.oblique_procrustes_batch: Batched oblique Procrustes target rotation over a cube of loading matrices

Description

Align each slice of a loading-matrix cube to a single shared target using the same oblique target rotation as .oblique_procrustes(), in one call. This removes the per-replicate marshalling overhead of looping efa_procrustes() in R over bootstrap or multiple-imputation arrays.

Usage

.oblique_procrustes_batch(
  A,
  B,
  eps = 1e-05,
  maxit = 1000L,
  max_line_search = 10L,
  step0 = 1,
  normalize = FALSE,
  random_starts = 0L,
  screen_keep = 2L,
  triage_maxit = 25L,
  triage_improve_tol = 0
)

Value

A named list with the aligned-loadings array loadings (n x m x b), the factor-correlation array Phi (m x m x b), and the per-slice diagnostics valid, convergence, value, iterations, and line_search_failed.

Arguments

A: Numeric array of dimension n x m x b: the b loading matrices to align.
B: Numeric n x m target loading matrix shared across all slices.
eps: Numeric scalar. Convergence tolerance for the projected-gradient norm.
maxit: Integer scalar. Maximum number of full projected-gradient updates.
max_line_search: Integer scalar. Maximum number of step-halving attempts after the initial trial step in each line-search phase.
step0: Numeric scalar. Initial step size used in the projected-gradient update.
normalize: Logical scalar. If TRUE, apply Kaiser normalization to the loadings (only) before rotation and reverse it afterwards, leaving the target unnormalized (ignored for single-factor slices).
random_starts: Integer scalar. Number of additional random starts per slice.
screen_keep: Integer scalar. Number of screened random starts retained for triage optimization.
triage_maxit: Integer scalar. Number of short optimization iterations used in the triage stage.
triage_improve_tol: Numeric scalar. Relative improvement required for a triaged start to be promoted to full optimization.

Details

Each slice A[, , i] is aligned to B. For a single-factor cube the alignment reduces to the closed-form sign match T = sign(crossprod(A_i, B)) with factor correlation 1, matching the one-factor short-circuit in efa_procrustes(). For two or more factors the slice is warm-started from the closed-form orthogonal Procrustes solution (mirroring efa_procrustes()) and optimized with the same multi-start oblique solver as .oblique_procrustes(). Random starts are drawn serially with R::rnorm in the calling process.

Slices are aligned independently. A slice that cannot be aligned (a non-finite loading matrix, a failed warm-start decomposition, an invalid fit, or any linear-algebra exception) is reported with valid = FALSE and NA for the loadings, factor correlations, and all other per-slice diagnostics, rather than aborting the whole call, so one degenerate replicate does not discard the rest.