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## Calculate Kullback-Leibler projection from ssden objects
project.ssden <- function(object,include,mesh=FALSE,...)
{
qd.pt <- object$quad$pt
qd.wt <- object$quad$wt
bias <- object$bias
## evaluate full model
mesh0 <- dssden(object,qd.pt)
qd.wt <- qd.wt*bias$qd.wt
qd.wt <- t(t(qd.wt)/apply(qd.wt*mesh0,2,sum))
## extract terms in subspace
nqd <- dim(qd.wt)[1]
nxi <- length(object$id.basis)
qd.s <- qd.r <- q <- NULL
theta <- d <- NULL
n0.wk <- nq.wk <- nq <- 0
for (label in object$terms$labels) {
x.basis <- object$mf[object$id.basis,object$term[[label]]$vlist]
qd.x <- qd.pt[,object$term[[label]]$vlist]
nphi <- object$term[[label]]$nphi
nrk <- object$term[[label]]$nrk
if (nphi) {
phi <- object$term[[label]]$phi
for (i in 1:nphi) {
n0.wk <- n0.wk + 1
if (!any(label==include)) next
d <- c(d,object$d[n0.wk])
qd.s <- cbind(qd.s,phi$fun(qd.x,nu=i,env=phi$env))
}
}
if (nrk) {
rk <- object$term[[label]]$rk
for (i in 1:nrk) {
nq.wk <- nq.wk + 1
if (!any(label==include)) next
nq <- nq + 1
theta <- c(theta,object$theta[nq.wk])
qd.r <- array(c(qd.r,rk$fun(x.basis,qd.x,nu=i,env=rk$env,out=TRUE)),
c(nxi,nqd,nq))
q <- cbind(q,rk$fun(x.basis,x.basis,nu=i,env=rk$env,out=FALSE))
}
}
}
if (is.null(qd.s)&is.null(qd.r))
stop("gss error in project.ssden: include some terms")
if (!is.null(qd.s)) {
nn <- nxi + ncol(qd.s)
qd.s <- t(qd.s)
}
else nn <- nxi
## calculate projection
rkl <- function(theta1=NULL) {
theta.wk <- 1:nq
theta.wk[fix] <- theta[fix]
if (nq-1) theta.wk[-fix] <- theta1
qd.rs <- 0
for (i in 1:nq) qd.rs <- qd.rs + 10^theta.wk[i]*qd.r[,,i]
qd.rs <- rbind(qd.rs,qd.s)
z <- .Fortran("drkl",
cd=as.double(cd), as.integer(nn),
as.double(t(qd.rs)), as.integer(nqd), as.integer(bias$nt),
as.double(bias$wt), as.double(t(qd.wt)),
mesh=as.double(mesh0), as.double(.Machine$double.eps),
as.double(1e-6), as.integer(30), integer(nn),
double(2*bias$nt*(nqd+1)+nn*(2*nn+4)), info=integer(1),
PACKAGE="gss")
if (z$info==1)
stop("gss error in project.ssden: Newton iteration diverges")
if (z$info==2)
warning("gss warning in project.ssden: Newton iteration fails to converge")
assign("cd",z$cd,inherits=TRUE)
assign("mesh1",z$mesh,inherits=TRUE)
sum(bias$wt*(apply(qd.wt*log(mesh0/mesh1)*mesh0,2,sum)+
log(apply(qd.wt*mesh1,2,sum))))
}
cv.wk <- function(theta) cv.scale*rkl(theta)+cv.shift
if (nq) {
## initialization
if (is.null(qd.s)) theta.wk <- 0
else {
qd.r.wk <- 0
for (i in 1:nq) qd.r.wk <- qd.r.wk + 10^theta[i]*qd.r[,,i]
vv.s <- vv.r <- 0
for (i in 1:bias$nt) {
mu.s <- apply(qd.wt[,i]*qd.s,2,sum)/sum(qd.wt[,i])
v.s <- apply(qd.wt[,i]*qd.s^2,2,sum)/sum(qd.wt[,i])
v.s <- v.s - mu.s^2
mu.r <- apply(qd.wt[,i]*qd.r.wk,2,sum)/sum(qd.wt[,i])
v.r <- apply(qd.wt[,i]*qd.r.wk^2,2,sum)/sum(qd.wt[,i])
v.r <- v.r - mu.r^2
vv.s <- vv.s + bias$wt[i]*v.s
vv.r <- vv.r + bias$wt[i]*v.r
}
theta.wk <- log10(sum(vv.s)/(nn-nxi)/sum(vv.r)*nxi) / 2
}
theta <- theta + theta.wk
tmp <- NULL
for (i in 1:nq) tmp <- c(tmp,10^theta[i]*sum(q[,i]))
fix <- rev(order(tmp))[1]
## projection
cd <- c(10^(-theta.wk)*object$c,d)
mesh1 <- NULL
if (nq-1) {
if (object$skip.iter) kl <- rkl(theta[-fix])
else {
if (nq-2) {
## scale and shift cv
tmp <- abs(rkl(theta[-fix]))
cv.scale <- 1
cv.shift <- 0
if (tmp<1&tmp>10^(-4)) {
cv.scale <- 10/tmp
cv.shift <- 0
}
if (tmp<10^(-4)) {
cv.scale <- 10^2
cv.shift <- 10
}
zz <- nlm(cv.wk,theta[-fix],stepmax=.5,ndigit=7)
}
else {
the.wk <- theta[-fix]
repeat {
mn <- the.wk-1
mx <- the.wk+1
zz <- nlm0(rkl,c(mn,mx))
if (min(zz$est-mn,mx-zz$est)>=1e-3) break
else the.wk <- zz$est
}
}
kl <- rkl(zz$est)
}
}
else kl <- rkl()
}
else {
nn <- nrow(qd.s)
z <- .Fortran("drkl",
cd=as.double(d), as.integer(nn),
as.double(qd.s), as.integer(nqd), as.integer(bias$nt),
as.double(bias$wt), as.double(t(qd.wt)),
mesh=as.double(mesh0), as.double(.Machine$double.eps),
as.double(1e-6), as.integer(30), integer(nn),
double(2*bias$nt*(nqd+1)+nn*(2*nn+4)), info=integer(1),
PACKAGE="gss")
if (z$info==1)
stop("gss error in project.ssden: Newton iteration diverges")
if (z$info==2)
warning("gss warning in project.ssden: Newton iteration fails to converge")
mesh1 <- z$mesh
kl <- sum(bias$wt*(apply(qd.wt*log(mesh0/mesh1)*mesh0,2,sum)+
log(apply(qd.wt*mesh1,2,sum))))
}
kl0 <- sum(bias$wt*(apply(qd.wt*log(mesh0)*mesh0,2,sum)+
log(apply(qd.wt,2,sum))))
kl <- sum(bias$wt*(apply(qd.wt*log(mesh0/mesh1)*mesh0,2,sum)+
log(apply(qd.wt*mesh1,2,sum))))
wt.wk <- t(t(qd.wt)/apply(qd.wt*mesh1,2,sum))
kl1 <- sum(bias$wt*(apply(wt.wk*log(mesh1)*mesh1,2,sum)+
log(apply(wt.wk,2,sum))))
obj <- list(ratio=kl/kl0,kl=kl,check=(kl+kl1)/kl0)
if (mesh) obj$mesh <- mesh1
obj
}
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