Octave/MATLAB basics

The codes found here should work for Octave 2.1 and 2.9

Start

Type octave (and then ``enter'') in the shell window; you will see Octave's prompt, octave:1> 
If you want Matlab, you can start it with matlab-nojvm; you will see Matlab's prompt, >> 
Try basic commands:

1+1
a=1+1
a=1+5;
a
sin(3.14)
sin(pi)

Matrices

v=[3,4,5]
size(v)
w=[3,4,5]'
size(w)
a=[0,7,0;3,0,0;0,0,0]
size(a)
a(1,2)
col2=a(:,2)
size(col2)
a*a
a.*a

Plotting

x=[0,1,2,3]'
y=x.^2
plot(x,y)
# To discard the plot, point a mouse on it and type q.
x=(0:0.1:3)'
# To discard the rest of the output, type q.
y=x.^2
plot(x,y)
# To discard the plot, point a mouse on it and type q.
z=cos(x);
w=sin(x);
plot(x,y,x,z,x,w)
# Here we plot y vs. x, z vs. x, and w vs. x

Solving ODEs

function ret=f(t,x); ret=x^2; endfunction;
# Test it: see what f(3,7) is

# t will be on the interval [0,1]; x(0)=0.9
[t,x]=rk4('f',[0,1],0.9);
# t will be the set of moments of time;
# x will be the values of the function at these moments of time.
plot(t,x)

Remark 1: In Matlab, function ret=f(t,x); ret=x^2; endfunction; generates an error message (Error: Function definitions are not permitted at the prompt or in scripts). You would need to describe a function f(t,x) in a separate file, f.m, with the following contents:

function ret=f(t,x); ret=x^2;

Remark 2: In Octave, instead of rk4, one could use the standard lsode function of the Octave package, with the only difference that lsode which uses slightly different syntax. The above example is to be modified as follows:

function ret=f(x,t); ret=x^2; endfunction;
# Test it: see what f(3,7) is!
# Note that now we need x to come first in the list of arguments of f(),
# because lsode expects it this way!
t=(0:0.01:1)';
x=lsode('f',0.9,t);
plot(t,x)

Writing scripts

## Octave script for solving dx/dt=f(t,x)=x^2
## with the Runge-Kutta method (implemented in rk4.m)
function ret=f(t,x); ret=x^2; endfunction;
[t,x]=rk4('f',[0,1],0.9);
plot(t,x);
pause(60);
## Press Ctrl-C to stop

Here is an example of solving a first order system:

## Octave script for solving dx/dt=v, dv/dt=-x-v/5
## with the Runge-Kutta method (implemented in rk4.m).
function ret = f(t,X); ret = [X(2),-X(1)-X(2)/5]; endfunction
[T,X]=rk4('f',[0,50],[-2,0],0.2); # added timestep parameter, dt=0.2
plot(X(:,1),X(:,2))
pause(60);

Incorporating graphics into LaTeX files

print('fig.eps','-deps')

\documentclass{article}
\usepackage{graphicx,color}
\begin{document}
Equation
$$
\frac{dx}{dt}=x^2
$$
\begin{figure}[htbp]
\includegraphics[width=4in]{fig.eps}
\end{figure}
\end{document}

Here is an example of this. Download the files oscillator.tex, fig.m, rk4.m.

octave fig.m
# This produces fig.eps

latex oscillator.tex
latex oscillator.tex
dvips -Ppdf oscillator.dvi -o oscillator.ps
ps2pdf oscillator.ps

For more examples on incorporating graphics and creating ``PowerPoint-like'' presentations, see Using Octave to prepare figures for LaTeX papers.

Remark: If you use Matlab, once you produced a graphical output in a separate window, in that window go to ``File'' -> ``Save As...'' and in ``Save as type:'' choose ``EPS file''.

Reference materials

• Octave on-line manual (see also Octave documentation)
• GNUplot documentation
• Running MATLAB jobs In Batch
• ODE Software for MATLAB

Written by Andrew Comech

ACKNOWLEDGMENT: This page resulted from the research that has been partially supported by the National Science Foundation under Grants DMS-0621257 and DMS-0600863.