Matrix multiplication (@ operator) is broken and needs to be ported to kernels (out of Numba)

[alexander-held]

Version of Awkward Array

1.7.0

Description and code to reproduce

While trying to use awkward arrays in matrix multiplication, I ran into two different kinds of unexpected behavior. The following code shows an example.

import awkward as ak
import numpy as np

v = np.asarray([1,2,3])
A = np.asarray([[1,0,0],[0,1,0],[0,0,1]])
vT1 = np.asarray([[1],[2],[3]])
vT2 = np.asarray([1,2,3])

print(v @ A @ vT1)  # [14]
print(v @ A @ vT2)  # 14

v = ak.Array([1,2,3])
A = ak.Array([[1,0,0],[0,1,0],[0,0,1]])
vT1 = ak.Array([[1],[2],[3]])
vT2 = ak.Array([1,2,3])

print(v @ A @ vT1)  # output [[a], [b], [c]], different values for a, b, c each time
print(v @ A @ vT2)  # ValueError: in ListOffsetArray64 attempting to get 3, stops[i] > len(content)

In the first case with vT1, uninitialized data seems to be accessed, leading to different outputs every time. The output shape also changes when compared to the numpy approach. I naively expected the second case with vT2 to also work, and to report the same result as numpy. I believe the different treatment for this may be on purpose and a design choice, but wanted to include it here as well to be sure this is expected.

[jpivarski]

I made #1324 and mentioned @lukasheinrich in it, but that's a duplicate of this one, so I'll close that and prioritize this.

[jpivarski]

This is harder than we thought and should be deferred beyond the next release.

np.matmul on Awkward Arrays should raise NotImplementedError for now.