compute_dW_dlambda_wrapper: Compute Derivative of Penalty Matrix G with Respect to Lambda...

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

Compute Derivative of Penalty Matrix G with Respect to Lambda (Wrapper)

Description

Wrapper function for computing the derivative of the weight matrix w.r.t lambda \lambda. This involves computing terms related to the derivative of 1/(1+\textbf{x}^{T}\textbf{U}\textbf{G}\textbf{x}).

Usage

compute_dW_dlambda_wrapper(
  G,
  A,
  GXX,
  Ghalf,
  dG_dlambda,
  dGhalf_dlambda,
  AGAInv,
  nc,
  K,
  parallel,
  cl,
  chunk_size,
  num_chunks,
  rem_chunks
)

Arguments

G	A list of penalty matrices \textbf{G} for each partition
A	Constraint matrix \textbf{A}
GXX	List of \textbf{G}\textbf{X}^{T}\textbf{X} products
Ghalf	List of \textbf{G}^{1/2} matrices
dG_dlambda	List of d\textbf{G}/d\lambda matrices
dGhalf_dlambda	List of d\textbf{G}^{1/2}/d\lambda matrices
AGAInv	Inverse of \textbf{A}^{T}\textbf{G}\textbf{A}
nc	Number of columns
K	Number of partitions minus 1 (K)
parallel	Logical to enable parallel processing
cl	Cluster object for parallel computation
chunk_size	Size of chunks for parallel processing
num_chunks	Number of chunks
rem_chunks	Remainder chunks

Value

Scalar value representing the trace derivative component.

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