This evaluator calculates the scalar products \(\int b_i b_j\). More...

#include <PolynomialScalarProductEvaluator.hpp>

Inheritance diagram for sgpp::combigrid::PolynomialScalarProductEvaluator:

Public Member Functions
std::shared_ptr< AbstractLinearEvaluator< FloatArrayVector > >	cloneLinear () override
	Clones this object and returns it as a shared pointer to AbstractLinearEvaluator<V>. More...

std::vector< double >	getBasisCoefficients () override

std::vector< FloatArrayVector >	getBasisValues () override
	This method is specific to AbstractLinearEvaluator and has to be implemented by all subclasses. More...

void	initializeBounds (std::shared_ptr< sgpp::combigrid::OrthogonalPolynomialBasis1D > orthogBasis)

bool	needsOrderedPoints () override

bool	needsParameter () override

	PolynomialScalarProductEvaluator ()

	PolynomialScalarProductEvaluator (sgpp::combigrid::SingleFunction weight_function, bool normalizeWeights=true, size_t numAdditionalPoints=10)

	PolynomialScalarProductEvaluator (std::shared_ptr< sgpp::combigrid::OrthogonalPolynomialBasis1D > orthogBasis)

	PolynomialScalarProductEvaluator (PolynomialScalarProductEvaluator const &other)

void	setBasisCoefficientsAtGridPoints (std::vector< double > &functionValues) override
	set the basis coefficients for the linear combination. More...

void	setGridPoints (std::vector< double > const &newXValues) override
	Sets the grid points for evaluation. More...

void	setParameter (FloatArrayVector const &param) override
	Via this method, the parameter can be set. More...

virtual	~PolynomialScalarProductEvaluator ()

Public Member Functions inherited from sgpp::combigrid::AbstractLinearEvaluator< FloatArrayVector >
virtual std::shared_ptr< AbstractEvaluator< FloatArrayVector > >	clone ()
	Clones the AbstractEvaluator object. More...

virtual FloatArrayVector	eval ()
	AbstractLinearEvaluator provides a standard implementation of this method based on getBasisCoefficients(). More...

virtual void	getBounds (double &a, double &b)

virtual void	getWeightFunction (sgpp::combigrid::SingleFunction &weight_function)

virtual bool	hasCustomWeightFunction ()

virtual void	setBounds (double a, double b)

virtual void	setWeightFunction (sgpp::combigrid::SingleFunction weight_function)

virtual	~AbstractLinearEvaluator ()

Public Member Functions inherited from sgpp::combigrid::AbstractEvaluator< FloatArrayVector >
virtual EvaluatorConfiguration	getConfig ()
	(Currently not used). More...

virtual void	setConfig (EvaluatorConfiguration newEvalConfig)

void	setLevel (size_t level)
	This is used to set the level in case an evaluator needs it. More...

virtual	~AbstractEvaluator ()

Additional Inherited Members
Protected Attributes inherited from sgpp::combigrid::AbstractEvaluator< FloatArrayVector >
EvaluatorConfiguration	evalConfig

size_t	level

Detailed Description

This evaluator calculates the scalar products \(\int b_i b_j\).

This is done via quadrature based on the given grid points. The quadrature weights are obtained by (numerically) integrating the Lagrange polynomials on the given grid points. In the constructor, a weight function may be passed whose values at the grid points are multiplied with the given function values.

Constructor & Destructor Documentation

◆ PolynomialScalarProductEvaluator() [1/4]

sgpp::combigrid::PolynomialScalarProductEvaluator::PolynomialScalarProductEvaluator ( )

References sgpp::combigrid::AbstractEvaluator< FloatArrayVector >::evalConfig, sgpp::combigrid::Multi_PolynomialScalarProduct, and sgpp::combigrid::EvaluatorConfiguration::type.

◆ PolynomialScalarProductEvaluator() [2/4]

sgpp::combigrid::PolynomialScalarProductEvaluator::PolynomialScalarProductEvaluator	(	sgpp::combigrid::SingleFunction	weight_function,
		bool	normalizeWeights = `true`,
		size_t	numAdditionalPoints = `10`
	)

Parameters

numAdditionalPoints	Specifies how many Gauss-Legrendre points should be used in addition to the default when integrating the Lagrange polynomials for computing the quadrature weights. This number should be higher if the weight function is hard to integrate.
weight_function	optional weight function w that can be included in the quadrature weights. The Quadrature evaluator then approximates the integral of f*w instead of the integral of f. This provides more precision by calling w more often than f, which might be useful if w can be evaluated much faster than f.
normalizeWeights	If this is set to true, the weights are normalized so that they sum up to 1. This might be useful if the weight function is (or should be) a probability distribution on the domain.

