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simulation::montecarlo − Monte Carlo simulations
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 ______________________________________________________________________________
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.
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:
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-init code: code to be run at start up | ||
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-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. | ||
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-final code: code to be run at the end | ||
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-trials n: number of trials in the experiment (required) | ||
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-reportfile file: opened file to send the output to (default: stdout) | ||
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-verbose: write the intermediate results (1) or not (0) (default: 0) | ||
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-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. | ||
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-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.
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.
math, montecarlo simulation, stochastic modelling
Mathematics
Copyright (c) 2008 Arjen Markus <[email protected]>