An Introduction to MATLAB for beginners

CONTENTS
•Introduction
•Desktop tools
•Creating arrays
•Mathematical operation with arrays
•Script files
•Two dimensional plots
•Functions
2

Introduction
 MATLAB is a program for doing numerical computation.
 originally designed for solving linear algebra type problems
using matrices.
 name 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.
3

Desktop Tools
•Command Window
-type commands
•Workspace
-view program variables
-clear to clear
-double click on a variable to see it in the Array Editor
•Command History
-view past commands
-save a whole session using diary
6

Command
Window
Current Directory
Workspace
Command
History
7

•Figure Window
-contains output from graphic commands
•Help Window
-provides help information
•Editor Window
-creates and debugs script and function files
•Current directory Window
-shows files in current directory
•Launch Pad Window
-provides access to tools,demos and
documentation
8

COMMAND WINDOW
 >> type code
Press enter
Command executed and output displayed
semicolon(;)
output not displayed
Ellipsis(…) if a command is too long to fit in one line
Command can continue line after line up to 4096
characters.
9

Matlab case sensitive
% -comment
clc -clear screen
↑ -recall previously typed commands
↓ -move down to previously typed
commands
11

Arithmetic Operations With
Scalars
Operation Symbol Example
Addition + 5+3
Subtraction - 5-3
Multiplication * 5*3
Right division / 5/3
Left division 53=3/5
Exponentiation ^ 5^3=125
12

text from a MATLAB screen
» %To get started, type one of these commands:
» a=5;
» b=a/2
b =
2.5000
»
13

Order of Precedence
Parentheses
Exponentiation
Multiplication and division
Addition and subtraction
14

Display Formats
 User can control format in which
MATLAB displays o/p on screen.
format command– To change o/p
format
Default format for numerical values
-short (fixed point with 4 decimal
digits)
15

Command Description
format short Fixed-point with 4
decimal digits
format long Fixed-point with 14
decimal digits
format bank 2 decimal digits
format compact Eliminates empty lines
format loose Adds empty lines
16

Elementary Math functions
Function Description
sqrt (x) Square root
exp (x) Exponential (ex )
abs (x) Absolute value
log (x) Natural logarithm
Base e logarithm
Log10(x) Base 10 logarithm
factorial(x) Factorial function x!
17

Trigonometric math functions
sin(x),cos(x), tan(x),cot(x)
Rounding functions
Function Description
round(x) Round to the nearest integer
fix(x) Round towards zero
ceil(x) Round towards infinity
floor(x) Round towards minus infinity
rem(x,y) Returns remainder after x is
divided by y
Sign(x) Signum function 18

Math Functions
Elementary functions (sin, cos, sqrt, abs, exp,
log10, round)
-type help elfun
Advanced functions (bessel, beta, gamma, erf)
-type help specfun
-type help elmat
19

Variables (Arrays) and Operators
20

Defining scalar variables
variable is a name made of a letter or a
combination of several letters that is assigned a
numerical value
- actually name of a memory location
-assignment operator ‘=‘
Variable_name=a numerical value or a computable
aaaaa
expression
>>x=15
>>x=3*x-12
21

• When new variable is created matlab assigns
appropriate memory space where assigned
value can be stored
• When variable is used stored data is used
• If assigned new value content of memory is
replaced
>>ABB=72;
>>ABB=9;
>>ABB
ABB=
9
22

Rules about 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.
• Must begin with a letter.
• Avoid using names of built-in functions for
variable.
23

Predefined variables
variable description
ans Value of last expression
eps Smallest difference
between 2 numbers
i √-1
inf Infinity
j Same as i
NaN Not a number
pi The number Π
24

Some Useful MATLAB commands
• who List known variables
• whos List known variables plus their size
• help >> help sqrt Help on using sqrt
• clear Clear all variables from work space
• clear x y Clear variables x and y from work space
• clc Clear the command window
25

Array
List of numbers arranged in row and/or columns.
• Simplest array
-1D array
-usually to represent vectors.
• Complex array
-2D array
-represent matrixes
26

Creating vector from a known list
of numbers
Variable_name = [type vector elements]
•Row vector-type elements with space or
comma
•Column vector-type elements with
semicolon(;) or press Enter key after each
element
27

Creating vector with constant
spacing
Variable_name = [m:q:n] Variable_name = m:q:n
or
First term spacing last term
First element last element no of elements(when omitted
default value 100)
Variable_name = linspace(xi,xf,n)
28

