MatLab08.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
The If Statement
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, plotting, executable files,
or
subroutines.
There are times when you want your code to make a decision. For example, if you are
approximating a differential equation, and the rate of change is discontinuous, you may
want to change the rate depending on what time step you are on.
Here we will define an executable file that contains an if statement. The file is called by
Matlab, and it constructs a second derivative finite difference matrix with boundary
conditions. There is a variable in the file called
decision.
If this variable is less than 3, the file
will find and plot the eigen values of the matrix, if it is greater than 3 the eigen values of the
inverse of the matrix are found and plotted, otherwise, the system is inverted to find an
approximation to y'=sin(x) according to the specified boundary conditions.
There are times when you want certain parts of your program to be executed only in limited
circumstances. The way to do that is to put the code within an "if" statement. The most basic
structure for an "if" statement is the following:
if
(condition statement)
(matlab commands)
end
More complicated structures are also possible including combinations like the following:
if
(condition statement)
(matlab commands)
elseif
(condition statement)
(matlab commands)
elseif
(condition statement)
(matlab commands)
.
.
.
else
(matlab commands)
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]
end
The conditions are boolean statements and the standard comparisons can be made. Valid
comparisons include "<" (less than), ">" (greater than), "<=" (less than or equal), ">="
(greater than or equal), "==" (equal - this is two equal signs with no spaces betweeen them),
and "˜=" (not equal). For example, the following code will set the variable j to be -1:
a = 2;
b = 3;
if (a<b)
j = -1;
end
Additional statements can be added for more refined decision making. The following code
sets the variable j to be 2.
a = 4;
b = 3;
if (a<b)
j = -1;
else if (a>b)
j = 2;
end
The
else
statement provides a catch all that will be executed if no other condition is met. The
following code sets the variable j to be 3.
a = 4;
b = 4;
if (a<b)
j = -1;
else if (a>b)
j = 2;
else
j=3
end
This last example demonstrates one of the bad habits that Matlab allows you to get away
with. With finite precision arithmetic two variables are rarely exactly the same. When using
C or FORTRAN you should never compare two floating numbers to see if they are the same.
Instead you should check to see if they are
close.
Matlab does not use integer arithmetic so
if you check to see if two numbers are the same it
automatically
checks to see if the
variables are
close.
If you were to use C or FORTRAN then that last example could get you
into big trouble. but Matlab does the checking for you in case the numbers are just really
close.
Matlab allows you to string together multiple boolean expressions using the standard logic
operators, "&"
(and),
¦
(or),
and
˜
(not).
For example to check to see if
a
is less than
b
and at
the same time
b
is greater than or equal to
c
you would use the following commands:
if (a < b) & (b >= c)
Matlab commands
end
[Wpisz tekst]
Example
If you are not familiar with creating executable files see our
tutorial
on the subject.
Otherwise, copy the following script into a file called
ifDemo.m.
decision = 3;
leftx = 0;
rightx = 1;
lefty = 1;
righty = 1;
N= 10;
h = (rightx-leftx)/(N-1);
x = [leftx:h:rightx]';
A = zeros(N);
for i=2:N-1,
A(i,i-1:i+1) = [1 -2 1];
end
A = A/h^2;
A(1,1) = 1;
A(N,N) = 1;
b = sin(x);
b(1) = lefty;
b(N) = righty;
if(decision<3)
% Find and plot the eigen values
[e,v] = eig(A);
e = diag(e);
plot(real(e),imag(e),'rx');
title('Eigen Values of the matrix');
elseif(decision>3)
% Find and plot the eigen values of inv(A)
[e,v] = eig(inv(A));
e = diag(e);
plot(real(e),imag(e),'rx');
title('Eigen Values of the inverse of the matrix');
else
% Solve the system
y = A\b;
linear = (lefty-righty+sin(leftx)-sin(rightx))/(leftx-rightx);
[Wpisz tekst]
constant = lefty + sin(leftx) - linear*leftx;
true = -sin(x) + linear*x + constant;
subplot(1,2,1);
plot(x,y,'go',x,true,'y');
title('True Solution and Approximation');
xlabel('x');
ylabel('y');
subplot(1,2,2);
plot(x,abs(y-true),'cx');
title('Error');
xlabel('x');
ylabel('|Error|');
end
You can execute the instructions in the file by simply typing
ifDemo
at the matlab prompt.
Try changing the value of the variable
decision
to see what actions the script will take. Also,
try changing the other variables and experiment.
The basic form of the
if-block
is demonstrated in the program above. You are not required to
have an
elseif
or
else
block, but you are required to end the
if-block
with the
endif
statement.

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