compute_dG_u_dlambda_xy: Compute Derivative of...

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

Compute Derivative of \textbf{U}\textbf{G}\textbf{X}^{T}\textbf{y} with Respect to Lambda

Description

Compute Derivative of \textbf{U}\textbf{G}\textbf{X}^{T}\textbf{y} with Respect to Lambda

Usage

compute_dG_u_dlambda_xy(
  AGAInv_AGXy,
  AGAInv,
  G,
  A,
  dG_dlambda,
  nc,
  nca,
  K,
  Xy,
  Ghalf,
  dGhalf,
  GhalfXy_temp,
  parallel,
  cl,
  chunk_size,
  num_chunks,
  rem_chunks
)

Arguments

AGAInv_AGXy	Product of (\textbf{A}^{T}\textbf{G}\textbf{A})^{-1} and \textbf{A}^{T}\textbf{G}\textbf{X}^{T}\textbf{y}
AGAInv	Inverse of \textbf{A}^{T}\textbf{G}\textbf{A}
G	List of \textbf{G} matrices
A	Constraint matrix \textbf{A}
dG_dlambda	List of d\textbf{G}/d\lambda matrices
nc	Number of columns
nca	Number of constraint columns
K	Number of partitions minus 1 (K)
Xy	List of \textbf{X}^{T}\textbf{y} products
Ghalf	List of \textbf{G}^{1/2} matrices
dGhalf	List of d\textbf{G}^{1/2}/d\lambda matrices
GhalfXy_temp	Temporary storage for \textbf{G}^{1/2}\textbf{X}^{T}\textbf{y}
parallel	Use parallel processing
cl	Cluster object
chunk_size	Size of parallel chunks
num_chunks	Number of chunks
rem_chunks	Remaining chunks

Details

Computes d(\textbf{U}\textbf{G}\textbf{X}^{T}\textbf{y})/d\lambda. Uses efficient implementation avoiding large matrix construction. For large problems (K \ge 10, nc > 4), uses chunked parallel processing. For smaller problems, uses simpler least squares approach based on \textbf{G}^{1/2}.

Value

Vector of derivatives

lgspline documentation built on June 8, 2025, 10:45 a.m.