advanced matlab (for electrical engineers)

Advanced MATLABAdvanced MATLAB(for Electrical Engineers)(for Electrical Engineers)

Instructor: Kamran ArshadEE Club, KFUPM28 March 2004

KFUPM

Advanced MATLAB Course for Electrical Engineers (Kamran Arshad)

Course Information

Course Destination Course is designed for non-professionals and

engineers who wish to expand his pervious skills in using MATLAB.

Prerequisite Preliminary skills in MATLAB are required for this

course.

Syllabus Course contents and syllabus is on the consent of

instructor.


Course Syllabus First Day

Introduction to MATLAB, Basics of Matrix Algebra, Iterative Calculations, Graphical Illustration

Second DaySpecifically deal with problems of Communication Engineering

Third DayDeal with problems of Digital Signal Processing and

Control Theory

MINOR MODIFICATIONS MAY TAKE PLACE


What is Matlab? A software environment for interactive numerical computations

Examples: Matrix computations and linear algebra Solving nonlinear equations Numerical solution of differential equations Statistics and data analysis Signal processing Modelling of dynamical systems Solving partial differential equations Simulation of engineering systems


Why should you attend this course?

Matlab used (on a daily basis) in many engineering companies


Matlab used in many courses at KFUPM

1. EE 370 Communication Engineering

2. EE 380 Control Theory

3. EE 270 Signals and Systems

Image Processing, Digital Signal Processing, and some courses at other departments of university

Why should you attend this course? (contd)


Matlab Background

Matlab = Matrix Laboratory Originally a user interface for numerical linear algebra

routines (Lapak/Linpak) Commercialized 1984 by The Mathworks Since then heavily extended (defacto-standard) Higher-level, similar to ‘C’ programming environment;

no compiler 2D (rectangular & polar) and 3D display of data,

functions, system responses


Iterative Calculations

Matlab is interactive, no need to declare variables >> 2+3*4/2 >> a=5e-3; b=1; a+b

Most elementary functions and constants are already defined

>> cos(pi) >> abs(1+i) >> sin(pi)

Last call gives answer 1.2246e-016 !?


Variable and Memory Management

Matlab uses double precision (approx. 16 significant digits)>> format long>> format compact

(see all other formats by typing help format on command prompt)

All variables are shown with>> who>> whos

Variables can be stored on file>> save filename>> clear>> load filename


The Help System

Search for appropriate function>> lookfor keyword

Rapid help with syntax and function definition >> help function

An advanced hyperlinked help system is launched by>> helpdesk

Complete manuals as PDF files


Some Useful Commands

whos shows the environment clear removes all variables from memory clear v1 ez removes variables v1 & ez from memory clf clears the current figure or graph clc clears the command window dir lists current directory delete fname deletes file named fname help matlab\general General purpose commands help matlab\ops Operators and special characters help matlab\lang Programming language

constructs help matlab\elmat Elementary matrices help matlab\elfun Elementary math functions

To abort type ctrl cTo abort type ctrl c


Vectors and Matrices

Vectors (arrays) are defined as >> v = [1, 2, 4, 5] >> w = [1; 2; 4; 5]

Matrices (2D arrays) defined similarly >> A = [1,2,3;4,-5,6;5,-6,7]


Matrix Operators

All common operators are overloaded>> v + 2

Common operators are available>> B = A’>> A*B>> A+B

Note: Matlab is case-sensitive

A and a are two different variables• Transponate conjugates complex entries; avoided by

>> B=A.’


