--- /dev/null
+###########################################################
+# CONTINUOUS WAVELET TRANSFORMATION OF A TIME SERIES OBJECT
+###########################################################
+
+cwt.ts <- function(ts,s0,noctave=5,nvoice=10,w0=2*pi){
+
+ if (class(ts)!="ts"){
+
+ cat("# This function needs a time series object as input. You may construct this by using the function ts(data,start,deltat). Try '?ts' for help.\n")
+
+ }
+ else{
+
+ t=time(ts)
+ dt=t[2]-t[1]
+
+ s0unit=s0/dt*w0/(2*pi)
+ s0log=as.integer((log2(s0unit)-1)*nvoice+1.5)
+
+ if (s0log<1){
+ cat(paste("# s0unit = ",s0unit,"\n",sep=""))
+ cat(paste("# s0log = ",s0log,"\n",sep=""))
+ cat("# s0 too small for w0! \n")
+ }
+ totnoct=noctave+as.integer(s0log/nvoice)+1
+
+ totts.cwt=cwt(ts,totnoct,nvoice,w0,plot=0)
+
+ ts.cwt=totts.cwt[,s0log:(s0log+noctave*nvoice)]
+
+ #Normalization
+ sqs <- sqrt(2^(0:(noctave*nvoice)/nvoice)*s0)
+ smat <- matrix(rep(sqs,length(t)),nrow=length(t),byrow=TRUE)
+
+ ts.cwt*smat
+
+ }
+
+}
+
+#####################################
+# WSP
+#####################################
+
+wsp <- function(ts,s0=1,noctave=5,nvoice=10,w0=2*pi,sw=0,tw=0,swabs=0,siglevel=0.95,critval=NULL,nreal=1000,arealsiglevel=0.9,kernel=0,markt=-999,marks=-999,logscale=FALSE,plot=TRUE,units="",device="screen",file="wsp",color=TRUE,pwidth=10,pheight=7,labsc=1,labtext="",sigplot=3){
+
+ if (class(ts)!="ts"){
+
+ cat("# This function needs a time series object as input. You may construct this by using the function ts(data,start,deltat). Try '?ts' for help.\n")
+
+ }
+ else{
+
+ if (sw!=0 & swabs==0)
+ swabs <- as.integer(sw*nvoice)
+ if (swabs!=0 & sw==0)
+ sw <- swabs/nvoice
+
+ sllist <- checkarealsiglevel(sw,tw,w0,arealsiglevel,siglevel,0)
+ arealsiglevel <- sllist$arealsiglevel
+ siglevel <- sllist$siglevel
+
+ at <- NULL
+
+ t <- time(ts)
+ dt <- deltat(ts)
+ s0rem <- s0
+ s0 <- adjust.s0(s0,dt)
+ dnoctave <- as.integer(log(s0/s0rem-0.000000000001)/log(2))+1
+
+ noctave <- adjust.noctave(length(ts),dt,s0,tw,noctave)
+ scalevector <- 2^(0:(noctave*nvoice)/nvoice)*s0
+ tsanom <- ts-mean(ts)
+
+ #WAVELET TRANSFORMATION
+ ts.cwt <- cwt.ts(tsanom,s0,noctave,nvoice,w0)
+
+ #SMOOTHING
+ wsp <- smooth.matrix(Mod(ts.cwt)^2,swabs)
+ smwsp <- smooth.time(wsp,tw,dt,scalevector)
+
+ #POINTWISE SIGNIFICANCE TEST
+ if (is.null(critval)==FALSE){ # is critval empty?
+ if (dim(critval)[2]!=dim(smwsp)[2]){ # is critval of the wrong dimension?
+ if (siglevel[1]!=0 & nreal!=0) critval <-
+ criticalvaluesWSP(tsanom,s0,noctave,nvoice,w0,swabs,tw,siglevel,nreal)
+ #critval is of wrong dimension and siglevel and nreal are given
+ else {
+ critval <- NULL # no test possible
+ arealsiglevel <- 0
+ cat("# dimension of critval is wrong \n")
+ cat("# areawise test only possible with pointwise test \n")
+ }
+ }
+ }
+ else{ # critval is empty, but nreal or siglevel is given
+ if (siglevel[1]!=0 & nreal!=0) critval <-
+ criticalvaluesWSP(tsanom,s0,noctave,nvoice,w0,swabs,tw,siglevel,nreal)
+ else {
+ critval <- NULL
+ arealsiglevel <- 0
+ cat("# areawise test only possible with pointwise test \n")
+ }
+ }
+
+ #AREAL SIGNIFICANCE TEST
+ if (arealsiglevel!=0){
+ v <- critval[1,]
+ v[v==0] <- 9999
+ cvmat <- matrix(rep(v,length(t)),nrow=length(t),byrow=TRUE)
+ atest <- arealtest(smwsp/cvmat,dt,s0,noctave,nvoice,w0,swabs,tw,siglevel,arealsiglevel,kernel,0)
+ at <- atest$at
+ kernel <- atest$kernel
+ }
+
+ if (s0rem<s0){
+ smwsp <- addvalues(nvoice,dnoctave,smwsp,NA)
+ critval <- addvalues(nvoice,dnoctave,critval,1)
+ #at <- addvalues(nvoice,dnoctave,at,NA)
+ noctave <- noctave+dnoctave
+ s0 <- s0/2^dnoctave
+ scalevector <- 2^(0:(noctave*nvoice)/nvoice)*s0
+ }
+
+ #PARAMETERS
+ wclist <-
+ list(modulus=smwsp,phase=NULL,time=t,s0=s0,noctave=noctave,nvoice=nvoice,w0=w0,scales=scalevector,critval=critval,at=at,kernel=kernel)
+
+ class(wclist) <- "wt"
+
+ #PLOTTING
+ if (plot)
+ plot(wclist,markt,marks,NULL,NULL,logscale,FALSE,units,"Wavelet Power Spectrum",device,file,FALSE,color,pwidth,pheight,labsc,labtext,sigplot)
+
+ wclist
+
+ }
+
+}
+
+#####################################
+# WCO
+#####################################
+
+wco <-
+ function(ts1,ts2,s0=1,noctave=5,nvoice=10,w0=2*pi,sw=0,tw=0,swabs=0,siglevel=0.95,arealsiglevel=0.9,kernel=0,markt=-999,marks=-999,sqr=FALSE,phase=TRUE,plot=TRUE,units="",device="screen",file="wcoh",split=FALSE,color=TRUE,pwidth=10,pheight=7,labsc=1,labtext="",sigplot=3){
+
+ if (class(ts1)!="ts"){
+
+ cat("# This function needs two time series objects as input. You may construct them by using the function ts(data,start,deltat). Try '?ts' for help.\n")
+
+ }
+ else{
+
+ if (sw!=0 & swabs==0)
+ swabs <- as.integer(sw*nvoice)
+ if (swabs!=0 & sw==0)
+ sw <- swabs/nvoice
+
