INITIA                 package:PTAk                 R Documentation

_I_n_i_t_i_a_l_i_s_a_t_i_o_n _u_s_e_d _i_n _S_I_N_G_V_A

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

     Gives the first Tucker1 components of a given tensor.

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

        INITIA(X,modesnam=NULL,method="Presvd",dim=1,...)

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

       X: a tensor (as an array) of order k

modesnam: a character vector of the names of the modes

  method: uses either the inbuilt SVD `method="svd"' or a power
          algorithm giving only the first `method="Presvd"' or any
          other function given applying to the column space of a matrix
          and returning a list with `v' (in columns vectors as in
          `svd') and `d'. 

     dim: default 1 in each space otherwise specify the number of
          dimensions e.g. `c(2,3..,2)' (with `"Presvd"' dim is
          obviously 1)

     ...: 

     extra arguments of the method `method': the first argument is
     fixed (see details).

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

     Computes the first (or `dim') right singular vector  (or other
     summaries) for every representation of the tensor as a matrix with
     `dim(X)[i]' columns, `i=1...k'.

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

     a list (of length k) of  lists  with arguments: 

       v: the singular vectors in rows

modesnam: a character object naming the mode, `"m i"' otherwise

       n: labels of mode `i' entries as given in `dimnames' of the
          data, can be `NULL'

       d: the corresponding first singular values

_N_o_t_e:

     The collection these eigenvectors, is known as the Tucker1
     solution or initialisation related to PCA-3modes or PCA-nmodes
     models. If a function is given  it may include `dim' as argument.

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

     Didier Leibovici didier@fmrib.ox.ac.uk

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

     Kroonenberg P.M (1983) Three-mode Principal Component Analysis:
     Theory and Applications.  DSWO Press, Leiden.

     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:

     `SINGVA', `PTAk'

