In the first example of the documentation http://docs.scipy.org/doc/numpy/reference/generated/numpy.gradient.html
x = np.array([1, 2, 4, 7, 11, 16], dtype=np.float)
np.gradient(x)
array([ 1. , 1.5, 2.5, 3.5, 4.5, 5. ])
Isn't the output should be:
array([ 1. , 1., 2., 3., 4., 5. ])
???
Numpy-gradient uses forward, backward, and central differences where appropriate.
Input:
x = np.array([1, 2, 4, 7, 11, 16], dtype=np.float)
np.gradient(x) # this uses default distance=1
Output:
array([ 1. , 1.5, 2.5, 3.5, 4.5, 5. ])
For the first item it uses forward (current -> next) difference:
- previous number: none
- current (first) number: 1
- next number: 2
(2 - 1) / 1 = 1.
For the last item it uses backward (previous -> current) difference:
- previous number: 11
- current (last) number: 16
- next number: none
(16 - 11) / 1 = 5.
And, for the items in between, the central difference is applied:
- previous number: 1
- current number: 2
- next number: 4
(4 - 1) / 2 = 1.5
- previous number: 2
- current number: 4
- next number: 7
(7 - 2) / 2 = 2.5
...
and so on:-
(11 - 4) / 2 = 3.5
(16 - 7) / 2 = 4.5
The differences are divided by the sample distance (default=1) for forward and backward differences, but twice the distance for the central difference to obtain appropriate gradients.
What you expect as output is what you will get when running np.diff, but then one element shorter:
np.diff(arr)
>>> array([ 1., 2., 3., 4., 5.])
np.gradient looks takes the i'th element and looks at the average between the differences for the (i+1)'th vs. i'th element and the (i-1)'th vs. i'th element. For the edge values it only can use one point. So value number two comes 1.5 comes from averaging (2-1) and (4-2).
