Matlab Basics MEE

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MMATLABATLAB BBASICSASICS

Sanjay R JoshiSanjay R Joshi

[email protected]@yahoo.com20-Jan-200720-Jan-2007

MATLAB for ELECTRICAL ENGINEERINGMATLAB for ELECTRICAL ENGINEERING

EE DEPTEE DEPTIIT BOMBAYIIT BOMBAY

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• MATLAB - developed by Math Works Inc.

•http://www.mathworks.com

•MATLAB - acronym for MATrix LABoratory

•Matrices and arrays - the heart of MATLAB

•Offers programming features - similar to other languages

•Offers GUI tools

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Why MATLAB is Why MATLAB is popular ?popular ?

1.1. No need to declare dimensions of a No need to declare dimensions of a matrix as in FORTRAN or C.matrix as in FORTRAN or C.

2.2. Very powerful and easy-to-learn Very powerful and easy-to-learn graphics capabilities.graphics capabilities.

3.3. MATLAB can be integrated with MATLAB can be integrated with FORTRAN and C/C++ programs.FORTRAN and C/C++ programs.

4.4. MATLAB has many MATLAB has many toolboxestoolboxes ((collections of MATLAB functionscollections of MATLAB functions) ) applied to specific topics like control applied to specific topics like control system, symbolic manipulation, FFT etc.system, symbolic manipulation, FFT etc.

5.5. MATLAB has proved to be extremely MATLAB has proved to be extremely efficient and hence very fast for solving efficient and hence very fast for solving some problems.some problems.

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•MATLAB is an interactive system for doing numerical computations

•Powerful operations can be performed using just one or two commands.

• There are more than 1000 functions in the basic MATLAB product alone.

•Modeling, simulation, Data analysis, exploration, and visualization and many more.

•Application development, including Graphical User Interface building.

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Easy to use

Platform independence

Predefined functions

Device –independent plotting

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MATLAB WINDOWS

COMMAND WINDOWCOMMAND WINDOW

To give MATLAB commands at the To give MATLAB commands at the promptprompt

EDIT/DEBUG WINDOWEDIT/DEBUG WINDOW

To create , edit and debug the To create , edit and debug the program. program.

Type edit at the command prompt.Type edit at the command prompt.

FIGURE WINDOWFIGURE WINDOW

To visualize graphs and plotsTo visualize graphs and plots

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• Provides a variety of graphic output displays:

• linear

• log-log

• semilog

• polar

• bar chart, and

•contour plots

• 2-D and 3-D views

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• Provides extensive numerical resources

• Over 200 reliable, accurate mathematical subprograms

• The subprograms provide solutions to broad range of mathematical problems including: matrix algebra ( Linear Algebra )

• complex arithmetic

• differential equations

• nonlinear systems, and

• many special functions

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• Available in all operating systems:

•DOS

•Windows9.x/NT

•Unix

•Macintosh

•Same syntax for all platforms

• Open system environment - access to source code

•Allows - to mix MATLAB with FORTRAN or C

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Simple MathSimple Math» 2+2.5+106

ans =

110.5000

» 4*25 + 2^3

ans =

108

» One can use it as a calculator/scratch pad

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MATLAB VariablesMATLAB Variables» a = 2

a =

2

»b = 3

b=

3

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MATLAB VariablesMATLAB Variables» c = 1000;» d = 0.001;» e = a*b*c/d

e =

6000000

»

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MATLAB VariablesMATLAB Variables

MATLAB variable are automatically MATLAB variable are automatically created created when they are initialized.when they are initialized.There are three way to initializing There are three way to initializing variable in MATLAB.variable in MATLAB. Assign data to the variable in an assignment Assign data to the variable in an assignment statement. statement.

Input data into the variable from the Input data into the variable from the keyboard.keyboard.

Read data from file.Read data from file.

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MATLAB WorkspaceMATLAB WorkspaceTo recall the variable

» a

a =

2

»

Use arrow keys for scrolling through previous commands

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MATLAB WorkspaceMATLAB WorkspaceList of variables in the workspace

» who

Your variables are:

a b c d e »

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Variable Naming RulesVariable Naming Rules•Variable names are case sensitive. For example NRe and nRe are different MATLAB variables

•Variable name can contain upto 31 characters. •Start with a letter, followed by letters, numbers or underscores.