+ sllist <- checkarealsiglevel(sw,tw,w0,arealsiglevel,siglevel,1)
+ arealsiglevel <- sllist$arealsiglevel
+ siglevel <- sllist$siglevel
+
+ if (sw==0 & tw==0 & swabs==0) {
+ cat("# coherence without averaging makes no sense! \n")
+ siglevel <- 0
+ arealsiglevel <- 0
+ }
+
+ if (phase==FALSE) phs <- NULL
+
+ at <- NULL
+
+ tsadjust <- adjust.timeseries(ts1,ts2)
+ ts1 <- tsadjust$ts1
+ ts2 <- tsadjust$ts2
+
+ t <- time(ts1)
+ dt <- deltat(ts1)
+
+ s0rem <- s0
+ s0 <- adjust.s0(s0,dt)
+ dnoctave <- as.integer(log(s0/s0rem-0.000000000001)/log(2))+1
+
+ noctave <- adjust.noctave(length(ts1),dt,s0,tw,noctave)
+
+ scalevector <- 2^(0:(noctave*nvoice)/nvoice)*s0
+
+ ts1anom <- ts1-mean(ts1)
+ ts2anom <- ts2-mean(ts2)
+
+ ts1.cwt <- cwt.ts(ts1anom,s0,noctave,nvoice,w0)
+ ts2.cwt <- cwt.ts(ts2anom,s0,noctave,nvoice,w0)
+
+ cosp <- Re(ts1.cwt)*Re(ts2.cwt) + Im(ts1.cwt)*Im(ts2.cwt)
+ quad <- Im(ts1.cwt)*Re(ts2.cwt) - Re(ts1.cwt)*Im(ts2.cwt)
+ wsp1 <- Mod(ts1.cwt)^2
+ wsp2 <- Mod(ts2.cwt)^2
+
+ smcosp <- smooth.matrix(cosp,swabs)
+ smquad <- smooth.matrix(quad,swabs)
+ smwsp1 <- smooth.matrix(wsp1,swabs)
+ smwsp2 <- smooth.matrix(wsp2,swabs)
+
+ smsmcosp <- smooth.time(smcosp,tw,dt,scalevector)
+ smsmquad <- smooth.time(smquad,tw,dt,scalevector)
+ smsmwsp1 <- smooth.time(smwsp1,tw,dt,scalevector)
+ smsmwsp2 <- smooth.time(smwsp2,tw,dt,scalevector)
+
+ if (sqr==FALSE)
+ wcoh <- sqrt((smsmcosp^2+smsmquad^2)/(smsmwsp1*smsmwsp2))
+ else
+ wcoh <- (smsmcosp^2+smsmquad^2)/(smsmwsp1*smsmwsp2)
+
+ if (phase)
+ phs <- atan2(smsmquad,smsmcosp)
+ else phs <- NULL
+
+ #POINTWISE SIGNIFICANCE TEST
+ if (siglevel[1]!=0) critval <- criticalvaluesWCO(s0,noctave,nvoice,w0,swabs,tw,siglevel)
+ else critval <- NULL
+ if (sqr==TRUE & is.null(critval)==FALSE)
+ critval <- critval^2
+
+ #AREAWISE SIGNIFICANCE TEST
+ if (arealsiglevel!=0){
+ atest <- arealtest(wcoh/critval,dt,s0,noctave,nvoice,w0,swabs,tw,siglevel,arealsiglevel,kernel,1)
+ at <- atest$at
+ kernel <- atest$kernel
+ }
+
+ wcoh[1,1] <- 0
+ wcoh[1,2] <- 1
+
+ if (phase){
+ phs[1,1] <- -pi
+ phs[1,2] <- pi
+ }
+
+ if (s0rem<s0){
+ wcoh <- addvalues(nvoice,dnoctave,wcoh,NA)
+ phs <- addvalues(nvoice,dnoctave,phs,NA)
+ noctave <- noctave+dnoctave
+ s0 <- s0/2^dnoctave
+ scalevector <- 2^(0:(noctave*nvoice)/nvoice)*s0
+ }
+
+ wclist <- list(modulus=wcoh,phase=phs,s0=s0,noctave=noctave,nvoice=nvoice,w0=w0,time=t,scales=scalevector,critval=critval,at=at,kernel=kernel)
+
+ class(wclist) <- "wt"
+
+ if (plot) plot(wclist,markt,marks,NULL,NULL,FALSE,phase,units,"Wavelet Coherence",device,file,split,color,pwidth,pheight,labsc,labtext,sigplot)
+
+ wclist
+
+ }
+
+ }
+
+#####################################
+# WCS
+#####################################
+
+wcs <- function(ts1,ts2,s0=1,noctave=5,nvoice=10,w0=2*pi,sw=0,tw=0,swabs=0,markt=-999,marks=-999,logscale=FALSE,phase=TRUE,plot=TRUE,units="",device="screen",file="wcsp",split=FALSE,color=TRUE,pwidth=10,pheight=7,labsc=1,labtext=""){
+
+ if (class(ts1)!="ts"){
+
+ cat("# This function needs two time series objects as input. You may construct them by using the function ts(data,start,deltat). Try '?ts' for help. \n")
+
+ }
+ else{
+
+ if (sw!=0 & swabs==0)
+ swabs <- as.integer(sw*nvoice)
+ if (swabs!=0 & sw==0)
+ sw <- swabs/nvoice
+
+ tsadjust <- adjust.timeseries(ts1,ts2)
+ ts1 <- tsadjust$ts1
+ ts2 <- tsadjust$ts2
+
+ t <- time(ts1)
+ dt <- deltat(ts1)
+
+ s0rem <- s0
+ s0 <- adjust.s0(s0,dt)
+ dnoctave <- as.integer(log(s0/s0rem-0.000000000001)/log(2))+1
+
+ noctave <- adjust.noctave(length(ts1),dt,s0,tw,noctave)
+
+ scalevector <- 2^(0:(noctave*nvoice)/nvoice)*s0
+
+ ts1anom <- ts1-mean(ts1)
+ ts2anom <- ts2-mean(ts2)
+
+ ts1.cwt <- cwt.ts(ts1anom,s0,noctave,nvoice,w0)
+ ts2.cwt <- cwt.ts(ts2anom,s0,noctave,nvoice,w0)
+
+ cosp <- Re(ts1.cwt)*Re(ts2.cwt) + Im(ts1.cwt)*Im(ts2.cwt)
+ quad <- Im(ts1.cwt)*Re(ts2.cwt) - Re(ts1.cwt)*Im(ts2.cwt)
+
+ smcosp <- smooth.matrix(cosp,swabs)
+ smquad <- smooth.matrix(quad,swabs)
+
+ smsmcosp <- smooth.time(smcosp,tw,dt,scalevector)
+ smsmquad <- smooth.time(smquad,tw,dt,scalevector)
+
+ wcsp <- smsmcosp^2+smsmquad^2
+
+ if (phase)
+ phs <- atan2(smsmquad,smsmcosp)
+ else phs <- NULL
+
+ if (phase){
+ phs[1,1] <- -pi
+ phs[1,2] <- pi
+ }
+
+ if (s0rem<s0){
+ wcsp <- addvalues(nvoice,dnoctave,wcoh,NA)
+ phs <- addvalues(nvoice,dnoctave,phs,NA)
+ noctave <- noctave+dnoctave
+ s0 <- s0/2^dnoctave
+ scalevector <- 2^(0:(noctave*nvoice)/nvoice)*s0
+ }
+
+ wclist <- list(modulus=wcsp,phase=phs,s0=s0,noctave=noctave,nvoice=nvoice,w0=w0,time=t,scales=scalevector,critval=NULL,at=NULL,kernel=NULL)
+
+ class(wclist) <- "wt"
+
+ if (plot) plot(wclist,markt,marks,NULL,NULL,logscale,phase,units,"Wavelet Cross Spectrum",device,file,split,color,pwidth,pheight,labsc,labtext)
+
