Matlab practical and lab session

MATLAB
Krishna K. Mohbey
Bhopal

MANIT

MATLAB introduction
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.

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

Assembly

What are we interested in?
Matlab is too broad for our purposes in this
course.
The features we are going to require is
Matlab

Series of
Matlab
commands

m-files

Input
Output
capability

Command
Line

mat-files

functions
Command
execution like DOS
command window

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

MATLAB Help
• MATLAB Help is an extremely
powerful assistance to learning
MATLAB
• Help not only contains the
theoretical background, but also
shows demos for
implementation
• MATLAB Help can be opened
by using the HELP pull-down
menu

MATLAB Help (cont.)
• Any command description
can be found by typing the
command in the search field
• As shown above, the
command to take square
root (sqrt) is searched
• We can also utilize
MATLAB Help from the
command window as shown

MATLAB Toolboxes

















Statistics Toolbox
Optimization Toolbox
Database Toolbox
Parallel Computing Toolbox
Image Processing Toolbox
Bioinformatics Toolbox
Fuzzy Logic Toolbox
Neural Network Toolbox
Data Acquisition Toolbox
MATLAB Report Generator
Signal Processing
Communications
System Identification
Wavelet Filter Design
Control System
Robust Control

Connecting to MATLAB
C/C++
Java
Perl

Excel /
COM

Database
Toolbox

Web

Instrument Control
Data Acquisition
Image Acquisition

File I/O

Deploying with MATLAB

C/C++
Stand-alone

COM

Excel

Web

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.

More about the Workspace
• who, whos – current variables in the
workspace
• save – save workspace variables to *.mat file
• load – load variables from *.mat file
• clear – clear workspace variables
- CODE

MATLAB

Everything in MATLAB is a matrix !

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

Variables
No need for types. i.e.,

int a;
double b;
float c;
All variables are created with double precision unless
specified and they are matrices.

Example:
>>x=5;
>>x1=2;

After these statements, the variables are 1x1 matrices with
double precision

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.

MATLAB Special Variables
1.
2.
3.
4.
5.
6.
7.
8.

ans
pi
eps
inf
NaN
i and j
realmin
realmax

Default variable name for results
Value of π
Smallest incremental number
Infinity
Not a number e.g. 0/0
i = j = square root of -1
The smallest usable positive real number
The largest usable positive real number

Different format
>> e=1/3
e=
0.3333
>> format long
>> e
e=
0.333333333333333
>> format short e
>> e
e=
3.3333e-001

%default

%long decimal

%long exponential

To clear a variable
» who
Your variables are:
D
NRe

ans
mu

rho
v

» clear D
» who
Your variables are:
NRe

ans

mu

rho

v

Complex Numbers
Complex number i or j stands for √-1
»i
ans =
0 + 1.0000i
» c1 = 2+3i
c1 =
2.0000 + 3.0000i
»

Complex Numbers
Some functions deal with complex number
>> c=1-2i
c = 1.0000 - 2.0000i
>> abs(c)
ans =

2.2361

ans =

1

>> real(c)
>> imag(c)
ans = -2
>> angle(c)
ans = -1.1071

Mathematical Functions
» x=sqrt(2)/2
x=
0.7071
» y=sin(x)
y=
0.6496
»

Built-in Functions
Trigonometric
functions

Exponential
functions
Complex
functions
Rounding and
Remainder
functions

sin, cos, tan, sin, acos, atan,
sinh, cosh, tanh, asinh,
acosh, atanh, csc, sec, cot,
acsc, …
exp, log, log10, sqrt
abs, angle, imag, real, conj
floor, ceil, round, mod, rem,
sign

Math & Assignment Operators
Power
Multiplication
Division
or
NOTE:

^ or .^
a^b
* or .*
a*b
/ or ./
a/b
or . ba or
56/8 = 856

- (unary) + (unary)
Addition
+
Subtraction Assignment =

a+b
a-b
a=b

or
a.^b
or
a.*b
or
a./b
b.a

(assign b to a)

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

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

<
<=
>
>=
==
~=

MATLAB Logical Operators
MATLAB supports three logical operators.
not
and
or

~
&
|

% highest precedence
% equal precedence with or
% equal precedence with and

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

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

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

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

MATLAB Matrices
A matrix can be created in MATLAB as follows (note the
commas AND semicolons):
» a = [1 , 2 , 3 ; 4 , 5 ,6 ; 7 , 8 , 9]
Or
» a = [1 2 3 ; 4 5 6 ; 7 8 9]
Or
>> a=[1 2 3
456
7 8 9]
a=
1
4
7

2
5
8

3
6
9

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.

