Matlab an Introduction_Lecture_for all.ppt

AM2032 JAYANTA MUKHERJEE
INTRODUCTION
TO
MATLAB

 Introduction to MATLAB
 Running MATLAB and MATLAB Environment
 Getting help
 Variables, Arithmetic and Logical Operators
 Matrices and Vectors
 Mathematical Functions
 Plotting
 Programming
 M-files
 User Defined Functions
 Miscellaneous
 Tips

Introduction to MATLAB

Running MATLAB &
the MATLAB
Environment
You can enter MATLAB
with system command
“matlab” , C:> matlab. Or,
it can be started by
clicking on the start-up
menu or a short-cut icon

MATLAB Desktop
Command
Window
Launch Pad
Command
History
After the “>>” symbol, you
can type the commands
Command History is
used to view previously
used functions, and
selected lines can be
copied and executed.
Launch Pad is used to
provide easy access to
tools, demos, and
documentation.
Command Window is
used to enter variables
and run functions and
M-files. The Command
window is where you
can interact with
Matlab directly. Default
working directory on
Windows is C:/
MATLAB / bin.

MATLAB Desktop – cont’d
Command
Window
Workspace
Current
Directory
Workspace
consists of the set of
variables (named arrays)
built up during a
MATLAB session and
stored in memory.
Current Directory
is used to change
directory that is
worked on, quickly.

MATLAB Editor
Access to
commands
Color keyed text with
auto indents
tabbed sheets for other
files being edited

Getting MATLAB Help
• Type one of the following
commands in the command
window:
>>help – lists all the help topics
>>help topic – provides help for the
specified topic
>>help command – provides help for the
specified command
>>helpwin – opens a separate help
window for navigation
>>Lookfor keyword – search all M-files
for keyword
• Online resource

MATLAB Variables
• 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.
• 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.
• Variable names and their types do not have to be declared in MATLAB.
• Any variable can take real, complex, and integer values.
• The name of variable is not accepted if it is reserved word.

MATLAB Variables – cont’d
• Special variables:
– ans: default variable name for the result.
– pi: π = 3.1415926 ……
– eps: ε= 2.2204e-016, smallest value by which two numbers can differ
– inf: ∞, infinity
– NAN or nan: not-a-number
• Commands involving variables:
– who: lists the names of the defined variables
– whos: lists the names and sizes of defined variables
– clear: clears all variables
– clear name: clears the variable name
– clc: clears the command window
– clf: clears the current figure and the graph window
– Ctrl+C: Aborts calculation

•You can think of computer memory as a large set of “boxes” in which
numbers can be stored. The values can be inspected and changed.
•Boxes can be labeled with a variable name.
>> A=3
A =
3
3
A

• Suppose we want to calculate the volume of a
cylinder.
• It’s radius and height are stored as variables in
memory.
>> volume = pi*radius^2*height
volume radius height

• Variable is a name given to a reserved
location in memory.
>>x = 111;
>>number_of_students = 75;
>>name = ‘University College Cork’;
>>radius = 5;
>>area = pi * radius^2;
>>x_value=23
x_value=23

MATLAB Arithmetic Operators
Operator Description
+ Addition
- Subtraction
.* Multiplication (element wise)
./ Right division (element wise)
. Left division (element wise)
= Assignment operator,e.g. a = b,(assign b to a)
: Colon operator (Specify Range )
.^ Power (element wise)
' Transpose
* Matrix multiplication
/ Matrix right division
Matrix left division
; Row separator in a Matrix
^ Matrix power

Logical Operators
in MATLAB
Operator Description
& Returns 1 for every element location that is true (nonzero) in both arrays, and
0 for all other elements.
| Returns 1 for every element location that is true (nonzero) in either one or the
other, or both, arrays and 0 for all other elements.
~ Complements each element of input array, A.
< Less than
<= Less than or equal to
> Greater than
>= Greater than or equal to
== Equal to
~= Not equal to

