code: def apply_parafac2_projections(parafac2_tensor):
      r"""Apply the projection matrices to the evolving factor.
  
      Parameters
      ----------
      parafac2_tensor : Parafac2Tensor
  
      Returns
      -------
      (weights, factors) : ndarray, tuple
          A tensor decomposition on the form A [B_i] C such that
          the :math:`X_{ijk}` is given by :math:`\sum_r A_{ir} [B_i]_{jr} C_{kr}`.
  
          This is also equivalent to a coupled matrix factorisation, where
          each matrix, :math:`X_i = C diag([a_{i1}, ..., a_{ir}] B_i)`.
  
          The first element of factors is the A matrix, the second element is
          a list of B-matrices and the third element is the C matrix.
      """
      _validate_parafac2_tensor(parafac2_tensor)
      weights, factors, projections = parafac2_tensor
  
      evolving_factor = [
          T.dot(projection, factors[1]) for projection in projections
      ]
  
      return weights, (factors[0], evolving_factor, factors[2])
  
imports: from .None import backend
  from .base import unfold, tensor_to_vec
  from ._factorized_tensor import FactorizedTensor
label_desc: Use image node_id 3 for calling a global function with example usage: apply_parafac2_projections(parafac2_tensor) and returns: weights,  factors,  evolving_factor,  factors