### Name: magic
### Title: Stable Multiple Smoothing Parameter Estimation by GCV or UBRE,
###   with optional fixed penalty
### Aliases: magic
### Keywords: models smooth regression

### ** Examples

library(mgcv)
set.seed(1);n<-400;sig2<-4
x0 <- runif(n, 0, 1);x1 <- runif(n, 0, 1)
x2 <- runif(n, 0, 1);x3 <- runif(n, 0, 1)
f <- 2 * sin(pi * x0)
f <- f + exp(2 * x1) - 3.75887
f <- f+0.2*x2^11*(10*(1-x2))^6+10*(10*x2)^3*(1-x2)^10-1.396
e <- rnorm(n, 0, sqrt(sig2))
y <- f + e
# set up additive model
G<-gam(y~s(x0)+s(x1)+s(x2)+s(x3),fit=FALSE)
# fit using magic
mgfit<-magic(G$y,G$X,G$sp,G$S,G$off,G$rank,C=G$C)
# and fit using gam as consistency check
b<-gam(G=G)
mgfit$sp;b$sp  # compare smoothing parameter estimates
edf<-magic.post.proc(G$X,mgfit,G$w)$edf  # extract e.d.f. per parameter
# get termwise e.d.f.s
twedf<-0;for (i in 1:4) twedf[i]<-sum(edf[((i-1)*10+1):(i*10)])
twedf;b$edf  # compare