Fix hypertoroidal MH defaults and infinite-angle handling (#5462)

* Fix hypertoroidal MH defaults and non-finite angle validation

* Add hypertoroidal sampling and angle regressions

Author: FlorianPfaff

src/pyrecest/distributions/hypertorus/abstract_hypertoroidal_distribution.py

@@ -21,7 +21,7 @@
     cos,
     int32,
     int64,
-    isnan,
+    isfinite,
     linspace,
     log,
     meshgrid,
@@ -171,8 +171,10 @@ def angular_error(alpha, beta):
         Returns:
             float or numpy array: The angular error(s) in radians.
         """
-        if bool(isnan(alpha).any()) or bool(isnan(beta).any()):
-            raise ValueError("Angles must not contain NaN values.")
+        if bool(backend_any(~isfinite(alpha))) or bool(backend_any(~isfinite(beta))):
+            raise ValueError(
+                "Angles must contain only finite values; NaN and infinite values are invalid."
+            )
         # Ensure the angles are between 0 and 2*pi
         alpha = mod(alpha, 2.0 * pi)
         beta = mod(beta, 2.0 * pi)
@@ -312,7 +314,12 @@ def proposal_np(x):
                 proposal = proposal_np
 
         if start_point is None:
-            start_point = self.mean_direction()
+            try:
+                start_point = self.mean_direction()
+            except ValueError:
+                # Uniform and other symmetric hypertoroidal distributions can have
+                # no unique mean direction even though MH sampling is well-defined.
+                start_point = zeros(self.dim)
 
         # pylint: disable=duplicate-code
         s = AbstractManifoldSpecificDistribution.sample_metropolis_hastings(

tests/distributions/test_hypertoroidal_sampling_and_angle_regressions.py

@@ -0,0 +1,28 @@
+import pytest
+from pyrecest.backend import array
+from pyrecest.distributions import AbstractHypertoroidalDistribution
+from pyrecest.distributions.hypertorus.hypertoroidal_uniform_distribution import (
+    HypertoroidalUniformDistribution,
+)
+
+
+def test_uniform_metropolis_hastings_does_not_require_unique_mean():
+    dist = HypertoroidalUniformDistribution(2)
+
+    samples = dist.sample_metropolis_hastings(4, burn_in=0, skipping=1)
+
+    assert samples.shape == (4, 2)
+
+
+@pytest.mark.parametrize(
+    ("alpha", "beta"),
+    [
+        (float("inf"), 0.0),
+        (float("-inf"), 0.0),
+        (0.0, float("inf")),
+        (0.0, float("-inf")),
+    ],
+)
+def test_angular_error_rejects_infinite_inputs(alpha, beta):
+    with pytest.raises(ValueError, match="finite"):
+        AbstractHypertoroidalDistribution.angular_error(array(alpha), array(beta))