Matlab introduction

11
Introduction to MATLAB
RAJASTHAN

2
Topics..
 What is MATLAB ??
 Basic Matrix Operations
 Script Files and M-files
 Some more Operations and Functions
APPLICATIONS:
 Plotting functions ..
 Image Processing Basics ..
 Robotics Applications ..

3
Topics..
APPLICATIONS:

4
MATLAB
 MATLAB is a program for doing numerical
computation. It was originally designed for solving
linear algebra type problems using matrices. It’s
name is derived from MATrix LABoratory.
MATLAB has since been expanded and now has
built-in functions for solving problems requiring data
analysis, signal processing, optimization, and several
other types of scientific computations. It also
contains functions for 2-D and 3-D graphics and
animation.

5
MATLAB
Everything in MATLAB is a matrix !

6
MATLAB
 The MATLAB environment is command oriented
somewhat like UNIX. A prompt appears on the screen and
a MATLAB statement can be entered. When the <ENTER>
key is pressed, the statement is executed, and another
prompt appears.
 If a statement is terminated with a semicolon ( ; ), no
results will be displayed. Otherwise results will appear
before the next prompt.

What is Matlab?
 Matlab is basically a high level language
 which has many specialized toolboxes for making
things easier for us
 How high?
Assembly
High Level
Languages such as
C, Pascal etc.
Matlab

What are we interested in?
 Matlab is too broad for our purposes in this
course.
 The features we are going to require is
Matlab
Command
Line
m-files
functions
mat-files
Command execution
like DOS command
window
Series of
Matlab
commands
Input
Output
capability
Data
storage/
loading

Matlab Screen
 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

11
MATLAB
To get started, type one of these commands: helpwin,
helpdesk, or demo
» a=5;
» b=a/2
b =
2.5000
»

12
MATLAB Variable Names
 Variable names ARE case sensitive
 Variable names can contain up to 63 characters (as of
MATLAB 6.5 and newer)
 Variable names must start with a letter followed by letters,
digits, and underscores.

13
MATLAB Special Variables
ans Default variable name for results
pi Value of 
eps Smallest incremental number
inf Infinity
NaN Not a number e.g. 0/0
i and j i = j = square root of -1
realmin The smallest usable positive real number
realmax The largest usable positive real number

14
Topics..
APPLICATIONS:
 GUI Design and Programming

15
Math & Assignment Operators
Power ^ or .^ a^b or a.^b
Multiplication * or .* a*b or a.*b
Division / or ./ a/b or a./b
or or . ba or b.a
NOTE: 56/8 = 856
- (unary) + (unary)
Addition + a + b
Subtraction - a - b
Assignment = a = b (assign b to a)

16
Other MATLAB symbols
>> prompt
. . . continue statement on next line
, separate statements and data
% start comment which ends at end of line
; (1) suppress output
(2) used as a row separator in a matrix
: specify range

17
MATLAB Relational Operators
 MATLAB supports six relational operators.
Less Than <
Less Than or Equal <=
Greater Than >
Greater Than or Equal >=
Equal To ==
Not Equal To ~=

18
MATLAB Logical Operators
 MATLAB supports three logical operators.
not ~ % highest precedence
and & % equal precedence with or
or | % equal precedence with and

19
MATLAB Matrices
 MATLAB treats all variables as matrices. For our purposes
a matrix can be thought of as an array, in fact, that is how
it is stored.
 Vectors are special forms of matrices and contain only one
row OR one column.
 Scalars are matrices with only one row AND one column

20
MATLAB Matrices
 A matrix with only one row AND one column is a scalar. A
scalar can be created in MATLAB as follows:
» a_value=23
a_value =
23

21
MATLAB Matrices
 A matrix with only one row is called a row vector. A row
vector can be created in MATLAB as follows (note the
commas):
» rowvec = [12 , 14 , 63]
rowvec =
12 14 63

22
MATLAB Matrices
 A matrix with only one column is called a column vector.
A column vector can be created in MATLAB as follows
(note the semicolons):
» colvec = [13 ; 45 ; -2]
colvec =
13
45
-2

23
MATLAB Matrices
 A matrix can be created in MATLAB as follows (note the
commas AND semicolons):
» matrix = [1 , 2 , 3 ; 4 , 5 ,6 ; 7 , 8 , 9]
matrix =
1 2 3
4 5 6
7 8 9

24
Extracting a Sub-Matrix
 A portion of a matrix can be extracted and stored in a
smaller matrix by specifying the names of both matrices
and the rows and columns to extract. The syntax is:
sub_matrix = matrix ( r1 : r2 , c1 : c2 ) ;
where r1 and r2 specify the beginning and ending rows
and c1 and c2 specify the beginning and ending columns
to be extracted to make the new matrix.

