generate force with autograd

generation_autograd.py

@@ -6,6 +6,8 @@ from numpy import fft as f
 from autograd import grad, jacobian
 from autograd import elementwise_grad as egrad
 
+##
+# parameters
 d=2
 
 #dx=0.02
@@ -24,8 +26,9 @@ l_cA=0.3
 alpha_A=1
 alpha_V=1
 
-v=1.0
-a=1.0
+e=0.2
+v=e
+a=1-e
 
 def gamma_V_func(r):
     return v**2*np.exp(-1/2*(r/l_cV)**(2*alpha_V))
@@ -84,9 +87,37 @@ def Gamma_AX(x,Y):
     r=npa.sqrt(((Y-x)**2).sum(axis=-1))
     return a**2*npa.exp(-(r/l_cA)**alpha_A)
 
+#potential and vector potential functions ready to use
+
 def V_func(x,Y=Y):
     return npa.dot(Gamma_VX(x,Y),KV)
 
 def A_func(x,Y=Y):
     return npa.tensordot(Gamma_AX(x,Y),KA,[[1],[2]])
 
+## generate force
+
+nablaV=egrad(V_func,argnum=0)
+
+
+coordA={}
+for i in range(1,d):
+    for j in range(i):
+        def A_coord(x,Y=Y):
+            AT=npa.tensordot(Gamma_AX(x,Y),KA,[[1],[2]]).T
+            return AT[i,j,:]
+        coordA[(i,j)]=egrad(A_coord)
+def jacobA(x,coordA=coordA):
+    JA=np.zeros((d,d)+x.shape)
+    for i in range(1,d):
+        for j in range(i):
+            JA[i,j,:]=coordA[(i,j)](x)
+            JA[j,i,:]=-JA[i,j,:]
+    return JA
+
+def rotA(x):
+    jacA=jacobA(x)*1/np.sqrt(2)
+    return np.einsum('ij...j -> ...i',jacA)
+
+
+