+ wclist
+
+ }
+
+}
+
+##########################################
+# POINTWISE SIGNIFICANCE TEST
+##########################################
+
+rawWSP <- function(ts,s0=1,noctave=5,nvoice=20,w0=2*pi,swabs=0,tw=0,scalevector){
+
+ tsanom <- ts-mean(ts)
+
+ ts.cwt <- cwt.ts(tsanom,s0,noctave,nvoice,w0)
+
+ wsp <- Mod(ts.cwt)^2
+
+ smwsp <- smooth.matrix(wsp,swabs)
+ smsmwsp <- smooth.time(smwsp,tw,deltat(ts),scalevector)
+
+ smsmwsp
+
+}
+
+criticalvaluesWSP <- function(ts,s0=1,noctave=5,nvoice=10,w0=2*pi,swabs=0,tw=0,siglevel=0.95,nreal=1000){
+
+ t=time(ts)
+ dt=deltat(ts)
+
+ s0 <- adjust.s0(s0,dt)
+ noctave <- adjust.noctave(length(ts),dt,s0,tw,noctave)
+
+ scalevector <- 2^(0:(noctave*nvoice)/nvoice)*s0
+
+ cat("# calculating critical values by means of MC-simulations \n")
+
+ s0unit=s0/dt*w0/(2*pi)
+ s0log=as.integer((log2(s0unit)-1)*nvoice+1.5)
+
+ wsp0 <- rawWSP(ts,s0,noctave,nvoice,w0,swabs,tw,scalevector)
+
+ S <- dim(wsp0)[2]
+
+ n1 <- 1 + 2*as.integer( sqrt(2) * 2^((S-swabs+s0log-1)/nvoice+1) )
+ n2 <- max(scalevector)*tw*2/dt*1.1
+ n3 <- 2*tw*s0*2^noctave/dt+100
+ n <- max(n1,n2,n3)
+
+ center <- (n-1)/2+1
+ cv <- matrix(rep(0,S*length(siglevel)),ncol=S)
+ rmatrix <- matrix(0,nrow=nreal,ncol=S)
+
+ # Fitting AR1-process (red noise) to data
+ arts0 <- ar(ts,order.max=1)
+ sdts0 <- sd(ts[1:length(ts)])
+
+ if (arts0$order==0){
+ se <- sqrt(arts0$var)
+ arts0$ar <- 0.000001
+ }
+ else
+ se <- sqrt(sdts0*sdts0*(1-arts0$ar*arts0$ar))
+
+ tsMC <- ts(data=rep(0,n),start=t[1],frequency=1/dt)
+
+ # MC Simulations
+ for (i in 1:nreal){
+
+ tsMC[1:n] <- arima.sim(list(ar = arts0$ar), n+1, sd = se)[2:(n+1)]
+
+ rmatrix[i,] <- rawWSP(tsMC,s0,noctave,nvoice,w0,swabs,tw,scalevector)[center,]
+
+ }
+
+ for (s in (1+swabs):(S-swabs)) rmatrix[,s] <- sort(rmatrix[,s])
+
+ for (i in 1:length(siglevel)){
+ sigindex <- as.integer(nreal*siglevel[i])
+ cvv <- rmatrix[sigindex,]
+ cvv[is.na(cvv)] <- 0
+ cv[i,] <- cvv
+ }
+
+ cv
+
+}
+
+###########
+
+criticalvaluesWCO <- function(s0,noctave,nvoice,w0,swabs,tw,siglevel=0.95){
+
+ cv=rep(0,length(siglevel))
+
+ for (i in 1:length(siglevel)){
+
+ if (siglevel[i]!=0.9 && siglevel[i]!=0.95 && siglevel[i]!=0.99) siglevel[i] <- 0.95
+
+ if (siglevel[i]==0.9){
+ cat("# significance level set to 0.90 \n")
+ sw <- 1.0*swabs/nvoice
+ cv[i] <- 0.00246872*w0^2*sw + 0.0302419*w0*sw^2 + 0.342056*sw^3 -
+ 0.000425853*w0^2 - 0.101749*w0*sw - 0.703537*sw^2 +
+ 0.00816219*w0 + 0.442342*sw + 0.970315
+ }
+
+ if (siglevel[i]==0.95){
+ cat("# significance level set to 0.95 \n")
+ sw <- swabs*100.0/3.0/nvoice
+ cv[i] <- 0.0000823*w0^3 + 0.0000424*w0^2*sw + 0.0000113*w0*sw^2 +
+ 0.0000154*sw^3 - 0.0023*w0^2 - 0.00219*w0*sw - 0.000751*sw^2 +
+ 0.0205*w0 + 0.0127*sw + 0.95
+ }
+
+ if (siglevel[i]==0.99){
+ cat("# significance level set to 0.99 \n")
+ sw <- 1.0*swabs/nvoice
+ cv[i] <- 0.00102304*w0^2*sw + 0.00745772*w0*sw^2 + 0.230035*sw^3 -
+ 0.000361565*w0^2 - 0.0502861*w0*sw - 0.440777*sw^2 +
+ 0.00694998*w0 + 0.29643*sw + 0.972964
+ }
+
+ if (cv[i]>1) cv[i] <- 1
+
+ cat(paste("# significance testing, cv=",cv[i]," \n",sep=""))
+
+ }
+
+ cv
+
+}
+
+#############################
+# AREAWISE SIGNIFICANCE TEST
+#############################
+
+slide <- function(data,kernellist,s0,noctave,nvoice,cv){
+
+ # slides kernel over data set
+ #----------------------------
+ # data: matrix containing data
+ # kernellist: matrix containing kernel
+ # s0: lowest scale
+ # noctave: number of octaves
+ # nvoice: number of voices per octave
+ # cv: critical value, all values higher are set to one
+
+ #Time: (rows) n,i the kernel is to be scaled in this direction
+ #Scale: (cols) m,j
+
+ data[data<cv] <- 0
+
+ kernel <- kernellist$bitmap
+
+ js <- kernellist$is
+
+ sm <- s0*2^noctave
+
+ dbin <- tobin(data)
+ kbin <- tobin(kernel)
+
+ dn <- nrow(dbin)
+ dm <- ncol(dbin)
+
+ kn <- nrow(kbin)
+ km <- ncol(kbin)
+
+ mark <- matrix(rep(0,dn*dm),nrow=dn)
+
+ for (j in 1:(dm-km+1)){
+
+ s <- s0*2^((j+js-1)/nvoice)
+ kscn <- as.integer(kn*s/sm);
+ if (kscn==0) kscn <- 1
+
+ ksc <- scaleKernel(kbin,kscn)
+ kscm <- km
+
+ for (i in 1:(dn-kscn+1)){
+
+ subbin <- dbin[i:(i+kscn-1),j:(j+kscm-1)]
+
+ if (sum(ksc*subbin)==sum(ksc))
+ mark[i:(i+kscn-1),j:(j+kscm-1)] <- mark[i:(i+kscn-1),j:(j+kscm-1)]+ksc
+
+ }
+
+ }
+
+ mark <- tobin(mark)
+
+ mark
+
+}
+
+arealtest <- function(wt,dt=1,s0=1,noctave=5,nvoice=20,w0=2*pi,swabs=0,tw=0,siglevel,arealsiglevel=0.9,kernel=0,type=0){
+
+ slp <- slope(w0,swabs,tw,nvoice,siglevel,arealsiglevel,type)
+
+ if (length(kernel)<2){
+ maxarea <- s0*2^noctave*slp/10*nvoice/dt
+ cat(paste("# calculating kernel (maxarea=",maxarea,")\n",sep=""))
+ cvkernel <-
+ kernelRoot(s0,w0,a=maxarea,noctave,nvoice,swabs,tw,dt)
+
+ cat("# building kernel bitmap \n")
