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
%
%  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, reading:

 
function [Rgyr_t]=singleRandWalk(randStream,tMax)
% Usage:  [Rgyr_t]=singleRandWalk(randStream,tMax)
% Input:
%   randStream - random number stream
%   tMax       - number of steps in random walk
% Output:
%   Rgyr_r     - array holding the radius of gyration
%                for all considered time steps

  x=0.;y=0.; % initial walker position
  Rgyr_t = zeros(tMax,1);
  for t = 1:tMax
    % implement random step
    phi=2.*pi*rand(randStream);
    x = x+cos(phi);
    y = y+sin(phi);
    % record radius of gyration for current time
    Rgyr_t(t)=sqrt(x*x+y*y);
  end
end
  

• averageRgyr.m, which computes the average radius of gyration of the random walks for time steps 1...tMax, reading:

 
function [avList,stdErrList]=averageRgyr(rawDat)
% Usage: [av]=averageRgyr(rawDat)
% Input:
%  rawData   - array of size [N,tMax] where N is the
%              number of independent random walks and
%              tMax is the number of steps taken by an
%              individual walk
% Returns:
%  av         - aveage radius of gyration for the steps

 [Lx,Ly]=size(rawDat);
  avList = zeros(Ly,1);
  stdErrList = zeros(Ly,1);
  for i = 1:Ly
    [av,var,stdErr] = basicStats(rawDat(:,i));
    avList(i) = av;
    stdErrList(i) = stdErr; 
  end
end

function [av,var,stdErr]=basicStats(x)
% usage: [av,var,stdErr]=basicStats(x)
% Input: 
%  x   - list of numbers
% Returns:
%  av  - average 
%  var - variance
%  stdErr - standard error
  av=sum(x)/length(x);
  var=sum((x-av).^2)/(length(x)-1);
  stdErr=sqrt(var/length(x));
end
  

For test purposes one might execute the myExample_2DRandWalk.m directly from within a Matlab session on a local Desktop PC.

Specifying file dependencies

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'...
                           }...
        );
  

In the above job submission script, all dependent files are listed as FileDependencies. I.e., the .m-files specified therein are copied from your local desktop PC to the HPC system at run time.

Now, from within a Matlab session I navigate to the Folder where the above .m-files are located in and call the job submission script, i.e.:

 
>> cd MATLAB/R2011b/example/myExamples_matlab/RandWalk/
>> mySubmitScript_v1
runtime    = 24:0:0 (default)
memory     = 1500M (default)
diskspace  = 50G (default)
  

before the job is actually submitted, I need to specify my user ID and password, of course. Once the job is successfully submitted, I can check the state of the job via typing jobRW.state. Once the job has finished, i.e.,

 
>> jobRW.state

ans =

finished
  

I might go on and load the results, giving

 
>> res=load(jobRW);
>> res

res = 

            N: 10000
      Rgyr_av: [100x1 double]
    Rgyr_sErr: [100x1 double]
       Rgyr_t: [10000x100 double]
          ans: 'finished'
          res: [1x1 struct]
         tMax: 100
  

However, note that there are several drawbacks related to the usage of FileDependencies: E.g.,

• each worker gets an own copy of the respective .m-files when the job starts (in particular, workers that participate in the computing process do not share a set of .m-files in a common location),
• the respective .m-files are not available on the HPC system once the job is finished,
• comparatively large input files need to be copied to the HPC system over and over again, if several computations on the same set of input data are performed.

In many cases a different procedure, based on specifying PathDependencies, outlined below in detail, might be recommendend.