant, sgpp::optimization::ResponseSurface::interpolantGradient, sgpp::optimization::ResponseSurface::lb, sgpp::base::ModBspline, sgpp::base::ModFundamentalSpline, sgpp::base::ModNakBspline, sgpp::base::ModPoly, sgpp::base::ModWeaklyFundamentalNakSpline, sgpp::base::NakBspline, sgpp::base::NakBsplineBoundary, sgpp::base::NakBsplineExtended, sgpp::base::NakPBspline, sgpp::optimization::ResponseSurface::numDim, sgpp::base::PolyBoundary, sgpp::optimization::ResponseSurface::ub, and sgpp::base::WeaklyFundamentalNakSplineBoundary.

◆ SplineResponseSurface() [3/3]

sgpp::optimization::SplineResponseSurface::SplineResponseSurface	(	std::shared_ptr< sgpp::base::Grid >	grid,
		sgpp::base::DataVector	coefficients,
		sgpp::base::DataVector	lb,
		sgpp::base::DataVector	ub,
		size_t	degree = `3`
	)

inline

Constructor.

Parameters

grid	grid
coefficients	coefficients matching the grid
lb	lower bounds
ub	upper bounds
degree	degree of the interpolants basis

References sgpp::base::Bspline, sgpp::base::BsplineBoundary, sgpp::base::BsplineClenshawCurtis, sgpp::base::FundamentalSpline, sgpp::optimization::ResponseSurface::interpolant, sgpp::optimization::ResponseSurface::interpolantGradient, sgpp::optimization::ResponseSurface::lb, sgpp::base::ModBspline, sgpp::base::ModFundamentalSpline, sgpp::base::ModNakBspline, sgpp::base::ModPoly, sgpp::base::ModWeaklyFundamentalNakSpline, sgpp::base::NakBspline, sgpp::base::NakBsplineBoundary, sgpp::base::NakBsplineExtended, sgpp::base::NakPBspline, sgpp::optimization::ResponseSurface::numDim, sgpp::base::PolyBoundary, sgpp::optimization::ResponseSurface::ub, and sgpp::base::WeaklyFundamentalNakSplineBoundary.

◆ ~SplineResponseSurface()

sgpp::optimization::SplineResponseSurface::~SplineResponseSurface ( )

inlineoverride

Destructor.

Member Function Documentation

◆ eval()

double sgpp::optimization::SplineResponseSurface::eval ( sgpp::base::DataVector v )

overridevirtual

evaluates this response surface

Parameters

v	point to evaluate in

Returns: the evaluation

Reimplemented from sgpp::optimization::ResponseSurface.

References sgpp::optimization::ResponseSurface::interpolant, sgpp::optimization::ResponseSurface::lb, sgpp::optimization::ResponseSurface::transformPoint(), and sgpp::optimization::ResponseSurface::ub.

Referenced by python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis::estimateDensity().

◆ evalGradient()

double sgpp::optimization::SplineResponseSurface::evalGradient	(	sgpp::base::DataVector	v,
		sgpp::base::DataVector &	gradient
	)

overridevirtual

evaluates the response surface and its gradient

Parameters

v	point to evaluate in
gradient	reference to return the repsonse surfaces gradient evaluted in v

Returns: the evaluation

Implements sgpp::optimization::ResponseSurface.

References sgpp::base::DataVector::getSize(), sgpp::optimization::ResponseSurface::interpolantGradient, sgpp::optimization::ResponseSurface::lb, sgpp::optimization::ResponseSurface::transformPoint(), and sgpp::optimization::ResponseSurface::ub.

