Extra MATLAB Info


The following Web Sites have tutorials on MATLAB:


   www.mathworks.com
   http://spicerack.sr.unh.edu/~mathadm/tutorial/software/matlab/
   http://www.engin.umich.edu/group/ctm/



Starting MATLAB


- On a PC, double click the MATLAB icon
- On a UNIX machine, enter the command: matlab



Exiting MATLAB


- To exit MATLAB, enter the command: quit or exit



Getting Help


- The command: help xxx
  Will get help on topic xxx


- The command: lookfor xxx
  Will look for functions whose first line of the
  help text contains the keyword xxx.  


- Use the command: lookfor -all xxx 
  to search all help text lines for each function.


- The command: helpdesk
  Give more detailed information on a function etc..
  including some examples.



Funny State?


- If MATLAB goes into a funny state (e.g. infinite loop)
  try pressing ctrl-c or ctrl-break.



Capturing MATLAB Commands/Output


Sometimes a record of commands and output entered in a 
MATLAB session needs to be recorded.  To do this, enter
the command:


diary  xxx


where xxx is a filename.  Output saved is only text based
and no graphics will be included.


To shut off the diary, enter the command:


diary off



Variables


- Must start with a letter
- The first 31 characters are unique
- Case sensitive


- To see the contents of a variable, enter the variable
  name and press the enter key.


- To erase a variable from memory, enter the command: clear xxx
  where xxx is the variable to remove.


- The command: clear 
  by itself will remove all variables.



Types of variables


- MATLAB's primary type is a matrix.
- 1 x 1 matrices are interpreted as scalars
- 1 x n matrices are interpreted as row vectors
- n x 1 matrices are interpreted as column vectors


Check out the help for more information on different
data types.



The MATLAB workspace


   The workspace is the area of memory accessible
from the MATLAB command line.  Variables are stored
in the workspace.  
The command: 


          whos    


Is used to see what is currently in the workspace.



Creating Statements, Expressions and Variables 
in the Workspace


MATLAB statements are usually of the form:


variable = expression
or
expression


Normally statements are placed one on a line.
Several statements can be placed on one line
as long as each statement is separated by
a comma or semi-colon.


   Expressions are usually composed of operators, 
functions and variable names.  If just the expression 
form is used, the result is stored in a variable 
called ans.  


   MATLAB does not require any type declarations or 
dimension statements.  When it encounters a new variable
name, the variable is automatically created and the 
appropriate storage is allocated.  If a variable already
exists, it will be overwritten and the storage may be
re-adjusted.  Use the equal sign (=) to assign a value 
to a variable and create it.


Scalars


Scalars are used as in programming languages such as
C or BASIC.


Try entering the following statements
(hit Enter key after each line):


a = 5, b = 6.327e3
c = 7
d = 5.5 + 7i
whos



Notice after each line is entered and the Enter key is
pressed, the variable shows up and then its value.


MATLAB can handle integers, reals, scientific notation
and complex numbers.  If complex numbers are used,
there can be no space between the i and the number
in the imaginary part.  The letter j can also be used
instead of i for the imaginary part.


To suppress the output of a variable, put a semi-colon
at the end of each statement.  This holds for any type 
of variable.  Try it for the same example.


Row vectors


   To create a row vector, enclose the values with
square brackets [].  Each value within the brackets
must be separated by either a comma or blanks.


Try:


a = [1 2 3 4 5.5]
b = [3 4e5]
c = [1 2 3 4 5 6 7 8 9 ...
10 11 12 13 14 15]



The last line is an example of continuing a statement
if there is no more space on the current line.
Add three periods at the end of the line and
press the Enter key and continue on the next line.
This method holds for any statement entered at
the command line.



Column Vectors


   To create a column vector, enclose the values with
square brackets [].  Each value within the brackets
must be separated by semi-colon.  The semi-colon
starts a new row.
   
Try:


c = [2;4;5;6]
d = [1;1;2;2;3;3]



Matrices


   Creating a matrix is the combination of a row
and column vector.  Enclose the values in the square
brackets and use the semi-colon to start a new row
in the matrix.


Try:


ff = [1 2 3; 234 34 3; 3 4 5]
gg = [4 5 6; 2 3 4]




Saving a MATLAB workspace


   Sometimes the workspace contains several variables and
it would be a pain to re-enter all of them.  To save the
current workspace enter the command:


save xxx


This will create a file called xxx.mat.  This file is
a binary file and is machine dependent.   NOTE, if
there is an existing workspace saved and the same name
is used, the previous workspace will get overwritten.


   To load a workspace back into MATLAB, enter the 
command: 


load xxx


This will load the file called xxx.mat into the workspace.
Duplicate variables will get overwritten.  Check the help 
for more details on these two commands.



Make sure there are some variables in memory
and try:


whos
save first
clear
whos
load first
whos



Expressions


Expressions can be composed of operators, numbers, functions 
or variables.  All operations are evaluated as a matrix.
Here are some matrix operators:


+   addition
-   subtraction
*   multiplication
/   right division
'   transpose
^   power


Note that matrices have to be the correct size.
Otherwise an error message will occur.


