Beam search decoder.

        :param batch_size: decoder batch size
        :param initial_input: initial input, usually tensor of BOS tokens
        :param initial_context: initial context, usually [encoder_context,
            src_seq_lengths, None]

        returns: (translation, lengths, counter)
            translation: (batch_size, max_seq_len) - indices of target tokens
            lengths: (batch_size) - lengths of generated translations
            counter: number of iterations of the decoding loop

def beam_search(self, batch_size, initial_input, initial_context=None):
        """
        Beam search decoder.

        :param batch_size: decoder batch size
        :param initial_input: initial input, usually tensor of BOS tokens
        :param initial_context: initial context, usually [encoder_context,
            src_seq_lengths, None]

        returns: (translation, lengths, counter)
            translation: (batch_size, max_seq_len) - indices of target tokens
            lengths: (batch_size) - lengths of generated translations
            counter: number of iterations of the decoding loop
        """
        beam_size = self.beam_size
        norm_const = self.len_norm_const
        norm_factor = self.len_norm_factor
        max_seq_len = self.max_seq_len
        cov_penalty_factor = self.cov_penalty_factor

        translation = torch.zeros(batch_size * beam_size, max_seq_len,
                                  dtype=torch.int64)
        lengths = torch.ones(batch_size * beam_size, dtype=torch.int64)
        scores = torch.zeros(batch_size * beam_size, dtype=torch.float32)

        active = torch.arange(0, batch_size * beam_size, dtype=torch.int64)
        base_mask = torch.arange(0, batch_size * beam_size, dtype=torch.int64)
        global_offset = torch.arange(0, batch_size * beam_size, beam_size,
                                     dtype=torch.int64)

        eos_beam_fill = torch.tensor([0] + (beam_size - 1) * [float('-inf')])

        if self.cuda:
            translation = translation.cuda()
            lengths = lengths.cuda()
            active = active.cuda()
            base_mask = base_mask.cuda()
            scores = scores.cuda()
            global_offset = global_offset.cuda()
            eos_beam_fill = eos_beam_fill.cuda()

        translation[:, 0] = BOS

        words, context = initial_input, initial_context

        if self.batch_first:
            word_view = (-1, 1)
            ctx_batch_dim = 0
            attn_query_dim = 1
        else:
            word_view = (1, -1)
            ctx_batch_dim = 1
            attn_query_dim = 0

        # replicate context
        if self.batch_first:
            # context[0] (encoder state): (batch, seq, feature)
            _, seq, feature = context[0].shape
            context[0].unsqueeze_(1)
            context[0] = context[0].expand(-1, beam_size, -1, -1)
            context[0] = context[0].contiguous().view(batch_size * beam_size,
                                                      seq, feature)
            # context[0]: (batch * beam, seq, feature)
        else:
            # context[0] (encoder state): (seq, batch, feature)
            seq, _, feature = context[0].shape
            context[0].unsqueeze_(2)
            context[0] = context[0].expand(-1, -1, beam_size, -1)
            context[0] = context[0].contiguous().view(seq, batch_size *
                                                      beam_size, feature)
            # context[0]: (seq, batch * beam,  feature)

        # context[1] (encoder seq length): (batch)
        context[1].unsqueeze_(1)
        context[1] = context[1].expand(-1, beam_size)
        context[1] = context[1].contiguous().view(batch_size * beam_size)
        # context[1]: (batch * beam)

        accu_attn_scores = torch.zeros(batch_size * beam_size, seq)
        if self.cuda:
            accu_attn_scores = accu_attn_scores.cuda()

        counter = 0
        for idx in range(1, self.max_seq_len):
            if not len(active):
                break
            counter += 1

            eos_mask = (words == EOS)
            eos_mask = eos_mask.view(-1, beam_size)

            terminating, _ = eos_mask.min(dim=1)

            lengths[active[~eos_mask.view(-1)]] += 1

            output = self.model.generate(words, context, beam_size)
            words, logprobs, attn, context = output

            attn = attn.float().squeeze(attn_query_dim)
            attn = attn.masked_fill(eos_mask.view(-1).unsqueeze(1), 0)
            accu_attn_scores[active] += attn

            # words: (batch, beam, k)
            words = words.view(-1, beam_size, beam_size)
            words = words.masked_fill(eos_mask.unsqueeze(2), EOS)

            # logprobs: (batch, beam, k)
            logprobs = logprobs.float().view(-1, beam_size, beam_size)

            if eos_mask.any():
                logprobs[eos_mask] = eos_beam_fill

            active_scores = scores[active].view(-1, beam_size)
            # new_scores: (batch, beam, k)
            new_scores = active_scores.unsqueeze(2) + logprobs

            if idx == 1:
                new_scores[:, 1:, :].fill_(float('-inf'))

            new_scores = new_scores.view(-1, beam_size * beam_size)
            # index: (batch, beam)
            _, index = new_scores.topk(beam_size, dim=1)
            source_beam = index / beam_size

            new_scores = new_scores.view(-1, beam_size * beam_size)
            best_scores = torch.gather(new_scores, 1, index)
            scores[active] = best_scores.view(-1)

            words = words.view(-1, beam_size * beam_size)
            words = torch.gather(words, 1, index)

            # words: (1, batch * beam)
            words = words.view(word_view)

            offset = global_offset[:source_beam.shape[0]]
            source_beam += offset.unsqueeze(1)

            translation[active, :] = translation[active[source_beam.view(-1)], :]
            translation[active, idx] = words.view(-1)

            lengths[active] = lengths[active[source_beam.view(-1)]]

            context[2] = context[2].index_select(1, source_beam.view(-1))

            if terminating.any():
                not_terminating = ~terminating
                not_terminating = not_terminating.unsqueeze(1)
                not_terminating = not_terminating.expand(-1, beam_size).contiguous()

                normalization_mask = active.view(-1, beam_size)[terminating]

                # length normalization
                norm = lengths[normalization_mask].float()
                norm = (norm_const + norm) / (norm_const + 1.0)
                norm = norm ** norm_factor

                scores[normalization_mask] /= norm

                # coverage penalty
                penalty = accu_attn_scores[normalization_mask]
                penalty = penalty.clamp(0, 1)
                penalty = penalty.log()
                penalty[penalty == float('-inf')] = 0
                penalty = penalty.sum(dim=-1)

                scores[normalization_mask] += cov_penalty_factor * penalty

                mask = base_mask[:len(active)]
                mask = mask.masked_select(not_terminating.view(-1))

                words = words.index_select(ctx_batch_dim, mask)
                context[0] = context[0].index_select(ctx_batch_dim, mask)
                context[1] = context[1].index_select(0, mask)
                context[2] = context[2].index_select(1, mask)

                active = active.masked_select(not_terminating.view(-1))

        scores = scores.view(batch_size, beam_size)
        _, idx = scores.max(dim=1)

        translation = translation[idx + global_offset, :]
        lengths = lengths[idx + global_offset]

        return translation, lengths, counter