From 8a6fccf3739febbb24a5bcb2264faa41954a75ad Mon Sep 17 00:00:00 2001
From: Shaurya Shukla <shauryabhushanshukla@gmail.com>
Date: Thu, 24 Sep 2026 18:10:29 -0400
Subject: [PATCH] fix modified inductance element La to match its documented
 definition

La computed (L * j * omega)^alpha, which also raises L to the power alpha.
The docs (and EC-Lab's definition) give Z = L * (j * omega)^alpha. Fix the
formula, update the La reference values in test_each_element, add a test
that Z is linear in L, and correct the units of L to H sec^(a - 1).

Fixes #312
---
 impedance/models/circuits/elements.py    |  4 ++--
 impedance/tests/test_circuit_elements.py | 15 ++++++++++++---
 2 files changed, 14 insertions(+), 5 deletions(-)

diff --git a/impedance/models/circuits/elements.py b/impedance/models/circuits/elements.py
index fa067407..d72009ec 100644
--- a/impedance/models/circuits/elements.py
+++ b/impedance/models/circuits/elements.py
@@ -208,7 +208,7 @@ def CPE(p, f):
     return Z
 
 
-@element(num_params=2, units=["H sec", ""])
+@element(num_params=2, units=["H sec^(a - 1)", ""])
 def La(p, f):
     """defines a modified inductance element as represented in [1]
 
@@ -225,7 +225,7 @@ def La(p, f):
     """
     omega = 2 * np.pi * np.array(f)
     L, alpha = p[0], p[1]
-    Z = (L * 1j * omega) ** alpha
+    Z = L * (1j * omega) ** alpha
     return Z
 
 
diff --git a/impedance/tests/test_circuit_elements.py b/impedance/tests/test_circuit_elements.py
index 5276c44e..d0199372 100644
--- a/impedance/tests/test_circuit_elements.py
+++ b/impedance/tests/test_circuit_elements.py
@@ -40,9 +40,9 @@ def test_each_element():
             (1.6541327179718126 - 0.537460300252313j),
         ],
         "La": [
-            (0.21769191 + 0.07073239j),
-            (0.86664712 + 0.28159072j),
-            (3.45018434 + 1.12103285j),
+            (0.03450184 + 0.01121033j),
+            (0.13735431 + 0.04462912j),
+            (0.54681737 + 0.17767173j),
         ],
         "G": [
             (0.09999994078244179 - 0.00006283179105931961j),
@@ -98,6 +98,15 @@ def test_each_element():
         circuit_elements["T"]([1, 2, 50, 100], [10000])
 
 
+def test_La_linear_in_L():
+    # Z = L * (j omega)^alpha, so doubling L must double Z for any alpha
+    freqs = [0.001, 1.0, 1000]
+    La = circuit_elements["La"]
+    Z1 = La([0.1, 0.7], freqs)
+    Z2 = La([0.2, 0.7], freqs)
+    assert np.isclose(Z2, 2 * Z1).all()
+
+
 def test_s():
     a = np.array([5 + 6 * 1j, 2 + 3 * 1j])
     b = np.array([5 + 6 * 1j, 2 + 3 * 1j])