.. _oneapi-mkl-rng-weibull:

oneapi::mkl::rng::weibull
=========================

Generates Weibull distributed random numbers.


.. contents::
    :local:
    :depth: 1

Description
***********

The ``oneapi::mkl::rng::weibull`` class object is used in the ``oneapi::mkl::rng::generate`` function to provide Weibull distributed random numbers with displacement ``a``, scalefactor ``β``, and shape :math:`\alpha`, where :math:`\alpha, \beta, a \in R ; \alpha > 0, \beta > 0`.


The probability density function is given by:

.. math::

   F_{a, \alpha, \beta}(x) =
   \begin{cases}
      \frac{\alpha}{\beta^\alpha} (x - a)^{\alpha - 1} \exp \left( - {\left( \frac{x-a}{\beta} \right)}^{\alpha} \right), & x \geq a \\
      0, & x < a
   \end{cases}


The cumulative distribution function is as follows:

.. math::

   F_{a, \alpha, \beta}(x) =
   \begin{cases}
      1 - \exp \left( - {\left( \frac{x-a}{\beta} \right)}^{\alpha} \right), & x \geq a \\
      0, & x < a
   \end{cases},
   - \infty < x < + \infty


.. list-table::
   :header-rows: 1

   * - Product and Performance Information
   * - Performance varies by use, configuration and other factors. Learn more at `https://www.intel.com/PerformanceIndex <https://www.intel.com/PerformanceIndex>`__. Notice revision #20201201


API
***


Syntax
------

.. code-block:: cpp

   namespace oneapi::mkl::rng {
   template<typename RealType = float, typename Method = weibull_method::by_default>
   class weibull {
   public:
       using method_type = Method;
       using result_type = RealType;
       weibull(): weibull((Real_Type)1.0, (RealType)0.0, (RealType)1.0){}
       explicit weibull(RealType alpha, RealType a, RealType beta);
       explicit weibull(const param_type& pt);
       RealType alpha() const;
       RealType a() const;
       RealType beta() 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
-------------------

.. list-table::
   :header-rows: 0

   * - ``typename RealType = float``
     - Type of the produced values. The specific values are as follows:

       ``float``

       ``double``
   * - ``typename Method = oneapi::mkl::rng::weibull_method::by_default``
     - Generation method. The specific values are as follows:
       ``oneapi::mkl::rng::weibull_method::icdf``

       ``oneapi::mkl::rng::weibull_method::icdf_accurate``

       See brief descriptions of the methods in :ref:`distributions-template-parameter-method`


Input Parameters
----------------

.. list-table::
   :header-rows: 1

   * - Name
     - Type
     - Description
   * - alpha
     - ``RealType (float, double)``
     - Shape α
   * - a
     - ``RealType (float, double)``
     - Displacement ``a``.
   * - beta
     - ``RealType (float, double)``
     - Scalefactor β.