.. _oneapi-mkl-rng-gamma:

oneapi::mkl::rng::gamma
=======================


Generates gamma distributed random values.


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

The ``oneapi::mkl::rng::gamma`` class object is used in the ``oneapi::mkl::rng::generate`` function to provide random numbers with gamma distribution that has shape parameter α, displacement ``a``, and scale parameter ``β``, where :math:`\alpha, \beta, and a \in R ; \alpha > 0, \beta > 0`.


The probability density function is given by:

.. math::

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


where ``Γ(α)`` is the complete gamma function.

The cumulative distribution function is as follows:

.. math::

   F_{\alpha, a, \beta}(x) =
   \begin{cases}
      \int_{a}^{x} \frac{1}{\Gamma (\alpha) \beta^\alpha} (y - a)^{\alpha - 1} e^{-\frac{(y-a)}{\beta}} dy, & x \geq a \\
      0, & x < a
   \end{cases},
   - \infty < x < + \infty




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   * - 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 = gamma_method::by_default>
   class gamma {
   public:
   using method_type = Method; using result_type = RealType;
   gamma(): gamma((RealType)1.0, (RealType)0.0, (RealType)1.0){}
   explicit gamma(RealType alpha, RealType a, RealType beta);
   explicit gamma(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
-------------------

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

       ``float``

       ``double``

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

       ``oneapi::mkl::rng::gamma_method::marsaglia``

       ``oneapi::mkl::rng::gamma_method::marsaglia_accurate``

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


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

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