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

.. _onemath_rng_chi_square:

chi_square
==========

Class is used for generation of chi-square distributed real types random numbers.

.. _onemath_rng_chi_square_description:

.. rubric:: Description

The class object is used in the :ref:`oneapi::math::rng::generate()<onemath_rng_generate>` function to provide random numbers chi-square distributed with :math:`n` degrees of freedom, :math:`n \in N; n > 0`.

The probability distribution is given by:

.. math::

    f_{n}(x) = \left\{ \begin{array}{rcl} \frac{x^{\frac{n - 2}{2}}e^{-\frac{x}{2}}}{2^{n/2}\Gamma(n/2)}, x \ge 0 \\ 0, x < 0 \end{array}\right.

The cumulative distribution function is as follows:

.. math::

    F_{n}(x) = \left\{ \begin{array}{rcl} \int^{x}_{0}\frac{y^{\frac{n - 2}{2}}e^{-\frac{x}{2}}}{2^{n/2}\Gamma(n/2)}dy, x \ge 0 \\ 0, x < 0 \end{array}\right.


.. _onemath_rng_chi_square_syntax:

class chi_square
----------------

.. rubric:: Syntax

.. code-block:: cpp

    namespace oneapi::math::rng {
    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();
        explicit chi_square(std::int32_t n);
        std::int32_t n() const;
    };
    }

.. container:: section

    .. rubric:: Template parameters

    .. container:: section

        typename RealType
            Type of the produced values. Supported types:
                * ``float``
                * ``double``

    .. container:: section

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

                * ``oneapi::math::rng::chi_square_method::by_default``
                * ``oneapi::math::rng::chi_square_method::gamma_based``

            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
        * - `chi_square()`_
          - Default constructor
        * - `explicit chi_square(std::int32_t n)`_
          - Constructor with parameters
        * - `std::int32_t n() const`_
          - Method to obtain number of degrees of freedom `n`

.. container:: section

    .. rubric:: Member types

    .. container:: section

        .. code-block:: cpp

            chi_square::method_type = Method

        .. container:: section

            .. rubric:: Description

            The type which defines transformation method for generation.

    .. container:: section

        .. code-block:: cpp

            chi_square::result_type = RealType

        .. container:: section

            .. rubric:: Description

            The type which defines type of generated random numbers.

.. container:: section

    .. rubric:: Constructors

    .. container:: section

        .. _`chi_square()`:

        .. code-block:: cpp

            chi_square::chi_square()

        .. container:: section

            .. rubric:: Description

            Default constructor for distribution, parameters set as `n` = 5.

    .. container:: section

        .. _`explicit chi_square(std::int32_t n)`:

        .. code-block:: cpp

            explicit chi_square::chi_square(std::int32_t n)

        .. container:: section

            .. rubric:: Description

            Constructor with parameters. `n` is the number of degrees of freedom.

        .. container:: section

            .. rubric:: Throws

            oneapi::math::invalid_argument
                Exception is thrown when :math:`n < 1`

.. container:: section

    .. rubric:: Characteristics

    .. container:: section

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

        .. code-block:: cpp

            std::int32_t chi_square::n() const

        .. container:: section

            .. rubric:: Return Value

            Returns the distribution parameter `n` - number of degrees of freedom.

**Parent topic:** :ref:`onemath_rng_distributions`