fixed the ordering of the matrix in takagi with diagonal matrix

added test to trigger both svd_order=True and False in takagi with diagonal matrix

thewalrus/decompositions.py

@@ -206,13 +206,14 @@ def takagi(A, svd_order=True):
     # If the matrix is diagonal, Takagi decomposition is easy
     if np.allclose(A, np.diag(np.diag(A)), rtol=1e-16):
         d = np.diag(A)
-        U = np.diag(np.exp(1j * 0.5 * np.angle(d)))
         l = np.abs(d)
         idx = np.argsort(l)
+        d = d[idx]
         l = l[idx]
-        U = U[idx]
+        U = np.diag(np.exp(1j * 0.5 * np.angle(d)))
+        U = U[::-1, :]
         if svd_order:
-            return l[::-1], U[::-1, :]
+            return l[::-1], U[:, ::-1]
         return l, U
 
     u, d, v = np.linalg.svd(A)

thewalrus/tests/test_decompositions.py

@@ -334,7 +334,8 @@ def test_takagi_error():
         takagi(A)
 
 
-def test_takagi_diagonal_matrix():
+@pytest.mark.parametrize("svd_order", [True, False])
+def test_takagi_diagonal_matrix(svd_order):
     """Test the takagi decomposition works well for a specific matrix that was not decomposed accurately in a previous implementation.
     See more info in PR #393 (https://github.com/XanaduAI/thewalrus/pull/393)"""
     A = np.array(
@@ -356,7 +357,7 @@ def test_takagi_diagonal_matrix():
             ],
         ]
     )
-    d, U = takagi(A)
+    d, U = takagi(A, svd_order=svd_order)
     assert np.allclose(A, U @ np.diag(d) @ U.T)
     assert np.allclose(U @ np.conjugate(U).T, np.eye(len(U)))
     assert np.all(d >= 0)