sgpp::optimization::ResponseSurface Class Reference

General response surface. More...

#include <ResponseSurface.hpp>

Inheritance diagram for sgpp::optimization::ResponseSurface:

Public Member Functions
virtual double	eval (sgpp::base::DataVector v)
	evaluates the response surface [Attention: this is not alway simply "interpolant->eval".
virtual double	evalGradient (sgpp::base::DataVector v, sgpp::base::DataVector &gradient)=0
	evaluates the response surface and its gradient
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.

Protected Member Functions
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
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

General response surface.

Represents an approximation of some function. Usually the approximation is created via interpolation. (But could also be regression for example)

Constructor & Destructor Documentation

ResponseSurface()

sgpp::optimization::ResponseSurface::ResponseSurface ( size_t  numDim )

inlineexplicit

Constructor.

~ResponseSurface()

virtual sgpp::optimization::ResponseSurface::~ResponseSurface ( )

inlinevirtual

Destructor.

Member Function Documentation

domainVolume()

double sgpp::optimization::ResponseSurface::domainVolume ( )

protected

calculates the volume of the tensor product domain given by lb and ub

Returns

volume

References lb, numDim, and ub.

Referenced by sgpp::optimization::SplineResponseSurface::getIntegral().

eval()

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

virtual

evaluates the response surface [Attention: this is not alway simply "interpolant->eval".

In context of active subspaces, for example, the argument v must first be transformed to the active subspace]

Parameters

v	point in which the response surface shall be evaulated

Returns

evaluation

Reimplemented in sgpp::optimization::SplineResponseSurface.

References interpolant.

Referenced by python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis::estimateDensity(), l2Error(), nrmsError(), and nrmsErrorFromTestData().

evalGradient()

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

pure virtual

evaluates the response surface and its gradient

Parameters

v	point in which the response surface shall be evaluated
gradient	reference to return the gradient evaluated in v

Returns

evaluation

Implemented in sgpp::optimization::SplineResponseSurface.

l2Error()

double sgpp::optimization::ResponseSurface::l2Error	(	std::shared_ptr< sgpp::base::ScalarFunction >	objectiveFunc,
		size_t	numMCPoints = 1000
	)

Calculates the l2 error between interpolant and objective function.

Parameters

objectiveFunc	the objectiveFunction
numMCPoints	number of Monte Carlo Points

Returns

l2 error

References eval(), sgpp::base::RandomNumberGenerator::getInstance(), sgpp::base::RandomNumberGenerator::getUniformRN(), lb, numDim, and ub.

nrmsError()

sgpp::base::DataVector sgpp::optimization::ResponseSurface::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.

Parameters

objectiveFunc	the objectiveFunction
numMCPoints	number of Monte Carlo Points

Returns

vector [NRMSE, l2 error, min, max]

References eval(), sgpp::base::RandomNumberGenerator::getInstance(), sgpp::base::RandomNumberGenerator::getUniformRN(), lb, numDim, and ub.

nrmsErrorFromTestData()

sgpp::base::DataVector sgpp::optimization::ResponseSurface::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)

Parameters

fileName	path to the stored data set
numMCPoints	the first numMCPoints of the data set are used
numDim	number of dimensions

Returns

vector [NRMSE, l2 error, min, max]

References eval(), fileName, sgpp::base::DataMatrix::fromFile(), and numDim.

precalculateErrorTestData()

void sgpp::optimization::ResponseSurface::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.

Parameters

objectiveFunc	the objective function
numMCPoints	number of Monte carlo Points
fileName	path specifying where to save the generated data

References fileName, sgpp::base::RandomNumberGenerator::getInstance(), sgpp::base::RandomNumberGenerator::getUniformRN(), lb, numDim, and ub.

transformPoint()

void sgpp::optimization::ResponseSurface::transformPoint ( sgpp::base::DataVector &  v, sgpp::base::DataVector  lBounds, sgpp::base::DataVector  uBounds, sgpp::base::DataVector  newlBounds, sgpp::base::DataVector  newuBounds  )

protected

transforms a point in hyper-rectangle [lBounds,rBounds] to the hyper-rectangle [newlBounds,newuBounds]

Parameters

v	point in [lBounds,uBounds]
lBounds	lower bounds
uBounds	upper bounds
newlBounds	new lower bounds
newuBounds	new upper bounds

References sgpp::base::DataVector::add(), sgpp::base::DataVector::componentwise_div(), sgpp::base::DataVector::componentwise_mult(), and sgpp::base::DataVector::sub().

