# Copyright (c) 2023, NVIDIA CORPORATION.  All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
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# See the License for the specific language governing permissions and
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import torch
from utils.constants import V_NEGATIVE_NUM


def viterbi_decoding(log_probs_batch, y_batch, T_batch, U_batch, viterbi_device):
    """
    Do Viterbi decoding with an efficient algorithm (the only for-loop in the 'forward pass' is over the time dimension). 
    Args:
        log_probs_batch: tensor of shape (B, T_max, V). The parts of log_probs_batch which are 'padding' are filled
            with 'V_NEGATIVE_NUM' - a large negative number which represents a very low probability.
        y_batch: tensor of shape (B, U_max) - contains token IDs including blanks in every other position. The parts of
            y_batch which are padding are filled with the number 'V'. V = the number of tokens in the vocabulary + 1 for
            the blank token.
        T_batch: tensor of shape (B, 1) - contains the durations of the log_probs_batch (so we can ignore the 
            parts of log_probs_batch which are padding)
        U_batch: tensor of shape (B, 1) - contains the lengths of y_batch (so we can ignore the parts of y_batch
            which are padding).
        viterbi_device: the torch device on which Viterbi decoding will be done.

    Returns:
        alignments_batch: list of lists containing locations for the tokens we align to at each timestep.
            Looks like: [[0, 0, 1, 2, 2, 3, 3, ...,  ], ..., [0, 1, 2, 2, 2, 3, 4, ....]].
            Each list inside alignments_batch is of length T_batch[location of utt in batch].
    """
    B, T_max, _ = log_probs_batch.shape
    U_max = y_batch.shape[1]

    # transfer all tensors to viterbi_device
    log_probs_batch = log_probs_batch.to(viterbi_device)
    y_batch = y_batch.to(viterbi_device)
    T_batch = T_batch.to(viterbi_device)
    U_batch = U_batch.to(viterbi_device)

    # make tensor that we will put at timesteps beyond the duration of the audio
    padding_for_log_probs = V_NEGATIVE_NUM * torch.ones((B, T_max, 1), device=viterbi_device)
    # make log_probs_padded tensor of shape (B, T_max, V +1 ) where all of
    # log_probs_padded[:,:,-1] is the 'V_NEGATIVE_NUM'
    log_probs_padded = torch.cat((log_probs_batch, padding_for_log_probs), dim=2)
    # make log_probs_reordered tensor of shape (B, T_max, U_max)
    # it contains the log_probs for only the tokens that are in the Ground Truth, and in the order
    # that they occur
    log_probs_reordered = torch.gather(input=log_probs_padded, dim=2, index=y_batch.unsqueeze(1).repeat(1, T_max, 1))

    # initialize tensors of viterbi probabilies and backpointers
    v_matrix = V_NEGATIVE_NUM * torch.ones_like(log_probs_reordered)
    backpointers = -999 * torch.ones_like(v_matrix)
    v_matrix[:, 0, :2] = log_probs_reordered[:, 0, :2]

    # Make a letter_repetition_mask the same shape as y_batch
    # the letter_repetition_mask will have 'True' where the token (including blanks) is the same
    # as the token two places before it in the ground truth (and 'False everywhere else).
    # We will use letter_repetition_mask to determine whether the Viterbi algorithm needs to look two tokens back or
    # three tokens back
    y_shifted_left = torch.roll(y_batch, shifts=2, dims=1)
    letter_repetition_mask = y_batch - y_shifted_left
    letter_repetition_mask[:, :2] = 1  # make sure dont apply mask to first 2 tokens
    letter_repetition_mask = letter_repetition_mask == 0

    # bp_absolute_template is a tensor we will need during the Viterbi decoding to convert our argmaxes from indices between 0 and 2,
    # to indices in the range (0, U_max-1) indicating from which token the mostly path up to that point came from.
    # it is a tensor of shape (B, U_max) that looks like
    # bp_absolute_template = [
    #   [0, 1, 2, ...,, U_max]
    #   [0, 1, 2, ...,, U_max]
    #   [0, 1, 2, ...,, U_max]
    #   ... rows repeated so there are B number of rows in total
    # ]
    bp_absolute_template = torch.arange(U_max, device=viterbi_device).unsqueeze(0).repeat(B, 1)

    for t in range(1, T_max):

        # e_current is a tensor of shape (B, U_max) of the log probs of every possible token at the current timestep
        e_current = log_probs_reordered[:, t, :]

        # v_prev is a tensor of shape (B, U_max) of the viterbi probabilities 1 timestep back and in the same token position
        v_prev = v_matrix[:, t - 1, :]

        # v_prev_shifted is a tensor of shape (B, U_max) of the viterbi probabilities 1 timestep back and 1 token position back
        v_prev_shifted = torch.roll(v_prev, shifts=1, dims=1)
        # by doing a roll shift of size 1, we have brought the viterbi probability in the final token position to the
        # first token position - let's overcome this by 'zeroing out' the probabilities in the firest token position
        v_prev_shifted[:, 0] = V_NEGATIVE_NUM

        # v_prev_shifted2 is a tensor of shape (B, U_max) of the viterbi probabilities 1 timestep back and 2 token position back
        v_prev_shifted2 = torch.roll(v_prev, shifts=2, dims=1)
        v_prev_shifted2[:, :2] = V_NEGATIVE_NUM  # zero out as we did for v_prev_shifted
        # use our letter_repetition_mask to remove the connections between 2 blanks (so we don't skip over a letter)
        # and to remove the connections between 2 consective letters (so we don't skip over a blank)
        v_prev_shifted2.masked_fill_(letter_repetition_mask, V_NEGATIVE_NUM)

        # we need this v_prev_dup tensor so we can calculated the viterbi probability of every possible
        # token position simultaneously
        v_prev_dup = torch.cat(
            (v_prev.unsqueeze(2), v_prev_shifted.unsqueeze(2), v_prev_shifted2.unsqueeze(2),), dim=2,
        )

        # candidates_v_current are our candidate viterbi probabilities for every token position, from which
        # we will pick the max and record the argmax
        candidates_v_current = v_prev_dup + e_current.unsqueeze(2)
        v_current, bp_relative = torch.max(candidates_v_current, dim=2)

        # convert our argmaxes from indices between 0 and 2, to indices in the range (0, U_max-1) indicating
        # from which token the mostly path up to that point came from
        bp_absolute = bp_absolute_template - bp_relative

        # update our tensors containing all the viterbi probabilites and backpointers
        v_matrix[:, t, :] = v_current
        backpointers[:, t, :] = bp_absolute

    # trace backpointers TODO: parallelize over batch_size
    alignments_batch = []
    for b in range(B):
        T_b = int(T_batch[b])
        U_b = int(U_batch[b])

        final_state = int(torch.argmax(v_matrix[b, T_b - 1, U_b - 2 : U_b])) + U_b - 2
        alignment_b = [final_state]
        for t in range(T_b - 1, 0, -1):
            alignment_b.insert(0, int(backpointers[b, t, alignment_b[0]]))
        alignments_batch.append(alignment_b)

    return alignments_batch