Support for complex numbers

[alexander-held]

Describe the potential feature

Currently the library does not support complex numbers, causing e.g.

import awkward as ak
import vector

arr = ak.Array(
    [{"x": 1, "y": 2, "z": 3 + 3j, "t": 5 + 3j}],
    with_name="Vector4D",
    behavior=vector.backends.awkward.behavior,
)
arr.tau

to fail since np.copysign does not seem to handle complex numbers (see e.g. np.copysign(ak.Array([1, 1j]), ak.Array([1, -1]))).

I ran into this while solving for object kinematics in constrained systems, where the violation of assumptions (e.g. on-shell decay) can result in imaginary contributions to the kinematics. Another example might be math with tachyons. For my use case I can in practice work around this by making all relevant numbers real before hitting any vector codepaths that would otherwise fail.

I am opening this issue to have a place to track the topic and potential interest in vector with complex numbers as I have not seen this discussed previously.

Motivation

No response

Possible Implementation

No response

[pfackeldey]

Hi @alexander-held,
np.copysign doesn't work with complex numpy arrays either. I suppose it's just not well-defined with complex numbers? I'm not sure if it would be always correct to run the copysign only on the real part?

In general, vector should already now work with complex numbers just as well as NumPy (or whatever .lib is) does, because we forward the NumPy operations to the underlying NumPy arrays of an Awkward Array (if you use the awkward backend). We're inheriting the same complex number constraints that also NumPy has.