MATLAB Matrices


A column vector can be extracted
from a matrix. As an example
we create a matrix below:



Here we extract column 2 of the
matrix and make a column vector:

» matrix=[1,2,3;4,5,6;7,8,9]

» coltwo=matrix( : , 2)

matrix =
1 2
4 5
7 8

coltwo =
3
6
9

2
5
8

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]

» rowvec=matrix(2 : 2 , 1 : 3)

matrix =
1
4
7

2
5
8

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.

3
6
9

rowvec =
4

5

6

Special Matrices
1
eye(3) = 0

0

1
ones(3) = 1

1


0 0
1 0

0 1

1 1
1 1

1 1


0 0 
zeros(3,2) = 0 0


0 0 


1 1 1 1
ones(2,4) = 
1 1 1 1



Special Matrices functions
>> a=magic(4)

%magic matrix

a=
16 2
5 11
9 7
4 14

3 13
10 8
6 12
15 1

>> b=rand(5)

%random matrix

b=
0.8147
0.9058
0.1270
0.9134
0.6324

0.0975
0.2785
0.5469
0.9575
0.9649

0.1576
0.9706
0.9572
0.4854
0.8003

0.1419
0.4218
0.9157
0.7922
0.9595

0.6557
0.0357
0.8491
0.9340
0.6787

Some matrix building functions
>> a
>> a
a=
a=
1 2
1 2
4 5
4 5
7 8
7 8
>> diag(a)
ans =
1
5
9

>> triu(a)
ans =
1 2 3
0 5 6
0 0 9

3
3
6
6
9
9
>> tril(a)
ans =
1 0
4 5
7 8

0
0
9

Concatenation of Matrices


x = [1 2], y = [4 5]
A = [ x y]
1 2 4 5
B = [x ; y]
12
45

Matrices Operations

Given A and B:

Addition

Subtraction

Product

Transpose

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

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

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

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

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

Mean and Median
Mean: Average or mean value of a distribution
Median: Middle value of a sorted distribution
M = mean(A),
M = mean(A,dim),

M = median(A)
M = median(A,dim)

M = mean(A), M = median(A): Returns the mean or median value of vector A.
If A is a multidimensional mean/median returns an array of mean values.
Example:
A = [ 0 2 5 7 20]

B = [1 2 3
336
468
4 7 7];

mean(A) = 6.8
mean(B) = 3.0000 4.5000 6.0000 (column-wise mean)
mean(B,2) = 2.0000 4.0000 6.0000 6.0000 (row-wise mean)

Mean and Median
Examples:

A = [ 0 2 5 7 20]

B = [1 2 3
336
468
4 7 7];

Mean:

mean(A) = 6.8
mean(B) = 3.0 4.5 6.0 (column-wise mean)
mean(B,2) = 2.0 4.0 6.0 6.0 (row-wise mean)
Median:

median(A) = 5
median(B) = 3.5 4.5 6.5 (column-wise median)
median(B,2) = 2.0
3.0
6.0
7.0 (row-wise median)

Standard Deviation and Variance








Standard deviation is calculated using the std() function
std(X) : Calcuate the standard deviation of vector x
If x is a matrix, std() will return the standard deviation of each column
Variance (defined as the square of the standard deviation) is calculated using
the var() function
var(X) : Calcuate the variance of vector x
If x is a matrix, var() will return the standard deviation of each column

X = [1 5 9;7 15 22]
s = std(X)
s = 4.2426 7.0711 9.1924

Histograms
•
•

Histograms are useful for showing the pattern of the
whole data set
Allows the shape of the distribution to be easily
visualized

Histograms
Matlab hist(y,m) command will generate a frequency histogram
of vector y distributed among m bins
Also can use hist(y,x) where x is a vector defining the bin
centers

Example:
>>b=sin(2*pi*t)
>>hist(b,10);

