Error of the spectral coarse graining (SCG) approximationSource:
scg_eps() 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
A numeric matrix of (eigen)vectors assumed normalized. The vectors are to be stored column-wise in
A vector of
nrow(V)integers labeling each group vertex in the partition.
The type of semi-projector used for the SCG. For now “symmetric”, “laplacian” and “stochastic” are available.
A probability vector of length
pis the stationary probability distribution of a Markov chain when
mtype= “stochastic”. This parameter is ignored otherwise.
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.
scg_eps() returns with a numeric vector whose \(i\)th
component is \(\Vert v_i-Pv_i\Vert\) (see Details).
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
David Morton de Lachapelle, http://people.epfl.ch/david.morton.