gamma#

Generates Gamma distributed random numbers.

Description#

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

The probability distribution is given by:

\[\begin{split}f_{a, \alpha, \beta}(x) = \left\{ \begin{array}{rcl} \frac{1}{\Gamma(\alpha)\beta^{\alpha}}(x - a)^{\alpha - 1}e^{-(x - a) / \beta}, x \ge a \\ 0, x < a \end{array}\right.\end{split}\]

The cumulative distribution function is as follows:

\[\begin{split}F_{a, \alpha, \beta}(x) = \left\{ \begin{array}{rcl} \int^x_a\frac{1}{\Gamma(\alpha)\beta^{\alpha}}(y - a)^{\alpha - 1}e^{-(y - a) / \beta}dy, x \ge a \\ 0, x < a \end{array}\right.\end{split}\]

API#

Syntax#

namespace oneapi::mkl::rng::device {
  template<typename RealType, typename Method>
  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;
    std::size_t count_rejected_numbers() const;
    void param(const param_type& pt);
  };
}

Include Files#

  • oneapi/mkl/rng/device.hpp

Template Parameters#

typename Type

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

  • float

  • double

typename Method

Generation method. The specific values are as follows:

  • oneapi::mkl::rng::device::gamma_method::by_default

  • oneapi::mkl::rng::device::gamma_method::marsaglia

  • oneapi::mkl::rng::device::gamma_method::marsaglia_accurate

See brief descriptions of the methods in Distributions Template Parameter Method

Note

To enable extra optimizations based on Vector Math functions, define the MKL_RNG_USE_BINARY_CODE macro and link static oneMKL libraries according to the output produced by Intel® oneAPI Math Kernel Library Link Line Advisor. It may improve performance on some hardware.

Input Parameters#

Name

Type

Description

alpha

RealType (float, double)

Shape \(\alpha\).

a

RealType (float, double)

Displacement a.

beta

RealType (float, double)

Scalefactor \(\beta\).

Special methods#

std::size_t count_rejected_numbers() const

Returns the amount of random numbers that were rejected during the last generate function call. If no generate calls, returns 0.