Creating 2D array(matrix)
•Matrix are used in science & eng to describe
many physical quantities.
Variable_name = [1st row elements;2nd row
elements;……;last row elements]
•All rows must have same number of elements
29

Zeros , ones and eye commands
•zeros(m,n)
mxn matrix of 0’s.
•ones(m,n)
mxn matrix of I’ s.
•eye(n)
nxn identity matrix
30

Transpose operator
•Type single quote (‘) following variable to be
transposed.
>> aa = [3 8 1]
aa=
3 8 1
>>bb=aa’
bb=
3
8
1
31

Array addressing
•Vector named ve
ve(k)
element in position k
•Matrix ma
ma(k,p)
refers to element in row k & column p
32

Using a colon : in addressing arrays
va(:) -all elements of vector va
va(m:n) -all elements m through n of vector va
A(:,n) -elements in all rows of column n of
matrix A
A(n,:) -elements in all columns of row n of
matrix A
A(:,m:n) -elements of all rows between columns
m and n
A(m:n,:) -elements in all columns between rows
m and n
33

Adding elements to existing
variables
•by assigning values to the elements.
>>DF = 1 2 3 4
DF =
1 2 3 4
>>DF(5:10)=10:5:35
DF =
1 2 3 4 10 15 20 25 30 35
>>AD = [5 7 2 ]
AD =
5 7 2
>>AD(8) = 4
AD=
5 7 2 0 0 0 0 4
>>RE = [3 8 1 ];
>>GT = 4:3:16;
>>KNH = [RE GT]
KNH =
3 8 1 4 7 10 13 16
>>E = [1 2 3 4;5 6 7 8]
E=
1 2 3 4
5 6 7 8
>>E(3,:) = [6:4:9]
E=
1 2 3 4
5 6 7 8
6 7 8 9
Appending
Adding elements
to a vector
Matlab add zeros
between last
original element
and new
element
Adding elements
to a matrix
34

Deleting Elements
By assigning nothing to these elements.
>>kt =[10 8 6 21 9]
kt=
10 8 6 21 9
>>kt(4) = []
Kt=
10 8 6 9
>>mtr = [5 56 75;23 54 12;64 12 76]
mtr=
5 56 75
23 54 12
64 12 76
>>mtr(:,2:3) = []
mtr=
5
23
64
>>
Eliminate the 4th
element
Eliminate all rows of
columns 2 through 3
35

Building function for handling arrays
Function Description Example
length(A) returns number of elements in
vector A
>>A =[ 5 9 2 4]
>>length(A)
ans =
4
size(A) returns a row vector of [m,n] >>A=[6 1 4 0;5 9 8 2]
A=
6 1 4
5 9 8
>>size(A)
ans =
2 3
reshape(A,m,n) rearrange r x s matrix to a m x n
matrix
>>B=reshape(A,3,2)
B=
6 5
1 9
4 8 36

contd…
diag(v) When v is a vector ,creates a square
matrix with the elements of v in the
diagonal.
>>v = [7 4 2];
>>A =diag(v)
A=
7 0 0
0 4 0
0 0 2
diag(A) When A is a matrix , creates a vector
from the diagonal elements of A .
>>A= [1 2 3;4 5 6;7 8 9]
A=
1 2 3
4 5 6
7 8 9
>>vec=diag(A)
Vec=
1
5
9
37

Strings And String As Variables
•In single quotes.
•Text on screen change to purple when 1st single quote is
typed then turns into maroon when string is typed.
•Used in
-o/p commands to display text messages.
-in formatting commands of plots.(labels to axes ,
title and plots).
-as i/p arguments for some functions.
>>Name = ‘murshida’
Name =
murshida
>>Name(2:8) = ‘idhya ‘
Name =
midhya 38

Character Strings
>> hi = ' hello';
>> class = 'MATLAB';
>> hi
hi =
hello
>> class
class =
MATLAB
>> greetings = [hi class]
greetings =
helloMATLAB
>> vgreetings = [hi;class]
vgreetings =
hello
MATLAB
concatenation with blank
or with “,”
semi-colon: join vertically
39

