1. Introduction to
Tharmarajah Thiruvaran
19-20 March 2007

2. Interactive Calculations
Matlab is interactive, no need to declare variables
>> 2+3*4/2
>> V = 50
>> V + 2
>> V
Ans = 52
>> a=5e-3; b=1; a+b
Most elementary functions and constants are already defined
>> cos(pi)
>> abs(1+i)
>> sin(pi)

3. 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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4. 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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5. Vectors and Matrices Vectors (arrays) are defined as
>> w = [1; 2; 4; 5]
Matrices (2D arrays) defined similarly
>> A = [1,2,3; 4,-5,6; 5,-6,7]

6. Matrices Generation eye - Identity matrix ones - Matrix with all
elements = 1
rand – Random matrix
zeros - Matrix with all
elements = 0
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7. Matrix Index
Given:
Always starts with 1 (not 0)
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8. Matrices Operations Given A and B: Addition Subtraction Product
Transpose
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9. The use of “.” – “Element” Operation
Given A:
Divide each element of A by 2
Multiply each element of A by 3
Square each element of A
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10. MATLAB Math & Assignment Operators
Power ^ or .^ a^b or a.^b
Multiplication * or .* a*b or a.*b
Division / or ./ a/b or a./b
or \ or .\ b\a or b.\a
NOTE: /8 = 8\56
- (unary) + (unary)
Addition a + b
Subtraction a - b
Assignment = a = b (assign b to a)
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11. Other MATLAB symbols >> prompt
. . . continue statement on next line
, separate statements and data
% start comment which ends at end of line
; (1) suppress output
(2) used as a row separator in a matrix
: specify range
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12. Matlab Desktop Launch Pad Command Window History >> radius = 50
Ans = 60
Command Window
History
We all hear about memory: RAM, bits, bytes, words, and more, but how does it all fit together?
It all starts with a desire to represent numbers electronically, manipulate them, and store or sometimes print the answers.
A computer program is simply a sequence of instructions that manipulate the contents of memory.
Most people don’t consider hard disks and CDROMs as “memory” but they are.
The key difference is the “permanence” and the “speed” of the memory. Cache and RAM require power to hold their values. Hard disks, CDROM, and Tape retain their contents even when the power is turned off.
Cache and RAM require power, but can change values very fast!
Faster memory also costs more!
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13. The Matlab Environment
Matlab is an interpreted language
Commands (Statements) are typed into the COMMAND Window and executed immediately
Variables are allocated in memory as soon as they are first used in an expression
Commands must be re-entered to be re-executed
MATLAB statements can also be put together to construct a Script which can be repeated executed as a MATLAB Program.
All variables created in the Command Window are in what is called the Base Workspace
Variables can be reassigned new values as needed
Variables can be selectively cleared from the workspace
The Workspace can be saved to a data file
File extension is .mat (ex: mydata.mat)
File is in binary and essentially unreadable by humans
.mat files can be reloaded back into the Matlab Workspace
Precision and accuracy are not the same!
A precise answer is not necessarily an accurate answer…
One should not demand more precision or accuracy than is necessary…
BE CONSISTENT!

14. Matlab Desktop – cont’d
Workspace
Command Window
Current DIrectory
[Instructors: you can spend as much or as little time talking to this picture. Have fun, be a story-teller.]
Key points:
differences in speed
temporary versus permanent
Faster memory is more expensive. (Note cost/megabyte for various storage devices.)
MATLAB variables are stored in RAM. We use LOAD/SAVE to move data from temporary storage (RAM) to permanent storage (hard disk.)
The CPU move memory from RAM to Register for actual computation, then moves the results back to RAM.
This picture highlights the differences between memory.
CPU registers are the fewest, most precious resources on the computer, and also the FASTEST!
The CPU cache either on the CPU (level1) or on the mother board (level 2) are very fast.
The RAM (physical or virtual) is where our normal variables are stored. When we create MATLAB arrays, or work with Word Documents, these data are stored in RAM.
CDROM, DVD, hard disks are “permanent storage devices.”
The input sources interact with memory at different levels, depending on the device.
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15. Matlab Programs Programs in Matlab are:
Scripts, or
Functions
Scripts: Matlab statements that are fed from a file into the Command Window and executed immediately
Functions: Program modules that are passed data (arguments) and return a result (i.e., sin(x))
These can be created in any text editor (but Matlab supplies a nice built-in editor)
We are trying to go from the “MACRO” view of memory, KB, MB, GB, etc. to the micro view.
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16. Matlab Editor Access to commands New, Load, Save, etc.
Color keyed text with auto indents
Comments
tabbed sheets for other files being edited
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17. Reserved Words…
Matlab has some special (reserved) words that you may not use…
switch
continue
else
try
catch
global
persistent
break
for
end if
while
function
return
elsif
case
otherwise
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18. Special Variable
Description
ans
default variable name for results
beep
make sound pi
mathematical constant
eps
smallest number that can be subtracted from 0 to make a negative
inf
infinity
NaN
not a number
i (or) j
imaginary number
realmin, realmax
smallest & largest positive real numbers
bitmax
largest positive integer
nargin, nargout
number of function in (or) out variables
varargin
variable number of function in arg’s
varaout
variable number of function out arg’s

