Compute a partial eigendecomposition.

Usage

eig_partial(
  A,
  k,
  target = largest(),
  B = NULL,
  method = auto(),
  tol = 1e-08,
  maxit = NULL,
  vectors = TRUE,
  seed = NULL,
  certify = TRUE,
  allow_dense_fallback = c("auto", "never", "always"),
  initial_subspace = NULL
)

Arguments

A: Matrix or eigencore operator.
k: Number of eigenpairs to compute.
target: Eigencore eigenvalue target descriptor.
B: Optional metric matrix or operator for generalized problems.
method: Solver method descriptor.
tol: Convergence and certification tolerance.
maxit: Optional iteration limit.
vectors: Whether to compute vectors.
seed: Optional random seed for stochastic solver components.
certify: Whether to compute certification diagnostics.
allow_dense_fallback: Dense fallback policy.
initial_subspace: Optional numeric matrix of starting directions (a warm start). Supported on standard real Hermitian Lanczos paths: the native paths for explicit dense double or dgCMatrix operators, the native matrix-free callback path selected by lanczos(block > 1), and the scalar matrix-free reference path selected by lanczos(block = 1); supplying it on any other planned path (generalized, shift-invert, dense fallback) is an error. Pass method = lanczos() to guarantee a Lanczos route: with the default method = auto(), sparse or nearest() problems may be planned as shift-invert, which does not consume a start and will reject the argument. The subspace is only a starting hint: projected quantities, residuals, orthogonality, convergence, and the certificate are recomputed for the current operator on every solve. The columns are orthonormalized at the solver boundary and fitted to the method's start block — when the accepted rank exceeds the block width the block is a seeded random rotation of the full accepted basis, so every supplied direction contributes. Because a residual certificate proves eigenpair accuracy but not target identity, a fully supplied subspace that is already invariant at tol is discarded in favor of a cold start; provenance records that guard decision. Diagnostics distinguish operator block calls, operator columns, and certification columns. NULL (the default) preserves the cold random start exactly.

Value

An eigencore_eigen_result containing computed values, optional vectors, certificate diagnostics, method/plan metadata, and convergence diagnostics.

Examples

A <- diag(c(5, 4, 3, 2, 1))
A[1, 2] <- A[2, 1] <- 0.1
fit <- eig_partial(A, k = 2, target = largest())
values(fit)
#> [1] 5.009902 3.990098
certificate(fit)$passed
#> [1] TRUE

# Generalized SPD problem A x = lambda B x
B <- diag(c(2, 1, 1, 1, 1))
gfit <- eig_partial(A, B = B, k = 2, target = smallest())
values(gfit)
#> [1] 1 2