NumPy should warn (eventually raise an error?) on comparisons between complex numbers

Python (version 3, at least) raises an error, but NumPy uses lexicographic order (see https://github.com/numpy/numpy/issues/11505 for discussion).

We should clean this up to match Python. This behavior is fine for sorting, but I don’t think it makes sense for comparisons between numbers. I think most comparisons between complex numbers are probably latent bugs (as was the case where I discovered this).

My suggestion would be to start by issuing a DeprecationWarning, and then maybe make it a true error at some point in the distance future.

Reproducing code example:

>>> x = 1 + 1j
>>> y = 2 + 1j
>>> x < y
TypeError: '<' not supported between instances of 'complex' and 'complex'
>>> np.array(x) < np.array(y)
True

Numpy/Python version information:

1.18.2 3.6.9 (default, Nov 7 2019, 10:44:02) [GCC 8.3.0]

[shoyer]

I could also imagine np.sort(c_arr, key=(c_arr.real, c_arr.imag)) as sugar for np.take_along_axis(c_arr, np.lexsort((c_arr.real, c_arr.imag), axis), axis)

[shoyer]

I think it would also be fair to require setting a special option in np.sort to handle complex values, but I can imagine that might get more push-back.