MatLab06.pdf

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LABORATORIUM MECHATRONIKI, DIAGNOSTYKI
I BEZPIECZEŃSTWA TECHNICZNEGO
INSTYTUT POJAZDÓW
WYDZIAŁ SAMOCHODÓW I MASZYN ROBOCZYCH
POLITECHNIKA WARSZAWSKA
ul. Narbutta 84, 02-524 Warszawa
Tel. (22) 234-8117 do 8119
e-mail :msekretariat@mechatronika.net.pl
http://www.mechatronika.net.pl
Laboratorium Inżynierii Oprogramowania
Matlab Tutorial
M Files
In this tutorial we will assume that you know how to create vectors and matrices, know how
to index into them, and know about loops. For more information on those topics see one of
our tutorials on
vectors, matrices, vector operations, loops,
or
plotting.
In this tutorial we will introduce the basic operations for creating executable files. Once you
have a general routine in a matlab file, it allows you to perform more complex operations,
and it is easier to repeat these operations. For example, you might have a set of instructions
to use Euler's approximation for a differential equation (see the tutorial on
loops),
but you
want to be able to use those instructions for different equations.
As an example, a simple file to approximate the D.E. y'= 1/y using Euler's method is found.
To execute the commands in the file, the step size and the initial value must be specified.
Once done, you can easily approximate the given D.E. for a wide variey of initial conditions
and step sizes.
First, you will need to create the file. The easiest editor on our system is to just use the built
in matlab editor. It will allow you to do some very simple file manipulations. The editor is
very simple and easy to start. It is not a very advanced editor, though.
Matlab executable files (called M-files) must have the extension ".m". In this example a file
called simpleEuler.m is created. To get Matlab to execute the commands in the file simply
type in "simpleEuler". Matlab will then search the current directory for the file
"simpleEuler", read the file, and execute the commands in the file. If matlab cannot find the
file you will get an error message:
??? Undefined function or variable 'simpleEuler'.
If this is the case then either you mistyped the name of the program, the program is
misnamed, or the file is located in directory that matlab does not know about. In the later
case you have to let matlab know which directory to search. The list of directories that is
searched for files is called the "path." For more information on how to set the path there are
two articles at the mathworks site that go into more detail:
text command
and
graphical.
If you are not familiar with a more advanced editor use matlab's built in editor to create the
file. Type in the following command at the matlab prompt:
This tutorial was originally written by
Kelly Black.
Modified by
Jędrzej Mączak.
It is licensed under a
Creative Commons Attribution-ShareAlike 2.5 License
[Wpisz tekst]
>> edit simpleEuler.m
Once the editor appears on the screen either type or cut and paste the necessary
matlab
commands:
% file: simpleEuler.m
% This matlab file will find the approximation to
%
% dy/dx = 1/y
% y(0) = starty
%
%
% To run this file you will first need to specify
% the step the following:
% h
: the step size
% starty : the initial value
%
% The routine will generate three vectors. The first
% vector is x which is the grid points starting at
% x0=0 and have a step size h.
%
% The second vector is an approximation to the specified
% D.E.
%
% The third vector is the true solution to the D.E.
%
% If you haven't guessed, you cna use the percent sign
% to add comments.
%
x = [0:h:1];
y = 0*x;
y(1) = starty;
for i=2:max(size(y)),
y(i) = y(i-1) + h/y(i-1);
end
true = sqrt(2*x+1);
Once the commands are in place, save the file. Go back to your original window and start up
matlab. The file is called up by simply typing in the base name (in this case simpleEuler).
>> simpleEuler
??? Undefined function or variable h.
Error in ==> /home/black/math/mat/examples/simpleEuler.m
On line 28 ==> x = [0:h:1];
[Wpisz tekst]
If you try to call the file without first defining the variables h and starty, you will get an error
message. You must first specify all of the variables that are not defined in the file itself.
>> h = 1/16;
>> starty = 1;
>> simpleEuler
>> whos
Name
Size
h
i
starty
true
x
y
1x1
1x1
1x1
1x17
1x17
1x17
Bytes Class
8 double array
8 double array
8 double array
136 double array
136 double array
136 double array
Grand total is 54 elements using 432 bytes
>> plot(x,y,'rx',x,true)
Once the necessary variables are defined, and you type in the command
simpleEuler,
matlab
searched the current directory for a file called simpleEuler.m. Once it found the file, it read
the file and executed the commands as if you had typed them from the keyboard.
If you would like to run the program again with a different step size, you have to be careful.
The program will write over the vectors x,y, and true. If you want to save these vectors, you
must do so explicitly!
>> x0 = x;
>> y0 = y;
>> true0 = true;
>> h = h/2;
>> simpleEuler
>> whos
Name
Size
h
i
starty
true
true0
x
x0
y
y0
1x1
1x1
1x1
1x33
1x17
1x33
1x17
1x33
1x17
Bytes Class
8 double array
8 double array
8 double array
264 double array
136 double array
264 double array
136 double array
264 double array
136 double array
Grand total is 153 elements using 1224 bytes
>> plot(x0,abs(true0-y0),'gx',x,abs(true-y),'yo');
Now you have two approximations. The first is with a step size of 1/16, and it is stored in the
vectors
x0
and
y0.
The second approximation is for a step size of 1/32 and is found in the
vectors
x
and
y.
[Wpisz tekst]

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