test Pauli matrices

test/test_lanzcos.py

@@ -35,6 +35,33 @@ def test_four(self):
             assert np.abs(np.linalg.norm(eigvec2[:, j]) - 1.) < tol
             assert np.all(np.abs(A @ eigvec2[:, j] / eigval2[j] - eigvec2[:, j]) < tol)
 
+    def test_paulix(self):
+        tol = 1e-8
+        A = np.array(
+            [
+                [0., 1.],
+                [1., 0.]
+            ]
+        )
+        eigval1, eigvec1 = np.linalg.eig(A)
+        eigval2, eigvec2 = lanzcos(A, A.shape[0])
+
+        assert len(eigval2) == A.shape[0] + 1
+
+        eig1dict = {}
+        for i in range(A.shape[0]):
+            for j in range(len(eigval2)):
+                if abs(eigval1[i] - eigval2[j]) < tol:
+                    eig1dict[i] = j
+                    break
+        assert len(set(eig1dict.values())) == len(eigval1)
+
+        for i in range(A.shape[0]):
+            j = eig1dict[i]
+            assert np.abs(np.linalg.norm(eigvec2[:, j]) - 1.) < tol
+            assert np.all(np.abs(A @ eigvec2[:, j] / eigval2[j] - eigvec2[:, j]) < tol)
+            assert abs(abs(eigvec2[0, j]) - np.sqrt(0.5)) < tol
+
 
 if __name__ == '__main__':
     unittest.main()