compute_dG_u_dlambda_xy {lgspline}R Documentation

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


[Package lgspline version 0.2.0 Index]