Octave
GNU Octave is a high-level language primarily intended for numerical computations. It's commands are in general compatible with those of Matlab. A simple Octave program and an associated submit script are as follows:
| Category of Software | |
|---|---|
| What is Octave | GNU Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command line interface for solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with Matlab. It may also be used as a batch-oriented language. Octave has extensive tools for solving common numerical linear algebra problems, finding the roots of nonlinear equations, integrating ordinary functions, manipulating polynomials, and integrating ordinary differential and differential-algebraic equations. It is easily extensible and customizable via user-defined functions written in Octave's own language, or using dynamically loaded modules written in C++, C, Fortran, or other languages. Octave is available from http://www.gnu.org/software/octave/ The Official Octave Manual is found at: http://www.gnu.org/software/octave/doc/interpreter/index.html |
| How to use | Free to use |
Sample Code
This example comes from http://www.smac.lps.ens.fr/index.php/Program:Direct_pi
%--------------------------------------------------------------
% plot_direct_pi.m -- Illustrative plot of SMAC algorithm 1.1
%
% usage: octave> plot_direct_pi( Ntrials )
%
% Octave version: 3.0.3
%--------------------------------------------------------------
%--------------------------------------------------------------
% plot_direct_pi -- run and plot results of direct_pi
%--------------------------------------------------------------
function plot_direct_pi( Ntrials )
[XYin,XYout,pi_estimate] = direct_pi( Ntrials );
clf; % clear graphics
plot(XYin(:,1),XYin(:,2),'ro'); % inner x,y: red 'o'
hold on; % use same graph
plot(XYout(:,1),XYout(:,2),'bx'); % outer x,y: blue 'x'
axis( [-1 1 -1 1],'square' ); % graph annotations
xlabel('x');
ylabel('y');
str1 = 'plot\_direct\_pi.m: SMAC Algorithm 1.1';
str2 = strcat( 'Ntrials=',num2str(Ntrials) );
str3 = strcat( ', pi\_estimate=',sprintf("%6.4f",pi_estimate) );
title( strcat( str1, "\n", str2, str3 ));
end
%------------------------------------------------------------------
% direct_pi -- SMAC algorithm 1.1: direct-sampling estimate of pi
%
% Ntrials: number of random points in a square of edge 2
%
% Nhits: number of trial points in inscribed unit circle
% TrueFalse: vector of T/F = 1/0 = inside/outside unit circle
%
% note: Octave fn 'find' gives indices of non-zero elements
%------------------------------------------------------------------
function [XYin,XYout,pi_estimate] = direct_pi( Ntrials )
XY = [ran( Ntrials,-1,1 ), ran( Ntrials,-1,1 )]; % x,y vectors
TrueFalse = (XY(:,1).^2 + XY(:,2).^2 < 1); % T/F=1/0 vector
XYin = XY( find( TrueFalse), : ); % inner x,y's
XYout = XY( find(!TrueFalse), : ); % outer x,y's
Nhits = size(XYin,1);
pi_estimate = 4 * Nhits / Ntrials; % pi/4 = area ratio
end
%-------------------------------------------------------------------
% ran -- use Octave fn 'rand' to get uniform random vector in (a,b)
%-------------------------------------------------------------------
function randvector = ran( rows,a,b )
randvector = (b-a)*rand(rows,1) + a;
end
Note, as this program plots a graph, you must have X11-forwarding enabled on your X-terminal session. See the Access (original) page for more information.
$module load octave $octave octave:1> plot_direct_pi(1000)
An Octave MPI toolbox is also available. The following script illustrates how it can be used to run one of the examples which comes with it:
$module load mptib To use MPITB you must include contents of $MPITB_HOME/.octaverc in ~/.octaverc $cp $MPITB_HOME/.octaverc ~/.octaverc
#!/bin/sh #$ -S /bin/sh #$ -cwd #$ -pe orte 4 #$ -l h_rt=12:00:00 #$ -l h_vmem=2G module load mpitb mpirun -wd $MPITB_HOME/Pi octave -q --eval "Pi(2E7,'r')"
results =
{
pi = 3.1416
err = -2.1094e-13
time = 1.8360
}