+ kernel <-
+ kernelBitmap(cvkernel,s0,w0,noctave,nvoice,swabs,tw,dt)
+
+ }
+
+ cat("# performing arealtest \n")
+ sl <- slide(wt,kernel,s0,noctave,nvoice,1)
+
+ list(at=sl,kernel=kernel)
+
+}
+
+#############################
+# PLOTTING
+#############################
+
+plotat <- function(t,wt,at,sigplot){
+
+ if (length(at)>1){
+ linewidth <- 1
+ if (sigplot==3)
+ linewidth <- 5
+
+ contour(x=t,z=at,levels=0.5,add=TRUE,drawlabels=FALSE,axes=FALSE,lwd=linewidth,col="black")
+ }
+
+}
+
+
+plotcv <- function(t,wt,cv){
+
+ if (length(dim(cv))==0)
+
+ contour(x=t,z=wt,levels=c(cv),drawlabels=FALSE,axes=FALSE,add=TRUE,col="black",lwd=1)
+
+ else{
+
+ for(i in 1:nrow(cv)){
+
+ v <- cv[i,]
+ v[v==0] <- 9999
+ m <- matrix(rep(v,length(t)),nrow=length(t),byrow=TRUE)
+
+ contour(x=t,z=wt/m,levels=1,drawlabels=FALSE,axes=FALSE,add=TRUE,col="black",lwd=1)
+
+ }
+
+ }
+
+}
+
+plotcoi <- function(t,s0,noctave,w0){
+
+ tv <- as.vector(t)
+ tvl <- tv[tv-tv[1]<(tv[length(tv)]-tv[1])/2]
+ tvr <- tv[tv-tv[1]>=(tv[length(tv)]-tv[1])/2]
+
+ lines(tvl,log2(((tvl-tv[1])*4*pi/((w0+sqrt(2+w0*w0))*sqrt(2)))/s0)/noctave,col="black")
+ lines(tvr,log2(((tv[length(tv)]-tvr)*4*pi/((w0+sqrt(2+w0*w0))*sqrt(2)))/s0)/noctave,col="black")
+
+}
+
+plotmarks <- function(t,s0,noctave,markt,marks){
+
+ if (markt[1]!=-999){
+
+ for (i in 1:length(markt)){
+ lines(c(markt[i],markt[i]),c(0,1),lty="dotted")
+ }
+
+ }
+
+ if (marks[1]!=-999){
+
+ for (i in 1:length(marks)){
+ lines(c(t[1],t[length(t)]),c(log2(marks[i]/s0)/noctave,log2(marks[i]/s0)/noctave),lty="dotted")
+ }
+
+ }
+
+}
+
+
+#####################
+# PLOT.WT
+#####################
+
+plot.wt <- function(wt,markt=-999,marks=-999,t1=NULL,t2=NULL,logscale=FALSE,phase=FALSE,units="",plottitle="",device="screen",file="wt",split=FALSE,color=TRUE,pwidth=10,pheight=5,labsc=1.5,labtext="",sigplot=3,xax=NULL,xlab=NULL,yax=NULL,ylab=NULL){
+
+ plotwt(wt$modulus,wt$phase,wt$time,wt$s0,wt$noctave,wt$w0,wt$critval,wt$at,markt,marks,t1,t2,logscale,phase,units,plottitle,device,file,split,color,pwidth,pheight,labsc,labtext,sigplot,xax,xlab,yax,ylab)
+
+}
+
+plotwt <-
+ function(wt,phs,t,s0,noctave,w0,cv=NULL,at=NULL,markt=-999,marks=-999,t1=NULL,t2=NULL,logscale=FALSE,phase=FALSE,units="",plottitle="Wavelet Plot",device="screen",file="wavelet",split=FALSE,color=TRUE,pwidth=10,pheight=7,labsc=1,labtext="",sigplot=1,xax=NULL,xlab=NULL,yax=NULL,ylab=NULL){
+
+ if (is.null(phs)) phase <- FALSE
+
+ mgpv <- c(3,1,0)
+ if (labsc>1) mgpv[1] <- 3-(labsc-1.5)
+
+ ncolors <- 64
+ colors <- wtcolors(ncolors)
+ if (color==FALSE) colors <- gray((0:ncolors)/ncolors*0.7+0.3)
+
+ rangev <- (0:(ncolors-1))/(ncolors-1)
+ rangebar <- matrix(rangev,nrow=2,ncol=64,byrow=TRUE)
+
+ s <- 2^(0:(noctave))*s0
+ sn <- (0:(noctave))/noctave
+
+ deltat <- (t[length(t)]-t[1])/(length(t)-1)
+ cut <- FALSE
+ if ((!is.null(t1)) | (!is.null(t2))){
+ if (t1<t2 & t1>=t[1] & t2<=t[length(t)]){
+
+ cut <- TRUE
+
+ i1 <- (t1-t[1])/deltat+1
+ i2 <- (t2-t[1])/deltat+1
+
+ t <- t[t>=t1 & t<=t2]
+
+ wt <- wt[i1:i2,]
+ if (phase) phs <- phs[i1:i2,]
+ if (length(at)>1) at <- at[i1:i2,]
+
+ }
+ }
+
+ #----------------
+ # Setting layout
+ #----------------
+
+ if (device=="ps" && split==FALSE){
+
+ file <- paste(file,".eps",sep="")
+
+ postscript(file,onefile=TRUE,horizontal=TRUE,paper="special",width=pwidth,height=pheight)
+ cat(paste("# writing",file," \n"))
+
+ }
+
+ if (device=="ps" && split==TRUE){
+
+ file1 <- paste(file,".mod.eps",sep="")
+
+ postscript(file1,onefile=TRUE,horizontal=TRUE,paper="special",width=pwidth,height=pheight)
+ cat(paste("# writing",file1," \n"))
+
+ }
+
+ if (phase==TRUE && split==FALSE) nlo <- layout(matrix(c(1,2,3,4),2,2,byrow=TRUE),widths=c(4,1))
+ else nlo <- layout(matrix(c(1,2),ncol=2,byrow=TRUE),widths=c(4,1))
+
+
+ #-----------------
+ # Plotting modulus
+ #-----------------
+
+ if (logscale){
+ if (units=="")
+ image(x=t,z=log10(wt),col = colors,axes=FALSE,xlab="Time",ylab="Scale",frame.plot=TRUE,cex.lab=labsc,mgp=mgpv)
+ else
+ image(x=t,z=log10(wt),col = colors,axes=FALSE,xlab=paste("Time ","[",units,"]",sep=""),ylab=paste("Scale ","[",units,"]",sep=""),frame.plot=TRUE,cex.lab=labsc,mgp=mgpv)
+ }
+ else{
+ if (units=="")
+ image(x=t,z=wt,col = colors,axes=FALSE,xlab="Time",ylab="Scale",frame.plot=TRUE,cex.lab=labsc,mgp=mgpv)
+ else
+ image(x=t,z=wt,col = colors,axes=FALSE,xlab=paste("Time ","[",units,"]",sep=""),ylab=paste("Scale ","[",units,"]",sep=""),frame.plot=TRUE,cex.lab=labsc,mgp=mgpv)
+ }
+
+ text(t[1+as.integer(length(t)*0.1)],0.8,labtext,cex=2)
+
+ if (sigplot==1 | sigplot==3){
+ if (is.null(cv)==FALSE){ #Critical values
+ if (cv[1]!=0 & cv[1]!=-1) plotcv(t,wt,cv)
+ }
+ }
+
+ if (sigplot>1) plotat(t,wt,at,sigplot)
+