◆ getCoefficients()

sgpp::base::DataVector sgpp::optimization::SplineResponseSurface::getCoefficients ( )

inline

Returns: the interpolation coefficients

◆ getGrid()

std::shared_ptr< sgpp::base::Grid > sgpp::optimization::SplineResponseSurface::getGrid ( )

inline

Returns: the interpolation grid

Referenced by python.uq.analysis.asgc.ASGCKnowledge.ASGCKnowledge::getSparseGridFunction(), python.uq.learner.SimulationLearner.SimulationLearner::learnData(), python.uq.learner.SimulationLearner.SimulationLearner::learnDataWithFolding(), python.uq.learner.SimulationLearner.SimulationLearner::learnDataWithTest(), and python.uq.learner.SimulationLearner.SimulationLearner::refineGrid().

◆ getIntegral()

double sgpp::optimization::SplineResponseSurface::getIntegral ( )

return the integral of the response surface

References sgpp::op_factory::createOperationQuadrature(), sgpp::optimization::ResponseSurface::domainVolume(), and sgpp::base::OperationQuadrature::doQuadrature().

◆ getLowerBounds()

sgpp::base::DataVector sgpp::optimization::SplineResponseSurface::getLowerBounds ( )

inline

Returns: the lower bounds of the domain

References sgpp::optimization::ResponseSurface::lb.

◆ getMean()

double sgpp::optimization::SplineResponseSurface::getMean	(	sgpp::base::DistributionsVector	pdfs,
		size_t	quadOrder
	)

return the mean of the response surface w.r.t.

a probability density function

Parameters

pdfs	the probability density function
quadOrder	order of the Gauss Legendre quadrature

References sgpp::op_factory::createOperationWeightedQuadrature(), and sgpp::base::OperationWeightedQuadrature::doWeightedQuadrature().

Referenced by getVariance().

◆ getSize()

size_t sgpp::optimization::SplineResponseSurface::getSize ( )

inline

Returns: the number of grid points

Referenced by python.uq.uq_setting.UQSetting.UQSetting::convert(), python.uq.uq_setting.UQSetting.UQSetting::getTimeDependentResults(), python.uq.uq_setting.UQSetting.UQSetting::runSamples(), and python.uq.uq_setting.UQSetting.UQSetting::runSamples_withoutDistribution().

◆ getUpperBounds()

sgpp::base::DataVector sgpp::optimization::SplineResponseSurface::getUpperBounds ( )

inline

Returns: the upper bounds of the domain

References sgpp::optimization::ResponseSurface::ub.

◆ getVariance()

sgpp::base::DataVector sgpp::optimization::SplineResponseSurface::getVariance	(	sgpp::base::DistributionsVector	pdfs,
		size_t	quadOrder
	)

return the variance of the response surface w.r.t.

a probability density function

Parameters

pdfs	the probability density function
quadOrder	order of the Gauss Legendre quadrature

Returns: vector [v,mS,m] containing the variance v and the meanSquare mS and mean m used to compute it

References sgpp::op_factory::createOperationWeightedSecondMoment(), sgpp::base::OperationWeightedSecondMoment::doWeightedQuadrature(), and getMean().

◆ nextSurplusAdaptiveGrid()

void sgpp::optimization::SplineResponseSurface::nextSurplusAdaptiveGrid	(	size_t	refinementsNum,
		bool	verbose = `false`
	)

refines the grid surplus adaptive but does not recalculate interpolation coefficients

Parameters

refinementsNum	number of grid points which should be refined
verbose	print information on the refine points

Referenced by refineSurplusAdaptive().

◆ optimize()

sgpp::base::DataVector sgpp::optimization::SplineResponseSurface::optimize ( )

calculates the minimimum with gradient descent

Returns: argmin of the response surface

The gradient method needs a starting point. We use the grid point with the smallest (most promising) function value and save it in x0.

References sgpp::optimization::optimizer::UnconstrainedOptimizer::getOptimalPoint(), sgpp::base::DataVector::getPointer(), sgpp::base::DataVector::getSize(), sgpp::optimization::ResponseSurface::interpolant, sgpp::optimization::ResponseSurface::interpolantGradient, sgpp::optimization::ResponseSurface::lb, sgpp::optimization::ResponseSurface::numDim, sgpp::optimization::optimizer::GradientDescent::optimize(), sgpp::optimization::optimizer::UnconstrainedOptimizer::setStartingPoint(), sgpp::optimization::ResponseSurface::transformPoint(), and sgpp::optimization::ResponseSurface::ub.

