R/single.norm.R

In changepoint: Methods for Changepoint Detection

single.mean.norm.calc <-
function(data,extrainf=TRUE,minseglen){
  singledim=function(data,extrainf=TRUE,minseglen){
    n=length(data)
    y=c(0,cumsum(data))
    y2=c(0,cumsum(data^2))
    null=y2[n+1]-y[n+1]^2/n
    taustar=minseglen:(n-minseglen+1)
    tmp=y2[taustar+1]-y[taustar+1]^2/taustar + (y2[n+1]-y2[taustar+1]) - ((y[n+1]-y[taustar+1])^2)/(n-taustar)
    
    tau=which(tmp==min(tmp,na.rm=T))[1]
    taulike=tmp[tau]
    tau=tau+minseglen-1 # correcting for the fact that we are starting at minseglen
    if(extrainf==TRUE){
      out=c(tau,null,taulike)
      names(out)=c('cpt','null','alt')
      return(out)
    }
    else{
      return(tau)
    }
  }
    

  if(is.null(dim(data))==TRUE || length(dim(data)) == 1){
    # single data set
    cpt=singledim(data,extrainf,minseglen)
    return(cpt)
  }
  else{
    rep=nrow(data)
    n=ncol(data)
    cpt=NULL
    if(extrainf==FALSE){
      for(i in 1:rep){
        cpt[i]=singledim(data[i,],extrainf,minseglen)
      }
    }
    else{
      cpt=matrix(0,ncol=3,nrow=rep)
      for(i in 1:rep){
        cpt[i,]=singledim(data[i,],extrainf,minseglen)
      }
      colnames(cpt)=c('cpt','null','alt')
    }
    return(cpt)
  }
}

single.mean.norm<-function(data,penalty="MBIC",pen.value=0,class=TRUE,param.estimates=TRUE,minseglen){
  if(is.null(dim(data))==TRUE || length(dim(data)) == 1){
    # single dataset
    n=length(data)
  }
  else{
    n=ncol(data)
  }
  if(n<2){stop('Data must have atleast 2 observations to fit a changepoint model.')}
  if(n<(2*minseglen)){stop('Minimum segment legnth is too large to include a change in this data')}
  
  pen.value = penalty_decision(penalty, pen.value, n, diffparam=1, asymcheck="mean.norm", method="AMOC")
  if(is.null(dim(data))==TRUE || length(dim(data)) == 1){ # single dataset
		tmp=single.mean.norm.calc(coredata(data),extrainf=TRUE,minseglen)
		if(penalty=="MBIC"){
		  tmp[3]=tmp[3]+log(tmp[1])+log(n-tmp[1]+1)
		}
		ans=decision(tmp[1],tmp[2],tmp[3],penalty,n,diffparam=1,pen.value)
    
		if(class==TRUE){
		  return(class_input(data, cpttype="mean", method="AMOC", test.stat="Normal", penalty=penalty, pen.value=ans$pen, minseglen=minseglen, param.estimates=param.estimates, out=c(0, ans$cpt)))
		}
		else{ 
		  alogn=(2*log(log(n)))^(-(1/2))
		  blogn=(alogn^(-1))+(1/2)*alogn*log(log(log(n)))  # Chen & Gupta (2000) pg10
		  out=c(ans$cpt,exp(-2*(pi^(1/2))*exp(-alogn*sqrt(abs(tmp[2]-tmp[3]))+(alogn^{-1})*blogn))-exp(-2*(pi^(1/2))*exp((alogn^{-1})*blogn)))
		  names(out)=c('cpt','conf.value')
		  return(out)
		}
	}
	else{ 
		tmp=single.mean.norm.calc(data,extrainf=TRUE,minseglen)
		if(penalty=="MBIC"){
		  tmp[,3]=tmp[,3]+log(tmp[,1])+log(n-tmp[,1]+1)
		}
		ans=decision(tmp[,1],tmp[,2],tmp[,3],penalty,n,diffparam=1,pen.value)
		if(class==TRUE){
			rep=nrow(data)
			out=list()
			for(i in 1:rep){
        out[[i]] = class_input(data, cpttype="mean", method="AMOC", test.stat="Normal", penalty=penalty, pen.value=ans$pen, minseglen=minseglen, param.estimates=param.estimates, out=c(0, ans$cpt[i]))
			}
			return(out)
		}
		else{ 
		  alogn=(2*log(log(n)))^(-(1/2))
		  blogn=(alogn^(-1))+(1/2)*alogn*log(log(log(n)))  # Chen & Gupta (2000) pg10
		  out=cbind(ans$cpt,exp(-2*(pi^(1/2))*exp(-alogn*sqrt(abs(tmp[,2]-tmp[,3]))+(alogn^{-1})*blogn))-exp(-2*(pi^(1/2))*exp((alogn^{-1})*blogn)))
		  colnames(out)=c('cpt','conf.value')
      rownames(out)=NULL
		  return(out)
		}
	}
}