19. Matlab Help
Let’s bring the memory discussion to MATLAB.
Examine the upper left pane on the MATLAB window. Several pieces of memory have been “allocated”, “named” and assigned variables.
We used an “assignment statement” (i= 10;) to assign a “value” to a “variable”.
On some computers (and in some languages) the memory must first be “allocated” before any values can be assigned.
KEY ITEMS TO DISCUSS:
A variable is piece of memory that has been given a name.
A value is the contents with the variable.
THE SCREEN SHOWS:
The screen shows the name of the variable,
The size of the variable (in elements and bytes),
The “class” - what kind of data is stored in the piece of memory
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20. Scripts (and Functions)
Matlab’s Command prompt is where you can enter commands to be executed immediately…
Just like a calculator
You can see what you’ve done but it must be re-entered at the command prompt to be recalculated
Only the results (variables) are retained in the Matlab workspace (diary on will log commands and results to a diary file; diary off disables this)
What if you want to enter different values for radius or length?
>> length=5.5;
>> radius=2.25;
>> volume=pi.*radius^2.*length
volume =
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21. Matlab Scripts Matlab scripts are the solution to this problem!
You can create a “script” that can be repeatedly executed
This is the basic Matlab “program”
Scripts are simply text files containing Matlab statements
You can use any text editor but the built-in editor indents and uses color to highlight the language syntax
Script files always have the “.m” extension, e.g., m-files
When a script (m-file) is executed, it is simply read sequentially and each line is presented to the Matlab command prompt just like it was typed by hand
Speed and repeatability are key features
Matlab control & loop statements (e.g., if, for, while…) can be executed in this way
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22. Example Script in an m-file
Use File/New/M-file to start Matlab editor
Save file with .m extension in directory in Matlab’s path
Type m-file name at prompt to execute
m file myscript is called by name
>> myscript
Enter the length of a cylinder: 8
Now enter the radius: 2.4
Volume of cylinder is:
Enter the length of a cylinder: 10
Now enter the radius: 1
Volume of cylinder is:
>>
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23. Script Workspace
When commands are executed, the results are left in the Matlab BASE workspace.
whos will list all the current variables in the workspace
Scripts can make use of variables already defined in the Base workspace
>> myscript
Enter the length of a cylinder: 10
Now enter the radius: 1
Volume of cylinder is:
>> whos
Name Size Bytes Class
length x double array
radius x double array
volume x double array
Grand total is 3 elements using 24 bytes
>>
>> density=100;
>> myscript
Enter the length of a cylinder: 10
Now enter the radius: 1
Weight of cylinder is:
>>
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24. Plot, Hold, Subplot and Figure
Example
PLOT Linear plot.
plot(X,Y) plots vector Y versus vector X
plot(Y) plots the columns of Y versus their index
plot(X,Y,S) with plot symbols and colors
See also semilogx, semilogy, title, xlabel, ylabel, axis, axes, hold, legend, subplot...
x = [ ];
y1 = (x.^2) -1;
plot(x, y1,'bo-.');
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25. Plot, Hold, Subplot and Figure
Example
XLABEL X-axis label.
xlabel('text') adds text beside the X-axis on the current axis.
YLABEL Y-axis label.
ylabel('text') adds text beside the Y-axis on the current axis.
...
xlabel('x values');
ylabel('y values');
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26. Plot, Hold, Subplot and Figure
Example
HOLD Hold current graph.
hold on holds the current plot and all axis properties so that subsequent graphing commands add to the existing graph.
hold off returns to the default mode
hold, by itself, toggles the hold state.
...
hold on;
y2 = x + 2;
plot(x, y2, 'g+:');
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27. Plot, Hold, Subplot and Figure
SUBPLOT Create axes in tiled positions.
subplot(m,n,p), or subplot(mnp), breaks the Figure window into an m-by-n matrix of small axes
Example
x = [ ];
y1 = (x.^2) -1;
% Plot y1 on the top
subplot(2,1,1);
plot(x, y1,'bo-.');
xlabel('x values');
ylabel('y values');
% Plot y2 on the bottom
subplot(2,1,2);
y2 = x + 2;
plot(x, y2, 'g+:');
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28. Plot, Hold, Subplot and Figure
FIGURE Create figure window.
FIGURE, by itself, creates a new figure window, and returns its handle.
Example
x = [ ];
y1 = (x.^2) -1;
% Plot y1 in the 1st Figure
plot(x, y1,'bo-.');
xlabel('x values');
ylabel('y values');
% Plot y2 in the 2nd Figure
figure
y2 = x + 2;
plot(x, y2, 'g+:');
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29. 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 m-files
what >> what a: List MATLAB files in a:
clear Clear all variables from work space
clear x y Clear variables x and y from work space
clc Clear the command window
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30. Some Useful MATLAB commands
what List all m-files in current directory
dir List all files in current directory
ls Same as dir
type test Display test.m in command window
delete test Delete test.m
cd a: Change directory to a:
chdir a: Same as cd
pwd Show current directory
which test Display directory path to ‘closest’ test.m
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31. 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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32. MATLAB Logical Operators
MATLAB supports three logical operators.
not ~ % highest precedence
and & % equal precedence with or
or | % equal precedence with and
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33. MATLAB Logical Functions
MATLAB also supports some logical functions.
xor (exclusive or) Ex: xor (a, b)
Where a and b are logical expressions. The xor operator evaluates to true if and only if one expression is true and the other is false. True is returned as 1, false as 0.
any (x) returns 1 if any element of x is nonzero
all (x) returns 1 if all elements of x are nonzero
isnan (x) returns 1 at each NaN in x
isinf (x) returns 1 at each infinity in x
finite (x) returns 1 at each finite value in x
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34. Matlab Selection Structures
An if - elseif - else structure in MATLAB.
Note that elseif is one word.
if expression1 % is true
% execute these commands
elseif expression2 % is true
else % the default
end
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35. MATLAB Repetition Structures
A for loop in MATLAB for x = array
for ind = 1:100
b(ind)=sin(ind/10)
end
Alternative:
x=0.1:0.1:10; b=sin(x); - Most of the loops can be avoided!!!
A while loop in MATLAB while expression
while x <= 10
% execute these commands
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36. Questions ?
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