FDA.concurrent <-
function(X,Y,intercept=TRUE,basis=NULL,Ld2.basis=NULL,basis.type=c("fourier"),nbasis=3,timeinv=c(0,1),timegrids=NULL,lambda=0.01)
{
N<-dim(X)[1] # # of subject
ntp<-dim(X)[2] # # of time points
# design matrix
X.design<-design.mat(X,intercept=intercept)
q<-X.design$q
W<-X.design$W
# time grids
if(is.null(timegrids))
{
timegrids<-seq(timeinv[1],timeinv[2],length.out=ntp)
}
# basis functions
if(is.null(basis))
{
if(basis.type[1]=="fourier")
{
basis<-fourier.basis(timeinv=timeinv,ntp=ntp,nbasis=nbasis)
Ld2.basis<-Ld2.fourier(timeinv=timeinv,ntp=ntp,nbasis=nbasis)
}
}else
{
nbasis<-ncol(basis)
}
# lambda
if(length(lambda)==1)
{
lambda<-rep(lambda,q)
}else
if(length(lambda)>q)
{
lambda<-lambda[1:q]
}else
{
lambda<-rep(lambda[1],q)
}
K<-nbasis*q
U<-matrix(0,K,K)
Theta<-array(0,c(q,K,ntp))
for(j in 1:q)
{
Utmp<-lambda[j]*apply(array(apply(Ld2.basis,1,function(x){return(x%*%t(x))}),c(nbasis,nbasis,ntp)),c(1,2),function(x){return(int.func(x,timeinv=timeinv,timegrids=timegrids))})
U[((j-1)*nbasis+1):(j*nbasis),((j-1)*nbasis+1):(j*nbasis)]<-Utmp
Theta[j,((j-1)*nbasis+1):(j*nbasis),]<-t(basis)
}
# W %*% Theta matrix
mat1<-array(NA,c(K,K,ntp))
mat2<-array(NA,c(K,1,ntp))
for(s in 1:ntp)
{
dtmp<-matrix(W[,s,],ncol=q)%*%matrix(Theta[,,s],nrow=q)
mat1[,,s]<-t(dtmp)%*%dtmp
mat2[,,s]<-t(matrix(Theta[,,s],nrow=q))%*%t(matrix(W[,s,],ncol=q))%*%Y[,s]
}
V1<-apply(mat1,c(1,2),int.func,timeinv=timeinv,timegrids=timegrids)
V2<-apply(mat2,c(1,2),int.func,timeinv=timeinv,timegrids=timegrids)
g<-solve(V1+U)%*%V2
# gamma.est<-matrix(apply(Theta,3,function(x){return(x%*%g)}),ncol=q)
gamma.est<-matrix(NA,ntp,q)
for(j in 1:q)
{
gamma.est[,j]<-basis%*%g[((j-1)*nbasis+1):(j*nbasis)]
}
if(intercept)
{
colnames(gamma.est)<-c("Intercept",paste0("X",1:(q-1)))
}else
{
colnames(gamma.est)<-paste0("X",1:q)
}
yfit<-t(apply(W,1,function(x){return(apply(x*gamma.est,1,sum))}))
re<-list(coefficients=c(g),basis=basis,gamma.curve=t(gamma.est),fitted=yfit)
return(re)
}
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