Functions and Structured Programming in MATLAB

Just as in mathematics, it is convenient to be able to define logical parts of a program as a single entity. This can be because it becomes easier to understand a large program when it is composed of small easily identified segments or because a small piece of code is going to be used in several places in a program.

We have already met a small number of the built-in functions found in MATLAB. However, much of the power of MATLAB is that you can extend the language by writing your own functions. (MATLAB functions are similar to sub-routines found in other programming languages such as FORTRAN)

Mathematical functions

In mathematics, one can define a function, as for example:

This function can then be used by specifying the name of the function and an argument. The argument is used to replace the variable x in the definition of the function by the value that results in evaluating the argument. So, for example, the following arguments give the results shown:

  Argument    Value

       0         5
       1         8
      -1         2
     2+3        20

and so on. Functions can have more than one argument, as in:

In this case, using the function requires specifying two arguments where the first one is used in lieu of x and the second for y. So, for example, the following table shows the result for a variety of argument values:

  Function   Value

   g(0,0)      10
   g(1,0)      11
   g(0,1)       9
   g(2,1)      13

Note, in particular, the difference in result for g(1,0) and g(0,1).

Functions in MATLAB

In MATLAB, one can define functions much as we define them in mathematics. Like script files these are also stored with the extension .m but the first line of the file must contain the word function. For example, the following code segment defines a MATLAB function which corresponds to the mathematical definition:

  function y = equ(x)
  % Any comments immediately following the function declaration
  % are used for the HELP file

    y = 3.0*x + 5.0;

In this case, the function equ takes a local variable x and returns a real result, y . The result of the function is whatever value y has when the end of the function is reached.

Note: The name assigned to the function by MATLAB is actually the name given to the saved m-file not that given on the function declaration line. Of course, in most cases, it makes sense to use the same name.

Functions can be called by other functions, script program files or interactively at the command prompt. For example we may have a program that uses the defined function:

%  test program
 d = input('Please input the value for d ');  
 Answer = equ(d);        % Calls function which carries out the calculation
 Answer                  % Print output to screen

Look carefully at this example and note the following:

The variables used in calling the function do not have the same names as the variables within the function. The value of d when the function is called is used to replace all occurrences of x in the function body. There is a one-to-one mapping between the arguments given when the function is used and the arguments in the declaration of the function itself.

Number of Inputs and Outputs

There is pretty much no limit on the number of inputs and outputs for a MATLAB function. For example, if we consider the multi-variable function above, we have :

  function z = multiin(x,y)

  z = x^2 - y + 10.0

The above example takes two inputs and calculates a single output. Whereas the following function has multiple outputs but only a single input:

  function [y,t] = multiout(x)

  y = 2*x^2;
  t = y - x;

In fact, if we applied the above function on array variable, x, this would create two outputs (equivalent to y and t) which were also arrays.

There doesn't even need to be an input or an output. For example, consider the following unhelpful error message function, which when called, displays an output to the screen:

  function errormessage

  disp('There is an error')
  disp('Please rectify')

When to use functions

When should one use a function?

In general, a function should be used when there is any piece of code that forms some type of logically cohesive unit (a set of calculations that pertain to one type of quantity for example) or when a piece of code is going to be needed in several places in a program (it's always best to minimise the amount of code you have to repeat as it's easier to fix something if it's only in one place).

Update on format of a program

With the introduction of functions, the format of a program discussed earlier has changed. A complete program now includes a main program (most likely a script file) which will then call a number of functions (which may themselves call other functions) to manipulate the data.

    %This is the  main program

    % Assign variables values
    x1 = input('Please enter first value ');
    x2 = input('Please enter second value ');
  
   % Calculations
    a = equ(x1); % call function
    b = equ(x2); % call function
    answer = a - b; 

    % Display output
    answer

Note that the function equ (defined earlier) and the MATLAB function input are called twice in this program. This type of programming is called structured programming .

Local or Global Variables

The variables used within the body of a function are local variables. This means that variables used by a MATALB function are generally seperate from those of other functions and those in the base MATLAB workspace.

This is in contrast to variables created in a script file (or entered at the MATLAB command prompt) which are global variables and will remain in the MATLAB workspace until cleared. Global variables can be used by other non-function MATLAB code.

An Exercise

Now try the exercise associated with this section.

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