sgpp::quadrature::OperationQuadratureMCAdvanced Class Reference

Quadrature on any sparse grid (that has OperationMultipleEval implemented) using various Monte Carlo Methods (Advanced). More...

#include <OperationQuadratureMCAdvanced.hpp>

Inheritance diagram for sgpp::quadrature::OperationQuadratureMCAdvanced:

Public Member Functions
virtual double	doQuadrature (sgpp::base::DataVector &alpha)
	Quadrature using advanced MC in \(\Omega=[0,1]^d\). More...
double	doQuadratureFunc (FUNC func, void *clientdata)
	Quadrature of an arbitrary function using advanced MC in \(\Omega=[0,1]^d\). More...
double	doQuadratureL2Error (FUNC func, void *clientdata, sgpp::base::DataVector &alpha)
	Quadrature of the \(L^2\)-norm of the error, \( ||f(x)-u(x)||_{L^2} \), between a given function and the current sparse grid function using advanced MC in \(\Omega=[0,1]^d\). More...
size_t	getDimensions ()
	Method returns the total number of samples which can be generated according to the sample generator settings (dimensions and subdivision into strata) More...
	OperationQuadratureMCAdvanced (sgpp::base::Grid &grid, size_t numberOfSamples, std::uint64_t seed=std::mt19937_64::default_seed)
	Constructor of OperationQuadratureMCAdvanced, specifying a grid object and the number of samples to use. More...
	OperationQuadratureMCAdvanced (size_t dimensions, size_t numberOfSamples, std::uint64_t seed=std::mt19937_64::default_seed)
	Constructor of OperationQuadratureMCAdvanced, specifying dimensions and the number of samples to use. More...
void	useLatinHypercubeMonteCarlo ()
	Initialize SampleGenerator for LatinHypercubeMC. More...
void	useNaiveMonteCarlo ()
	Initialize SampleGenerator for NaiveMC. More...
void	useQuasiMonteCarloWithHaltonSequences ()
	Initialize SampleGenerator for HaltonSequenceGenerator. More...
void	useQuasiMonteCarloWithScrambledSobolSequences ()
	Initialize SampleGenerator for ScrambledSobolSequenceGenerator. More...
void	useQuasiMonteCarloWithSobolSequences ()
	Initialize SampleGenerator for SobolSequenceGenerator. More...
void	useStratifiedMonteCarlo (std::vector< size_t > &n)
	Initialize SampleGenerator for StratifiedMC. More...
virtual	~OperationQuadratureMCAdvanced ()
	Descructor. More...
Public Member Functions inherited from sgpp::base::OperationQuadrature
	OperationQuadrature ()
	Constructor. More...
virtual	~OperationQuadrature ()
	Destructor. More...

Protected Attributes
size_t	dimensions
sgpp::base::Grid *	grid
sgpp::quadrature::SampleGenerator *	myGenerator
size_t	numberOfSamples
std::uint64_t	seed

Detailed Description

Quadrature on any sparse grid (that has OperationMultipleEval implemented) using various Monte Carlo Methods (Advanced).

Constructor & Destructor Documentation

OperationQuadratureMCAdvanced() [1/2]

sgpp::quadrature::OperationQuadratureMCAdvanced::OperationQuadratureMCAdvanced	(	sgpp::base::Grid &	grid,
		size_t	numberOfSamples,
		std::uint64_t	seed = std::mt19937_64::default_seed
	)

Constructor of OperationQuadratureMCAdvanced, specifying a grid object and the number of samples to use.

Parameters

grid	Reference to the grid object
numberOfSamples	Number of Monte Carlo samples
seed	Custom seed (defaults to default seed of mt19937_64)

References dimensions, sgpp::base::Grid::getDimension(), and myGenerator.

OperationQuadratureMCAdvanced() [2/2]

sgpp::quadrature::OperationQuadratureMCAdvanced::OperationQuadratureMCAdvanced	(	size_t	dimensions,
		size_t	numberOfSamples,
		std::uint64_t	seed = std::mt19937_64::default_seed
	)

Constructor of OperationQuadratureMCAdvanced, specifying dimensions and the number of samples to use.

Parameters

dimensions	dimensionality of this problem
numberOfSamples	Number of Monte Carlo samples
seed	Custom seed (defaults to default seed of mt19937_64)

References myGenerator.

~OperationQuadratureMCAdvanced()

sgpp::quadrature::OperationQuadratureMCAdvanced::~OperationQuadratureMCAdvanced ( )

virtual

Descructor.

References myGenerator.

Member Function Documentation

doQuadrature()

double sgpp::quadrature::OperationQuadratureMCAdvanced::doQuadrature ( sgpp::base::DataVector &  alpha )

virtual

Quadrature using advanced MC in \(\Omega=[0,1]^d\).

Parameters

alpha

Coefficient vector for current grid

Implements sgpp::base::OperationQuadrature.

References sgpp::op_factory::createOperationMultipleEval(), dimensions, sgpp::quadrature::SampleGenerator::getSamples(), grid, sgpp::base::OperationMultipleEval::mult(), myGenerator, numberOfSamples, and sgpp::base::DataVector::sum().

doQuadratureFunc()

double sgpp::quadrature::OperationQuadratureMCAdvanced::doQuadratureFunc	(	FUNC	func,
		void *	clientdata
	)

Quadrature of an arbitrary function using advanced MC in \(\Omega=[0,1]^d\).

