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
Description
diag
eye
magic
ones
rand
return diagonal M.E as a vector
identity matrix
magic squares
matrix of ones
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
.*
./
.^
.‘
element-by-element mul
element-by-element div
element-by-element power
transpose
* If the sizes of the matrices are incompatible for the matrix
operation, an error message will result.
Matrix Operations
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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 >,
•
If - elseif - end Construct:
if < condition1 >,
< program >
end
•
< program 1>
elseif <condition2>
< program2 >
If - else - end Construct:
if < condition 1 >,
< program 1>
else
< program2 >
end
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 add
x = 3;
z=x+y
y = 5;
– 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)
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plot (x,y)
plot (x,y1,x,y2)
mesh(z)
stem (x)
xlabel (‘X-axis label ’)
ylabel (‘Y-axis label ’)
title (‘title of plot’)
subplot (m,n,p)
grid
hold
zoom
figure
pause
linear plot
multiple plots on the same graph
3-D graph
discrete plot
add X-axis label
add Y-axis label
add graph title
divide figure window
add grid lines
hold current graph in the figure
allow zoom in/out using mouse
create new figure window
wait for user response