oneapi::mkl::rng::cauchy

Generates Cauchy distributed random values.

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

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, β∈R ; β > 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

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.