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 `solutions.PTAk object' see `is.solutions.PTAk'

     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 `solutions.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-kmodes
     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 didier@fmrib.ox.ac.uk

_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'

