Quaternion multiplication wrong, because of Tensor.cross

[yzhhr]

Describe the bug

The expression c should give the same result but it actually goes wrong.

import torch
torch.manual_seed(42)
import kornia
from kornia.geometry.quaternion import Quaternion
x = Quaternion.random(3)
a = x * x
b = x[0] * x[0]
c = x[[0,0,0]] * x
d = x[[0,1,2]] * x
print(a[0], b, c[0], d[0])

The code gives

Parameter containing:
tensor([-0.9849, -0.0576, -0.1629,  0.0067], requires_grad=True) Parameter containing:
tensor([-0.9849, -0.0576, -0.1629,  0.0067], requires_grad=True) Parameter containing:
tensor([-0.9849, -0.1930,  0.4901, -0.0056], requires_grad=True) Parameter containing:
tensor([-0.9849, -0.0576, -0.1629,  0.0067], requires_grad=True)

May affect more behaviors

For example the so3 and se3 lie group actions also depend on quaternions.

Tracing the bug

The bug is caused by a call to Tensor.cross, which finds the first dimension of size=3 as vec3. The code can be found in Quaternion.__mul__. Replacing the call with a more stable torch.linalg.cross can fix the issue, according to my experiment.

It is weird that only expression c actually triggers the bug. PyTorch actually gives a warning of Tensor.cross deprecated but no one seems to be caring?

Can I possibly help fix it in a PR?

One more question

Is Quaternion class designed to be not supporting broadcasting? Why those modules default to be requires_grad=True even when initializers are requires_grad=False?

Reproduction steps

Just run the sample code.

Expected behavior

All four expressions should give the same result.

Environment

kornia 0.7.2.dev0, torch 2.2.1

Additional context

No response

[cjpurackal]

Good catch, please go ahead with the PR and it would be great if you can update the tests as well!