content: # Copyright (c) Meta Platforms, Inc. and affiliates.
  #
  # This source code is licensed under the MIT license found in the
  # LICENSE file in the root directory of this source tree.
  
  import numpy as np
  import pytest  # noqa: F401
  import torch
  
  import theseus as th
  from theseus.constants import TEST_EPS
  from theseus.geometry.lie_group_check import set_lie_group_check_enabled
  from theseus.utils import numeric_jacobian
  
  from .common import (
      BATCH_SIZES_TO_TEST,
      check_adjoint,
      check_compose,
      check_exp_map,
      check_inverse,
      check_jacobian_for_local,
      check_log_map,
      check_projection_for_compose,
      check_projection_for_exp_map,
      check_projection_for_inverse,
      check_projection_for_log_map,
      check_projection_for_rotate_and_transform,
      check_so3_se3_normalize,
  )
  
  
  def check_SO3_log_map(tangent_vector, atol=1e-7, enable_functorch=False):
      with set_lie_group_check_enabled(not enable_functorch, silent=True):
          error = (tangent_vector - th.SO3.exp_map(tangent_vector).log_map()).norm(dim=1)
          error = torch.minimum(error, (error - 2 * np.pi).abs())
          assert torch.allclose(error, torch.zeros_like(error), atol=atol)
  
  
  def check_SO3_to_quaternion(so3: th.SO3, atol=1e-10, enable_functorch=False):
      with set_lie_group_check_enabled(not enable_functorch, silent=True):
          quaternions = so3.to_quaternion()
          assert torch.allclose(
              th.SO3(quaternion=quaternions).to_matrix(), so3.to_matrix(), atol=atol
          )
  
  
  def _create_tangent_vector(batch_size, ang_factor, rng, dtype):
      tangent_vector = torch.rand(batch_size, 3, generator=rng, dtype=dtype) - 0.5
      tangent_vector /= tangent_vector.norm(dim=1, keepdim=True)
      tangent_vector *= ang_factor
      return tangent_vector
  
  
  @pytest.mark.parametrize("batch_size", BATCH_SIZES_TO_TEST)
  @pytest.mark.parametrize("dtype", [torch.float32, torch.float64])
  @pytest.mark.parametrize(
      "ang_factor", [None, 1e-5, 3e-3, 2 * np.pi - 1e-11, np.pi - 1e-7, np.pi - 1e-11]
  )
  @pytest.mark.parametrize("enable_functorch", [True, False])
  def test_exp_map(batch_size, dtype, ang_factor, enable_functorch):
      rng = torch.Generator()
      rng.manual_seed(0)
      ATOL = 2e-4 if dtype == torch.float32 else 1e-6
  
      if ang_factor is None:
          ang_factor = (
              torch.rand(batch_size, 1, generator=rng, dtype=dtype) * 2 * np.pi - np.pi
          )
  
      tangent_vector = _create_tangent_vector(batch_size, ang_factor, rng, dtype)
      check_exp_map(tangent_vector, th.SO3, atol=ATOL, enable_functorch=enable_functorch)
      check_projection_for_exp_map(
          tangent_vector, th.SO3, atol=ATOL, enable_functorch=enable_functorch
      )
  
  
  @pytest.mark.parametrize("batch_size", BATCH_SIZES_TO_TEST)
  @pytest.mark.parametrize("dtype", [torch.float32, torch.float64])
  @pytest.mark.parametrize(
      "ang_factor", [None, 1e-5, 3e-3, 2 * np.pi - 1e-11, np.pi - 1e-11]
  )
  @pytest.mark.parametrize("enable_functorch", [True, False])
  def test_log_map(batch_size, dtype, ang_factor, enable_functorch):
      if dtype == torch.float32 and ang_factor == np.pi - 1e-11:
          return
  
      rng = torch.Generator()
      rng.manual_seed(0)
      ATOL = 1e-3 if dtype == torch.float32 else 1e-8
      PROJECTION_ATOL = 1e-2 if dtype == torch.float32 else 1e-8
  
