# tensorly.parafac2_tensor.parafac2_to_slice

parafac2_to_slice(parafac2_tensor, slice_idx, validate=True)[source]

Generate a single slice along the first mode from the PARAFAC2 tensor.

The decomposition is on the form such that the i-th frontal slice, , of is given by

where is the diagonal matrix whose nonzero entries are equal to the -th row of the factor matrix , is a factor matrix such that the cross product matrix is constant for all , and is a factor matrix. To compute this decomposition, we reformulate the expression for such that

where is a orthogonal matrix and is a matrix.

An alternative formulation of the PARAFAC2 decomposition is that the tensor element is given by

with the same constraints hold for as above.

Parameters: parafac2_tensorParafac2Tensor - (weight, factors, projection_matrices) weights1D array of shape (rank, )weights of the factors factorsList of factors of the PARAFAC2 decompositionContains the matrices , and described above projection_matricesList of projection matrices used to create evolvingfactors. ndarrayFull tensor of shape [P[slice_idx].shape[1], C.shape[1]], where P is the projection matrices and C is the last factor matrix of the Parafac2Tensor.