cauchy#

Generates Cauchy distributed random values.

Description#

The cauchy class object is used in the 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#

namespace oneapi::mkl::rng {
  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: 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.