.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation
..
.. SPDX-License-Identifier: CC-BY-4.0

.. _onemkl_rng_hypergeometric:

hypergeometric
==============

Class is used for generation of hypergeometrically distributed integer types random numbers.

.. _onemkl_rng_hypergeometric_description:

.. rubric:: Description

The class object is used in the :ref:`oneapi::mkl::rng::generate()<onemkl_rng_generate>` function to provide random numbers hypergeometrically distributed with lot size :math:`l`, size of sampling :math:`s`, and number of marked elements in the lot :math:`m`, where :math:`l, m, s \in N \bigcup \{0\}; l \ge max (s, m)`.

Consider a lot of :math:`l` elements comprising :math:`m` marked and :math:`l` - :math:`m` unmarked elements. A trial sampling without replacement of exactly :math:`s` elements from this lot helps to define the hypergeometric distribution, which is the probability that the group of :math:`s` elements contains exactly :math:`k` marked elements.

The probability distribution is given by:

.. math::

     P_(X = k) = \frac{C^k_mC^{s-k}_{l-m}}{C^s_l}, k \in \{max(0, s + m - l), ... , min(s, m)\}.

The cumulative distribution function is as follows:

.. math::

     F_{l, s, m}(x) = \left\{ \begin{array}{rcl} 0, x < max(0, s + m - l) \\ \sum^{\lfloor x \rfloor}_{k = max(0, s + m - l)}\frac{C^k_mC^{s-k}_{l-m}}{C^s_l}, max(0, s + m - l) \leq x \leq min(s, m) \\ 1, x > min(s, m) \end{array}\right.

.. _onemkl_rng_hypergeometric_syntax:

class hypergeometric
--------------------

.. rubric:: Syntax

.. code-block:: cpp

    namespace oneapi::mkl::rng {
    template<typename IntType = std::int32_t, typename Method = hypergeometric_method::by_default>
    class hypergeometric {
    public:
        using method_type = Method;
        using result_type = IntType;
        hypergeometric();
        explicit hypergeometric(std::int32_t l, std::int32_T s, std::int32_T m);
        std::int32_t s() const;
        std::int32_t m() const;
        std::int32_t l() const;
    };
    }

.. container:: section

    .. rubric:: Template parameters

    .. container:: section

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

    .. container:: section

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

                * ``oneapi::mkl::rng::hypergeometric_method::by_default``
                * ``oneapi::mkl::rng::hypergeometric_method::h2pe``

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

.. container:: section

    .. rubric:: Class Members

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

        * - Routine
          - Description
        * - `hypergeometric()`_
          - Default constructor
        * - `explicit hypergeometric(std::int32_t l, std::int32_T s, std::int32_T m)`_
          - Constructor with parameters
        * - `std::int32_t s() const`_
          - Method to obtain lot size
        * - `std::int32_t m() const`_
          - Method to obtain size of sampling without replacement
        * - `std::int32_t l() const`_
          - Method to obtain number of marked elements

.. container:: section

    .. rubric:: Member types

    .. container:: section

        .. code-block:: cpp

            hypergeometric::method_type = Method

        .. container:: section

            .. rubric:: Description

            The type which defines transformation method for generation.

    .. container:: section

        .. code-block:: cpp

            hypergeometric::result_type = IntType

        .. container:: section

            .. rubric:: Description

            The type which defines type of generated random numbers.

.. container:: section

    .. rubric:: Constructors

    .. container:: section

        .. _`hypergeometric()`:

        .. code-block:: cpp

            hypergeometric::hypergeometric()

        .. container:: section

            .. rubric:: Description

            Default constructor for distribution, parameters set as `l` = 1, `s` = 1, `m` = 1.

    .. container:: section

        .. _`explicit hypergeometric(std::int32_t l, std::int32_T s, std::int32_T m)`:

        .. code-block:: cpp

            explicit hypergeometric::hypergeometric(std::int32_t l, std::int32_T s, std::int32_T m)

        .. container:: section

            .. rubric:: Description

            Constructor with parameters. `l` is a lot size, `s` is a size of sampling without replacement, `m` is a number of marked elements.

        .. container:: section

            .. rubric:: Throws

            oneapi::mkl::invalid_argument
                Exception is thrown when :math:`s < 0`, or :math:`m < 0`, or :math:`l < (s > m ? s : m)`

.. container:: section

    .. rubric:: Characteristics

    .. container:: section

        .. _`std::int32_t l() const`:

        .. code-block:: cpp

            std::int32_t hypergeometric::l() const

        .. container:: section

            .. rubric:: Return Value

            Returns the distribution parameter `l` - lot size value.

    .. container:: section

        .. _`std::int32_t s() const`:

        .. code-block:: cpp

            std::int32_t hypergeometric::s() const

        .. container:: section

            .. rubric:: Return Value

            Returns the distribution parameter `s` - size of sampling without replacement.

    .. container:: section

        .. _`std::int32_t m() const`:

        .. code-block:: cpp

            std::int32_t hypergeometric::m() const

        .. container:: section

            .. rubric:: Return Value

            Returns the distribution parameter `m` - number of marked elements.

**Parent topic:** :ref:`onemkl_rng_distributions`