>>hist(b,[-1 -0.75 0 0.25 0.5 0.75
40

45
40

35

35

30

30

25

25

20
20

15
15

10
10

5

5
0
-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0
-1.5

-1

-0.5

0

0.5

1

1.5

Histograms
The histc function is a bit more powerful and allows bin edges to
be defined
[n, bin] = histc(x, binrange)
x = statistical distribution
binrange = the range of bins to plot e.g.: [1:1:10]
n = the number of elements in each bin from vector x
bin = the bin number each element of x belongs


Use the bar function to plot the histogram

Histograms
Example:
>> test = round(rand(100,1)*10)
>> histc(test,[1:1:10])
>> Bar(test)

14

12

10

8

6

4

2

0

1

2

3

4

5

6

7

8

9

10

Some Useful MATLAB commands
who
whos
help
lookfor
what
clear
clear x y
clc

List known variables
List known variables plus their size
>> help sqrt
Help on using sqrt
>> lookfor sqrt Search for
keyword sqrt in m-files
>> what a: List MATLAB files in a:
Clear all variables from work space
Clear variables x and y from work space
Clear the command window

Some Useful MATLAB commands
what
dir
ls
type test
delete test
cd a:
chdir a:
pwd

List all m-files in current directory
List all files in current directory
Same as dir
Display test.m in command window
Delete test.m
Change directory to a:
Same as cd
Show current directory

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)
all (x)
isnan (x)
isinf (x)
finite (x)

returns 1 if any element of x is nonzero
returns 1 if all elements of x are nonzero
returns 1 at each NaN in x
returns 1 at each infinity in x
returns 1 at each finite value in x

Input and fprintf
>> x=input('please enter a number')
please enter a number100
x=
100
>> fprintf('%d',x)
100>>
>>

Text string,error message
Text string are entered into matlab surrounded by
single quotes
s=‘this is a text’
Text string can be displayed with
disp(‘this is message’)
Error message are best display with
error(‘sorry, this is error’)

Flow Control
if
for
while
switch case
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)
elseif (b~=5)
end
if (a<3)
else
end

Control Structures
Some Dummy Examples

For loop syntax
for i=Index_Array
Matlab Commands
end
%................................
for i=start:inc_value:stop
Matlab Commands
end

for i=1:100
end
for j=1:3:200
end
for m=13:-0.2:-21
end
for k=[0.1 0.3 -13 12 7 -9.3]
end

Control Structures
While Loop Syntax
Dummy Example

while (condition)
Matlab Commands
end

while ((a>3) & (b==5))
end

switch
• switch – Switch among several cases based on
expression
• The general form of SWITCH statement is:
switch switch_expr
case case_expr,

statement, …, statement
case {case_expr1, case_expr2, case_expr3, …}

…
otherwise

end

switch (cont.)
• Note:
– Only the statements between the matching CASE and
the next case, otherwise, or end are executed
– Unlike C, the switch statement does not fall
through (so breaks are unnecessary)

• CODE

Some Examples
>> x=20
x=

20

y=

30

>> y=30
>> if x>y
'greater x'
else
'greater y'
end
ans =greater y
>>

Some Examples
>> for p=1:10
fprintf('%dt',p)
end
1 2 3 4 5 6 7 8 9 10 >>

>> for p=1:2:10
fprintf('%dt',p)
end
1
3
5

7

9

>>

Reading Data from files
MATLAB supports reading an entire file and creating a matrix of
the data with one statement.
>> load fcmdata.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 (fcmdata)

>> length (fcmdata)

% size will return the number
% of rows and number of
% columns in the matrix
% length will return the total
% no. of elements in myvector

MATLAB Graphics
One of the best things about MATLAB is interactive
graphics
“plot” is the one you will be using most often
Many other 3D plotting functions -- plot3, mesh, surfc,
etc.
Use “help plot” for plotting options
To get a new figure, use “figure”
logarithmic plots available using semilogx, semilogy
and loglog

Plotting Commands
plot(x,y) defaults to a blue line
plot(x,y,’ro’) uses red circles
plot(x,y,’g*’) uses green asterisks
If you want to put two plots on the same graph, use
“hold on”
plot(a,b,’r:’)
hold on
plot(a,c,’ko’)

(red dotted line)
(black circles)

Color, Symbols, and Line Types
Use “help plot” to find available Specifiers
Colors

Symbols

Line Types

b

blue

.

point

-

solid

g

green

o

circle

:

dotted

r

red

x

x-mark

-.

dashdot

c

cyan

+

plus

--

dashed

m

magenta

*

star

y

yellow

s

square

k

black

d

diamond

v

triangle (down)

^

triangle (up)

<

triangle (left)

>

triangle (right)

p

pentagram

h

hexagram

Plotting
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...