      if ang_factor is None:
          ang_factor = (
              torch.rand(batch_size, 1, generator=rng, dtype=dtype) * 2 * np.pi - np.pi
          )
  
      tangent_vector = _create_tangent_vector(batch_size, ang_factor, rng, dtype)
      check_SO3_log_map(tangent_vector, atol=ATOL, enable_functorch=enable_functorch)
      if tangent_vector.norm(dim=1).max() < 2 * np.pi - 1e-3:
          check_log_map(
              tangent_vector, th.SO3, atol=ATOL, enable_functorch=enable_functorch
          )
      check_projection_for_log_map(
          tangent_vector, th.SO3, atol=PROJECTION_ATOL, enable_functorch=enable_functorch
      )
  
  
  @pytest.mark.parametrize("batch_size", BATCH_SIZES_TO_TEST)
  @pytest.mark.parametrize("dtype", [torch.float32, torch.float64])
  @pytest.mark.parametrize("enable_functorch", [True, False])
  def test_inverse(batch_size, dtype, enable_functorch):
      rng = torch.Generator()
      rng.manual_seed(0)
  
      group = th.SO3.rand(batch_size, generator=rng, dtype=dtype)
  
      check_inverse(group, enable_functorch=enable_functorch)
  
  
  @pytest.mark.parametrize("batch_size", BATCH_SIZES_TO_TEST)
  @pytest.mark.parametrize("dtype", [torch.float32, torch.float64])
  @pytest.mark.parametrize(
      "ang_factor", [None, 1e-5, 3e-3, 2 * np.pi - 1e-11, np.pi - 1e-11]
  )
  @pytest.mark.parametrize("enable_functorch", [True, False])
  def test_quaternion(batch_size, dtype, ang_factor, enable_functorch):
      rng = torch.Generator()
      rng.manual_seed(0)
      ATOL = 1e-3 if dtype == torch.float32 else 1e-8
  
      if ang_factor is None:
          ang_factor = (
              torch.rand(batch_size, 1, generator=rng, dtype=dtype) * 2 * np.pi - np.pi
          )
  
      tangent_vector = _create_tangent_vector(batch_size, ang_factor, rng, dtype)
      so3 = th.SO3.exp_map(tangent_vector)
      check_SO3_to_quaternion(so3, atol=ATOL, enable_functorch=enable_functorch)
  
  
  @pytest.mark.parametrize("batch_size", BATCH_SIZES_TO_TEST)
  @pytest.mark.parametrize("dtype", [torch.float32, torch.float64])
  @pytest.mark.parametrize("enable_functorch", [True, False])
  def test_adjoint(batch_size, dtype, enable_functorch):
      rng = torch.Generator()
      rng.manual_seed(0)
      so3 = th.SO3.rand(batch_size, generator=rng, dtype=dtype)
      tangent = torch.randn(batch_size, 3, dtype=dtype)
      check_adjoint(so3, tangent, enable_functorch)
  
  
  @pytest.mark.parametrize("batch_size", BATCH_SIZES_TO_TEST)
  @pytest.mark.parametrize("dtype", [torch.float32, torch.float64])
  def test_compose(batch_size, dtype):
      rng = torch.Generator()
      rng.manual_seed(0)
      so3_1 = th.SO3.rand(batch_size, generator=rng, dtype=dtype)
      so3_2 = th.SO3.rand(batch_size, generator=rng, dtype=dtype)
      check_compose(so3_1, so3_2)
  
  
  @pytest.mark.parametrize("dtype", [torch.float32, torch.float64])
  def test_rotate_and_unrotate(dtype):
      rng = torch.Generator()
      rng.manual_seed(0)
      for _ in range(10):  # repeat a few times
          for batch_size_group in BATCH_SIZES_TO_TEST:
              for batch_size_pnt in BATCH_SIZES_TO_TEST:
                  if (
                      batch_size_group != 1
                      and batch_size_pnt != 1
                      and batch_size_pnt != batch_size_group
                  ):
                      continue
  
                  so3 = th.SO3.rand(batch_size_group, generator=rng, dtype=dtype)
                  point_tensor = torch.randn(
                      batch_size_pnt, 3, generator=rng, dtype=dtype
                  )
  
                  jacobians_rotate = []
                  rotated_point = so3.rotate(point_tensor, jacobians=jacobians_rotate)
                  expected_rotated_data = so3.to_matrix() @ point_tensor.unsqueeze(2)
                  jacobians_unrotate = []
                  unrotated_point = so3.unrotate(rotated_point, jacobians_unrotate)
  
