Multimedia Security:
Introduction to Matlab
Riccardo Lazzeretti
lazzeretti@diism.unisi.it
Lab LTT (240, second floor)
Outline
•
•
•
•
•
•
•
•
•
What is Matlab?
Matlab layout
Variables, array, matrix, string, indexing
Operators (Arithmetic, relational, logical )
Display Facilities
Flow Control
Using of M-File
Writing User Defined Functions
Workspace
What is Matlab?
• Matlab (MATrix LABoratory) is basically a high level
language which has many specialized toolboxes for
making data analysis easy
• Interactive environment
▫ Commands interpreted one line at a time
▫ Own functions or procedures may be scripted
• Enriched by thematic toolbox
▫
▫
▫
▫
Image acquisition
Financial
Signal processing
…
• Too broad for our purposes in this course
Matlab Layout
• Command Window
▫ type commands
• Current Directory
▫ View folders and m-files
• Workspace
▫ View program variables
▫ Double click on a variable
to see it in the Array Editor
• Command History
▫ view past commands
▫ save a whole session
using diary
• Configurable Intarface
▫
Other windows…

Help!!!
Variables
• No need for type declaration:
int a;
double b;
float c;
• Matlab works with double precision (unless specified) matrices
• Variables are 1x1 matrices
Example:
>>x=5;
>>x1=2;
• Particular values predefined:
▫
▫
▫
▫
▫
pi : π
eps: Euler’s number
i or j: imaginary unit
inf: infinite (division by 0 is allowed)
NaN: Not a Number (inf - inf)
• Matlab is case sensitive
▫ A is different from a
Array, Matrix
• a vector
In the help:
Matlab
 Mathematics
 Matrices and arrays
x = [1 2 5 1]
x =
1
2
5
• a matrix
1
M = [1 2 3; 5 1 4; 3 2 -1]
M =
1
5
3
2
1
2
3
4
-1
• Column vector and transpose
y = x’
w = [3 5 7]’
z = [1; 9; 2]
y =
w =
1
2
5
1
z =
3
5
7
1
9
2
Series
•
t =1:10
t =
1
2
k =2:-0.5:-1
•
3
4
1
0.5
5
6
7
8
k =
2
•
B
1.5
= [1:4; 5:8]
x =
1
5
2
6
3
7
4
8
0
-0.5
-1
9
10
Matrices automatically generated
• zeros(M,N), MxN matrix of zeros
• zeros(M) stands for zeros(M,M)
• ones(M,N) MxN matrix of ones
• ones(M) stands for ones(M,M)
• eye(M)generates the identity matrix
• rand(M,N) MxN matrix of uniformly
distributed random numbers on
[0,1)
▫ randn(M,N) for normal distribution
• magic(M) ???
x = zeros(1,3)
x =
0
0
x = ones(1,3)
x =
1
1
0
1
x = eye(2)
x =
1
0
0
1
x = rand(1,3)
x =
0.9501 0.2311
0.6068
Other data types
• Boolean
In the help:
Matlab
 Programming Fundamentals
 Classes (Data Types)
▫ logical
• Integers
▫ int8, int16, int32, int64
▫ uint8, uint16, uint32, uint64
• Text
▫ char
• Containers
▫ cell
▫ struct
Matrix Index
• The matrix indices begin from 1 (not 0 (as in C))
• The matrix indices must be positive integer
Given:
A(-2), A(0)
Error: ??? Subscript indices must either be real positive integers or logicals.
A(4,2)
Error: ??? Index exceeds matrix dimensions.
Matrix index (2)
•
end indicates the last element
• End
• «:» indicates all the elements and can
be used to select a row, a column or a
sub-matrix
Variable display
1. Writing the variable name
▫
«;» prevents displaying the variable
2. By using the command disp
3. From the workspace
▫
▫
It provides a variable preview
Variable editor can be opened by
double-clicking on the variable name
Concatenation of Matrices
• x = [1 2], y = [4 5], z=[ 0 0]
A = [ x y]
1
2
4
5
B = [x ; y]
1 2
4 5
C = [x y ;z]
Error:
??? Error using ==> vertcat CAT arguments dimensions are not consistent.
