APSOLUk                 package:PTAk                 R Documentation

_A_s_s_o_c_i_a_t_e_d _k-_m_o_d_e_s _P_r_i_n_c_i_p_a_l _T_e_n_s_o_r_s _o_f _a _k-_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 (k-1)-modes associated solutions to the given
     Principal Tensor of the given tensor. Calls recursively PTAk.

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

      APSOLUk(X,solu,nbPT,nbPT2=1,
                            smoothing=FALSE,smoo=list(NA),
                             minpct=0.1,ptk=NULL,
                              verbose=getOption("verbose"),file=NULL,
                               modesnam=NULL)

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

       X: a tensor (as an array) of order _k_, 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 

    nbPT: a number or a vector of dimension _(k-2)_

   nbPT2: integer, if 0 no 2-modes solutions will be computed, 1 means
          all, >1 otherwise

smoothing: see 'SVDgen'

    smoo: see 'PTA3'

  minpct: numerical 0-100 to control of computation of future solutions
          at this level and below

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

 verbose: control printing

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

modesnam: character vector of the names of the modes, if 'NULL' "'mo
          1'" ..."'mo k'"

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

     For each component of the identified  Principal Tensor given in
     'solutions', a PTA-_(k-1)_modes of the contracted product of X and
     the component is done. This gives all the associated Principal
     Tensors which updates  'solutions' supposed to contain a Principal
     Tensors of X at the first place. For full description of arguments
     see 'PTAk'.

_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
     'solutions'). 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. This function is usually called by
     'PTAk' but can be used on its own to carry on a 'PTAk' analysis if
     'X' is the projected (of the original data) on the orthogonal of
     all the _k_modes Principal Tensor. In other words the 'ptk'
     rank-one tensor in 'solutions' should be the first best rank-one
     tensor approximating 'X' for this decomposition analysis to be
     called PTA-_k_modes.

_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:

     'PTAk'