Scalars


Scalars follow the normal mathematical rules with
the operators.


Try the following and examine the results:


a = 5 
b = 6
c = a + b
d = a + b * c
a = b*c+a^2
e = a/0
e-e
f = 2e200/e


The last three statements are an example that infinity
and Not a Number (NaN) can be handled by MATLAB .  
This could be beneficial in some cases.



Vectors and Matrices


Vectors and matrices have to follow the matrix 
operator rules.


Try the following and examine the results:


clear
a = [1;2]
b = 3
c = a + b
b * a
d = b * a
row = [1 2 3 4 5 6 7 8 9]
row = row'
col = [1 2 3 4 5]'
r = [1 2 3 4 5]
c = [6 7 8 9 0]'
r*c
c*r
b2 = [1 2 3; 4 5 6]
b3 = [3 3 3; 4 4 4]
5*b2
b2+b3
b3-b2
b2*b3'


Building Matrices


So far the elements in the matrices have been numbers.
MATLAB allows expressions and even other matrices
as elements to create larger matrices.


Try the following and examine the results:


a = 5
b = [5*a a]
c = [b;b]
d = [c c; c c]


a=[1 2; 3 4]
b=[5 6; 7 8]
[a+b a-b; 2*a 3*b; b a]



Functions


MATLAB has several functions, here are some that will
create matrices.  Check the help for other functions.


Try the following, use help to check out the functions:


clear
z = zeros(5,5)
o = ones(3,3)
ident =  eye(7)
five = 5*ones(4,4)
mix = rand(2,5)
normdist =  randn(3,4)


p = [zeros(5,6) ones(5,3)]



Accessing Elements in a Matrix


For row and column vectors a single subscript can be used.
For example:


k=3
a= [1 2 3]
b= [4 5 6]'
a(2)
a(k)
b(3)


For matrices, two subscripts can be used.  The first indicates
the row, the second the column.  A single subscript notation
can be used as well.  With the single subscript, the matrix is
considered to be a single array.  Each COLUMN of elements are
placed one after each other to represent the array.


For example:


a=[1 2 3 4; 5 6 7 8; 9 10 11 12]
a(1,2)
a(2,2)
a(3,1)
a(1)
a(5)
a(10)
a(6) = 99
a


Colon Operator (:)


This is one of MATLAB's most important operators.
Proper use of this operator will improve efficiency.
There are two forms of the colon operator, one is


start : inc : end


where start is the initial starting value, inc is an increment value
and end is the ending value.  If the inc expression is left out,
an increment of 1 is used.  Either form creates a row vector.


Try the following and examine the results:


1:3
1:0.5:4.7
55:-3:22
1:-1:3
x= 3, y=2, z=9 
x:y:z


x = 1:10
y = [1:5;6:10]



The colon operator can also be used to access parts of
a matrix.  If the colon is used by itself in a row or column
subscript, it accesses the whole row or column.


For example:


a(:,3) - the third column
a(1,:) - the first row
a(1:4,3) - the first 4 rows of the third column
a(1:3,:) - the first 3 rows


Try the following out:


a=[1:4;5:8;9:12;13:16]
a(:,3)
a(1,:)
a(2:4,2:3)
a(2,:) = [1 1 1 1]
a(:,2) = [2 2 2 2]'



Comparing Efficiency


Two ways in MATLAB to compare the efficiency of
algorithms is by count the number of floating point
operations (flops) or elapsed time.



flops(0) - Reset floating point operations to zero
flops    - Display current number of floating point operations
tic      - Starts clock (in seconds)
toc      - Stops clock


Examples:


a = rand(100,100);
b = rand(100,200);
tic, x=a*b; toc
flops(0), x=a*b; flops


Saving space


If a matrix is very large, but the majority of the matrix
is zero, then using the sparse command will save some space
and possibly computational time.  To convert a sparse matrix
to a full matrix, use the full command.


Try the following:


a= floor(10*rand(1000)/9);
b = sparse(a);
whos
tic, a*a; toc
tic, b*b; toc





Scripts


   Scripts (sometimes called M-files) in MATLAB are text 
files which contain MATLAB commands.  When a script is invoked, 
MATLAB reads in the file and executes each command in it.
If several commands need to be executed repeatedly, 
then creating a script would save time.  Any variables
created by the script remain in the workspace.


   The name of the script can be any valid filename
with a .m extension (e.g.  start.m).  To invoke a script,
enter the name of the file without the extension.


   Using a text editor, create the following script
and name it script1.m :


%  Percent sign is used as a comment
%  Identify your script
%  
%  Author: Your name
%


a = [1 2 3; 4 5 6; 7 8 9]     % create a 3x3 matrix
sum(a)
  


At the command line prompt in MATLAB, enter
the command:


script1

This should run the script.