Importance sampling Monte Carlo integrator. More...

Inheritance diagram for mc::integrators::ISMontecarloIntegrator< dim >:

Collaboration diagram for mc::integrators::ISMontecarloIntegrator< dim >:

Public Member Functions
	ISMontecarloIntegrator (const mc::domains::IntegrationDomain< dim > &d)
	Construct an importance sampling integrator.

double	integrate (const std::function< double(const mc::geom::Point< dim > &)> &f, int n_samples, const mc::proposals::Proposal< dim > &proposal, std::uint32_t seed) override
	Compute the integral using importance sampling.

Public Member Functions inherited from mc::integrators::Integrator< dim >
	Integrator (const mc::domains::IntegrationDomain< dim > &d)
	Constructs an integrator for a specific domain.

virtual	~Integrator ()=default
	Virtual destructor for proper polymorphic cleanup.

Additional Inherited Members
Protected Member Functions inherited from mc::integrators::Integrator< dim >
std::vector< mc::geom::Point< dim > >	initializeRandomizer (int numbers)
	Initializes random samples uniformly distributed in the domain.

Protected Attributes inherited from mc::integrators::Integrator< dim >
const mc::domains::IntegrationDomain< dim > &	domain
	Reference to the integration domain.

std::vector< std::mt19937 >	randomizer
	Per-thread random number generators.

Detailed Description

template<std::size_t dim>
class mc::integrators::ISMontecarloIntegrator< dim >

Importance sampling Monte Carlo integrator.

Template Parameters

dim	Dimensionality of the integration domain.

Computes the integral using importance sampling: ∫_Ω f(x) dx = ∫_Ω [f(x)/q(x)] · q(x) dx ≈ (1/N) ∑ᵢ [f(xᵢ)/q(xᵢ)]

where q(x) is a proposal distribution chosen to approximate f(x). This reduces variance compared to uniform sampling when q resembles f.

Note: The proposal should be chosen carefully to match the integrand's shape.

Definition at line 40 of file ISintegrator.hpp.

Constructor & Destructor Documentation

template<std::size_t dim>

mc::integrators::ISMontecarloIntegrator< dim >::ISMontecarloIntegrator ( const mc::domains::IntegrationDomain< dim > & d )

explicit

Construct an importance sampling integrator.

Parameters

d	Reference to the integration domain.

template<std::size_t dim>

double mc::integrators::ISMontecarloIntegrator< dim >::integrate	(	const std::function< double(const mc::geom::Point< dim > &)> &	f,
		int	n_samples,
		const mc::proposals::Proposal< dim > &	proposal,
		std::uint32_t	seed
	)

overridevirtual

Compute the integral using importance sampling.

Parameters

f	Integrand function: ℝⁿ → ℝ.
n_samples	Number of samples drawn from the proposal.
proposal	Custom sampling distribution q(x). Should approximate f(x) to minimize variance.
seed	Random seed for reproducibility.

Uses ISMeanEstimator to compute weighted average: (1/N) ∑ᵢ [f(xᵢ)/q(xᵢ)] where xᵢ ~ q.

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