From bf886c98b03b82b6907aba1d316f51069be85fa9 Mon Sep 17 00:00:00 2001
From: Florian Pfaff <6773539+FlorianPfaff@users.noreply.github.com>
Date: Fri, 7 Aug 2026 11:12:44 +0800
Subject: [PATCH 1/2] Preserve Complex Bingham single-point backend scalar

---
 .../hypersphere_subset/complex_bingham_distribution.py          | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/pyrecest/distributions/hypersphere_subset/complex_bingham_distribution.py b/src/pyrecest/distributions/hypersphere_subset/complex_bingham_distribution.py
index 05810152da..809d3c1e48 100644
--- a/src/pyrecest/distributions/hypersphere_subset/complex_bingham_distribution.py
+++ b/src/pyrecest/distributions/hypersphere_subset/complex_bingham_distribution.py
@@ -148,7 +148,7 @@ def pdf(self, xs):
         Bxs = self.B @ xs  # (d, n)
         vals = real(einsum("ij,ij->j", conj(xs), Bxs))  # shape (n,)
         p = exp(self.log_norm_const + vals)
-        return float(p[0]) if single else p
+        return p[0] if single else p
 
     def sample(self, n):
         """Draw samples from the complex Bingham distribution.

From 9a3884efc0d1abcf42e8f864ab34b2ed72c71389 Mon Sep 17 00:00:00 2001
From: Florian Pfaff <6773539+FlorianPfaff@users.noreply.github.com>
Date: Fri, 7 Aug 2026 11:13:04 +0800
Subject: [PATCH 2/2] Test Complex Bingham single-point autograd

---
 .../test_complex_bingham_pytorch_autograd.py  | 43 +++++++++++++++++++
 1 file changed, 43 insertions(+)
 create mode 100644 tests/distributions/test_complex_bingham_pytorch_autograd.py

diff --git a/tests/distributions/test_complex_bingham_pytorch_autograd.py b/tests/distributions/test_complex_bingham_pytorch_autograd.py
new file mode 100644
index 0000000000..337c52f9c0
--- /dev/null
+++ b/tests/distributions/test_complex_bingham_pytorch_autograd.py
@@ -0,0 +1,43 @@
+from __future__ import annotations
+
+import pytest
+
+import pyrecest.backend
+from pyrecest.distributions import ComplexBinghamDistribution
+
+torch = pytest.importorskip("torch")
+
+pytestmark = pytest.mark.skipif(
+    pyrecest.backend.__backend_name__ != "pytorch",
+    reason="PyTorch backend regression",
+)
+
+
+def test_single_point_pdf_preserves_pytorch_autograd() -> None:
+    distribution = ComplexBinghamDistribution(
+        torch.tensor(
+            [[-3.0, 0.0], [0.0, 0.0]],
+            dtype=torch.complex128,
+        )
+    )
+    point = torch.tensor(
+        [0.5 + 0.5j, 0.5 - 0.5j],
+        dtype=torch.complex128,
+        requires_grad=True,
+    )
+
+    density = distribution.pdf(point)
+
+    assert torch.is_tensor(density)
+    assert density.ndim == 0
+    assert density.dtype == torch.float64
+    assert density.device == point.device
+    assert density.requires_grad
+    assert torch.isfinite(density)
+    assert density > 0.0
+
+    density.backward()
+
+    assert point.grad is not None
+    assert torch.all(torch.isfinite(point.grad))
+    assert torch.any(point.grad != 0.0)