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=0.01,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 `solutions.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 `solutions.PTAk' object see `is.solutions.PTAk'

_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-kmodes
     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
     kmodes 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-kmodes.

_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:

     `PTAk'

