% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/get_B.R
\name{.get_B_gaussian_nocorr}
\alias{.get_B_gaussian_nocorr}
\title{Path 2: Gaussian Identity Link, No Correlation}
\usage{
.get_B_gaussian_nocorr(
  Xy,
  Ghalf,
  GhalfInv,
  A,
  K,
  p_expansions,
  R_constraints,
  constraint_value_vectors,
  family,
  return_G_getB,
  quadprog,
  qp_Amat,
  qp_bvec,
  qp_meq,
  qp_score_function,
  parallel_aga,
  parallel_matmult,
  cl,
  chunk_size,
  num_chunks,
  rem_chunks,
  X,
  y,
  Lambda,
  order_list,
  observation_weights,
  iterate,
  tol,
  glm_weight_function,
  schur_correction_function,
  need_dispersion_for_estimation,
  dispersion_function,
  unique_penalty_per_partition,
  L_partition_list,
  VhalfInv,
  homogenous_weights,
  ...
)
}
\arguments{
\item{Xy}{List of cross-products \eqn{\mathbf{X}_k^{\top}\mathbf{y}_k}
by partition.}

\item{Ghalf, GhalfInv}{Lists of \eqn{\mathbf{G}^{1/2}_k} and
\eqn{\mathbf{G}^{-1/2}_k} matrices by partition.}

\item{A}{Constraint matrix \eqn{\mathbf{A}}.}

\item{K, p_expansions, R_constraints}{Integer dimensions.}

\item{constraint_value_vectors}{Constraint RHS list encoding
\eqn{\mathbf{A}^{\top}\boldsymbol{\beta} = \mathbf{c}}.}

\item{family}{GLM family object.}

\item{return_G_getB}{Logical; return covariance components.}

\item{quadprog}{Logical; apply QP refinement for inequality constraints.}

\item{qp_Amat, qp_bvec, qp_meq}{QP constraint specification.}

\item{qp_score_function}{Score function for QP step.}

\item{parallel_aga, parallel_matmult}{Logical flags.}

\item{cl, chunk_size, num_chunks, rem_chunks}{Parallel parameters.}

\item{X, y, Lambda, order_list, observation_weights}{Standard arguments
passed through for optional QP refinement.}

\item{iterate, tol, glm_weight_function, schur_correction_function, }{need_dispersion_for_estimation,dispersion_function,
unique_penalty_per_partition,L_partition_list,VhalfInv,
homogenous_weights Standard arguments passed through.}

\item{...}{Passed to sub-functions.}
}
\value{
Same structure as \code{get_B}.
}
\description{
For the canonical Gaussian case without correlation structures, the
unconstrained estimate has the closed form
\eqn{\hat{\boldsymbol{\beta}}_k = \mathbf{G}_k \mathbf{X}_k^{\top}
\mathbf{y}_k} and the constrained estimate follows by a single
Lagrangian projection. No iteration is needed.
}
\details{
When \eqn{K = 0} and there are no inequality constraints or nonzero
constraint values, the function returns
\eqn{\hat{\boldsymbol{\beta}} = \mathbf{G}\mathbf{X}^{\top}\mathbf{y}}
directly without forming the full \eqn{P}-dimensional OLS system.
}
\keyword{internal}
