Extract a result certificate.

Usage

certificate(x, ...)

Arguments

x: An eigencore result object.
...: Reserved for future methods.

Value

The eigencore_certificate object stored on x, or NULL if the result does not carry a certificate field.

Details

Backward errors use the standard normwise 2-norm definition: ||A x - lambda B x|| / ((||A||_2 + |lambda| ||B||_2) ||x||) for eigenpairs and sqrt(||A v - sigma u||^2 + ||A^H u - sigma v||^2) / ||A||_2 for singular triplets. The norms in the denominator are exact or LOWER bounds (never estimates), so the reported backward error is never smaller than the true one and passed is sound. Fields describing the scale:

norm_bound_type: "two_norm_exact" or "two_norm_lower_bound" (eigen certificates report A+B parts; B = I is "identity_exact").
norm_source: Where each value came from: "diagonal", "full_spectrum", "metadata" (an operator's metadata$two_norm), "column_norms", "applied_vectors" (||A x|| / ||x|| for the certified vectors), "ritz" (residual-corrected Ritz values), "frobenius_rank_bound", or "lanczos" (a short deterministic Krylov estimate run only when it could change the verdict).
norm_values: The values used, named A (and B).
scale_is_estimate: Always FALSE for built-in certificates.

Examples

fit <- eig_partial(diag(c(3, 2, 1)), k = 1, target = largest())
cert <- certificate(fit)
cert$passed
#> [1] TRUE
cert$max_residual
#> [1] 0