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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
Plotting
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,
or
loops.
In this tutorial we will introduce the basic operations for creating plots. To show how the
plot
command is used, an approximation using Euler's Method is found and the results
plotted. We will approximate the solution to the D.E. y'= 1/y, y(0)=1. A step size of h=1/16 is
specified and Euler's Method is used. Once done, the true solution is specified so that we
can compare the approximation with the true value. (This example comes from the tutorial
on
loops.)
>> h = 1/16;
>> x = 0:h:1;
>> y = 0*x;
>> size(y)
ans =
1 17
>> max(size(y))
ans =
17
>> y(1) = 1;
>> for i=2:max(size(y)),
y(i) = y(i-1) + h/y(i-1);
end
>> true = sqrt(2*x+1);
Now, we have an approximation and the true solution. To compare the two, the true
solution is plotted with the approximation plotted at the grid points as a green 'o'. The
plot
command is used to generate plots in matlab. There is a wide variety of arguments that it
will accept. Here we just want one plot, so we give it the range, the domain, and the format.
This tutorial was originally written by
Kelly Black.
Modified by
Jędrzej Mączak.
It is licensed under a
Creative Commons Attribution-ShareAlike 2.5 License
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
>> plot(x,y,'go',x,true)
That's nice, but it would also be nice to plot the error:
>> plot(x,abs(true-y),'mx')
Okay, let's print everything on one plot. To do this, you have to tell matlab that you want
two plots in the picture. This is done with the
subplot
command. Matlab can treat the
window as an array of plots. Here we will have one row and two columns giving us two plots.
In plot #1 the function is plotted, while in plot #2 the error is plotted.
>> subplot(1,2,1);
>> plot(x,y,'go',x,true)
>> subplot(1,2,2);
>> plot(x,abs(true-y),'mx')
Figure 1.
The two plots from the first approximation
This tutorial was originally written by
Kelly Black.
Modified by
Jędrzej Mączak.
It is licensed under a
Creative Commons Attribution-ShareAlike 2.5 License
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
Let's start over. A new approximation is found by cutting the step size in half. But first, the
picture is completely cleared and reset using the
clf
comand. (Note that I am using new
vectors
x1
and
y1.)
>> clf
>> h = h/2;
>> x1 = 0:h:1;
>> y1 = 0*x1;
>> y1(1) = 1;
>> for i=2:max(size(y1)),
y1(i) = y1(i-1) + h/y1(i-1);
end
>> true1 = sqrt(2*x1+1);
The new approximation is plotted, but be careful! The vectors passed to
plot
have to match.
The labels are given for the axis and a title is given to each plot in the following example. The
following example was chosen to show how you can use the
subplot
command to cycle
through the plots at any time.
>> plot(x,y1,'go',x,true1)
??? Error using ==> plot
Vectors must be the same lengths.
>> plot(x1,y1,'go',x1,true1)
>> plot(x1,abs(true1-y1),'mx')
>> subplot(1,2,1);
>> plot(x,abs(true-y),'mx')
>> subplot(1,2,2);
>> plot(x1,abs(true1-y1),'mx')
>> title('Errors for h=1/32')
>> xlabel('x');
>> ylabel('|Error|');
>> subplot(1,2,1);
>> xlabel('x');
>> ylabel('|Error|');
>> title('Errors for h=1/16')
This tutorial was originally written by
Kelly Black.
Modified by
Jędrzej Mączak.
It is licensed under a
Creative Commons Attribution-ShareAlike 2.5 License
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
Figure 2.
The errors for the two approximations
Finally, if you want to print the plot, you must first print the plot to a file. To print a
postscript file of the current plot you can use the
print
command. The following example
creates a postscript file called error.ps which resides in the current directory. This new file
(error.ps) can be printed from the UNIX prompt using the lpr command.
>> print -dps error.ps
This tutorial was originally written by
Kelly Black.
Modified by
Jędrzej Mączak.
It is licensed under a
Creative Commons Attribution-ShareAlike 2.5 License

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