MAINT:linalg.det:Return scalars for singleton inputs (scipy#18763)

scipy/linalg/_basic.py

@@ -1001,7 +1001,8 @@ def det(a, overwrite_a=False, check_finite=True):
     det : (...) float or complex
         Determinant of `a`. For stacked arrays, a scalar is returned for each
         (m, m) slice in the last two dimensions of the input. For example, an
-        input of shape (p, q, m, m) will produce a result of shape (p, q).
+        input of shape (p, q, m, m) will produce a result of shape (p, q). If
+        all dimensions are 1 a scalar is returned regardless of ndim.
 
     Notes
     -----
@@ -1066,11 +1067,17 @@ def det(a, overwrite_a=False, check_finite=True):
 
     # Scalar case
     if a1.shape[-2:] == (1, 1):
-        if a1.dtype.char in 'dD':
-            return np.squeeze(a1)
+        # Either ndarray with spurious singletons or a single element
+        if max(*a1.shape) > 1:
+            temp = np.squeeze(a1)
+            if a1.dtype.char in 'dD':
+                return temp
+            else:
+                return (temp.astype('d') if a1.dtype.char == 'f' else
+                        temp.astype('D'))
         else:
-            return (np.squeeze(a1).astype('d') if a1.dtype.char == 'f' else
-                    np.squeeze(a1).astype('D'))
+            return (np.float64(a1.item()) if a1.dtype.char in 'fd' else
+                    np.complex128(a1.item()))
 
     # Then check overwrite permission
     if not _datacopied(a1, a):  # "a"  still alive through "a1"

scipy/linalg/tests/test_basic.py

@@ -932,6 +932,23 @@ class TestDet:
     def setup_method(self):
         self.rng = np.random.default_rng(1680305949878959)
 
+    def test_1x1_all_singleton_dims(self):
+        a = np.array([[1]])
+        deta = det(a)
+        assert deta.dtype.char == 'd'
+        assert np.isscalar(deta)
+        assert deta == 1.
+        a = np.array([[[[1]]]], dtype='f')
+        deta = det(a)
+        assert deta.dtype.char == 'd'
+        assert np.isscalar(deta)
+        assert deta == 1.
+        a = np.array([[[1 + 3.j]]], dtype=np.complex64)
+        deta = det(a)
+        assert deta.dtype.char == 'D'
+        assert np.isscalar(deta)
+        assert deta == 1.+3.j
+
     def test_1by1_stacked_input_output(self):
         a = self.rng.random([4, 5, 1, 1], dtype=np.float32)
         deta = det(a)