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fEBA_Rfns.R
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fEBA_Rfns.R
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#function to simulate functional white noise data
fws.sim <- function(nb=15,gsz=20,Ts,seed){
set.seed(seed)
#create b-spline basis
bspl1.1 <- create.bspline.basis(norder=nb)
#plot(bspl1.1)
eval.bspl1.1 <- eval.basis(seq(0, 1, length.out=gsz), bspl1.1)
# draw coefficients for fourier basis
covmat <- diag(exp(((1:nb)-1)/20)); # covariance matrix for coefficients
fcf <- sqrt(covmat)%*%matrix(rnorm(nb*Ts),ncol=Ts);
# draw one time point realization for process
fwn <- t(fcf)%*%t(eval.bspl1.1);
#standardize variance across components
fwn <- apply(fwn,2,function(x) 1*(x/sd(x)))
return(fwn);
}
#function to simulate nonstationary 3 band linear data
f3bL.sim <- function(nb,gsz,Ts,seed){
set.seed(seed)
seed2<-sample(1:600,3);
#low frequencies
X <- fws.sim(nb=nb,gsz=gsz,T=Ts,seed=seed2[1]);
Ts <- nrow(X);
Fs <- floor(Ts/2)+1;
f <- seq(from=0,by=1/Ts,length.out=floor(Ts/2)+1);
f <- c(f,rev(f[c(-1,-which(f==0.5))]));
dft <- mvfft(X)/Ts;
dft[which(f>0.15),] <- 0;
fwn1.lf <- Re(mvfft(dft,inverse=TRUE));
fwn1.lf <- apply(fwn1.lf,2,function(x) x/sd(x));
# fwn1.lf <- fwn1.lf/sd(fwn1.lf);
#middle frequencies
X <- fws.sim(nb=nb,gsz=gsz,T=Ts,seed=seed2[2]);
Ts <- nrow(X);
Fs <- floor(Ts/2)+1;
f <- seq(from=0,by=1/Ts,length.out=floor(Ts/2)+1);
f <- c(f,rev(f[c(-1,-which(f==0.5))]));
dft <- mvfft(X)/Ts;
dft[which(f<=0.15 | f>0.35),] <- 0;
fwn1.mf <- Re(mvfft(dft,inverse=TRUE));
fwn1.mf <- apply(fwn1.mf,2,function(x) x/sd(x));
# fwn1.mf <- fwn1.mf/sd(fwn1.mf);
#high frequencies
X <- fws.sim(nb=nb,gsz=gsz,T=Ts,seed=seed2[3]);
Ts <- nrow(X);
Fs <- floor(Ts/2)+1;
f <- seq(from=0,by=1/Ts,length.out=floor(Ts/2)+1);
f <- c(f,rev(f[c(-1,-which(f==0.5))]));
dft <- mvfft(X)/Ts;
dft[which(f<=0.35),] <- 0;
fwn1.hf <- Re(mvfft(dft,inverse=TRUE));
fwn1.hf <- apply(fwn1.hf,2,function(x) x/sd(x));
# fwn1.hf <- fwn1.hf/sd(fwn1.hf);
#nonstationary 3 segments linear
#combine
coef1 <- seq(from=10,to=1,length.out=Ts);
coef2 <- seq(from=5,to=5,length.out=Ts);
coef3 <- seq(from=1,to=10,length.out=Ts);
X.3bL <- coef1*fwn1.lf*sqrt(.3) + coef2*fwn1.mf*sqrt(.4) + coef3*fwn1.hf*sqrt(.3);
return(X.3bL)
}
#function to simulate nonstationary 3 band sinusoidal data
f3bS.sim <- function(nb,gsz,Ts,seed){
set.seed(seed)
seed2<-sample(1:600,4);
#low frequencies
X <- fws.sim(nb=nb,gsz=gsz,T=Ts,seed=seed2[1]);
Ts <- nrow(X);
Fs <- floor(Ts/2)+1;
f <- seq(from=0,by=1/Ts,length.out=floor(Ts/2)+1);
f <- c(f,rev(f[c(-1,-which(f==0.5))]));
dft <- mvfft(X)/Ts;
dft[which(f>0.15),] <- 0;
fwn1.lf <- Re(mvfft(dft,inverse=TRUE));
fwn1.lf <- apply(fwn1.lf,2,function(x) x/sd(x));
# fwn1.lf <- fwn1.lf/sd(fwn1.lf);
#middle frequencies
X <- fws.sim(nb=nb,gsz=gsz,T=Ts,seed=seed2[2]);
Ts <- nrow(X);
Fs <- floor(Ts/2)+1;
f <- seq(from=0,by=1/Ts,length.out=floor(Ts/2)+1);
f <- c(f,rev(f[c(-1,-which(f==0.5))]));
dft <- mvfft(X)/Ts;
dft[which(f<=0.15 | f>0.35),] <- 0;
fwn1.mf <- Re(mvfft(dft,inverse=TRUE));
fwn1.mf <- apply(fwn1.mf,2,function(x) x/sd(x));
# fwn1.mf <- fwn1.mf/sd(fwn1.mf);
#high frequencies
X <- fws.sim(nb=nb,gsz=gsz,T=Ts,seed=seed2[3]);
Ts <- nrow(X);
Fs <- floor(Ts/2)+1;
f <- seq(from=0,by=1/Ts,length.out=floor(Ts/2)+1);
f <- c(f,rev(f[c(-1,-which(f==0.5))]));
dft <- mvfft(X)/Ts;
dft[which(f<=0.35),] <- 0;