•For example: SRe_2_electrical_power2by3

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Special VariablesSpecial Variables

ans Default variable name used f or resuts

pi Value of

inf Stands f or infi nity (e.g., 1/ 0)

NaN Stands f or Not-a-Number (e.g., 0/ 0)

i, j i = j = -1

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To Clear a VariableTo Clear a Variable» who

Your variables are:

a b c d e » clear a;» who

Your variables are:

b c d e

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To clear all variablesTo clear all variables» who

Your variables are:

b c d e

» clear» who»

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Complex NumbersComplex Numbers» i

ans =

0 + 1.0000i

» c1 = 2+3i

c1 =

2.0000 + 3.0000i»

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Mathematical Mathematical FunctionsFunctions

» x=sqrt(2)/2

x =

0.7071

» y=sin(x)

y =

0.6496»

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Built-in FunctionsTrigonometric f unctions

sin, cos, tan, sin, acos, atan, sinh, cosh, tanh, asinh, acosh, atanh, csc, sec, cot, acsc, …

Exponential f unctions

exp, log, log10, sqrt

Complex functions

abs, angle, imag, real, conj

Rounding and Remainder f unctions

floor, ceil, round, mod, rem, sign

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Saving & Loading Data

>> A=[2 0; 0 5];>> [M l]=eig(A);>> save data1 M l; clear all;>> who>> load data1>> who

Your variables are:

M l

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Array Operations» x = [1 2 3 4 5 6 7 8 9 10]

x =

1 2 3 4 5 6 7 8 9 10» a = 1:2:10 Note : operator

a =

1 3 5 7 9

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Array Operations» y = sin(x)

y =

Columns 1 through 7

0.8415 0.9093 0.1411 -0.7568 -0.9589 -0.2794 0.6570

Columns 8 through 10

0.9894 0.4121 -0.5440

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Array Addressing» y(3)

ans =

0.1411

» y(1:5)

ans =

0.8415 0.9093 0.1411 -0.7568 -0.9589

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Array Orientation» z = [1; 2; 3; 4]

z =

1 2 3 4 » z'

ans =

1 2 3 4

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Array Manipulation» A = [1 2; 3 4; 5 6]

A =

1 2 3 4 5 6

» B = [1 2 3; 4 5 6];» A+B??? Error using ==> +Matrix dimensions must agree.

»

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Array Manipulation» A*B

ans =

9 12 15 19 26 33 29 40 51

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Significance of .» clear» A = [1 2; 3 4];» B = [1 1; 2 2];» A.*B

ans =

1 2 6 8

»

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Significance of .» A./B

ans =

1.0000 2.0000 1.5000 2.0000

» A/BWarning: Matrix is singular to working precision.

ans =

Inf Inf Inf Inf»

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Matrix Operations» [A B]

ans =

1 2 1 1 3 4 2 2

» ans-1

ans =

0 1 0 0 2 3 1 1

»

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>> D = A +B>> D = A +B

D =D =

2 32 3

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Matrix Matrix OperationsOperations

>> G= A - B>> G= A - B

G =G =

0 10 1

1 21 2

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Matrix Operations» C = [A B]

C =

1 2 1 1 3 4 2 2

» C(1,:)

ans =

1 2 1 1

»

» C(:,2)

ans =

2 4

» C(:,2:end)

ans =

2 1 1 4 2 2

»

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Matrix Functions» size(C)

ans =

2 4

» determ(A) ans = -2 »

» A

A =

1 2 3 4

» inv(A)

ans =

-2.0000 1.0000 1.5000 -0.5000

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Matrix FunctionsSome functions: determ, inv, diag, triu, tril, rank, eig, size

» eig(A)

ans =

-0.3723 5.3723

Show eigshow

» [a b] = eig(A)

a =

-0.8246 -0.4160 0.5658 -0.9094

b =

-0.3723 0 0 5.3723

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» eye(2)

ans =

1 0 0 1

» eye(2,3)

ans =

1 0 0 0 1 0

»

Other such arrays:

ones(n), ones(r, c)

zeros(n), zeros(r, c)

rand(n), rand(r,c)

Standard ArraysStandard Arrays

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ones(3)

ans =

1 1 1 1 1 1 1 1 1

>> ones(3,2)

ans =

1 1 1 1 1 1

Standard ArraysStandard Arrayszeros(2)

ans =

0 0 0 0>> zeros (3,2)

ans =

0 0 0 0 0 0

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Plots» x = 1:2:50;» y = x.^2;» plot(x,y)»

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Plots» plot(x,y,'*-')» xlabel('Values of x')» ylabel('y')»

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Relational Operators

<>

<=>===~=

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Control Flow Statementsfor n=1:10…end

while expression…end

if expression…else...end

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MATLAB FilesMATLAB Files

M-files Script Files Function Files

MAT-files

MEX-files

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M FilesM Files

Useful for extending the MATLAB language for your application

Useful for automating a series of steps you need to perform many times

Internal variables are local to the function by default

Operate on data in the workspace

Can accept input arguments and return output arguments

Do not accept input arguments or return output arguments

Function M-FilesScript M-Files

M-files are ordinary ASCII (text) files having extension .m containing MATLAB commands

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SCRIPTSSCRIPTSVariables created by scripts Variables created by scripts remains in workspace even after remains in workspace even after the execution of it.the execution of it.

