make so3_log_map torch script compatible

Summary:
* HAT_INV_SKEW_SYMMETRIC_TOL was a global variable and torch script gives an error when compiling that function. Move it to the function scope.
* torch script gives error when compiling acos_linear_extrapolation because bound is a union of tuple and float. The tuple version is kept in this diff.

Reviewed By: patricklabatut

Differential Revision: D30614916

fbshipit-source-id: 34258d200dc6a09fbf8917cac84ba8a269c00aef

Author: shchhan123456

pytorch3d/transforms/math.py

@@ -9,10 +9,12 @@
 
 import torch
 
+DEFAULT_ACOS_BOUND = 1.0 - 1e-4
+
 
 def acos_linear_extrapolation(
     x: torch.Tensor,
-    bound: Union[float, Tuple[float, float]] = 1.0 - 1e-4,
+    bounds: Tuple[float, float] = (-DEFAULT_ACOS_BOUND, DEFAULT_ACOS_BOUND),
 ) -> torch.Tensor:
     """
     Implements `arccos(x)` which is linearly extrapolated outside `x`'s original
@@ -21,23 +23,20 @@ def acos_linear_extrapolation(
 
     More specifically:
     ```
-    if -bound <= x <= bound:
+    bounds=(lower_bound, upper_bound)
+    if lower_bound <= x <= upper_bound:
         acos_linear_extrapolation(x) = acos(x)
-    elif x <= -bound: # 1st order Taylor approximation
-        acos_linear_extrapolation(x) = acos(-bound) + dacos/dx(-bound) * (x - (-bound))
-    else:  # x >= bound
-        acos_linear_extrapolation(x) = acos(bound) + dacos/dx(bound) * (x - bound)
+    elif x <= lower_bound: # 1st order Taylor approximation
+        acos_linear_extrapolation(x) = acos(lower_bound) + dacos/dx(lower_bound) * (x - lower_bound)
+    else:  # x >= upper_bound
+        acos_linear_extrapolation(x) = acos(upper_bound) + dacos/dx(upper_bound) * (x - upper_bound)
     ```
-    Note that `bound` can be made more specific with setting
-    `bound=[lower_bound, upper_bound]` as detailed below.
 
     Args:
         x: Input `Tensor`.
-        bound: A float constant or a float 2-tuple defining the region for the
+        bounds: A float 2-tuple defining the region for the
             linear extrapolation of `acos`.
-            If `bound` is a float scalar, linearly interpolates acos for
-            `x <= -bound` or `bound <= x`.
-            If `bound` is a 2-tuple, the first/second element of `bound`
+            The first/second element of `bound`
             describes the lower/upper bound that defines the lower/upper
             extrapolation region, i.e. the region where
             `x <= bound[0]`/`bound[1] <= x`.
@@ -46,11 +45,7 @@ def acos_linear_extrapolation(
         acos_linear_extrapolation: `Tensor` containing the extrapolated `arccos(x)`.
     """
 
-    if isinstance(bound, float):
-        upper_bound = bound
-        lower_bound = -bound
-    else:
-        lower_bound, upper_bound = bound
+    lower_bound, upper_bound = bounds
 
     if lower_bound > upper_bound:
         raise ValueError("lower bound has to be smaller or equal to upper bound.")

pytorch3d/transforms/so3.py

@@ -12,9 +12,6 @@
 from ..transforms import acos_linear_extrapolation
 
 
-HAT_INV_SKEW_SYMMETRIC_TOL = 1e-5
-
-
 def so3_relative_angle(
     R1: torch.Tensor,
     R2: torch.Tensor,
@@ -104,7 +101,8 @@ def so3_rotation_angle(
         return phi_cos
     else:
         if cos_bound > 0.0:
-            return acos_linear_extrapolation(phi_cos, 1.0 - cos_bound)
+            bound = 1.0 - cos_bound
+            return acos_linear_extrapolation(phi_cos, (-bound, bound))
         else:
             return torch.acos(phi_cos)
 
@@ -250,6 +248,8 @@ def hat_inv(h: torch.Tensor) -> torch.Tensor:
         raise ValueError("Input has to be a batch of 3x3 Tensors.")
 
     ss_diff = torch.abs(h + h.permute(0, 2, 1)).max()
+
+    HAT_INV_SKEW_SYMMETRIC_TOL = 1e-5
     if float(ss_diff) > HAT_INV_SKEW_SYMMETRIC_TOL:
         raise ValueError("One of input matrices is not skew-symmetric.")
 

tests/test_acos_linear_extrapolation.py

@@ -101,11 +101,6 @@ def _one_acos_test(self, x: torch.Tensor, lower_bound: float, upper_bound: float
         self._test_acos_outside_bounds(
             x[x_lower], y[x_lower], dacos_dx[x_lower], lower_bound
         )
-        if abs(upper_bound + lower_bound) <= 1e-5:  # lower_bound==-upper_bound
-            # check that passing bounds=upper_bound gives the same
-            # resut as bounds=[lower_bound, upper_bound]
-            y_one_bound = acos_linear_extrapolation(x, upper_bound)
-            self.assertClose(y_one_bound, y)
 
     def test_acos(self, batch_size: int = 10000):
         """

tests/test_so3.py

@@ -7,6 +7,7 @@
 
 import math
 import unittest
+from distutils.version import LooseVersion
 
 import numpy as np
 import torch
@@ -268,6 +269,11 @@ def test_so3_cos_bound(self, batch_size: int = 100):
                 # all grad values have to be finite
                 self.assertTrue(torch.isfinite(r.grad).all())
 
+    @unittest.skipIf(LooseVersion(torch.__version__) < "1.9", "recent torchscript only")
+    def test_scriptable(self):
+        torch.jit.script(so3_exp_map)
+        torch.jit.script(so3_log_map)
+
     @staticmethod
     def so3_expmap(batch_size: int = 10):
         log_rot = TestSO3.init_log_rot(batch_size=batch_size)