X-Git-Url: https://git.auder.net/?a=blobdiff_plain;f=codes_Jairo_stage2%2Fsowas-superseded.r;fp=codes_Jairo_stage2%2Fsowas-superseded.r;h=dca33536ce316493b67ff989bd2f7064e4d45580;hb=ad642dc605bbbd0b3fa890c78fa8d634b1d6f703;hp=0000000000000000000000000000000000000000;hpb=f1fea2229d365a222b5aff0cb1b4d346c4437e8b;p=epclust.git

diff --git a/codes_Jairo_stage2/sowas-superseded.r b/codes_Jairo_stage2/sowas-superseded.r
new file mode 100644
index 0000000..dca3353
--- /dev/null
+++ b/codes_Jairo_stage2/sowas-superseded.r
@@ -0,0 +1,1563 @@
+###########################################################
+# 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
+  
+}