celeritas::NormalDistribution< RealType > Class Template Reference

Sample from a normal distribution. More...

#include <NormalDistribution.hh>

Public Types
Type aliases
using	real_type = RealType
using	result_type = real_type
using	RecordT = NormalDistributionRecord

Public Member Functions
	NormalDistribution (real_type mean, real_type stddev)
	Construct with mean and standard deviation.
	NormalDistribution (real_type mean)
	Construct with unit deviation.
	NormalDistribution (RecordT const &record)
	NormalDistribution ()
	Construct with unit deviation and zero mean.
template<class Generator >
result_type	operator() (Generator &rng)
template<class Generator >
auto	operator() (Generator &rng) -> result_type
	Sample a random number according to the distribution.

Detailed Description

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

Sample from a normal distribution.

The normal (Gaussian) distribution is

\[ p(x) = \exp\!\left( -\frac{(x - \mu)^{2}}{2\sigma^{2}} \right) \]

with mean \(\mu\) and standard deviation \(\sigma\).

This implementation uses the Box-Muller transform to generate pairs of independent, normally distributed random numbers, and returns them one at a time. Two random numbers uniformly distributed on [0, 1] are mapped to two independent, standard, normally distributed samples using the relations:

\[ x_1 = \sqrt{-2 \ln \xi_1} \cos(2 \pi \xi_2) x_2 = \sqrt{-2 \ln \xi_1} \sin(2 \pi \xi_2) \]

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

• NormalDistribution.hh