[Numpy-discussion] 2-D FFT input/ouput storage

[Robert Kern]

Daniel Sheltraw wrote:
> Hello All
> 
> Now that I have Numeric loading properly at the Python command line I
> went in search of some docs on the 2-D FFT. How are the input and output
> to the forward and inverse 2-D FFTs stored? Is it simply a 2-D version
> of the 1-D storage? When I do "print FFT.inverse_fft2d.__doc__" I get no
> helpful info about storage.

The 2-D layout follows directly as a consequence of the 1-D layout and 
the definition of a 2-D FFT.

In [14]: import FFT

In [15]: def my2dfft(A):
    ....:     A = array(A, Complex)
    ....:     for i in range(A.shape[0]):
    ....:         A[i] = FFT.fft(A[i])
    ....:     for i in range(A.shape[-1]):
    ....:         A[:,i] = FFT.fft(A[:,i])
    ....:     return A
    ....:

In [16]: A = reshape(arange(16.), (4,4))

In [17]: my2dfft(A)
Out[17]:
array([[ 120. +0.j,   -8. +8.j,   -8. +0.j,   -8. -8.j],
        [ -32.+32.j,    0. +0.j,    0. +0.j,    0. +0.j],
        [ -32. +0.j,    0. +0.j,    0. +0.j,    0. +0.j],
        [ -32.-32.j,    0. +0.j,    0. +0.j,    0. +0.j]])

In [18]: FFT.fft2d(A)
Out[18]:
array([[ 120. +0.j,   -8. +8.j,   -8. +0.j,   -8. -8.j],
        [ -32.+32.j,    0. +0.j,    0. +0.j,    0. +0.j],
        [ -32. +0.j,    0. +0.j,    0. +0.j,    0. +0.j],
        [ -32.-32.j,    0. +0.j,    0. +0.j,    0. +0.j]])

-- 
Robert Kern
rkern at ucsd.edu

"In the fields of hell where the grass grows high
  Are the graves of dreams allowed to die."
   -- Richard Harter