◆ refineSurplusAdaptive()

void sgpp::optimization::SplineResponseSurface::refineSurplusAdaptive	(	size_t	refinementsNum,
		bool	verbose = `false`
	)

refines the grid surplus adaptive and recalculates the interpoaltion coefficients

Parameters

refinementsNum	number of grid points which should be refined
verbose	print information on the refine points

References nextSurplusAdaptiveGrid().

Referenced by surplusAdaptive().

◆ regular()

void sgpp::optimization::SplineResponseSurface::regular ( size_t level )

creates a regular sparse grid interpolant

Parameters

level level of the regular sparse grid

References sgpp::optimization::ResponseSurface::interpolant, sgpp::optimization::ResponseSurface::interpolantGradient, level, sgpp::base::ModPoly, and sgpp::base::PolyBoundary.

Referenced by surplusAdaptive().

◆ regularByPoints()

void sgpp::optimization::SplineResponseSurface::regularByPoints	(	size_t	numPoints,
		bool	verbose = `false`
	)

creates a regular grid of the lowest level with more grid points than specified

Parameters

numPoints	desired number of grid points
verbose	print extra info

References sgpp::optimization::ResponseSurface::interpolant, sgpp::optimization::ResponseSurface::interpolantGradient, level, sgpp::base::ModPoly, and sgpp::base::PolyBoundary.

◆ ritterNovak()

void sgpp::optimization::SplineResponseSurface::ritterNovak	(	size_t	maxNumGridPoints,
		double	gamma,
		size_t	initialLevel = `3`,
		bool	verbose = `false`
	)

creates an adaptive grid based on Ritter-Novak this is favourable for optimization

Parameters

maxNumGridPoints	maximum number of grid points of the interpolants grid
gamma	Ritter Novak adaptivity parameter between 0 and1
initialLevel	initial level for the refinement
verbose	print extra info

References sgpp::optimization::IterativeGridGeneratorRitterNovak::generate(), sgpp::optimization::ResponseSurface::interpolant, and sgpp::optimization::ResponseSurface::interpolantGradient.

◆ surplusAdaptive()

void sgpp::optimization::SplineResponseSurface::surplusAdaptive	(	size_t	maxNumGridPoints,
		size_t	initialLevel,
		size_t	refinementsNum = `3`,
		bool	verbose = `false`
	)

creates a surplus adaptive sparse grid interpolant

Parameters

maxNumGridPoints	maximum number of grid points of the interpolants grid
initialLevel	first a regular grid of initialLevel is created.
refinementsNum	max number of grid points, added in each refinement step
verbose	print extra info

References sgpp::optimization::ResponseSurface::interpolant, sgpp::optimization::ResponseSurface::interpolantGradient, sgpp::base::ModPoly, sgpp::base::PolyBoundary, refineSurplusAdaptive(), and regular().

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

optimization/src/sgpp/optimization/function/scalar/SplineResponseSurface.hpp
optimization/src/sgpp/optimization/function/scalar/SplineResponseSurface.cpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ SplineResponseSurface() [1/3]

◆ SplineResponseSurface() [2/3]

◆ SplineResponseSurface() [3/3]

◆ ~SplineResponseSurface()

Member Function Documentation

◆ eval()

◆ evalGradient()

◆ getCoefficients()

◆ getGrid()

◆ getIntegral()

◆ getLowerBounds()

◆ getMean()

◆ getSize()

◆ getUpperBounds()

◆ getVariance()

◆ nextSurplusAdaptiveGrid()

◆ optimize()

◆ refineSurplusAdaptive()

◆ regular()

◆ regularByPoints()

◆ ritterNovak()

◆ surplusAdaptive()