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periodoframe.R
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periodoframe.R
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library(minpack.lm)
source('periodograms.R')
#library(lomb)
tol <- 1e-18
tol2 <- 1e-20
tol3 <- 1e-30
#trend <- FALSE
RV.model <- function(par,data){
####
t <- data$data[,1]
y <- data$data[,2]
dy <- data$data[,3]
Indices <- data$Indices
Nma <- data$Nma
NI <- data$NI
if(!any('A'==names(par))){
A <- B <- phi <- omega <- 0
}else{
phi <- data$par.fix$phi
omega <- data$par.fix$omega
}
var <- names(par)
d <- c()
m <- c()
for(k in 1:length(var)){
assign(var[k],par[[var[k]]])
if(grepl('^d',var[k])) d <- c(d,par[[var[k]]])
if(grepl('^m',var[k])) m <- c(m,par[[var[k]]])
}
ind <- sort(t,index.return=TRUE)$ix
if(NI>0){
r <- A*cos(omega*t-phi)+B*sin(omega*t-phi)+gamma+beta*t+partI(d,Indices,NI)
}else{
r <- A*cos(omega*t-phi)+B*sin(omega*t-phi)+gamma+beta*t
}
val <- r
if(Nma>0){
for(k in 1:Nma){
t2 <- c(rep(0,k),t[-(1:k)])
t1 <- c(rep(0,k),t[-(length(t)+1-(1:k))])
ys <- c(rep(0,k),y[-(length(t)+1-(1:k))])
rs <- c(rep(0,k),r[-(length(t)+1-(1:k))])
val <- val+m[k]*exp(-abs(t2-t1)/exp(logtau))*(ys-rs)
}
}
return(val)
}
partI <- function(d,Is,NI){
if(NI==1){
d*Is[,1]
}else{
d%*%t(Is[,1:NI])
}
}
wI <- function(w,Is,NI){
unlist(lapply(1:NI,function(i) sum(w*Is[,i])))
}
me <- function(m,t,logtau,x){
if(length(m)==1){
m*exp(-abs(t[-1]-t[-length(t)])/exp(logtau))*x[-length(x)]
}else{
# unlist(lapply(1:length(m), function(i) m[i]*exp(-abs(t[-c(1:i)]-t[-(length(t)+1-c(1:i))])/exp(logtau))*x[-(length(x)+1-c(1:i))]))
}
}
rv.res <- function(par,data){
y <- data$data[,2]
dy <- data$data[,3]
###add a large constant to make the logL always positive and thus avoid errors
# tmp <- sqrt((y-RV.model(par,data))^2/(2*(dy^2+par$sj^2)) + 0.5*log(dy^2+par$sj^2)+100)
tmp <- sqrt((y-RV.model(par,data))^2/(2*(dy^2+par$sj^2)) + 0.5*log(dy^2+par$sj^2)+0.5*log(2*pi))
if(any(is.na(tmp))){
cat('inside=',head((y-RV.model(par,data))^2/(2*(dy^2+par$sj^2))),'\n')
}
return(tmp)
}
######optimize all parameters using the LM algorithm
nlopt <- function(pars,type='noise'){
var <- names(pars)
for(k in 1:length(var)){
assign(var[k],pars[[var[k]]])
}
par.opt <- NULL
chi2 <- NULL
if(type=='period'){
par.fix <- list(omega=omega,phi=phi)
}else{
par.fix <- NULL
}
tmp <- data.frame(t,y,dy)
df <- list(data=tmp,Indices=Indices,par.fix=par.fix,Nma=Nma,NI=NI)
trace <- FALSE
if(type!='noise'){
start <- list(A=Aini,B=Bini,gamma=gamma.ini,beta=beta.ini)
par.low <- c(A=Amin,B=Bmin,gamma=gamma.min,beta=beta.min)
par.up <- c(A=Amax,B=Bmax,gamma=gamma.max,beta=beta.max)
}else{
start <- list(gamma=gamma.ini,beta=beta.ini)
par.low <- c(gamma=gamma.min,beta=beta.min)
par.up <- c(gamma=gamma.max,beta=beta.max)
}
if(NI>0){
for(k in 1:NI){
start[[paste0('d',k)]] <- dini
par.low <- c(par.low,d=dmin)
par.up <- c(par.up,d=dmax)
}
}
cat('par.up=',par.up,'\n')
start$sj <- sj.ini
par.low <- c(par.low,sj=sj.min)
par.up <- c(par.up,sj=sj.max)
if(Nma>0){
for(k in 1:Nma){
start[[paste0('m',k)]] <- mini#[k]
par.low <- c(par.low,m=mmin)
par.up <- c(par.up,m=mmax)
}
start <- c(start,logtau=logtau.ini)
