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

From: Alexey Balakin
Subject: Re: [Bug-gsl] Discrete Hankel Transform (possible bug)
Date: Wed, 10 Feb 2010 05:07:49 +0300

Dear Brian,

2010/2/10 Brian Gough <address@hidden>:
> 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.

It's a pity but I can write my own wrapper function (what I really do now).

All the best,
Alexey Balakin

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