.. _oneapi-mkl-rng-poisson_v:

oneapi::mkl::rng::poisson_v
===========================


Generates Poisson distributed random values with varying mean.


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

The ``oneapi::mkl::rng::poisson_v`` class object is used in the ``oneapi::mkl::rng::generate`` function to provide ``n`` Poisson distributed random numbers ``x``\ :sub:`i`\ (``i`` = 1, ..., ``n``) with distribution parameter ``λi``, where ``λi∈R``; ``λi > 0``.


The probability distribution is given by:

.. math::

   P(X_i = k) =
   \frac{\lambda_i^k \exp(-\lambda_i)}{k!},
   k \in \{0, 1, 2, \ldots \}


The cumulative distribution function is as follows:

.. math::

   F_{\lambda_i} (x) =
   \begin{cases}
      \sum_{k = 0}^{\lfloor x \rfloor}
      \frac{\lambda_i^k e^{-\lambda_i}}{k!}, & x \geq 0 \\
      0, & x < 0
   \end{cases},
   x \in R


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   * - Product and Performance Information
   * - Performance varies by use, configuration and other factors. Learn more at `https://www.intel.com/PerformanceIndex <https://www.intel.com/PerformanceIndex>`__. Notice revision #20201201


API
***


Syntax
------

.. code-block:: cpp


   template<typename IntType = std::int32_t, typename Method = poisson_v_method::by_default>
   class poisson_v {
   public:
   using method_type = Method;
   using result_type = IntType;
   explicit poisson_v(std::vector<double> lambda
   explicit poisson_v(const param_type& pt);
   std::vector<double> lambda() 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
-------------------

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   * - ``typename IntType = std::int32_t``
     - Type of the produced values. The specific values are as follows:

       ``std::int32_t``

       ``std::uint32_t``
   * - ``typename Method =  oneapi::mkl::rng::poisson_v_method:: by_default``
     - Generation method. The specific values are as follows:

       ``oneapi::mkl::rng::poisson_v_method::gaussian_icdf_based``

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


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

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   * - Name
     - Type
     - Description
   * - lambda
     - ``std::vector<double>``
     - Array of ``n`` distribution parameters λ.