Finding stable orthogonal re-parameterization of the square...

gam.reparam {mgcv}

R Documentation

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 <simon.wood@r-project.org>.

[Package mgcv version 1.8-28 Index]