Nothing
FDA.historical2 <-
function(X1,X2,Y,delta.grid1=1,delta.grid2=1,intercept=TRUE,basis1=NULL,Ld2.basis1=NULL,basis2=NULL,Ld2.basis2=NULL,basis.type=c("fourier"),
nbasis1=3,nbasis2=3,timeinv=c(0,1),timegrids=NULL,lambda1=0.01,lambda2=0.01)
{
N<-dim(X1)[1] # # of subject
ntp<-dim(X1)[2] # # of time points
# design matrix
X.dim<-function(X)
{
q0<-dim(X)[3]
if(is.na(q0))
{
if(intercept)
{
q<-2
W<-array(NA,c(N,ntp,q))
W[,,1]<-matrix(1,nrow=N,ncol=ntp)
W[,,2]<-X
}else
{
q<-1
W<-array(NA,c(N,ntp,q))
W[,,1]<-X
}
}else
if(intercept)
{
q<-q0+1
W<-array(NA,c(N,ntp,q))
W[,,1]<-matrix(1,nrow=N,ncol=ntp)
W[,,2:q]<-X
}else
{
q<-q0
W<-X
}
return(list(q=q,W=W))
}
X.dim.re1<-X.dim(X1)
X.dim.re2<-X.dim(X2)
q1<-X.dim.re1$q
W1<-X.dim.re1$W
q2<-X.dim.re2$q
W2<-X.dim.re2$W
q<-q1+q2
# time grids
if(is.null(timegrids))
{
timegrids<-seq(timeinv[1],timeinv[2],length.out=ntp)
}
# basis functions
if(is.null(basis1))
{
if(basis.type[1]=="fourier")
{
basis1<-fourier.basis(timeinv=timeinv,ntp=ntp,nbasis=nbasis1)
Ld2.basis1<-Ld2.fourier(timeinv=timeinv,ntp=ntp,nbasis=nbasis1)
}
}else
{
nbasis1<-ncol(basis1)
}
if(is.null(basis2))
{
if(basis.type[1]=="fourier")
{
basis2<-fourier.basis(timeinv=timeinv,ntp=ntp,nbasis=nbasis2)
Ld2.basis2<-Ld2.fourier(timeinv=timeinv,ntp=ntp,nbasis=nbasis2)
}
}else
{
nbasis2<-ncol(basis2)
}
# lambda
if(length(lambda1)==1)
{
lambda1<-rep(lambda1,q)
}else
if(length(lambda1)>q)
{
lambda1<-lambda1[1:q]
}else
{
lambda1<-rep(lambda1[1],q)
}
if(length(lambda2)==1)
{
lambda2<-rep(lambda2,q)
}else
if(length(lambda2)>q)
{
lambda2<-lambda2[1:q]
}else
{
lambda2<-rep(lambda2[1],q)
}
K1<-c(nbasis1*q1,nbasis1*q2)
K2<-c(nbasis2*q1,nbasis2*q2)
K<-c((nbasis1*nbasis2)*q1,(nbasis1*nbasis2)*q2)
######################################################
D.func<-function(W,K1,K2,K,q,delta.grid)
{
U<-matrix(0,K,K)
V<-matrix(0,K,K)
D<-array(0,c(N,K,ntp))
for(j in 1:q)
{
U1tmp<-apply(array(apply(basis2,1,function(x){return(x%*%t(x))}),c(nbasis2,nbasis2,ntp)),c(1,2),function(x){return(int.func(x,timeinv=timeinv,timegrids=timegrids))})
U2tmp<-apply(array(apply(Ld2.basis1,1,function(x){return(x%*%t(x))}),c(nbasis1,nbasis1,ntp)),c(1,2),function(x){return(int.func(x,timeinv=timeinv,timegrids=timegrids))})
U[((j-1)*(nbasis1*nbasis2)+1):(j*(nbasis1*nbasis2)),((j-1)*(nbasis1*nbasis2)+1):(j*(nbasis1*nbasis2))]<-lambda1[j]*kronecker(U1tmp,U2tmp)
V1tmp<-apply(array(apply(Ld2.basis2,1,function(x){return(x%*%t(x))}),c(nbasis2,nbasis2,ntp)),c(1,2),function(x){return(int.func(x,timeinv=timeinv,timegrids=timegrids))})
V2tmp<-apply(array(apply(basis1,1,function(x){return(x%*%t(x))}),c(nbasis1,nbasis1,ntp)),c(1,2),function(x){return(int.func(x,timeinv=timeinv,timegrids=timegrids))})