References sgpp::combigrid::AbstractEvaluator< FloatArrayVector >::evalConfig, sgpp::combigrid::Multi_PolynomialScalarProduct, and sgpp::combigrid::EvaluatorConfiguration::type.

◆ PolynomialScalarProductEvaluator() [3/4]

sgpp::combigrid::PolynomialScalarProductEvaluator::PolynomialScalarProductEvaluator ( std::shared_ptr< sgpp::combigrid::OrthogonalPolynomialBasis1D > orthogBasis )

References sgpp::combigrid::AbstractEvaluator< FloatArrayVector >::evalConfig, initializeBounds(), sgpp::combigrid::Multi_PolynomialScalarProduct, and sgpp::combigrid::EvaluatorConfiguration::type.

◆ PolynomialScalarProductEvaluator() [4/4]

sgpp::combigrid::PolynomialScalarProductEvaluator::PolynomialScalarProductEvaluator ( PolynomialScalarProductEvaluator const & other )

References sgpp::combigrid::AbstractEvaluator< FloatArrayVector >::evalConfig, sgpp::combigrid::Multi_PolynomialScalarProduct, and sgpp::combigrid::EvaluatorConfiguration::type.

◆ ~PolynomialScalarProductEvaluator()

sgpp::combigrid::PolynomialScalarProductEvaluator::~PolynomialScalarProductEvaluator ( )

virtual

Member Function Documentation

◆ cloneLinear()

std::shared_ptr< AbstractLinearEvaluator< FloatArrayVector > > sgpp::combigrid::PolynomialScalarProductEvaluator::cloneLinear ( )

overridevirtual

Clones this object and returns it as a shared pointer to AbstractLinearEvaluator<V>.

Implements sgpp::combigrid::AbstractLinearEvaluator< FloatArrayVector >.

Referenced by getBasisCoefficients().

◆ getBasisCoefficients()

std::vector<double> sgpp::combigrid::PolynomialScalarProductEvaluator::getBasisCoefficients ( )

inlineoverridevirtual

Implements sgpp::combigrid::AbstractLinearEvaluator< FloatArrayVector >.

References cloneLinear(), initializeBounds(), needsOrderedPoints(), needsParameter(), setBasisCoefficientsAtGridPoints(), setGridPoints(), and setParameter().

◆ getBasisValues()

std::vector<FloatArrayVector> sgpp::combigrid::PolynomialScalarProductEvaluator::getBasisValues ( )

inlineoverridevirtual

This method is specific to AbstractLinearEvaluator and has to be implemented by all subclasses.

It should return the coefficients used for the linear combination of function values. Example: If you want to do a linear interpolation and have the grid points 0.0 and 0.5 and an evaluation point (the parameter) of 0.2, you would return the weights (0.6, 0.4), because the interpolated value is 0.6 * f(0) + 0.4 * f(0.5).

In the case of multi-evaluation, this returns several coefficients for each grid point. Continuing the example above, if you would have evaluation points 0.2 and 0.4, the basis coefficients returned should be ((0.6, 0.2), (0.4, 0.8)).

Implements sgpp::combigrid::AbstractLinearEvaluator< FloatArrayVector >.

◆ initializeBounds()

void sgpp::combigrid::PolynomialScalarProductEvaluator::initializeBounds ( std::shared_ptr< sgpp::combigrid::OrthogonalPolynomialBasis1D > orthogBasis )

References sgpp::combigrid::FloatArrayVector::at(), sgpp::combigrid::LagrangePolynom::degree(), sgpp::combigrid::LagrangePolynom::evaluate(), sgpp::combigrid::GaussLegendreQuadrature::evaluate_iteratively(), sgpp::combigrid::LagrangePolynom::initialize(), and python.leja::points.

Referenced by getBasisCoefficients(), and PolynomialScalarProductEvaluator().