[Numpy-discussion] Re: Weird (wrong?) real fft 2d behavior

[Andrew Jaffe]

Dear Warren,
 >
 > On Wed, 25 Jan 2006, Andrew Jaffe wrote:
 >
 >> Andrew Jaffe wrote:
 >>> If I start with what I thought was an appropriate (n, n/2+1) complex
 >>> matrix which should have a real inverse fft, and then take its real 
fft,
 >>> I don't get back the original matrix.
 >>>
 >>> Note the presence of very small but nonzero reals in the final matrix,
 >
 > That's just roundoff.
 >
 >>> and the fact that the 2d and 4th rows are duplicates. This seems to 
be a
 >>>  mistake somewhere.
 >>>
 >>> Or am I just misunderstanding/misremembering something about 2d 
real ffts?
 >
 > It looks wrong to me, and I think I wrote those functions.  I get the 
same
 > results in Numeric.  I'll try to look into the problem.
 >
 >> and I should point out that
 >> 	delta_rp = N.dft.real_fft2d(delta_kp)
 >> is 'allclose' to the original delta_r (which leads me to believe that I
 >> may indeed be misunderstanding something).
 >
 > "Stable" does not neccessarily imply "correct".

Indeed! And more to the point, it's actually the case that "delta_kp" 
doesn't actually have the requisite 16 (non-small) real degrees of 
freedom -- so it can't really be right.

Andrew