WOLFRAM SYSTEM MODELER
randomPseudo random number generator |
SystemModel["Modelica.Clocked.RealSignals.Sampler.Utilities.Internal.random"]
This information is part of the Modelica Standard Library maintained by the Modelica Association.
Random generates a sequence of uniform distributed pseudo-random numbers. The algorithm is a variant of the multiplicative congruential algorithm, known as the Wichmann-Hill generator:
x(k) = (a1*x(k-1)) mod m1 y(k) = (a2*y(k-1)) mod m2 z(k) = (a3*z(k-1)) mod m3 U(k) = (x(k)/m1 + y(k)/m2 + z(k)/m3) mod 1
This generates pseudo-random numbers U(k) uniformly distributed in the interval (0,1). There are many forms of generators depending on the parameters m (prime numbers) and a. The sequence needs an initial Integer vector {x,y,z} known as the seed. The use of the same seed will lead to the same sequence of numbers.
Remarks
Random number generators (RNG) are pseudo-functions which are not true functions but algorithms which deliver a fixed sequence of (usually Integer) numbers which should have a very large period before they repeat itself and appropriate statistic properties such that the sequence appears to be a random draw. For real-valued random numbers, the integers are scaled to the real interval 0.0-1.0. They result in a uniformly distributed random variate between 0-1, which has to be transformed to give a random variate of a wanted distribution. There are two types of techniques for transforming random variates:
Acceptance-Rejection techniques throw away some of the generated variates and are thus less efficient. They can not be avoided for all distributions. A good summary about random number generation and most of the transformation techniques used below is given in:
Discrete Event SimulationSome of the other references are quoted below.
WICHMANN-HILL RANDOM NUMBER GENERATOR Wichmann, B. A. & Hill, I. D. (1982) Algorithm AS 183: An efficient and portable pseudo-random number generator Applied Statistics 31 (1982) 188-190 see also: Correction to Algorithm AS 183 Applied Statistics 33 (1984) 123 McLeod, A. I. (1985) A remark on Algorithm AS 183 Applied Statistics 34 (1985),198-200 In order to completely avoid external functions, all seeds are set via parameters. For simulation purposes this is almost always the desired behaviour. Translated by Hubertus Tummescheit from Python source provided by Guido van Rossum translated from C source by Adrian Baddeley. http://www.python.org/doc/current/lib/module-random.html R A N D O M V A R I A B L E G E N E R A T O R S distributions on the real line: ------------------------------ normal (Gaussian) 2 versions
Copyright © Hubertus Tummescheit and Department of Automatic Control, Lund University, Sweden.
This Modelica function is free software; it can be redistributed and/or modified under the terms of the BSD-3-Clause license.
seedIn |
Type: Integer[3] Description: Integer vector defining random number sequence, e.g., {23,87,187} |
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x |
Type: Real Description: Random number between 0 and 1 |
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seedOut |
Type: Integer[3] Description: Modified seed to be used for next call of random() |
2019-05-20: Changed license to BSD-3-Clause after consultation with Hubertus Tummescheit.