Summary:
GitHub issue #2002 (https://github.com/facebookresearch/pytorch3d/issues/2002)
points out that the near-pi branch of `matrix_to_axis_angle(..., fast=True)`
normalizes with `torch.norm(n)`, which reduces over the whole batch. That is
real, and there were two further problems next to it.
`matrix_to_axis_angle(..., fast=True)`:
- The axis was read from row 0 of `(R + I) / 2`, which is `n_x * n`. That is
exactly zero whenever the axis is perpendicular to x, giving `nan` (for
example for an exact rotation by pi about y), and is dominated by rounding
when `abs(n_x)` is small. It is now read from
`R + R^T - 2*cos(angle)*I == 2*(1 - cos(angle))*nnT`, taking the column whose
diagonal entry is largest so that the multiplier is at least `1/sqrt(3)`.
Symmetrizing also makes the identity exact at every angle rather than only at
pi. The sign, which `nnT` does not determine, comes from `omegas`.
- `torch.norm(n)` becomes a per-row `torch.linalg.vector_norm`, which is the
reported bug: with more than one near-pi rotation in a batch, every one of
them was scaled wrongly.
- The branch threshold was `isclose(angle, pi)`. `omegas` is `2*sin(angle)`
times the axis, so the other branch loses relative precision like
`1/(pi - angle)`, and just outside `isclose` the float32 round-trip error
reached 9.6e-4. The threshold is now `pi - 1e-2`, which leaves under 1% of
uniformly random rotations on the more expensive branch.
- The `torch.isclose(angles, 0)` guard on `omegas` is removed. `torch.sinc(0)`
is 1, so a zero angle was never a special case, and `torch.norm` has a zero
rather than `nan` gradient at zero. The guard only zeroed the answer for
angles below its `atol` of 1e-8, returning 0 instead of an exact 1e-9
rotation, and cost 24% at a batch of 100k.
Worst-case float32 round-trip matrix error over random axes, before -> after:
exactly pi `nan` or 2.0 -> 3.6e-07; `pi - 1e-5` 2.0 -> 4.2e-07; `pi - 1e-4`
9.6e-04 -> 3.6e-07. The worst case at any angle is now 9.9e-06, at the branch
boundary, against 4.8e-07 for `fast=False`.
On the choice of `pi - 1e-2`: the new near-pi branch is accurate at any
threshold, so the threshold only decides how much of the batch takes the
slower branch, and the worst case is always the angle just below it. Measured
on one batch of 100k random float32 rotations on CPU, where `fast=False` took
11.4 ms, threshold against fraction of uniformly random rotations selected,
time, and worst-case round-trip error:
- `isclose(angle, pi)`, the previous behaviour: 0.003%, 8.6 ms, 1e-03
- `pi - 1e-3`: 0.1%, 8.9 ms, 9e-05
- `pi - 1e-2`, chosen: 0.7%, 8.9 ms, 1e-05
- `pi - 0.05`: 3.2%, 10.2 ms, 3e-06
- `3.0` radians: 9.0%, 17.6 ms, 9e-07
So `pi - 1e-2` buys two orders of magnitude of accuracy over the old threshold
for no measurable time, and it is the last threshold that is free; at `3.0`
radians `fast=True` would be slower than `fast=False`. The errors are sampled
over random axes, so they move in the last digit between runs.
`axis_angle_to_matrix(..., fast=True)` is Rodrigues' formula rewritten with
`cross_product_matrix^2 == outer_product - angle^2 * I` and
`(1 - cos(angle)) / angle^2 == sinc(angle / (2*pi))^2 / 2`. The first removes a
batched 3x3 matrix multiplication, which `bmm` serves poorly at that size, and
folds the leftover `-angle^2 * I` into the identity term as `cos(angle) * I`;
the second is defined at zero, so the `angles_sqrd == 0` special case goes
away. Values are unchanged to 8.9e-16.
`matrix_to_axis_angle` also used eight separate boolean mask indexes, each of
which re-runs `nonzero` over the whole batch and, on CUDA, synchronizes. The
cheap branch is now evaluated densely and the near-pi minority is selected
with a single `nonzero`.
Evaluating the near-pi branch densely too, which would remove the last
`nonzero` and so every data-dependent shape, was tried and rejected: against
this version it is 1.24x to 1.60x faster on CUDA at batches of 1k to 100k but
0.88x at 1M, and about 2x slower on CPU, and it does not survive
`torch.jit.script` without further work. It is the version to revisit if
export or `torch.compile` friendliness ever matters more than speed.
Speedups, before -> after:
- `matrix_to_axis_angle`: CUDA 1.88x at a batch of 1k, 1.66x at 100k, 1.47x at
1M; CPU 1.26x at 1k, 2.01x at 100k, 1.71x at 1M.
- `axis_angle_to_matrix`: CUDA 1.26x at 1k, 1.81x at 100k, 5.49x at 1M; CPU
unchanged.
Before this change `matrix_to_axis_angle(..., fast=True)` was slower than
`fast=False` on CUDA at a batch of 100k, 0.587 against 0.463 ms, because the
selection synchronized.
