APSOLU3 {PTAk}

Associated 3-modes Principal Tensors of a 3-modes Principal Tensor

Description

Computes all the 2-modes solutions associated to the given Principal Tensor of the given tensor.

Usage

APSOLU3(X,solu,pt3=NULL,nbPT2=1,
                 smoothing=FALSE,smoo=list(NA),
                        verbose=getOption("verbose"),file=NULL, ...)

Arguments

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’

...

any other arguments passed to SVDGen or other functions

Details

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.

Value

an updated PTAk object

Note

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.

Author(s)

Didier G. Leibovici

References

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

See Also

PTA3, APSOLUk