+ if (!cut) plotcoi(t,s0,noctave,w0) #cone of influence
+ plotmarks(t,s0,noctave,markt,marks) #additional guiding lines
+
+ if (is.null(xax))
+ axis(side=1,at=axTicks(1),cex.axis=labsc)
+ else
+ if (is.null(xlab))
+ axis(side=1,xax,labels=as.character(xax),cex.axis=labsc)
+ else
+ axis(side=1,xax,labels=xlab,cex.axis=labsc)
+
+ if (is.null(yax))
+ axis(side=2,sn,labels=as.character(s),cex.axis=labsc)
+ else
+ if (is.null(ylab))
+ axis(side=2,yax,labels=as.character(yax),cex.axis=labsc)
+ else
+ axis(side=2,yax,labels=ylab,cex.axis=labsc)
+
+ title(main=plottitle,cex=labsc)
+
+ image(z=rangebar,axes=FALSE,col=colors,frame.plot=TRUE,cex.lab=labsc,mgp=mgpv)
+
+ if (is.null(cv)==FALSE){
+ if (length(dim(cv))==0){
+ for (i in 1:length(cv))
+ if (cv[i]!=0) lines(c(-1,2),c(cv[i],cv[i]))
+ }
+ }
+
+ if (!logscale)
+ axis(side=2,(0:5)/5,labels=c("0","","","","","1"),cex.axis=labsc)
+ else{
+ labelv <- substr(as.character(c(0:5)*(max(log10(wt),na.rm=TRUE)-min(log10(wt),na.rm=TRUE))/5),1,4)
+ axis(side=2,(0:5)/5,labels=labelv,cex.axis=labsc)
+ }
+
+
+ #-----------------
+ # Plotting phase
+ #-----------------
+ if (phase==TRUE){
+
+ if (device=="ps" && split==TRUE){
+
+ dev.off()
+
+ file2 <- paste(file,".phs.eps",sep="")
+
+ postscript(file2,onefile=TRUE,horizontal=TRUE,paper="special",width=10,height=5)
+ cat(paste("# writing",file2," \n"))
+
+ }
+
+ colors <- rainbow(ncolors)
+ if (color==FALSE){
+ dummy <- gray((0:ncolors)/ncolors)
+ colors[1:(ncolors/2)] <- dummy[(ncolors/2+1):ncolors]
+ colors[(ncolors/2+1):ncolors] <- dummy[1:(ncolors/2)]
+ }
+
+ if (units=="")
+ image(x=t,z=phs,col=colors,axes=FALSE,xlab="Time",ylab="Scale",frame.plot=TRUE,cex.lab=labsc,mgp=mgpv)
+ else
+ image(x=t,z=phs,col=colors,axes=FALSE,xlab=paste("Time ","[",units,"]",sep=""),ylab=paste("Scale ","[",units,"]",sep=""),frame.plot=TRUE,cex.lab=labsc,mgp=mgpv)
+
+ if (is.null(cv)==FALSE) plotcv(t,wt,cv)
+ if (sigplot>1) plotat(t,wt,at,sigplot)
+ if (!cut) plotcoi(t,s0,noctave,w0)
+ plotmarks(t,s0,noctave,markt,marks)
+
+ if (is.null(xax))
+ axis(side=1,at=axTicks(1),cex.axis=labsc)
+ else
+ if (is.null(xlab))
+ axis(side=1,xax,labels=as.character(xax),cex.axis=labsc)
+ else
+ axis(side=1,xax,labels=xlab,cex.axis=labsc)
+
+ if (is.null(yax))
+ axis(side=2,sn,labels=as.character(s),cex.axis=labsc)
+ else
+ if (is.null(ylab))
+ axis(side=2,yax,labels=as.character(yax),cex.axis=labsc)
+ else
+ axis(side=2,yax,labels=ylab,cex.axis=labsc)
+
+
+ title(main="Phase")
+
+ image(z=rangebar,axes=FALSE,col=colors,frame.plot=TRUE,cex.lab=labsc,mgp=mgpv)
+ axis(side=2,(0:4)/4,labels=c("-PI","","0","","PI"),cex.axis=labsc)
+
+ }
+
+ if (device=="ps") dev.off()
+
+ }
+
+##############################
+# Surrogates
+##############################
+
+createwavesurrogates <- function(nsurr=1,wt=1,n,dt=1,s0=1,noctave=5,nvoice=10,w0=2*pi){
+
+ surrmat <- matrix(rep(0,n*nsurr),ncol=nsurr)
+
+ for (i in 1:nsurr){
+
+ cat(paste("# Creating realization ",i,"\n",sep=""))
+
+ x <- rnorm(n)
+ xts <- ts(x,start=0,deltat=dt)
+
+ xwt <- cwt.ts(xts,s0,noctave,nvoice,w0)
+ wtsurr <- wt*xwt
+
+ surri <- as.vector(invmorlet(wtsurr,0,dt,s0,noctave,nvoice,w0))
+
+ surrmat[,i] <- Re(surri)
+
+ }
+
+ surrmat
+
+}
+
+surrwave <- function(x,...)
+ UseMethod("surrwave")
+
+surrwave.wt <- function(wt,nsurr=1,spec=TRUE){
+
+ n <- length(wt$time)
+ t0 <- wt$time[1]
+ dt <- (wt$time[13]-t0)/12
+ s0 <- wt$s0
+ noctave <- wt$noctave
+ nvoice <- wt$nvoice
+ w0 <- wt$w0
+
+ wt <- wt$modulus
+ if (spec==TRUE)
+ wt <- sqrt(wt)
+
+ surrmat <- createwavesurrogates(nsurr,wt,n,dt,s0,noctave,nvoice,w0)
+
+ surrts <- ts(surrmat,start=t0,deltat=dt)
+
+ surrts
+
+}
+
+surrwave.matrix <- function(mat,nsurr=1,t0=0,dt=1,s0=1,noctave=5,nvoice=10,w0=2*pi,sw=0,tw=0,swabs=0,spec=FALSE){
+
+ if (sw!=0 & swabs==0)
+ swabs <- as.integer(sw*nvoice)
+
+ scalevector <- 2^(0:(noctave*nvoice)/nvoice)*s0
+
+ if ((noctave*nvoice+1)!=dim(mat)[2])
+ cat("# ERROR! nscales unequal noctave*nvoice+1 ! \n")
+
+ n <- dim(mat)[1]
+
+ if (spec==FALSE)
+ mat <- Mod(mat)
+ else
+ mat <- sqrt(Mod(mat))
+
+ wtsm <- smooth.matrix(mat,swabs)
+ wt <- smooth.time(wtsm,tw,dt,scalevector)
+
+ surrmat <- createwavesurrogates(nsurr,wt,n,dt,s0,noctave,nvoice,w0)
+
+ surrts <- ts(surrmat,start=t0,deltat=dt)
+
+ surrts
+
+}
+
+surrwave.character <-
+ function(file,nsurr=1,t0=0,dt=1,s0=1,noctave=5,nvoice=10,w0=2*pi,sw=0,tw=0,swabs=0,transpose=TRUE,spec=FALSE){
+
+ if (sw!=0 & swabs==0)
+ swabs <- as.integer(sw*nvoice)
+
+ scalevector <- 2^(0:(noctave*nvoice)/nvoice)*s0
+
+ if (transpose==FALSE)
+ mat <- matrix(scan(file,comment.char="#"),ncol=nvoice*noctave+1,byrow=TRUE)
+ else
+ mat <- matrix(scan(file,comment.char="#"),ncol=nvoice*noctave+1,byrow=FALSE)
+
+ if ((noctave*nvoice+1)!=dim(mat)[2])