Example
x = [-3 -2 -1 0
1 2 3];
y1 = (x.^2) -1;
plot(x,
y1,'bo-.');

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.

Example
...
xlabel('x
values');
ylabel('y
values');

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.

Example
...
hold on;
y2 = x + 2;
plot(x, y2,
'g+:');

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

Example
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+:');

Figure
FIGURE Create figure window.
FIGURE, by itself, creates a new
figure window, and returns its
handle.

Example
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+:');

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

2D line plot
0.8
0.6
0.4
0.2
amplitude

>> x=0:0.05:5;
>> y=sin(x.^2);
>> plot(x,y);
>> xlabel('time');
>> plot(x,y);
>> xlabel('time');
>>ylabel('amplitude');

1

0
-0.2
-0.4
-0.6
-0.8
-1

0

0.5

1

1.5

2

2.5
time

3

3.5

4

4.5

5

Bar plot
>> x=-2.9:0.2:2.9;
>> bar(x,exp(-x.*x));
>>

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-3

-2

-1

0

1

2

3

Stairstep plot of sine wave
>> x=0:0.25:10;
>> stairs(x,sin(x));

1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1

0

1

2

3

4

5

6

7

8

9

10

M-Files
Script file: a collection of MATLAB commands
Function file: a definition file for one function

Script Files
Any valid sequence of MATLAB commands can
be in the script files.
Variables defined/used in script files are global,
i.e., they present in the workspace.

Matlab practical and lab session

Using Script M-files
» what
M-files in the current directory
C:WINDOWSDesktopMatlab-Tutorials
abc abc1
» abc
1
3
5
.
.
.

File Name

M-file Example

%test.m
for i=1:5
for j=1:i
fprintf('*');
end
fprintf('n');
end

%output
>> test
*
**
***
****
*****

Writing 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

Examples
Write a function : out=squarer (A, ind)

Which takes the square of the input matrix if the input
indicator is equal to 1
And takes the element by element square of the input
matrix if the input indicator is equal to 2

Same Name

Another 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 or an m-file as

Function Example1
multiply.m
function y = multiply(a,b)
y=a*b;
end

output
>> multiply(23,3)
ans =
69

Function Example2
function1.m
function [out1,out2] = function1(a,b)
out1=sin(a);
out2=sin(b);
end

output
[a,b]=function1(2,4)
a=
0.9093
b=
-0.7568

Cluster Analysis?
Finding groups of objects such that the objects in a group will
be similar (or related) to one another and different from (or
unrelated to) the objects in other groups

Clustering techniques
Clustering
Clustering

Partitional
Partitional
k-mean

Hierarchical
Hierarchical

agglomerative

divisive

Hierarchical clustering
Algorithm Description

1. Determine the distance between each pair of
points
2. Iteratively group points into a binary
hierarchical cluster tree(linkage)
3. cut the hierarchical tree into cluster

Hierarchical clustering

1.
0.075

0.07

0.065

2.

0.06

0.055

0.05

2 28 7 24 27 21 18 12 6 9 15 26 10 3 8 29 5 17 22 13 30 16 1 23 4 11 20 19 25 14

3.

Hierarchical clustering using matlab
load fisheriris
X=meas
Y = pdist(X)
z=linkage(Y)
dendrogram(z)

0.075

0.07

0.065

0.06

0.055

0.05

2 28 7 24 27 21 18 12 6 9 15 26 10 3 8 29 5 17 22 13 30 16 1 23 4 11 20 19 25 14

Hierarchical clustering using matlab
7

load fisheriris
X=meas
Y = pdist(X)
z=linkage(Y)
dendrogram(z)
hidx=cluster(z,'MaxClust',3)
ptsymb = {'bs','r^','md','go','c+'};
for i=1:max(hidx)
clust=find(hidx==i)
plot3(X(clust,1),X(clust,2),X(clust,3),ptsymb{i});
hold on;
end
6
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2

1
4.5

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3.5

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2.5

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7.5

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Matlab practical and lab session

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