MATLAB Ch 3 – Functions & Files
EGR1302
Outline
Introduction
 Elementary mathematical operations
 User-defined functions
 Working with data files

Introduction

Review from Ch 1

MATLAB mathematical functions
 Pair
of parentheses after function name
encloses function’s argument
 Can be part of mathematical expression
Users can define functions
 MATLAB has commands and functions
for managing the work session

Introduction
MATLAB has many built-in functions
 Users may define functions

Convenient use
 Advanced function capability

 Function
handles
 Anonymous functions
 Subfunctions
 Nested functions

MATLAB allows input/output of data
files
Section 3.1
ELEMENTARY
MATHEMATICAL FUNCTIONS
Finding relevant functions

Command – lookfor

Seeks the word in the help descriptions
of the MATLAB help system
 If
user does not know the name of function
>> lookfor imaginary
i
- Imaginary unit.
j
- Imaginary unit.
complex - Construct complex result
from real and imaginary
parts.
imag
- Complex imaginary part.
Finding relevant functions
Finding relevant functions

Command – disp

If user knows correct spelling of a
MATLAB function
 Same
output as selecting complex
hyperlink after using lookfor command
>> disp complex
Tables 3.1-1, 3.1-2, 3.1-3

List of some common mathematical
functions (pp. 142, 146, 148)
Exponential & logarithmic
 Complex number
 Numeric
 Trigonometric
 Hyperbolic

Example – complex functions
>> x=-3+4i;
>> y=6-8i;
>> mag_x = abs(x)
mag_x =
5
>> mag_y = abs(y)
mag_y =
10
>> mag_product = abs(x*y)
mag_product =
50
Example – complex functions
>> angle_x = angle(x)
angle_x =
2.2143
>> angle_y = angle(y)
angle_y =
-0.9273
>> sum_angles = angle_x + angle_y
sum_angles =
1.2870
>> angle_product = angle(x*y)
angle_product =
1.2870
Section 3.2
USER-DEFINED FUNCTIONS
Functions files

Differences between script &
functions M-files

All functions variables are local
 Values
available only within function
 Useful when repeating a set of commands
multiple times


Building blocks of larger programs
First line in function  function
definition line
 List
of inputs and outputs
Function definition line

Distinguishes function from script
function[output vars]=func_name(input vars)

function – must be lower case

Output variables must be enclosed in

Input variables must be enclosed in
square brackets
parentheses
 func_name must be same as name of
M-file
 Use
exist function before naming a function
Simple function example
function z = fun(x,y)
u = 3*x;
z = u + 6*y.^2;
>> fun(3,7)
ans =
303
>> z = fun(3,7)
z=
303
>> y = [3 4 5];
>> z = fun(y,7)
z=
303 306 309
>> z
??? Undefined function or variable 'z'.
>> u
??? Undefined function or variable 'u'.
Functions
Suppress output of function by
putting semicolon after the function
call
 Only order of arguments is important,
not names of arguments
 Arrays can be used as input
arguments
 May have more than one output

Variations in function line

One input, one output:
 Brackets
are optional
function [area_square] = square(side)
OR
function area_square = square(side)
 Two inputs, one output
function
[volume_box] = box(height,width,length)


One input, two outputs
function [area_circle,circumf] = circle(radius)

No named output: function sqplot(side)
function sqplot(side)
2nd simple function example
function [A, C] = circle(r)
A = pi*r.^2;
C = 2*pi*r;
>> [A, C] = circle(4)
A=
50.2655
C=
25.1327
>> r = [3 4 5];
>> [A, C] = circle(r)
A=
28.2743 50.2655 78.5398
C=
18.8496 25.1327 31.4159
Comments in functions
Comment lines, starting with %, may
be placed anywhere in function file
 If user types help to obtain
information about function



All comment lines immediately following
function definition line up to first blank
or executable line is displayed
If user types lookfor command

First comment line is displayed
Local variables

Names of input variables given in
function are local to the function


Other variable names can be used when
calling the function
All variables inside a function are
erased after the function finishes
executing

Except when the same variable names
appear in the output variable list used in
the function call
Global variables

global command declares certain
variables global

Their values are available to the basic
workspace and to other functions that
declare these variables global.
global a x q