Rewriting `axis_angle_to_matrix` to compute all nine entries in one
`torch.stack`, as `quaternion_to_matrix` does, was also tried and is not
faster: 0.96x, 0.74x and 1.10x on CUDA at 1k, 100k and 1M, because the extra
kernel launches cost about what the saved intermediates gain.
Reviewed By: MichaelRamamonjisoa
Differential Revision: D115714860
fbshipit-source-id: cf19695f67bf2e2e6f8719419e9f902d5c58c309
Summary:
This is an extension of https://github.com/facebookresearch/pytorch3d/issues/1544 with various speed, stability, and readability improvements. (I could not find a way to make a commit to the existing PR). This PR is still based on the [Rodrigues' rotation formula](https://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions#Rotation_matrix_%E2%86%94_Euler_axis/angle).
The motivation is the same; this change speeds up the conversions up to 10x, depending on the device, batch size, etc.
### Notes
- As the angles get very close to `π`, the existing implementation and the proposed one start to differ. However, (my understanding is that) this is not a problem as the axis can not be stably inferred from the rotation matrix in this case in general.
- bottler , I tried to follow similar conventions as existing functions to deal with weird angles, let me know if something needs to be changed to merge this.
Pull Request resolved: https://github.com/facebookresearch/pytorch3d/pull/1948
Reviewed By: MichaelRamamonjisoa
Differential Revision: D69193009
Pulled By: bottler
fbshipit-source-id: e5ed34b45b625114ec4419bb89e22a6aefad4eeb
Summary: Update all FB license strings to the new format.
Reviewed By: patricklabatut
Differential Revision: D33403538
fbshipit-source-id: 97a4596c5c888f3c54f44456dc07e718a387a02c
Summary:
Make sure the functions from `rotation_conversion` are jittable, and add some type hints.
Add tests to verify this is the case.
Pull Request resolved: https://github.com/facebookresearch/pytorch3d/pull/898
Reviewed By: patricklabatut
Differential Revision: D31926103
Pulled By: bottler
fbshipit-source-id: bff6013c5ca2d452e37e631bd902f0674d5ca091
Summary: Because rotations and (rotation) quaternions live on curved manifolds, it doesn't make sense to optimize them directly. Having a prominent option to require gradient on random ones may cause people to try, and isn't particularly useful.
Reviewed By: theschnitz
Differential Revision: D29160734
fbshipit-source-id: fc9e320672349fe334747c5b214655882a460a62
Summary:
As reported on github, `matrix_to_quaternion` was incorrect for rotations by 180˚. We resolved the sign of the component `i` based on the sign of `i*r`, assuming `r > 0`, which is untrue if `r == 0`.
This diff handles special cases and ensures we use the non-zero elements to copy the sign from.
Reviewed By: bottler
Differential Revision: D29149465
fbshipit-source-id: cd508cc31567fc37ea3463dd7e8c8e8d5d64a235
Summary: We can represent a rotation as a vector in the axis direction, whose length is the rotation anticlockwise in radians around that axis.
Reviewed By: gkioxari
Differential Revision: D24306293
fbshipit-source-id: 2e0f138eda8329f6cceff600a6e5f17a00e4deb7
Summary: Issue #119. The function `sqrt(max(x, 0))` is not convex and has infinite gradient at 0, but 0 is a subgradient at 0. Here we implement it in such a way as to give 0 as the gradient.
Reviewed By: gkioxari
Differential Revision: D24306294
fbshipit-source-id: 48d136faca083babad4d64970be7ea522dbe9e09
Summary: Conversion to/from the 6D representation of rotation from the paper http://arxiv.org/abs/1812.07035 ; based on David’s implementation.
Reviewed By: davnov134
Differential Revision: D22234397
fbshipit-source-id: 9e25ee93da7e3a2f2068cbe362cb5edc88649ce0
Summary: The shebang line `#!<path to interpreter>` is only required for Python scripts, so remove it on source files for class or function definitions. Additionally explicitly mark as executable the actual Python scripts in the codebase.
Reviewed By: nikhilaravi
Differential Revision: D20095778
fbshipit-source-id: d312599fba485e978a243292f88a180d71e1b55a
Summary:
Lint related fixes: Improve internal/OSS consistency. Fix the fight between black and certain pyre-ignore markers by moving them to the line before.
Use clang-format-8 automatically if present. Small number of pyre fixes.
arc doesn't run pyre at the moment, so I put back the explicit call to pyre. I don't know if there's an option somewhere to change this.
Reviewed By: nikhilaravi
Differential Revision: D19780518
fbshipit-source-id: ef1c243392322fa074130f6cff2dd8a6f7738a7f
Summary: Fixed the rotation matrices generated by the RotateAxisAngle class and updated the tests. Added documentation for Transforms3d to clarify the conventions.
Reviewed By: gkioxari
Differential Revision: D19912903
fbshipit-source-id: c64926ce4e1381b145811557c32b73663d6d92d1