par.low <- c(par.low,logtau=logtau.min)
par.up <- c(par.up,logtau=logtau.max)
}
names(par.up) <- names(par.low) <- names(start)
###########
out <- nls.lm(par = start,lower=par.low,upper=par.up,fn = rv.res,data=df,control=nls.lm.control(maxiter=500))#ftol=1e-8
opt.par <- pars <- as.list(coef(out))
yp.full <- RV.model(par=pars,data = df)
if(type=='period'){
pars$A <- 0
pars$B <- 0
yp.noise <- RV.model(par=pars,data=df)
}else{
yp.noise <- yp.full
}
res <- as.numeric(y-yp.full)
res.sig <- as.numeric(y-(yp.full-yp.noise))
chi2 <- sum(res^2/dy^2)
chi2.noise <- sum((y-yp.noise)^2/dy^2)
logLmax <- sum(-res^2/(2*(opt.par$sj^2+dy^2))-0.5*log(2*pi)-0.5*log(opt.par$sj^2+dy^2))
return(list(res=res,res.sig=res.sig,chi2=chi2,chi2.noise=chi2.noise,par=opt.par,logLmax=logLmax))
}
rv.red <- function(par,df){
#####setting up
var <- names(df)
for(k in 1:length(var)){
assign(var[k],df[[var[k]]])
}
if(!is.null(par.fix)){
phi <- par.fix$phi
omega <- par.fix$omega
}
t <- data[,1]
y <- data[,2]
dy <- data[,3]
logtau <- par$logtau
m <- c()
if(Nma>0){
for(j in 1:Nma){
m <- c(m,par[[paste0('m',j)]])
}
}else{
m <- 0
}
sj <- par$sj
#####notations
W <- sum(1/(sj^2+dy^2))
w <- 1/(sj^2+dy^2)/W
es <- c()
if(Nma>0){
for(i in 1:Nma){
ei <- c(rep(0,i),exp(-abs(t[-(length(t)+1-(1:i))]-t[-(1:i)])/exp(logtau)))
es <- rbind(es,ei)
}
yp <- y-m%*%(es*ys)
wp <- 1-m%*%es
tp <- t-m%*%(es*ts)
if(type=='period'){
cp <- cos(omega*t)-m%*%(es*cs)
sp <- sin(omega*t)-m%*%(es*ss)
}
}else{
yp <- y
wp <- 1
tp <- t
if(type=='period'){
cp <- cos(omega*t)
sp <- sin(omega*t)
}
}
WIp <- ip <- TIp <- YIp <- CIp <- SIp <- c()
IIp <- array(data=NA,dim=c(NI,NI))
if(NI>0){
for(j in 1:NI){
if(Nma>0){
ip <- rbind(ip,Indices[j,]-m%*%(es*Is[,j,]))
}else{
ip <- rbind(ip,Indices[j,])
}
YIp <- c(YIp,sum(w*yp*ip[j,]))
WIp <- c(WIp,sum(w*wp*ip[j,]))
TIp <- c(TIp,sum(w*tp*ip[j,]))
if(type=='period'){
CIp <- c(CIp,sum(w*cp*ip[j,]))
SIp <- c(SIp,sum(w*sp*ip[j,]))
}
}
for(j in 1:NI){
for(i in j:NI){
IIp[j,i] <- IIp[i,j] <- sum(w*ip[i,]*ip[j,])
}
}
}
WWp <- sum(w*wp*wp)
YWp <- sum(w*wp*yp)
YTp <- sum(w*yp*tp)
Wp <- sum(w*wp)
WTp <- sum(w*wp*tp)
TTp <- sum(w*tp^2)
if(type=='period'){
Cp <- sum(w*cp)
Sp <- sum(w*sp)
YCp <- sum(w*yp*cp)
YSp <- sum(w*yp*sp)
CCp <- sum(w*cp^2)
SSp <- sum(w*sp^2)
CSp <- sum(w*cp*sp)
CTp <- sum(w*cp*tp)
CWp <- sum(w*cp*wp)
STp <- sum(w*sp*tp)
SWp <- sum(w*sp*wp)
}
if(type=='noise'){
if(NI>0){
lin.mat <- matrix(c(WWp,WTp,WIp,WTp,TTp,TIp),byrow=TRUE,ncol=2+NI)
for(j in 1:NI){
lin.mat <- rbind(lin.mat,c(WIp[j],TIp[j],IIp[j,]))
}
vec.rh <- c(YWp,YTp,YIp)
}else{
dI <- 0
d <- 0
lin.mat <- matrix(c(WWp,WTp,WTp,TTp),byrow=TRUE,ncol=2)
vec.rh <- c(YWp,YTp)
}
###optimized parameterse for the trend model
}else if(type=='period'){
#####calculate the optimal white noise model parameters:gamma,beta,dj
lin.mat <- c()
if(NI>0){
for(j in 1:(4+NI)){
if(j==1){
lin.mat <- rbind(lin.mat,c(CCp,CSp,CWp,CTp,CIp))
}
if(j==2){
lin.mat <- rbind(lin.mat,c(CSp,SSp,SWp,STp,SIp))
}
if(j==3){
lin.mat <- rbind(lin.mat,c(CWp,SWp,WWp,WTp,WIp))
}
if(j==4){
lin.mat <- rbind(lin.mat,c(CTp,STp,WTp,TTp,TIp))
}
if(j>4){
