[SciPy-user] FFTs broken on Mac OSX

[Rob Managan]

I can't get rid of errors in the fftpack stuff in the new scipy. When 
I installed fftw2.1.5 I did a make check and it said it all was fine. 
This is on Mac OSX 10.3.9

Here is a test script based on the first failure I get in scipy.test()
The k=1 case is OK, the k=2 case gives effectively zeros and should 
be a -1*sine curve if I understand this properly.

******

from scipy.fftpack import diff,fft,ifft
from scipy.fftpack import fftfreq

import scipy.base as Numeric
from scipy.base import arange, add, array, sin, cos, pi,exp,tanh,sum

def direct_diff(x,k=1,period=None):
     print 'x',x
     fx = fft(x)
     print ' '
     print 'fx', fx
     n = len (fx)
     print 'n',n
     if period is None:
         period = 2*pi
     print 'fftfreq',fftfreq(n)
     w = fftfreq(n)*2j*pi/period*n
     print 'k, w', k,w
     if k<0:
         w = 1 / w**k
         w[0] = 0.0
     else:
         w = w**k
     print 'w', w
     if n>2000:
         w[250:n-250] = 0.0

     print "result",ifft(w*fx)
     return ifft(w*fx).real

def check_definition():
     n=16
     x = arange(n)*2*pi/n
     print ' k= 1 test '
     aaaaa = direct_diff(sin(x),1)
     print ' k= 2 test '
     aaaaa = direct_diff(sin(x),2)

check_definition()

***
OUTPUT

  k= 1 test
x [  0.00000000e+00   3.82683432e-01   7.07106781e-01   9.23879533e-01
    1.00000000e+00   9.23879533e-01   7.07106781e-01   3.82683432e-01
    1.22464680e-16  -3.82683432e-01  -7.07106781e-01  -9.23879533e-01
   -1.00000000e+00  -9.23879533e-01  -7.07106781e-01  -3.82683432e-01]

fx [  1.77975831e-16 +0.00000000e+00j  -1.35945820e-15 -8.00000000e+00j
   -3.87815369e-16 -8.43346956e-16j   5.48376387e-17 -5.45964141e-16j
    1.14423775e-17 -4.99600361e-16j   4.98926849e-16 -5.45964141e-16j
    6.32744729e-16 -1.77213142e-16j   3.15834992e-16 +0.00000000e+00j
    2.88998134e-16 +0.00000000e+00j   3.15834992e-16 -0.00000000e+00j
    6.32744729e-16 +1.77213142e-16j   4.98926849e-16 +5.45964141e-16j
    1.14423775e-17 +4.99600361e-16j   5.48376387e-17 +5.45964141e-16j
   -3.87815369e-16 +8.43346956e-16j  -1.35945820e-15 +8.00000000e+00j]
n 16
fftfreq [ 0.      0.0625  0.125   0.1875  0.25    0.3125  0.375   0.4375 -0.5
  -0.4375 -0.375  -0.3125 -0.25   -0.1875 -0.125  -0.0625]
k, w 1 [ 0.+0.j  0.+1.j  0.+2.j  0.+3.j  0.+4.j  0.+5.j  0.+6.j  0.+7.j  0.-8.j
   0.-7.j  0.-6.j  0.-5.j  0.-4.j  0.-3.j  0.-2.j  0.-1.j]
w [  0.00000000e+00+0.j   6.12323400e-17+1.j   1.22464680e-16+2.j
    1.83697020e-16+3.j   2.44929360e-16+4.j   3.06161700e-16+5.j
    3.67394040e-16+6.j   4.28626380e-16+7.j   4.89858720e-16-8.j
    4.28626380e-16-7.j   3.67394040e-16-6.j   3.06161700e-16-5.j
    2.44929360e-16-4.j   1.83697020e-16-3.j   1.22464680e-16-2.j
    6.12323400e-17-1.j]
result [  1.00000000e+00 +0.00000000e+00j   9.23879533e-01 -2.77555756e-17j
    7.07106781e-01 +0.00000000e+00j   3.82683432e-01 +5.26704453e-33j
   -9.39464148e-17 -0.00000000e+00j  -3.82683432e-01 -5.26704453e-33j
   -7.07106781e-01 -0.00000000e+00j  -9.23879533e-01 -2.77555756e-17j
   -1.00000000e+00 +0.00000000e+00j  -9.23879533e-01 +2.77555756e-17j
   -7.07106781e-01 +0.00000000e+00j  -3.82683432e-01 +5.26704453e-33j
   -9.39464148e-17 +0.00000000e+00j   3.82683432e-01 -5.26704453e-33j
    7.07106781e-01 -0.00000000e+00j   9.23879533e-01 +2.77555756e-17j]

