This evaluator calculates the scalar products int b_i(x) b_j(x) dx for B splines b_i and b_j. More...

#include <BSplineScalarProductEvaluator.hpp>

Inheritance diagram for sgpp::combigrid::BSplineScalarProductEvaluator:

Public Member Functions
	BSplineScalarProductEvaluator ()

	BSplineScalarProductEvaluator (size_t degree)

	BSplineScalarProductEvaluator (size_t degree, sgpp::combigrid::SingleFunction weight_function, double a=0, double b=1, bool normalizeWeights=true, size_t numAdditionalPoints=0)

	BSplineScalarProductEvaluator (BSplineScalarProductEvaluator const &other)

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	getBounds (double &a, double &b) override

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

bool	hasCustomWeightFunction () override

bool	needsOrderedPoints () override

bool	needsParameter () override

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

void	setBounds (double a, double b) override

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...

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

virtual	~BSplineScalarProductEvaluator ()

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	~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(x) b_j(x) dx for B splines b_i and 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

◆ BSplineScalarProductEvaluator() [1/4]

sgpp::combigrid::BSplineScalarProductEvaluator::BSplineScalarProductEvaluator ( )

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

Referenced by cloneLinear().

◆ BSplineScalarProductEvaluator() [2/4]

sgpp::combigrid::BSplineScalarProductEvaluator::BSplineScalarProductEvaluator ( size_t degree )

explicit

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

◆ BSplineScalarProductEvaluator() [3/4]

sgpp::combigrid::BSplineScalarProductEvaluator::BSplineScalarProductEvaluator	(	size_t	degree,
		sgpp::combigrid::SingleFunction	weight_function,
		double	a = `0`,
		double	b = `1`,
		bool	normalizeWeights = `true`,
		size_t	numAdditionalPoints = `0`
	)

Parameters

degree	degree of the B spline basis
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.
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.
a	lower bound of bounding box
b	upper bound of bounding box
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::EvaluatorConfiguration::degree, sgpp::combigrid::AbstractEvaluator< FloatArrayVector >::evalConfig, sgpp::combigrid::Multi_BSplineScalarProduct, and sgpp::combigrid::EvaluatorConfiguration::type.

◆ BSplineScalarProductEvaluator() [4/4]

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

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

◆ ~BSplineScalarProductEvaluator()

sgpp::combigrid::BSplineScalarProductEvaluator::~BSplineScalarProductEvaluator ( )

virtual

Member Function Documentation

◆ cloneLinear()

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

overridevirtual

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

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

References BSplineScalarProductEvaluator().

Referenced by getBounds().

◆ getBasisCoefficients()

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

inlineoverridevirtual

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

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

◆ getBasisValues()

std::vector<FloatArrayVector> sgpp::combigrid::BSplineScalarProductEvaluator::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 >.

Referenced by sgpp::combigrid::BSplineInterpolationCoefficientEvaluator::setGridPoints().