lin.mat <- rbind(lin.mat,c(CIp[j-4],SIp[j-4],WIp[j-4],TIp[j-4],IIp[j-4,]))
}
}
vec.rh <- c(YCp,YSp,YWp,YTp,YIp)
}else{
lin.mat <- rbind(lin.mat,c(CCp,CSp,CWp,CTp))
lin.mat <- rbind(lin.mat,c(CSp,SSp,SWp,STp))
lin.mat <- rbind(lin.mat,c(CWp,SWp,WWp,WTp))
lin.mat <- rbind(lin.mat,c(CTp,STp,WTp,TTp))
vec.rh <- c(YCp,YSp,YWp,YTp)
}
}
white.par <- try(solve(lin.mat,vec.rh,tol=tol),TRUE)#gamma,beta,dj
if(class(white.par)=='try-error') white.par <- try(solve(lin.mat,vec.rh,tol=tol2),TRUE)
if(class(white.par)=='try-error') white.par <- solve(lin.mat,vec.rh,tol=tol3)
ind0 <- length(white.par)-NI-1
if(length(white.par)==1){
cat('white.par=',white.par,'\n')
cat('lin.mat=',c(lin.mat),'\n')
cat('det(lin.mat)=',det(lin.mat),'\n')
cat('dim(lin.mat)=',dim(lin.mat),'\n')
cat('NI=',NI,'\n')
cat('length(white.par)=',length(white.par),'\n')
cat('ind0=',ind0,'\n')
}
r <- white.par[ind0]+white.par[ind0+1]*t
if(NI>0){
r <- r+white.par[(ind0+2):length(white.par)]%*%Indices[1:NI,]
}
if(type=='period'){
r <- r+white.par[1]*cos(omega*t)+white.par[2]*sin(omega*t)
}
if(Nma>0){
r <- as.numeric(r)
rs <- c()
for(i in 1:Nma){
ri <- c(rep(0,i),r[-(length(t)+1-(1:i))])
rs <- rbind(rs,ri)
}
v <- as.numeric(r+m%*%(es*(ys-rs)))
}else{
v <- as.numeric(r)
}
opt.par <- white.par
return(list(v=v,par=opt.par))
}
rv.white <- function(par,df){
#####setting up
var <- names(df)
for(k in 1:length(var)){
assign(var[k],df[[var[k]]])
}
if(!is.null(par.fix)){
phi <- par.fix$phi
omega <- par.fix$omega
}
t <- data[,1]
y <- data[,2]
dy <- data[,3]
sj <- par$sj
#####notations
W <- sum(1/(sj^2+dy^2))
w <- 1/(sj^2+dy^2)/W
if(type=='period'){
c <- cos(omega*t)
s <- sin(omega*t)
}
Y <- sum(w*y)
YT <- sum(w*y*t)
T <- sum(w*t)
TT <- sum(w*t^2)
if(NI>0){
I <- TI <- YI <- c()
II <- array(data=NA,dim=c(NI,NI))
for(j in 1:NI){
I <- c(I,sum(w*Indices[j,]))
TI <- c(TI,sum(w*t*Indices[j,]))
YI <- c(YI,sum(w*y*Indices[j,]))
for(i in j:NI){
II[j,i] <- II[i,j] <- sum(w*Indices[i,]*Indices[j,])
}
}
if(type=='period'){
CI <- SI <- c()
for(j in 1:NI){
CI <- c(CI,sum(w*cos(omega*t)*Indices[j,]))
SI <- c(SI,sum(w*sin(omega*t)*Indices[j,]))
}
}
}
####
# if w is normalized, 1 is used; otherwise, W is used.
if(type=='noise'){
if(NI>0){
lin.mat <- matrix(c(1,T,I,T,TT,TI),byrow=TRUE,ncol=2+NI)
for(j in 1:NI){
lin.mat <- rbind(lin.mat,c(I[j],TI[j],II[j,]))
}
vec.rh <- c(Y,YT,YI)
white.par <- try(solve(lin.mat,vec.rh,tol=tol),TRUE)#gamma,beta,dj
if(class(white.par)=='error') white.par <- solve(lin.mat,vec.rh,tol=tol2)
indd <- (length(white.par)-NI+1):length(white.par)
}else{
dI <- 0
d <- 0
lin.mat <- matrix(c(1,T,T,TT),byrow=TRUE,ncol=2)
vec.rh <- c(Y,YT)
white.par <- try(solve(lin.mat,vec.rh,tol=tol),TRUE)
if(class(white.par)=='error') white.par <- solve(lin.mat,vec.rh,tol=tol2)
}
###optimized parameterse for the trend model
}else if(type=='period'){
C <- sum(w*cos(omega*t))
S <- sum(w*sin(omega*t))
CC <- sum(w*cos(omega*t)^2)
SS <- sum(w*sin(omega*t)^2)
CS <- sum(w*sin(omega*t)*cos(omega*t))
CT <- sum(w*t*cos(omega*t))
ST <- sum(w*t*sin(omega*t))
YC <- sum(w*y*cos(omega*t))
YS <- sum(w*y*sin(omega*t))
#####calculate the optimal white noise model parameters:gamma,beta,dj
