oneapi::mkl::rng::gamma

Generates gamma distributed random values.

Description

The oneapi::mkl::rng::gamma class object is used in the oneapi::mkl::rng::generate function to provide random numbers with gamma distribution that has shape parameter α, displacement a, and scale parameter β, where \(\alpha, \beta, and a \in R ; \alpha > 0, \beta > 0\).

The probability density function is given by:

\[\begin{split}f_{\alpha, a, \beta}(x) = \begin{cases} \frac{1}{\Gamma (\alpha) \beta^\alpha} (x - a)^{\alpha - 1} e^{-\frac{(x-a)}{\beta}}, & x \geq a \\ 0, & x < a \end{cases}, - \infty < x < + \infty\end{split}\]

where Γ(α) is the complete gamma function.

The cumulative distribution function is as follows:

\[\begin{split}F_{\alpha, a, \beta}(x) = \begin{cases} \int_{a}^{x} \frac{1}{\Gamma (\alpha) \beta^\alpha} (y - a)^{\alpha - 1} e^{-\frac{(y-a)}{\beta}} dy, & x \geq a \\ 0, & x < a \end{cases}, - \infty < x < + \infty\end{split}\]

Product and Performance Information

Performance varies by use, configuration and other factors. Learn more at https://www.intel.com/PerformanceIndex. Notice revision #20201201

API

Syntax

template<typename RealType = float, typename Method = gamma_method::by_default>
class gamma {
public:
  using method_type = Method; using result_type = RealType;
  gamma(): gamma((RealType)1.0, (RealType)0.0, (RealType)1.0){}
  explicit gamma(RealType alpha, RealType a, RealType beta);
  explicit gamma(const param_type& pt);
  RealType alpha() const;
  RealType a() const;
  RealType beta() const;
  param_type param() const;
  void param(const param_type& pt);
};

Devices supported: CPU and GPU.

Include Files

  • oneapi/mkl/rng.hpp

Template Parameters

typename RealType = float

Type of the produced values. The specific values are as follows:

float

double

typename Method = oneapi::mkl::rng::gamma_method::by_default

Generation method. The specific values are as follows:

oneapi::mkl::rng::gamma_method::marsaglia

oneapi::mkl::rng::gamma_method::marsaglia_accurate

See brief descriptions of the methods in Distributions Template Parameter Method.

Input Parameters

Name

Type

Description

alpha

RealType (float, double)

Shape α

a

RealType (float, double)

Displacement a.

beta

RealType (float, double)

Scalefactor β.