integration_benchmarks.cpp File Reference

Benchmark suite for Monte Carlo integration algorithms. More...

#include "apps/benchmarks.hpp"
#include <montecarlo/integrators/ISintegrator.hpp>
#include <montecarlo/utils/muParserXInterface.hpp>
#include <montecarlo/rng/rng_global.hpp>
#include <cmath>
#include <cstdint>
#include <iostream>
#include <functional>
#include <limits>
#include <random>
#include <string>

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Functions
template<size_t dim, typename Func >
void	executeBenchmark (const std::string &title, const std::string &filename, mc::integrators::MontecarloIntegrator< dim > &integrator, const mc::domains::IntegrationDomain< dim > &domain, Func &&f, bool useGnuplot, const std::string &rawDataFile, const std::string &functionExpr)
	Generic execution loop for integration benchmarks.
template<typename Func >
void	runCircleBenchmark (Func f, const std::string &modeLabel, bool useGnuplot, const std::string &funcStr)
template<typename Func >
void	runSphereBenchmark (Func f, const std::string &modeLabel, bool useGnuplot, const std::string &funcStr)
template<typename Func >
void	runRectBenchmark (Func f, const std::string &modeLabel, bool useGnuplot, const std::string &funcStr)
template<typename Func >
void	runCylinderBenchmark (Func f, const std::string &modeLabel, bool useGnuplot, const std::string &funcStr)
void	circleIntegration (bool useGnuplot)
void	sphereIntegration (bool useGnuplot)
void	rectangularIntegration (bool useGnuplot)
void	cylinderIntegration (bool useGnuplot)
void	circleIntegrationParser (const std::string &expr, bool useGnuplot)
void	sphereIntegrationParser (const std::string &expr, bool useGnuplot)
void	rectangularIntegrationParser (const std::string &expr, bool useGnuplot)
void	cylinderIntegrationParser (const std::string &expr, bool useGnuplot)
void	runBenchmarks (bool useGnuplot)
	Run integration benchmarks with hardcoded integrands.
void	runBenchmarksMH ()
	Run Metropolis-Hastings MCMC integration benchmarks.
void	runBenchmarks (const std::string &expression, bool useGnuplot)
	Run integration benchmarks with custom mathematical expression.

Detailed Description

Benchmark suite for Monte Carlo integration algorithms.

Comprehensive evaluation of integration accuracy and performance across:

• Multiple algorithms: Uniform MC, Importance Sampling, MCMC
• Various dimensions: 1D through 12D
• Different domain types: rectangles, spheres, cylinders, hyperrectangles
• Parser-based and hardcoded function expressions

Methodology:

• Sweep across sample counts (logarithmic scale)
• Time execution of each integration
• Compute error relative to analytical reference when available
• Generate CSV output for statistical analysis
• Produce Gnuplot scripts for visualization

Key Benchmarks:

• uniDimIntegration(): ∫₀¹ x² dx = 1/3
• circleIntegration(): ∫ (x²+y²) dA over unit disk
• sphereIntegration(): ∫ (x²+y²+z²) dV over unit ball
• Higher-dimensional tests to study curse of dimensionality

See also

runBenchmarks(), executeBenchmark(), saveResults()

Definition in file integration_benchmarks.cpp.

Function Documentation

circleIntegration()

void circleIntegration

(

bool

useGnuplot

)

Definition at line 213 of file integration_benchmarks.cpp.

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circleIntegrationParser()

void circleIntegrationParser	(	const std::string &	expr,
		bool	useGnuplot
	)

Definition at line 242 of file integration_benchmarks.cpp.

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cylinderIntegration()

void cylinderIntegration

(

bool

useGnuplot

)

Definition at line 231 of file integration_benchmarks.cpp.

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cylinderIntegrationParser()

void cylinderIntegrationParser	(	const std::string &	expr,
		bool	useGnuplot
	)

Definition at line 278 of file integration_benchmarks.cpp.

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executeBenchmark()

template<size_t dim, typename Func >

void executeBenchmark	(	const std::string &	title,
		const std::string &	filename,
		mc::integrators::MontecarloIntegrator< dim > &	integrator,
		const mc::domains::IntegrationDomain< dim > &	domain,
		Func &&	f,
		bool	useGnuplot,
		const std::string &	rawDataFile,
		const std::string &	functionExpr
	)

Generic execution loop for integration benchmarks.

Template Parameters

dim	Dimensionality of the integration domain.
Func	Function type (integrand).

Parameters

title	Display title for the benchmark
filename	Output CSV filename
integrator	Integration engine to benchmark
domain	Integration domain (used for visualization)
f	Integrand function
useGnuplot	If true, generate visualization script
rawDataFile	Raw data filename for plotting
functionExpr	String representation of the integrand

GENERIC execution loop. Runs the integration for increasing sample sizes, measures time, plots results, and saves to file.

Definition at line 57 of file integration_benchmarks.cpp.

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rectangularIntegration()

void rectangularIntegration

(

bool

useGnuplot

)

Definition at line 225 of file integration_benchmarks.cpp.

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rectangularIntegrationParser()

void rectangularIntegrationParser	(	const std::string &	expr,
		bool	useGnuplot
	)

Definition at line 266 of file integration_benchmarks.cpp.

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runBenchmarks() [1/2]

void runBenchmarks

(

bool

useGnuplot

)

Run integration benchmarks with hardcoded integrands.

Parameters

useGnuplot

If true, generate gnuplot script for visualization.

Definition at line 292 of file integration_benchmarks.cpp.

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runBenchmarks() [2/2]

void runBenchmarks	(	const std::string &	expression,
		bool	useGnuplot
	)

Run integration benchmarks with custom mathematical expression.

Parameters

expression	Mathematical function string (muParserX syntax)
useGnuplot	If true, generate gnuplot script

Definition at line 449 of file integration_benchmarks.cpp.

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runBenchmarksMH()

void runBenchmarksMH

(

)

Run Metropolis-Hastings MCMC integration benchmarks.

Definition at line 309 of file integration_benchmarks.cpp.

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runCircleBenchmark()

template<typename Func >

void runCircleBenchmark	(	Func	f,
		const std::string &	modeLabel,
		bool	useGnuplot,
		const std::string &	funcStr
	)

Definition at line 160 of file integration_benchmarks.cpp.

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runCylinderBenchmark()

template<typename Func >

void runCylinderBenchmark	(	Func	f,
		const std::string &	modeLabel,
		bool	useGnuplot,
		const std::string &	funcStr
	)

Definition at line 195 of file integration_benchmarks.cpp.

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runRectBenchmark()

template<typename Func >

void runRectBenchmark	(	Func	f,
		const std::string &	modeLabel,
		bool	useGnuplot,
		const std::string &	funcStr
	)

Definition at line 183 of file integration_benchmarks.cpp.

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runSphereBenchmark()

template<typename Func >

void runSphereBenchmark	(	Func	f,
		const std::string &	modeLabel,
		bool	useGnuplot,
		const std::string &	funcStr
	)

Definition at line 171 of file integration_benchmarks.cpp.

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sphereIntegration()

void sphereIntegration

(

bool

useGnuplot

)

Definition at line 219 of file integration_benchmarks.cpp.

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sphereIntegrationParser()

void sphereIntegrationParser	(	const std::string &	expr,
		bool	useGnuplot
	)

Definition at line 254 of file integration_benchmarks.cpp.

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