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sp_random.h
Go to the documentation of this file.
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/** @file sp_random.h Evaluating random variables */
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/*
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FAU Discrete Event System Simulator
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Copyright (C) 2007 Christoph Doerr
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Exclusive copyright is granted to Thomas Moor
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*/
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#ifndef FAUDES_SP_RANDOM_H
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#define FAUDES_SP_RANDOM_H
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#include "
tp_timeinterval.h
"
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#include "
sp_executor.h
"
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namespace
faudes {
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/**
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@defgroup SimRandomVariables Random Variables
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@ingroup SimulatorPlugin
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Sampling or evaluating random variables for simulation
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This module implements the evaluation (also known as sampling) of random
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variables with various distributions. It specialises on restricted support
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PDFs, since this is required for the ProposingExecutor.
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Random variables and their simulation is a highly involved topic and we give credit
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to the sources from which this module stems:
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1)
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Implementation of a random number generator from Stave Park and Dave Geyer, which
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we use in original form up to minor cosmetic changes.
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2)
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Inverse gaussian CDF by rational approxomation coefficients, presumably by Peter J, Acjlam,
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which we use in its original form up to minor cosmetic changes.
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3)
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Gaussian CDF by an aproximation that we found in "Handbook of Mathematical Functions" by
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Abromowitz and Stegun.
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All sources were available freely and we did not find any restricting licensing terms.
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Thanks!
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---------------------------------------------------------------------
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Regarding 1), from the header of rngs.c
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This is an ANSI C library for multi-stream random number generation.
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The use of this library is recommended as a replacement for the ANSI C
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rand() and srand() functions, particularly in simulation applications
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where the statistical 'goodness' of the random number generator is
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important. The library supplies 256 streams of random numbers; use
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SelectStream(s) to switch between streams indexed s = 0,1,...,255.
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The streams must be initialized. The recommended way to do this is by
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using the function PlantSeeds(x) with the value of x used to initialize
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the default stream and all other streams initialized automatically with
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values dependent on the value of x. The following convention is used
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to initialize the default stream: \n
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if x > 0 then x is the state \n
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if x < 0 then the state is obtained from the system clock \n
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if x = 0 then the state is to be supplied interactively. \n
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The generator used in this library is a so-called 'Lehmer random number
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generator' which returns a pseudo-random number uniformly distributed
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0.0 and 1.0. The period is (m - 1) where m = 2,147,483,647 and the
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smallest and largest possible values are (1 / m) and 1 - (1 / m)
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respectively. For more details see:
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"Random Number Generators: Good Ones Are Hard To Find" \n
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Steve Park and Keith Miller \n
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Communications of the ACM, October 1988 \n
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Name : rngs.c (Random Number Generation - Multiple Streams) \n
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Authors : Steve Park & Dave Geyer \n
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Language : ANSI C \n
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Latest Revision : 09-22-98
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---------------------------------------------------------------------
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Regarding 2), from the header of rngs.c
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This function returns an approximation of the inverse cumulative
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standard normal distribution function. I.e., given P, it returns
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an approximation to the X satisfying P = Pr{Z <= X} where Z is a
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random variable from the standard normal distribution.
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The algorithm uses a minimax approximation by rational functions
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and the result has a relative error whose absolute value is less
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than 1.15e-9.
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Author: Peter J. Acklam \n
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Time-stamp: 2002-06-09 18:45:44 +0200 \n
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E-mail: jacklam at math dot uio dor no \n
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WWW URL: http www dot math dot uio dot no /~jacklam \n
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C implementation adapted from Peter's Perl version \n
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---------------------------------------------------------------------
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Regarding 3), found as code example in Wikipedia
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---------------------------------------------------------------------
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*/
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/**
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* Use this function to set the state of all the random number generator
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* streams by "planting" a sequence of states (seeds), one per stream,
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* with all states dictated by the state of the default stream.
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* The sequence of planted states is separated one from the next by
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* 8,367,782 calls to ran().
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*/
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void
ran_plant_seeds
(
long
x);
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/**
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* Use this function to set the current random number generator
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* stream -- that stream from which the next random number will come.
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*/
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void
ran_select_stream
(
int
index);
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/**
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* Put a seed
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* @param seed
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* Random generator seed
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*/
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void
ran_put_seed
(
long
seed);
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/**
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* Initialize random generator
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* @param seed
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* Random generator seed
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*/
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void
ran_init
(
long
seed);
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/**
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* Run random generator
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* Random Number Generator
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* (for more details see "Random Number Generators: Good Ones Are Hard To Find"
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* Steve Park and Keith Miller
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* Communications of the ACM, October 1988)
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* @return
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* Random value in [0,1) ( excluding 1 (?))
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*/
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double
ran
(
void
);
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/**
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* Sample a random variable uniformly on interval [a;b)
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* Distribution: f(t) dt= {1/(b-a)} dt for t, a <=t< b, else 0
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* @param a
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* Lower bound
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* @param b
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* Upper bound
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* @return
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* Random value
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*/
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double
ran_uniform
(
double
a,
double
b);
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/**
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* Sample a discrete random variable uniformly on interval [a;b)
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* Distribution: p(n) = 1/(b-a-1)
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* @param a
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* Lower bound
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* @param b
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* Upper bound
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* @return
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* Random value
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*/
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long
ran_uniform_int
(
long
a,
long
b);
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/**
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* Sample a random variable exponentially
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* Distribution: f(t) dt = 1/mu exp(-t/mu) dt for t>=0
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* @param mu
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* mu
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* @return
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* Random variabe
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*/
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double
ran_exponential
(
double
mu);
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/**
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* Sample a random variable exponentially on a restricted interval
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* Distribution: f(t) dt = 1/mu exp(-t/mu) dt for t>=0
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* @param mu
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* mu
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* @param tossLB
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* Lower interval bound
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* @param tossUB
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* Upper interval bound
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*/
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double
ran_exponential
(
double
mu,
Time::Type
tossLB,
Time::Type
tossUB);
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/**
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* Sample a random variable gaussian distributed on a restricted interval
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* Distribution: f(t) = 1 / sqrt(2 pi sigma^2) * exp( -1/2 ((t-mu)/sigma)^2) for t>=0
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* @param mu
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* mu
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* @param sigma
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* sigma
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* @param tossLB
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* Lower interval bound
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* @param tossUB
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* Upper interval bound
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*/
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double
ran_gauss
(
double
mu,
double
sigma,
Time::Type
tossLB,
Time::Type
tossUB);
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/**
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* Help function: calculate gaussian CDF
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* using an approximation from
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* Abromowitz and Stegun: Handbook of Mathematical Functions
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* @param x
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* @return CDF(x)
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*/
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double
ran_gaussian_cdf_P
(
double
x);
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/** @} doxygen group */
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}
// namespace
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#define FAUDES_STOCHRAN_H
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#endif
libFAUDES 2.28a
--- 2016.09.13 --- c++ api documentaion by
doxygen
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