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.

Type	Name	Mode
string	keyword
	Given keyword (without leading minus)

::simulation::montecarlo::hasOption keyword

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

Type	Name	Mode
string	keyword
	Given keyword (without leading minus)

::simulation::montecarlo::setOption keyword value

Set the value of the given option.

Type	Name	Mode
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

Type	Name	Mode
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).

Type	Name	Mode
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.

Type	Name	Mode
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.

Type	Name	Mode
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