Transcript Introduction to MATLAB

Introduction to MATLAB
1
SAJID GUL KHAWAJA
Introduction
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 What is MATLAB ?
•
MATLAB is a computer program that combines computation and
visualization power that makes it particularly useful tool for engineers.
•
MATLAB is an executive program, and a script can be made with a list
of MATLAB commands like other programming language.
 MATLAB Stands for MATrix LABoratory.
• The system was designed to make matrix computation particularly
easy.

The MATLAB environment allows the user to:
•
•
•
•
•
manage variables
import and export data
perform calculations
generate plots
develop and manage files for use with MATLAB.
MATrix LABoratory
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 www.mathworks.com
 Advantages of MATLAB
 Ease of use
 Platform independence
 Predefined functions
 Plotting
 Disadvantages of MATLAB
 Can be slow
 Commercial software
MATLAB Screen
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
Command Window
 type commands

Current Directory
 View folders and mfiles

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
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 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
Variables Types
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 Variable types
 Numeric
 Logical
 Character and string
 Cell and Structure
 Function handle
Variables (con’t…)
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 Variable names:

Must start with a letter




You’ll get an error if this doesn’t happen
May contain only letters, digits, and the underscore “_”
MATLAB is case sensitive, i.e. one & OnE are different variables.
MATLAB only recognizes the first 31 characters in a variable name.
 Assignment statement:


Variable = number;
Variable = expression;
 Example:
>> tutorial = 1234;
>> tutorial = 1234
tutorial =
1234
NOTE: when a semi-colon ”;” is
placed at the end of each command,
the result is not displayed.
Variables (con’t…)
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 Don’t name your variables the same as functions


min, max, sqrt, cos, sin, tan, mean, median, etc
Funny things happen when you do this
 MATLAB reserved words don’t work either


i, j, eps, nargin, end, pi, date, etc
i, j are reserved as complex numbers initially

Will work as counters in my experience so they can be redefined as
real numbers
 Give meaningful (descriptive and easy-to-remember)
names for the variables. Never define a variable with
the same name as a MATLAB function or command.
Special Variables
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Special Values
• MATLAB includes a number of predefined special values.
These values can be used at any time without initializing
them.
• These predefined values are stored in ordinary variables.
They can be overwritten or modified by a user.
• If a new value is assigned to one of these variables, then that
new value will replace the default one in all later calculations.
>> circ1 = 2 * pi * 10;
>> pi = 3;
>> circ2 = 2 * pi * 10;
Never change the values of predefined variables.
Special Variables (con’t…)
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 Special variables:





ans : default variable name for the result
pi:  = 3.1415926…………
eps:  = 2.2204e-016, smallest amount by which 2 numbers can differ.
Inf or inf : , infinity
NaN or nan: not-a-number
 Commands involving variables:






