Introduction to matlab

An Introduction to MATLAB

Santosh K Venu 1

What is MATLAB?

• MATLAB
– MATrix LABoratory: 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.

2

• Stands for MATrix LABoratory
• Interpreted language
• Scientific programming environment
• Very good tool for the manipulation of matrices
• Great visualisation capabilities
• Loads of built-in functions
• Easy to learn and simple to use

3

MATLAB Overview

• Strengths of MATLAB
• Weaknesses of MATLAB

4

Strengths of MATLAB

• MATLAB is relatively easy to learn
• MATLAB code is optimized to be relatively quick
when performing matrix operations
• MATLAB may behave like a calculator or as a
programming language
• MATLAB is interpreted, errors are easier to fix

5

Weaknesses of MATLAB

• MATLAB is NOT a general purpose programming
language
• MATLAB is an interpreted language (making it for the
most part slower than a compiled language such as C, C++)
• MATLAB is designed for scientific computation and is
not suitable for some things (such as design an interface)

6

Matlab Desktop

• Command Window
– type commands
• Workspace
– view program variables
– clear to clear
• clear all: removes all variables, globals, functions and MEX
links
• clc: clear command window
– double click on a variable to see it in the Array Editor
• Command History
– view past commands
• Launch Pad
– access help, tools, demos and documentation
7

Matlab Desktop - con’t

Launch Pad

Workspace

Current
DIrectory
Command
Window History

8

How to Resume Default Desktop

9

Matlab Help

• Different ways to find information
– help
– help general, help mean, sqrt...
– helpdesk - an html document with links to further
information

10

Matlab Help - con’t

11

Matlab Help - con’t

12

Command window

• 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.

» a=5;
» b=a/2

b=

2.5000

»
13

MATLAB Special Variables

ans Default variable name for results
pi Value of 
inf Infinity
NaN Not a number e.g. 0/0
i and j i = j = square root of minus one: (-1) (imaginary number)
e.g. sqrt(-1) ans= 0 + 1.0000i
realmin The smallest usable positive real number
realmax The largest usable positive real number

14

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

Working with Matrices and Arrays

• Since Matlab makes extensive use of matrices, the best
way for you to get started with MATLAB is to learn how
to handle matrices.
– Separate the elements of a row with blanks or commas.
– Use a semicolon ; to indicate the end of each row.
– Surround the entire list of elements with square brackets, [ ].

A = [16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15 14 1]

MATLAB displays the matrix you just entered:
A=
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1

• Once you have entered the matrix, it is automatically
remembered in the MATLAB workspace. You can
simply refer to it as A.

• Keep in mind, variable names are case-sensitive

Manipulating Matrices
A=
16 3 2 13
5 10 11 8
• Access elements of a matrix 9 6 7 12
>>A(1,2) 4 15 14 1

ans=
3 indices of matrix element(s)
• Remember Matrix(row,column)
• Naming convention Matrix variables start with a capital
letter while vectors or scalar variables start with a simple
letter

18

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 ~=

19

MATLAB Logical Operators

• MATLAB supports three logical operators.

not ~ % highest precedence
and & % equal precedence with or
or | % equal precedence with and

20

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 （1,1）are matrices with only one row AND one
column

21

MATLAB Matrices

• A matrix with only one row AND one column is a scalar.
A scalar can be created in MATLAB as follows:

» a=23

a=

23

22

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] or rowvec = [12 14 63]

rowvec =

12 14 63

23

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

24

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

25

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, the rows and
columns. 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.