fwn1.hf <- Re(mvfft(dft,inverse=TRUE));
fwn1.hf <- apply(fwn1.hf,2,function(x) x/sd(x));
# fwn1.hf <- fwn1.hf/sd(fwn1.hf);
#nonstationary 3 segments linear
#combine
coef1 <- sqrt(9)*sin(2*pi*seq(0,1,length=Ts));
coef2 <- sqrt(9)*cos(2*pi*seq(0,1,length=Ts));
coef3 <- sqrt(9)*cos(4*pi*seq(0,1,length=Ts));
X.3bS <- coef1*fwn1.lf*sqrt(.3) + coef2*fwn1.mf*sqrt(.4) + coef3*fwn1.hf*sqrt(.3)+fws.sim(nb=nb,gsz=gsz,T=Ts,seed=seed2[4]);
return(X.3bS)
}
#function to run iterative eba algorithm
fEBA.wrapper <- function(X,Rsel,K,N,ndraw,alpha,std,blockdiag,dcap=10^10){
freq <- seq(from=0,by=1/N,length.out=floor(N/2)+1);
R<-min(ncol(X),Rsel);
#multitaper estimator of power spectrum
pse <- fhat(X,N,K,Rsel,std);
B <- dim(pse)[3];
dimnames(pse) <- list(freq,apply(expand.grid(1:R,1:R),1,paste,collapse = "-"),1:B);
#demeaned multitaper estimator of power spectrum
gpse <- ghat(pse);
dimnames(pse) <- list(freq,apply(expand.grid(1:R,1:R),1,paste,collapse = "-"),1:B);
#initialization
f.part=c(1,floor(N/2)+1); #starting partition
stp <- 0; #stopping condition
idx <- 1; #partition index
logfile <- list(); #initialize log file
sumfile <- matrix(NA,nrow=0,ncol=4); #initalize summary file
partlst <- list(freq[f.part]); #initialize list of partitions
bw <- floor((K+1)*(N/(N+1)))+1; #bandwidth in terms of # of frequencies + 1
passctr <- 0;
dctr <- 0;
#recursive loop to generate new partition points
while(stp==0){
if(min(f.part[idx+1]-bw,f.part[idx]+bw+(dctr+1)*dcap)>(f.part[idx]+bw+dctr*dcap)){ #endf>startf
#display pass counter
passctr <- passctr + 1;
message(paste("Pass ",passctr,sep=""));
#identify changepoint candidates (Cpp functions)
startf <- f.part[idx]+bw+dctr*dcap;
endf <- min(f.part[idx+1]-bw,startf+dcap);
tmp <- fEBA(fhat=pse[startf:endf,,,drop=FALSE],ghat=gpse[startf:endf,,,drop=FALSE],
K,ndraw,alpha,blockdiag)
#reformat and add labeling
names(tmp) <- c('Qts','Qint','Qpv','Qhb');
rownames(tmp$Qts) <- freq[(startf+1):endf];
rownames(tmp$Qint) <- freq[(startf+1):endf];
rownames(tmp$Qpv) <- freq[(startf+1):endf];
rownames(tmp$Qhb) <- c('freq','pval','threshold','sig');
colnames(tmp$Qts) <- apply(expand.grid(1:R,1:R),1,paste,collapse = "-");
colnames(tmp$Qint) <- "Qint";
colnames(tmp$Qpv) <- c(apply(expand.grid(1:R,1:R),1,paste,collapse = "-"),"Qint");
colnames(tmp$Qhb) <- c(apply(expand.grid(1:R,1:R),1,paste,collapse = "-"),"Qint");
tmp$Qhb[1,] <- freq[startf+1+tmp$Qhb[1,]];
#append run to log file
logfile <- c(logfile,list(tmp));
#append to summary
sumfile <- rbind(sumfile,tmp$Qhb[,'Qint']);
#print results from pass
print(tmp$Qhb[,'Qint']);
#update partition, list, and starting points
f.part.curr <- f.part;
len.curr <- length(f.part.curr);
if(as.logical(tmp$Qhb[4,"Qint"]) && tmp$Qhb['freq','Qint']!=freq[f.part.curr[idx+1]]){
f.part <- as.vector(sort(c(f.part,which(freq==tmp$Qhb['freq','Qint']))));
}
if(length(f.part)>len.curr){
#if updates
#append new partition to partition list
partlst <- c(partlst,list(freq[f.part]));
#increment idx
idx <- idx+1;
#reset dctr
dctr <- 0;
} else {
#if no updates
#increment dctr
dctr <- dctr + 1;
}
}else{
idx <- idx+1; #move to next segment if too small
}
#stop once reached last partition point
stp <- as.numeric(length(f.part)==idx);
}
#compile results
rownames(sumfile) <- 1:nrow(sumfile);
results <- list(part.final=freq[f.part],part.list=partlst,
summary=sumfile,fhat=pse,ghat=gpse,log=logfile);
return(results)
}