code: #!/usr/bin/env python
  # Copied from fftpack.helper by Pearu Peterson, October 2005
  """ Test functions for fftpack.helper module
  """
  
  from numpy.testing import *
  from numpy.fft import fftshift,ifftshift,fftfreq
  
  from numpy import pi
  
  def random(size):
      return rand(*size)
  
  class TestFFTShift(TestCase):
      def test_definition(self):
          x = [0,1,2,3,4,-4,-3,-2,-1]
          y = [-4,-3,-2,-1,0,1,2,3,4]
          assert_array_almost_equal(fftshift(x),y)
          assert_array_almost_equal(ifftshift(y),x)
          x = [0,1,2,3,4,-5,-4,-3,-2,-1]
          y = [-5,-4,-3,-2,-1,0,1,2,3,4]
          assert_array_almost_equal(fftshift(x),y)
          assert_array_almost_equal(ifftshift(y),x)
  
      def test_inverse(self):
          for n in [1,4,9,100,211]:
              x = random((n,))
              assert_array_almost_equal(ifftshift(fftshift(x)),x)
  
  
  class TestFFTFreq(TestCase):
      def test_definition(self):
          x = [0,1,2,3,4,-4,-3,-2,-1]
          assert_array_almost_equal(9*fftfreq(9),x)
          assert_array_almost_equal(9*pi*fftfreq(9,pi),x)
          x = [0,1,2,3,4,-5,-4,-3,-2,-1]
          assert_array_almost_equal(10*fftfreq(10),x)
          assert_array_almost_equal(10*pi*fftfreq(10,pi),x)
  
  
  if __name__ == "__main__":
      run_module_suite()
  
apis: numpy.fft.fftshift numpy.fft.fftfreq numpy.fft.ifftshift