docstr: Computes RNN outputs by unrolling the LSTM starting with a initial
  input and state.
  
  Parameters
  ----------
  static_feat : Tensor
      static features. Shape: (batch_size, num_static_features).
  past_target : Tensor
      target history. Shape: (batch_size, history_length).
  time_feat : Tensor
      time features. Shape: (batch_size, prediction_length,
      num_time_features).
      Note: They still need to be for all `prediction_length` time steps.
      This function will slice the features it needs.
  scale : Tensor
      tensor containing the scale of each element in the batch.
      Shape: (batch_size, 1, 1).
  begin_states : List
      list of initial states for the LSTM layers. The shape of each
      tensor of the list should be (batch_size, num_cells)
  Returns
  --------
  Tensor
      A tensor containing sampled paths.
      Shape: (batch_size, num_sample_paths, window_size).
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code: def _decode_one_window(
      self,
      F,
      model: DeepARPredictionNetwork,
      window_size: int,
      offset: int,
      static_feat: Tensor,
      past_target: Tensor,
      time_feat: Tensor,
      scale: Tensor,
      begin_states: List,
  ) -> Tuple[Tensor, Tensor]:
      """
      Computes RNN outputs by unrolling the LSTM starting with a initial
      input and state.
  
      Parameters
      ----------
      static_feat : Tensor
          static features. Shape: (batch_size, num_static_features).
      past_target : Tensor
          target history. Shape: (batch_size, history_length).
      time_feat : Tensor
          time features. Shape: (batch_size, prediction_length,
          num_time_features).
          Note: They still need to be for all `prediction_length` time steps.
          This function will slice the features it needs.
      scale : Tensor
          tensor containing the scale of each element in the batch.
          Shape: (batch_size, 1, 1).
      begin_states : List
          list of initial states for the LSTM layers. The shape of each
          tensor of the list should be (batch_size, num_cells)
      Returns
      --------
      Tensor
          A tensor containing sampled paths.
          Shape: (batch_size, num_sample_paths, window_size).
      """
  
      rnn_outputs_ls = []
  
      # for each future time-units we draw new samples for this time-unit and
      # update the state
      for k in range(offset, offset + window_size):
          # (batch_size * num_samples, 1, *target_shape, num_lags)
          lags = model.get_lagged_subsequences(
              F=F,
              sequence=past_target,
              sequence_length=model.history_length + k,
              indices=model.shifted_lags,
              subsequences_length=1,
          )
  
          # (batch_size * num_samples, 1, *target_shape, num_lags)
          lags_scaled = F.broadcast_div(
              lags, scale.expand_dims(axis=-1)
          )
  
          # from (batch_size * num_samples, 1, *target_shape, num_lags)
          # to (batch_size * num_samples, 1, prod(target_shape) * num_lags)
          input_lags = F.reshape(
              data=lags_scaled,
              shape=(
                  -1,
                  1,
                  prod(model.target_shape) * len(model.lags_seq),
              ),
          )
  
          # (batch_size * num_samples, 1, prod(target_shape) * num_lags +
          # num_time_features + num_static_features)
          decoder_input = F.concat(
              input_lags,
              time_feat.slice_axis(axis=1, begin=k, end=k + 1),
              # observed_values.expand_dims(axis=1),
              static_feat,
              dim=-1,
          )
  
          # output shape: (batch_size * num_samples, 1, num_cells)
          # state shape: (batch_size * num_samples, num_cells)
          rnn_outputs, begin_states = model.rnn.unroll(
              inputs=decoder_input,
              length=1,
              begin_state=begin_states,
              layout="NTC",
              merge_outputs=True,
          )
          rnn_outputs_ls.append(rnn_outputs)
  
          distr_args = model.proj_distr_args(rnn_outputs)
  
          # compute likelihood of target given the predicted parameters
          distr = model.distr_output.distribution(
              distr_args, scale=scale
          )
  
          # (batch_size * num_samples, 1, *target_shape)
  
          new_samples = distr.sample(dtype=self.dtype)
  
          # (batch_size * num_samples, seq_len, *target_shape)
          past_target = F.concat(past_target, new_samples, dim=1)
  
      # (batch_size * num_samples, prediction_length, *target_shape)
      rnn_outputs = F.concat(*rnn_outputs_ls, dim=1)
  
      return rnn_outputs, begin_states
  
imports: from typing import Dict, List, Optional, Tuple
  import mxnet
  import numpy
  from gluonts.core.component import Type, validated
  from gluonts.itertools import prod
  from gluonts.mx.model.deepar import DeepAREstimator
  from gluonts.mx.model.deepar._network import DeepARPredictionNetwork
  from gluonts.mx.model.deepvar_hierarchical._estimator import projection_mat
  from gluonts.mx.model.deepvar_hierarchical._network import coherency_error
  from gluonts.mx.distribution import Distribution, EmpiricalDistribution
  from gluonts.mx import Tensor
  from gluonts.mx.distribution import TransformedPiecewiseLinear
  from gluonts.nursery.temporal_hierarchical_forecasting.utils import utils
  from gluonts.nursery.temporal_hierarchical_forecasting.model.cop_deepar import gluonts_fixes, gnn
label_desc: Use image node_id 2 for calling the COPDeepARPredictionNetwork obj's underlying member method code with example usage: obj._decode_one_window(F, model, window_size, offset, static_feat, past_target, time_feat, scale, begin_states) and returns: rnn_outputs,  begin_states