Difference between revisions of "Matlab Examples using MDCS"
Line 58: | Line 58: | ||
As liste above, the .m-file depends on the following files: | As liste above, the .m-file depends on the following files: | ||
* singleRandWalk.m, implementing a single random walk, | * singleRandWalk.m, implementing a single random walk, | ||
<nowiki> | |||
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 | |||
</nowiki> | |||
* averageRgyr.m, which computes the average radius of gyration of the random walks for time steps 1...tMax. | * averageRgyr.m, which computes the average radius of gyration of the random walks for time steps 1...tMax. | ||
<nowiki> | |||
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 | |||
</nowiki> | |||
For test purposes one might execute the myExample_2DRandWalk.m | For test purposes one might execute the myExample_2DRandWalk.m |
Revision as of 18:00, 6 June 2013
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,
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.
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. 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'... }... );