  k= 2 test
x [  0.00000000e+00   3.82683432e-01   7.07106781e-01   9.23879533e-01
    1.00000000e+00   9.23879533e-01   7.07106781e-01   3.82683432e-01
    1.22464680e-16  -3.82683432e-01  -7.07106781e-01  -9.23879533e-01
   -1.00000000e+00  -9.23879533e-01  -7.07106781e-01  -3.82683432e-01]

fx [  1.77975831e-16 +0.00000000e+00j  -1.35945820e-15 -8.00000000e+00j
   -3.87815369e-16 -8.43346956e-16j   5.48376387e-17 -5.45964141e-16j
    1.14423775e-17 -4.99600361e-16j   4.98926849e-16 -5.45964141e-16j
    6.32744729e-16 -1.77213142e-16j   3.15834992e-16 +0.00000000e+00j
    2.88998134e-16 +0.00000000e+00j   3.15834992e-16 -0.00000000e+00j
    6.32744729e-16 +1.77213142e-16j   4.98926849e-16 +5.45964141e-16j
    1.14423775e-17 +4.99600361e-16j   5.48376387e-17 +5.45964141e-16j
   -3.87815369e-16 +8.43346956e-16j  -1.35945820e-15 +8.00000000e+00j]
n 16
fftfreq [ 0.      0.0625  0.125   0.1875  0.25    0.3125  0.375   0.4375 -0.5
  -0.4375 -0.375  -0.3125 -0.25   -0.1875 -0.125  -0.0625]
k, w 2 [ 0.+0.j  0.+1.j  0.+2.j  0.+3.j  0.+4.j  0.+5.j  0.+6.j  0.+7.j  0.-8.j
   0.-7.j  0.-6.j  0.-5.j  0.-4.j  0.-3.j  0.-2.j  0.-1.j]
w [  0. +0.00000000e+00j  -1. +1.22464680e-16j  -4. +4.89858720e-16j
   -9. +1.10218212e-15j -16. +1.95943488e-15j -25. +3.06161700e-15j
  -36. +4.40872848e-15j -49. +6.00076932e-15j -64. -7.83773951e-15j
  -49. -6.00076932e-15j -36. -4.40872848e-15j -25. -3.06161700e-15j
  -16. -1.95943488e-15j  -9. -1.10218212e-15j  -4. -4.89858720e-16j
   -1. -1.22464680e-16j]
result [ -7.09525200e-15 +0.00000000e+00j   5.93691289e-15 -1.64869810e-32j
   -1.14813636e-15 +0.00000000e+00j  -1.52577697e-15 +1.31424439e-31j
    1.47456631e-15 -0.00000000e+00j  -4.63227633e-16 -1.31424439e-31j
   -1.11807920e-15 -0.00000000e+00j   6.76061857e-16 -2.79335858e-31j
   -5.69389769e-16 +0.00000000e+00j   6.76061857e-16 +2.79335858e-31j
   -1.11807920e-15 +0.00000000e+00j  -4.63227633e-16 +1.31424439e-31j
    1.47456631e-15 +0.00000000e+00j  -1.52577697e-15 -1.31424439e-31j
   -1.14813636e-15 -0.00000000e+00j   5.93691289e-15 +1.64869810e-32j]

-- 
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
Rob Managan               email managan at llnl.gov
LLNL                      phone: 925-423-0903
P.O. Box 808, L-095       FAX:   925-422-3389
Livermore, CA  94551-0808