rayleigh

oneMKL - Data Parallel C++ Developer Reference

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ID 772045

Date 10/15/2026

Version

Public

rayleigh

Generates Rayleigh distributed random values.

Description
API

Description

The oneapi::mkl::rng::rayleigh class object is used by the oneapi::mkl::rng::generate function to provide Rayleigh distributed random numbers with displacement (a) and scalefactor (b, β), where \(a, \beta \in R ; \beta > 0\).

The Rayleigh distribution is a special case of the Weibull distribution, where the shape parameter \(\alpha = 2\).

The probability density function is given by:

\[\begin{split}f_{a, \beta}(x) = \begin{cases} \frac{2(x-a)}{\beta^2} \exp (-\frac{(x-a)^2}{\beta^2}), & x \geq a \\ 0, & x < a \end{cases}, - \infty < x < + \infty\end{split}\]

The cumulative distribution function is as follows:

\[\begin{split}F_{\alpha, \beta} (x) = \begin{cases} 1 - \exp\left(-\frac{(x-\alpha)^2}{\beta^2}\right), & x \geq \alpha) \\ 0, & x < \alpha \end{cases}, - \infty < x < + \infty\end{split}\]

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

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

    rayleigh(): rayleigh((RealType)0.0, (RealType)1.0){}
    explicit rayleigh(RealType a, RealType b);
    explicit rayleigh(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

typename RealType = float

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

float

double

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

Generation method. The specific values are as follows:

oneapi::mkl::rng::rayleigh_method::icdf

oneapi::mkl::rng::rayleigh_method::icdf_accurate

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`.

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oneMKL - Data Parallel C++ Developer Reference

rayleigh

Description

API