who: lists the names of defined variables
whos: lists the names and sizes of defined variables
clear: clears all varialbes, reset the default values of special variables.
clear name: clears the variable name
clc: clears the command window
clf: clears the current figure and the graph window.
Interactive Commands
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 Format of output
 Defaults to 4 decimal places
 Can change using format statement
 format long changes output to 15 decimal places
Operators (arithmetic)
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+ addition
- subtraction
* multiplication
/ division
^ power
‘ complex conjugate transpose
Operators
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• Scalar arithmetic operations
Operation
–
–
–
–
–
–
Exponentiation: ^
Multiplication: *
Right Division: /
Left Division: \
Addition:
+
Subtraction: - a
MATLAB form
ab
ab
a / b = a/b
a \ b = b/a
a+b
–b
a^b
a*b
a/b
a\b
a+b
a-b
• MATLAB ignores white space between variables
and operators
Operators (relational, logical)
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 == Equal to
 ~= Not equal to
 < Strictly smaller
 > Strictly greater
 <= Smaller than or equal to
 >= Greater than equal to
 & And operator
 | Or operator
Operators (Element by Element)
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.*
./
.^
element-by-element multiplication
element-by-element division
element-by-element power
Order of Operations
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• Parentheses
• Exponentiation
• Multiplication and division have equal precedence
• Addition and subtraction have equal precedence
• Evaluation occurs from left to right
• When in doubt, use parentheses
– MATLAB will help match parentheses for you
Vectors, Matrices and Arrays
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 Vectors
 Array Operations
 Matrices
Vectors, Matrices and Arrays
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Arrays
 The fundamental unit of data in MATLAB
 Scalars are also treated as arrays by MATLAB (1
row and 1 column).
 Row and column indices of an array start from 1.
 Arrays can be classified as vectors and
matrices.
Vectors, Matrices and Arrays
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 Vector: Array with one dimension
 Matrix: Array with more than one dimension
 Size of an array is specified by the number of rows
and the number of columns, with the number of
rows mentioned first (For example: n x m array).
Total number of elements in an array is the product
of the number of rows and the number of columns.
Arrays
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Variables and Arrays
 Array: A collection of data values organized into rows
and columns, and known by a single name.
Row 1
Row 2
Row 3
arr(3,2)
Row 4
Col 1 Col 2 Col 3 Col 4 Col 5
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1 2
a= 3 4
5 6
3x2 matrix  6 elements
b=[1 2 3 4]
1x4 array  4 elements, row vector
1
c= 3
5
3x1 array  3 elements, column vector
a(2,1)=3
Row #
Column #
b(3)=3
c(2)=3
Vectors
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 A row vector in MATLAB can be created by an explicit list, starting with a left
bracket, entering the values separated by spaces (or commas) and closing the
vector with a right bracket.
 A column vector can be created the same way, and the rows are separated by
semicolons.
 Example:
>> x = [ 0 0.25*pi 0.5*pi 0.75*pi pi ] OR x = [ 0 0.25*pi, 0.5*pi, 0.75*pi , pi]
x=
0 0.7854 1.5708 2.3562 3.1416
x is a row vector.
>> y = [ 0; 0.25*pi; 0.5*pi; 0.75*pi; pi ]
y=
0
0.7854
y is a column vector.
1.5708
2.3562
3.1416
Vectors (con’t…)
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 Vector Addressing – A vector element is addressed in MATLAB with an
integer index enclosed in parentheses.
 Example:
>> x(3)
ans =
1.5708
 3rd element of vector x
• The colon notation may be used to address a block of elements.
(start : increment : end)
start is the starting index, increment is the amount to add to each successive
index, and end is the ending index. A shortened format (start : end) may be
used if increment is 1.
• Example:
>> x(1:3)
ans = 0 0.7854 1.5708
 1st to 3rd elements of vector x
NOTE: MATLAB index starts at 1.
Vectors
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Some useful commands:
x = start:end
create row vector x starting with start,
counting by one, ending at end
x=
start:increment:end
create row vector x starting with start,
counting by increment, ending at or before
end
length(x)
returns the length of vector x
y = x’
transpose of vector x
dot (x, y)
returns the scalar dot product of the vector x
and y.
Arrays and Matrices
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Initializing with Shortcut Expressions
first: increment: last
• Colon operator: a shortcut notation used to initialize
arrays with thousands of elements
>> x = 1 : 2 : 10;
>> angles = (0.01 : 0.01 : 1) * pi;
• Transpose operator: (′) swaps the rows and columns of
an array
1 1
2 2
>> g = [1:4];
h=
3 3
>> h = [ g′ g′ ];
4 4
Long Array, Matrix
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
t =1:10
t =
1
2
3
k =2:-0.5:-1

4
5
6
7
8
k =
2
B

1.5
1
0.5
= [1:4; 5:8]
x =
1
5
2
6
3
7
4
8
0
-0.5
-1
9
10
Matrices Addressing
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 Matrix Addressing:
-- matrixname(row, column)
-- colon may be used in place of a row or column reference to select the
entire row or column.
Example:
>> f(2,3)
ans =
6
>> h(:,1)
ans =
2
1
recall:
f=
1
4
h=
2
1
2
5
3
6
4
3
6
5
Generating Vectors/Matrices from functions
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 zeros(M,N)
MxN matrix of
zeros
 ones(M,N)
MxN matrix of ones
 rand(M,N)
MxN matrix of
uniformly
distributed random
numbers on (0,1)
x = zeros(1,3)
x =
0
0
0
x = ones(1,3)
x =
1
1
1
x = rand(1,3)
x =
0.9501 0.2311 0.6068
Array Operations
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Scalar-Array Mathematics
For addition, subtraction, multiplication, and division of an
array by a scalar simply apply the operations to all elements of
the array.
 Example:
>> f = [ 1 2; 3 4]
f=
1 2
3 4
>> g = 2*f – 1
Each element in the array f is
g=
multiplied by 2, then subtracted
1 3
by 1.
5 7

