% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/blockfit_solve.R
\name{.bf_case_gauss_no_corr}
\alias{.bf_case_gauss_no_corr}
\title{Gaussian Identity Backfitting Without Correlation (Case b)}
\usage{
.bf_case_gauss_no_corr(
  X_spline,
  X_flat,
  y,
  K,
  Ghalf_sp,
  GhalfA_sp,
  XfXf_pen_inv,
  constraint_values_spline,
  nc_spline,
  nc_flat,
  A_spline,
  tol,
  max_backfit_iter,
  verbose,
  split = NULL,
  constraint_values = list(),
  Lambda_flat = NULL,
  p_expansions = NULL
)
}
\arguments{
\item{X_spline, X_flat}{Lists of per-partition submatrices.}

\item{y}{List of response vectors.}

\item{K}{Integer.}

\item{Ghalf_sp}{List of \eqn{\mathbf{G}_s^{1/2}} matrices.}

\item{GhalfA_sp}{Pre-computed \eqn{\mathbf{G}_s^{1/2}
\mathbf{A}_s}.}

\item{XfXf_pen_inv}{Penalised inverse of the pooled flat Gram
matrix.}

\item{constraint_values_spline}{Spline-only constraint RHS.}

\item{nc_spline, nc_flat}{Integers.}

\item{A_spline}{Spline-only constraint matrix.}

\item{tol}{Convergence tolerance.}

\item{max_backfit_iter}{Maximum iterations.}

\item{verbose}{Logical.}

\item{split}{Output of \code{.bf_split_components}, needed for
mixed-constraint enforcement on the flat step.}

\item{constraint_values}{Full constraint RHS list.}

\item{Lambda_flat}{Flat penalty submatrix.}

\item{p_expansions}{Integer; columns per partition.}
}
\value{
A named list with \code{beta_spline} and
  \code{beta_flat}.
}
\description{
Standard block-coordinate descent on the convex quadratic
objective, alternating between the spline step (Lagrangian
projection) and the flat step (pooled penalized regression).
}
\keyword{internal}
