oneapi::mkl::rng::cauchy

Generates Cauchy distributed random values.

Description

The oneapi::mkl::rng::cauchy class object is used in the oneapi::mkl::rng::generate function to provide Cauchy 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}
{\pi \beta
\left(
   1 + {\left( \frac{x-a}{\beta} \right)}^2
\right)},
- \infty < x < + \infty

The cumulative distribution function is as follows:

F_{a, \beta}(x) =
\frac{1}{2} +
\frac{1}{\pi} \arctan (\frac{x-a}{\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

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

Devices supported: Host, 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::cauchy_method::by_default

Generation method. The specific values are as follows: oneapi::mkl::rng::cauchy_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.