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An Introduction to MATLAB

Santosh K Venu

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What is MATLAB?

• MATLAB– MATrix LABoratory: MATLAB is a program for doing numerical

computation. It was originally designed for solving linear algebra type problems using matrices. It’s name is derived from MATrix LABoratory.

– MATLAB has since been expanded and now has built-in functions for solving problems requiring data analysis, signal processing, optimization, and several other types of scientific computations. It also contains functions for 2-D and 3-D graphics and animation.

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• Stands for MATrix LABoratory• Interpreted language• Scientific programming environment• Very good tool for the manipulation of matrices• Great visualisation capabilities• Loads of built-in functions• Easy to learn and simple to use

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MATLAB Overview

• Strengths of MATLAB

• Weaknesses of MATLAB

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Strengths of MATLAB

• MATLAB is relatively easy to learn• MATLAB code is optimized to be relatively quick

when performing matrix operations• MATLAB may behave like a calculator or as a

programming language• MATLAB is interpreted, errors are easier to fix

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Weaknesses of MATLAB

• MATLAB is NOT a general purpose programming language

• MATLAB is an interpreted language (making it for the most part slower than a compiled language such as C, C++)

• MATLAB is designed for scientific computation and is not suitable for some things (such as design an interface)

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Matlab Desktop

• Command Window– type commands

• Workspace– view program variables– clear to clear

• clear all: removes all variables, globals, functions and MEX links

• clc: clear command window– double click on a variable to see it in the Array Editor

• Command History– view past commands

• Launch Pad– access help, tools, demos and documentation

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Matlab Desktop - con’t

Workspace

Current DIrectory

Command Window History

Launch Pad

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How to Resume Default Desktop

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Matlab Help

• Different ways to find information

– help

– help general, help mean, sqrt...

– helpdesk - an html document with links to further information

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Matlab Help - con’t

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Matlab Help - con’t

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Command window

• 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.

» a=5;» b=a/2

b =

2.5000

»

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MATLAB Special Variables

ans Default variable name for resultspi Value of inf InfinityNaN Not a number e.g. 0/0i and j i = j = square root of minus one: (-1) (imaginary number)

e.g. sqrt(-1) ans= 0 + 1.0000irealmin The smallest usable positive real numberrealmax The largest usable positive real number

Variables

• No need for types. i.e.,

• All variables are created with double precision unless specified and they are matrices.

• After these statements, the variables are 1x1 matrices with double precision

int a;double b;float c;

Example:>>x=5;>>x1=2;

Working with Matrices and Arrays

• Since Matlab makes extensive use of matrices, the best way for you to get started with MATLAB is to learn how to handle matrices.– Separate the elements of a row with blanks or commas.– Use a semicolon ; to indicate the end of each row.– Surround the entire list of elements with square brackets, [ ].

A = [16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15 14 1]

MATLAB displays the matrix you just entered:A =

16 3 2 135 10 11 89 6 7 124 15 14 1

• Once you have entered the matrix, it is automatically remembered in the MATLAB workspace. You can simply refer to it as A.

• Keep in mind, variable names are case-sensitive

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Manipulating Matrices

• Access elements of a matrix>>A(1,2)ans=3• Remember Matrix(row,column)• Naming convention Matrix variables start with a capital

letter while vectors or scalar variables start with a simple letter

A =16 3 2 135 10 11 89 6 7 124 15 14 1

indices of matrix element(s)

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MATLAB Relational Operators

• MATLAB supports six relational operators.

Less Than <Less Than or Equal <=Greater Than >Greater Than or Equal >=Equal To ==Not Equal To ~=

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MATLAB Logical Operators

• MATLAB supports three logical operators.

not ~ % highest precedenceand & % equal precedence with oror | % equal precedence with and

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MATLAB Matrices

• MATLAB treats all variables as matrices. For our purposes a matrix can be thought of as an array, in fact, that is how it is stored.

• Vectors are special forms of matrices and contain only one row OR one column.

• Scalars （1,1）are matrices with only one row AND one column

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MATLAB Matrices

• A matrix with only one row AND one column is a scalar. A scalar can be created in MATLAB as follows:

» a=23

a =

23

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MATLAB Matrices

• A matrix with only one row is called a row vector. A row vector can be created in MATLAB as follows (note the commas):

» rowvec = [12 , 14 , 63] or rowvec = [12 14 63]

rowvec =

12 14 63

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MATLAB Matrices

• A matrix with only one column is called a column vector. A column vector can be created in MATLAB as follows (note the semicolons):

» colvec = [13 ; 45 ; -2]

colvec =

1345-2

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MATLAB Matrices

• A matrix can be created in MATLAB as follows (note the commas AND semicolons):

» matrix = [1 , 2 , 3 ; 4 , 5 ,6 ; 7 , 8 , 9]

matrix =

1 2 34 5 67 8 9

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Extracting a Sub-Matrix

• A portion of a matrix can be extracted and stored in a smaller matrix by specifying the names of both matrices, the rows and columns. The syntax is:

sub_matrix = matrix ( r1 : r2 , c1 : c2 ) ;

where r1 and r2 specify the beginning and ending rows and c1and c2 specify the beginning and ending columns to be extracted to make the new matrix.

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MATLAB Matrices

• A column vector can be extracted from a matrix. As an example we create a matrix below:

» matrix=[1,2,3;4,5,6;7,8,9]

matrix =1 2 34 5 67 8 9

• Here we extract column 2 of the matrix and make a column vector:

» col_two=matrix( : , 2)

col_two =258

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MATLAB Matrices

• A row vector can be extracted from a matrix. As an example we create a matrix below:

» matrix=[1,2,3;4,5,6;7,8,9]

matrix =

1 2 34 5 67 8 9

• Here we extract row 2 of the matrix and make a row vector. Note that the 2:2 specifies the second row and the 1:3 specifies which columns of the row.