Indexing Matrices

Indexing using parentheses>> A(2,3)

Index submatrices using vectorsof row and column indices >> A([2 3],[1 2])

Ordering of indices is important!>> B=A([3 2],[2 1])>> B=[A(3,2),A(3,1); A(2,2);A(2,1)]


Indexing Matrices(Cond)

Index complete row or column using the colon operator >> A(1,:)

Can also add limit index range>> A(1:2,:)>> A([1 2],:)

General notation for colon operator>> v=1:5>> w=1:2:5


Arithmetic Operations and Precedence

Operation Algebraic Matlab Form Scalar

addition a + b a + bsubtraction a – b a – bmultiplication a x b a * bdivision a ÷ b a / bexponentiation ab a ^ b

Precedence Operation

1 Parenthesis, innermost first.

2 Exponentiation, left to right

3 Multiplication & division, left to right

4 Addition & subtraction, left to right


Precedence - Example

% Compute the area of the trapezoid » base = 5 » height_1 = 3 » height_2 = 7 » area = 0.5*base*(height_1 + height_2) % What is the area?

» area = 0.5*base*height_1 + height_2 % What is the area?

% Where are the parentheses assumed?


Matrix Functions Many elementary matrices predefined

>> help elmat;>> I=eye(3)

Elementary functions are often overloaded>> help elmat>> sin(A)

Specialized matrix functions and operators>> As=sqrtm(A)>> As^2>> A.*A

Note: in general, ”.<operator>” is elementwise operation


Numerical Linear Algebra

Basic numerical linear algebra>> z=[1;2;3]; x=inv(A)*z>> x=A\z

Many standard functions predefined>> det(A)>> rank(A)>> eig(A)

The number of input/output arguments can often be varied>> [V,D]=eig(A)


The programming environment

Matlab can’t tell if identifier is variable or function >> z=theta;

Matlab searches for identifier in the following order1. variable in current workspace2. built-in variable3. built-in m-file4. m-file in current directory5. m-file on search path

Note: m-files can be located in current directory, or in path


Script files

Script-files contain a sequence of Matlab commands

Executed by typing its name>> factscript

Operates on variables in global workspace Variable n must exist in workspace Variable y is created (or over-written)

Use comment lines (starting with %) to document file

%FACTSCRIPT – Compute n-factorial, n!=1*2*...*n

y = prod(1:n);

%FACTSCRIPT – Compute n-factorial, n!=1*2*...*n

y = prod(1:n);

factscript.mfactscript.m


Displaying code and getting help

To list code, use type command >> type factscript

The help command displays first consecutive comment lines

>> help factscript


Functions

Functions describe subprograms Take inputs, generate outputs Have local variables (invisible in global

workspace)[output_arguments]= function_name(input_arguments)

% Comment lines <function body>

function [z]=factfun(n)% FACTFUN – Compute factorial% Z=FACTFUN(N)

z = prod(1:n);

function [z]=factfun(n)% FACTFUN – Compute factorial% Z=FACTFUN(N)

z = prod(1:n);

factfun.mfactfun.m


Scripts or function: when use what?

Functions Take inputs, generate outputs, have internal

variables Solve general problem for arbitrary parameters

Scripts Operate on global workspace Document work, design experiment or test Solve a very specific problem once

% FACTTEST – Test factfun

N=50;y=factfun(N);

% FACTTEST – Test factfun

N=50;y=factfun(N);

facttest.mfacttest.m


Flow control - selection

The if-elseif-else constructionif <logical expression>

<commands>

elseif <logical expression>

<commands>

else

<commands>

end

if height>170

disp(’tall’)

elseif height<150

disp(’small’)

else

disp(’average’)

end

if height>170

disp(’tall’)

elseif height<150

disp(’small’)

else

disp(’average’)

end


Logical expressions Relational operators (compare arrays of same sizes)

== (equal to) ~= (not equal) < (less than) <= (less than or equal to)> (greater than) >= (greater than or equal to)

Logical operators (combinations of relational operators)& (and)| (or)~ (not)

Logical functionsxorisemptyanyall

if (x>=0) & (x<=10)

disp(‘x is in range [0,10]’)

else

disp(‘x is out of range’)

end

if (x>=0) & (x<=10)

disp(‘x is in range [0,10]’)

else

disp(‘x is out of range’)

end


Flow control - repetition

Repeats a code segment a fixed number of timesfor index=<vector>

<statements>

end

The <statements> are executed repeatedly.At each iteration, the variable index is assigneda new value from <vector>.

