INTRODUCTION TO MATLAB LAB# 01

INTRODUCTION TO MATLAB

LAB# 01

Introduction to Matlab

• What is Matlab?

– Matlab is a commercial “MATrix LABoratory” package by

Mathworks, which operates as an interactive programming

environment with graphical output.

– The MATLAB programming language is exceptionally straight

forward since almost every data object is assumed to be an Array.

– In engineering MATLAB is displacing popular programming

languages, due to its interactive interface, reliable algorithmic

foundation, fully extensible environment and availability of

different tool boxes.

Introduction to MATLAB

• Entering and Running MATLAB– On a system running Microsoft Windows double click on the

Matlab icon to launch Matlab.

– A command window will appear with the prompt >> you are now in MATLAB.

• Leaving Matlab– A MATLAB session may be terminated by simply typing

>> quit or by typing >>exit at the MATLAB prompt.

• Online Help

Online help is available from the MATLAB prompt both generally and for specific commands.

>> help

>> help demo

Desktop Tools (Matlab v7)

• 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

Variables

• MATLAB is case sensitive, that is‘a’ is not the same as ‘A’

– MATLAB has built in variables like pi, eps and ans.

– The variable ans will keep track of the last output which was not assigned to another variable.

• Variable Assignment:– The equality sign is used to assigned values to variables.

• >> x = 3 y = x ^ 2

– Out put can be suppressed by appending a semicolon to the command lines.

• >> x = 3 ; y = x ^ 2 ;

Variables

• Active Variables:– Who

• Removing Variables– Clear x

– Clear

• Saving and Restoring Variables– Save filename

– Load filename

Variable Arithmetic

• Operator precedence– 2 + 3 *4 ^ 2

• Double Precision Arithmetic– Normally the results will be displayed in a shorter form.

• a = sqrt( 2 ) >> a = 1.4142

– Format long• b = sqrt ( 2 ) >> b = 1.41421356……….

– Format short

• Command Line Editing– The arrow keys allow “ command line editing”

Built in Mathematical Functions

Functions Meaning Examples

Sin sine sin ( pi )=0.0

Cos cosine cos ( pi )=1.0

Tan tangent tan ( pi / 4)=1.0

Exp exponential exp(1.0)=2.7183

log natural log log(2.7183)=1.0

• Arguments to trigonometric functions are given in radians.– x= pi / 3;

– sin( x ) ^ 2 + cos ( x ) ^ 2 = ?

Matrices

• The element within a row of a matrix may be separated by a commas as well as a blank.

• The elements of a matrix being created are enclosed by brackets.

• A matrix is entered in “row major order” [i.e. all of the first row, then all of the second row; etc];

• Rows are separated by semicolon [or a new line], and the elements of the row may be separated by either a comma or space.

• The following commands will create a 3 x 3 matrix and assigned it to the variable A.

– >> A = [1 2 3; 4 5 6; 7 8 9]; or A = [1,2,3;4,5,6;7,8,9]

– >> A = [ 1 2 3

4 5 6

7 8 9 ]

Matrices

• The matrix element located in the i-th row and j-th column of A is referred to in the usual way:– >> A (1 , 2), A ( 2 , 3)

• Matrices can be easily modified:– A ( 2 , 3 ) = 10;

• Building Matrices from a Block:– Large matrices can be assembled from smaller matrix blocks i.e.

• C = [A;10 11 12];

• [A; A; A]

• [A, A, A]

• >> B = [A, zeros(3,2); zeros(2,3), eye( 2 ) ] ?

Built in Matrix Functions

Function Descriptiondiag return diagonal M.E as a vector

eye identity matrix

magic magic squares

ones matrix of ones

rand randomly generated matrix

zeros matrix of zeros

Built in Matrix Functions

• Matrices of Random Entries:– >> rand ( 3 )– >> rand ( m , n )

• Magic Squares: – A magic square is a square matrix which has equal sums along all its rows

and columns.– >> magic ( 4 )

• Matrix of Ones:– >> eye ( m , n )– >> eye ( n )

• Matrices of Zeros:– >> zeros ( m , n )– >> zeros ( n )

• Diagonal Matrices:– >> diag (A)

• diag ( diag ( A ) ) ?