lin.mat <- c()#matrix(c(CC,CS,C,CT,CIW,T,I,T,TT,TI),byrow=TRUE,ncol=2+NI)
if(NI>0){
for(j in 1:(4+NI)){
if(j==1){
lin.mat <- rbind(lin.mat,c(CC,CS,C,CT,CI))
}
if(j==2){
lin.mat <- rbind(lin.mat,c(CS,SS,S,ST,SI))
}
if(j==3){
lin.mat <- rbind(lin.mat,c(C,S,W,T,I))
}
if(j==4){
lin.mat <- rbind(lin.mat,c(CT,ST,T,TT,TI))
}
if(j>4){
lin.mat <- rbind(lin.mat,c(CI[j-4],SI[j-4],I[j-4],TI[j-4],II[j-4,]))
}
}
vec.rh <- c(YC,YS,Y,YT,YI)
white.par <- try(solve(lin.mat,vec.rh,tol=tol),TRUE)#gamma,beta,dj
if(class(white.par)=='error') white.par <- solve(lin.mat,vec.rh,tol=tol2)
indd <- (length(white.par)-NI+1):length(white.par)
}else{
lin.mat <- rbind(lin.mat,c(CC,CS,C,CT))
lin.mat <- rbind(lin.mat,c(CS,SS,S,ST))
lin.mat <- rbind(lin.mat,c(C,S,W,T))
lin.mat <- rbind(lin.mat,c(CT,ST,T,TT))
vec.rh <- c(YC,YS,Y,YT)
white.par <- try(solve(lin.mat,vec.rh,tol=tol),TRUE)#gamma,beta,dj
if(class(white.par)=='error') white.par <- solve(lin.mat,vec.rh,tol=tol2)
}
}
ind0 <- length(white.par)-NI-1
r <- white.par[ind0]+white.par[ind0+1]*t
if(NI>0){
r <- r+white.par[(ind0+2):length(white.par)]%*%Indices[1:NI,]
}
if(type=='period'){
r <- r+white.par[1]*cos(omega*t)+white.par[2]*sin(omega*t)
}
if(NI>0){
indd <- (length(white.par)-NI+1):length(white.par)
opt.par <- c(white.par[-indd],d=white.par[indd])
}else{
opt.par <- white.par
}
return(list(v=r,par=opt.par))
}
rv.red.res <- function(par,df){
y <- df$data[,2]
dy <- df$data[,3]
# if(df$Nma>0){
v <- rv.red(par,df)$v
# }else{
# v <- rv.white(par,df)$v
# }
sj <- par$sj
# tmp <- sqrt((y-v)^2/(2*(dy^2+sj^2)) + 0.5*log(dy^2+sj^2)+100)
tmp <- sqrt((y-v)^2/(2*(dy^2+sj^2)) + 0.5*log(dy^2+sj^2)+0.5*log(2*pi))
return(tmp)
}
######express other parameters as functions of correlated noise parameters, optimize correlated noise parameters using the LM algorithm
sopt <- function(pars,type='noise'){
var <- names(pars)
for(k in 1:length(var)){
assign(var[k],pars[[var[k]]])
}
####transpose Indices to make the computation faster
if(!is.null(Indices) & !any(is.na(Indices))){
if(nrow(Indices)==length(t)) Indices <- t(Indices)
}
if(type=='period'){
par.fix <- list(omega=omega,phi=phi)
}else{
par.fix <- NULL
}
ts <- cs <- ys <- ss <- c()
if(NI>0){
Is <- array(data=NA,dim=c(Nma,NI,length(t)))
}else{
Is <- c()
}
if(Nma>0){
for(i in 1:Nma){
yi <- c(rep(0,i),y[-(length(t)+1-(1:i))])
ys <- rbind(ys,yi)
ti <- c(rep(0,i),t[-(length(t)+1-(1:i))])
ts <- rbind(ts,ti)
if(type=='period'){
ci <- c(rep(0,i),cos(omega*t[-(length(t)+1-(1:i))]))
cs <- rbind(cs,ci)
si <- c(rep(0,i),sin(omega*t[-(length(t)+1-(1:i))]))
ss <- rbind(ss,si)
}
if(NI==1){
Is[i,,] <- c(rep(0,i*NI),Indices[1,-(length(t)+1-(1:i))])
}else if(NI>1){
Is[i,,] <- c(matrix(rep(0,i*NI),nrow=NI),Indices[1:NI,-(length(t)+1-(1:i))])
}
}
}
tmp <- data.frame(t,y,dy)
df <- list(data=tmp,Indices=Indices,par.fix=par.fix,Nma=Nma,NI=NI,type=type,ts=ts,cs=cs,ss=ss,Is=Is,ys=ys)
####
start <- list()
par.low <- par.up <- c()
start$sj <- sj.ini
par.low <- c(par.low,sj=sj.min)
par.up <- c(par.up,sj=sj.max)
if(Nma>0){
for(k in 1:Nma){
start[[paste0('m',k)]] <- mini
par.low <- c(par.low,mmin)
par.up <- c(par.up,mmax)
}
start <- c(start,logtau=logtau.ini)
par.low <- c(par.low,logtau=logtau.min)
