Introduction to Matlab-1
Lecture 1 – Matlab Basics
Laboratoire Mathématiques,
Informatique et Applications
Introduction to Matlab
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What is Matlab?
 A software environment for interactive numerical
computations
 Examples:
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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
Chemical Process Control
Signal and Systems I
Control Project Course
Signals and Systems II
Signal Theory
Modeling of Dynamical Systems
Digital Signal Processing
Automatic Control, Basic Course
Adaptive Signal Processing
Automatic Control, Advanced Course
Signal Processing Project
Nonlinear Control
Communication theory
Hybrid and Embedded Control Systems
Advanced Communication Theory
<and many, many more>
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Today’s Lecture
Matlab Basics
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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
Complements
Matrix-X
Octave
Lyme
Maple
Mathematica
(free; GNU)
(free; Palm)
(symbolic)
(symbolic)
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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
Sig. Proc
C-kernel
Contr. Syst.
m-files
Simulink
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Matlab Desktop
Launch Pad
Command
Window
History
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Matlab Desktop – cont’d
Workspace
Command
Window
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 : operator
VERY 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
>>A(:,2)
ans =
7
A=
3
5
2
2
1
1
1
0
7
2
1
1
What’ll happen if you type A(:,:) ?
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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]
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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
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Indexing Matrices
Indexing using parentheses
>> A(2,3)
Index submatrices using vectors
of row and column indices
>> A([2 3],[1 2])
Rows no. 2, 3
Column no. 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)]
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Indexing Matrices
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
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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
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Manipulating Matrices
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A=
3
5
2
>> 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)
B=
1
4
2
2
1
1
1
0
7
3
9
7
1
5
2
Enter matrix B
into the Matlab
workspace
Create matrices A and B and try out the the matrix operators in this slide
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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)
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Matrix vs Element Math
Element Math
1 2  1 2  1 4 
3 4  *3 4  9 16
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Matrix Math
1 2  1 2  7 10
3 4 * 3 4  15 22
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 
 

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Circuit Example
+
10V
-
10 Ohms
3uF
0.01 H
I=V/R=10 / 10 
1
 j *  * 0.01
6
j *  * 3 *10
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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 1
unless its redefined
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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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Sample Plots
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Sin()
Cos()
0.8
0.6
0.4
y
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
1
2
3
4
5
6
7

% 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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Graphics
Three-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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Graphics
Bitmap 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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