# fields, Tools for spatial data
# Copyright 2004-2007, Institute for Mathematics Applied Geosciences
# University Corporation for Atmospheric Research
# Licensed under the GPL -- www.gpl.org/licenses/gpl.html
"Krig.flplike" <- function(lam, obj) {
    #  - log profile likelihood for lambda
    # See section 3.4 from Nychka  Spatial Processes as Smoothers paper.
    # for equation and derivation
    lD <- obj$matrices$D * lam
    nn <- length(lD)
    #
    num <- log(sum((obj$matrices$u^2) * lD/(1 + lD))) * (nn - 
        obj$nt)
    # note subtle differences between den and RSS in Krig.fgcv
    #   log determinant of I-A restricted to nonzero eigenvalues
    #   log det is the sum of the logs of the eigenvalues
    den <- sum(ifelse(lD > 0, log(lD/(1 + lD)), 0))
    # NOTE: minus the log likelihood!
    0.5 * (num - den)
}