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dssmoother <- function(X,Y=NULL,lambda,m,s) {
n <- nrow(X)
d <- ncol(X)
Sgu <- DuchonS(X,m)
qrSgu <- qr(Sgu)
F2 <- qr.Q(qrSgu,complete=TRUE)[,-(1:ncol(Sgu))]
Qgu <- DuchonQ(X,0,m,s,symmetric=TRUE)
ainv <- t(F2)%*%Qgu%*%F2
diag(ainv) <- diag(ainv)+lambda
Sp <- -lambda*F2%*%(solve(ainv))%*%t(F2)
if (! is.null(Y)) {
cgu <- as.vector(Sp%*%Y)/(-lambda)
dgu <- solve(qr.R(qrSgu))%*%(t(qr.Q(qrSgu))%*%(as.matrix(Y)-Qgu%*%cgu))
diag(Sp) <- rep(1,n)+diag(Sp)
return(list(H=Sp,Sgu=Sgu,Qgu=Qgu,dgu=dgu,cgu=cgu))
} else {
diag(Sp) <- rep(1,n)+diag(Sp)
return(list(H=Sp,Sgu=Sgu,Qgu=Qgu,dgu=NULL,cgu=NULL))
}
}
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