def forward(self,x):
'''
Implement the symmetries of the state
:param x: nsamplesx12 vector, where the first (last) 6 components correspond to a single spin
:return: <x|psi>
'''
x.to(self.device)
# We start by implementing the c3v+I slicing
# output -> inv nsamples*24x12
inv = torch.zeros(size=(self.group_elements * x.shape[0], x.shape[1]))
for i, T in enumerate(self.Ts):
inv[i::self.group_elements, :] = x.mm(T)
# We then apply the first convolutional network to each element
for l in self.conv1:
inv = torch.relu(l.forward(inv))
inv=self.conv1_output.forward(inv)
# Then we apply the rolling step
#index = np.asarray([np.roll(np.arange(self.group_elements) + i * self.group_elements, j) for i in np.arange(x.shape[0]) for j in np.arange(self.group_elements)])
#inv2 = inv[index,:].flatten(1)
# Now we can get perform the dense operations
# We then apply the first convolutional network to each element
#for l in self.dense:
# inv2 = torch.relu(l.forward(inv2))
#inv = self.dense_output.forward(inv2)
# Finally, we perform the pooling
pool = torch.nn.AvgPool1d(self.group_elements)
value = pool.forward(inv.flatten().unsqueeze(0).unsqueeze(1)).squeeze()
# We still have to define the sign before the value, because of the anticommutation rules
state = x.cpu().detach().numpy()[0]
hex_order = [0,1,3,5,4,2,6,7,9,11,10,8]
# keep track of the current order
order = state * np.arange(1, 13)
# then, put it in the hex order
state_in_hex = order[hex_order]
# get the non-0 elements
state_in_hex = state_in_hex[np.where(state_in_hex > 0.1)]
# get the ordered indices
order = np.argsort(state_in_hex)
# create a permutation
perm = Permutation(order)
# print the sign
sign = perm.signature()
return sign*value
