diff --git a/input.py b/input.py
index 6eb96dee68c81fbd8fd157e60e8d439e0b01e62c..9efa77b83d269d3775c2b9f2f1021505e2639a8b 100644
--- a/input.py
+++ b/input.py
@@ -20,77 +20,77 @@ class FluxDataSingle:
 
 single_data = {}
 single_data["Case a:x"] = FluxDataSingle(
-        "2 4 4 4 20,1 1 1 1 5.5",
-        "4 11.2 8 8 46.4,1 2.6 1 1 7.1",
-        ("2. 2. 2. 3.4966629547095764 0.5033370452904236,"
+        states_str="2 4 4 4 20,1 1 1 1 5.5",
+        fluxes_str="4 11.2 8 8 46.4,1 2.6 1 1 7.1",
+        lam_str=("2. 2. 2. 3.4966629547095764 0.5033370452904236,"
             "1. 1. 1. 2.4966629547095764 -0.49666295470957644"),
-        "x")
+        direction="x")
 single_data["Case a:y"] = FluxDataSingle(
-        "2 4 4 4 20,1 1 1 1 5.5",
-        "4 8 11.2 8 46.4,1 1 2.6 1 7.1",
-        ("2. 2. 2. 3.4966629547095764 0.5033370452904236,"
+        states_str="2 4 4 4 20,1 1 1 1 5.5",
+        fluxes_str="4 8 11.2 8 46.4,1 1 2.6 1 7.1",
+        lam_str=("2. 2. 2. 3.4966629547095764 0.5033370452904236,"
             "1. 1. 1. 2.4966629547095764 -0.49666295470957644"),
-        "y")
+        direction="y")
 single_data["Case a:z"] = FluxDataSingle(
-        "2 4 4 4 20,1 1 1 1 5.5",
-        "4 8 8 11.2 46.4,1 1 1 2.6 7.1",
-        ("2. 2. 2. 3.4966629547095764 0.5033370452904236,"
+        states_str="2 4 4 4 20,1 1 1 1 5.5",
+        fluxes_str="4 8 8 11.2 46.4,1 1 1 2.6 7.1",
+        lam_str=("2. 2. 2. 3.4966629547095764 0.5033370452904236,"
             "1. 1. 1. 2.4966629547095764 -0.49666295470957644"),
-        "z")
+        direction="z")
 single_data["Case b:x"] = FluxDataSingle(
-        "1 -1 -1 -1 5.5,2 -4 -4 -4 20",
-        "-1 2.6 1 1 -7.1,-4 11.2 8 8 -46.4",
-        ("-1. -1. -1. 0.49666295470957644 -2.4966629547095764,"
+        states_str="1 -1 -1 -1 5.5,2 -4 -4 -4 20",
+        fluxes_str="-1 2.6 1 1 -7.1,-4 11.2 8 8 -46.4",
+        lam_str=("-1. -1. -1. 0.49666295470957644 -2.4966629547095764,"
             "-2. -2. -2. -0.5033370452904236 -3.4966629547095764"),
-        "x")
+        direction="x")
 single_data["Case b:y"] = FluxDataSingle(
-        "1 -1 -1 -1 5.5,2 -4 -4 -4 20",
-        "-1 1 2.6 1 -7.1,-4 8 11.2 8 -46.4",
-        ("-1. -1. -1. 0.49666295470957644 -2.4966629547095764,"
+        states_str="1 -1 -1 -1 5.5,2 -4 -4 -4 20",
+        fluxes_str="-1 1 2.6 1 -7.1,-4 8 11.2 8 -46.4",
+        lam_str=("-1. -1. -1. 0.49666295470957644 -2.4966629547095764,"
             "-2. -2. -2. -0.5033370452904236 -3.4966629547095764"),
-        "y")
+        direction="y")
 single_data["Case b:z"] = FluxDataSingle(
-        "1 -1 -1 -1 5.5,2 -4 -4 -4 20",
-        "-1 1 1 2.6 -7.1,-4 8 8 11.2 -46.4",
-        ("-1. -1. -1. 0.49666295470957644 -2.4966629547095764,"
+        states_str="1 -1 -1 -1 5.5,2 -4 -4 -4 20",
+        fluxes_str="-1 1 1 2.6 -7.1,-4 8 8 11.2 -46.4",
+        lam_str=("-1. -1. -1. 0.49666295470957644 -2.4966629547095764,"
             "-2. -2. -2. -0.5033370452904236 -3.4966629547095764"),