par.up <- c(par.up,logtau=logtau.max)
}
names(par.up) <- names(par.low) <- names(start)
##########numerical fit
Ntry <- 1
if(type=='noise'){
# if(TRUE){
start0 <- start
pars <- c()
likes <- c()
for(kk in 1:Ntry){
for(j in 1:5){
start <- as.list(rnorm(length(start0),unlist(start0),as.numeric((par.up-par.low)/100)))
if(all(unlist(start)>par.low & unlist(start)<par.up)) break()
}
names(start) <- names(start0)
out <- try(nls.lm(par = start,lower=par.low,upper=par.up,fn = rv.red.res,df=df,control=nls.lm.control(maxiter=500)),TRUE)#ftol=1e-16,ptol=1e-16#ftol=tol,ptol=tol
# out <- nls.lm(par = start,lower=par.low,upper=par.up,fn = rv.red.res,df=df,control=nls.lm.control(maxiter=500))
if(class(out)!='try-error'){
opt.par <- as.list(coef(out))
yp <- rv.red(par=opt.par, df=df)$v
pars <- rbind(pars,unlist(start))
logLmax <- sum(-(y-yp)^2/(2*(dy^2+opt.par$sj^2))-0.5*log(2*pi)-0.5*log((dy^2+opt.par$sj^2)))
likes <- c(likes,logLmax)
}
}
ind <- which.max(likes)
start <- as.list(pars[ind,])
names(start) <- names(start0)
}
out <- nls.lm(par = start,lower=par.low,upper=par.up,fn = rv.red.res,df=df,control=nls.lm.control(maxiter=500))
#####retrieve parameters
opt.par <- as.list(coef(out))
tmp <- rv.red(par=opt.par,df = df)
nams <- c('gamma','beta')
if(NI>0) nams <- c(nams,paste0('d',1:NI))
if(type=='period') nams <- c('A','B',nams)
names(tmp$par) <- nams
yp.full <- tmp$v
opt.par <- c(unlist(tmp$par),opt.par)
####model prediction and chi2
res <- as.numeric(y-yp.full)
logLmax <- sum(-res^2/(2*(dy^2+opt.par$sj^2))-0.5*log(2*pi)-0.5*log((dy^2+opt.par$sj^2)))
chi2 <- sum(res^2/dy^2)
####
pars <- opt.par
if(type=='period'){
pars$A <- 0
pars$B <- 0
df$Indices <- t(df$Indices)
yp.noise <- as.numeric(RV.model(par=pars,data = df))
}else{
yp.noise <- yp.full
}
res.sig <- as.numeric(y-(yp.full-yp.noise))
return(list(res=res,res.sig=res.sig,chi2=chi2,logLmax=logLmax,par=opt.par))#chi2.noise=chi2.noise
}
par.optimize <- function(data,Indices,NI,Nma,opt.type='sl',type='noise',omega=0,pars=NULL){
###pars is a list containing different variables
###Indices include indices which linear correlate with y in the model
###data include t,y,dy
opt.type0 <- opt.type
var <- names(pars)
for(k in 1:length(var)){
assign(var[k],pars[[var[k]]])
}
opt.type <- opt.type0
if(!exists('pars$Nma')){
pars$Nma <- Nma
}
if(!exists('pars$NI')){
pars$NI <- NI
}
t <- data[,1]
y <- data[,2]
dy <- data[,3]
err2 <- dy^2
W <- sum(1/err2)#new weight sum is 1.
w <- 1/err2/W#normalized weighting
Nrep <- 1
if(opt.type=='rep'){
Nrep <- 2
}
xs <- array(0,dim=c(1,length(t)))
for(ii in 1:Nrep){
########linear optimization
if(opt.type=='l'){
tmp <- lopt(pars=pars,type=type)
}else if(opt.type=='nl'){
tmp <- nlopt(pars=pars,type=type)
}else if(opt.type=='sl'){
tmp <- sopt(pars=pars,type=type)
}
}
###the returned variables are chi2 and best fitted parameters
return(tmp)
}
par.integral <- function(data,Indices,sj,m,d,type='noise',logtau=NULL,omega=NULL,Nma=0, NI=0){
if(NI==0){
dI <- 0
}else{
dI <- partI(d,Indices,NI)
}
t <- data[,1]
y <- data[,2]
dy <- data[,3]
ind <- which(dy==0)
dy[ind] <- 1e-6
W <- sum(1/(dy^2+sj^2))#new weight sum is 1.
