MATLAB, a product of Mathworks, is a software widely used
for exploring, refining, and understanding the numerical algorithms used in
many scientific and technological fields.
Engineers nowadays can hardly survive without the use of MATLAB as a
test platform for their codes. Useful
applications in different fields include processing of medical images, stress
and strain study in structural mechanics, earthquake data analysis in seismology,
reaction-diffusion processes in ecology and kinetic chemistry, and Markov
processes in mathematical economy.
MATLAB, an acronym for MATRIX LABORATORY, is also very efficient at
visualizing pure mathematical problems.
Complicated non-linear equations, differential and integral equations,
and evaluation of integrals can all be solved numerically, and to a good extent
symbolically.
MATLAB is mainly a programming language. However, in contrast to many programming
languages, MATLAB is extremely easy to use.
It is flexible to the user’s needs and requires almost no so-called
“programming skills.” For the expert,
MATLAB is an interpreted language but can also be translated to C or C++ code
if desired. We will not discuss this
advanced topic in this session.
This class provides you with basic manipulations and
techniques for the use of MATLAB. It is
assumed that you have some knowledge of elementary Calculus and that you know
the concept of vector (although we will give a brief review of it). This tutorial is intended for MATLAB on a
PC/Windows workstation, but if you need information about Macs or Unix, do no
hesitate to ask.
This course lasts for three hours and is structured into
three parts. There will be two breaks
of five to ten minutes each hour.
Please stop the
instructors and ask for explanations if something is not clear or is not
working properly!
MATLAB Course Outline
Part 1: Elementary Steps
1. Starting
Up and Closing Down
2. Asking
for Help
3. Command
Line Editing
4. Matrices
and Vectors
5. Basic
Operations
6. Scalar
Functions
7. Array
Operations (dot notation)
8. Matrix and Vector Functions
9. Examples
Part 2: Graphics, Output Format, and
Symbolic Computations
1. Two
Dimensional Graphics
2. Symbolic
Computations
3. Exercises
Part 3:
Programming with MATLAB
1. The
M-files
2. Loops and Conditions: For, While, If Loops
3. Exercises
Part 4: Managing
MATLAB
1. Printing and
Exporting
2. Saving and loading
MATLAB sessions
3. Submitting MATLAB
work
Part 1: Elementary Steps
1. Starting Up and Closing Down
A.
How to Start?
MATLAB can be used in both interactive and silent
modes. During this class we will be
operating in the more commonly used interactive mode.
If you are on a Windows workstation, click on
the Start
button. A pop-up menu will fly
out. Select successively Programs, Applications,
and then MATLAB 5.3.
If you are on a different PC, click on Start, then Find
(Files or Folders) and look for MATLAB through the dialog
window. Double click on the MATLAB
file.
After some loading time (usually 10 to 30
seconds), the MATLAB Command Window will appear. The command window in MATLAB is referred to as the shell.
You will see the following output on your shell:
To get
started, type one of these commands: helpwin, helpdesk, or demo.
For information on all of the MathWorks
products, type tour.
>>
This is MATLAB's greeting as the program begins.
Remark: Always check the Version number when
you are using MATLAB on a different network. This can be done by typing:
>> version
B.
How to End?
You can end a MATLAB session with the command
line:
>>
quit
Exit
will also work. Either one of these
commands will bring you back to the shell prompt.
2.
Asking for Help
A.
MATLAB Online Manual
There are several ways for getting help with
MATLAB. A good way to start is to type:
>>
helpdesk
The helpdesk command opens an HTML document, which contains the MATLAB
reference book. This is quite a large
document—don’t be overwhelmed! Useful
sections for beginners include Getting
Started and MATLAB Functions. You might want to browse them before
beginning your first session.
It’s helpful to keep this browser window open while you are working with
MATLAB, so that you can refer to it easily.
B.
Other Sources of Help
There are other ways of getting help with MATLAB
that do not make you search through the whole reference book. If you already know the name of a MATLAB
Function--for example, quit--and you want to
learn about its use, enter:
>>
help quit
You will see a description of the command quit.
During your first experiences with MATLAB you
should from time to time take a:
>>
demo
session which will show you various features of
MATLAB.
Another very useful feature is the lookfor
command. It looks for all the commands related to a given topic. Try:
>>
lookfor 'help'
It
will list all of the commands we just discussed.
3.
Command Line Editing
A.
