Introduction to matlab

Introduction to Matlab

By: İ.Yücel
Özbek

Outline:
 What is Matlab?
 Matlab Screen
 Variables, array, matrix, indexing
 Operators (Arithmetic, relational, logical )
 Display Facilities
 Flow Control
 Using of M-File
 Writing User Defined Functions
 Conclusion

What is 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
Command
m-files mat-files
Line

functions Command execution Data
Input like DOS command storage/
Output window loading
capability

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

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

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 x = zeros(1,3)
x =
0 0 0
 ones(M,N) MxN matrix of ones
x = ones(1,3)
x =
1 1 1
 rand(M,N) MxN matrix of uniformly
distributed random x = rand(1,3)
numbers on (0,1) 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.

Operators (arithmetic)
+ addition
- subtraction
* multiplication
/ division
^ power
‘ complex conjugate transpose

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

The use of “.” – “Element” Operation
A = [1 2 3; 5 1 4; 3 2 1]
A=
1 2 3
5 1 4
3 2 -1

b = x .* y c=x./y d = x .^2
x = A(1,:) y = A(3 ,:)
b= c= d=
x= y= 3 8 -3 0.33 0.5 -3 1 4 9
1 2 3 3 4 -1

K= x^2
Erorr:
??? Error using ==> mpower Matrix must be square.
B=x*y
Erorr:
??? Error using ==> mtimes Inner matrix dimensions must agree.

Basic Task: Plot the function sin(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-array1

0.8

0.6

>>y=sin(x); 0.4

0.2

0

 Plot the y-array -0.2

-0.4

-0.6

>>plot(y) -0.8

-1
0 10 20 30 40 50 60 70 80 90 100

Plot the function 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;

Plot the function e-x/3sin(x) between
0≤x≤4π
 Multiply the arrays y and y1 correctly
>>y2=y.*y1;

 Plot the y2-array
0.7

>>plot(y2) 0.6

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 0.7

0.6

0.5

 plot(.) 0.4

0.3

Example:
0.2

0.1

>>x=linspace(0,4*pi,100); 0

>>y=sin(x); -0.1

>>plot(y) -0.2

>>plot(x,y)
-0.3
0 10 20 30 40 50 60 70 80 90 100

0.7

 stem(.) 0.6

0.5

0.4

0.3

Example:
0.2

0.1

>>stem(y) 0

>>stem(x,y) -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’)
This is the sinus function
1

0.8

 xlabel(.) 0.6

0.4

>>xlabel(‘x (secs)’) 0.2

sin(x)
0

 ylabel(.)
-0.2

-0.4

-0.6

-0.8
>>ylabel(‘sin(x)’) -1
0 10 20 30 40 50 60 70 80 90 100
x (secs)

Operators (relational, logical)

 == Equal to
 ~= Not equal to
 < Strictly smaller
 > Strictly greater
 <= Smaller than or equal to
 >= Greater than equal to
 & And operator
 | Or operator

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;
Matlab Commands elseif (b~=5)
elseif (Condition_3) end
Matlab Commands
if (a<3)
else Some Matlab Commands;
Matlab Commands else
end end

Control Structures
Some Dummy Examples
 For loop syntax for i=1:100
end

for i=Index_Array for j=1:3:200
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)
Matlab Commands while ((a>3) & (b==5))
end end

Use of M-File
Click to create
a new M-File

• Extension “.m”
• A text file containing script or function or program to run

Use of M-File Save file as Denem430.m

If you include “;” at the
end of each statement,
result will not be shown
immediately

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

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

Useful Commands

 The two commands used most by Matlab
users are
>>help functionname

>>lookfor keyword

Questions

 ?
 ?
 ?
 ?
 ?

Introduction to matlab

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