Function M-File
Numerical Computing
with
.
MATLAB
for Scientists and Engineers
You will be able to



Write a function m-file,
Tell the differences between local and global
variables,
Use sub-functions and nested functions.
2
Anatomy of Function
mmempty.m
keyword
H1 Line (lookfor)
function d = mmempty(a,b)
%MMEMPTY Substitute Value if EMpty
% MMEMPTY(A,B) returns A if A is not empty,
input arguments
% otherwise
B
is
returned.
output
%
arguments
Help Message
if isempty(a)
function name = file name
d = b;
1~63 lower case
else
alphanumeric characters
d = a;
Function Body
end
3
Demo: Simple Function

Write a function m-file 'func1.m' for the
following expression.
f ( x)  e
x
cos  x 
func1.m

Run the function in the command window.
>> func1(4)
>> a = 0:0.1:5;
>> plot(a, func1(a))
4
Input – Output Arguments

Various forms of function definitions
function [mpay, tpay] = loan(amount, rate, years)
function [A] = RectArea(a, b)
function
A
= RectArea(a, b)
function
[V, S] = SphereVolArea(r)
function
trajectory(v, h, g)
5
Exercise 1: Polar Function

Write a function m-file for
r ( )  sin(3 ) cos( )

Use the function to calculate:
r ( / 4), r (5 / 2)

Use the function to plot (polar plot)
r ( ) for 0    2
6
Solution 1

Function m-file

Commands and Screenshot
7
Local and Global Variables



All variables in a function m-file is local.
Local variables are not shared between
function files / the command window.
Use global keyword for global variables.
global SPEED_OF_LIGHT;
8
Script and Function M-Files
Item
Script m-file
Function m-file
extension
.m
.m
1st line
any
function definition
variable
recognized in command
window
local to the function
usage
batch job
function, procedure
I/O
through variables
through arguments
file name
any
the function name
9
Anonymous Function

Simple one-line user-defined function
name = @ (arglist) expr

Examples
cube = @ (x) x^3
ex3r = @ (x, y) sqrt(x.^2+y.^2)

Usage
y = cube(23.4)
z = ex3r( [1 2], [2 0])
10
Exercise 2: Set of Parabolic Curves

Define an anonymous function for
f (a, b, x)  ( x  a)( x  b)

where a and b are scalar values while x can
be a vector.
Use the anonymous function to plot a set of
parabolic curves for -5<x<5 with
a=-b= 1, 1.5, 2, 2.5
11
Solution 2

Script and Screenshot
parabolas.m
12
Sub-functions 1/2


A function m-file may contain several function
definitions.
The 1st function is the primary function and
the others are sub-functions, which are
available only to the primary function.
f1.m
funciton y = f1( a, b, c )
% f1 is the main funciton
z = f2(a);
w = f3(b,c);
y = z .* w;
Why sub-functions?
Divide and conquer.
function k = f2( x)
...
13
Sub-functions 2/2



Variables in each function are private to the
function.
Only the primary function may be called from
outside.
Each function can call each other in the
function m-file.
14
Exercise 3 Determinant of 3x3 Matrix

Write a function m-file, det3x3.m, for calculating
the determinant of 3x3 matrix using the following
formula.
det( A)  A11

A22
A23
A32
A33
 A12
A21
A23
A31
A33
 A13
A21
A22
A31
A32
Use d = det3x3(A), where A is a 3x3 matrix. Use
a sub-function that calculates the 2x2
determinant.
e
3
3 2 1   




Calculate the determinant 6 5 7   e
2 e 




9
4
8
 
of the matrices on the right. 
  5 e
15
Solution 3

Function m-file
det3x3
16
Solution 3

Commands and Screenshot
17
Variable Number of Arguments


0+ Input Arguments / 0+ Output Arguments
Can be called with fewer arguments


nargin : # of actual input arguments
nargout : # of actual output arguments
18