Command lines
Once you open a MATLAB session, you start
entering command lines. A command line consists of one or more statements separated by a
semicolon. A statement is defined as "the smallest executable piece of
MATLAB code.”
We already saw some examples of command lines
above, other examples are:
>>
sqrt(2)
(which extracts the square root of 2 and returns
it as an output)
or:
>>
A = sqrt(2);
(this assigns to the variable A the
value of square root of 2).
Observations:
1.
When you enter the command lines the >> should not be
typed in. This is not part of the command line, but rather indicates its
beginning.
2.
Every command line terminates with a <return>
(or <enter> if you prefer).
3.
MATLAB has very flexible syntax, and the same command line can be entered in
different ways. We will discuss this
more later.
4.
A single command line can contain more statements. For example:
sqrt(2);
B = 3;
5.
Notice that the <return> should
be typed in only at the end of the command line.
B.
The use of the semicolon
If you tried to type in the three command lines
above you may have noticed some differences in MATLAB’s reaction to them. For
example:
>>
sqrt(2)
furnishes the output:
ans =
1.4142
whereas the command line:
>>
A = sqrt(2);
seems to have no effect. Actually it has, but we
do not see the effect because of the semicolon ";"
at the end of the command line. The
semicolon is a request for MATLAB not to show the outcome of the operation.
This is useful in programs when MATLAB performs a lot of intermediary
calculations.
The command line above is an assignment
operation. To make sure that MATLAB performed it just type in:
>>
A
and the output should read:
A =
1.4142
This would have been the output of the command
line defining A if we hadn't typed the semicolon at the
end of the command line.
C.
Recalling old command lines
During a MATLAB interactive session it is
possible to recall one of the former command lines by typing <arrow up> as many times as needed
to reach the desired line. This feature can save a lot of time, especially if a
simple command line must be repeated many times. The <arrow down> key will scroll down the history of command
lines.
Try this command to recall what you have entered
in your MATLAB session so far.
D.
Stopping MATLAB calculations
Often one needs to interrupt MATLAB while it is
computing. This is done by typing
<control>
and C
at the same time.
E.
Variables
When creating a large matrix, it is useful to
name it with a variable name.
Upper or lower case letters can be used to form
a variable name. They can contain
digits, but not in the first position. All other characters (space included)
are not allowed in variable names. The only non-alphanumeric character that is
allowed is the underscore "_"
which is used in accordance to tradition as a space since the latter is not
allowed.
Examples:
Legal choices for variable names in MATLAB are M , m , A ,
Wronsk
, _A
, WRONSK
, wRoNsK
, Wronsk_A
, w1
, w0
, w234i
, f_prime
etc. Notice that some of these,
although legal, are not really aesthetic.
The following are illegal choices for variable
names in MATLAB: 2 , #2 , a#
, Wronsk!
, Wronsk
A , w@1 , w1,2 , f'
etc.
Remark:
MATLAB distinguishes between upper and lower case letters! All the variables above are different.
To use variables, we type the variable name
followed by an equals sign, followed by what we want that variable to
represent. For instance:
>>
myvariable=3
And the computer will respond with:
myvariable =
3
There are a few commands that make managing the
variables you use easier.
>> who
will list the variables you have used:
Your variables
are:
A myvariable
While the command:
>>whos
will list the variables you have used, along
with some other pertinent information, including the size of the matrix that
the variable represents, the type of variable, and the amount of memory taken
up by that variable:
Name Size
Bytes Class
A 1x1 8 double array
myvariable 1x1 8 double array
Grand total is 2 elements using 16 bytes
* Remember, MATLAB stores ALL variables as
matrices, including single numbers (which are recorded as 1x1 matrices).
Finally, if we want to clear one or all of our
variables, we use:
>>clear
myvariable
or:
>>clear all
to clear all of our variables we have used.
If we want to see what a variable is designated
as, we type the variable name:
>>A
A =
1.4142
There is one other type of variable we will be
discussing later in the class, which is the 'symbolic variable.' Using symbolic variables, we are able to
solve equations symbolically instead of numerically.
4. Matrices and Vectors
A.
Matrices
The basic data structures that MATLAB uses are
objects known as matrices. A matrix
is a rectangular table consisting of numbers. These numbers are referred to as entries or elements of the matrix. Matrices are very handy objects widely used
in mathematical applications and are very simple conveyors of information. An
example of a matrix is:
1 3 4 5
-1 0 2 2
1
-1 -1 1
Since this matrix has three rows and four
columns, it is referred to as a 3x4 (three by four)
matrix.
