Re: [Bug-gsl] Discrete Hankel Transform (possible bug)

[Brian Gough]

At Tue, 2 Feb 2010 08:12:53 +0300,
Alexey Balakin wrote:
> I think a formula for discrete Hankel transform (DHT) contain a bug.
> The following code should give the same arrays b[i]=a[i] (at least
> with accuracy of numeric error). But it is possible only if one
> introduce additional multiplier f=j_{\nu, M} (in notation of GSL
> documentation). Note, here I use f*f because I do 2 transforms (like
> forward and backward).
> 
> So, I suggest to note this in documentation (as GSL "feature"), or
> change the formula and the code of gsl_dht_apply() function to
> additional multiplication by j_{\nu, M}.

Thanks for the email.  I agree this is a bit confusing, I've added an
extra note to the documentation about the overall scaling factor.  The
choice of factors in the transform is intentional because the test
code mentions it explicitly.  I think the convention may come from one
of the original papers.

> One more comment. I think that it will be nice if gsl_dht_apply()
> can handle the same arrays for input and output :) .

Unfortunately I don't think it's possible to do the transform
in-place.

-- 
Brian Gough

GNU Scientific Library -
http://www.gnu.org/software/gsl/