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# simulation::montecarlo

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## NAME

simulation::montecarlo − Monte Carlo simulations

## SYNOPSIS

package require Tcl ?8.4?

package require simulation::montecarlo 0.1

package require simulation::random

package require math::statistics

::simulation::montecarlo::getOption keyword

::simulation::montecarlo::hasOption keyword

::simulation::montecarlo::setOption keyword value

::simulation::montecarlo::setTrialResult values

::simulation::montecarlo::setExpResult values

::simulation::montecarlo::getTrialResults

::simulation::montecarlo::getExpResult

::simulation::montecarlo::transposeData values

::simulation::montecarlo::integral2D ...

::simulation::montecarlo::singleExperiment args ______________________________________________________________________________

## DESCRIPTION

The technique of Monte Carlo simulations is basically simple:

 • generate random values for one or more parameters. • evaluate the model of some system you are interested in and record the interesting results for each realisation of these parameters. • after a suitable number of such trials, deduce an overall characteristic of the model.

You can think of a model of a network of computers, an ecosystem of some kind or in fact anything that can be quantitatively described and has some stochastic element in it.

The package simulation::montecarlo offers a basic framework for such a modelling technique:

#
# MC experiments:
# Determine the mean and median of a set of points and compare them
#
::simulation::montecarlo::singleExperiment -init {
package require math::statistics

set prng [::simulation::random::prng_Normal 0.0 1.0]
} -loop {
set numbers {}
for { set i 0 } { \$i < [getOption samples] } { incr i } {
lappend numbers [\$prng]
}
set mean [::math::statistics::mean \$numbers]
set median [::math::statistics::median \$numbers] ;# ? Exists?
setTrialResult [list \$mean \$median]
} -final {
set result [getTrialResults]
set means {}
set medians {}
foreach r \$result {
foreach {m M} \$r break
lappend means \$m
lappend medians \$M
}
puts [getOption reportfile] "Correlation: [::math::statistics::corr \$means \$medians]"

} -trials 100 -samples 10 -verbose 1 -columns {Mean Median}

This example attemps to find out how well the median value and the mean value of a random set of numbers correlate. Sometimes a median value is a more robust characteristic than a mean value - especially if you have a statistical distribution with "fat" tails.

## PROCEDURES

The package defines the following auxiliary procedures:
::simulation::montecarlo::getOption
keyword

Get the value of an option given as part of the singeExperiment command.
string keyword

Given keyword (without leading minus)

::simulation::montecarlo::hasOption keyword

Returns 1 if the option is available, 0 if not.
string keyword

Given keyword (without leading minus)

::simulation::montecarlo::setOption keyword value

Set the value of the given option.
string keyword

Given keyword (without leading minus)

string value

(New) value for the option

::simulation::montecarlo::setTrialResult values

Store the results of the trial for later analysis
list values

List of values to be stored

::simulation::montecarlo::setExpResult values

Set the results of the entire experiment (typically used in the final phase).
list values

List of values to be stored

::simulation::montecarlo::getTrialResults

Get the results of all individual trials for analysis (typically used in the final phase or after completion of the command).

::simulation::montecarlo::getExpResult

Get the results of the entire experiment (typically used in the final phase or even after completion of the singleExperiment command).

::simulation::montecarlo::transposeData values

Interchange columns and rows of a list of lists and return the result.
list values

List of lists of values

There are two main procedures: integral2D and singleExperiment.
::simulation::montecarlo::integral2D
...

Integrate a function over a two-dimensional region using a Monte Carlo approach.

Arguments PM

::simulation::montecarlo::singleExperiment args

Iterate code over a number of trials and store the results. The iteration is gouverned by parameters given via a list of keyword-value pairs.

 int n List of keyword-value pairs, all of which are available during the execution via the getOption command.

The singleExperiment command predefines the following options:

 • -init code: code to be run at start up • -loop body: body of code that defines the computation to be run time and again. The code should use setTrialResult to store the results of each trial (typically a list of numbers, but the interpretation is up to the implementation). Note: Required keyword. • -final code: code to be run at the end • -trials n: number of trials in the experiment (required) • -reportfile file: opened file to send the output to (default: stdout) • -verbose: write the intermediate results (1) or not (0) (default: 0) • -analysis proc: either "none" (no automatic analysis), standard (basic statistics of the trial results and a correlation matrix) or the name of a procedure that will take care of the analysis. • -columns list: list of column names, useful for verbose output and the analysis

Any other options can be used via the getOption procedure in the body.

## TIPS

The procedure singleExperiment works by constructing a temporary procedure that does the actual work. It loops for the given number of trials.

As it constructs a temporary procedure, local variables defined at the start continue to exist in the loop.

## KEYWORDS

math, montecarlo simulation, stochastic modelling

Mathematics

## COPYRIGHT

Copyright (c) 2008 Arjen Markus <arjenmarkus@users.sourceforge.net>

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