Parameters

func	The function to integrate
clientdata	Optional data to pass to FUNC

References dimensions, sgpp::base::DataVector::getPointer(), sgpp::base::DataMatrix::getRow(), sgpp::quadrature::SampleGenerator::getSamples(), python.statsfileInfo::i, myGenerator, and numberOfSamples.

doQuadratureL2Error()

double sgpp::quadrature::OperationQuadratureMCAdvanced::doQuadratureL2Error	(	FUNC	func,
		void *	clientdata,
		sgpp::base::DataVector &	alpha
	)

Quadrature of the \(L^2\)-norm of the error, \( ||f(x)-u(x)||_{L^2} \), between a given function and the current sparse grid function using advanced MC in \(\Omega=[0,1]^d\).

Parameters

func	The function \(f(x)\)
clientdata	Optional data to pass to FUNC
alpha	Coefficient vector for current grid

References sgpp::op_factory::createOperationEval(), dimensions, sgpp::base::OperationEval::eval(), sgpp::base::DataMatrix::get(), sgpp::quadrature::SampleGenerator::getSamples(), grid, python.statsfileInfo::i, myGenerator, numberOfSamples, friedman::p, chess::point, and sgpp::combigrid::pow().

getDimensions()

size_t sgpp::quadrature::OperationQuadratureMCAdvanced::getDimensions

(

)

Method returns the total number of samples which can be generated according to the sample generator settings (dimensions and subdivision into strata)

Returns

size_t dimension of samples

References dimensions.

useLatinHypercubeMonteCarlo()

void sgpp::quadrature::OperationQuadratureMCAdvanced::useLatinHypercubeMonteCarlo

(

)

Initialize SampleGenerator for LatinHypercubeMC.

References dimensions, myGenerator, numberOfSamples, and seed.

useNaiveMonteCarlo()

void sgpp::quadrature::OperationQuadratureMCAdvanced::useNaiveMonteCarlo

(

)

Initialize SampleGenerator for NaiveMC.

References dimensions, myGenerator, and seed.

useQuasiMonteCarloWithHaltonSequences()

void sgpp::quadrature::OperationQuadratureMCAdvanced::useQuasiMonteCarloWithHaltonSequences

(

)

Initialize SampleGenerator for HaltonSequenceGenerator.

References dimensions, and myGenerator.

useQuasiMonteCarloWithScrambledSobolSequences()

void sgpp::quadrature::OperationQuadratureMCAdvanced::useQuasiMonteCarloWithScrambledSobolSequences

(

)

Initialize SampleGenerator for ScrambledSobolSequenceGenerator.

useQuasiMonteCarloWithSobolSequences()

void sgpp::quadrature::OperationQuadratureMCAdvanced::useQuasiMonteCarloWithSobolSequences

(

)

Initialize SampleGenerator for SobolSequenceGenerator.

useStratifiedMonteCarlo()

void sgpp::quadrature::OperationQuadratureMCAdvanced::useStratifiedMonteCarlo

(

std::vector< size_t > &

n

)

Initialize SampleGenerator for StratifiedMC.

Parameters

n	Array of dimension proerties

References myGenerator, and seed.

Member Data Documentation

dimensions

size_t sgpp::quadrature::OperationQuadratureMCAdvanced::dimensions

protected

Referenced by doQuadrature(), doQuadratureFunc(), doQuadratureL2Error(), getDimensions(), OperationQuadratureMCAdvanced(), useLatinHypercubeMonteCarlo(), useNaiveMonteCarlo(), and useQuasiMonteCarloWithHaltonSequences().

grid

sgpp::base::Grid* sgpp::quadrature::OperationQuadratureMCAdvanced::grid

protected

Referenced by python.uq.learner.Interpolant.Interpolant::doLearningIteration(), doQuadrature(), doQuadratureL2Error(), python.learner.Classifier.Classifier::evalError(), python.uq.learner.Interpolant.Interpolant::evalError(), python.uq.learner.SimulationLearner.SimulationLearner::getCollocationNodes(), python.uq.learner.SimulationLearner.SimulationLearner::getGrid(), python.uq.learner.SimulationLearner.SimulationLearner::getLearner(), python.uq.learner.Regressor.Regressor::learnData(), python.uq.learner.Regressor.Regressor::learnDataWithFolding(), python.uq.learner.Regressor.Regressor::learnDataWithTest(), python.learner.Classifier.Classifier::refineGrid(), python.learner.Regressor.Regressor::refineGrid(), python.uq.learner.Regressor.Regressor::refineGrid(), python.uq.learner.SimulationLearner.SimulationLearner::refineGrid(), python.learner.Classifier.Classifier::updateResults(), python.learner.Regressor.Regressor::updateResults(), and python.uq.learner.Regressor.Regressor::updateResults().

myGenerator

sgpp::quadrature::SampleGenerator* sgpp::quadrature::OperationQuadratureMCAdvanced::myGenerator

protected

Referenced by doQuadrature(), doQuadratureFunc(), doQuadratureL2Error(), OperationQuadratureMCAdvanced(), useLatinHypercubeMonteCarlo(), useNaiveMonteCarlo(), useQuasiMonteCarloWithHaltonSequences(), useStratifiedMonteCarlo(), and ~OperationQuadratureMCAdvanced().

numberOfSamples

size_t sgpp::quadrature::OperationQuadratureMCAdvanced::numberOfSamples

protected

Referenced by doQuadrature(), doQuadratureFunc(), doQuadratureL2Error(), and useLatinHypercubeMonteCarlo().

seed

std::uint64_t sgpp::quadrature::OperationQuadratureMCAdvanced::seed

protected

Referenced by useLatinHypercubeMonteCarlo(), useNaiveMonteCarlo(), and useStratifiedMonteCarlo().

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

• quadrature/src/sgpp/quadrature/operation/hash/OperationQuadratureMCAdvanced.hpp
• quadrature/src/sgpp/quadrature/operation/hash/OperationQuadratureMCAdvanced.cpp