eig_full: Compute a full dense eigendecomposition

In eigencore: Certified Partial Eigenvalue and Singular Value Computation

Compute a full dense eigendecomposition

Description

eig_full() is the dense/full eigencore surface for standard and generalized eigenproblems. Sparse and operator inputs are not silently densified.

Usage

eig_full(
  A,
  B = NULL,
  structure = NULL,
  vectors = TRUE,
  tol = 1e-08,
  allow_dense_fallback = c("auto", "never", "always"),
  ...
)

Arguments

A	Base dense square matrix.
B	Optional base dense square matrix for generalized problems.
structure	Optional structure descriptor. Use general() to force the general-pencil path for dense generalized inputs.
vectors	Whether to return right eigenvectors.
tol	Certification tolerance.
allow_dense_fallback	Reserved dense fallback policy. Sparse/operator inputs still fail unless a future issue explicitly opens an opt-in dense fallback contract for eig_full().
...	Reserved for future options.

Value

An eigencore_eigen_result. Dense general-pencil results additionally carry alpha, beta, classification, classification_policy, left_vectors (left generalized eigenvectors satisfying ⁠w^H A = lambda w^H B⁠), and conditioning. For real pencils the decomposition runs through the expert LAPACK driver DGGEVX with balancing, so conditioning contains reciprocal condition numbers rconde/rcondv and the balanced pencil norms abnrm/bbnrm. Complex pencils use ZGGEV (R's bundled LAPACK subset has no ZGGEVX), so they return left vectors but conditioning$available is FALSE.

Examples

A <- diag(c(1, 4, 9))
B <- diag(c(1, 2, 3))
fit <- eig_full(A, B = B)
values(fit)
certificate(fit)$passed

# Force the dense general-pencil path when alpha/beta diagnostics matter.
pencil <- eig_full(A, B = B, structure = general())
pencil$alpha
pencil$beta
pencil$classification

eigencore documentation built on July 26, 2026, 1:06 a.m.