» rowvec=matrix(2 : 2 , 1 : 3)

rowvec =

4 5 6

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Matrices transpose

• a vector x = [1 2 5 1]

x =

1 2 5 1

• transpose y = x’ y =

1

2

5

1

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Scalar - Matrix Addition

» a=3;» b=[1, 2, 3;4, 5, 6]b =

1 2 34 5 6

» c= b+a % Add a to each element of bc =

4 5 67 8 9

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Scalar - Matrix Subtraction

» a=3;» b=[1, 2, 3;4, 5, 6]b =

1 2 34 5 6

» c = b - a %Subtract a from each element of bc =

-2 -1 01 2 3

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Scalar - Matrix Multiplication

» a=3;» b=[1, 2, 3; 4, 5, 6]b =

1 2 34 5 6

» c = a * b % Multiply each element of b by ac =

3 6 912 15 18

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Scalar - Matrix Division

» a=3;» b=[1, 2, 3; 4, 5, 6]b =

1 2 34 5 6

» c = b / a % Divide each element of b by ac =

0.3333 0.6667 1.00001.3333 1.6667 2.0000

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Math & Assignment Operators

Power ^ or .^ a^b or a.^b

Multiplication * or .* a*b or a.*b

Division / or ./ a/b or a./b

- (unary) + (unary)Addition + a + bSubtraction - a - bAssignment = a = b (assign b to a)

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Other operators

[ ] concatenation

( ) subscription

x = [ zeros(1,3) ones(1,2) ]

x =

0 0 0 1 1

x = [ 1 3 5 7 9]

x =

1 3 5 7 9

y = x(2)

y =

3

y = x(2:4)

y =

3 5 7

Introduction to Matlab Sumitha Balasuriya

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The : operator

• VERY important operator in Matlab• Means ‘to’>> 1:10ans =

1 2 3 4 5 6 7 8 9 10>> 1:2:10ans =

1 3 5 7 9

Try the following >> x=0:pi/12:2*pi;>> y=sin(x)

• Length• Max• Mean• Median• Min• Prod• Size• Var• Sum• Det• Rank• Eig• sort/flipr 37

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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')

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Multiple Graphs

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

y1=sin(t);

y2=sin(t+pi/2);

plot(t,y1,t,y2)

grid on

• Plotting Multiple Data Sets in One Graph– Multiple x-y pair arguments create multiple graphs with a

single call to plot.For example: x = 0:pi/100:2*pi;

y = sin(x);y2 = sin(x-.25);y3 = sin(x-.5);plot(x,y,x,y2,x,y3)

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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)

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Graph Functions (summary)

• plot linear plot• stem discrete plot• grid add grid lines• xlabel add X-axis label• ylabel add Y-axis label• title add graph title• subplot divide figure window • figure create new figure window• pause wait for user response

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Some Useful MATLAB commands

• who List known variables• whos List known variables plus their size• help >> help sqrt Help on using sqrt• lookfor >> lookfor sqrt

Search for keyword sqrt in on MATLABPATH.• what >> what ('directory')

List MATLAB files in directory • clear Clear all variables from work space• clear x y Clear variables x and y from work space• clc Clear the command window

Flow Control

• if • for • while • break • ….

Control Structures

• If Statement Syntax

if (Condition_1)Matlab Commands

elseif (Condition_2)Matlab Commands

elseif (Condition_3)Matlab Commands

elseMatlab Commands

end

Some Dummy Examples

if ((a>3) & (b==5))Some Matlab Commands;

end

if (a<3)Some Matlab Commands;

elseif (b~=5) Some Matlab Commands;

end

if (a<3)Some Matlab Commands;

else Some Matlab Commands;

end

Control Structures

• For loop syntax

for i=Index_ArrayMatlab Commands

end

Some Dummy Examples

for i=1:100Some Matlab Commands;

end

for j=1:3:200Some Matlab Commands;

end

for m=13:-0.2:-21Some Matlab Commands;

end

for k=[0.1 0.3 -13 12 7 -9.3]Some Matlab Commands;

end

Control Structures

• While Loop Syntax

while (condition)Matlab Commands

end

Dummy Example

while ((a>3) & (b==5))Some Matlab Commands;

end

Classification of flow

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%|-------------------------------------|This function classifies a flow |according to the values of the Reynolds (Re) and Mach (Ma). |Re <= 2000, laminar flow 2000 < Re <= 5000, transitional flowRe > 5000, turbulent flow Ma < 1, sub-sonic flow Ma = 1, sonic flow Ma > 1, super-sonic flow %|-------------------------------------|

Vector Function

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Consider now a vector function f(x) = [f1(x1,x2,x3) f2(x1,x2,x3) f3(x1,x2,x3)]T, where x =[x1,x2,x3]T (The symbol []T indicates the transpose of a matrix). Specifically,f1(x1,x2,x3) = x1 cos(x2) + x2 cos(x1) + x3f2(x1,x2,x3) = x1x2 + x2x3 + x3x1f3(x1,x2,x3) = x12 + 2x1x2x3 + x32A function to evaluate the vector function f(x) is shown below.

Summation

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%Check if m or n are matricesif length(n)>1 | length(m)>1 thenerror('sum2 - n,m must be scalar values')abortend%Calculate summation if n and m are scalarsS = 0; %initialize sumfor i = 1:n %sweep by index ifor j = 1:m %sweep by index jS = S + 1/((i+j)^2+1);endend

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Thank U