25
MATLAB Matrices
 A column vector can be
extracted from a matrix.
As an example we create a
matrix below:
» matrix=[1,2,3;4,5,6;7,8,9]
matrix =
1 2 3
4 5 6
7 8 9
 Here we extract column 2
of the matrix and make a
column vector:
» col_two=matrix( : , 2)
col_two =
2
5
8

26
MATLAB Matrices
 A row vector can be
extracted from a matrix.
As an example we create
a matrix below:
» matrix=[1,2,3;4,5,6;7,8,9]
matrix =
1 2 3
4 5 6
7 8 9
 Here we extract row 2 of
the matrix and make a
row vector. Note that
the 2:2 specifies the
second row and the 1:3
specifies which columns
of the row.
» rowvec=matrix(2 : 2 , 1 :
3)
rowvec =
4 5 6

Array, Matrix
 a vector x = [1 2 5 1]
x =
1 2 5 1
 a matrix x = [1 2 3; 5 1 4; 3 2 -1]
x =
1 2 3
5 1 4
3 2 -1
 transpose y = x’ y =
1
2
5
1

Long Array, Matrix
 t =1:10
t =
1 2 3 4 5 6 7 8 9 10
 k =2:-0.5:-1
k =
2 1.5 1 0.5 0 -0.5 -1
 B = [1:4; 5:8]
x =
1 2 3 4
5 6 7 8

Generating Vectors from functions
 zeros(M,N) MxN matrix of zeros
 ones(M,N) MxN matrix of ones
 rand(M,N) MxN matrix of uniformly
distributed
random
numbers on (0,1)
x = zeros(1,3)
x =2
0 0 0
x = ones(1,3)
x =
1 1 1
x = rand(1,3)
x =
0.9501 0.2311 0.6068

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.

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.

Matrices Operations
Given A and B:
Addition Subtraction Product Transpose

The use of “.” – “Element” Operation
K= x^2
Erorr:
??? Error using ==> mpower Matrix must be square.
B=x*y
Erorr:
??? Error using ==> mtimes Inner matrix dimensions must agree.
A = [1 2 3; 5 1 4; 3 2 1]
A =
1 2 3
5 1 4
3 2 -1
y = A(3 ,:)
y=
3 4 -1
b = x .* y
b=
3 8 -3
c = x . / y
c=
0.33 0.5 -3
d = x .^2
d=
1 4 9
x = A(1,:)
x=
1 2 3

Vectors and Matrices

















18
16
14
12
10
B
 How do we assign values to vectors?
>>> A = [1 2 3 4 5]
A =
1 2 3 4 5
>>>
>>> B = [10;12;14;16;18]
B =
10
12
14
16
18
>>>
A row vector –
values are
separated by
spaces
A column vector
– values are
separated by
semi–colon (;)
 54321A 

 How do we assign values to matrices ?
Columns separated by
space or a comma
Rows separated by
semi-colon
>>> A=[1 2 3;4 5 6;7 8 9]
A =
1 2 3
4 5 6
7 8 9
>>> 









987
654
321

 How do we access elements in a matrix or a vector?
Try the followings:
>>> A(2,3)
ans =
6
>>> A(:,3)
ans =
3
6
9
>>> A(1,:)
ans =
1 2 3
>>> A(2,:)
ans =
4 5 6

 Arithmetic operations – Matrices
Performing operations to every entry in a matrix
Add and subtract>>> A=[1 2 3;4 5 6;7 8
9]
A =
1 2 3
4 5 6
7 8 9
>>>
>>> A+3
ans =
4 5 6
7 8 9
10 11 12
>>> A-2
ans =
-1 0 1
2 3 4
5 6 7

Multiply and divide>>> A=[1 2 3;4 5 6;7 8 9]
A =
1 2 3
4 5 6
7 8 9
>>>
>>> A*2
ans =
2 4 6
8 10 12
14 16 18
>>> A/3
ans =
0.3333 0.6667 1.0000
1.3333 1.6667 2.0000
2.3333 2.6667 3.0000

Power
>>> A=[1 2 3;4 5 6;7 8 9]
A =
1 2 3
4 5 6
7 8 9
>>>
A^2 = A * A
To square every element in A, use
the element–wise operator .^
>>> A.^2
ans =
1 4 9
16 25 36
49 64 81
>>> A^2
ans =
30 36 42
66 81 96
102 126 150

