laplace#

Generates random numbers with Laplace distribution.

Description#

The laplace class object is used in the generate function to provide random numbers with Laplace distribution with mean value (or average) a and scalefactor ( b, β), where \(a, \beta \in R ; \beta > 0\). The scalefactor value determines the standard deviation as:

\[\sigma = \beta \sqrt{2}\]

The probability density function is given by:

\[f_{a, \beta}(x) = \frac{1}{\sqrt {2\beta}} \exp \left( -\frac{|x-a|}{\beta} \right), - \infty < x < + \infty\]

The cumulative distribution function is as follows:

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

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 = laplace_method::by_default>
  class laplace {
  public:
    using method_type = Method;
    using result_type = RealType;

    laplace(): laplace((RealType)0.0, (RealType)1.0){}
    explicit laplace(RealType a, RealType b);
    explicit laplace(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::laplace_method::by_default

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

See brief descriptions of the methods in Distributions Template Parameter Method

Input Parameters#

Name

Type

Description

a

RealType (float, double)

Mean value a.

b

RealType (float, double)

Scalefactor b.