w <- 1/(dy^2+sj^2)/W#normalized weighting
if(Nma>0){
Is <- c()
vs <- c()
ts <- c()
trep <- c()
for(k in 1:Nma){
if(NI>1){
Is <- rbind(Is,c(rep(0,k),partI(d,Indices[-(length(t)+1-(1:k)),],NI)))
}else{
Is <- 0
}
ts <- rbind(ts,c(rep(0,k),t[-(length(t)+1-(1:k))]))#shift forward by k points
trep <- rbind(trep,c(rep(0,k),t[-(1:k)]))#unshifted but with the previous points chopped
vs <- rbind(vs,c(rep(0,k),y[-(length(t)+1-(1:k))]))
}
c <- m*exp(-abs(trep-ts)/exp(logtau))
}else{
c <- 0
ts <- 0
vs <- 0
Is <- 0
}
if(Nma>0){
if(is.matrix(Is) | is.data.frame(Is)){
yp <- y-colSums(c*vs)-dI-colSums(c*Is)
}else if(length(Is)>1){
yp <- y-colSums(c*vs)-dI-c*Is
}else{
yp <- y-colSums(c*vs)-dI
}
tp <- t+colSums(c*ts)
wp <- 1+colSums(c)
}else{
yp <- y-dI
tp <- t
wp <- 1
}
YWp <- sum(w*wp*yp)
Wp <- sum(w*wp)
WWp <- sum(w*wp^2)
WTp <- sum(w*wp*tp)
TTp <- sum(w*tp^2)
WTp <- sum(w*wp*tp)
YTp <- sum(w*yp*tp)
YWp <- sum(w*yp*wp)
YYp <- sum(w*yp^2)
logL0 <- log(2*pi/sqrt(WWp*TTp-WTp^2))-log(W)+W*(((YTp*WWp-WTp*YWp)^2/(WWp*TTp-WTp^2)+YWp^2-YYp*WWp)/(2*WWp))
logLp <- logL <- logL0
if(type=='period'){
###determine phase to eliminate CS
if(Nma>0){
cc <- colSums(c*cos(omega*ts))
ss <- colSums(c*sin(omega*ts))
}else{
ss <- cc <- 0
}
CCpp <- sum(w*(cos(omega*t)-cc)^2)
SSpp <- sum(w*(sin(omega*t)-ss)^2)
CSpp <- sum(w*(sin(omega*t)-ss)*(cos(omega*t)-cc))
phi <- 0.5*atan(2*CSpp/(CCpp-SSpp))
phip <- 0.5*atan(sum(w*sin(2*omega*t))/sum(w*cos(2*omega*t)))
###define notations using the determined phase
if(Nma>0){
cc <- colSums(c*cos(omega*ts-phi))
ss <- colSums(c*sin(omega*ts-phi))
}else{
ss <- cc <- 0
}
cp <- cos(omega*t-phi)-cc
sp <- sin(omega*t-phi)-ss
Cp <- sum(w*cp)
Sp <- sum(w*sp)
CCp <- sum(w*cp^2)
SSp <- sum(w*sp^2)
CSp <- sum(w*sp*cp)
CTp <- sum(w*cp*tp)
STp <- sum(w*sp*tp)
CWp <- sum(w*cp*wp)
SWp <- sum(w*sp*wp)
YCp <- sum(w*yp*cp)
YSp <- sum(w*yp*sp)
U <- WWp-CWp^2/CCp-SWp^2/SSp
R <- CWp*CTp/CCp+SWp*STp/SSp-WTp
Q <- YWp-CWp*YCp/CCp-SWp*YSp/SSp
V <- CCp*SSp*TTp*U-SSp*CTp^2*U-CCp*STp^2*U-CCp*SSp*R^2
if(V<=0){
cat('V=',V,'is not positive for f=',omega/(2*pi),'!\n')
# V <- V+1e-30
cat('Q=',Q,'\n')
cat('U=',U,'\n')
cat('R=',R,'\n')
}
X <- SSp*YCp^2*U+CCp*YSp^2*U-YYp*CCp*SSp*U+CCp*SSp*Q^2
logL <- log((2*pi)^2/sqrt(abs(V)))-2*log(W)+W*((X+(CCp*SSp*YTp*U-YCp*CTp*SSp*U-YSp*STp*CCp*U+CCp*SSp*Q*R)^2/V)/(2*CCp*SSp*U))
}
return(list(logL0=logL0,logL=logL,logLp=logLp))
}
#notations depending on frequency omega
local.notation <- function(t,y,dy,Indices,NI,omega,phi){
W <- sum(1/dy^2)
w <- 1/dy^2/W
C <- sum(w*cos(omega*t-phi))
S <- sum(w*sin(omega*t-phi))
YC <- sum(w*y*cos(omega*t-phi))
YS <- sum(w*y*sin(omega*t-phi))
CC <- sum(w*cos(omega*t-phi)^2)
SS <- sum(w*sin(omega*t-phi)^2)
CS <- sum(w*sin(omega*t-phi)*cos(omega*t-phi))
ST <- sum(w*sin(omega*t-phi)*t)
CT <- sum(w*cos(omega*t-phi)*t)
if(NI>0){
CI <- (w*cos(omega*t-phi))%*%Indices[,1:NI]
SI <- (w*sin(omega*t-phi))%*%Indices[,1:NI]
}else{
CI <- SI <- rep(0,NI)
}
vars <- unique(c('omega','phi','C','S','CC','SS','CS','CT','ST','SI','CI','YC','YS'))
pars <- list()
for(k in 1:length(vars)){
if(exists(vars[k])){
pars[[vars[k]]] <- eval(parse(text = vars[k]))
}
}
return(pars)
}
#####definition of notations
global.notation <- function(t,y,dy,Indices,Nma,NI){
#######notations
data <- cbind(t,y,dy)
W <- sum(1/dy^2)
w <- 1/dy^2/W
T <- sum(w*t)
Y <- sum(w*y)
if(NI>0){
I <- w%*%Indices[,1:NI,drop=FALSE]
}else{
I <- 0
