Introduction to Matlab-1

Introduction to Matlab-1Introduction to Matlab-1Lecture 1 – Matlab Basics

Laboratoire Mathématiques, Informatique et Applications

2Introduction to MatlabIntroduction to Matlab

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What is Matlab? A software environment for interactive

numerical computations Examples:

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


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


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Matlab used in many courses

Numerical analysis

Signal and Systems I

Signals and Systems II

Modeling of Dynamical Systems

Automatic Control, Basic Course

Automatic Control, Advanced Course

Nonlinear Control

Hybrid and Embedded Control Systems

Chemical Process Control

Control Project Course

Signal Theory

Digital Signal Processing

Adaptive Signal Processing

Signal Processing Project

Communication theory

Advanced Communication Theory

<and many, many more>


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Today’s Lecture

Matlab Basics Background to Matlab Interactive calculations Vectors and matrices Graphical illustrations

Next lecture: Matlab programming


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Matlab Background

Matlab = Matrix Laboratory Originally a user interface for numerical linear algebra routines Commercialized 1984 by The Mathworks Since then heavily extended (defacto-standard)

Alternatives ComplementsMatrix-X Maple (symbolic)Octave (free; GNU) Mathematica (symbolic)Lyme (free; Palm)


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Construction

Core functionality: compiled C-routines

Most functionality is given as m-files, grouped into toolboxes

m-files contain source code, can be copied and altered m-files are platform independent (PC, Unix/Linux, MAC)

Simulation of dynamical systems is performed in Simulink

m-filesC-kernel

Sig. Proc

Simulink

Contr. Syst.


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Matlab Desktop

Command Window

Launch Pad

History


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Matlab Desktop – cont’d

Command Window

Workspace

Current DIrectory


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Matlab Help


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MATLAB Demo

Demonstrations are invaluable since they give an indication of the MATLAB capabilities.

A comprehensive set are available by typing the command >>demo in MATLAB prompt.


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Interactive 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 !?


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Variable and Memory Management

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

All variables are shown with>> who>> whos

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


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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


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Variables Don’t have to declare type Don’t even have to initialise Just assign in command window

>>

>> a=12; % variable a is assigned 12

Matlab prompt

assign operator

suppress command output

comment operator

Try the same line without the semicolon and comments


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Variables (continued …)

View variable contents by simply typing the variable name at the command prompt

>> a

a =

12

>>

>> a*2

a =

24

>>


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Workspace

The workspace is Matlab’s memory Can manipulate variables stored in the

workspace>> b=10;

>> c=a+b

c =

22

>>


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Workspace (continued …)

Display contents of workspace>> whos

Name Size Bytes Class

a 1x1 8 double array

b 1x1 8 double array

c 1x1 8 double array

Grand total is 3 elements using 24 bytes

>>Delete variable(s) from workspace

>> clear a b; % delete a and b from workspace

>> whos

>> clear all; % delete all variables from workspace

>> whos


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The : operatorVERY important operator in Matlab

Means ‘to’>> 1:10

ans =

1 2 3 4 5 6 7 8 9 10

>> 1:2:10

ans =

1 3 5 7 9 Try the following >> x=0:pi/12:2*pi;>> y=sin(x)


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The : operator and matrices

>>A(3,2:3)

ans =

1 7

>>A(:,2)

ans =

2

1

1

A =

3 2 1

5 1 0

2 1 7

What’ll happen if you type A(:,:) ?


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Vectors and MatricesVectors (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]


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Matrix OperatorsAll 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


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Indexing MatricesIndexing 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)]

Rows no. 2, 3 Column no. 1, 2


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Indexing MatricesIndex 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


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Matrix FunctionsMany 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


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Manipulating Matrices

>> A ' % transpose

>> B*A % matrix multiplication

>> B.*A % element by element multiplication

>> B/A % matrix division

>> B./A % element by element division

>> [B A] % Join matrices (horizontally)

>> [B; A] % Join matrices (vertically)

A =

3 2 1

5 1 0

2 1 7

B =

1 3 1

4 9 5

2 7 2

Create matrices A and B and try out the the matrix operators in this slide

Enter matrix B into the Matlab workspace


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Numerical Linear AlgebraBasic 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)


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Matrix vs Element Math

Element Math

16 9

4 1

4 3

2 1*

4 3

2 1

Matrix Math

22 15

10 7

4 3

2 1*

4 3

2 1


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Circuit Example

+10V

-

10 Ohms3uF

0.01 H

I=V/R=10 / 01.0**10*3**

110

6

j

j


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RLC Series .m File%Example4.m - RLC

w=linspace(1,40000,1000);

i=10./(10+(1./(j.*w.*3.*10^-6))+(j.*w.*0.01));

plot(w,abs(v));

j is intrinsically unless its redefined1


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RLC series result


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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)’);


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0 1 2 3 4 5 6 7-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1Sample Plots

y

Sin()Cos()

% print the cosine and sine u = 0:pi/20:2*pi; w = sin(u);v = cos(u);figure(1);plot(u,w,'ro-') ;hold on;plot(u,v,'gs:');xlabel('\theta');ylabel('y');legend('Sin(\theta)','Cos(\theta)');title('Sample Plots');


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Can change plot properties in Figure menu, or via ”handle”

>> h=plot(x,y); set(h, ’LineWidth’, 4);

Many other plot functions available

>> v=1:4; pie(v)


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Graphics

Three-dimensional graphics>> A = zeros(32);

>> A(14:16,14:16) = ones(3);

>> F=abs(fft2(A));

>> mesh(F)

>> rotate3d on


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Three-dimensional graphics>> A = zeros(32);

>> A(14:16,14:16) = ones(3);

>> F=abs(fft2(A));

>> mesh(F)

>> rotate3d on


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GraphicsThree-dimensional graphics>> A = zeros(32);>> A(14:16,14:16) = ones(3);>> F=abs(fft2(A));>> mesh(F)>> rotate3d on

Several other plot functions available >> surfl(F)

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


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GraphicsBitmap images can also be visualized

>> load mandrill

>> image(X); colormap(map)

>> axis image off


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MATLAB - Reference:A Partial List of On-Line Matlab Tutorials and Matlab

Books http://www.duke.edu/~hpgavin/matlab.html

Getting started with Matlab http://www.engr.iupui.edu/ee/courses/matlab/tutorial_start.htm

A quick reference to some of the key features of Matlab http://science.ntu.ac.uk/msor/ccb/matlab.html#MATLAB

Matlab tutorial, with lots of links to other tutorials http://www.glue.umd.edu/~nsw/ench250/matlab.htm

Control Tutorial for Matlab http://www.engin.umich.edu/group/ctm/home.text.html

A Practical Introduction to Matlab http://www.math.mtu.edu/~msgocken/intro/intro.html

Matlab Tutorial Information from UNH http://spicerack.sr.unh.edu/~mathadm/tutorial/software/matlab/


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Next Lecture

Programming in MATLAB

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Introduction to Matlab-1