ENH: Distances between distributions with complex samples

[jmoraispk]

Is your feature request related to a problem? Please describe.

When I try to compute

scipy.stats.wasserstein_distance(u,v) or scipy.stats.wasserstein_distance_nd(u,v) between distributions with complex samples, I get this warning:

/home/joao/mambaforge/envs/my-env/lib/python3.9/site-packages/scipy/stats/_stats_py.py:10628:
ComplexWarning: Casting complex values to real discards the imaginary part

Which means the distance is not happening between complex numbers, but between real numbers.

Describe the solution you'd like.

I'm not sure if this is the correct way of doing it, but I would like the distances to work normally for complex vectors. I tried the following changes, and they seem to be working.

Changing line 10628 in _stats_py.py from

values = np.asarray(values, dtype=float)
to:

if type(values) == np.ndarray and values.dtype in [np.complex64, np.complex128]:
    pass
else:
    values = np.asarray(values, dtype=float)

Describe alternatives you've considered.

I considered unfolding the complex into a 2*N vector with real and imaginary parts separated. But this will compute distances differently. Instead of shortest distances in the complex plane, it would sum the real distance with the imaginary.

(like summing the 2 sides of the rectangular triangle instead of the diagonal)the

Additional context (e.g. screenshots, GIFs)

No response