Operators (arithmetic)
• Arithmetic operators
In the help:
+ addition
Matlab
- subtraction
 Programming Fundamentals
* multiplication
 Basic Program Components
 Operators
/ division
^ power
 complex conjugate transpose
• Logical operators
~ not
| or
& and
• Relational operators
<, <= lower than
>, >= greater than
==
equal to
~=
Not equal to
Matrices Operations
Given A and B:
Addition
Subtraction
Product
Transpose
Operators (Element by Element)
.*
./
.^
element-by-element multiplication
element-by-element division
element-by-element power
Defined x=A(1,:) and y=A(2,:)
K= x^2
Error:
??? Error using ==> mpower Matrix must be square.
B=x*y
Error:
??? Error using ==> mtimes Inner matrix dimensions must agree.
Fuctions
• A function is used as usual
▫ <output>=function(<inputs>)
▫ A function in Matlab can return more output
matrices
 A=function(X) stores the first output in A
 [A,B]=function(X) stores the first output in A
and the second in B
• The most important functions:
▫ help <name> provides a function descritpion in
the command window
▫ doc <name> opens the help
Some Built-in functions
•
•
•
•
•
•
•
•
•
•
mean(A):mean value of a vector
max(A), min (A): maximum and minimum
sum(A): summation.
sort(A): sorted vector
median(A): median value
std(A): standard deviation.
det(A) : determinant of a square matrix
dot(a,b): dot product of two vectors
Cross(a,b): cross product of two vectors
Inv(A): Inverse of a matrix A
• ATTENTION: If applied to a matrix, many of them
operate on columns
Dimensional functions
• Given A=rand(3,4), B=[],
x=[1,2,3]
• isempty() returns logical 1
(true) if the matrix is an empty
array and logical 0 (false)
otherwise.
• size() returns the number of
row and columns of a matrix
▫ Can be used to obtain only the
number of rows [size(…,1)] or
columns [size(…,2)]
• length() returns the number
of elements in an array or the
number of columns in a matrix
▫ If applied to a matrix returns the
biggest among the number of rows
and columns
Function Plot
sin(x) between 0≤x≤4π
• Create an x-array of 100 samples between 0 and
4π.
Equivalent to
>>x=linspace(0,4*pi,100);
x=0:4*pi/100:100
• Calculate sin(.) of the x-array
1
>>y=sin(x);
0.8
0.6
0.4
0.2
• Plot the y-array
>>plot(y)
0
-0.2
-0.4
-0.6
-0.8
-1
0
10
20
30
40
50
60
70
80
90
• doc plot to see plot parameters and configuration
100
Alternative way to plot variables
3. Matlab plots the variable
2. Click plot button
1. Select the variable
Exercise:
Plot e-x/3sin(x) between 0≤x≤4π
• Create an x-array of 100 samples between 0 and 4π.
>>x=linspace(0,4*pi,100);
• Calculate sin(.) of the x-array
>>y=sin(x);
• Calculate e-x/3 of the x-array
>>y1=exp(-x/3);
• Multiply the arrays y and y1
>>y2=y*y1;
Exercise:
Plot e-x/3sin(x) between 0≤x≤4π
• Multiply the arrays y and y1 correctly
>>y2=y.*y1;
• Plot the y2-array
0.7
0.6
>>plot(y2)
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
0
10
20
30
40
50
60
70
80
90
100
Display Facilities
• title(.)
>>title(‘This is the sinus function’)
• xlabel(.)
This is the sinus function
1
0.8
>>xlabel(‘x (secs)’)
0.6
0.4
sin(x)
• ylabel(.)
0.2
0
-0.2
>>ylabel(‘sin(x)’)
-0.4
-0.6
-0.8
-1
0
10
20
30
40
50
60
x (secs)
70
80
90
100
Display Facilities
0.7
0.6
• plot(.)
0.5
0.4
0.3
0.2
>>x=linspace(0,4*pi,100);
>>y=sin(x).*exp(-x/3);
>>plot(y)
>>plot(x,y)
• stem(.)
