.. _oneapi-mkl-rng-laplace:

oneapi::mkl::rng::laplace
=========================


Generates random numbers with Laplace distribution.


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

The ``oneapi::mkl::rng::laplace`` class object is used in the
``oneapi::mkl::rng::generate`` function to provide random numbers with Laplace distribution with mean value (or average) ``a`` and scalefactor ( ``b``, ``β``), where :math:`a, \beta \in R ; \beta > 0`. The scalefactor value determines the standard deviation as


.. math::

   \sigma = \beta \sqrt{2}


The probability density function is given by:

.. math::

   F_{a, \beta}(x) =
   \frac{1}{\sqrt {2\beta}}
   \exp \left( -\frac{|x-a|}{\beta} \right),
   - \infty < x < + \infty

The cumulative distribution function is as follows:

.. math::

   F_{\alpha, \beta}(x) =
   \begin{cases}
      \frac{1}{2}\exp\left(-\frac{|x-\alpha|}{\beta}\right), & x \geq \alpha \\
      1 - \frac{1}{2}\exp\left(-\frac{|x-\alpha|}{\beta}\right), & x < \alpha
   \end{cases},
   - \infty < x < + \infty


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

   * - 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 RealType = float, typename Method = laplace_method::by_default>
   class laplace {
   public:
   using method_type = Method;
   using result_type = RealType;
   laplace(): laplace((RealType)0.0, (RealType)1.0){}
   explicit laplace(RealType a, RealType b);
   explicit laplace(const param_type& pt);
   RealType a() const;
   RealType b() 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 RealType = float``
     -     Type of the produced values. The specific values are as follows:

           ``float``

           ``double``
   * -        ``typename Method = oneapi::mkl::rng::laplace_method::by_default``
     -     Generation method. The specific values are as follows:
           ``oneapi::mkl::rng::laplace_method::icdf``

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


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

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   :header-rows: 1

   * - Name
     - Type
     - Description
   * - a
     - ``RealType (float, double)``
     - Mean value ``a``.
   * - b
     - ``RealType (float, double)``
     - Scalefactor b.