BUG: interpolate: Fix wrong warning message if degree=-1 in `interpol…

…ate.RBFInterpolator` (#20364)

* BUG: optimize: Fix wrong warning message if degree=-1 in interpolate.RBFInterpolator

* BUG: optimize: add a comment for test

scipy/interpolate/_rbfinterp.py

@@ -342,10 +342,11 @@ def __init__(self, y, d,
             degree = int(degree)
             if degree < -1:
                 raise ValueError("`degree` must be at least -1.")
-            elif degree < min_degree:
+            elif -1 < degree < min_degree:
                 warnings.warn(
-                    f"`degree` should not be below {min_degree} when `kernel` "
-                    f"is '{kernel}'. The interpolant may not be uniquely "
+                    f"`degree` should not be below {min_degree} except -1 "
+                    f"when `kernel` is '{kernel}'."
+                    f"The interpolant may not be uniquely "
                     f"solvable, and the smoothing parameter may have an "
                     f"unintuitive effect.",
                     UserWarning, stacklevel=2

scipy/interpolate/tests/test_rbfinterp.py

@@ -369,9 +369,18 @@ def test_degree_warning(self):
         y = np.linspace(0, 1, 5)[:, None]
         d = np.zeros(5)
         for kernel, deg in _NAME_TO_MIN_DEGREE.items():
-            match = f'`degree` should not be below {deg}'
-            with pytest.warns(Warning, match=match):
-                self.build(y, d, epsilon=1.0, kernel=kernel, degree=deg-1)
+            # Only test for kernels that its minimum degree is not 0.
+            if deg >= 1:
+                match = f'`degree` should not be below {deg}'
+                with pytest.warns(Warning, match=match):
+                    self.build(y, d, epsilon=1.0, kernel=kernel, degree=deg-1)
+
+    def test_minus_one_degree(self):
+        # Make sure a degree of -1 is accepted without any warning.
+        y = np.linspace(0, 1, 5)[:, None]
+        d = np.zeros(5)
+        for kernel, _ in _NAME_TO_MIN_DEGREE.items():
+            self.build(y, d, epsilon=1.0, kernel=kernel, degree=-1)
 
     def test_rank_error(self):
         # An error should be raised when `kernel` is "thin_plate_spline" and