```
## Use `magic' for a standard additive model fit ...
library(mgcv)
set.seed(1);n <- 200;sig <- 1
dat <- gamSim(1,n=n,scale=sig)
k <- 30
## set up additive model
G <- gam(y~s(x0,k=k)+s(x1,k=k)+s(x2,k=k)+s(x3,k=k),fit=FALSE,data=dat)
## fit using magic (and gam default tolerance)
mgfit <- magic(G$y,G$X,G$sp,G$S,G$off,rank=G$rank,
control=list(tol=1e-7,step.half=15))
## 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)$edf # get e.d.f. per param
range(edf-b$edf) # compare
## p>n example... fit model to first 100 data only, so more
## params than data...
mgfit <- magic(G$y[1:100],G$X[1:100,],G$sp,G$S,G$off,rank=G$rank)
edf <- magic.post.proc(G$X[1:100,],mgfit,G$w[1:100])$edf
## constrain first two smooths to have identical smoothing parameters
L <- diag(3);L <- rbind(L[1,],L)
mgfit <- magic(G$y,G$X,rep(-1,3),G$S,G$off,L=L,rank=G$rank,C=G$C)
## Now a correlated data example ...
library(nlme)
## simulate truth
set.seed(1);n<-400;sig<-2
x <- 0:(n-1)/(n-1)
f <- 0.2*x^11*(10*(1-x))^6+10*(10*x)^3*(1-x)^10
## produce scaled covariance matrix for AR1 errors...
V <- corMatrix(Initialize(corAR1(.6),data.frame(x=x)))
Cv <- chol(V) # t(Cv)%*%Cv=V
## Simulate AR1 errors ...
e <- t(Cv)%*%rnorm(n,0,sig) # so cov(e) = V * sig^2
## Observe truth + AR1 errors
y <- f + e
## GAM ignoring correlation
par(mfrow=c(1,2))
b <- gam(y~s(x,k=20))
plot(b);lines(x,f-mean(f),col=2);title("Ignoring correlation")
## Fit smooth, taking account of *known* correlation...
w <- solve(t(Cv)) # V^{-1} = w'w
## Use `gam' to set up model for fitting...
G <- gam(y~s(x,k=20),fit=FALSE)
## fit using magic, with weight *matrix*
mgfit <- magic(G$y,G$X,G$sp,G$S,G$off,rank=G$rank,C=G$C,w=w)
## Modify previous gam object using new fit, for plotting...
mg.stuff <- magic.post.proc(G$X,mgfit,w)
b$edf <- mg.stuff$edf;b$Vp <- mg.stuff$Vb
b$coefficients <- mgfit$b
plot(b);lines(x,f-mean(f),col=2);title("Known correlation")
```

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