Array Operations (con’t…)
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 Element-by-Element Array-Array Mathematics.
Operation
Algebraic Form
MATLAB
Addition
a+b
a+b
Subtraction
a–b
a–b
Multiplication
axb
a .* b
Division
ab
a ./ b
ab
a .^ b
Exponentiation
• Example:
>> x = [ 1 2 3 ];
>> y = [ 4 5 6 ];
>> z = x .* y
z = 4 10 18
Each element in x is multiplied by
the corresponding element in y.
Matrices Some Useful Commands
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Length(A)
returns the larger of the number of rows or columns in A.
Size(A)
for a m x n matrix A, returns the row vector [m,n] containing the number of
rows and columns in matrix.
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 = A, where  is a scalar.
Matrix Multiplication
C = A*B
Matrix Inverse
B = inv(A), A must be a square matrix in this case.
rank (A)  returns the rank of the matrix A.
Matrix Powers
B = A.^2  squares each element in the matrix
C = A * A  computes A*A, and A must be a square matrix.
Determinant
det (A), and A must be a square matrix.
A, B, C are matrices, and m, n,  are scalars.
Initializing with Keyboard Input
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• The input function displays a prompt string in the
Command Window and then waits for the user to respond.
my_val = input( ‘Enter an input value: ’ );
in1 = input( ‘Enter data: ’ );
in2 = input( ‘Enter data: ’ ,`s`);
Displaying Data in MATLAB
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The disp (Array/String) function
>> disp( 'Hello' )
Hello
>> disp(5)
5
>> disp( [ ‘Hello ' ‘World!' ] )
Hello World!
>> name = ‘World!';
>> disp( [ 'Hello ' name ] )
Hello World!
Display Windows
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 Graphic (Figure) Window
 Displays plots and graphs
 Created in response to graphics commands.
 M-file editor/debugger window
 Create and edit scripts of commands called M-files.
Plotting
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 For more information on 2-D plotting, type help graph2d
 Plotting a point:
the function plot ()
>> plot ( variablename, ‘symbol’)
Example : Complex number
>> z = 1 + 0.5j;
>> plot (z, ‘.’)
creates a graphics
window, called a Figure
window, and named by
default “Figure No. 1”
Basic Task: Plot the function sin(x) between
0≤x≤4π
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 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);
 Plot the y-array
>>plot(y)
Display Facilities
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 plot(.)
0.7
0.6
0.5
Example:
>>x=linspace(0,4*pi,100);
>>y=sin(x);
>>plot(y)
>>plot(x,y)
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
 stem(.)
Example:
>>stem(y)
>>stem(x,y)
0
10
20
30
40
50
60
70
80
90
100
Display Facilities
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 title(.)
>>title(‘This is the sinus function’)
 xlabel(.)
>>xlabel(‘x (secs)’)
 ylabel(.)
>>ylabel(‘sin(x)’)
MATLAB Graphs
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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
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t = 0:pi/100:2*pi;
y1=sin(t);
y2=sin(t+pi/2);
plot(t,y1,t,y2)
grid on
Selection Programming
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 Flow Control
 Loops
Flow Control (if/else)
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 Simple if statement:
if logical expression
commands
end
 Example: (Nested)
if d <50
count = count + 1;
disp(d);
if b>d
b=0;
end
end
 Example: (else and elseif clauses)
if temperature > 100
disp (‘Too hot – equipment malfunctioning.’)
elseif temperature > 90
disp (‘Normal operating range.’);
elseif (‘Below desired operating range.’)
else
disp (‘Too cold – turn off equipment.’)
end
Switch, Case, and Otherwise
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switch input_num
case -1
input_str = 'minus one';
case 0
input_str = 'zero';
case 1
input_str = 'plus one';
case {-10,10}
input_str = '+/- ten';
otherwise
input_str = 'other value';
end
 More efficient than
elseif statements
 Only the first
matching case is
executed
Loops
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 for loop
for variable = expression
commands
end
 while loop
while expression
commands
end
o
•Example (for loop):
for t = 1:5000
y(t) = sin (2*pi*t/10);
end
•Example (while loop):
EPS = 1;
while ( 1+EPS) >1
EPS = EPS/2;
end
EPS = 2*EPS
the break statement
break – is used to terminate the execution of the loop.
M-Files
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So far, we have discussed the execution of commands in the
command window. But a more practical way is to create a M-file.
 The M-file is a text file that consists a group of
MATLAB commands.
 MATLAB can open and execute the commands
exactly as if they were entered at the MATLAB
command window.
 To run the M-files, just type the file name in the
command window. (make sure the current working
directory is set correctly)
All MATLAB commands are M-files.
User-Defined Function
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 Add the following command in the beginning of your m-file:
function [output variables] = function_name (input variables);
NOTE: the function_name should
be the same as your file name to
avoid confusion.
 calling your function:
-- a user-defined function is called by the name of the m-file, not
the name given in the function definition.
-- type in the m-file name like other pre-defined commands.
 Comments:
-- The first few lines should be comments, as they will be
displayed if help is requested for the function name. the first
comment line is reference by the lookfor command.
Built-in MATLAB Functions
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result = function_name( input );
–
–
–
–
–
–
–
–
–
abs, sign
log, log10, log2
exp
sqrt
sin, cos, tan
asin, acos, atan
max, min
round, floor, ceil, fix
mod, rem
• help elfun  help for elementary math functions
Getting Help
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 For help type one of following commands in
the command window:
help – lists all the help topic
 help topic – provides help for the specified topic
 help command – provides help for the specified command


help help – provides information on use of the help command
helpwin – opens a separate help window for navigation
 lookfor keyword – Search all M-files for keyword
