celeritas::RejectionSampler< RealType > Class Template Reference

Return whether a rejection loop needs to continue trying. More...

#include <RejectionSampler.hh>

Public Types
Type aliases
using	real_type = RealType
using	result_type = bool

Public Member Functions
constexpr	RejectionSampler (real_type fmax)
	Construct with acceptance probability and maximum probability.
constexpr	RejectionSampler ()
	Construct when the distribution's maximum is normalized.
template<class Generator >
bool	operator() (real_type f, Generator &rng) const
template<class Generator >
auto	operator() (real_type f, Generator &rng) const -> result_type
	Reject with a given probability.

Static Public Member Functions
static constexpr real_type	tolerance ()
	Allow a priori estimate of fmax to be slightly unconservative.

Detailed Description

template<class RealType = ::celeritas::real_type>
class celeritas::RejectionSampler< RealType >

Return whether a rejection loop needs to continue trying.

A common implementation of sampling from a "difficult" (non-analytically invertible) probability distribution function is to bound the difficult distribution f(x) with another easily sampled proposal distribution g(x) . Given a constant M such that \( f(x) < M g(x) \) over the x interval being sampled, it is equivalent to sampling f(x) by instead sampling from g(x) and rejecting with probability

\[ \frac{f(x)}{M g(x)} \]

.

This rejection sampler is constructed with the maximum M and is invoked with the sampled ratio \( f(x)/g(x) \) and an RNG. It allows an underestimate of the constant M by \( 10 \epsilon_\textrm{mach} \) which may result in an imperceptible bias against selecting the peak of the PDF.

These invocations generate statistically equivalent results:

• BernoulliDistribution(1 - p / pmax)(rng);
• !BernoulliDistribution(p / pmax)(rng);
• p < pmax * UniformDistribution{}(rng)
• RejectionSampler(pmax)(p, rng);

Example

This rejects over a cross section distribution with a known maximum bound.

RejectionSampler reject{xs_max}
do {
  xs = sample_xs(rng);
} while (reject(xs, rng));

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

• RejectionSampler.hh