Any assignment to those variables, in
any function or in the base workspace, is
available to all the other functions
declaring them global.
Finding the zeros of a
function
fzero(‘function’, x0)
function is a string containing the
name of the function
 x0 is a user-supplied guess for the zero
 Returns a value of x that is near x0


Identifies only points where the function
crosses the x-axis
 Not
points where the function just touches
the axis.
>> fzero('cos',2)
ans =
1.5708
Using fzero with userdefined functions

To find the zeros of more complicated
functions, it is more convenient to
define the function in a function file
function y = f1(x)
y = x + 2*exp(-x) - 3;
>> x = fzero('f1',-1)
x=
-0.5831
>> x = fzero('f1',2)
x=
2.8887
Finding the minimum of a
function
fminbnd(‘function’, x1,x2)

function is a string containing the
name of the function

Returns a value of x that minimizes the
function in the interval x1 ≤ x ≤ x2
>> fminbnd('cos', 0,4)
ans =
3.1416
Finding the minimum of a
function

For functions of more than one
variable
fminsearch(‘function’, x0)
function is a string containing the
name of the function
 Vector x0 is a guess that must be
supplied by the user.

function f = f4(x)
f = x(1).*exp(-x(1).^2-x(2).^2);
>> fminsearch('f4',[0,0])
ans =
-0.7071 0.0000
Design optimization example

Example 3.2-2, p. 161
Section 3.4
WORKING WITH DATA FILES
Importing data files

Typical ASCII file

Header lines
 One
or more lines of text
 Contain comments, creation date, column
headings

Data
 Arranged
in rows & columns
 Each number in a row may be separated



Spaces
Commas
Tab
Importing data files

Importing an externally generated file
in ASCII format
Matlab can not import data that is
separated (i.e., delimited) by commas
 To import a comma-delimited ASCII file,
some pre-processing is required

 First,
open data file in a text editor (e.g.,
Notepad)
 Second, delete the text header lines
 Third, replace each comma with at least one
space (i.e., use Replace function)
Importing data files

Importing an externally generated file
in ASCII format
load filename

Matrix is generated
 Name
of matrix is filename with extension
stipped off
load tensile_test.txt
 This
command creates a matrix named
“tensile_test”
Importing data files

Excel spreadsheets may be imported
into Matlab

Save Excel file in 2003 format (i.e., .xls
extension)
A = xlsread(‘filename’)
 Imports
file into array A
[A, B] = xlsread(‘filename’)
 Imports
all numeric data into array A and all
text data into array B
Import Wizard

Allows for importing a variety of
ASCII file formats
Space-delimited files
 Mixed text and numeric files
 Files with text headers
 Files with non-space delimiters

 Commas
 Semi-colons
 Tabs
Import Wizard

What you must know before you may
import the data file
How many data items are in each row?
 Are the data items numeric, text strings,
or a mixture of both types?
 Does each row or column have a
descriptive text header?
 What character is used as the delimiter
that separates items in each row into
columns?

Import Wizard

Caution


Import Wizard overwrites any existing
variable in the workspace with no
warning message!
Dialog boxes ask you to:
Specify the name of the file you want to
import
 Specify the delimiter used in the file
 Select the variables that you want to
import

Import Wizard
End of Chapter 3
Slides that I do not plan to
use
Outline
Introduction
 Elementary mathematical operations
 User-defined functions
 Advanced function programming
 Working with data files

Section 3.3
ADVANCED FUNCTION
PROGRAMMING
Function handles

Create a function handle to any
function by using the at sign, @,
before the function name.
Name the handle
 Use the handle to reference the function

>>sine_handle = @sin;
 sine_handle
the handle
is a user-selected name for
Function handles

A common use
Pass the function as an argument to
another function
 Example - plot sin x over 0  x  6 as
follows:

>>plot([0:0.01:6],sine_handle,[0:0.01:6])
 Cumbersome
way to plot the sine function
 However, the concept can be extended to
create a general purpose plotting function
that accepts a function as an input
Function handles
function x =
gen_plot(fun_handle,
interval)
 plot(interval, fun_handle,
interval)

You may call this function to plot the
sin x over 0  x  6 as follows:
 >>gen_plot(sine_handle,[0:0.
01:6])