Strings placed as matrix
Done by typing ‘;’ or by pressing ‘Enter’ key
at the end of each row.
Each row must be placed as strings.(ie
enclosed in single quotes).
Each row with words of equal size.add space
for making words of equal size.
>>a=[‘abcd’;’efg ‘]
a=
abcd
efg
>>a=[‘ab cd’;’ef gh’]
a=
ab cd
ef gh
40

Built-in function char
•Create an array with rows that have same
number of characters from an input of
characters which are not of same length.
•MATLAB makes length of all rows equal to the
longest line by adding spaces to the short line.
Variable_name = char( ‘ string 1 ’ , ’ string 2 ’ , ’string 3 ’ )
>>info = char(‘student name:’,’john smith’,’grade:’,’A+’)
Info =
student name:
john smith
grade:
A+ 41

>>X=‘156’
X=
156
>>Y=156
Y=
156
>>
both X & Y look the
same .But X cannot
be used for
mathematical
calculation.
42

Addition and subtraction
>>vectA = [8 5 4]; vectB = [10 2 7];
>>vectC = vectA + vectB
vectC =
18 7 11
>>A = [ 5 -3 8;9 2 10]
A =
5 -3 8
9 2 10
>>B = [10 7 4;-11 15 1]
B =
10 7 4
-11 15 1
>>A - B
ans=
-5 -10 4
20 -13 9
44

Array multiplication
>>F = [1 3; 5 7]
F=
1 3
5 7
>>G = [ 4 2; 1 6 ]
G=
4 2
1 6
>>F*G
ans =
7 20
27 52
>>b=3
b=
3
>>b*F
ans =
3 9
15 21
45

Array division
•Determinants
|A|
in matlab use det(A)
•Identity matrix
AI = IA = A
In matlab use eye(A)
•Inverse of a matrix
BA = AB = I
In matlab use A ^-1 or inv(A)
46

Contd..
Left division
to solve matrix eqn AX = B
X = AB
Right division
to solve matrix eqn XC = D
X = D/C
What happens: B is
divided by A
What happens: D is
divided by A
47

example
Q. Solve three linear equations using
matrix 4x - 2y + 6z = 8
2x + 8y +2z = 4
6x + 10y+3z= 0
Eqns are of the form AX = B or XC =D
4 -2 6 x 8
2 8 2 y = 4
6 10 3 z 0
or
4 2 6
x y z -2 8 10 = 8 4 0
6 2 3
48

Operators (Element by Element)
.* element-by-element multiplication
./ element-by-element right division
. element-by-element left division
.^ element-by-element exponentiation
49

element-by-element operations
>>A = [ 2 6 3; 5 8 4]
A=
2 6 3
5 8 4
>>B = [ 1 4 10; 3 2 7]
B=
1 4 10
3 2 7
>>A .*B
ans=
2 24 30
15 16 28
>>C = A/B
C=
2.0000 1.5000 0.3000
1.6667 4.0000 0.5714
>>B .*3
ans=
1 64 1000
27 8 343
>>A * B
???Error using ==>
Inner matrix dimensions must
agree.
50

mean(A) mean value of the elements of the vector A. >> A=[5 9 2 4];
>>mean(A)
ans =
5
C=max(A)
[d,n]=max(A)
C= is the largest element in vector A.( If A is a
matrix,
C =row vector containing the largest element of
each column of A.)
d =largest element in vector A,
n =position of the element ( the first if several
have the max value ).
>>A=[5 9 2 4 11 6 7 11 0 1];
>>C=max(A)
C=
11
>>[d,n]=max(A)
d =
11
n =
5
min(A)
[d,n]=min(A)
Same as max(A) , but for
smallest element.
Same as [d,n]= max(A), but for the smallest
element .
>>A=[5 9 2 4];
>>min(A)
ans =
2
Std(A) standard deviation of the element of the vector
A.
>>A=[5 9 2 4];
>>std(A)
Ans=
2.9439 52

dot (A) scalar (dot) product of two vectors a and b.
The vectors can each be row or column
vector.
>>a=[1 2 3];
>>b=[ 3 4 5];
>>dot(A)
Ans=
26
cross(A) cross product of two vectors a and b , (a*b).
The vectors must have 3 element.
>>a=[1 3 2];
>>b=[2 4 1];
>>cross(a,b)
Ans=
-5 3 -2
sum(A) sum of the elements of the vector A. >>A=[5 9 2 4];
>>sum(A)
ans=
20
sort(A) arranges the elements of the vector A in
ascending order.
>>A=[5 9 2 4 ];
>>sort(A)
ans=
2 4 5 9
Median(A) median value of the elements of the vector
A.
>>A=[5 9 2 4];
>>median(A)
ans=
4.5000 53

