RSpectra-compatible eigen shim. — eigs • eigencore

Mirrors RSpectra::eigs(). which uses ARPACK codes ("LM", "SM", "LR", "SR", "LI", "SI"). Unlike ARPACK, "LI"/"SI" rank by the signed imaginary part (see largest_imaginary()), not by its magnitude. A non-NULL real sigma with which = "LM" requests the eigenvalues nearest sigma, computed by shift-invert Krylov-Schur Arnoldi on a factorised A - sigma I (dense QR or sparse LU).

Usage

eigs(
  A,
  k,
  which = "LM",
  sigma = NULL,
  opts = list(),
  ...,
  n = NULL,
  args = NULL,
  left = FALSE
)

Arguments

A: Matrix, eigencore operator, or a function f(x, args) returning A %*% x (then n is required).
k: Number of eigenpairs to compute.
which: RSpectra-style target selector.
sigma: Optional real shift; eigenvalues nearest sigma are returned.
opts: RSpectra options list. tol, ncv (Krylov subspace size, passed as auto(max_subspace = ncv) so the planner still chooses the route), maxitr (passed as the iteration limit maxit) and retvec are honoured; other keys raise a warning.
...: Additional arguments passed to eig_partial().
n: Dimension of the operator when A is a function.
args: Extra argument passed to a function A.
left: Whether to compute and certify left eigenvectors (left_vectors = "auto" in eig_partial()). FALSE (default) skips the adjoint solve and its certificate entirely.

Value

A list compatible with RSpectra::eigs(), including values, vectors, convergence counts, operation counts, certificate diagnostics, and, with left = TRUE, left_vectors, right_vectors, left_certificate and biorthogonality.

Details

Like RSpectra::eigs(), only right eigenvectors are computed by default; left = TRUE also computes and certifies left eigenvectors and their biorthogonality with the right ones (the eig_partial() default).

Examples

A <- diag(c(5, 4, 3, 2, 1))
A[1, 2] <- 0.5
res <- eigs(A, k = 2, which = "LM")
res$values
#> [1] 5 4