Prev: Changing the save button in figure windows
Next: Tracing xPC execution times
From: Greg Heath on 7 Jul 2010 21:10
On Jul 7, 4:41 am, "Jan Simon" <matlab.THIS_Y...(a)nMINUSsimon.de>
wrote:
> Dear Cesare,
>
> > I don't know if this is related, however I've noticed that for
> > x = start:step:stop;
> > d = x(2:end) - x(1:end-1);
> > e = eps(d);
> > then unique(e) is tipically (well at least for my random tests) a scalar. I was wondering whether an observation like this or some other idea could be used to set the smallest possible threshold for determining whether x could be of the form start:step:stop.
>
> The method used in INTERP1, Matlab 6.5, to determine equally spaced input:
>   eqsp = (norm(diff(x), Inf) < eps*norm(x, Inf));
> Matlab 2009a:
>   h = diff(x);
>   eqsp = (norm(diff(h), Inf) <= eps(norm(x, Inf)));
>   if any(~isfinit(x)), eqsp = 0; end
> ??? Is it correct to check the norm of DIFF(h) instead of DIFF(x) ???

Of course. A straight line is the only curve
with a constant zero 2nd derivative.

Greg
From: Jan Simon on 8 Jul 2010 03:39
Dear Greg,

> > The method used in INTERP1, Matlab 6.5, to determine equally spaced input:
> >   eqsp = (norm(diff(x), Inf) < eps*norm(x, Inf));
> > Matlab 2009a:
> >   h = diff(x);
> >   eqsp = (norm(diff(h), Inf) <= eps(norm(x, Inf)));
> > ??? Is it correct to check the norm of DIFF(h) instead of DIFF(x) ???

> Of course. A straight line is the only curve
> with a constant zero 2nd derivative.

Mathematically. With floating point arithmetics the problem is to determine the almost constant 2nd difference quotients. For this task I expected something like:
all(abs(diff(x)) < eps(x)) % *Invalid*, DIFF(x) is shorter
e.g. to catch [1:1e7:1e14], [1+1e-5, 1e7:1e7:1e14] and [1e14 + (1:0.00001:2)]. The Inf-norm is not really helpful here and the the accuracy of the 2nd difference quotient is not directly related to the accuracy of the single steps. Do I miss the important idea behind the Inf-norm here?
The problem is to distiunguish noisy steps (not equidistant) from noise caused by the limited floating point precision.

Kind regards, Jan
First  |  Prev  | 
Pages: 1 2 3 4
Prev: Changing the save button in figure windows
Next: Tracing xPC execution times