compute_GhalfXy_temp_wrapper: Compute Component...

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

Compute Component \textbf{G}^{1/2}\textbf{A}(\textbf{A}^{T}\textbf{G}\textbf{A})^{-1}\textbf{A}^{T}\textbf{G}\textbf{X}^{T}\textbf{y}

Description

Compute Component \textbf{G}^{1/2}\textbf{A}(\textbf{A}^{T}\textbf{G}\textbf{A})^{-1}\textbf{A}^{T}\textbf{G}\textbf{X}^{T}\textbf{y}

Usage

compute_GhalfXy_temp_wrapper(
  G,
  Ghalf,
  A,
  AGAInv,
  Xy,
  nc,
  K,
  parallel,
  cl,
  chunk_size,
  num_chunks,
  rem_chunks
)

Arguments

G	List of \textbf{G} matrices
Ghalf	List of \textbf{G}^{1/2} matrices
A	Constraint matrix \textbf{A}
AGAInv	Inverse of \textbf{A}^{T}\textbf{G}\textbf{A}
Xy	List of \textbf{X}^{T}\textbf{y} products
nc	Number of columns
K	Number of partitions minus 1 (K)
parallel	Use parallel processing
cl	Cluster object
chunk_size	Size of parallel chunks
num_chunks	Number of chunks
rem_chunks	Remaining chunks

Details

Computes the least-squares projection component \mathbf{G}^{1/2}\mathbf{A}(\mathbf{A}^{T}\mathbf{G}\mathbf{A})^{-1} \mathbf{A}^{T}\mathbf{G}\mathbf{X}^{T}\mathbf{y} together with the intermediate product (\mathbf{A}^{T}\mathbf{G}\mathbf{A})^{-1}\mathbf{A}^{T}\mathbf{G}\mathbf{X}^{T}\mathbf{y} for reuse downstream.

Value

Unnamed two-element list containing the projected result vector and the intermediate (\mathbf{A}^{T}\mathbf{G}\mathbf{A})^{-1}\mathbf{A}^{T}\mathbf{G}\mathbf{X}^{T}\mathbf{y} product.

lgspline documentation built on May 8, 2026, 5:07 p.m.