A numeric matrix of (eigen)vectors assumed normalized.
The vectors are to be stored column-wise in V).
groups
A vector of nrow(V) integers labeling
each group vertex in the partition.
mtype
The type of semi-projector used for the SCG. For
now symmetric, laplacian and stochastic
are available.
p
A probability vector of length nrow(V).
p is the stationary probability distribution of a Markov chain
when mtype = stochastic. This parameter is ignored otherwise.
norm
Either row or col. If set to row
the rows of the Laplacian matrix sum to zero and the rows of the
stochastic matrix sum to one; otherwise it is the columns.
Value
normEps returns with a numeric vector whose $i$th component is
$\Vert v_i-Pv_i\Vert$ (see Details).
Details
scgNormEps computes $\Vert v_i-Pv_i\Vert$,
where $v_i$ is the $i$th eigenvector in V and
$P$ is the projector corresponding to the mtype argument.
References
D. Morton de Lachapelle, D. Gfeller, and P. De Los Rios, Shrinking
Matrices while Preserving their Eigenpairs with Application to the
Spectral Coarse Graining of Graphs. Submitted to SIAM Journal on
Matrix Analysis and Applications, 2008.
http://people.epfl.ch/david.morton