                  # Check the operation result
                  assert torch.allclose(
                      expected_rotated_data.squeeze(2),
                      rotated_point.tensor,
                      atol=TEST_EPS,
                  )
                  assert torch.allclose(
                      point_tensor, unrotated_point.tensor, atol=TEST_EPS
                  )
  
                  # Check the jacobians
                  # function_dim = 3 because rotate(so3, (x, y, z)) --> (x_new, y_new, z_new)
                  so3_double = so3.copy()
                  so3_double.to(torch.float64)
                  expected_jac = numeric_jacobian(
                      lambda groups: groups[0].rotate(groups[1]),
                      [so3_double, th.Point3(point_tensor.double())],
                      function_dim=3,
                  )
                  assert torch.allclose(
                      jacobians_rotate[0].double(), expected_jac[0], atol=TEST_EPS
                  )
                  assert torch.allclose(
                      jacobians_rotate[1].double(), expected_jac[1], atol=TEST_EPS
                  )
                  expected_jac = numeric_jacobian(
                      lambda groups: groups[0].unrotate(groups[1]),
                      [so3_double, th.Vector(tensor=rotated_point.tensor.double())],
                      delta_mag=1e-5,
                      function_dim=3,
                  )
                  assert torch.allclose(
                      jacobians_unrotate[0].double(), expected_jac[0], atol=TEST_EPS
                  )
                  assert torch.allclose(
                      jacobians_unrotate[1].double(), expected_jac[1], atol=TEST_EPS
                  )
  
  
  @pytest.mark.parametrize("dtype", [torch.float32, torch.float64])
  @pytest.mark.parametrize("enable_functorch", [True, False])
  def test_projection(dtype, enable_functorch):
      rng = torch.Generator()
      rng.manual_seed(0)
      for _ in range(10):  # repeat a few times
          for batch_size in BATCH_SIZES_TO_TEST:
              # Test SO3.rotate
              check_projection_for_rotate_and_transform(
                  th.SO3, th.Point3, th.SO3.rotate, batch_size, rng, dtype=dtype
              )
  
              # Test SO3.unrotate
              check_projection_for_rotate_and_transform(
                  th.SO3, th.Point3, th.SO3.unrotate, batch_size, rng, dtype=dtype
              )
  
              # Test SO3.compose
              check_projection_for_compose(
                  th.SO3, batch_size, rng, dtype=dtype, enable_functorch=enable_functorch
              )
  
              # Test SO3.inverse
              check_projection_for_inverse(
                  th.SO3, batch_size, rng, dtype=dtype, enable_functorch=enable_functorch
              )
  
  
  @pytest.mark.parametrize("dtype", [torch.float32, torch.float64])
  def test_local_map(dtype):
      rng = torch.Generator()
      rng.manual_seed(0)
      ATOL = 3e-5 if dtype == torch.float32 else 1e-7
  
      for batch_size in BATCH_SIZES_TO_TEST:
          group0 = th.SO3.rand(batch_size, dtype=dtype)
          group1 = th.SO3.rand(batch_size, dtype=dtype)
  
          check_jacobian_for_local(
              group0, group1, Group=th.SO3, is_projected=True, atol=ATOL
          )
  
  
  @pytest.mark.parametrize("batch_size", BATCH_SIZES_TO_TEST)
  @pytest.mark.parametrize("dtype", [torch.float32, torch.float64])
  def test_normalization(batch_size, dtype):
      check_so3_se3_normalize(th.SO3, batch_size, dtype)
  