ldetS Getting log generalized determinant of penalty matrices

Description

INTERNAL function calculating the log generalized determinant of penalty matrix S stored blockwise in an Sl list (which is the output of Sl.setup).

Usage

ldetS(Sl, rho, fixed, np, root = FALSE, repara = TRUE,
      nt = 1,deriv=2,sparse=FALSE)

Arguments

Sl	the output of Sl.setup.
rho	the log smoothing parameters.
fixed	an array indicating whether the smoothing parameters are fixed (or free).
np	number of coefficients.
root	indicates whether or not to return the matrix square root, E, of the total penalty S_tot.
repara	if TRUE multi-term blocks will be re-parameterized using gam.reparam, and a re-parameterization object supplied in the returned object.
nt	number of parallel threads to use.
deriv	order of derivative to use
sparse	should E be sparse?

Value

A list containing:

• ldetS: the log-determinant of S.

• ldetS1: the gradient of the log-determinant of S.

• ldetS2: the Hessian of the log-determinant of S.

• Sl: with modified rS terms, if needed and rho added to each block

• rp: a re-parameterization list.

• rp: E a total penalty square root such that t(E)%*%E = S_tot (if root==TRUE).

Author(s)

Simon N. Wood <[email protected]>.