Calculations at the Command
Line / Workspace
» -5/(4.8+5.32)^2
ans =
-0.0488
» (3+4i)*(3-4i)
ans =
25
» cos(pi/2)
ans =
6.1230e-017
» exp(acos(0.3))
ans =
3.5470
» a = 2;
» b = 5;
» a^b
ans =
32
» x = 5/2*pi;
» y = sin(x)
y =
1
» z = asin(y)
z =
1.5708
Results
assigned to
“ans” if name
not specified
() parentheses for
function inputs
Semicolon
suppresses
screen output
MATLAB as a calculator Assigning Variables
Copyright  1984 - 1998 by The MathWorks, Inc.

Vector & Matrix
in MATLAB
4 10 1 6 2
8 1.2 9 4 25
7.2 5 7 1 11
0 0.5 4 5 56
23 83 13 0 10
1
2
Rows (m) 3
4
5
Columns
(n)
1 2 3 4 5
1 6 11 16 21
2 7 12 17 22
3 8 13 18 23
4 9 14 19 24
5 10 15 20 25
A = A (2,4)
A (17)
Rectangular Matrix:
Scalar: 1-by-1 array
Vector: m-by-1 array
1-by-n array
Matrix: m-by-n array
Matrix elements can be EITHER
numbers OR characters
How do you specify this 5ⅹ 5 matrix ‘A’ in MATLAB ?
>>A=[4 10 1 6 2
8 1.2 9 4 25
7.2 5 7 1 11
0 0.5 4 5 56
23 83 13 0 10 ];
>>A=[4 10 1 6 2; 8 1.2 9 4 25; 7.2 5 7 1 11; 0 0.5 4 5 56; 23 83 13 0 10 ];

2 7 4
2
7
4
2 7 4
3 8 9
?
Examples (Vectors)
X=[2 7 4];
X=[2; 7; 4];
X=[2 7 4]’;
X=[2 7 4;3 8 9];
Y=[X X];
2 7 4
3 8 9
2 7 4
3 8 9
Row Vector
Column Vector
Matrix or a
2D array
Matrix
of
matrices

More on Vectors
x = start:end Creates row vector x starting with start, counting by 1 ,
ending at end
x = initial value : increment : final
value
Creates row vector x starting with start, counting by
increment, ending at or before end
x = linspace(start,end,number) Creates linearly spaced row vector x starting with start,
ending at end, having number elements
x = logspace(start,end,number) Creates logarithmically spaced row vector x starting
with start, ending with end, having number elements
length(x) Returns the length of vector x
y = x’ Transpose of vector x
dot(x,y),cross(x,y) Returns the scalar dot and vector cross product of the
vector x and y

More on Matrices
zeros(n) Returns a n ⅹ n matrix of zeros
zeros(m,n) Returns a m ⅹ n matrix of zeros
rand(m,n) Returns a m ⅹ n matrix of random numbers
eye(m,n) Returns a m ⅹ n Identity matrix
ones(n) Returns a n ⅹ n matrix of ones
ones(m,n) Returns a m ⅹ n matrix of ones
size(A)
For a m ⅹ n matrix A, returns the row vector [m,n]
containing the number of rows and columns in matrix
length(A) Returns the larger of the number of rows or columns in A

Any MATLAB expression can
be entered as a matrix element
Entering Numeric Arrays
» a=[1 2;3 4]
a =
1 2
3 4
» b=[-2.8, sqrt(-7), (3+5+6)*3/4]
b =
-2.8000 0 + 2.6458i 10.5000
» b(2,5) = 23
b =
-2.8000 0 + 2.6458i 10.5000 0 0
0 0 0 0 23.0000
Row separator:
semicolon (;)
Column separator:
space / comma (,)
Use square
brackets [ ]
Matrices must be rectangular/same
height. (Set undefined elements to zero)
MATLAB does not allow this !

