.. _oneapi-mkl-rng-gumbel:

oneapi::mkl::rng::gumbel
========================


Generates Gumbel distributed random values.


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

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

The ``oneapi::mkl::rng::gumbel`` class object is used in the ``oneapi::mkl::rng::generate`` function to provide Gumbel distributed random numbers with displacement (a) and scalefactor (``b``, ``β``), where :math:`a, \beta \in R ; \beta > 0`.


The probability density function is given by:


.. math::

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


The cumulative distribution function is as follows:

.. math::

   F_{\alpha, \beta} (x) = 1 - \exp (- \exp(\frac{x - \alpha}{\beta})),
   - \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


   template<typename RealType = float, typename Method = gumbel_method::by_default>
   class gumbel {
   public:
   using method_type = Method; using result_type =
   RealType; gumbel(): gumbel((RealType)0.0,
   (RealType)1.0){} explicit gumbel(RealType a,
   RealType b);
   explicit gumbel(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``


Template Parameters
-------------------

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

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

       ``float``

       ``double``

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

       ``oneapi::mkl::rng::gumbel_method::icdf``

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


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

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

   * - Name
     - Type
     - Description
   * - a
     - ``RealType (float, double)``
     - Displacement ``a``.
   * - b
     - ``RealType (float, double)``
     - Scalefactor ``b``.