sp_random.h
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1 /** @file sp_random.h Evaluating random variables */
2 
3 /*
4  FAU Discrete Event System Simulator
5 
6  Copyright (C) 2007 Christoph Doerr
7  Exclusive copyright is granted to Thomas Moor
8 
9 */
10 
11 #ifndef FAUDES_SP_RANDOM_H
12 #define FAUDES_SP_RANDOM_H
13 
14 #include "tp_timeinterval.h"
15 #include "sp_executor.h"
16 
17 
18 namespace faudes {
19 
20 /**
21 
22 @defgroup SimRandomVariables Random Variables
23 
24 @ingroup SimulatorPlugin
25 
26 Sampling or evaluating random variables for simulation
27 
28 This module implements the evaluation (also known as sampling) of random
29 variables with various distributions. It specialises on restricted support
30 PDFs, since this is required for the ProposingExecutor.
31 
32 Random variables and their simulation is a highly involved topic and we give credit
33 to the sources from which this module stems:
34 
35 1)
36 Implementation of a random number generator from Stave Park and Dave Geyer, which
37 we use in original form up to minor cosmetic changes.
38 
39 2)
40 Inverse gaussian CDF by rational approxomation coefficients, presumably by Peter J, Acjlam,
41 which we use in its original form up to minor cosmetic changes.
42 
43 
44 3)
45 Gaussian CDF by an aproximation that we found in "Handbook of Mathematical Functions" by
46 Abromowitz and Stegun.
47 
48 All sources were available freely and we did not find any restricting licensing terms.
49 Thanks!
50 
51 
52 ---------------------------------------------------------------------
53 
54 Regarding 1), from the header of rngs.c
55 
56 This is an ANSI C library for multi-stream random number generation.
57 The use of this library is recommended as a replacement for the ANSI C
58 rand() and srand() functions, particularly in simulation applications
59 where the statistical 'goodness' of the random number generator is
60 important. The library supplies 256 streams of random numbers; use
61 SelectStream(s) to switch between streams indexed s = 0,1,...,255.
62 
63 The streams must be initialized. The recommended way to do this is by
64 using the function PlantSeeds(x) with the value of x used to initialize
65 the default stream and all other streams initialized automatically with
66 values dependent on the value of x. The following convention is used
67 to initialize the default stream: \n
68 if x > 0 then x is the state \n
69 if x < 0 then the state is obtained from the system clock \n
70 if x = 0 then the state is to be supplied interactively. \n
71 
72 The generator used in this library is a so-called 'Lehmer random number
73 generator' which returns a pseudo-random number uniformly distributed
74 0.0 and 1.0. The period is (m - 1) where m = 2,147,483,647 and the
75 smallest and largest possible values are (1 / m) and 1 - (1 / m)
76 respectively. For more details see:
77 
78  "Random Number Generators: Good Ones Are Hard To Find" \n
79  Steve Park and Keith Miller \n
80  Communications of the ACM, October 1988 \n
81 
82 Name : rngs.c (Random Number Generation - Multiple Streams) \n
83 Authors : Steve Park & Dave Geyer \n
84 Language : ANSI C \n
85 Latest Revision : 09-22-98
86 
87 ---------------------------------------------------------------------
88 
89 Regarding 2), from the header of rngs.c
90 
91 This function returns an approximation of the inverse cumulative
92 standard normal distribution function. I.e., given P, it returns
93 an approximation to the X satisfying P = Pr{Z <= X} where Z is a
94 random variable from the standard normal distribution.
95 
96 The algorithm uses a minimax approximation by rational functions
97 and the result has a relative error whose absolute value is less
98 than 1.15e-9.
99 
100 Author: Peter J. Acklam \n
101 Time-stamp: 2002-06-09 18:45:44 +0200 \n
102 E-mail: jacklam at math dot uio dor no \n
103 WWW URL: http www dot math dot uio dot no /~jacklam \n
104 
105 C implementation adapted from Peter's Perl version \n
106 
107 ---------------------------------------------------------------------
108 
109 Regarding 3), found as code example in Wikipedia
110 
111 ---------------------------------------------------------------------
112 
113 
114 @{
115 
116 */
117 
118 
119 
120 
121 /**
122  * Use this function to set the state of all the random number generator
123  * streams by "planting" a sequence of states (seeds), one per stream,
124  * with all states dictated by the state of the default stream.
125  * The sequence of planted states is separated one from the next by
126  * 8,367,782 calls to ran().
127  */
128 void ran_plant_seeds(long x);
129 
130 /**
131  * Use this function to set the current random number generator
132  * stream -- that stream from which the next random number will come.
133  */
134 void ran_select_stream(int index);
135 
136 /**
137 * Put a seed
138 * @param seed
139 * Random generator seed
140 */
141 void ran_put_seed(long seed);
142 
143 /**
144 * Initialize random generator
145 * @param seed
146 * Random generator seed
147 */
148 void ran_init(long seed);
149 
150 /**
151 * Run random generator
152 * Random Number Generator
153 * (for more details see "Random Number Generators: Good Ones Are Hard To Find"
154 * Steve Park and Keith Miller
155 * Communications of the ACM, October 1988)
156 * @return
157 * Random value in [0,1) ( excluding 1 (?))
158 */
159 double ran(void);
160 
161 
162 /**
163 * Sample a random variable uniformly on interval [a;b)
164 * Distribution: f(t) dt= {1/(b-a)} dt for t, a <=t< b, else 0
165 * @param a
166 * Lower bound
167 * @param b
168 * Upper bound
169 * @return
170 * Random value
171 */
172 double ran_uniform(double a, double b);
173 
174 /**
175 * Sample a discrete random variable uniformly on interval [a;b)
176 * Distribution: p(n) = 1/(b-a-1)
177 * @param a
178 * Lower bound
179 * @param b
180 * Upper bound
181 * @return
182 * Random value
183 */
184 long ran_uniform_int(long a, long b);
185 
186 /**
187 * Sample a random variable exponentially
188 * Distribution: f(t) dt = 1/mu exp(-t/mu) dt for t>=0
189 * @param mu
190 * mu
191 * @return
192 * Random variabe
193 */
194 double ran_exponential(double mu);
195 
196 /**
197 * Sample a random variable exponentially on a restricted interval
198 * Distribution: f(t) dt = 1/mu exp(-t/mu) dt for t>=0
199 * @param mu
200 * mu
201 * @param tossLB
202 * Lower interval bound
203 * @param tossUB
204 * Upper interval bound
205 */
206 double ran_exponential(double mu, tpTime::Type tossLB, tpTime::Type tossUB);
207 
208 /**
209 * Sample a random variable gaussian distributed on a restricted interval
210 * Distribution: f(t) = 1 / sqrt(2 pi sigma^2) * exp( -1/2 ((t-mu)/sigma)^2) for t>=0
211 * @param mu
212 * mu
213 * @param sigma
214 * sigma
215 * @param tossLB
216 * Lower interval bound
217 * @param tossUB
218 * Upper interval bound
219 */
220 double ran_gauss(double mu, double sigma, tpTime::Type tossLB, tpTime::Type tossUB);
221 
222 /**
223 * Help function: calculate gaussian CDF
224 * using an approximation from
225 * Abromowitz and Stegun: Handbook of Mathematical Functions
226 * @param x
227 * @return CDF(x)
228 */
229 double ran_gaussian_cdf_P(double x);
230 
231 /** @} doxygen group */
232 
233 
234 } // namespace
235 
236 
237 #define FAUDES_STOCHRAN_H
238 #endif

libFAUDES 2.26g --- 2015.08.17 --- c++ api documentaion by doxygen