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Newsgroups: comp.soft-sys.matlab
Subject: Re: fractional loop
Date: Tue, 20 Mar 2012 20:55:16 +0000 (UTC)
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"Sanaa" wrote in message <jkajf8\$h28\$1@newscl01ah.mathworks.com>...
> Greetings,
> I am having a problem with the fraction iteration in Matlab. Actually, I have this code to plot the trajectory of the following map
>
> x_n = -0.5 x_(n-1)+1,    x0 = 0, n = 1,2,3,......
> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
> clear;
> x0=0;
> x(1) = x0;
> itermax = 50;
> for i = 1:itermax-1
>     %x(1)= x0;
>     x(i+1) = - 0.5*x(i)+1;
> end
> hold off;
> plot(x,'r*');
> hold on;
> plot(x,'y');
> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
> The problem????
>
> Now I want to do the same for this problem
> x_n = -0.5 x_(n-1/2) + 1,    x0 = 0
> n = 1/2, 1, 3/2, 2, ...
>
> n here is a fraction!!!!
>
> Any help will be appreciated.
- - - - - - - - -
This latter definition of x will give you the same sequence of values as the first one.  Just define

y(m) = x((m-1)/2) for m = 1, 2, 3, ...

Then y(1) = x(0) = 0 and y(m+1) = x(m/2) = -.5*x(m/2-1/2)+1 = -.5*y(m)+1 .  This shows that y, the second x, and the previous x, all have the same sequence of values.

Why is this a problem for you?  As you must be aware, matlab will only accept arrays that are indexed by positive integers, so a revised definition like this from x to y is necessary to represent such a sequence as an array in matlab.

Roger Stafford
```