Sl.setup: Setting up a list representing a block diagonal penalty...

In mgcv: Mixed GAM Computation Vehicle with Automatic Smoothness Estimation

Setting up a list representing a block diagonal penalty matrix

Description

INTERNAL function for setting up a list representing a block diagonal penalty matrix from the object produced by gam.setup.

Usage

Sl.setup(G,cholesky=FALSE,no.repara=FALSE,sparse=FALSE,keepS=FALSE)

Arguments

G	the output of gam.setup.
cholesky	re-parameterize using Cholesky only.
no.repara	set to TRUE to turn off all initial reparameterization.
sparse	sparse setup?
keepS	store original penalties in S0? (after any splitting of multiple penalties into singletons, but before reparameterization)

Value

A list with an element for each block. For block, b, Sl[[b]] is a list with the following elements

• repara: should re-parameterization be applied to model matrix, etc? Usually FALSE if non-linear in coefficients.

• start, stop: such that start:stop are the indexes of the parameters of this block.

• S: a list of penalty matrices for the block (dim = stop-start+1) If length(S)==1 then this will be an identity penalty. Otherwise it is a multiple penalty, and an rS list of square root penalty matrices will be added. S (if repara==TRUE) and rS (always) will be projected into range space of total penalty matrix.

• rS: square root of penalty matrices if multiple penalties are used.

• D: a reparameterization matrix for the block. Applies to cols/params in start:stop. If numeric then X[,start:stop]%*%diag(D) is re-parametrization of X[,start:stop], and b.orig = D*b.repara (where b.orig is the original parameter vector). If matrix then X[,start:stop]%*%D is re-parametrization of X[,start:stop], and b.orig = D%*%b.repara (where b.orig is the original parameter vector).

• S0: original penalties if requested.

Author(s)

Simon N. Wood <[e-mail]>.

mgcv documentation built on April 11, 2025, 6:11 p.m.