'\"
'\" Generated from file '/usr/obj/ports/tcllib-1.11.1/tcllib-1.11.1/modules/simulation/montecarlo.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2008 Arjen Markus <arjenmarkus@users.sourceforge.net>
'\"
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.TH "simulation::montecarlo" n 0.1 simulation "Tcl Simulation Tools"
.BS
.SH NAME
simulation::montecarlo \- Monte Carlo simulations
.SH SYNOPSIS
package require \fBTcl  ?8.4?\fR
.sp
package require \fBsimulation::montecarlo  0.1\fR
.sp
package require \fBsimulation::random \fR
.sp
package require \fBmath::statistics \fR
.sp
\fB::simulation::montecarlo::getOption\fR \fIkeyword\fR
.sp
\fB::simulation::montecarlo::hasOption\fR \fIkeyword\fR
.sp
\fB::simulation::montecarlo::setOption\fR \fIkeyword\fR \fIvalue\fR
.sp
\fB::simulation::montecarlo::setTrialResult\fR \fIvalues\fR
.sp
\fB::simulation::montecarlo::setExpResult\fR \fIvalues\fR
.sp
\fB::simulation::montecarlo::getTrialResults\fR
.sp
\fB::simulation::montecarlo::getExpResult\fR
.sp
\fB::simulation::montecarlo::transposeData\fR \fIvalues\fR
.sp
\fB::simulation::montecarlo::integral2D\fR \fI...\fR
.sp
\fB::simulation::montecarlo::singleExperiment\fR \fIargs\fR
.sp
.BE
.SH DESCRIPTION
.PP
The technique of \fIMonte Carlo simulations\fR is basically simple:
.IP \(bu
generate random values for one or more parameters.
.IP \(bu
evaluate the model of some system you are interested in and record the
interesting results for each realisation of these parameters.
.IP \(bu
after a suitable number of such trials, deduce an overall characteristic
of the model.
.PP
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.
.PP
The package \fIsimulation::montecarlo\fR offers a basic framework for
such a modelling technique:
.nf

#
# 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}

.fi
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.
.SH PROCEDURES
The package defines the following auxiliary procedures:
.TP
\fB::simulation::montecarlo::getOption\fR \fIkeyword\fR
Get the value of an option given as part of the \fIsingeExperiment\fR command.
.RS
.TP
string \fIkeyword\fR
Given keyword (without leading minus)
.RE
.sp
.TP
\fB::simulation::montecarlo::hasOption\fR \fIkeyword\fR
Returns 1 if the option is available, 0 if not.
.RS
.TP
string \fIkeyword\fR
Given keyword (without leading minus)
.RE
.sp
.TP
\fB::simulation::montecarlo::setOption\fR \fIkeyword\fR \fIvalue\fR
Set the value of the given option.
.RS
.TP
string \fIkeyword\fR
Given keyword (without leading minus)
.TP
string \fIvalue\fR
(New) value for the option
.RE
.sp
.TP
\fB::simulation::montecarlo::setTrialResult\fR \fIvalues\fR
Store the results of the trial for later analysis
.RS
.TP
list \fIvalues\fR
List of values to be stored
.RE
.sp
.TP
\fB::simulation::montecarlo::setExpResult\fR \fIvalues\fR
Set the results of the entire experiment (typically used in the final
phase).
.RS
.TP
list \fIvalues\fR
List of values to be stored
.RE
.sp
.TP
\fB::simulation::montecarlo::getTrialResults\fR
Get the results of all individual trials for analysis (typically used in
the final phase or after completion of the command).
.sp
.TP
\fB::simulation::montecarlo::getExpResult\fR
Get the results of the entire experiment (typically used in the final
phase or even after completion of the \fIsingleExperiment\fR command).
.sp
.TP
\fB::simulation::montecarlo::transposeData\fR \fIvalues\fR
Interchange columns and rows of a list of lists and return the result.
.RS
.TP
list \fIvalues\fR
List of lists of values
.RE
.PP
There are two main procedures: \fIintegral2D\fR and \fIsingleExperiment\fR.
.TP
\fB::simulation::montecarlo::integral2D\fR \fI...\fR
Integrate a function over a two-dimensional region using a Monte Carlo
approach.
.sp
Arguments PM
.sp
.TP
\fB::simulation::montecarlo::singleExperiment\fR \fIargs\fR
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.
.RS
.TP
int \fIn\fR
List of keyword-value pairs, all of which are available
during the execution via the \fIgetOption\fR command.
.RE
.PP
The \fIsingleExperiment\fR command predefines the following
options:
.IP \(bu
\fI-init code\fR: code to be run at start up
.IP \(bu
\fI-loop body\fR: body of code that defines the computation to
be run time and again. The code should use \fIsetTrialResult\fR
to store the results of each trial (typically a list of numbers,
but the interpretation is up to the implementation). Note: Required keyword.
.IP \(bu
\fI-final code\fR: code to be run at the end
.IP \(bu
\fI-trials n\fR: number of trials in the experiment (required)
.IP \(bu
\fI-reportfile file\fR: opened file to send the output to (default: stdout)
.IP \(bu
\fI-verbose\fR: write the intermediate results (1) or not (0) (default: 0)
.IP \(bu
\fI-analysis proc\fR: 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.
.IP \(bu
\fI-columns list\fR: list of column names, useful for verbose output
and the analysis
.PP
Any other options can be used via the getOption procedure
in the body.
.SH TIPS
The procedure \fIsingleExperiment\fR works by constructing a
temporary procedure that does the actual work. It loops for the given
number of trials.
.PP
As it constructs a temporary procedure, local variables defined at the
start continue to exist in the loop.
.SH KEYWORDS
math, montecarlo simulation, stochastic modelling
.SH COPYRIGHT
.nf
Copyright (c) 2008 Arjen Markus <arjenmarkus@users.sourceforge.net>

.fi