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mgcv (version 1.9-0)

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)

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.

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.

Author

Simon N. Wood <simon.wood@r-project.org>.