Entering Numeric Arrays - cont.
» w=[1 2;3 4] + 5
w =
6 7
8 9
» x = 1:5
x =
1 2 3 4 5
» y = 2:-0.5:0
y =
2.0000 1.5000 1.0000 0.5000 0
» z = rand(2,4)
z =
0.9501 0.6068 0.8913 0.4565
0.2311 0.4860 0.7621 0.0185
Scalar expansion
Creating sequences
colon operator (:)
Utility functions for
creating matrices.

Numerical Array Concatenation - [ ]
» a=[1 2;3 4]
a =
1 2
3 4
» cat_a=[a, 2*a; 3*a, 4*a; 5*a, 6*a]
cat_a =
1 2 2 4
3 4 6 8
3 6 4 8
9 12 12 16
5 10 6 12
15 20 18 24
Use [ ] to combine
existing arrays as
matrix “elements”
Row separator:
semicolon (;)
Column separator:
space / comma (,)
Use square
brackets [ ]
The resulting
matrix must
be rectangular.
4*a

Array Subscripting / Indexing
4 10 1 6 2
8 1.2 9 4 25
7.2 5 7 1 11
0 0.5 4 5 56
23 83 13 0 10
1
2
3
4
5
1 2 3 4 5
1 6 11 16 21
2 7 12 17 22
3 8 13 18 23
4 9 14 19 24
5 10 15 20 25
A =
A(3,1)
A(3)
A(1:5,5)
A(:,5)
A(21:25)
A(4:5,2:3)
A([9 14;10 15])
• Use () parentheses to specify index
• colon operator (:) specifies range / ALL
• [ ] to create matrix of index subscripts
• ‘end’ specifies maximum index value
A(1:end,end)
A(:,end)
A(21:end)’

Some operations should be
handled with care
>>A=[1 2;4 5];
>>B=A*A % prints
9 12
24 33 % Proper matrix multiplication
>>
>>B=A.*A % prints
1 4
16 25 % Element by element multiplication

Operations on Matrices
Transpose B=A’
Identity Matrix
eye(n) -> returns an n X n identity matrix
eye(m,n) -> returns an m X n matrix with ones on the
main diagonal and zeros elsewhere
Addition and Subtraction C =A +B C =A - B
Scalar Multiplication B = α A, where α is a scalar
Matrix Multiplication C = A * B
Matrix Inverse B = inv(A), A must be a square matrix in this case
Matrix powers B = A * A , A must be a square matrix
Determinant det(A), A must be a square matrix

Multidimensional Arrays
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
» A = Pascal(4);
» A(:,:,2) = magic(4)
A(:,:,1)
1 1 1 1
1 2 3 4
1 3 6 10
1 4 10 20
A(:,:,2)
16 2 3 13
5 11 10 8
9 7 6 12
4 14 15 1
» A(:,:,9) = diag(ones(1,4));
Page N
Page 1
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
16 2 3 13
5 11 10 8
9 7 6 12
4 14 15 1
1 1 1 1
1 2 3 4
1 3 6 10
1 4 10 20
>>A = 1;
while length(A) < 4
A = [0 A] + [A 0];
end

Operating on Matrices

Operating on Matrices - cont.
• Matrices must have the same dimensions
• Dimensions of resulting matrix = dimensions of
multiplied matrices
• Resulting elements = product of corresponding
elements from the original matrices
Array Multiplication
» a = [1 2 3 4; 5 6 7 8];
» b = [1:4; 1:4];
» c = a.*b
c =
1 4 9 16
5 12 21 32 c(2,4) = a(2,4)*b(2,4)
Same rules apply for other
array operations too !

