simulation::montecarlo(n)    Tcl Simulation Tools    simulation::montecarlo(n)



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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

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DESCRIPTION
       The technique of Monte Carlo simulations is basically simple:

       o      generate random values for one or more parameters.

       o      evaluate the model of some system you are interested in and
              record the interesting results for each realisation of these
              parameters.

       o      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:

       o      -init code: code to be run at start up

       o      -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.

       o      -final code: code to be run at the end

       o      -trials n: number of trials in the experiment (required)

       o      -reportfile file: opened file to send the output to (default:
              stdout)

       o      -verbose: write the intermediate results (1) or not (0)
              (default: 0)

       o      -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.

       o      -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

CATEGORY
       Mathematics

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




simulation                            0.1            simulation::montecarlo(n)