+ cat("# ERROR! nscales unequal noctave*nvoice+1 ! \n")
+
+ n <- dim(mat)[1]
+
+ if (spec==FALSE)
+ mat <- Mod(mat)
+ else
+ mat <- sqrt(Mod(mat))
+
+ wtsm <- smooth.matrix(mat,swabs)
+ wt <- smooth.time(wtsm,tw,dt,scalevector)
+
+ surrmat <- createwavesurrogates(nsurr,wt,n,dt,s0,noctave,nvoice,w0)
+
+ surrts <- ts(surrmat,start=t0,deltat=dt)
+
+ surrts
+
+ }
+
+surrwave.ts <- function(ts,nsurr=1,s0=1,noctave=5,nvoice=10,w0=2*pi,sw=0,tw=0,swabs=0){
+
+ n <- length(ts)
+ t0 <- time(ts)[1]
+ dt <- deltat(ts)
+ if (sw!=0 & swabs==0)
+ swabs <- as.integer(sw*nvoice)
+
+ scalevector <- 2^(0:(noctave*nvoice)/nvoice)*s0
+
+ wt <- Mod(cwt.ts(ts,s0,noctave,nvoice,w0))
+
+ wtsm <- smooth.matrix(wt,swabs)
+ wt <- smooth.time(wtsm,tw,dt,scalevector)
+
+ surrmat <- createwavesurrogates(nsurr,wt,n,dt,s0,noctave,nvoice,w0)
+
+ surrts <- ts(surrmat,start=t0,deltat=dt)
+
+ surrts
+
+}
+
+invmorlet <- function(wt,t0=0,dt=1,s0=1,noctave=5,nvoice=10,w0=2*pi){
+
+ if ((noctave*nvoice+1)!=dim(wt)[2])
+ cat("# ERROR! nscales unequal noctave*nvoice+1 ! \n")
+
+ n <- dim(wt)[1]
+
+ wt[is.na(wt)] <- 0
+
+ tsRe <- rep(0,n)
+ tsIm <- rep(0,n)
+
+ wtRe <- t(Re(wt))
+ wtIm <- t(Im(wt))
+
+ z <- .C("invmorlet",
+ as.double(as.vector(wtRe)),
+ as.double(as.vector(wtIm)),
+ as.integer(n),
+ as.double(dt),
+ as.double(s0),
+ as.integer(noctave),
+ as.integer(nvoice),
+ as.double(w0),
+ tsRetmp = as.double(tsRe),
+ tsImtmp = as.double(tsIm),
+ PACKAGE="sowas")
+
+ invvec=complex(real=z$tsRetmp,imaginary=z$tsImtmp)
+ invts <- ts(data=invvec,start=t0,deltat=dt)
+
+ invts
+
+}
+
+#################################
+# INPUT / OUTPUT
+#################################
+
+readmatrix <- function(file,M){
+
+ A <- matrix(scan(file,comment.char="#"),ncol=M,byrow=TRUE)
+
+ A
+
+}
+
+
+readts <- function(file){
+
+ A <- matrix(scan(file,comment.char="#"),ncol=2,byrow=TRUE)
+
+ Adum <- A
+
+ Adum[is.na(Adum)] <- 0
+
+ t <- Adum %*% c(1,0)
+ x <- A %*% c(0,1)
+
+ N=length(t)
+ f=1/(t[13]-t[1])*12
+
+ if ((f>11) && (f<13)) f <- 12
+
+ timeseries<-ts(data=x,start=t[1],frequency=f)
+
+ timeseries
+
+}
+
+writematrix <- function(file,data,header="# R Matrix"){
+
+ write(header,file)
+ write(t(data),file,ncol(data),append=TRUE)
+
+}
+
+############################
+# HELP FUNCTIONS
+############################
+
+smooth.matrix <- function(wt,swabs){
+
+ if (swabs != 0)
+ smwt <- t(filter(t(wt),rep(1,2*swabs+1)/(2*swabs+1)))
+ else
+ smwt <- wt
+
+ smwt
+
+}
+
+smooth.time <- function(wt,tw,dt,scalevector){
+
+ smwt <- wt
+
+ if (tw != 0){
+ for (i in 1:length(scalevector)){
+
+ twi <- as.integer(scalevector[i]*tw/dt)
+ smwt[,i] <- filter(wt[,i],rep(1,2*twi+1)/(2*twi+1))
+
+ }
+ }
+
+ smwt
+
+}
+
+
+adjust.noctave <- function(N,dt,s0,tw,noctave){
+
+ if (tw>0){
+ dumno <- as.integer((log(N*dt)-log(2*tw*s0))/log(2))
+ if (dumno<noctave){
+ cat("# noctave adjusted to time smoothing window \n")
+ noctave <- dumno
+ }
+ }
+
+ noctave
+
+}
+
+adjust.s0 <- function(s0,dt){
+
+ if (s0<2*dt){
+ s0 <- 2*dt
+ cat(paste("# s0 set to ",s0," \n"))
+ }
+
+ s0
+
+}
+
+adjust.timeseries <- function(ts1,ts2){
+
+ if (length(ts1)!=length(ts2)){
+ tsint <- ts.intersect(ts1,ts2)
+ dt <- deltat(ts1)
+ ts1 <- ts(data=tsint[,1],start=time(tsint)[1],frequency=1/dt)
+ ts2 <- ts(data=tsint[,2],start=time(tsint)[1],frequency=1/dt)
+ t <- time(ts1)
+ }
+
+ list(ts1=ts1,ts2=ts2)
+
+}
+
+checkarealsiglevel <- function(sw,tw,w0,arealsiglevel,siglevel,type){
+
+ if (type==0){
+
+ swv <- c(0,0.5,1)
+ twv <- c(0,1.5,3)
+ w0v <- c(pi,2*pi)
+
+ if (length(swv[swv==sw])==0 || length(twv[twv==tw])==0 ||
+ length(w0v[w0v==w0])==0){
+ arealsiglevel <- 0
+ cat("# areawise test for spectrum currently \n")
+ cat("# only possible for \n")
+ cat("# sw = 0 \n")
+ cat("# tw = 0 \n")
+ cat("# w0 = 2pi \n")
+ cat("# No areawise test performed \n")
+ }
+ }
+
+ if (type==1){
+
+ swv <- c(0.5)
+ twv <- c(1.5)
+ w0v <- c(2*pi)
+
+ if (length(swv[swv==sw])==0 || length(twv[twv==tw])==0 ||
+ length(w0v[w0v==w0])==0){
+ arealsiglevel <- 0
+ cat("# areawise test for coherence currently \n")
+ cat("# only possible for \n")
+ cat("# sw = 0.5 \n")
+ cat("# tw = 1.5 \n")
+ cat("# w0 = 2pi \n")
+ cat("# No areawise test performed \n")
+ }
+ }
+
+
+ if (arealsiglevel!=0){
+ arealsiglevel <- 0.9
+ siglevel <- 0.95
+ cat("# currently only siglevel=0.95 and arealsiglevel=0.9 possible for areawise test \n")
+ }
+
+ list(siglevel=siglevel,arealsiglevel=arealsiglevel)
+
+}
+
+########################
+
+as.wt <- function(modulus,phase=NULL,s0=NULL,noctave=NULL,nvoice=NULL,w0=NULL,dt=1,time=NULL,scales=NULL,critval=NULL,at=NULL,kernel=NULL,N=NULL,t0=NULL){
+
+ if (is.null(scales))
+ gotscales <- FALSE
+ else
+ gotscales <- TRUE
+
+ if ((!gotscales) & (!is.null(s0)) & (!is.null(noctave)) &(!is.null(nvoice))){
