Extract homogeneous generalized coordinates.

Generalized dense-pencil and generalized Schur results store eigenvalues in homogeneous form as alpha / beta; generalized SVD results use the same alpha/beta convention for generalized singular values. alpha_beta() exposes those coordinates along with the finite/infinite/undefined classification computed by eigencore.

Usage

alpha_beta(x, ...)

Arguments

x

An eigencore result with homogeneous alpha and beta fields.

...

Reserved for future methods.

Value

A list containing alpha, beta, and any available values, classification, finite, infinite, and undefined fields. Results that record how the finite/infinite/undefined labels were decided also include a classification_policy list with the policy name, the tolerance, the per-coordinate zero thresholds, and the pencil norms used for norm-scaled classification.

Examples

A <- diag(c(2, 3, 0))
B <- diag(c(1, 0, 0))
fit <- eig_full(A, B = B, structure = general())
alpha_beta(fit)$classification
#> [1] "finite"    "infinite"  "undefined"