From df85740fb00a695bb47b310e43da5e40ff8e2411 Mon Sep 17 00:00:00 2001
From: Florian Pfaff <6773539+FlorianPfaff@users.noreply.github.com>
Date: Mon, 18 May 2026 11:50:07 +0200
Subject: [PATCH 1/3] Guard undefined hyperspherical mean directions

---
 .../abstract_hypersphere_subset_distribution.py       | 11 +++++------
 1 file changed, 5 insertions(+), 6 deletions(-)

diff --git a/src/pyrecest/distributions/hypersphere_subset/abstract_hypersphere_subset_distribution.py b/src/pyrecest/distributions/hypersphere_subset/abstract_hypersphere_subset_distribution.py
index 52228908a..de627a5f3 100644
--- a/src/pyrecest/distributions/hypersphere_subset/abstract_hypersphere_subset_distribution.py
+++ b/src/pyrecest/distributions/hypersphere_subset/abstract_hypersphere_subset_distribution.py
@@ -1,4 +1,3 @@
-import warnings
 from abc import abstractmethod
 from collections.abc import Callable
 from typing import Union
@@ -117,13 +116,13 @@ def fangles_array(*args):
         else:
             raise ValueError("Unsupported")
 
-        if linalg.norm(mu) < 1e-9:
-            warnings.warn(
-                "Warning: Density may not actually have a mean direction because integral yields a point very close to the origin."
+        norm_mu = linalg.norm(mu)
+        if norm_mu < 1e-9:
+            raise ValueError(
+                "Mean direction is undefined because the first moment is too close to the origin."
             )
 
-        mu = mu / linalg.norm(mu)
-        return mu
+        return mu / norm_mu
 
     def gen_pdf_hyperspherical_coords(self):
         """

From b480757771cfc958783aec5c4a86e1c769aa4f32 Mon Sep 17 00:00:00 2001
From: Florian Pfaff <6773539+FlorianPfaff@users.noreply.github.com>
Date: Mon, 18 May 2026 12:39:48 +0200
Subject: [PATCH 2/3] Guard undefined hyperhemispherical mean directions

---
 .../abstract_hyperhemispherical_distribution.py        | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/src/pyrecest/distributions/hypersphere_subset/abstract_hyperhemispherical_distribution.py b/src/pyrecest/distributions/hypersphere_subset/abstract_hyperhemispherical_distribution.py
index c5b4cb046..0fa01a93b 100644
--- a/src/pyrecest/distributions/hypersphere_subset/abstract_hyperhemispherical_distribution.py
+++ b/src/pyrecest/distributions/hypersphere_subset/abstract_hyperhemispherical_distribution.py
@@ -125,13 +125,13 @@ def mean_direction_numerical(self, integration_boundaries=None):
             p = self.pdf(r)
             mu = r @ p / n * Sd
 
-        if linalg.norm(mu) < 1e-9:
-            warnings.warn(
-                "Density may not have actually have a mean direction because integral yields a point very close to the origin."
+        norm_mu = linalg.norm(mu)
+        if norm_mu < 1e-9:
+            raise ValueError(
+                "Mean direction is undefined because the first moment is too close to the origin."
             )
 
-        mu = mu / linalg.norm(mu)
-        return mu
+        return mu / norm_mu
 
     @staticmethod
     def get_full_integration_boundaries(dim: Union[int, int32, int64]):

From df4d83043860792a0ad6a1b734fc3cc49f93a4f7 Mon Sep 17 00:00:00 2001
From: Florian Pfaff <6773539+FlorianPfaff@users.noreply.github.com>
Date: Mon, 18 May 2026 12:52:41 +0200
Subject: [PATCH 3/3] Add undefined mean-direction regression test

---
 .../test_abstract_hyperspherical_distribution.py      | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/tests/distributions/test_abstract_hyperspherical_distribution.py b/tests/distributions/test_abstract_hyperspherical_distribution.py
index bd242b770..7e9b9766b 100644
--- a/tests/distributions/test_abstract_hyperspherical_distribution.py
+++ b/tests/distributions/test_abstract_hyperspherical_distribution.py
@@ -7,6 +7,7 @@
 from pyrecest.backend import array, linalg, log, pi, sqrt
 from pyrecest.distributions import (
     AbstractHypersphericalDistribution,
+    HypersphericalUniformDistribution,
     VonMisesFisherDistribution,
 )
 
@@ -68,6 +69,16 @@ def test_mean_direction_numerical(self):
         vmf = VonMisesFisherDistribution(mu, kappa)
         self.assertLess(linalg.norm(vmf.mean_direction_numerical() - mu), 1e-6)
 
+    @unittest.skipIf(
+        pyrecest.backend.__backend_name__ == "jax",
+        reason="Not supported on this backend",
+    )
+    def test_mean_direction_numerical_undefined_for_uniform_circle(self):
+        """Tests that undefined mean directions are reported explicitly."""
+        uniform_circle = HypersphericalUniformDistribution(1)
+        with self.assertRaisesRegex(ValueError, "Mean direction is undefined"):
+            uniform_circle.mean_direction_numerical()
+
     def test_plotting_error_free_1d(self):
         """Tests the plotting function for circular distributions."""