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cauchy

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cauchy#

Class is used for generation of Cauchy distributed real types random numbers.

Description

The class object is used in the oneapi::math::rng::generate() function to provide random numbers Cauchy distributed with displacement \(a\), and scale parameter \((b, \beta)\), where \(a, \beta \in R; \beta > 0\).

The probability distribution is given by:

\[f_{a, \beta}(x) = \frac{1}{\pi\beta(1 + (\frac{x - a}{\beta})^2)}, x \in R.\]

The cumulative distribution function is as follows:

\[F_{a, \beta}(x) = \frac{1}{2} + \frac{1}{\pi} \arctan{(\frac{x - a}{\beta})}, x \in R.\]

class cauchy#

Syntax

namespace oneapi::math::rng {
template<typename RealType = float, typename Method = cauchy_method::by_default>
class cauchy {
public:
    using method_type = Method;
    using result_type = RealType;
    cauchy();
    explicit cauchy(RealType a, RealType b);
    RealType a() const;
    RealType b() const;
};
}

Template parameters

typename RealType
Type of the produced values. Supported types:

  • float

  • double

typename Method = oneapi::math::rng::cauchy_method::by_default

Transformation method, which will be used for generation. Supported types:

  • oneapi::math::rng::cauchy_method::by_default

  • oneapi::math::rng::cauchy_method::icdf

See description of the methods in Distributions methods template parameter.

Class Members

Routine

Description

cauchy()

Default constructor

explicit cauchy(RealType a, RealType b)

Constructor with parameters

RealType a() const

Method to obtain displacement value

RealType b() const

Method to obtain scalefactor value

Member types

cauchy::method_type = Method

Description

The type which defines transformation method for generation.

cauchy::result_type = RealType

Description

The type which defines type of generated random numbers.

Constructors

cauchy::cauchy()

Description

Default constructor for distribution, parameters set as a = 0.0, and b = 1.0.

explicit cauchy::cauchy(RealType a, RealType b)

Description

Constructor with parameters. a is a displacement value, b is a scalefactor value.

Throws

oneapi::math::invalid_argument

Exception is thrown when \(b \leq\) static_cast<RealType>(0.0)

Characteristics

RealType cauchy::a() const

Return Value

Returns the distribution parameter a - displacement value.

RealType cauchy::b() const

Return Value

Returns the distribution parameter b - scalefactor value.

Parent topic: Host Distributions

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