eigs_sym.undirected_factor_model {fastRG}

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.