.. SPDX-FileCopyrightText: 2024 Intel Corporation
..
.. SPDX-License-Identifier: CC-BY-4.0

.. _onemath_device_rng_geometric:

geometric
=========

Generates geometrically distributed random values.

.. rubric:: Description

The ``geometric`` class object is used in the ``generate`` and function
to provide geometrically distributed random numbers with probability ``p`` of a single trial success,
where :math:`p \in R; 0 \leq p \leq 1`.

The probability distribution is given by:

.. math::

     P(X = k) = p * (1 - p)^k, k = \{0, 1, 2, ... \}.

The cumulative distribution function is as follows:

.. math::

   F_p(x) =
   \begin{cases}
      0, x < 0 \\
      1 - (1 - p)^{\lfloor x + 1 \rfloor}, x \ge 0
   \end{cases}


class geometric
---------------

.. rubric:: Syntax

.. code-block:: cpp

   namespace oneapi::math::rng::device {
     template<typename IntType, typename Method>
     class geometric {
     public:
       using method_type = Method;
       using result_type = IntType;

       geometric();
       explicit geometric(float p);
       
       float p() const;
     };
   }


.. container:: section

    .. rubric:: Template parameters

    .. container:: section

        typename IntType
            Type of the produced values. Supported types:
                * ``std::int32_t``
                * ``std::uint32_t``
                * ``std::int64_t``
                * ``std::uint64_t``

    .. container:: section

        typename Method = oneapi::math::rng::geometric_method::by_default
            Transformation method, which will be used for generation. Supported types:

                * ``oneapi::math::rng::geometric_method::by_default``
                * ``oneapi::math::rng::geometric_method::icdf``

            See description of the methods in :ref:`Distributions methods template parameter<onemath_rng_distributions_template_parameter_onemath_rng_method_values>`.

.. container:: section

    .. rubric:: Class Members

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

        * - Routine
          - Description
        * - `geometric()`_
          - Default constructor
        * - `explicit geometric(float p)`_
          - Constructor with parameters
        * - `float p() const`_
          - Method to obtain probability `p`

.. container:: section

    .. rubric:: Member types

    .. container:: section

        .. code-block:: cpp

            geometric::method_type = Method

        .. container:: section

            .. rubric:: Description

            The type which defines transformation method for generation.

    .. container:: section

        .. code-block:: cpp

            geometric::result_type = IntType

        .. container:: section

            .. rubric:: Description

            The type which defines type of generated random numbers.

.. container:: section

    .. rubric:: Constructors

    .. container:: section

        .. _`geometric()`:

        .. code-block:: cpp

            geometric::geometric()

        .. container:: section

            .. rubric:: Description

            Default constructor for distribution, parameters set as `p` = 0.5f.

    .. container:: section

        .. _`explicit geometric(float p)`:

        .. code-block:: cpp

            explicit geometric::geometric(float p)

        .. container:: section

            .. rubric:: Description

            Constructor with parameters. `p` is a probability value.

        .. container:: section

            .. rubric:: Throws

            oneapi::math::invalid_argument
                Exception is thrown when :math:`p \ge 1.0f`, or :math:`p \leq 0.0f`

.. container:: section

    .. rubric:: Characteristics

    .. container:: section

        .. _`float p() const`:

        .. code-block:: cpp

            float geometric::p() const

        .. container:: section

            .. rubric:: Return Value

            Returns the distribution parameter `p` - probability value.

**Parent topic:** :ref:`onemath_device_rng_distributions`