+ gotscales <- TRUE
+ scales=2^(0:(noctave*nvoice)/nvoice)*s0
+ }
+
+ if (gotscales & (is.null(s0) | is.null(noctave) |
+ is.null(nvoice))){
+ s0 <- scales[1]
+ noctave <- log(scales[length(scales)]/s0)/log(2)
+ nvoice <- (length(scales)-1)/noctave
+ }
+
+
+ if (!gotscales)
+ cat("# ERROR! No scales given! \n")
+
+ if (is.null(time)) gottimes <- FALSE
+ else gottimes <- TRUE
+
+ if ((!gottimes) & (!is.null(dt)) & (!is.null(t0)) &(!is.null(N))){
+ gottimes <- TRUE
+ time=(0:(N-1))*dt+t0
+ }
+
+ if (!gottimes)
+ cat("# ERROR! No time vector given! \n")
+
+ wcolist <- list(modulus=modulus,phase=phase,s0=s0,noctave=noctave,nvoice=nvoice,w0=w0,time=time,scales=scales,critval=critval,at=at,kernel=kernel)
+
+ class(wcolist) <- "wt"
+
+ wcolist
+
+}
+
+########################
+
+wtcolors <- function(ncolors){
+
+ upside <- rainbow(ncolors,start=0,end=.7)
+ #upside <- heat.colors(ncolors+5)
+ #upside <- upside[1:ncolors]
+
+
+ down <- upside
+
+ for (i in 1:ncolors){
+ down[i] <- upside[ncolors+1-i]
+ }#
+
+ down
+
+}
+
+####################
+
+createwgn <- function(N,sig,dt){
+
+ timeseries<-ts(data=rnorm(N,0,sig),start=0,deltat=dt)
+
+ timeseries
+
+}
+
+
+createar <- function(N,a,sig,dt){
+
+ if (a==0) a <- 0.000000001
+
+ se <- sqrt(sig*sig*(1-a*a))
+ tsMC <- ts(data=rep(0,N),start=0,deltat=dt)
+
+ tsMC[1:N] <- arima.sim(list(ar = a), N, sd = se)
+
+}
+
+######################
+
+rk <- function(N=1000,s=8,noctave=5,nvoice=10,w0=2*pi,plot=TRUE){
+
+ t <- 1:N
+
+ sunit <- s*(w0+sqrt(2+w0*w0))/(4*pi)
+
+ s0 <- 4
+ #s0unit <- s0*(w0+sqrt(2+w0*w0))/(4*pi)
+ s0unit=s0/dt*w0/(2*pi) #(CORRECT)
+ s0log <- as.integer((log2(s0unit)-1)*nvoice+1.5)
+
+ totnoct <- noctave+as.integer(s0log/nvoice)+1
+
+ x <- morlet(N,N/2,sunit,w0)
+
+ totts.cwt <- Mod(cwt(x,totnoct,nvoice,w0,plot=0))
+ wt=totts.cwt[,s0log:(s0log+noctave*nvoice)]
+
+ wt <- wt/max(wt)
+
+ if (plot==TRUE) plotwt(wt,0,t,s0,noctave,w0,units="",plottitle="Reproducing Kernel")
+
+ wt
+
+}
+
+###################
+
+addvalues <- function(nvoice,dnoctave,x,value){
+
+ nr <- dim(x)[1]
+ nc <- dim(x)[2]
+ dnc <- nvoice*dnoctave
+
+ y <- matrix(rep(value,nr*(nc+dnc)),nrow=nr)
+
+ y[,(dnc+1):(dnc+nc)] <- x
+
+ y
+
+}
+
+####################
+
+scalematrix <- function(wt){
+
+ # scales matrix, such that the maximal value is one
+ # wt: matrix to be scaled
+
+ mval <- max(wt,na.rm=TRUE)
+
+ wt <- wt/mval
+
+ wt
+
+}
+
+
+foldKernel <- function(F,swabs,tw,s,dt){
+
+ # folds a matrix (e.g. kernel with smoothing window
+ # F: matrix input
+ # swabs: smooting window width
+
+ smsF <- smooth.matrix(F,swabs)
+ smsF[is.na(smsF)] <- 0
+
+ smtsF <- smooth.time(smsF,tw,dt,s)
+
+ smtsF[is.na(smtsF)] <- 0
+
+ scF <- scalematrix(smtsF)
+
+ scF
+
+}
+
+kernelBitmap <- function(c,s0=1,w0=6,noctave=6,nvoice=20,swabs=0,tw=0,dt=1){
+ # produces kernel bitmap
+ # c: height of contour, that defines area
+ # s0: lowest scale
+ # noctave: number of octaves
+ # nvoice: number of voices per octave
+ # swabs: smoothing window length in scale direction
+ # dt: sampling time
+
+ s <- s0*2^noctave
+ is <- noctave*nvoice
+
+ x <- s0*2^(((1:(nvoice*(noctave+2)))-1)/nvoice)
+
+ t <- max(2000,max(x)*tw*2/dt*1.1)
+
+ y <- ((0:(2*t))-t)/2*dt
+
+ X <- matrix(x,ncol=nvoice*(noctave+2),nrow=2*t+1,byrow=T)
+ Y <- matrix(y,ncol=nvoice*(noctave+2),nrow=2*t+1)
+
+ F <- sqrt(2*s*X/(s*s+X*X))*exp(-0.5*(Y*Y+w0*w0*(X-s)*(X-s))/(s*s+X*X))
+
+ F <- foldKernel(F,swabs,tw,x,dt)
+
+ F[F<c] <- 0
+ F[F>=c] <- 1
+
+ is1 <- 1
+ is2 <- nvoice*(noctave+1)
+ it1 <- 1
+ it2 <- 2*t+1
+
+ L <- F[1:(2*t+1),is1]
+
+ while (length(L[L!=0])==0) {
+ is1 <- is1+1
+ L <- F[1:(2*t+1),is1]
+ }
+
+ L <- F[1:(2*t+1),is2]
+
+ while (length(L[L!=0])==0) {
+ is2 <- is2-1
+ L <- F[1:(2*t+1),is2]
+ }
+
+
+ L <- F[it1,1:(nvoice*(noctave+2))]
+
+ while (length(L[L!=0])==0) {
+ it1 <- it1+1
+ L <- F[it1,1:(nvoice*(noctave+2))]
+ }
+
+ L <- F[it2,1:(nvoice*(noctave+2))]
+
+ while (length(L[L!=0])==0) {
+ it2 <- it2-1
+ L <- F[it2,1:(nvoice*(noctave+2))]
+ }
+
+ kernel <- list(bitmap=F[(it1-1):(it2+1),(is1-1):(is2+1)],is=is-is1)
+
+ kernel
+
+}
+
+kernelRoot <- function(s0=1,w0=6,a=0,noctave=6,nvoice=20,swabs=0,tw=0,dt=1){
+
+ tol <- 0.005
+ cmin <- 0
+ cmax <- 1
+ cntr <- 0.5
+ da <- a
+
+ while (abs(da/a)>tol){
+
+ da <- kernelArea(cntr,s0,w0,a,noctave,nvoice,swabs,tw,dt)
+ if (da>0){
+ cmin <- cntr
+ cntr <- mean(c(cntr,cmax))
+ }
+ if (da<0){
+ cmax <- cntr
+ cntr <- mean(c(cntr,cmin))
+ }
+ }
+
+ cntr
+
+}
+
+kernelArea <- function(cntr,s0=1,w0=6,a=0,noctave=6,nvoice=20,swabs=0,tw=0,dt=1){
+
+ # calulates area of reproducing kernel for smoothed data at scale s0*2^noctave
+ # cntr: height of contour line to define kernel area. This
+ # parameter is to be estimated!
