dot-bf_split_components: Split Design and Penalty into Spline and Flat Components
In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

.bf_split_components

R Documentation

Split Design and Penalty into Spline and Flat Components

Description

Partitions the per-partition design matrices, penalty matrices, and constraint matrix into "spline" (columns receiving partition-specific coefficients) and "flat" (columns receiving a single shared coefficient across all partitions) subsets.

Usage

.bf_split_components(
  X,
  flat_cols,
  p_expansions,
  K,
  Lambda,
  L_partition_list,
  A,
  qr_pivot_smoothing_constraints = TRUE,
  parallel_qr = FALSE,
  cl = NULL,
  constraint_values
)

Arguments

`X`	List of `K+1` design matrices (`N_k \times p_expansions`).
`flat_cols`	Integer vector of flat column indices.
`p_expansions`	Integer; total columns per partition.
`K`	Integer; number of interior knots.
`Lambda`	`p_expansions \times p_expansions` shared penalty matrix.
`L_partition_list`	List of partition-specific penalty matrices.
`A`	Full `P \times R_constraints` constraint matrix.
`constraint_values`	List of constraint right-hand sides.

Value

A named list with elements:

X_spline: List of K+1 matrices, spline columns only.
X_flat: List of K+1 matrices, flat columns only.
Lambda_spline: nc_s \times nc_s penalty submatrix.
Lambda_flat: nc_f \times nc_f penalty submatrix.
L_part_spline: List of partition-specific penalty submatrices for the spline columns.
A_spline: Spline-only constraint matrix (columns pruned and rank-reduced via pivoted QR).
nca_spline: Integer; number of columns in A_spline.
constraint_values_spline: List of constraint RHS vectors restricted to spline rows.
spline_cols: Integer vector of spline column indices.
nc_spline: Integer; number of spline columns.
nc_flat: Integer; number of flat columns.
A_flat: Flat-only constraint matrix (rows for flat coefficients, columns pruned and rank-reduced). Used to enforce mixed constraints on the flat update step.
nca_flat: Integer; number of columns in A_flat.
A_full: The original full constraint matrix A, retained for mixed-constraint enforcement.
flat_rows_all: Integer vector of flat-coefficient row indices in the full P-space.
spline_rows_all: Integer vector of spline-coefficient row indices in the full P-space.
has_mixed_constraints: Logical; TRUE if any constraint column in A has nonzero entries on both spline and flat rows.
mixed_constraint_cols: Integer vector of column indices in the original A that are mixed (touch both spline and flat rows).