Replace jnp.interp with interpax.interp1d in thermo.py

Follow-up to PR #16 which replaced jnp.interp with interpax in abundances.py.
This change applies the same improvement to thermo.py for consistency and
better performance.

Changes:
- Import interpax module
- Flip QED correction tables at load time (instead of at each call) for
  monotonically increasing x coordinates required by interpax
- Replace 6 jnp.interp calls with interpax.interp1d:
  - rho_EM_std: 2 calls for QED corrections
  - p_EM_std: 1 call for QED correction
  - rho_plus_p_EM_std: 1 call for QED correction
  - G_nue_with_me: 1 call for collision factor interpolation
  - G_numt_with_me: 1 call for collision factor interpolation

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

Author: smsharma

linx/thermo.py

@@ -1,10 +1,11 @@
-import os 
+import os
 
 import numpy as np
 
-import jax.numpy as jnp 
+import jax.numpy as jnp
 import jax.lax as lax
 from jax import grad, vmap, device_put, devices
+import interpax
 
 import linx.const as const 
 from linx.special_funcs import Li, K1, K2
@@ -633,10 +634,10 @@ def p_massive_MB(T, mu, m, g):
 
 file_dir = os.path.dirname(__file__)
 
-# QED Corrections
-P_QED_tab = np.loadtxt(file_dir+"/data/background/"+"QED_P_int.txt")
-dPdT_QED_tab = np.loadtxt(file_dir+"/data/background/"+"QED_dP_intdT.txt")
-d2PdT2_QED_tab = np.loadtxt(file_dir+"/data/background/"+"QED_d2P_intdT2.txt")
+# QED Corrections - flip to ensure monotonically increasing T for interpax.interp1d
+P_QED_tab = np.flip(np.loadtxt(file_dir+"/data/background/"+"QED_P_int.txt"), axis=0)
+dPdT_QED_tab = np.flip(np.loadtxt(file_dir+"/data/background/"+"QED_dP_intdT.txt"), axis=0)
+d2PdT2_QED_tab = np.flip(np.loadtxt(file_dir+"/data/background/"+"QED_d2P_intdT2.txt"), axis=0)
 
 # Effect of standard value of electron mass in scattering matrix elements
 f_nue_scat_tab = np.loadtxt(file_dir+"/data/background/"+"nue_scatt.txt")
@@ -704,13 +705,13 @@ def rho_EM_std(T_g, mu=0, LO=True, NLO=True):
     """ 
 
     corr_QED = (
-        -jnp.interp(
-            T_g, jnp.flip(P_QED_tab[:,0]), 
-            jnp.flip(LO*P_QED_tab[:,1]+NLO*P_QED_tab[:,2])
-        ) 
-        + T_g*jnp.interp(
-            T_g, jnp.flip(dPdT_QED_tab[:,0]),
-            jnp.flip(LO*dPdT_QED_tab[:,1]+NLO*dPdT_QED_tab[:,2])
+        -interpax.interp1d(
+            T_g, P_QED_tab[:,0],
+            LO*P_QED_tab[:,1]+NLO*P_QED_tab[:,2]
+        )
+        + T_g*interpax.interp1d(
+            T_g, dPdT_QED_tab[:,0],
+            LO*dPdT_QED_tab[:,1]+NLO*dPdT_QED_tab[:,2]
         )
     )
 
@@ -745,9 +746,9 @@ def p_EM_std(T_g, mu=0, LO=True, NLO=True):
         Units of MeV^4. 
     """ 
 
-    corr_QED = jnp.interp(
-        T_g, jnp.flip(P_QED_tab[:,0]),
-        jnp.flip(LO*P_QED_tab[:,1] + NLO*P_QED_tab[:,2])
+    corr_QED = interpax.interp1d(
+        T_g, P_QED_tab[:,0],
+        LO*P_QED_tab[:,1] + NLO*P_QED_tab[:,2]
     )
 
     return (
@@ -781,9 +782,9 @@ def rho_plus_p_EM_std(T_g, mu=0, LO=True, NLO=True):
         Units of MeV^4. 
     """ 
 
-    corr_QED = T_g * jnp.interp(
-        T_g, jnp.flip(dPdT_QED_tab[:,0]),
-        jnp.flip(LO*dPdT_QED_tab[:,1] + NLO*dPdT_QED_tab[:,2])
+    corr_QED = T_g * interpax.interp1d(
+        T_g, dPdT_QED_tab[:,0],
+        LO*dPdT_QED_tab[:,1] + NLO*dPdT_QED_tab[:,2]
     )
 
     return (
@@ -1018,10 +1019,10 @@ def G(T_1, mu_1, T_2, mu_2):
 
     def G_nue_with_me(T_1, mu_1, T_2, mu_2):
 
-        def interp_f(f_tab): 
-
-            return jnp.interp(
-                T_1, f_tab[:,0], f_tab[:,1], left=f_tab[0,1], right=f_tab[-1,1]
+        def interp_f(f_tab):
+            # Tables have boundary values 0.0 (low T) and 1.0 (high T)
+            return interpax.interp1d(
+                T_1, f_tab[:,0], f_tab[:,1], extrap=(0.0, 1.0)
             )
 
         f_nue_ann  = lax.cond(
@@ -1042,12 +1043,12 @@ def interp_f(f_tab):
             )
         )
 
-    def G_numt_with_me(T_1, mu_1, T_2, mu_2): 
-
-        def interp_f(f_tab): 
+    def G_numt_with_me(T_1, mu_1, T_2, mu_2):
 
-            return jnp.interp(
-                T_1, f_tab[:,0], f_tab[:,1], left=f_tab[0,1], right=f_tab[-1,1]
+        def interp_f(f_tab):
+            # Tables have boundary values 0.0 (low T) and 1.0 (high T)
+            return interpax.interp1d(
+                T_1, f_tab[:,0], f_tab[:,1], extrap=(0.0, 1.0)
             )
 
         f_numt_ann  = lax.cond(