Performing operations between matrices
>>> A=[1 2 3;4 5 6;7 8 9]
A =
1 2 3
4 5 6
7 8 9
>>> B=[1 1 1;2 2 2;3 3 3]
B =
1 1 1
2 2 2
3 3 3
A*B 



















333
222
111
987
654
321
A.*B










3x93x83x7
2x62x52x4
1x31x21x1










272421
12108
321
=
=










505050
323232
141414

A/B
A./B










0000.36667.23333.2
0000.35000.20000.2
0000.30000.20000.1
=
? (matrices
singular)










3/93/83/7
2/62/52/4
1/31/21/1

A^B
A.^B










729512343
362516
321
=
??? Error using ==> ^
At least one operand must be scalar










333
222
111
987
654
321

Basic Task: Plot the function sin(x)
between 0≤x≤4π
 Create an x-array of 100 samples between 0 and 4π.
 Calculate sin(.) of the x-array
 Plot the y-array
>>x=linspace(0,4*pi,100);
>>y=sin(x);
>>plot(y)
0 10 20 30 40 50 60 70 80 90 100
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1

Plot the function e-x/3sin(x) between
0≤x≤4π Create an x-array of 100 samp
 Calculate sin(.) of the x-array
 Calculate e-x/3 of the x-array
 Multiply the arrays y and y1
>>y=sin(x);
>>y1=exp(-x/3);
>>y2=y*y1;

Display Facilities
 plot(.)
 stem(.)
Example:
>>y=sin(x);
>>plot(y)
>>plot(x,y)
Example:
>>stem(y)
>>stem(x,y)
0 10 20 30 40 50 60 70 80 90 100
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 10 20 30 40 50 60 70 80 90 100
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7

46
Topics..
APPLICATIONS:

47
Use of M-File
 There are two kinds of M-files:
Scripts, which do not accept input
arguments or return output arguments. They
operate on data in the workspace.
Functions, which can accept input
arguments and return output arguments.
Internal variables are local to the function.
Click to create
a new M-File

48
M-File as script file
Save file as filename.m
Type what you want to
do, eg. Create matrices
If you include “;” at the
end of each statement,
result will not be shown
immediately
Run the file by typing the filename in the command window

49
Reading Data from files
 MATLAB supports reading an entire file and creating a
matrix of the data with one statement.
>> load mydata.dat; % loads file into matrix.
% The matrix may be a scalar, a vector, or a
% matrix with multiple rows and columns. The
% matrix will be named mydata.
>> size (mydata) % size will return the number
% of rows and number of
% columns in the matrix
>> length (myvector) % length will return the total
% no. of elements in
myvector

50
Some Useful MATLAB commands
 who List known variables
 whos List known variables plus their size
 help >> help sqrt Help on using sqrt
 lookfor >> lookfor sqrt Search for
keyword sqrt in m-files
 what >> what a: List MATLAB files in a:
 clear Clear all variables from work space
 clear x y Clear variables x and y from work space
 clc Clear the command window

51
Some Useful MATLAB commands
 what List all m-files in current directory
 dir List all files in current directory
 ls Same as dir
 type test Display test.m in command window
 delete test Delete test.m
 cd a: Change directory to a:
 chdir a: Same as cd
 pwd Show current directory
 which test Display directory path to ‘closest’
test.m

52
MATLAB Logical Functions
 MATLAB also supports some logical functions.
xor (exclusive or) Ex: xor (a, b)
Where a and b are logical expressions. The xor
operator evaluates to true if and only if one
expression is true and the other is false. True is
returned as 1, false as 0.
any (x) returns 1 if any element of x is nonzero
all (x) returns 1 if all elements of x are nonzero
isnan (x) returns 1 at each NaN in x
isinf (x) returns 1 at each infinity in x
finite (x) returns 1 at each finite value in x

53
Matlab Selection Structures
 An if - elseif - else structure in MATLAB.
Note that elseif is one word.
if expression1 % is true
% execute these commands
elseif expression2 % is true
else % the default
end

54
MATLAB Repetition Structures
A for loop in MATLAB for x = array
for ind = 1:100
b(ind)=sin(ind/10)
end
while loop in MATLAB while expression
while x <= 10
end
x=0.1:0.1:10; b=sin(x); - Most of the loops can be
avoided!!!

