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

Usage

# S3 method for 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 \(A\).