.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation
..
.. SPDX-License-Identifier: CC-BY-4.0
.. _onemkl_rng_overview:
Random Number Generators (RNG)
==============================
.. rubric:: Definitions
The pseudo-random number generator is defined by a structure(:math:`S`, :math:`\mu`, :math:`f`, :math:`U`, :math:`g`), where:
- :math:`S` is a finite set of states (the state space)
- :math:`\mu` is a probability distribution on :math:`S` for the initial state
(or seed) :math:`s_0`
- :math:`f:S \rightarrow S` is the transition function
- :math:`U` â€“ a finite set of output symbols
- :math:`g:S \rightarrow U` an output function
The generation of random numbers is as follows:
#. Generate the initial state (called the seed) :math:`s_0` according to :math:`\mu` and compute :math:`u_0 = g(s_0)`.
#. Iterate for :math:`i = 1 , ... , ` :math:`s_i = f(s_{i-1})` and :math:`u_i = g(s_i)`. Output values :math:`u_i` are the so-called random numbers produced by the PRNG.
In computational statistics, random variate generation is usually made in two steps:
#. Generating imitations of independent and identically distributed
(i.i.d.) random variables having the uniform distribution over the
interval :math:`(0, 1)`
#. Applying transformations to these i.i.d. :math:`U(0, 1)` random variates
in order to generate (or imitate) random variates and random
vectors from arbitrary distributions.
.. rubric:: Structure
RNG domain contains two classes types:
- Engines (basic random number generators) classes, which holds
the state of generator and is a source of i.i.d. random. Refer to
:ref:`onemkl_rng_engines_basic_random_number_generators`
for a detailed description.
- Distribution classes templates (transformation classes) for different types of statistical
distributions, for example, uniform, normal (Gaussian), binomial,
etc. These classes contain all of the distributionâ€™s parameters
(including generation method). Refer to :ref:`onemkl_rng_distributions` for
a detailed description of the distributions.
The RNG domain also contains two types of free functions:
- Generation routines. The current routines are used to obtain random
numbers from a given engine with proper statistics defined by a
given distribution. Refer to the :ref:`onemkl_rng_generate_routine`
section for a detailed description.
- Service routines. The routines are used to modify the engine state. Refer to :ref:`onemkl_rng_service_routines` for a
description of these routines.
Engine classes work with both generation and service routines. Distribution classes are used in
generation routines only. Refer to the :ref:`onemkl_rng_usage_model`
section for the description of typical RNG scenario.
.. toctree::
:hidden:
onemkl-rng-usage-model.rst
generate-routine.rst
engines-basic-random-number-generators.rst
service-routines.rst
distributions.rst
bibliography.rst
**Parent topic:** :ref:`onemkl_rng`