Using and Defining Functions in MATLAB

 

 

Elementary Mathematical Functions

 

·       In our work in the past few weeks, we have used several mathematical functions without much discussion. As you might expect, MATLAB provides an extensive library of built-in functions covering most of the common mathematical operations including exponential and logarithm functions, trigonometric and hyperbolic functions, and some common rounding functions.  The functions have a common, and by now familiar, syntax: 

 

output = function_name(input);

 

For example y=sin(x);

 

·       Typically we refer to x as the input or argument of the function that has a function name of sin. The output or returned variable, which would be sin(x), is said to be returned by the function.

 

·       These standard or built-in functions in MATLAB are fairly powerful and often operate on both scalar and array arguments. In addition, it is possible to use functions in the arguments of other functions (a technique which is known as function composition) e.g. y=sin(sqrt(x)).

 

User-Defined Functions

 

·       If there is some operation you use frequently that is not already a predefined function in MATLAB, you can create a user-defined function.  These function files are simply m-files with a specific structure.

 

·       Using the MATLAB editor we are able to construct our own function files that can be used repeatedly by other scripts files or other functions. This process is analogous to the use of subroutines in other languages such as C and Fortran. Essentially, this means that we can construct our own library of functions relevant to our own interests and applications. The main benefit or consequence is that complicated programming problems can be decomposed into smaller tasks and programs can then be developed in a modularized and structured manner.

·       To do this we define and code function files – a special type of m-file, that have a well specified structure or syntax. The first line on the function file must contain a function definition line that defines the function name and specifies a list of input and output variables:

          function [output variables]=function_name(input variables);

 

q       output variables is a comma separated list of variables calculated within the function file and enclosed within square brackets in the function definition. These are the values that the function will return to the MATLAB workspace.

q       input variables is a comma separated list of variables that need to be passed to the function when you use it. They are akin to the argument of the trigonometric functions we looked at earlier.

q       function_name is the name that you have chosen for the function and MUST be the same as the filename that you use to save the m-file (but it does not include the .m extension)

q       Any other variables defined inside the function but not in the output variable list are local variables and are not returned to or shown in your workspace.  You may use variable names inside a function even if those variables are used in a different way in the calling function.

 

Some guidelines and rules

 

·       The word function in the function definition line must be in lower case.

·       Comments can be placed anywhere within a function definition but those immediately following the function statement will be printed when you type help ‘function name’ at the command prompt.

 

An example

 

·       There are many instances where two variables are related by a square-law relationship, particularly in terms of energy and power calculations. Since these must be calculated on a frequent basis it is useful to define a special function for this purpose. Some illustrative relationships are:

 

Power dissipated in a resistor:  

Kinetic energy calculations:      

 

·       Let’s now write a function file whose sole purpose is to compute the square law relationship for some input…

 

·       Open a new m-file and copy-and-paste the commands below into that m-file.  Name the m-file the same name as the function name on the first line (squarelaw.m).  Add you name and the date in the comment lines.  Note that when copying-and-pasting you may get blank lines between the comment lines.  You MUST delete these blank lines in your m-file so that the first group of comment lines are not interrupted by spaces.

 

function  [out]=squarelaw(in,param)

%

% [out]=squarelaw(in,param)

%

% Computes square-law relationship

% out=(in^2)*param

%

% Author: …

% date:  …

 

out=(in^2)*param;

 

·       Type help squarelaw in the command window and you should see the comment lines to remind you what this function does and what its input and output arguments are.

 

·       Test it out…  Run the function as follows at the command prompt:

>>     out=squarelaw(10,2)

 

·       Now, modify this function so that it will allow both scalar inputs and vector (array) inputs and outputs and test it.  Hint:  make mathematical operations array operations rather than scalar operations.  Test it like so at the command prompt…

 

>>     v=linspace(0,10,100);

>>     R=1000;

>>     p=squarelaw(v,1/R);

>>     plot(v,p)

>>     xlabel('Voltage (V) ')

>>     ylabel('Power (W) ');

>>     title('Power Dissapation for a 1000 Ohm Resistor');

 

·       Note that all these commands above can be put in a script file (m-file).  So m-files can call functions and one function can call another.  Thus, it is helpful to build a library of commonly used functions.  You write an operation once as a well-written function, then you can use it anytime you need to perform that operation without having to retype it.  This is called modular programming. 

 

 

 

This document was originally created by Dr. Malcolm Daniels of the Department of Electrical and Computer Engineering and modified by Dr. Russell Hardie.