}
YY <- sum(w*y^2)
YT <- sum(w*y*t)
if(NI>0){
YI <- (w*y)%*%Indices[,1:NI,drop=FALSE]
}else{
YI <- 0
}
TT <- sum(w*t^2)
if(NI>0){
TI <- (w*t)%*%Indices[,1:NI,drop=FALSE]
}else{
TI <- 0
}
II <- array(data=NA,dim=c(NI,NI))
if(NI>0){
for(i in 1:NI){
II[i,] <- (w*Indices[,i])%*%Indices[,1:NI,drop=FALSE]
}
}
#####parameter boundaries
gamma.min <- min(y)
gamma.max <- max(y)
gamma.ini <- (gamma.min+gamma.max)/2
if(NI>0){
dmin <- -2*(max(y)-min(y))/(max(Indices)-min(Indices))
dmax <- 2*(max(y)-min(y))/(max(Indices)-min(Indices))
dini <- rep((dmin+dmax)/2,1)
}else{
dini <- dmin <- dmax <- 0#rep(0,NI)
}
beta.min <- -(max(y)-min(y))/(max(t)-min(t))
beta.max <- (max(y)-min(y))/(max(t)-min(t))
beta.ini <- (beta.min+beta.max)/2
trend <- TRUE
if(!trend){
beta.min <- -1e-6
beta.max <- 1e-6
beta.ini <- 0
}
sj.min <- 0
sj.max <- 2*sd(y)
sj.ini <- (sj.min+sj.max)/2
mmin <- -1
mmax <- 1
rr <- 1
mini <- rep((mmin+rr*mmax)/(1+rr),1)
logtau.min <- log(max(min(diff(t)),-10))
logtau.max <- log(2*(max(t)-min(t)))
logtau.ini <- (logtau.min+rr*logtau.max)/(1+rr)
Amin <- Bmin <- -2*(max(y)-min(y))
Amax <- Bmax <- 2*(max(y)-min(y))
Aini <- Bini <- (Amin+Amax)/2
vars <- unique(c('t','dy','err2','II','T','TT','TI','II','w','W','I','Y','YT','YI','data','Indices','y','logtau','phi','m','xs','Amin','Bmin','Amax','Bmax','logtau.min','logtau.max','mmin','mmax','beta.min','beta.max','dmin','dmax','gamma.max','gamma.min','Aini','Bini','gamma.ini','beta.ini','dini','mini','logtau.ini','sj.ini','sj.max','sj.min'))
pars <- list()
for(k in 1:length(vars)){
if(exists(vars[k])){
pars[[vars[k]]] <- eval(parse(text = vars[k]))
}
}
return(pars)
}
####Marginalized likelihood periodogram
MLP <- function(t, y, dy, Nma=0, Inds=0,mar.type='part',sj=0,logtau=NULL,ofac=1,fmax=NULL,fmin=NULL,tspan=NULL,model.type='MA',opt.par=NULL,Indices=NA,MLP.type='sub',sampling='combined',section=1){
# unit <- 365.24#to make the elements of the matrix in the function of 'solve' on the same order
unit <- 1
if(length(Inds)>0 & !is.null(Indices) & !all(is.na(Indices))){
if(all(Inds==0)){
NI <- 0
}else{
Inds <- Inds[Inds>0]
NI <- length(Inds)
Indices <- as.matrix(Indices[,Inds,drop=FALSE])
for(j in 1:ncol(Indices)){
Indices[,j] <- scale(Indices[,j])
}
}
}else{
Inds <- 0
NI <- 0
}
if(NI==0) d <- 0
if(Nma==0) m <- 0
if(is.null(tspan)){
tspan <- max(t)-min(t)
}
step <- 1/(tspan*ofac)
if(is.null(fmin)){
fmin <- 1/(tspan*ofac)
}
fnyq <- 0.5*length(y)/tspan
if(is.null(fmax)){
fmax <- fnyq
}
f <- fsample(fmin,fmax,sampling,section,ofac,unit)
nout <- length(f)
t <- (t-min(t))/unit#
Ndata <- length(t)
omegas <- 2*pi*f
phi <- 0
#######define notations and variables
y0 <- y
vars <- global.notation(t,y,dy,Indices,Nma,NI)
var <- names(vars)
for(k in 1:length(var)){
assign(var[k],vars[[var[k]]])
}
data <- cbind(t,y,dy)
############################################################
#####optimization; select the initial condition
############################################################
####fix the non-marginzed parameters at their optimal values
if(is.null(opt.par) | MLP.type=='sub'){
tmp <- par.optimize(data,Indices=Indices,NI=NI,Nma=Nma,opt.type='sl',type='noise',pars=vars)
opt.par <- tmp$par
if(MLP.type=='sub'){
y <- tmp$res
data[,2] <- y
vars$y <- y
vars$data <- data
}
}
if(Nma>0 & MLP.type=='assign'){
ind <- grep('^m',names(opt.par))
m <- unlist(lapply(ind,function(i) opt.par[[i]]))