Limitations of command
window
•commands cannot be saved and executed
again.
•not interactive.
•for change or correction all commands are to
be entered & executed again.
54

create a file with list
of commands . save
it & run the file
Script files
55

Use of M-File
Click to create a
new M-File
• Extension “.m”
• A text file containing script or function or program to run
57

SAVING A SCRIPT FILE
FILE
SAVE As..
enter name of file
with .m extension
59

Input to a script file
1. Variable is defined & assigned value in the script
file.
1
2. Variable is defined & assigned value in the
command window.
2
3. Variable is defined in script file, but a specific
value is entered in the command window when
the script file is executed.
3
GO
61

%this script file calculates the avg points scored in 3
%games
game1=75;
game2=93;
game3=68;
avg_point=(game1+game2+game3)/3
>>ex1
avg_points=
78.6667
62

%games .
%values of game1,game2 & game3 is done in
%command window.
>>game1=75;
>>game2=90;
>>game3=68
>>ex2
avg_points=
78.6667 63

%games .
%values of game1,game2 & game3 is assigned using
%input command.
game1=input(‘enter points scored in game1 : ’);
>>ex2
enter points scored in game1 : 75
avg_points=
78.6667 64

Initializing with Keyboard Input
• The input function displays a prompt string in the
Command Window and then waits for the user to
respond.
my_val = input( ‘Enter an input value: ’ );
in1 = input( ‘Enter data: ’ );
in2 = input( ‘Enter data: ’ ,`s`);
65

Output Commands
• disp command
displays o/p on the screen
or
disp(name of a variable) disp(‘text as string’)
• fprintf command
to display o/p(text & data) on the screen or save it to
a file
fprint(‘text typed in as string’)
66

Plotting with MATLAB
 MATLAB will plot one vector vs. another. The first one
will be treated as the abscissa (or x) vector and the
second as the ordinate (or y) vector. The vectors have
to be the same length.
 MATLAB will also plot a vector vs. its own index. The
index will be treated as the abscissa vector. Given a
vector “time” and a vector “dist” we could say:
>> plot (time, dist)
>> plot (dist)
plot(x,y)
68

formating a plot
There are commands in MATLAB to "annotate" a plot to put on
axis labels, titles, and legends. For example:
>> % To put a label on the axes we would use:
>> xlabel ('X-axis label')
>> ylabel ('Y-axis label')
>> % To put a title on the plot, we would use:
>> title ('Title of my plot')
>>%To put a text label in the plot,we would use:
>>text(x,y,’text as string’)
>>gtext(‘text as string’)
% user specifies the position in figure window with mouse
69

>> x = [0: pi/100: pi]; % [start: increment: end]
>> y = sin(x);
>> plot(x,y), title('Simple Plot')
70

Matlab Graphics
x = 0:pi/100:2*pi;
y = sin(x);
plot(x,y)
xlabel('x = :2pi')
ylabel('Sine of x')
title('Plot of the
Sine Function')
71

plot command
plot(x, y, ‘line specifiers’ , ‘PropertyName’ , PropertyValue)
vector (optional)
defines the
style and color
of line and
markers
(optional) properties
with values that can
be used to specify
the line width ,
marker’s size & edge,
and fill colors.
72

line specifiers
Line Style Specifier
Solid(default) -
Dashed --
Dotted :
dash-dot -.
Line color Specifier
Red r
Green g
Blue b
Cyan c
Magenta m
Yellow y
Black k
White w
73

line specifiers contd..
Marker Type Specifier
Plus sign +
Circle o
Asterisk *
Point .
Marker Type Specifier
Square S
Diamond d
Five-pointed
p
star
Six-pointed
star
h
74

plot(x,y) a blue solid line (default)
plot(x,y, ’r’) a red solid line connects the points
plot(x,y, ’--y’) yellow dashed line connects the points
plot(x,y, ’*’) points are marked with *(no line
between the points)
75

Property Name and Property Value
Property Name Possible Property Value
LineWidth
( or linewidth)
A number in units of
points(default 0.5).
MarkerSize
( or markersize)
A number in units of
points.
MarkerEdgeColor
( or
markeredgecolor)
Color specifiers typed as
string
MarkerFaceColor
( or
markerfacecolor)
Color specifiers typed as
string
76

