[SciPy-dev] rfft different in numpy vs scipy

Andrew Jaffe a.h.jaffe at gmail.com
Mon Sep 11 10:06:36 CDT 2006

Steven G. Johnson wrote:
 > Andrew Jaffe wrote:
 >> numpy returns n/2+1 complex numbers (so the first and last numbers are
 >> actually real) with the frequencies equivalent to the positive part of
 >> the fftfreq, whereas scipy returns n real numbers with the frequencies
 >> as in rfftfreq (i.e., two real numbers at the same frequency, except for
 >> the highest and lowest) [All of the above for even n; but the difference
 >> between numpy and scipy remains for odd n.]
 >> I think the numpy behavior makes more sense, as it doesn't require any
 >> unpacking after the fact, at the expense of a tiny amount of wasted
 >> space. But would this in fact require scipy doing extra work from
 >> whatever the 'native' real_fft (fftw, I assume) produces?
 > As an author of FFTW, let me interject a couple of points into this
 > discussion.
 > First, if you are using FFTW, then its real-input r2c routines
 > "natively" produce output in the "unpacked" numpy format as described
 > above: an array of n/2+1 complex numbers.  Any "packed" format would
 > require some data permutations.  Other FFT implementations use a
 > variety of formats.
 > Second, the *reason* why FFTW's r2c routines produce unpacked output is
 > largely because "packed" formats do not generalize well to
 > multi-dimensional FFTs, while the "unpacked" format does.  (Packed
 > formats are *possible* for multidimensional transforms, but become
 > increasingly intricate as you add more dimensions.)  Additionally, I
 > personally find the unpacked format more convenient in most
 > applications.
 > I hope this is helpful.

OK -- so it appears that all (three) of the votes so far are in support
of the numpy convention -- a complex result.

If this is something that can be done in pure python, I'm willing to
give it a stab, but I'm probably not capable of handling any python/C
issues. Does anyone out there understand the interaction between fftpack
(C & python?), fftw (C), scipy and numpy in this context well enough to
give some advice?



Andrew Jaffe a.jaffe at imperial.ac.uk
Astrophysics Group +44 207 594-7526
Blackett Laboratory, Room 1013 FAX 7541
Imperial College, Prince Consort Road
London SW7 2AZ ENGLAND http://astro.imperial.ac.uk/~jaffe

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