Data structure for discretized sparse data

Is your feature request related to a problem? Please describe. We need a FData subclass capable of storing discretized functions where:

The points in which the functions are measured are NOT in a grid (specially relevant for high dimensional functions such as surfaces).
The points in which each function is measured are different, and probably a different number of points per observation.
There are typically few points measured per observation (sparse instead of dense).

This structure is necessary for efficient storage and computation with this kind of data.

Describe the solution you'd like The proposal for the implementation is to have three arrays:

A first array containing the (concatenated) input points for the observations. For example, for three functional observations $f_1$, $f_2$, $f_3$, evaluated at $f_1(1, 2) = (3, 4, 5), f_1(2, 4) = (1, 7, 3), f_2(0, 0) = (1, 0, 1), f_3(0, 1) = (2, 2, 2), f_3(3, 5) = (1, 0, 0)$, this array would contain [(1, 2), (2, 4), (0, 0), (0, 1), (3, 5)].
A second array with the corresponding values. In the previous example it would be [(3, 4, 5), (1, 7, 3), (1, 0, 1), (2, 2, 2), (1, 0, 0)].
A third array with the indexes where the points of each observation start. In this case [0, 2, 3].

This approach has a compact representation and also allows for vectorization to be applied. The indexes can be used to apply the reduceat method of NumPy ufuncs.

Describe alternatives you've considered A more high-level API should be also exposed and used when possible.

GAA-UAM / scikit-fda

Data structure for discretized sparse data #498