-        "z")
+        direction="z")
 single_data["Case c:x"] = FluxDataSingle(
-        "2 4 8 12 64,1 1 2 3 11",
-        "4 11.2 16 24 134.4,1 2.6 2 3 12.6",
-        ("2. 2. 2. 3.4966629547095764 0.5033370452904236,"
+        states_str="2 4 8 12 64,1 1 2 3 11",
+        fluxes_str="4 11.2 16 24 134.4,1 2.6 2 3 12.6",
+        lam_str=("2. 2. 2. 3.4966629547095764 0.5033370452904236,"
             "1. 1. 1. 2.4966629547095764 -0.49666295470957644"),
-        "x")
+        direction="x")
 single_data["Case c:y"] = FluxDataSingle(
-        "2 4 8 12 64,1 1 2 3 11",
-        "8 16 35.2 48 268.8,2 2 5.6 6 25.2",
-        ("4. 4. 4. 5.496662954709576 2.5033370452904236,"
+        states_str="2 4 8 12 64,1 1 2 3 11",
+        fluxes_str="8 16 35.2 48 268.8,2 2 5.6 6 25.2",
+        lam_str=("4. 4. 4. 5.496662954709576 2.5033370452904236,"
             "2. 2. 2. 3.4966629547095764 0.5033370452904236"),
-        "y")
+        direction="y")
 single_data["Case c:z"] = FluxDataSingle(
-        "2 4 8 12 64,1 1 2 3 11",
-        "12 24 48 75.2 403.2,3 3 6 10.6 37.8",
-        ("6. 6. 6. 7.496662954709576 4.503337045290424,"
+        states_str="2 4 8 12 64,1 1 2 3 11",
+        fluxes_str="12 24 48 75.2 403.2,3 3 6 10.6 37.8",
+        lam_str=("6. 6. 6. 7.496662954709576 4.503337045290424,"
             "3. 3. 3. 4.496662954709576 1.5033370452904236"),
-        "z")
+        direction="z")
 single_data["Case d:x"] = FluxDataSingle(
-        "1 -1 -2 -3 11,2 -4 -8 -12 64",
-        "-1 2.6 2 3 -12.6,-4 11.2 16 24 -134.4",
-        ("-1. -1. -1. 0.49666295470957644 -2.4966629547095764,"
+        states_str="1 -1 -2 -3 11,2 -4 -8 -12 64",
+        fluxes_str="-1 2.6 2 3 -12.6,-4 11.2 16 24 -134.4",
+        lam_str=("-1. -1. -1. 0.49666295470957644 -2.4966629547095764,"
             "-2. -2. -2. -0.5033370452904236 -3.4966629547095764"),
-        "x")
+        direction="x")
 single_data["Case d:y"] = FluxDataSingle(
-        "1 -1 -2 -3 11,2 -4 -8 -12 64",
-        "-2 2 5.6 6 -25.2,-8 16 35.2 48 -268.8",
-        ("-2. -2. -2. -0.5033370452904236 -3.4966629547095764,"
+        states_str="1 -1 -2 -3 11,2 -4 -8 -12 64",
+        fluxes_str="-2 2 5.6 6 -25.2,-8 16 35.2 48 -268.8",
+        lam_str=("-2. -2. -2. -0.5033370452904236 -3.4966629547095764,"
             "-4. -4. -4. -2.5033370452904236 -5.496662954709576"),
-        "y")
+        direction="y")
 single_data["Case d:z"] = FluxDataSingle(
-        "1 -1 -2 -3 11,2 -4 -8 -12 64",
-        "-3 3 6 10.6 -37.8,-12 24 48 75.2 -403.2",
-        ("-3. -3. -3. -1.5033370452904236 -4.496662954709576,"
+        states_str="1 -1 -2 -3 11,2 -4 -8 -12 64",
+        fluxes_str="-3 3 6 10.6 -37.8,-12 24 48 75.2 -403.2",
+        lam_str=("-3. -3. -3. -1.5033370452904236 -4.496662954709576,"
             "-6. -6. -6. -4.503337045290424 -7.496662954709576"),
-        "z")
+        direction="z")
 
 
 @pytest.fixture(scope="session", params=[