testfft.py running, using numpy.fft
a=
[ 0.      0.7071  1.      0.7071  0.     -0.7071 -1.     -0.7071]
b=fft(a)=
[  0.00000000e+00 +0.00000000e+00j  -3.20820844e-15 -3.99998082e+00j
   0.00000000e+00 +0.00000000e+00j   9.95839695e-17 +1.91800920e-05j
   0.00000000e+00 +0.00000000e+00j  -9.95839695e-17 -1.91800920e-05j
   0.00000000e+00 +0.00000000e+00j   3.20820844e-15 +3.99998082e+00j]
abs(b)=
[  0.00000000e+00   3.99998082e+00   0.00000000e+00   1.91800920e-05
   0.00000000e+00   1.91800920e-05   0.00000000e+00   3.99998082e+00]
fftshift(abs(b))=
[  0.00000000e+00   1.91800920e-05   0.00000000e+00   3.99998082e+00
   0.00000000e+00   3.99998082e+00   0.00000000e+00   1.91800920e-05]
c=ifft(b)=
[ 0.0000 +0.00000000e+00j  0.7071 +2.77555756e-16j  1.0000 -8.26948102e-16j
  0.7071 -2.77555756e-16j  0.0000 +0.00000000e+00j -0.7071 -2.77555756e-16j
 -1.0000 +8.26948102e-16j -0.7071 +2.77555756e-16j]
abs(c)=
[ 0.      0.7071  1.      0.7071  0.      0.7071  1.      0.7071]

dir(numpy.fft)
['fft', 'fft2', 'fftfreq', 'fftn', 'fftpack', 'fftpack_lite', 'fftshift',
 'helper', 'hfft', 'ifft', 'ifft2', 'ifftn', 'ifftshift', 'ihfft', 'info',
 'irefft', 'irefft2', 'irefftn', 'irfft', 'irfft2', 'irfftn', 'refft',
 'refft2', 'refftn', 'rfft', 'rfft2', 'rfftn', 'test']