code: def test_numerical_stability_pi(self, k):
      # geometric_slerp should have excellent numerical
      # stability for angles approaching pi between
      # the start and end points
      angle = np.pi - k
      ts = np.linspace(0, 1, 100)
      P = np.array([1, 0, 0, 0])
      Q = np.array([np.cos(angle), np.sin(angle), 0, 0])
      # the test should only be enforced for cases where
      # geometric_slerp determines that the input is actually
      # on the unit sphere
      with np.testing.suppress_warnings() as sup:
          sup.filter(UserWarning)
          result = geometric_slerp(P, Q, ts, 1e-18)
          norms = np.linalg.norm(result, axis=1)
          error = np.max(np.abs(norms - 1))
          assert error < 4e-15
  
imports: import numpy
  from numpy.testing import assert_allclose
  import pytest
  from scipy.spatial import geometric_slerp
label_desc: Use image node_id 18 for calling the TestGeometricSlerp obj's underlying member method code with example usage: obj.test_numerical_stability_pi(k) without return types