The entries of a matrix have their position
identified by the number of the column and the number of the row they sit in.
For example, in the matrix above, the [3,2] entry is -1, and the [2,3] entry is
2.
To enter the above matrix in MATLAB we type:
>>
M = [1 3 4 5; -1 0 2 2; 1 -1 -1 1]
or alternatively:
>>
M = [1 3 4 5
-1 0 2 2
0 2 2 2]
B.
Building matrices
MATLAB provides a lot of different ways for
generating matrices and vectors. Some are built-in functions. Try the following
matrix constructions:
>>
Noise = rand(4)
>>
diag([1 4 5 6 -1])
>>
I = eye(3)
>>
zeros(2,4)
There are many other built-in matrix building
functions, and as you become more expert you will be able to define your
private ones.
Remark:
When you enter matrices you are not required to assign a variable name to them.
Although this can sometimes be useful (such as when you try new commands), it
is poor practice when effectively using MATLAB.
C.
Building vectors
Since vectors form a particular subclass of matrices,
all that has been said about matrices applies to vectors (with the appropriate
restrictions). For example:
>>
zeros(1,3)
will construct a row vector of length 3 whose
entries are zeros.
However, an easier way to build vectors is by
using the colon " : "
vector builder.
The colon builder has two required arguments:
the starting point and the ending point.
For example, the following command line:
>>
v = 1:9
yields:
v =
1
2 3 4 5 6
7 8 9
The colon builder can be made more sophisticated
by adding a third (optional argument) between the starting and ending point.
This argument indicates the stepsize.
For instance:
>>
w = 1:0.5:9
yields:
w =
Columns 1 through 7
1.0000
1.5000 2.0000 2.5000
3.0000 3.5000 4.0000
Columns 8 through 14
4.5000
5.0000 5.5000 6.0000
6.5000 7.0000 7.5000
Columns 15 through 17
8.0000
8.5000 9.0000
Remark:
The output of the last example looks quite different from the previous one.
There are two reasons for this:
1.
The vector v consisted solely of integer entries.
This makes MATLAB output its entries in the integer format, while the entries
of the vector w are in floating point format. The floating point format is how computers
understand what we usually call decimal numbers. Sometime these are incorrectly
called real numbers.
2.
The vector v is shorter than w, and MATLAB was able
to write it out in one single line. This type of output was not possible for
the vector w because the screen is too small, and the
row vector was thus split into several lines. However, since these several
lines still represent a single row, MATLAB indicates this fact by appending the
"Columns
n
through n+k
" label above each line.
D.
Accessing and manipulating entries
Consider the matrix:
>>
M=[1,2,3;6,3,4;5,4,3]
M =
1
2 3
6
3 4
5
4 3
and suppose that we are interested in accessing
the entry sitting in row 2 and column 3 (the value being 4). We type in:
>>
M(2,3)
ans =
4
Remark:
Notice the way we entered the matrix M, using commas and
semicolons.
Exercise:
Access the entries (1,2), (2,1) and (4,1) of the matrix M
above.
The entries of a matrix can also be modified.
For example:
>>
M(2,3)=-1
M =
1
2 3
2
3 -1
5
4 3
Exercise:
Set the entries (1,2) and (2,1) of to -12 and 56, respectively.
We can also access the entries of a matrix not
only individually but also in blocks (called submatrices). Assume for example
that we are given the matrix:
>>
A = rand(4)
then if we wanted to remove the 3x3 matrix
consisting of the first three rows of the last three columns, we would type:
>>
B = A(1:3,2:4)
To get the second row or fourth column of A
we enter, respectively:
>>
second_row = A(2,:)
>>
fourth_col = A(:,4)
This syntax can be used also to modify the
entries, for example:
>>
clear A
>>
A(1,:) = 1:7
>>
clear A
>>
A(:,1) = (1:7)'
5.
Basic Operations
Matrices, vectors and scalars can be added,
subtracted and multiplied. Scalars can be divided, and we will see that
matrices and vectors can also be divided.
A.
Scalar operations
Operations on scalars with MATLAB resemble those
performed by pocket calculators. Here are some examples to try:
>>
2+3
>>
2-3
>>
2*3
>>
3/2
>>
a = 4; b = 5; c = a*b
