Better compatibility with uncertainties package

Description

The uncertainties package is an extremely powerful tool for error propagation that is well integrated with NumPy.

Currently Astropy QTable objects work with uncertainties’ uarrays (essentially NumPy arrays). However, multiplying or dividing a uarray by an astropy unit returns the following error: TypeError: unsupported operand type(s) for *: 'numpy.ndarray' and 'IrreducibleUnit'

Likewise, uncertainties’ scalar type, ufloat, is not supported - multiplying a ufloat by a unit returns the following error: TypeError: unsupported operand type(s) for *: 'Variable' and 'IrreducibleUnit'

Fixing these incompatibilities and probably others I haven’t found could be a boon to Astropy.

Additional context

[mhvk]

The branch is definitely meant for astropy! Part of what was holding it up is how to deal with reductions (like mean()) and in particular when to drop the covariances (subtracting the mean of a 1000x1000 image would otherwise create a covariance matrix of 10^12 points…). But also how to sensibly deal with, say, dividing all rows in a 1000x1000 image by a 1000-length column.

Any help with it would definitely be appreciated. Though partially it is really about defining expectations and writing tests.

(Sorry this is a bit vague, I haven’t looked at it recently.)

[mhvk]

As far as I’m aware, none of those handle covariances – this is the really nice part of the uncertainties package: with c = a+b-a, your variable will not just equal b, but also have its uncertainty; in nddata and so on, it would have the uncertainty of a included since the parts are assumed to be independent.