gumbel#

Generates Gumbel distributed random values.

Description#

The gumbel class object is used in the generate function to provide Gumbel distributed random numbers with displacement a and scalefactor (b, β), where \(a, \beta \in R ; \beta > 0\).

The probability density function is given by:

\[f_{a, \beta} (x) = \frac{1}{\beta} \exp \left( \frac{x-a}{\beta} \right) \exp ( - \exp \left( \frac{x-a}{\beta} \right) ), - \infty < x < + \infty\]

The cumulative distribution function is as follows:

\[F_{\alpha, \beta} (x) = 1 - \exp (- \exp(\frac{x - \alpha}{\beta})), - \infty < x < + \infty\]

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#

namespace oneapi::mkl::rng {
  template<typename RealType = float,
           typename Method = gumbel_method::by_default>
  class gumbel {
  public:
    using method_type = Method;
    using result_type = RealType;

    gumbel(): gumbel((RealType)0.0, (RealType)1.0){}
    explicit gumbel(RealType a, RealType b);
    explicit gumbel(const param_type& pt);

    RealType a() const;
    RealType b() const;
    param_type param() const;
    void param(const param_type& pt);
  };
}

Devices supported: CPU and GPU

Include Files#

  • oneapi/mkl/rng.hpp

Template Parameters#

Name

Description

typename RealType = float

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

float

double

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

Generation method. The specific values are as follows:

oneapi::mkl::rng::gumbel_method::icdf

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

Input Parameters#

Name

Type

Description

a

RealType (float, double)

Displacement a.

b

RealType (float, double)

Scalefactor b.