Referenced by sgpp::optimization::SplineResponseSurface::eval(), sgpp::optimization::SplineResponseSurface::evalGradient(), and sgpp::optimization::SplineResponseSurface::optimize().

Member Data Documentation

interpolant

std::shared_ptr<sgpp::base::ScalarFunction> sgpp::optimization::ResponseSurface::interpolant

protected

Referenced by eval(), sgpp::optimization::SplineResponseSurface::eval(), sgpp::optimization::SplineResponseSurface::optimize(), sgpp::optimization::SplineResponseSurface::regular(), sgpp::optimization::SplineResponseSurface::regularByPoints(), sgpp::optimization::SplineResponseSurface::ritterNovak(), sgpp::optimization::SplineResponseSurface::SplineResponseSurface(), sgpp::optimization::SplineResponseSurface::SplineResponseSurface(), and sgpp::optimization::SplineResponseSurface::surplusAdaptive().

interpolantGradient

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

protected

Referenced by sgpp::optimization::SplineResponseSurface::evalGradient(), sgpp::optimization::SplineResponseSurface::optimize(), sgpp::optimization::SplineResponseSurface::regular(), sgpp::optimization::SplineResponseSurface::regularByPoints(), sgpp::optimization::SplineResponseSurface::ritterNovak(), sgpp::optimization::SplineResponseSurface::SplineResponseSurface(), sgpp::optimization::SplineResponseSurface::SplineResponseSurface(), and sgpp::optimization::SplineResponseSurface::surplusAdaptive().

lb

sgpp::base::DataVector sgpp::optimization::ResponseSurface::lb

protected

Referenced by domainVolume(), sgpp::optimization::SplineResponseSurface::eval(), sgpp::optimization::SplineResponseSurface::evalGradient(), sgpp::optimization::SplineResponseSurface::getLowerBounds(), l2Error(), nrmsError(), sgpp::optimization::SplineResponseSurface::optimize(), precalculateErrorTestData(), sgpp::optimization::SplineResponseSurface::SplineResponseSurface(), sgpp::optimization::SplineResponseSurface::SplineResponseSurface(), and sgpp::optimization::SplineResponseSurface::SplineResponseSurface().

numDim

size_t sgpp::optimization::ResponseSurface::numDim

protected

Referenced by domainVolume(), l2Error(), nrmsError(), nrmsErrorFromTestData(), sgpp::optimization::SplineResponseSurface::optimize(), precalculateErrorTestData(), sgpp::optimization::SplineResponseSurface::SplineResponseSurface(), sgpp::optimization::SplineResponseSurface::SplineResponseSurface(), and sgpp::optimization::SplineResponseSurface::SplineResponseSurface().

ub

sgpp::base::DataVector sgpp::optimization::ResponseSurface::ub

protected

Referenced by domainVolume(), sgpp::optimization::SplineResponseSurface::eval(), sgpp::optimization::SplineResponseSurface::evalGradient(), sgpp::optimization::SplineResponseSurface::getUpperBounds(), l2Error(), nrmsError(), sgpp::optimization::SplineResponseSurface::optimize(), precalculateErrorTestData(), sgpp::optimization::SplineResponseSurface::SplineResponseSurface(), sgpp::optimization::SplineResponseSurface::SplineResponseSurface(), and sgpp::optimization::SplineResponseSurface::SplineResponseSurface().

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

• optimization/src/sgpp/optimization/function/scalar/ResponseSurface.hpp
• optimization/src/sgpp/optimization/function/scalar/ResponseSurface.cpp