code: def construct_full_a(A_reduced, original_factor_idx, num_states):
      """
      Utility function for reconstruction a full A matrix from a reduced A matrix, using known factor indices
      to tile out the reduced A matrix along the 'non-informative' dimensions
      Parameters:
      ==========
      - `A_reduced` [np.ndarray]:
          The reduced A matrix or likelihood array that encodes probabilistic relationship
          of the generative model between hidden state factors (lagging dimensions, columns, slices, etc...)
          and observations (leading dimension, rows).
      - `original_factor_idx` [list]:
          List of hidden state indices in terms of the full hidden state factor list, that comprise
          the lagging dimensions of `A_reduced`
      - `num_states` [list]:
          The list of all the dimensionalities of hidden state factors in the full generative model.
          `A_reduced.shape[1:]` should be equal to `num_states[original_factor_idx]`
      Returns:
      =========
      - `A` [np.ndarray]:
          The full A matrix, containing all the lagging dimensions that correspond to hidden state factors, including
          those that are statistically independent of observations
  
      @ NOTE: This is the "inverse" of the reduce_a_matrix function,
      i.e. `reduce_a_matrix(construct_full_a(A_reduced, original_factor_idx, num_states)) == A_reduced, original_factor_idx`
      """
  
      o_dim = A_reduced.shape[
          0
      ]  # dimensionality of the support of the likelihood distribution (i.e. the number of observation levels)
      full_dimensionality = [
          o_dim
      ] + num_states  # full dimensionality of the output (`A`)
      fill_indices = [0] + [
          f + 1 for f in original_factor_idx
      ]  # these are the indices of the dimensions we need to fill for this modality
      fill_dimensions = np.delete(full_dimensionality, fill_indices)
  
      original_factor_dims = [
          num_states[f] for f in original_factor_idx
      ]  # dimensionalities of the relevant factors
      prefilled_slices = [slice(0, o_dim)] + [
          slice(0, ns) for ns in original_factor_dims
      ]  # these are the slices that are filled out by the provided `A_reduced`
  
      A = np.zeros(full_dimensionality)
  
      for item in itertools.product(
          *[list(range(d)) for d in fill_dimensions]
      ):
          slice_ = list(item)
          A_indices = insert_multiple(
              slice_, fill_indices, prefilled_slices
          )  # here we insert the correct values for the fill indices for this slice
          A[tuple(A_indices)] = A_reduced
  
      return A
  
imports: import numpy
  import pandas
  import seaborn
  import matplotlib.pyplot
  import warnings
  import itertools
label_desc: Use image node_id 28 for calling a global function with example usage: construct_full_a(A_reduced, original_factor_idx, num_states) and returns: A