Create a script file and edit it in Create a script file and edit it in MATLAB Editor called M-File MATLAB Editor called M-File EditorEditor

e.g e.g

% This is a sample Script M-file% This is a sample Script M-file

A = [ 1 2 3; 4 7 1; 9 5 0];A = [ 1 2 3; 4 7 1; 9 5 0];

[x,v] = eig(A) [x,v] = eig(A)

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Note script here

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Using Script M-files

» what

M-files in the current directory C:\WINDOWS.000\Desktop\MEE\ASSIGN-1

solu_AC_Series_Ckt

» solu_AC_Series_Ckt

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Using Script M-files» Supply frequency in Hertz = 50Supply Volatage in Volts =230Resistance in Ohms = 10Inductance in Henry = 0.5Capacitance in Micro Farad = 1000

» save data1 P Q V I pf

This is one of the saving option of MATLAB

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FUNCTIONSFUNCTIONS

They operate on variables of their own work space.

This is not the same , we access at the MATLAB command prompt.

Create a M-File , Save it and then call it.

You may call it to execute at command prompt or within any other function also.

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FUNCTION M-FilesFUNCTION M-Files

Function file and Script file can call each other.Multiple functions can appear in a single function M file. [Sub function] All the sub functions follow the rules of M-files. Try to use vectorized commands. Execute the program timings.m

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General structure of a Function M-file

function [o1,o2,...] = fun_name(i1,i2...) % This is the H1 line or first help text line % The rest of the help text... % ...% ... function body here (All MATLAB code doing the actual calculations come here) % Comments, if any.

Keyword

Output argument(s) Function name

Input argument(s)

Function definition line

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Function M-filesfunction [maxpower,rs,rl] = maxpow(V,rs)% [Max Power , Rs , RL ] = maxpow(Voltage,Rs)clc;maxpower=0.0; range = rs/10;Rl= (rs- range/2):range/6:(rs + range/2);for i = 1:length(Rl) I(i)=V/(rs + Rl(i)); power(i)= I(i)^2*Rl(i); if power(i) > maxpower maxpower = power(i); rl=Rl(i); endend

maxpow.m

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MAT FilesMAT FilesMAT-files are the data file format files that MATLAB uses for saving data and workspace to disk. They are machine dependent binary files. However, they can be ported to different architectures as MATLAB can sniff out the architecture information from the MAT-files. Thus a sort of machine independence is achieved with MAT-files. Whenever we want to save MATLAB Workspace or only some variables in the Workspace, we can do so by issuing the command `save filename' at the MATLAB prompt. If we leave out the filename, by default it is saved to `matlab.mat'.

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MEX FilesMEX Files Possible to call FORTRAN and C Possible to call FORTRAN and C

subroutines from inside MATLAB as subroutines from inside MATLAB as if they are built-in functions.if they are built-in functions.

The way to do it is through what are The way to do it is through what are

called called MMATLAB ATLAB EXEXecutable files ecutable files (MEX-files).(MEX-files).

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Why MEX-files?Why MEX-files? There is no need to rewrite long There is no need to rewrite long

preexisting C or FORTRAN code into preexisting C or FORTRAN code into M-filesM-files

Serious constraints like for-loops, Serious constraints like for-loops, which tend to slow down MATLAB which tend to slow down MATLAB can be made to run faster by can be made to run faster by recoding into C or FORTRAN and recoding into C or FORTRAN and running as MEX-filesrunning as MEX-files

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Calling a Function» [mp rs rl] = maxpow(200,5)

mp =

2000

rs = 5rl = 5

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Calling a FunctionYou may call your function by less number of output arguments

[mp r ] = maxpow(200,5)

mp = 2000r = 5Here r is our second argument variable

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Polynomials

Representing Polynomials:x4 - 12x3 + 25x + 116

» P = [1 -12 0 25 116];» roots(P)

ans =

11.7473 2.7028 -1.2251 + 1.4672i -1.2251 - 1.4672i

» r = ans;

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Polynomials from the Roots

» PP = poly(r)

PP =

1.0000 -12.0000 -0.0000 25.0000 116.0000

»

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Polynomial Multiplication

a = x3 + 2x2 + 3x + 4b = 4x2 + 9x + 16

» a = [1 2 3 4];» b = [4 9 16];» c = conv(a,b)

c =

4 17 46 75 84 64

»

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Recommended books• Mastering MATLAB

Duane Hanselman, Bruce LittlefieldThe MATLAB Curriculum Series, Prentice Hall Inc.

• MATLAB Programming for EngineersStephan J. ChapanThomson Publication

• Introduction to Matlab 6.0 2nd edition • Delores M. Etter• David C.Kuncicky• Doug Hull Pearson Education

•http://www.mathworks.com

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LET’S STARTLET’S START

MMATLABATLABinging

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THANK YOU THANK YOU

VERY MUCHVERY MUCH