single.var.norm.calc <- function(data,mu,extrainf=TRUE,minseglen){
  n=length(data)
  y=c(0,cumsum((data-mu)^2))
  null=n*log(y[n+1]/n)
  taustar=minseglen:(n-minseglen+1)
  sigma1=y[taustar+1]/taustar
  neg=sigma1<=0
  sigma1[neg==TRUE]=1*10^(-10)
  sigman=(y[n+1]-y[taustar+1])/(n-taustar)
  neg=sigman<=0
  sigman[neg==TRUE]=1*10^(-10)
  tmp=taustar*log(sigma1) + (n-taustar)*log(sigman)
  
  tau=which(tmp==min(tmp,na.rm=T))[1]
  taulike=tmp[tau]
  tau=tau+minseglen-1 # correcting for the fact that we are starting at minseglen
  if(extrainf==TRUE){
    out=c(tau,null,taulike)
    names(out)=c('cpt','null','alt')
    return(out)
  }
  else{
    return(tau)
  }
}    


single.var.norm<-function(data,penalty="MBIC",pen.value=0,know.mean=FALSE,mu=NA,class=TRUE,param.estimates=TRUE,minseglen){
  if(is.null(dim(data))==TRUE || length(dim(data)) == 1){
    # single dataset
    n=length(data)
    mu=mu[1]
  }
  else{
    n=ncol(data)
  }
  if(n<4){stop('Data must have atleast 4 observations to fit a changepoint model.')}
  if(n<(2*minseglen)){stop('Minimum segment legnth is too large to include a change in this data')}
  
  pen.value = penalty_decision(penalty, pen.value, n, diffparam=1, asymcheck="var.norm", method="AMOC")
  
  if(is.null(dim(data))==TRUE || length(dim(data)) == 1){
    if((know.mean==FALSE)&(is.na(mu))){
      mu=mean(coredata(data))
    }
    tmp=single.var.norm.calc(coredata(data),mu,extrainf=TRUE,minseglen)
		if(penalty=="MBIC"){
		  tmp[3]=tmp[3]+log(tmp[1])+log(n-tmp[1]+1)
		}
		ans=decision(tmp[1],tmp[2],tmp[3],penalty,n,diffparam=1,pen.value)
		if(class==TRUE){
		  out=class_input(data, cpttype="variance", method="AMOC", test.stat="Normal", penalty=penalty, pen.value=pen.value, minseglen=minseglen, param.estimates=param.estimates, out=c(0, ans$cpt))
		  param.est(out)=c(param.est(out),mean=mu)
		  return(out)
		}
		else{ 
		  alogn=sqrt(2*log(log(n)))
		  blogn=2*log(log(n))+ (log(log(log(n))))/2 - log(gamma(1/2))
		  out=c(ans$cpt,exp(-2*exp(-alogn*sqrt(abs(tmp[2]-tmp[3]))+blogn))-exp(-2*exp(blogn)))  # Chen & Gupta (2000) pg27
		  names(out)=c('cpt','conf.value')
		  return(out)
		}
	}
	else{ 
	  rep=nrow(data)
	  tmp=matrix(0,ncol=3,nrow=rep)
	  if(length(mu)!=rep){
	    mu=rep(mu,rep)
	  }
    for(i in 1:rep){
      if((know.mean==FALSE)&(is.na(mu[i]))){
        mu=mean(coredata(data[i,]))
      }
      tmp[i,]=single.var.norm.calc(data[i,],mu[i],extrainf=TRUE,minseglen)
    }

    if(penalty=="MBIC"){
		  tmp[,3]=tmp[,3]+log(tmp[,1])+log(n-tmp[,1]+1)
		}
		ans=decision(tmp[,1],tmp[,2],tmp[,3],penalty,n,diffparam=1,pen.value)
		if(class==TRUE){
			out=list()
			for(i in 1:rep){
          out[[i]] = class_input(data, cpttype="variance", method="AMOC", test.stat="Normal", penalty=penalty, pen.value=ans$pen, minseglen=minseglen, param.estimates=param.estimates, out=c(0, ans$cpt[i]))
          param.est(out[[i]])=c(param.est(out[[i]]),mean=mu[i])
			}
			return(out)
		}
		else{ 
		  alogn=sqrt(2*log(log(n)))
		  blogn=2*log(log(n))+ (log(log(log(n))))/2 - log(gamma(1/2))
		  out=cbind(ans$cpt,exp(-2*exp(-alogn*sqrt(abs(tmp[,2]-tmp[,3]))+blogn))-exp(-2*exp(blogn)))  # Chen & Gupta (2000) pg27
		  colnames(out)=c('cpt','conf.value')
      rownames(out)=NULL
		  return(out)
		}
	}
}






