solve_gep_subspace: Fast sub-space solver for a small block of generalized...

In genpca: Generalized Principal Component Analysis

Fast sub-space solver for a small block of generalized eigen-pairs

Description

Uses pre-conditioned sub-space iteration on the operator S_2^{-1} S_1 (or its inverse) to obtain the q largest or smallest generalized eigen-values/vectors of S_1 v = \lambda S_2 v.

Usage

solve_gep_subspace(
  S1,
  S2,
  q = 2,
  which = c("largest", "smallest"),
  max_iter = 100,
  tol = 1e-06,
  V0 = NULL,
  seed = NULL,
  reg_S = 0.001,
  reg_T = 1e-06,
  verbose = FALSE
)

Arguments

S1, S2	Symmetric positive-(semi)definite dgCMatrix (or dense) matrices of the same dimension d\times d.
q	Number of eigen-pairs required (⁠q << d⁠).
which	"largest" or "smallest".
max_iter, tol	Stopping rule - iteration stops when max(abs(lambda_new - lambda_old)/abs(lambda_old)) < tol.
V0	Optional ⁠d x q⁠ initial block (will be orthonormalised).
seed	Optional integer seed for reproducible random initialisation.
reg_S, reg_T	Ridge terms added to S1/S2 and the small ⁠q x q⁠ Gram matrix to guarantee invertibility.
verbose	Logical - print convergence info.

Value

A list with components

values

length-q numeric vector of Ritz eigen-values.

vectors

⁠d x q⁠ matrix, columns are orthonormal eigen-vectors in the original S-inner-product.

genpca documentation built on Sept. 17, 2026, 1:09 a.m.