Test SVD and Eig(h): allow benign sign change

tests/tensor/test_nlinalg.py

@@ -165,10 +165,33 @@ class TestSvd(utt.InferShapeTester):
         pt_outputs = fn(a)
 
         np_outputs = np_outputs if isinstance(np_outputs, tuple) else [np_outputs]
+        if compute_uv:
+            # In this case we sometimes get a sign flip on some columns in one impl and not the thore
+            # The results are both correct, and we test that by reconstructing the original input
+            U, S, Vh = pt_outputs
+            S_diag = np.expand_dims(S, -2) * np.eye(S.shape[-1])
+
+            diff = a.shape[-2] - a.shape[-1]
+            if full_matrix:
+                if diff > 0:
+                    # tall
+                    S_diag = np.pad(S_diag, [(0, 0), (0, diff), (0, 0)][-a.ndim :])
+                elif diff < 0:
+                    # wide
+                    S_diag = np.pad(S_diag, [(0, 0), (0, 0), (0, -diff)][-a.ndim :])
+
+            a_r = U @ S_diag @ Vh
+            rtol = 1e-3 if config.floatX == "float32" else 1e-7
+            np.testing.assert_allclose(a_r, a, rtol=rtol)
+
+            for np_val, pt_val in zip(np_outputs, pt_outputs, strict=True):
+                # Check values are equivalent up to sign change
+                np.testing.assert_allclose(np.abs(np_val), np.abs(pt_val), rtol=rtol)
 
-        rtol = 1e-5 if config.floatX == "float32" else 1e-7
-        for np_val, pt_val in zip(np_outputs, pt_outputs, strict=True):
-            np.testing.assert_allclose(np_val, pt_val, rtol=rtol)
+        else:
+            rtol = 1e-5 if config.floatX == "float32" else 1e-7
+            for np_val, pt_val in zip(np_outputs, pt_outputs, strict=True):
+                np.testing.assert_allclose(np_val, pt_val, rtol=rtol)
 
     def test_svd_infer_shape(self):
         self.validate_shape((4, 4), full_matrices=True, compute_uv=True)
@@ -428,8 +451,8 @@ class TestEig(utt.InferShapeTester):
 
         w, v = fn(A_val)
         w_np, v_np = np.linalg.eig(A_val)
-        np.testing.assert_allclose(w, w_np)
-        np.testing.assert_allclose(v, v_np)
+        np.testing.assert_allclose(np.abs(w), np.abs(w_np))
+        np.testing.assert_allclose(np.abs(v), np.abs(v_np))
         assert_array_almost_equal(np.dot(A_val, v), w * v)
 
         # Asymmetric input (real eigenvalues)
@@ -438,16 +461,16 @@ class TestEig(utt.InferShapeTester):
 
         w, v = fn(A_val)
         w_np, v_np = np.linalg.eig(A_val)
-        np.testing.assert_allclose(w, w_np)
-        np.testing.assert_allclose(v, v_np)
+        np.testing.assert_allclose(np.abs(w), np.abs(w_np))
+        np.testing.assert_allclose(np.abs(v), np.abs(v_np))
         assert_array_almost_equal(np.dot(A_val, v), w * v)
 
         # Asymmetric input (complex eigenvalues)
         A_val = self.rng.normal(size=(5, 5))
         w, v = fn(A_val)
         w_np, v_np = np.linalg.eig(A_val)
-        np.testing.assert_allclose(w, w_np)
-        np.testing.assert_allclose(v, v_np)
+        np.testing.assert_allclose(np.abs(w), np.abs(w_np))
+        np.testing.assert_allclose(np.abs(v), np.abs(v_np))
         assert_array_almost_equal(np.dot(A_val, v), w * v)
 
 
@@ -464,11 +487,14 @@ class TestEigh(TestEig):
 
         w, v = fn(A_val)
         w_np, v_np = np.linalg.eigh(A_val)
-        np.testing.assert_allclose(w, w_np)
-        np.testing.assert_allclose(v, v_np)
+        # There are multiple valid results up to some sign changes
+        # Check we can reconstruct input
         rtol = 1e-2 if self.dtype == "float32" else 1e-7
         np.testing.assert_allclose(np.dot(A_val, v), w * v, rtol=rtol)
 
+        np.testing.assert_allclose(np.abs(w), np.abs(w_np), rtol=rtol)
+        np.testing.assert_allclose(np.abs(v), np.abs(v_np), rtol=rtol)
+
     def test_uplo(self):
         S = self.S
         a = matrix(dtype=self.dtype)