1simulation::montecarlo(n) Tcl Simulation Tools simulation::montecarlo(n)
2______________________________________________________________________________
6
8 simulation::montecarlo - Monte Carlo simulations
9
11 package require Tcl ?8.4?
12 package require simulation::montecarlo 0.1
14 package require simulation::random
16 package require math::statistics
18 ::simulation::montecarlo::getOption keyword
20 ::simulation::montecarlo::hasOption keyword
22 ::simulation::montecarlo::setOption keyword value
24 ::simulation::montecarlo::setTrialResult values
26 ::simulation::montecarlo::setExpResult values
28 ::simulation::montecarlo::getTrialResults
30 ::simulation::montecarlo::getExpResult
32 ::simulation::montecarlo::transposeData values
34 ::simulation::montecarlo::integral2D ...
36 ::simulation::montecarlo::singleExperiment args
38______________________________________________________________________________
40
42 The technique of Monte Carlo simulations is basically simple:
43 · generate random values for one or more parameters.
45 · evaluate the model of some system you are interested in and
47 record the interesting results for each realisation of these
48 parameters.
49 · after a suitable number of such trials, deduce an overall char‐
51 acteristic of the model.
52 You can think of a model of a network of computers, an ecosystem of
54 some kind or in fact anything that can be quantitatively described and
55 has some stochastic element in it.
56 The package simulation::montecarlo offers a basic framework for such a
58 modelling technique:
59 #
62 # MC experiments:
63 # Determine the mean and median of a set of points and compare them
64 #
65 ::simulation::montecarlo::singleExperiment -init {
66 package require math::statistics
67 set prng [::simulation::random::prng_Normal 0.0 1.0]
69 } -loop {
70 set numbers {}
71 for { set i 0 } { $i < [getOption samples] } { incr i } {
72 lappend numbers [$prng]
73 }
74 set mean [::math::statistics::mean $numbers]
75 set median [::math::statistics::median $numbers] ;# ? Exists?
76 setTrialResult [list $mean $median]
77 } -final {
78 set result [getTrialResults]
79 set means {}
80 set medians {}
81 foreach r $result {
82 foreach {m M} $r break
83 lappend means $m
84 lappend medians $M
85 }
86 puts [getOption reportfile] "Correlation: [::math::statistics::corr $means $medians]"
87 } -trials 100 -samples 10 -verbose 1 -columns {Mean Median}
89 This example attemps to find out how well the median value and the mean
91 value of a random set of numbers correlate. Sometimes a median value is
92 a more robust characteristic than a mean value - especially if you have
93 a statistical distribution with "fat" tails.
94
96 The package defines the following auxiliary procedures:
97 ::simulation::montecarlo::getOption keyword
99 Get the value of an option given as part of the singeExperiment
100 command.
101 string keyword
103 Given keyword (without leading minus)
104 ::simulation::montecarlo::hasOption keyword
107 Returns 1 if the option is available, 0 if not.
108 string keyword
110 Given keyword (without leading minus)
111 ::simulation::montecarlo::setOption keyword value
114 Set the value of the given option.
115 string keyword
117 Given keyword (without leading minus)
118 string value
120 (New) value for the option
121 ::simulation::montecarlo::setTrialResult values
124 Store the results of the trial for later analysis
125 list values
127 List of values to be stored
128 ::simulation::montecarlo::setExpResult values
131 Set the results of the entire experiment (typically used in the
132 final phase).
133 list values
135 List of values to be stored
136 ::simulation::montecarlo::getTrialResults
139 Get the results of all individual trials for analysis (typically
140 used in the final phase or after completion of the command).
141 ::simulation::montecarlo::getExpResult
144 Get the results of the entire experiment (typically used in the
145 final phase or even after completion of the singleExperiment
146 command).
147 ::simulation::montecarlo::transposeData values
150 Interchange columns and rows of a list of lists and return the
151 result.
152 list values
154 List of lists of values
155 There are two main procedures: integral2D and singleExperiment.
157 ::simulation::montecarlo::integral2D ...
159 Integrate a function over a two-dimensional region using a Monte
160 Carlo approach.
161 Arguments PM
163 ::simulation::montecarlo::singleExperiment args
166 Iterate code over a number of trials and store the results. The
167 iteration is gouverned by parameters given via a list of key‐
168 word-value pairs.
169 int n List of keyword-value pairs, all of which are available
171 during the execution via the getOption command.
172 The singleExperiment command predefines the following options:
174 · -init code: code to be run at start up
176 · -loop body: body of code that defines the computation to be run
178 time and again. The code should use setTrialResult to store the
179 results of each trial (typically a list of numbers, but the
180 interpretation is up to the implementation). Note: Required key‐
181 word.
182 · -final code: code to be run at the end
184 · -trials n: number of trials in the experiment (required)
186 · -reportfile file: opened file to send the output to (default:
188 stdout)
189 · -verbose: write the intermediate results (1) or not (0)
191 (default: 0)
192 · -analysis proc: either "none" (no automatic analysis), standard
194 (basic statistics of the trial results and a correlation matrix)
195 or the name of a procedure that will take care of the analysis.
196 · -columns list: list of column names, useful for verbose output
198 and the analysis
199 Any other options can be used via the getOption procedure in the body.
201
203 The procedure singleExperiment works by constructing a temporary proce‐
204 dure that does the actual work. It loops for the given number of tri‐
205 als.
206 As it constructs a temporary procedure, local variables defined at the
208 start continue to exist in the loop.
209
211 math, montecarlo simulation, stochastic modelling
212
214 Mathematics
215
217 Copyright (c) 2008 Arjen Markus <arjenmarkus@users.sourceforge.net>
218tcllib 0.1 simulation::montecarlo(n)