[Numpy-discussion] BSD C port of FFTPACK incl. bluestein algorithm
Dag Sverre Seljebotn
Fri Nov 18 06:18:10 CST 2011
On 11/18/2011 12:58 PM, David Cournapeau wrote:
> On Fri, Nov 18, 2011 at 11:42 AM, Robert Kern<email@example.com> wrote:
>> On Fri, Nov 18, 2011 at 11:19, Dag Sverre Seljebotn
>> <firstname.lastname@example.org> wrote:
>>> I've been in touch with Martin Reinecke, author of the libpsht code for
>>> spherical harmonic transforms, about licensing issues.
>>> libpsht itself will remain under the GPL, but he is likely to release
>>> his C port of FFTPACK under BSD in the near future, as it is based on
>>> the public domain FFTPACK.
>>> I'm grateful for this change for my own purposes (allows releasing my
>>> own competing SHT library under the BSD) -- but it could perhaps be
>>> useful for NumPy or SciPy as well, depending on how complete the port
>>> is? E.g., perhaps make numpy.fft more complete (is the
>>> numpy.fft/scipy.fftpack split simply because of the Fortran dependency?).
>> It used to be the case that scipy.fftpack allowed one to build against
>> multiple different, usually faster, FFT libraries like FFTW. I think
>> we have backed away from that since the cost of maintaining the build
>> configuration for all of those different backends was so high. It's
>> worth noting that numpy.fft is already using a C translation of
>> FFTPACK. I'm not sure what the differences are between this
>> translation and Martin's.
Here's some more info forwarded from Martin:
- only FFTs are supported (no DCTs/DSTs)
- only double precision is supported (extension to single precision might
not be much work, though)
- both complex and real FFTs are supported
- real FFTs allow various storage schemes for the (half)complex frequency
domain data (classic FFTPACK scheme, FFTW or halfcomplex scheme,
uncompressed complex storage)
- precision of transforms involving large prime factors should be slightly
better than with original FFTPACK
- Bluestein's algorithm is automatically selected if considered profitable
- small accuracy self-testing code is provided.
Fairly complete interface documentation is available in Doxygen format.
I'll prepare a source package later in the afternoon and send it around.
> Having a Bluestein transformation alone would be worthwhile, as it
> would avoid the N^2 penalty for prime sizes.
> I am wondering about precision issues, though (when I tried
> implementing bluestein transforms on top of fftpack, it gave very bad
> results numerically-wise). A comparison with fftw would be good here.
Well, there's an indirect comparison: My SHT code currently uses FFTW3,
and it manages to agree with Reinecke's SHT code to a precision of
better than ~1e-12 for full SHTs. That includes several other sources of
(That's an average over several different-sized FFTs, of which half has
n=8192 and the other half all have different size, starting from 4 and
increasing up to 8192 in steps of 4 -- meaning prime factors on the
order of 1000).
I agree, a more direct comparison with FFTW would be good.
In more detail from the README:
I replaced the iterative sine and cosine calculations in radfg() and
17 by an exact calculation, which slightly improves the transform
18 real FFTs with lengths containing large prime factors.
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