Scipy 1.15.2 complaining about our estimated rotations

[garrettwrong]

Breaks CI. Looking into it now.

It related to an improvement made in Scipy's rotation class that is supposed to better handle non orthonormal matrix inputs. It will now raise on left handed rotations or reflections.

I believe our CL methods often return orientations with reflections and so can yield dets near -1.

[garrettwrong]

I think in this case of returning orientations, we may need to be applying a reflection about the origin to the estimated orientations to achieve a rotation in the det -1 case. Currently we just pass through the orientation as was done in MATLAB; the backproject code is (afaik) agnostic to whether we're a pure rotation or not, so long as it could transform the pts grid... but now the scipy utils we use to convert between euler and matrices care...

I need to confirm applying this reflection about the origin does not negatively impact the reconstruction results (which I've just got working acceptably after a long slog). Josh pointed out there was an attempt at making this work in the past with a correction in nearest_rotation, but I think the math was just a little off (reflection about axis instead of origin). I will report back.

[garrettwrong]

Unfortunately, despite passing tests and yielding an acceptable recon, the nearest_rotation method does not work in general with a basic application of any plane reflection, or origin reflection. I'll try looking into it more tomorrow to see if I can salvage something there.

I was incorrect, I believe the nearest_rotation function is correctly applying Kabsch's algorithm.

What I saw that made me think it was incorrect was our (sim) code (using the older scipy) internally changing test orientations that were not pure rotations when converting to angles then back to matrices. I'll need to retry comparing using projections and matrices directly.

[garrettwrong]

The function was in fact applying Kabsch's algorithm, but I think that was solving the wrong problem...

I changed the linear algebra to solve the problem we need to (I'm not sure if it has a fancy name) and added a test to confirm. I left the process I followed as a code comment.

I plan to merge this code once all tests pass. Besides solving a long standing shortfall in virtually all the groups' CL methods, it should resolve the CI issue following the scipy package upgrade.

[garrettwrong]

Closed by #1232