V[((j-1)*(nbasis1*nbasis2)+1):(j*(nbasis1*nbasis2)),((j-1)*(nbasis1*nbasis2)+1):(j*(nbasis1*nbasis2))]<-lambda2[j]*kronecker(V1tmp,V2tmp)
Ws<-array(NA,c(N,nbasis1,ntp))
Wstmp<-array(NA,c(N,nbasis1,ntp))
for(i in 1:ntp)
{
Wstmp[,,i]<-matrix(W[,i,j],nrow=N)%*%matrix(basis1[i,],ncol=nbasis1)
rtmp<-max(i-delta.grid,1)
Ws[,,i]<-apply(array(Wstmp[,,rtmp:i],c(N,nbasis1,length(rtmp:i))),c(1,2),int.func,timeinv=c(timegrids[rtmp],timegrids[i]),timegrids=timegrids[rtmp:i])
D[,((j-1)*(nbasis1*nbasis2)+1):(j*(nbasis1*nbasis2)),i]<-kronecker(t(basis2[i,]),Ws[,,i])
}
}
return(list(D=D,U=U,V=V))
}
re.D1<-D.func(W1,K1[1],K2[1],K[1],q1,delta.grid1)
re.D2<-D.func(W2,K1[2],K2[2],K[2],q2,delta.grid2)
D1<-re.D1$D
D2<-re.D2$D
D<-array(NA,c(dim(D1)[1],dim(D1)[2]+dim(D2)[2],dim(D1)[3]))
D[,1:(dim(D1)[2]),]<-D1
D[,(dim(D1)[2]+1):(dim(D1)[2]+dim(D2)[2]),]<-D2
mat1<-array(NA,c(sum(K),sum(K),ntp))
mat2<-array(NA,c(sum(K),1,ntp))
for(i in 1:ntp)
{
mat1[,,i]<-t(D[,,i])%*%D[,,i]
mat2[,,i]<-t(D[,,i])%*%Y[,i]
}
Q1<-apply(mat1,c(1,2),int.func,timeinv=timeinv,timegrids=timegrids)
Q2<-apply(mat2,c(1,2),int.func,timeinv=timeinv,timegrids=timegrids)
U1<-re.D1$U
V1<-re.D1$V
U2<-re.D2$U
V2<-re.D2$V
U=V<-matrix(0,sum(K),sum(K))
U[1:K[1],1:K[1]]<-U1
U[(K[1]+1):sum(K),(K[1]+1):sum(K)]<-U2
V[1:K[1],1:K[1]]<-V1
V[(K[1]+1):sum(K),(K[1]+1):sum(K)]<-V2
g<-solve(Q1+U+V)%*%Q2
g1<-g[1:K[1]]
g2<-g[(K[1]+1):sum(K)]
Gmat.func<-function(K1,K2,q,g)
{
Gmat<-matrix(0,K1,K2)
for(j in 1:q)
{
Gmat[((j-1)*nbasis1+1):(j*nbasis1),((j-1)*nbasis2+1):(j*nbasis2)]<-matrix(g[((j-1)*(nbasis1*nbasis2)+1):(j*(nbasis1*nbasis2))],nbasis1,nbasis2)
}
return(Gmat)
}
Gmat1<-Gmat.func(K1[1],K2[1],q1,g1)
Gmat2<-Gmat.func(K1[2],K2[2],q2,g2)
Gmat<-matrix(0,dim(Gmat1)[1]+dim(Gmat2)[1],dim(Gmat1)[2]+dim(Gmat2)[2])
Gmat[1:(dim(Gmat1)[1]),1:(dim(Gmat1)[2])]<-Gmat1
Gmat[(dim(Gmat1)[1]+1):(dim(Gmat1)[1]+dim(Gmat2)[1]),(dim(Gmat1)[2]+1):(dim(Gmat1)[2]+dim(Gmat2)[2])]<-Gmat2
######################################################
gamma.func<-function(Gmat,q)
{
gamma.est<-array(NA,c(ntp,ntp,q))
for(j in 1:q)
{
for(u in 1:ntp)
{
for(s in 1:ntp)
{
gamma.est[u,s,j]<-t(basis1[u,])%*%Gmat[((j-1)*nbasis1+1):(j*nbasis1),((j-1)*nbasis2+1):(j*nbasis2)]%*%basis2[s,]
}
}
}
return(gamma.est)
}
gamma.est1<-gamma.func(Gmat1,q1)
gamma.est2<-gamma.func(Gmat2,q2)
gamma.est<-array(NA,c(ntp,ntp,q))
gamma.est[,,1:q1]<-gamma.est1
gamma.est[,,(q1+1):q]<-gamma.est2
if(intercept)
{
dimnames(gamma.est)[[3]]<-c("Intercept",paste0("X",1:(q-1)))
}else
{
dimnames(gamma.est)<-list(NULL)
dimnames(gamma.est)[[3]]<-paste0("X",1:q)
}
yfit<-apply(D,c(1,3),function(x){return(t(x)%*%g)})
re<-list(coefficients=Gmat,coef.vec=g,coef1=Gmat1,coef2=Gmat2,basis1=basis1,basis2=basis2,gamma.curve=gamma.est,fitted=yfit)
return(re)
}
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