single.meanvar.norm.calc <-
function(data,extrainf=TRUE,minseglen){
  singledim=function(data,extrainf=TRUE,minseglen){
    n=length(data)
    y=c(0,cumsum(data))
    y2=c(0,cumsum((data)^2))
    null=n*log((y2[n+1]-(y[n+1]^2/n))/n)
    taustar=minseglen:(n-minseglen+1)
    sigma1=((y2[taustar+1]-(y[taustar+1]^2/taustar))/taustar)
    neg=sigma1<=0
    sigma1[neg==TRUE]=1*10^(-10)
    sigman=((y2[n+1]-y2[taustar+1])-((y[n+1]-y[taustar+1])^2/(n-taustar)))/(n-taustar)
    neg=sigman<=0
    sigman[neg==TRUE]=1*10^(-10)
    tmp=taustar*log(sigma1) + (n-taustar)*log(sigman)
    
    tau=which(tmp==min(tmp,na.rm=T))[1]
    taulike=tmp[tau]
    tau=tau+minseglen-1 # correcting for the fact that we are starting at minseglen
    if(extrainf==TRUE){
      out=c(tau,null,taulike)
      names(out)=c('cpt','null','alt')
      return(out)
    }
    else{
      return(tau)
    }
  }
    

  if(is.null(dim(data))==TRUE || length(dim(data)) == 1){
    # single data set
    cpt=singledim(data,extrainf,minseglen)
    return(cpt)
  }
  else{
    rep=nrow(data)
    n=ncol(data)
    cpt=NULL
    if(extrainf==FALSE){
      for(i in 1:rep){
        cpt[i]=singledim(data[i,],extrainf,minseglen)
      }
    }
    else{
      cpt=matrix(0,ncol=3,nrow=rep)
      for(i in 1:rep){
        cpt[i,]=singledim(data[i,],extrainf,minseglen)
      }
      colnames(cpt)=c('cpt','null','alt')
    }
    return(cpt)
  }
}

single.meanvar.norm<-function(data,penalty="MBIC",pen.value=0,class=TRUE,param.estimates=TRUE,minseglen){
  if(is.null(dim(data))==TRUE || length(dim(data)) == 1){
    # single dataset
    n=length(data)
  }
  else{
    n=ncol(data)
  } 
  if(n<4){stop('Data must have atleast 4 observations to fit a changepoint model.')}
  if(n<(2*minseglen)){stop('Minimum segment legnth is too large to include a change in this data')}
  
  pen.value = penalty_decision(penalty, pen.value, n, diffparam=1, asymcheck="meanvar.norm", method="AMOC")
  
  if(is.null(dim(data))==TRUE || length(dim(data)) == 1){
		tmp=single.meanvar.norm.calc(coredata(data),extrainf=TRUE,minseglen)
		if(penalty=="MBIC"){
		  tmp[3]=tmp[3]+log(tmp[1])+log(n-tmp[1]+1)
		}
		ans=decision(tmp[1],tmp[2],tmp[3],penalty,n,diffparam=2,pen.value)
		if(class==TRUE){
      return(class_input(data, cpttype="mean and variance", method="AMOC", test.stat="Normal", penalty=penalty, pen.value=ans$pen, minseglen=minseglen, param.estimates=param.estimates, out=c(0,ans$cpt)))
		}
		else{ 
		  alogn=sqrt(2*log(log(n)))
		  blogn=2*log(log(n))+ (log(log(log(n))))
		  out=c(ans$cpt,exp(-2*exp(-alogn*sqrt(abs(tmp[2]-tmp[3]))+blogn))-exp(-2*exp(blogn)))   # Chen & Gupta (2000) pg54
		  names(out)=c('cpt','conf.value')
		  return(out)
		}
	}
	else{ 
		tmp=single.meanvar.norm.calc(data,extrainf=TRUE,minseglen)
		if(penalty=="MBIC"){
		  tmp[,3]=tmp[,3]+log(tmp[,1])+log(n-tmp[,1]+1)
		}
		ans=decision(tmp[,1],tmp[,2],tmp[,3],penalty,n,diffparam=2,pen.value)
		if(class==TRUE){
			rep=nrow(data)
			out=list()
			for(i in 1:rep){
        out[[i]]= class_input(data[i,], cpttype="mean and variance", method="AMOC", test.stat="Normal", penalty=penalty, pen.value=ans$pen, minseglen=minseglen, param.estimates=param.estimates, out=c(0,ans$cpt[i]))
			}
			return(out)
		}
		else{ 
		  alogn=sqrt(2*log(log(n)))
		  blogn=2*log(log(n))+ (log(log(log(n))))
		  out=cbind(ans$cpt,exp(-2*exp(-alogn*sqrt(abs(tmp[,2]-tmp[,3]))+blogn))-exp(-2*exp(blogn)))   # Chen & Gupta (2000) pg54
		  colnames(out)=c('cpt','conf.value')
      rownames(out)=NULL
		  return(out)
		}
	}
}