for k=1:12 kfac=prod(1:k); disp([num2str(k),’ ‘,num2str(kfac)])end

for k=1:12 kfac=prod(1:k); disp([num2str(k),’ ‘,num2str(kfac)])end


Example – selection and repetition

function y=fact(n)% FACT – Display factorials of integers 1..nif nargin < 1 error(’No input argument assigned’)elseif n < 0 error(’Input must be non-negative’)elseif abs(n-round(n)) > eps error(’Input must be an integer’)end

for k=1:n kfac=prod(1:k);

disp([num2str(k),’ ’,num2str(kfac)])

y(k)=kfac;

end;

function y=fact(n)% FACT – Display factorials of integers 1..nif nargin < 1 error(’No input argument assigned’)elseif n < 0 error(’Input must be non-negative’)elseif abs(n-round(n)) > eps error(’Input must be an integer’)end

for k=1:n kfac=prod(1:k);

disp([num2str(k),’ ’,num2str(kfac)])

y(k)=kfac;

end;

fact.mfact.m


Flow control – conditional repetition

while-loops

<statements> are executed repeatedly as long as the <logical expression> evaluates to true

while <logical expression>

<statements>

end

k=1;

while prod(1:k)~=Inf,

k=k+1;

end

disp([‘Largest factorial in Matlab:’,num2str(k-1)]);

k=1;

while prod(1:k)~=Inf,

k=k+1;

end

disp([‘Largest factorial in Matlab:’,num2str(k-1)]);


Programming tips and tricks

Programming style has huge influence on program speed!

tic; X=-250:0.1:250;for ii=1:length(x) if x(ii)>=0, s(ii)=sqrt(x(ii)); else s(ii)=0; end;end;toc

tic; X=-250:0.1:250;for ii=1:length(x) if x(ii)>=0, s(ii)=sqrt(x(ii)); else s(ii)=0; end;end;toc

ticx=-250:0.1:250;s=sqrt(x); s(x<0)=0;toc;

ticx=-250:0.1:250;s=sqrt(x); s(x<0)=0;toc;

slow.mslow.m

fast.mfast.m

Loops are slow: Replace loops by vector operations!


MATLAB Graphics

MATLAB also provides a powerful set of graphics commands to create and manipulate graphics

Many commands can be entered from the Figure window

Advanced commands must be entered from the Command window or a script


Graphics

Visualization of vector data is available>> x=-pi:0.1:pi; y=sin(x);>> plot(x,y)>> plot(x,y,’s-’)>> xlabel(’x’); ylabel(’y=sin(x)’);

Can change plot properties in Figure menu, >> h=plot(x,y); set(h, ’LineWidth’, 4);

Many other plot functions available>> v=1:4; pie(v)


Graphics

Three-dimensional graphics>> A = zeros(32);>> A(14:16,14:16) = ones(3);>> F=abs(fft2(A));>> subplot(211),mesh(A);>> subplot(212),mesh(F);>> rotate3d on % Turn on mouse based movement

Several other plot functions available >> surfl(F)

Can change lightning and material properties>> cameramenu>> material metal


Practice Using Matlab

MatLab >>numerator = x^3 - 2*x^2 + 6.3; >>denominator = x^2 + 0.05005x – 3.14; >>f = numerator / denominator

Advice Use several statements … easier to debug … will

save you time. Use parenthesis … do not rely on precedence rules

3 2

2

2 6.3

0.05005 3.14

x x xf

x x


Practice Using Matlab2

2

0

4

2

ax bx c

b b acx

a

Calculate roots of quadratic equation .

Advice Take as input the values of a, b and c. Apply check for different type of roots, and calculate

roots. Print out the values of roots on the screen !!!


Summary

Lecture Understand the

MATLAB environment Understand various

commands of MTALAB Run small MATLAB

segments Graph data Summary

Action Items Review the lecture Record what you

learned and how this relates to your Learning Objectives for this class

Explore MATLAB. Practice commands Come prepared to ask

questions about MATLAB

advanced matlab (for electrical engineers)

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