On Mon, Apr 20, 2009 at 9:49 AM, Rob Clewley <rob.clew...@gmail.com> wrote:
> On Mon, Apr 20, 2009 at 10:48 AM, David Cournapeau > <da...@ar.media.kyoto-u.ac.jp> wrote: > > Rob Clewley wrote: > >> David, > >> > >> I'm confused about your reply. I don't think Ruben was only asking why > >> you'd ever get non-zero error after the forward and inverse transform, > >> but why his implementation using lists gives zero error but using > >> arrays he gets something of order 1e-15. > >> > > > > That's more likely just an accident. Forward + inverse = id is the > > surprising thing, actually. In any numerical package, if you do > > ifft(fft(a)), you will not recover a exactly for any non trivial size. > > For example, with floating point numbers, the order in which you do > > operations matters, so: > <SNIP ARITHMETIC> > > Will give you different values for d and c, even if you "on paper", > > those are exactly the same. For those reasons, it is virtually > > impossible to have exactly the same values for two different > > implementations of the same algorithm. As long as the difference is > > small (if the reconstruction error falls in the 1e-15 range, it is > > mostly likely the case), it should not matter, > > I understand the numerical mathematics behind this very well but my > point is that his two algorithms appear to be identical (same > operations, same order), he simply uses lists in one and arrays in the > other. It's not like he used vectorization or other array-related > operations - he uses for loops in both cases. Of course I agree that > 1e-15 error should be acceptable, but that's not the point. I think > there is legitimate curiosity in wondering why there is any difference > between using the two data types in exactly the same algorithm. > Well, without an example it is hard to tell. Maybe the print formats are different precisions and the list values are just getting rounded. Chuck <snip>
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