Matlab Examples using MDCS

A few examples for Matlab applications using MDCS (prepared using Matlab version R2011b) are illustrated below.

Example application

Consider the Matlab .m-file myExample_2DRandWalk.m (listed below), which among other things illustrates the use of sliced variables and independent stremas of random numbers for use with parfor-loops.

This example program generates a number of N independent 2D random walks (a single step has steplength 1 and a random direction). Each random walk performs tMax steps. At each step t, the radius of gyration (Rgyr) of walk i is stored in the array Rgyr_t in the entry Rgyr_t(i,t). While the whole data is availabe for further postprocessing, only the average radius of gyration Rgyr_av and the respective standard error Rgyr_sErr for the time steps 1...tMax are computed immediately and stored in an output file on HERO.

 
%% FILE:  myExample_2DRandWalk.m
%  BRIEF: illustrate sliced variables and independent streams 
%         of random numbers for use with parfor-loops
%         
%  DEPENDENCIES:
%    singleRandWalk.m   - implements single random walk
%    averageRgyr.m      - computes average radius of gyration
%                         for time steps 1...tMax
%    basicStats.m       - implements basic stat summary measures
%
%  AUTHOR: Oliver Melchert
%  DATE:   2013-06-05
%

N       = 10000;         % number of independent walks
tMax    = 100;           % number of steps in individual walk
Rgyr_t  = zeros(N,tMax); % matrix to hold results: row=radius 
                         % of gyration as fct of time; 
                         % col=independent random walk instances

parfor n=1:N

        % create random number stream seeded by the
        % current value of n; you can obtain a list
        % of all possible random number streams by
        % typing RandStream.list in the command window
        myStream = RandStream('mt19937ar','Seed',n);

        % obtain radius of gyration as fct of time for 
        % different independent random walks (indepence 
        % of RWs is ensured by connsidering different 
        % random number streams for each RW instance)
        Rgyr_t(n,:) = singleRandWalk(myStream,tMax);

end

% compute average Rgyr and its standard error for all steps
[Rgyr_av,Rgyr_sErr] = averageRgyr(Rgyr_t);

  

As liste above, the .m-file depends on the following files:

• singleRandWalk.m, implementing a single random walk,
• averageRgyr.m, which computes the average radius of gyration of the random walks for time steps 1...tMax,
• basicStats.m, implenting routines for the three basic summary statistic average, corrected variance and standard error.

For test purposes one might execute the myExample_2DRandWalk.m directly from within a Matlab session on a local Desktop PC. So as to sumbit the respective job to the local HPC system one might assemble the following job submission script, called mySubmitScript.m:

 
sched = findResource('scheduler','Configuration','HERO');

jobRW =...
   batch(...
        sched,...    
        'myExample_2DRandWalk',...
        'matlabpool',2,...
        'FileDependencies',{...
                           'singleRandWalk.m',...
                           'averageRgyr.m',...
                           'basicStats.m'...
                           }...
        );