compute_G_eigen: Compute Eigenvalues and Related Matrices for G

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

Compute Eigenvalues and Related Matrices for G

Description

Compute Eigenvalues and Related Matrices for G

Usage

compute_G_eigen(
  X_gram,
  Lambda,
  K,
  parallel,
  cl,
  chunk_size,
  num_chunks,
  rem_chunks,
  family,
  unique_penalty_per_partition,
  L_partition_list,
  keep_G = TRUE,
  shur_corrections
)

Arguments

X_gram	Gram matrix list (\textbf{X}^{T}\textbf{X})
Lambda	Penalty matrix (\boldsymbol{\Lambda})
K	Number of partitions minus 1 (K)
parallel	Use parallel processing
cl	Cluster object
chunk_size	Chunk size for parallel
num_chunks	Number of chunks
rem_chunks	Remaining chunks
family	GLM family
unique_penalty_per_partition	Use partition penalties
L_partition_list	Partition penalty list (\textbf{L}_\text{partition\_list})
keep_G	Return full G matrix (\textbf{G})
shur_corrections	List of Shur complement corrections (\textbf{S})

Details

Computes \textbf{G}, \textbf{G}^{1/2} and \textbf{G}^{-1/2} matrices via eigendecomposition of \textbf{X}^{T}\textbf{X} + \boldsymbol{\Lambda}_\text{effective} + \textbf{S}. Handles partition-specific penalties and parallel processing. For non-identity link functions, also returns \textbf{G}^{-1/2}.

Value

List containing combinations of:

• G - Full \textbf{G} matrix (if keep_G=TRUE)

• Ghalf - \textbf{G}^{1/2} matrix

• GhalfInv - \textbf{G}^{-1/2} matrix (for non-identity links)

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