APSOLU3                 package:PTAk                 R Documentation

_A_s_s_o_c_i_a_t_e_d _3-_m_o_d_e_s _P_r_i_n_c_i_p_a_l _T_e_n_s_o_r_s _o_f _a _3-_m_o_d_e_s
_P_r_i_n_c_i_p_a_l _T_e_n_s_o_r

_D_e_s_c_r_i_p_t_i_o_n:

     Computes all the 2-modes solutions associated to the given
     Principal Tensor of the given tensor.

_U_s_a_g_e:

     APSOLU3((X,solu,pt3=NULL,nbPT2=1,
                      smoothing=FALSE,smoo=list(NA),
                             verbose=getOption("verbose"),file=NULL )

_A_r_g_u_m_e_n_t_s:

       X: a tensor (as an array) of order _3_, if non-identity metrics
          are used 'X' is a list with 'data'  as the array and 'met' a
          list of metrics 

    solu: a 'PTAk' object

     pt3: a number identifying in 'solu' the Principal Tensor to use or
          the last (if 'NULL')

   nbPT2: integer, if 1 all solutions will be computed otherwise at
          maximum nbPT2  solutions

smoothing: see 'SVDgen'

    smoo: see 'PTA3'

 verbose: control printing

    file: output printed at the prompt if 'NULL', or printed in the
          given  'file'

_D_e_t_a_i_l_s:

     For each component of the identified Principal Tensor given in
     'solu', an SVD of the contracted product of 'X' and the component
     is done. This gives all the associated Principal Tensors which
     updates 'solu' supposed to contain Principal Tensors of 'X'.

_V_a_l_u_e:

     an updated 'PTAk' object

_N_o_t_e:

     Usually (i.e. as in 'PTA3' and 'PTAk') the principal tensor used
     is the first Principal Tensor of X (and is the last updated in
     'solu'). If it is another Principal Tensor, the obtained
     associated solutions do not _stricto sensu_ refer to the
     SVD-_k_modes decomposition (because the orthogonality is defined
     in the whole tensor space not necessarily on each component space)
     but are still meaningful.

_A_u_t_h_o_r(_s):

     Didier Leibovici c3s2i@free.fr

_R_e_f_e_r_e_n_c_e_s:

     Leibovici D and Sabatier R (1998) _A Singular Value Decomposition
     of a k-ways array for a Principal Component Analysis of multi-way
     data, the PTA-k_. Linear Algebra and its Applications, 269:307-329

_S_e_e _A_l_s_o:

     'PTA3', 'APSOLUk'

