.. _oneapi-mkl-rng-device-gaussian:

oneapi::mkl::rng::device::gaussian
==================================


Generates normally distributed random numbers.


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

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

The ``oneapi::mkl::rng::device::gaussian`` class object is used in the
``oneapi::mkl::rng::device::generate``
function to provide random numbers with normal (Gaussian)
distribution with mean (``a``) and standard deviation
(``stddev, σ``), where ``a``, ``σ ∈ R`` ; ``σ`` > 0.

The probability density function is given by:

.. math::

   f_{a, \sigma} (x) =
   \frac{1}{\sigma \sqrt{2 \pi}}
   \exp
   \left(
      - \frac{(y-a)^2}{2\sigma^2}
   \right) dy,
   - \infty < x < + \infty


The cumulative distribution function is as follows:

.. math::

   F_{a, \sigma} (x) =
   \int_{-\infty}^{x}
   \frac{1}{\sigma \sqrt{2 \pi}}
   \exp
   \left(
      - \frac{(y-a)^2}{2\sigma^2}
   \right) dy,
   - \infty < x < + \infty



The cumulative distribution function :math:`Fa,\sigma (x)` can be expressed
in terms of standard normal distribution :math:`\phi(x)` as


.. math::


   F

        a,\sigma
     (x) = \phi((x - a)/\sigma)


API
***


Syntax
------

.. code-block:: cpp


   template<typename RealType, typename Method>
   class gaussian {
   public:
   using method_type = Method;
   using result_type = RealType;
   gaussian(): gaussian((RealType)0.0, (RealType)1.0){}
   explicit gaussian(RealType mean, RealType stddev);
   explicit gaussian(const param_type& pt);
   RealType mean() const;
   RealType stddev() const;
   param_type param() const;
   void param(const param_type& pt);
   };


Include Files
-------------

- ``oneapi/mkl/rng/device.hpp``


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

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

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

           ``float``

           ``double``
      * -  ``typename Method``
        -  Generation method. The specific values are as follows:

           ``oneapi::mkl::rng::device::gaussian_method::box_muller2``


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

      * - Name
        - Type
        - Description
      * - mean
        - ``RealType (float, double)``
        - Mean value ``a``.
      * - stddev
        - ``RealType (float, double)``
        - Standard deviation ``σ``.