55
Scalar - Matrix Addition
» a=3;
» b=[1, 2, 3;4, 5, 6]
b =
1 2 3
4 5 6
» c= b+a % Add a to each element of b
c =
4 5 6
7 8 9

56
Scalar - Matrix Subtraction
» a=3;
» b=[1, 2, 3;4, 5, 6]
b =
1 2 3
4 5 6
» c = b - a %Subtract a from each element of b
c =
-2 -1 0
1 2 3

57
Scalar - Matrix Multiplication
» a=3;
» b=[1, 2, 3; 4, 5, 6]
b =
1 2 3
4 5 6
» c = a * b % Multiply each element of b by a
c =
3 6 9
12 15 18

58
Scalar - Matrix Division
» a=3;
» b=[1, 2, 3; 4, 5, 6]
b =
1 2 3
4 5 6
» c = b / a % Divide each element of b by a
c =
0.3333 0.6667 1.0000
1.3333 1.6667 2.0000

59
The use of “.” – “Element” Operation
Given A:
Divide each element of
A by 2
Multiply each
element of A by 3
Square each
element of A

6060
MATLAB Toolboxes
 MATLAB has a number of add-on software modules, called
toolbox , that perform more specialized computations.
 Signal Processing
 Image Processing
 Communications
 System Identification
 Wavelet Filter Design
 Control System
 Fuzzy Logic
 Robust Control
 µ-Analysis and Synthesis
 LMI Control
 Model Predictive Control
 …

6161
MATLAB Demo
 Demonstrations are invaluable since they give an indication
of the MATLAB capabilities.
 A comprehensive set are available by typing the command
>>demo in MATLAB prompt.

62
An Interesting, MATLAB command
why
In case you ever needed a reason

63
Topics..
APPLICATIONS:

64
Plot
PLOT Linear plot.
 PLOT(X,Y) plots vector Y
versus vector X
 PLOT(Y) plots the columns of
Y versus their index
 PLOT(X,Y,S) with plot
symbols and colors
 See also SEMILOGX,
SEMILOGY, TITLE,
XLABEL, YLABEL, AXIS,
AXES, HOLD, COLORDEF,
LEGEND, SUBPLOT...
x = [-3 -2 -1 0 1 2 3];
y1 = (x.^2) -1;
plot(x, y1,'bo-.');
Example

65
Plot Properties
XLABEL X-axis label.
 XLABEL('text') adds text
beside the X-axis on the
current axis.
YLABEL Y-axis label.
 YLABEL('text') adds text
beside the Y-axis on the
current axis.
...
xlabel('x values');
ylabel('y values');
Example

66
Hold
HOLD Hold current graph.
 HOLD ON holds the current
plot and all axis properties so
that subsequent graphing
commands add to the existing
graph.
 HOLD OFF returns to the
default mode
 HOLD, by itself, toggles the
hold state.
...
hold on;
y2 = x + 2;
plot(x, y2, 'g+:');
Example

67
Subplot
SUBPLOT Create axes in tiled
positions.
 SUBPLOT(m,n,p), or
SUBPLOT(mnp), breaks the Figure
window into an m-by-n matrix of
small axes
x = [-3 -2 -1 0 1 2 3];
y1 = (x.^2) -1;
% Plot y1 on the top
subplot(2,1,1);
plot(x, y1,'bo-.');
xlabel('x values');
ylabel('y values');
% Plot y2 on the bottom
subplot(2,1,2);
y2 = x + 2;
plot(x, y2, 'g+:');
Example

68
Figure
FIGURE Create figure window.
 FIGURE, by itself, creates a
new figure window, and
returns its handle.
x = [-3 -2 -1 0 1 2 3];
y1 = (x.^2) -1;
% Plot y1 in the 1st Figure
plot(x, y1,'bo-.');
xlabel('x values');
ylabel('y values');
% Plot y2 in the 2nd Figure
figure
y2 = x + 2;
plot(x, y2, 'g+:');
Example

69
Surface Plot
x = 0:0.1:2;
y = 0:0.1:2;
[xx, yy] = meshgrid(x,y);
zz=sin(xx.^2+yy.^2);
surf(xx,yy,zz)
xlabel('X axes')
ylabel('Y axes')

70
contourf-colorbar-plot3-waterfall-contour3-mesh-surf
3 D Surface Plot

71
Convolution
The behavior of a linear, continuous-time, time-invariant system with
input signal x(t) and output signal y(t) is described by the convolution
integral
- h(t), assumed known, the response of the system to a unit impulse
input
For example,
x = [1 1 1 1 1];  [1 1 1 1 1]
h = [0 1 2 3];  [3 2 1 0]
conv(x,h)
yields y = [0 1 3 6 6 6 5 3]
stem(y);
ylabel(‘Conv');
xlabel(‘sample number’);

