.. _oneapi-mkl-rng-chi_square:

oneapi::mkl::rng::chi_square
============================


Generates chi-square distributed random values.


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

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

The ``oneapi::mkl::rng::chi_square`` class object is used in the ``oneapi::mkl::rng::generate`` function to provide random numbers with chi-square distribution and ``ν`` degrees of freedom, ``n``\ ∈\ *N*, ``n`` > 0.


The probability density function is:

.. math::

   F_{v}(x) =
   \begin{cases}
         \frac {x^{\frac {n-2}{2}} e^{-\frac{x}{2}}}
               {2^{n/2} \Gamma (\frac {n}{2})} dy,
               & x \geq 0 \\
      0, & x < 0
   \end{cases}

The cumulative distribution function is:


.. math::

   F_{v}(x) =
   \begin{cases}
      \int _{0}^{x}
         \frac {y^{\frac {n-2}{2}} e^{-\frac{n}{2}}}
               {2^{n/2} \Gamma (\frac {n}{2})} dy,
               & x \geq 0 \\
      0, & x < 0
   \end{cases}


API
***


Syntax
------

.. code-block:: cpp


   template<typename RealType = float, typename Method = chi_square_method::by_default>
   class chi_square {
   public:
   using method_type = Method;
   using result_type = RealType;
   chi_square(): chi_square(5){}
   explicit chi_square(std::int32_t n);
   explicit chi_square(const param_type& pt);
   std::int32_t n() 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 = oneamkl::rng::chi_square_method::by_default``
     - Generation method. The specific values are as follows:

       ``oneapi::mkl::rng::chi_square_method::gamma_based``

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


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

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

   * - Name
     - Type
     - Description
   * - n
     - ``std::int32_t``
     - Degrees of freedom.