It seems that numpy.gradient() computes the boundary values incorrectly in version 1.9.0 (but correctly in e.g. version 1.8.1)

To reproduce:
Alternative 1:

>>> x = np.array([1, 2, 4], dtype=np.float)
>>> np.gradient(x)
array([ 0.5,  1.5,  2.5])

although the resulting array should be [(2-1)/1, (4-1)/2, (4-2)/1] = [1, 1.5, 2]

Alternative 2:
Just run the first example in the documentation for numpy.gradient():

>>> x = np.array([1, 2, 4, 7, 11, 16], dtype=np.float)
>>> np.gradient(x)

The result is

array([ 0.5,  1.5,  2.5,  3.5,  4.5,  5.5])

although the documentation says that it should be

array([ 1. , 1.5, 2.5, 3.5, 4.5, 5. ])

the latter also seems right, while the former seems wrong.

(see also http://stackoverflow.com/questions/26361007/numpy-gradient-seems-to-produce-erroneous-boundary-values-using-first-differe)