Executable Files

In this tutorial we will introduce the basic operations for creating executable files. Once you have a general routine in a matlab file, it allows you to perform more complex operations, and it is easier to repeat these operations. For example, you might have a set of instructions to use Euler's approximation for a differential equation (see the tutorial on loops), but you want to be able to use those instructions for different equations.

As an example, a simple file to approximate the D.E. y'= 1/y using Euler's method is found. To execute the commands in the file, the step size and the initial value must be specified. Once done, you can easily approximate the given D.E. for a wide variey of initial conditions and step sizes.

First, you will need to create the file. The easiest editor on our system (SGI's IRIX) is called "jot". It will allow you to do some very simple file manipulations. The editor is very simple and easy to start. It is not a very advanced editor, though.

Matlab executable files (called M-files) must have the extension ".m". In this example a file called simpleEuler.m is created. To get Matlab to execute the commands in the file simply type in "simpleEuler". Matlab will then search the current directory for the file "simpleEuler", read the file, and execute the commands in the file.

If you are not familiar with a more advanced editor use jot to create the file. Type in the following command at the unix prompt:
% jot simpleEuler.m

% file: simpleEuler.m
% This matlab file will find the approximation to
%
% dy/dx =  1/y
% y(0) = starty
%
%
%  To run this file you will first need to specify
%  the step the following:
%      h       : the step size
%      starty  : the initial value
%
%  The routine will generate three vectors.  The first
%  vector is x which is the grid points starting at
%  x0=0 and have a step size h.  
%
%  The second vector is an approximation to the specified
%  D.E. 
%
%  The third vector is the true solution to the D.E.
%
%  If you haven't guessed, you cna use the percent sign
%  to add comments.
%



x = [0:h:1];

y = 0*x;
y(1) = starty;

for i=2:max(size(y)),
   y(i) = y(i-1) + h/y(i-1);
end

true = sqrt(2*x+1);

Once the commands are in place, save the file. Go back to your original window and start up matlab. The file is called up by simply typing in the base name (in this case simpleEuler).

>> simpleEuler
??? Undefined function or variable h.

Error in ==> /home/black/math/mat/examples/simpleEuler.m
On line 27  ==> x = [0:h:1];

If you try to call the file without first defining the variables h and starty, you will get an error message. You must first specify all of the variables that are not defined in the file itself.

>> h = 1/16;
>> starty = 1;
>> starty = 1;
>> simpleEuler
>> whos
              Name        Size       Elements     Bytes    Density   Complex

                 h       1 by 1             1         8       Full      No 
                 i       1 by 1             1         8       Full      No 
            starty       1 by 1             1         8       Full      No 
              true       1 by 17           17       136       Full      No 
                 x       1 by 17           17       136       Full      No 
                 y       1 by 17           17       136       Full      No 

Grand total is 54 elements using 432 bytes

>> plot(x,y,'rx',x,true)

Once the necessary variables are defined, and you type in the command simpleEuler, matlab searched the current directory for a file called simpleEuler.m. Once it found the file, it read the file and executed the commands as if you had typed them from the keyboard.

If you would like to run the program again with a different step size, you have to be careful. The program will write over the vectors x,y, and true. If you want to save these vectors, you must do so explicitly!

>> x0 = x;
>> y0 = y;
>> true0 = true;
>> h = h/2;
>> simpleEuler
>> whos
              Name        Size       Elements     Bytes    Density   Complex

                 h       1 by 1             1         8       Full      No 
                 i       1 by 1             1         8       Full      No 
            starty       1 by 1             1         8       Full      No 
              true       1 by 33           33       264       Full      No 
             true0       1 by 17           17       136       Full      No 
                 x       1 by 33           33       264       Full      No 
                x0       1 by 17           17       136       Full      No 
                 y       1 by 33           33       264       Full      No 
                y0       1 by 17           17       136       Full      No 

Grand total is 153 elements using 1224 bytes

>> plot(x0,abs(true0-y0),'gx',x,abs(true-y),'yo');

This tutorial written by Kelly Black.