Plot of a Function
plot or fplot command
to plot a y=f(x)
create a vector of values of x
vector y is created with corrosponding values of
f(x) using element-by-element calculations.
once two vectors are created
plot(x,y)
77

Plot of a Function contd…
eg: plot function y =3.5-0.5x cos(6x) for -2 ≤ x ≤ 4.
%script file that create plot of function
% 3.5.^(-0.5*x).*cos(6*x)
x = [-2: 0.01: 4];
y = 3.5.^(-0.5*x).*cos(6*x);
plot(x,y)
78

Plot of a Function contd…
fplot command
plot function of form y=f(x) between
specified limits
fplot( ‘function ‘ , limits, line specifiers)
[xmin,xmax]
or
[xmin,xmax,ymin,ymax]
79

Multiple Graphs using plot command
plot(x,y,u,v,t,h)
t = 0:pi/100:2*pi;
y1=sin(t);
y2=sin(t+pi/2);
plot(t,y1,t,y2)
grid on
add grid lines to
the plot
80

Multiple Graphs using hold on,
hold off command
•one graph is plotted 1st with plot command.
•hold on command is typed.
this keeps the figure window with the 1st
plot open,including the axis properties &
formating
•additional graphs drawn with plot command that
follows.
•each plot command creates a graph that is added
to that figure.
•hold off command stop this process.
81

Multiple Graphs using line
command
additional graphs (lines) can be added to plot
that already exists.
line(x,y, ‘PropertyName’ ,PropertyValue)
x = [-2:0.01:4]
y = 3*x.^3 – 26*x + 6;
yd = 9*x.^2 – 26;
plot(x,y,’linestyle’, ’-’ ,’color’,’b’)
line(x,yd,’linestyle’, ’--’ ,’color’,’r’)
82

Multiple Plots
subplot(m , n , p)
t = 0:pi/100:2*pi;
y1=sin(t);
y2=sin(t+pi/2);
subplot(2,2,1)
plot(t,y1)
subplot(2,2,2)
plot(t,y2)
83

plots with logarithmic axis
•semilogy(x,y)
•semilogx(x,y)
•loglog(x,y)
84

use edit and insert to
format
click this button
to start the plot
edit mode
86

Histograms
•plots that show distribution of data
•overall range of a given set of data points is
divided into smaller subranges(bins)
•and the histogram shows how many data
points are there in each bin
hist (y)
87

>> y=[58 73 73 53 50 48 56 73 73 66 69 63 74 82 84 91 93 89 91 80
59 69 56 64 63 66 64 74 63 69];
>> hist(y)
>>
88

Random Numbers
x=rand(100,1);
stem(x);
hist(x,100)
89

polar plots
To plot a function r = f(θ)
polar(theta,radius, ‘line specifiers ‘)
vector
90

>> t=linspace(0,2*pi,200);
>> r=3*cos(0.5*t).^2+t;
>> polar(t,r)
91

Graph Functions (summary)
•plot linear plot
•stem discrete plot
•grid add grid lines
•xlabel add X-axis label
•ylabel add Y-axis label
•title add graph title
•subplot divide figure window
•figure create new figure window
•pause wait for user response
92

Scripts and Functions
• 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.
93

if/elseif/else Statement
>> A = 2; B = 3;
>> if A > B
'A is bigger'
elseif A < B
'B is bigger'
elseif A == B
'A equals B'
else
error('Something odd is happening')
end
ans =
B is bigger
94

switch Statement
>> n = 8
n =
8
>> switch(rem(n,3))
case 0
m = 'no remainder'
case 1
m = ‘the remainder is one'
case 2
m = ‘the remainder is two'
otherwise
error('not possible')
end
m =
the remainder is two
95

For Loop
>> for i = 2:5
for j = 3:6
a(i,j) = (i + j)^2
end
end
>> a
a =
0 0 0 0 0 0
0 0 25 36 49 64
0 0 36 49 64 81
0 0 49 64 81 100
0 0 64 81 100 121
96

while Loop
>> b = 4; a = 2.1; count = 0;
>> while b - a > 0.01
a = a + 0.001;
count = count + 1;
end
>> count
count =
1891
97

Common OS Commands
•ls / dir provide a directory listing
of the current directory
• pwd shows the current directory
98

An Introduction to MATLAB for beginners

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