% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/RcppExports.R
\name{.rotation_se_jacobian}
\alias{.rotation_se_jacobian}
\title{Rotation Jacobians for analytic rotation standard errors}
\usage{
.rotation_se_jacobian(
  A,
  T_init,
  method,
  param,
  normalize,
  oblique,
  eps,
  general_col = 0L
)
}
\arguments{
\item{A}{Numeric matrix. The unrotated loading matrix at the solution.}

\item{T_init}{Numeric matrix. The converged transformation that warm-starts each re-rotation.}

\item{method}{Character scalar. The criterion family: one of \code{"cf"}, \code{"oblimin"}, \code{"geomin"},
\code{"bentler"}, \code{"bifactor"}.}

\item{param}{Numeric scalar. The criterion's tuning argument (\code{kappa} for \code{"cf"}, \code{gam} for
\code{"oblimin"}, \code{delta} for \code{"geomin"}); ignored for \code{"bentler"} and \code{"bifactor"}.}

\item{normalize}{Logical scalar. Apply Kaiser normalization before rotation and reverse it after.}

\item{oblique}{Logical scalar. Use the oblique (column-normalized) manifold; otherwise orthogonal.}

\item{eps}{Numeric scalar. The forward-difference step on the loadings.}

\item{general_col}{Integer scalar. For \code{method = "bifactor"}, the zero-based column holding the
general factor in the (factor-reordered) reported solution; ignored by the other criteria.}
}
\value{
A named list with the Jacobian \code{J_L} (\verb{pk x pk}), the re-rotated \code{base_loadings}, a
validity flag, and -- when oblique -- the Jacobian \code{J_Phi} (\verb{k^2 x pk}) and \code{base_Phi}.
}
\description{
Forward-difference the warm-started re-rotation map \verb{A -> (rotated loadings, Phi)} over the
unrotated loadings \code{A} to obtain the rotation Jacobians used by the analytic standard errors for
rotated loadings (\code{se = "information"} in \code{\link[=efa_fit]{efa_fit()}}). The full \code{nrow(A) * ncol(A)} finite-
difference loop runs in compiled code, re-solving the rotation from the converged transformation
\code{T_init} at each perturbation; the caller forms \verb{J V J'} in R.
}
\references{
Jennrich, R. I. (1973). Standard errors for obliquely rotated factor loadings.
\emph{Psychometrika}, 38, 593-604.
}
\keyword{internal}