0.1
0
-0.1
-0.2
-0.3
0
10
20
30
40
50
60
70
80
90
100
0
10
20
30
40
50
60
70
80
90
100
0.7
0.6
0.5
0.4
>>stem(y)
>>stem(x,y)
0.3
0.2
0.1
0
-0.1
• Others…
-0.2
-0.3
Graphics - Overlay Plots
Use hold on for overlaying graphs
So the following:
Gives:
>>
>>
>>
>>
>>
>>
x=linspace(0,4*pi,100);
y=sin(x);
z=sin(x).*exp(-x/3);
plot(x,y, ‘b’);
hold on;
plot(x, z, ’r’);
Histogram
• hist() shows the distribution of data values
• Defined A= floor(rand(20)*50)
hist(A)
hist(A(:))
hist(A(:),50)
Flow Control
•
•
•
•
•
if
for
while
break
….
Control Structures
• If Statement Syntax
if (Condition_1)
Matlab Commands
elseif (Condition_2)
Matlab Commands
elseif (Condition_3)
Matlab Commands
else
Matlab Commands
end
Some Dummy Examples
if ((a>3) && (b==5))
Some Matlab Commands;
end
if (a<3)
Some Matlab Commands;
elseif (b~=5)
Some Matlab Commands;
end
if (a<3)
Some Matlab Commands;
else
Some Matlab Commands;
end
Control Structures
• For loop syntax
for i=Index_Array
Matlab Commands
end
Some Dummy Examples
for i=1:100
Some Matlab Commands;
end
for j=1:3:200
Some Matlab Commands;
end
for m=13:-0.2:-21
Some Matlab Commands;
end
for k=[0.1 0.3 -13 12 7 -9.3]
Some Matlab Commands;
end
Control Structures
• While Loop Syntax
while (condition)
Matlab Commands
end
Dummy Example
while ((a>3) && (b==5))
Some Matlab Commands;
end
Editor
Click to create
a new M-File
Click to open an
existing M-File
• Extension “.m”
• A text file containing script or function or program to run
Use of M-File
File saved as Denem430.m
If you include “;” at the
end of each statement,
result will not be shown
immediately
User Defined Functions
• Functions are m-files which can be executed by specifying
some inputs and supply some desired outputs.
• The code telling the Matlab that an m-file is actually a
function is
function out1=functionname(in1)
function out1=functionname(in1,in2,in3)
function [out1,out2]=functionname(in1,in2)
• You should write this command at the beginning of the
m-file and you should save the m-file with a file name
same as the function name
• A .m file must contain a single function
• Example
▫ Write a function : out=squarer (A, ind)
 Which takes the square of the input matrix if the input
indicator is equal to 1
 Or takes the element by element square of the input matrix
if the input indicator is equal to 2
Same Name
Writing User Defined Functions
• Other example:
▫ A function which takes an
input array and returns
the sum and product of its
elements as outputs
▫ The function sumprod(.)
can be called from
command window
Notes:
• “%” is the neglect sign for Matlab (equaivalent of
“//” in C). Anything after it on the same line is
neglected by Matlab compiler.
• Sometimes slowing down the execution is done
deliberately for observation purposes. You can
use the command “pause” for this purpose
pause %wait until any key
pause(3) %wait 3 seconds
Files in Matlab
•
•
•
•
•
c-like functions to manage file exist
fopen(), fclose() open and close files
fread(), fscanf() read from the file
fwrite(), fprintf() write in the file
…
• There is a easier way!!!
In the help:
Matlab
 Function reference
 File I/O
Workspace
Open the
variable editor
Import data
(workspace, text, images…)
• Commands:
▫ load
▫ save
• Unfortunately it cannot
be done automatically
Save the workspace
in a .mat file
Loading text file
• The file is placed in a cell having the
name of the file (without extension)
• Conversion to string (array of
characters):
▫ str=char(<filename>);
• The i-th character can be addressed as
usual
▫ str(i)
Debugging
Temporary variables
can be evaluated in
the workspace
Flow controls
Breakpoint
The command window can be used to
evaluate other functionalities, display
values or plot variables as usual
Suggestion
• Matlab is an interpreted
language
• Standard functions are more
efficient than user defined
functions
Avoid cicles, if possible