+ # s0: lowest scale
+ # w0: parameter of Morlet Wavelet
+ # a: area offset (only needed, when finding root. Is set to
+ # desired area
+ # noctave: number of octaves
+ # nvoice: number of voices per octave
+ # swabs: smoothing window width in scale direction
+ # dt: sampling time
+
+ s <- s0*2^noctave
+
+ x <- s0*2^(((1:(nvoice*(noctave+2)))-1)/nvoice)
+
+ t <- max(2000,max(x)*tw*2/dt*1.1)
+
+ y <- ((0:(2*t))-t)/2*dt
+
+ X <- matrix(x,ncol=nvoice*(noctave+2),nrow=2*t+1,byrow=T)
+ Y <- matrix(y,ncol=nvoice*(noctave+2),nrow=2*t+1)
+
+ F <- sqrt(2*s*X/(s*s+X*X))*exp(-0.5*(Y*Y+w0*w0*(X-s)*(X-s))/(s*s+X*X))
+
+ F <- foldKernel(F,swabs,tw,x,dt)
+
+ F[F>=cntr] <- 1
+ F[F<cntr] <- 0
+
+ area <- length(F[F==1])-a
+
+ area
+
+}
+
+
+tobin <- function(x){
+
+ # sets nonzero values to one
+
+ y <- x/x
+ y[is.na(y)] <- 0
+
+ y
+
+}
+
+scaleKernel <- function(kernel,l){
+
+ # scales kernel length in time direction proportional to scale
+ # kernel: data bitmap of width n
+ # l: new width of kernel
+
+ n <- nrow(kernel)
+ m <- ncol(kernel)
+
+ newKernel <- matrix(rep(0,m*l),nrow=l)
+
+ d <- as.double(n)/as.double(l)
+
+ for (i in 1:l){
+ j <- as.integer((i-0.5)*d)
+ if (j==0) j <- 1
+ newKernel[i,1:m] <- kernel[j,1:m]
+ }
+
+ newKernel
+
+}
+
+slope <- function(w0,swabs,tw,nvoice,siglevel,arealsiglevel,type){
+
+ sw <- swabs/nvoice
+
+ if (type==0){ # wavelet spectrum
+
+ if (tw == 0 & sw == 0 & w0 == 1 *pi) slp <- 5.82518 # w = 18.35831
+ if (tw == 1.5 & sw == 0 & w0 == 1 *pi) slp <- 24.69852 # w = 14.30709
+ if (tw == 3 & sw == 0 & w0 == 1 *pi) slp <- 35.48368 # w = 14.72354
+ if (tw == 0 & sw == 5 & w0 == 1 *pi) slp <- 7.347707 # w = 17.96942
+ if (tw == 1.5 & sw == 5 & w0 == 1 *pi) slp <- 28.24291 # w = 12.65993
+ if (tw == 3 & sw == 5 & w0 == 1 *pi) slp <- 51.13723 # w = 10.96359
+ if (tw == 0 & sw == 10 & w0 == 1 *pi) slp <- 10.47856 # w = 15.5941
+ if (tw == 1.5 & sw == 10 & w0 == 1 *pi) slp <- 45.07387 # w = 15.29793
+ if (tw == 3 & sw == 10 & w0 == 1 *pi) slp <- 52.82886 # w = 12.72361
+
+ if (tw == 0 & sw == 0 & w0 == 2 *pi) slp <- 8.718912 # w = 17.75933
+ if (tw == 1.5 & sw == 0 & w0 == 2 *pi) slp <- 11.88006 # w = 15.39648
+ if (tw == 3 & sw == 0 & w0 == 2 *pi) slp <- 26.55977 # w = 1.064384
+ if (tw == 0 & sw == 5 & w0 == 2 *pi) slp <- 14.64761 # w = 16.27518
+ if (tw == 1.5 & sw == 5 & w0 == 2 *pi) slp <- 28.27798 # w = 14.57059
+ if (tw == 3 & sw == 5 & w0 == 2 *pi) slp <- 63.54121 # w = 12.83778
+ if (tw == 0 & sw == 10 & w0 == 2 *pi) slp <- 27.78735 # w = 11.95813
+ if (tw == 1.5 & sw == 10 & w0 == 2 *pi) slp <- 41.27260 # w = 12.03379
+ if (tw == 3 & sw == 10 & w0 == 2 *pi) slp <- 67.37015 # w = 10.63935
+
+ }
+
+ if (type==1){ # wavelet coherence
+
+ if (tw==0 & sw==0 & w0==pi) slp <- 999 #not valid
+ if (tw==1.5 & sw==0 & w0==pi) slp <- 1
+ if (tw==3 & sw==0 & w0==pi) slp <- 1
+ if (tw==0 & sw==0.5 & w0==pi) slp <- 1
+ if (tw==1.5 & sw==0.5 & w0==pi) slp <- 1
+ if (tw==3 & sw==0.5 & w0==pi) slp <- 1
+ if (tw==0 & sw==1 & w0==pi) slp <- 1
+ if (tw==1.5 & sw==1 & w0==pi) slp <- 1
+ if (tw==3 & sw==1 & w0==pi) slp <- 1
+
+ if (tw==0 & sw==0 & w0==2*pi) slp <- 999 #not valid
+ if (tw==1.5 & sw==0 & w0==2*pi) slp <- 1
+ if (tw==3 & sw==0 & w0==2*pi) slp <- 1
+ if (tw==0 & sw==0.5 & w0==2*pi) slp <- 1
+ if (tw==1.5 & sw==0.5 & w0==2*pi) slp <- 8.3
+ if (tw==3 & sw==0.5 & w0==2*pi) slp <- 1
+ if (tw==0 & sw==1 & w0==2*pi) slp <- 1
+ if (tw==1.5 & sw==1 & w0==2*pi) slp <- 1
+ if (tw==3 & sw==1 & w0==2*pi) slp <- 1
+
+ if (tw==0 & sw==0 & w0==3*pi) slp <- 999 #not valid
+ if (tw==1.5 & sw==0 & w0==3*pi) slp <- 1
+ if (tw==3 & sw==0 & w0==3*pi) slp <- 1
+ if (tw==0 & sw==0.5 & w0==3*pi) slp <- 1
+ if (tw==1.5 & sw==0.5 & w0==3*pi) slp <- 1
+ if (tw==3 & sw==0.5 & w0==3*pi) slp <- 1
+ if (tw==0 & sw==1 & w0==3*pi) slp <- 1
+ if (tw==1.5 & sw==1 & w0==3*pi) slp <- 1
+ if (tw==3 & sw==1 & w0==3*pi) slp <- 1
+
+ if (tw==0 & sw==0 & w0==4*pi) slp <- 999 #not valid
+ if (tw==1.5 & sw==0 & w0==4*pi) slp <- 1
+ if (tw==3 & sw==0 & w0==4*pi) slp <- 1
+ if (tw==0 & sw==0.5 & w0==4*pi) slp <- 1
+ if (tw==1.5 & sw==0.5 & w0==4*pi) slp <- 1
+ if (tw==3 & sw==0.5 & w0==4*pi) slp <- 1
+ if (tw==0 & sw==1 & w0==4*pi) slp <- 1
+ if (tw==1.5 & sw==1 & w0==4*pi) slp <- 1
+ if (tw==3 & sw==1 & w0==4*pi) slp <- 1
+
+ }
+
+ cat(paste("# slope ",slp,"\n",sep=""))
+
+ slp
+
+}
projects / epclust.git / blobdiff