APSOLU3 {PTAk} | R Documentation |
Computes all the 2-modes solutions associated to the given Principal Tensor of the given tensor.
APSOLU3(X,solu,pt3=NULL,nbPT2=1, smoothing=FALSE,smoo=list(NA), verbose=getOption("verbose"),file=NULL )
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’ |
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
.
an updated PTAk
object
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.
Didier Leibovici c3s2i@free.fr
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