[Numpy-discussion] making np.gradient support unevenly spaced data

[alebarde at gmail.com]

Hi all,

I have implemented a proposed enhancement for the np.gradient function that
allows to compute the gradient on non uniform grids. (PR:
https://github.com/numpy/numpy/pull/8446)
The proposed implementation has a behaviour/signature is similar to that of
Matlab/Octave. As argument it can take:
1. A single scalar to specify a sample distance for all dimensions.
2. N scalars to specify a constant sample distance for each dimension.
   i.e. `dx`, `dy`, `dz`, ...
3. N arrays to specify the coordinates of the values along each
   dimension of F. The length of the array must match the size of
   the corresponding dimension
4. Any combination of N scalars/arrays with the meaning of 2. and 3.

e.g., you can do the following:

    >>> f = np.array([[1, 2, 6], [3, 4, 5]], dtype=np.float)
    >>> dx = 2.
    >>> y = [1., 1.5, 3.5]
    >>> np.gradient(f, dx, y)
    [array([[ 1. ,  1. , -0.5], [ 1. ,  1. , -0.5]]),
     array([[ 2. ,  2. ,  2. ], [ 2. ,  1.7,  0.5]])]

It should not break any existing code since as of 1.12 only scalars or list
of scalars are allowed.
A possible alternative API could be pass arrays of sampling steps instead
of the coordinates.
On the one hand, this would have the advantage of having "differences" both
in the scalar case and in the array case.
On the other hand, if you are dealing with non uniformly-spaced data (e.g,
data is mapped on a grid or it is a time-series), in most cases you already
have the coordinates/timestamps. Therefore, in the case of difference as
argument, you would almost always have a call np.diff before np.gradient.

In the end, I would rather prefer the coordinates option since IMHO it is
more handy, I don't think that would be too much "surprising" and it is
what Matlab already does. Also, it could not easily lead to "silly"
mistakes since the length have to match the size of the corresponding
dimension.

What do you think?

Thanks

Alessandro

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