gam.reparam Finding stable orthogonal re-parameterization of the square root penalty.

Description

INTERNAL function for finding an orthogonal re-parameterization which avoids "dominant machine zero leakage" between components of the square root penalty.

Usage

gam.reparam(rS, lsp, deriv)

Arguments

rS	list of the square root penalties: last entry is root of fixed penalty, if fixed.penalty==TRUE (i.e. length(rS)>length(sp)). The assumption here is that rS[[i]] are in a null space of total penalty already; see e.g. totalPenaltySpace and mini.roots.
lsp	vector of log smoothing parameters.
deriv	if deriv==1 also the first derivative of the log-determinant of the penalty matrix is returned, if deriv>1 also the second derivative is returned.

Value

A list containing

• S: the total penalty matrix similarity transformed for stability.

• rS: the component square roots, transformed in the same way.

• Qs: the orthogonal transformation matrix S = t(Qs)%*%S0%*%Qs, where S0 is the untransformed total penalty implied by sp and rS on input.

• det: log|S|.

• det1: dlog|S|/dlog(sp) if deriv >0.

• det2: hessian of log|S| wrt log(sp) if deriv>1.

Author(s)

Simon N. Wood <[email protected]>.