Numerical Methods Course Notes Version 0.1 (UCSD Math 174, Fall ...

16 CHAPTER 2. A “CRASH” COURSE IN OCTAVE/MATLAB
• eig(M) returns the eigenvalues of M. [V, LAMBDA] = eig(M) returns the eigenvectors, and
eigenvalues of M.
2.3 Programming and Control
If you are going to do any serious programming in octave, you should keep your commands in a
file. octave loads commands from ‘.m’ files. 2 If you have the following in a file called myfunc.m:
function [y1,y2] = myfunc(x1,x2)
% comments start with a ‘%’
% this function is useless, except as an example of functions.
% input:
% x1 a number
% x2 another number
% output:
% y1 some output
% y2 some output
y1 = cos(x1) .* sin(x2);
y2 = norm(y1);
then you can call this function from octave, as follows:
octave:1> myfunc(2,3)
ans = -0.058727
octave:2> [a,b] = myfunc(2,3)
a = -0.058727
b = 0.058727
octave:3> [a,b] = myfunc([1 2 3 4],[1 2 3 4])
a =
0.45465 -0.37840 -0.13971 0.49468
b = 0.78366
Note this silly function will throw an error if x1 and x2 are not of the same size.
It is recommended that you write your functions so that they can take scalar and vector input
where appropriate. For example, the octave builtin sine function can take a scalar and output a
scalar, or take a vector and output a vector which is, elementwise, the sine of the input. It is not
too difficult to write functions this way, it often only requires judicious use of .* multiplies instead
of * multiplies. For example, if the file myfunc.m were changed to read
y1 = cos(x1) * sin(x2);
it could easily crash if x1 and x2 were vectors of the same size because matrix multiplication is not
defined for an n × 1 matrix times another n × 1 matrix.
An .m file does not have to contain a function, it can merely contain some octave commands.
For example, putting the following into runner.m:
2 The ‘m’ stands for ‘octave.’