eigs_sym.undirected_factor_model: Compute the eigendecomposition of the expected adjacency...

In fastRG: Sample Generalized Random Dot Product Graphs in Linear Time

Compute the eigendecomposition of the expected adjacency matrix of an undirected factor model

Description

Compute the eigendecomposition of the expected adjacency matrix of an undirected factor model

Usage

## S3 method for class 'undirected_factor_model'
eigs_sym(A, k = A$k, which = "LM", sigma = NULL, opts = list(), ...)

Arguments

A	An undirected_factor_model().
k	Desired rank of decomposition.
which	Selection criterion. See Details below.
sigma	Shift parameter. See section Shift-And-Invert Mode.
opts	Control parameters related to the computing algorithm. See Details below.
...	Unused, included only for consistency with generic signature.

Details

The which argument is a character string that specifies the type of eigenvalues to be computed. Possible values are:

"LM"	The k eigenvalues with largest magnitude. Here the magnitude means the Euclidean norm of complex numbers.
"SM"	The k eigenvalues with smallest magnitude.
"LR"	The k eigenvalues with largest real part.
"SR"	The k eigenvalues with smallest real part.
"LI"	The k eigenvalues with largest imaginary part.
"SI"	The k eigenvalues with smallest imaginary part.
"LA"	The k largest (algebraic) eigenvalues, considering any negative sign.
"SA"	The k smallest (algebraic) eigenvalues, considering any negative sign.
"BE"	Compute k eigenvalues, half from each end of the spectrum. When k is odd, compute more from the high and then from the low end.

eigs() with matrix types "matrix", "dgeMatrix", "dgCMatrix" and "dgRMatrix" can use "LM", "SM", "LR", "SR", "LI" and "SI".

eigs_sym() with all supported matrix types, and eigs() with symmetric matrix types ("dsyMatrix", "dsCMatrix", and "dsRMatrix") can use "LM", "SM", "LA", "SA" and "BE".

The opts argument is a list that can supply any of the following parameters:

ncv

Number of Lanzcos basis vectors to use. More vectors will result in faster convergence, but with greater memory use. For general matrix, ncv must satisfy k+2\le ncv \le n, and for symmetric matrix, the constraint is k < ncv \le n. Default is min(n, max(2*k+1, 20)).

tol

Precision parameter. Default is 1e-10.

maxitr

Maximum number of iterations. Default is 1000.

retvec

Whether to compute eigenvectors. If FALSE, only calculate and return eigenvalues.

initvec

Initial vector of length n supplied to the Arnoldi/Lanczos iteration. It may speed up the convergence if initvec is close to an eigenvector of A.

fastRG documentation built on Aug. 8, 2025, 6:09 p.m.