Matrix Operations

+ Addition

- Subtraction

* Multiplication

^ Power

‘ Transpose

/ Division

* If the sizes of the matrices are incompatible for the matrix operation, an error message will result.

.* element-by-element mul

./ element-by-element div

.^ element-by-element power

.‘ transpose

Matrix Operations

• Matrix Transpose:– >> A’

• Matrix Addition / Subtraction:– A + B, A – B

• Matrix Multiplication;– A * B , B * A.

• Round Floating Point Numbers to Integers:– >> f = [-.5 .1 .5 ]– round (f)– ceil (f)– floor (f)– sum (f)– prod (f)

• Matrix Element Level Operations:– The matrix operation of addition and subtraction are already operates on

an element by element basis but other operation given above do not.– Matlab has a convention in which a dot in front of the operations is used.– i.e [1 , 2 , 3 , 4 ] . * [ 1 , 2 , 3 , 4 ]– [ 1 , 2 , 3 , 4 ] . ^ 2

Operators (relational, logical)

== equal

~= not equal

< less than

<= less than or equal

> greater than

>= greater than or equal

& AND

| OR

~ NOT

Branching Constructs

• If – end Construct:

if < condition >,

< program >

end

• If - else - end Construct:

if < condition 1 >,< program 1>

else < program2 >end

• If - elseif - end Construct:

if < condition1 >,

< program 1>

elseif <condition2>

< program2 >

end

Looping Constructs

• For Loops:

for i = 1 : n ,< program>,

end

• While Loops:

while < condition >,< program >,

end

• Nested For Loops:

for i = 1 : n ,

for j = 1 : n ,

A(i,j) = i/j ;

end

end

Matlab M-files

• Matlab commands can be run from one file without having to enter each command one by one at Matlab prompt.

• In order to use the programs later in Matlab they are to be saved first.

• For this purpose programs should be written in the editor / debugger.– In command window go to File menu, new and select M-file.

– Code your algorithm

– Execute it from the command window by typing file name

Matlab User Defined Function

• Matlab User Defined Function can have an input and output.

• Arguments can be passed to a function for computation

• For this purpose programs should be written in the editor / debugger.– In command window go to File menu, new and select M-file.

– function addx = 3; y = 5;

z = x + y

– Save the file and write add at the command prompt

– function addv (x,y)Z = x + y

– Save the file and write addv(5,6) at the command prompt

– % is used for commenting in front of a statement

Input/ Output

• Request User Input– data=input(‘message’);

– data=input(‘message’,’s’)

• Ouput Data– disp(‘message’)

– disp(variable_name)

Matlab Graphics

x = 0:pi/100:2*pi;

y = sin(x);

plot(x,y)

xlabel('x = 0:2\pi')

ylabel('Sine of x')

title('Plot of the Sine Function')

Multiple Graphs

t = 0:pi/100:2*pi;

y1=sin(t);

y2=sin(t+pi/2);

plot(t,y1,t,y2)

grid on

Multiple Graphs

x = 0 : .01 : 2 * pi;

y1= sin (x);

y2 =sin (2*x);

y3 = sin (4*x);

plot(x,y1,‘--',x,y2,‘-‘,x,y3,‘+')

grid

title ('Dashed line and dotted line graph')

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)

Three Dimensional Graphics

x = -1:.1:1 ;

y = -1:.1:1;

for i=1:1:length(x)

for j=1:1:length(y)

z(i,j)=x(i)^2+y(j)^2;

end

end

mesh(z);

Graph Functions (summary)

• plot (x,y) linear plot

• plot (x,y1,x,y2) multiple plots on the same graph

• mesh(z) 3-D graph

• stem (x) discrete plot

• xlabel (‘X-axis label ’) add X-axis label

• ylabel (‘Y-axis label ’) add Y-axis label

• title (‘title of plot’) add graph title

• subplot (m,n,p) divide figure window • grid add grid lines

• hold hold current graph in the figure

• zoom allow zoom in/out using mouse

• figure create new figure window

• pause wait for user response