2nd order derivative w.r.t. h

dhotrg.py

@@ -74,13 +74,16 @@ def main(beta, h=0.):
 
     T = build_tensor(beta, beta*h)
     lnZ = model.forward(T, args.use_checkpoint)
-    lnZ.backward()
-
-    m = h.grad/beta # m = 1/beta * dlnZ / dh
-
+    lnZ.backward(create_graph=True)
+    m = (h.grad).item() # dlnZ /d h  
+    
+    h.grad.backward()
+    m2 = (h.grad).item() -m # second order gradient d^2 lnZ/dh^2 
+    
+    m = torch.sqrt(m2/beta**2/2.0**args.niter)
     print ('beta, lnZ, m', beta.item(), lnZ.item(), m.item())
 
-    return lnZ, m  
+    return lnZ, m
 
 def scan_beta():