MATH/CMSC 206 - Introduction to Matlab

Function M-files Part 1

What is a Function M-File?
A Simple Function M-File
The General Idea
A (More) Complicated Function M-File
Self-Test

What is a Function M-File?

Suppose you wished to write your own function which you could access every time you loaded up Matlab. Suppose it couldn't be as simple as we've seen before - perhaps it needs to test the values passed to it like a piecewise function in calculus. Suppose the function is a process that needs to calculate and return a value. How can we do this?

Matlab allows all of this very conveniently using function M-files. At its most basic level an M-file is a text file containing a series of Matlab commands. Typically these files have the extension .m which is where they get their name. The location of these files is important also since otherwise Matlab won't know where to find them. The best and perhaps most obvious place to put them is in the current working directory. This is the directory indicted in the leftmost directory window "Current Directory" on Matlab. If you wish to store your M-files in another directory you'll have to add that directory to the path. You can do this by hunting under the "File" pull-down menu.

A Simple Function M-File

Let's start by creating a function M-file which you'll then have in your directory for future use. We'll make it something useful from calculus. We know that an object dropped from a height of h meters will strike the ground in sqrt(h/4.9) seconds. Let's create a function M-file named HowLong. To do this type:

edit HowLong.m

Matlab will verify that you'd like to open a new file (in the current working directory) so click "Yes".

If you prefer you can also open this file using any text editor you wish - it's not necessary to use Matlab's.

In the editor window which opens type the following code:

function t=HowLong(h) t=sqrt(h/4.9); end

Note: The end at the end of the m-file is not critical but it is good programming practice and I will always do it. I recommend you do too.

Save the M-file. From now on we can access our function simply by calling the HowLong function. You can do this anytime you ever run Matlab (now or in the future) because the file (and hence the function) will be there until you delete it.

HowLong(100)

ans =

   4.517539514526256

Stop to anaylze for a minute how this function works. The keyword function tells Matlab that we're writing a function. The t= indicates the variable which we'll use to return the result. The name HowLong is the name of the function and the parenthetical h indicates that a single value will be passed to the function and in that function the value will be called h.

We don't need any sort of end command here because as soon as Matlab runs out of commands in the HowLong.m file it merely stops and the value of t is passed back.

We can also do things like:

syms x;
HowLong(x)

 
ans =
 
((10*x)/49)^(1/2)

or:

syms q;
HowLong(q)

 
ans =
 
((10*q)/49)^(1/2)

The General Idea

The general outline of a function M-file is as follows:

function r=functionname(a,b,...)
do stuff
any matlab stuff
by the end assign
r = whatever you want to return
end

You can do any Matlab commands you like in the middle provided that you assign your return value r before you end the function. Note that the use of r is arbitrary. The functionname must correspond to the filename functionname.m you use. Here are some other simple function m-files and what they do:

Example 1: This will accept one value a and return that value plus 3.

function r=justin1(a)
r=a+3;
end

Example 2: This will accept two values a and b, solves a*x+b, printing the result since the line does not end with a semicolon ;, and then assigns (and therefore returns) s=a-b.

function s=justin2(a,b)
syms x;
solve(a*x+b);
s=a-b;
end

Example 3: This does ezplot on a*x^2 and returns a-8. It completely ignores b.

function t=justin3(a,b)
syms x;
ezplot(a*x^2);
t=a-8;
end

A (More) Complicated Function M-File

Function M-files do not need to be so simple. We can define a piecewise function. Try this new M-file:

edit pwisef.m

In the function place the following:

function y=pwisef(x) if (x <= 0) y = -x; else y = sin(x); end end

Note: The first end ends the if/else and the second end ends the function. The result is as expected:

pwisef(-1)

ans =

     1

versus

pwisef(pi/4)

ans =

   0.707106781186547

But if you try the following you'll get an error:

pwisef(x)

Why is this? The answer is fairly straightforward. The pwisef takes the value x as a parameter and then hits a brick wall when it tries to execute if (x<=0). How can it compare x to 0 if it doesn't know x? It can't. This will cause some problems as we'll see later.

Self-Test

Write a function M-file defining a function add which accepts a vector with two entries and adds those two entries, returning the result.
Write a function M-file defining a function maxheight which accepts two values, an initial velocity and an initial height, and returns the maximum height of an object with those criteria.
Write a function M-file defining a function area which accepts a value b and returns the area under the function 1/x from x=1 to x=b.

Answers to Self-Test