diff --git a/mbtrack2/utilities/misc.py b/mbtrack2/utilities/misc.py
index 87cb942cef012e5e156a2245d5c5ac9a802c20ef..7e29f9fd9980a7a08bc04288c91f3eb6a6551efa 100644
--- a/mbtrack2/utilities/misc.py
+++ b/mbtrack2/utilities/misc.py
@@ -301,7 +301,7 @@ def yokoya_elliptic(x_radius, y_radius):
 
             ip_range = np.arange(50)
             il_range = np.arange(50)
-            ip, il = np.meshgrid(ip_range, il_range, indexing='ij')
+            ip, il = np.meshgrid(ip_range, il_range, indexing="ij")
 
             ff_values = np.array(function_ff(small_semiaxis_th, F_th, mu_b_th, ip, il))
             L_values = np.array(function_L(mu_b_th, ip, il))
@@ -341,7 +341,7 @@ def yokoya_elliptic(x_radius, y_radius):
 
             ip_range = np.arange(50)
             il_range = np.arange(50)
-            ip, il = np.meshgrid(ip_range, il_range, indexing='ij')
+            ip, il = np.meshgrid(ip_range, il_range, indexing="ij")
 
             ff_values = np.array(function_ff(small_semiaxis, F, mu_b, ip, il))
             L_values = np.array(function_L(mu_b, ip, il))