26

MATLAB Matrices

• A column vector can be • Here we extract column 2 of
extracted from a matrix. As the matrix and make a
an example we create a column vector:
matrix below:

» matrix=[1,2,3;4,5,6;7,8,9] » col_two=matrix( : , 2)

matrix = col_two =
1 2 3 2
4 5 6 5
7 8 9 8

27

MATLAB Matrices

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

4 5 6

28

Matrices transpose

• a vector x = [1 2 5 1]

x =
1 2 5 1

• transpose y = x’ y =
1
2
5
1
29

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

30

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

31

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
32

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
33

Math & Assignment Operators

Power ^ or .^ a^b or a.^b
Multiplication * or .* a*b or a.*b
Division / or ./ a/b or a./b

- (unary) + (unary)
Addition + a+b
Subtraction - a-b
Assignment = a=b (assign b to a)
34

Other operators

[ ] concatenation x = [ zeros(1,3) ones(1,2) ]
x =
0 0 0 1 1

( ) subscription x = [ 1 3 5 7 9]
x =
1 3 5 7 9

y = x(2)
y =
3
y = x(2:4)
y =
3 5 7 35

The : operator

• VERY important operator in Matlab
• Means ‘to’
>> 1:10
ans =
1 2 3 4 5 6 7 8 9 10
>> 1:2:10
Try the following
ans = >> x=0:pi/12:2*pi;
>> y=sin(x)
1 3 5 7 9
Introduction to Matlab 36
Sumitha Balasuriya

• Length
• Max
• Mean
• Median
• Min
• Prod
• Size
• Var
• Sum
• Det
• Rank
• Eig
• sort/flipr 37

Matlab Graphics

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

38

Multiple Graphs

t = 0:pi/100:2*pi;
y1=sin(t);
y2=sin(t+pi/2);
plot(t,y1,t,y2)
grid on

39

• Plotting Multiple Data Sets in One Graph
– Multiple x-y pair arguments create multiple graphs with a
single call to plot.
For example: x = 0:pi/100:2*pi;
y = sin(x);
y2 = sin(x-.25);
y3 = sin(x-.5);
plot(x,y,x,y2,x,y3)

Multiple Plots

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)

41

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

42

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 on MATLABPATH.
• what >> what ('directory')
List MATLAB files in directory
• clear Clear all variables from work space
• clear x y Clear variables x and y from work space
• clc Clear the command window

43

Flow Control

• if
• for
• while
• break
• ….

Control Structures
Some Dummy Examples
• If Statement Syntax
if ((a>3) & (b==5))
Some Matlab Commands;
if (Condition_1) end
Matlab Commands if (a<3)
elseif (Condition_2) Some Matlab Commands;
elseif (b~=5)
Matlab Commands Some Matlab Commands;
elseif (Condition_3) end
Matlab Commands
if (a<3)
else Some Matlab Commands;
Matlab Commands else
end end

Control Structures
Some Dummy Examples

for i=1:100
• For loop syntax end

for j=1:3:200
for i=Index_Array Some Matlab Commands;
Matlab Commands end

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

Classification of flow
%|-------------------------------------|
This function classifies a flow |
according to the values of the Reynolds (Re) and Mach (Ma). |
Re <= 2000, laminar flow
2000 < Re <= 5000, transitional flow
Re > 5000, turbulent flow
Ma < 1, sub-sonic flow
Ma = 1, sonic flow
Ma > 1, super-sonic flow
%|-------------------------------------|

48

Vector Function

Consider now a vector function f(x) = [f1(x1,x2,x3) f2(x1,x2,x3)
f3(x1,x2,x3)]T, where x =
[x1,x2,x3]T (The symbol []T indicates the transpose of a matrix).
Specifically,
f1(x1,x2,x3) = x1 cos(x2) + x2 cos(x1) + x3
f2(x1,x2,x3) = x1x2 + x2x3 + x3x1
f3(x1,x2,x3) = x1
2 + 2x1x2x3 + x3
2
A function to evaluate the vector function f(x) is shown below.
49

Summation

%Check if m or n are matrices
if length(n)>1 | length(m)>1 then
error('sum2 - n,m must be scalar values')
abort
end
%Calculate summation if n and m are scalars
S = 0; %initialize sum
for i = 1:n %sweep by index i
for j = 1:m %sweep by index j
S = S + 1/((i+j)^2+1);
end
end
50

Introduction to matlab

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