72
Topics..
APPLICATIONS:

7373
Image Processing Toolbox
 The Image Processing Toolbox is a collection of functions
that extend the capability of the MATLAB ® numeric
computing environment. The toolbox supports a wide
range of image processing operations, including:
 Geometric operations
 Neighborhood and block operations
 Linear filtering and filter design
 Transforms
 Image analysis and enhancement
 Binary image operations
 Region of interest operations

7474
MATLAB Image Types
 Indexed images : m-by-3 color map
 Intensity images : [0,1] or uint8
 Binary images : {0,1}
 RGB images : m-by-n-by-3

7575
Indexed Images
» [x,map] =
imread('trees.tif');
» imshow(x,map);

7676
Intensity Images
» image =
ind2gray(x,map);
» imshow(image);

7777
Binary Images
» imshow(edge(image));

7979
Image Display
 image - create and display image object
 imagesc - scale and display as image
 imshow - display image
 colorbar - display colorbar
 getimage- get image data from axes
 truesize - adjust display size of image
 zoom - zoom in and zoom out of 2D plot

8080
Image Conversion
 Gray2ind - intensity image to index image
 im2bw - image to binary
 Im2double - image to double precision
 Im2uint8 - image to 8-bit unsigned integers
 Im2uint16 - image to 16-bit unsigned integers
 Ind2gray - indexed image to intensity image
 mat2gray - matrix to intensity image
 rgb2gray - RGB image to grayscale
 rgb2ind - RGB image to indexed image

81
GEOMETRIC OPERATIONS
“imcrop” crops an image to a specified rectangle.
imcrop displays the input image and waits for you to
specify the crop rectangle with the mouse.

82
IMAGE ENHANCEMENT
 Adjust intensity
 imadjust
 histeq
 Noise removal
 linear filtering
 median filtering
 adaptive filtering
>>im2 = histeq(im);
>>imshow(im2)

8383
TRANSFORMS
Fourier Transform
-fft2, fftshift, ifft2
Discrete Cosine Transform (DCT)
-dct2, idct2, dctmtx, dctdemo
Radon Transform
-radon, iradon, phantom

84
Topics..
APPLICATIONS:

85
Robotics Application
Lez Concorrenza - The Automation-Robotics Event, Techniche 2005

86
Concept
 take image
 filter using medfilt2
 take the subarray of ball region, find cluster of max
area ,find its centroid
 take the subarray of robot region , find cluster of max
area, find its centroid
 interpolate the ball using the ball's current and
previous coordinate , give output

87
MATLAB Code
parport=digitalio('parallel','LPT1');
addline(parport,0:7,'out');
ball_x_prev = 1;
ball_y_prev = 1;
while (1)
% code for acquiring image
filtered_image=medfilt2(bw,[3 3]); % filter the image
region_ball = filtered_image[20:460,10:575]; % ball region
region_bot = filtered_image[20:460,575:630]; % robot region
label = bwlabel(region_ball,4); %label the clusters in the region
data = regionprops(label,'basic'); % data ontains properties of clusters in the region
object = find([data.Area]==max([data.Area])) % object conatains the label of the cluster with max
area

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ball_x = data(object).Centroid(1); %x coordinates of the ball
ball_y = data(object).Centroid(2);
label = bwlabel(region_bot,4); %label the clusters in the region
data = regionprops(label,'basic'); % data ontains properties of clusters in the region
object =find([data.Area]==max([data.Area])) % object conatains the label of the cluster with max
area
robot_x = data(object).Centroid(1); %x coordinates of the bot
robot_y = data(object).Centroid(2);
% Algorithm for movement of robot
if (ball_x > ball_x_prev) % the ball is returning to the bot
% Do something
if (robot_y > y_proj)
% Do something else
Etc.

89
Topics..
APPLICATIONS:

90
Graphical User Interface
What is GUI: A graphical user interface (GUI) is a
user interface built with graphical objects such as
 Buttons
 Text fields
 Sliders
 Menus
If the GUI is designed well-designed, it should be
intuitively obvious to the user how its components
function.

91
Push ButtonsRadio Buttons
Frames
Checkbox Slider
Edit text
static textAxes

92
Graphical User Interface
Guide Editor
Property InspectorResult Figure

Matlab introduction

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