def _forward_alg(self, feats):# Do the forward algorithm to compute the partition functioninit_alphas = torch.Tensor(1, self.tagset_size).fill_(-10000.)# START_TAG has all of the score.init_alphas[0][self.tag_to_ix[START_TAG]] = 0.# Wrap in a variable so that we will get automatic backpropforward_var = autograd.Variable(init_alphas)# Iterate through the sentencefor feat in feats:alphas_t = []  # The forward variables at this timestepfor next_tag in range(self.tagset_size):# broadcast the emission score: it is the same regardless of# the previous tagemit_score = feat[next_tag].view(1, -1).expand(1, self.tagset_size)# the ith entry of trans_score is the score of transitioning to# next_tag from itrans_score = self.transitions[next_tag].view(1, -1)# The ith entry of next_tag_var is the value for the# edge (i -> next_tag) before we do log-sum-expnext_tag_var = forward_var + trans_score + emit_score# The forward variable for this tag is log-sum-exp of all the# scores.alphas_t.append(log_sum_exp(next_tag_var))forward_var = torch.cat(alphas_t).view(1, -1)terminal_var = forward_var + self.transitions[self.tag_to_ix[STOP_TAG]]alpha = log_sum_exp(terminal_var)return alpha

def _viterbi_decode(self, feats):backpointers = []# Initialize the viterbi variables in log spaceinit_vvars = torch.Tensor(1, self.tagset_size).fill_(-10000.)init_vvars[0][self.tag_to_ix[START_TAG]] = 0# forward_var at step i holds the viterbi variables for step i-1forward_var = autograd.Variable(init_vvars)for feat in feats:bptrs_t = []  # holds the backpointers for this stepviterbivars_t = []  # holds the viterbi variables for this stepfor next_tag in range(self.tagset_size):# next_tag_var[i] holds the viterbi variable for tag i at the# previous step, plus the score of transitioning# from tag i to next_tag.# We don't include the emission scores here because the max# does not depend on them (we add them in below)next_tag_var = forward_var + self.transitions[next_tag]best_tag_id = argmax(next_tag_var)bptrs_t.append(best_tag_id)viterbivars_t.append(next_tag_var[0][best_tag_id])# Now add in the emission scores, and assign forward_var to the set# of viterbi variables we just computedforward_var = (torch.cat(viterbivars_t) + feat).view(1, -1)backpointers.append(bptrs_t)# Transition to STOP_TAGterminal_var = forward_var + self.transitions[self.tag_to_ix[STOP_TAG]]best_tag_id = argmax(terminal_var)path_score = terminal_var[0][best_tag_id]# Follow the back pointers to decode the best path.best_path = [best_tag_id]for bptrs_t in reversed(backpointers):best_tag_id = bptrs_t[best_tag_id]best_path.append(best_tag_id)# Pop off the start tag (we dont want to return that to the caller)start = best_path.pop()assert start == self.tag_to_ix[START_TAG]  # Sanity checkbest_path.reverse()return path_score, best_path