String Arrays
• Created using single quote delimiter (')
• Each character is a separate matrix element
(16 bits of memory per character)
» str = 'Hi there,'
str =
Hi there,
» str2 = 'Isn't MATLAB great?'
str2 =
Isn't MATLAB great?
1x9 vector
str = H i t h e r e ,

Mathematical Functions of MATLAB-1
Elemantary Mathematical (Trigonometric) Functions
Trigonometric
functions
Remarks
sin(x)
cos(x)
tan(x)
asin(x)
acos(x)
atan(x)
atan2(y,x)
sinh(x)
cosh(x)
tanh(x)
asinh(x)
acosh(x)
atanh(x)
- pi/2 ≤ atan(x) ≥ pi/2, Same as atan(y/x) but –pi ≥ atan(y,x) ≥ pi

Other elemantary
functions
Remarks
abs(x)
angle(x)
sqrt(x)
real(x)
imag(x)
conj(x)
round(x)
fix(x)
floor(x)
ceil(x)
sign(x)
exp(x)
log(x)
log10(x)
factor(x)
Absolute value of x
Phase angle of complex value: If x = real, angle = 0. If x = √-1, angle =
pi/2
Square root of x
Real part of complex value x
Imaginary part of complex value x
Complex conjugate x
Round to do nearest integer
Round a real value toward zero
Round x toward - ∞
Round x toward + ∞
+1 if x > 0; -1 if x < 0
Exponential base e
Log base e
Log base 10
1 if x is a prime number, 0 if not
Mathematical Functions of MATLAB-2
And there are many many more !

Plotting in MATLAB
• Specify x-data and/or y-data
• Specify color, line style and marker symbol
• Syntax: 2-D Plotting
– Plotting single line:
– Plotting multiple lines:
plot(x1, y1, 'clm1', x2, y2, 'clm2', ...)
plot(xdata, ydata, 'color_linestyle_marker')

2-D Plotting - example
Create a Blue
(default color)
Sine Wave
» x = 0:1:2*pi;
» y = sin(x);
» plot(x,y);

2-D Plotting : example-cont.
• GRID ON creates a
grid on the current
figure
• GRID OFF turns off
the grid from the
current figure
• GRID toggles the grid
state
» x = 0:1:2*pi;
» y = sin(x);
» plot(x,y);grid on;
Adding a Grid

Adding additional plots to a
figure
• HOLD ON holds the
current plot
• HOLD OFF releases
hold on current plot
• HOLD toggles the
hold state
» x = 0:.1:2*pi;
» y = sin(x);
» plot(x,y,'b')
» grid on;
» hold on;
» plot(x,exp(-x),'r:*');

Controlling Viewing Area
• ZOOM ON allows user
to select viewing area
• ZOOM OFF prevents
zooming operations
• ZOOM toggles the
zoom state
• AXIS sets axis range
[xmin xmax ymin ymax]
» axis([0 2*pi 0 1]);

Graph Annotation
TITLE
TEXT
or
GTEXT
XLABEL
YLABEL
LEGEND

Subplots
SUBPLOT- display multiple axes in the same figure window
»subplot(2,2,1);
»plot(1:10);
»subplot(2,2,2);
»x = 0:.1:2*pi;
»plot(x,sin(x));
»subplot(2,2,3);
»x = 0:.1:2*pi;
»plot(x,exp(-x),’r’);
»subplot(2,2,4);
»plot(peaks);
subplot(#rows, #cols, index);

Alternative Scales for Axes
SEMILOGY
log Y
linear X
PLOTYY
2 sets of
linear axes
LOGLOG
Both axes
logarithmic
SEMILOGX
log X
linear Y

3-D Line Plotting
» z = 0:0.1:40;
» x = cos(z);
» y = sin(z);
» plot3(x,y,z);grid on;
plot3(xdata, ydata, zdata, 'clm', ...)

3-D Surface Plotting

Example:Advanced 3-D Plotting
» B = -0.2;
» x = 0:0.1:2*pi;
» y = -pi/2:0.1:pi/2;
» [x,y] = meshgrid(x,y);
» z = exp(B*x).*sin(x).*cos(y);
» surf(x,y,z)

Next Lecture: Programming with
Matlab
Lecture notes can be found at the following link:
http://euclid.ucc.ie/framesets/fset_staffdirectory.htm
Then click on my name and then on Lecture Notes

Questions?

Matlab an Introduction_Lecture_for all.ppt

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