logtau <- opt.par$logtau
}else{
m <- 0
logtau <- 1
}
if(NI>0 & MLP.type=='assign'){
ind <- grep('^d',names(opt.par))
d <- unlist(lapply(ind,function(i) opt.par[[i]]))
}else{
d <- rep(0,NI)
}
if(sj==0 & any(sj==names(opt.par))){
sj <- opt.par$sj
}
########################################
########marginalized posterior
########################################
if(!exists('m')) m <- 0
tmp <- par.integral(data,Indices,sj=sj,m=m,d=d,logtau=logtau,Nma=Nma,NI=NI,type='noise')
logL0 <- tmp$logL0
logBFmax <- 0
p <- pn <- rep(NA,length(omegas))
logBF.noise <- rep(NA,length(omegas))
logBF <- rep(NA,length(omegas))
logLp <- rep(NA,length(omegas))
for(kk in 1:length(f)){
omega <- omegas[kk]
tmp <- par.integral(data,Indices,sj=sj,m=m,d=d,type='period',logtau=logtau,omega=omega,Nma=Nma,NI=NI)
logL1 <- tmp$logL0#signal dependent noise model log likelihood
logL <- tmp$logL#likelihood for the full model for f=f[k]
logLp[kk] <- tmp$logLp
logBF.noise[kk] <- logL1-logL0
logBF[kk] <- logL-logL0
}
P <- unit/f
ind <- which(logBF>(max(logBF)+log(0.01)))
Popt <- (unit/f)[ind]
omega.opt <- 2*pi*(f[which.max(logBF)]/unit)
####optimized parameter
#opt <- par.optimize(data,Indices,NI,Nma,opt.type=opt.type,type='period',omega=omega,pars=var.new)
vars <- global.notation(t,y0,dy,Indices,Nma,NI)
tmp <- local.notation(t,y0,dy,Indices,NI,omega.opt,phi=0)
var.new <- c(vars,tmp)
# var.new$y <- y0
data[,2] <- y0
tmp <- par.optimize(data,Indices=Indices,NI=NI,Nma=Nma,opt.type='sl',type='period',pars=var.new)
opt.par <- tmp$par
inds <- sort(logBF,decreasing=TRUE,index.return=TRUE)$ix
ps <- P[inds[1:5]]
power.opt <- logBF[inds[1:5]]
return(list(P=unit/f, logp=power, ps=ps,power.opt=power.opt,logBF.opt=logBF[ind],logBF=logBF,power=logBF,logBF.noise=logBF.noise,Nma=Nma,NI=NI,par=opt.par,res=tmp$res,sig.level=log(c(10,100,1000))))
}
#####BFP-based model inference/selection
bfp.inf <- function(vars,Indices,Nmas=NULL,NI.inds=NULL){
var <- names(vars)
for(k in 1:length(var)){
assign(var[k],vars[[var[k]]])
}
Ndata <- length(t)
if(is.null(Nmas)){
Nmas <- c(0,1,2)
}
if(is.null(NI.inds)){
NI.inds <- list(0,1:3,1:5,c(1:3,6:10),c(1:3,11:18))
}
nis <- c()
for(j in 1:length(NI.inds)){
if(any(NI.inds[[j]]==0)){
nis <- c(nis,0)
}else{
nis <- c(nis,length(NI.inds[[j]]))
}
}
ni.min <- min(nis)
Nma.opt <- Nmas[1]
Inds.opt <- NI.inds[[1]]
NI.opt <- length(Inds.opt)
logLmaxs <- array(data=NA,dim=c(length(NI.inds),length(Nmas)))
logBFs <- array(data=NA,dim=c(length(NI.inds),length(Nmas)))
lbm <- 0#maximum logBF
withProgress(message = 'Calculating log(BF) table', value = 0, {
for(i in 1:length(Nmas)){
nma <- Nmas[i]
for(j in 1:length(NI.inds)){
incProgress(1/(length(Nmas)*length(NI.inds)), detail = paste("MA:", nma,'; Proxies:',paste(NI.inds[[j]],collapse=',')))
if(!all(NI.inds[[j]]==0)){
ni <- length(NI.inds[[j]])
Inds <- NI.inds[[j]]
if(length(Inds)==1){
indices <- matrix(Indices[,Inds],ncol=1)
}else{
indices <- Indices[,Inds]
}
}else{
ni <- 0
indices <- Indices
Inds <- 0
}
Ntry <- 10*(round(ni/3)+2*nma)
lls <- c()
vars <- global.notation(t,y,dy,Indices=indices,Nma=nma,NI=ni)
tmp <- par.optimize(data,Indices=indices,NI=ni,Nma=nma,opt.type='sl',type='noise',pars=vars)
ps.opt <- c(logtau=vars$logtau.ini,m=vars$mini,d=vars$dini,sj=vars$sj.ini)
pp <- tmp$par
if(i==1 & j==1) pss <- pp
lls <- c(lls,tmp$logLmax)
Nsd <- 100
if(Ntry>1){
for(kk in 1:Ntry){
vars$NI <- ni
vars$Nma <- nma
if(nma>0){