R/generate.PrecipitationOccurenceModel.R
In ecor/RGENERATEPREC: Tools to Generate Daily-Precipitation Time Series
Defines functions
generate.PrecipitationOccurrenceMultiSiteModel
generate.CCGammaObjectListPerEachMonth
generate.PrecipitationOccurrenceModel
Documented in
generate.CCGammaObjectListPerEachMonth
generate.PrecipitationOccurrenceModel
generate.PrecipitationOccurrenceMultiSiteModel
NULL
#' Stochastic Generation of a \code{PrecipitationOccurrenceModel} or \code{PrecipitationOccurrenceMultiSiteModel} model object
#'
#' It is an implentation of \code{\link{generate}} method
#'
#' @param x model returned by \code{\link{PrecipitationOccurrenceModel}} or \code{\link{PrecipitationOccurrenceMultiSiteModel}}
#' @param newdata predictor or exogenous variables. See \code{\link{predict.PrecipitationOccurrenceModel}}
#' @param exogen predictor or exogenous variables
#' @param monthly.factor vector of factors indicating the month of the days
#' @param random vector of random or calculated numbers ranging between 0 and 1
#' @param origin,end character strings (yyyy-dd-mm) indicating the start and/or end date of the daily weather generation.
#' @param n number of generations. See \code{\link{generate}}. Here it is ignored and the number of generations is given by \code{origin},\code{end} or \code{monthly.factor}.
#' @param previous logical vector containing previously occurred states
#' @param ... further arguments
#'
#' @seealso \code{\link{generate}},\code{\link{predict.glm}},\code{\link{PrecipitationOccurrenceModel}},\code{\link{PrecipitationOccurrenceMultiSiteModel}}
#' @export
#' @method generate PrecipitationOccurrenceModel
#### @S3method generate PrecipitationOccurrenceModel
#' @aliases generate generate.PrecipitationOccurrenceModel
#' @rdname generate
#' @importFrom RGENERATE generate
#' @return A vector or a data frame reporting generated time series for each station.
#' @references
#' D.S. Wilks (1998), Multisite Generalization of a Daily Stochastic Precipitation Generation Model, Journal of Hydrology, Volume 210, Issues 1-4, September 1998, Pages 178-191,
#' \url{https://www.sciencedirect.com/science/article/pii/S0022169498001863}
#'
#' Muamaraldin Mhanna and Willy Bauwens (2011) A Stochastic Space-Time Model for the Generation of Daily Rainfall in the Gaza Strip, International Journal of Climatology, Volume 32, Issue 7, pages 1098-1112,
#' \doi{10.1002/joc.2305}, \url{https://rmets.onlinelibrary.wiley.com/doi/abs/10.1002/joc.2305}
#'
#'
#'
#'
#' @examples
#'
#' library(RGENERATEPREC)
#'
#'
#' ## A function example can be found in the following script file:
#' scriptfile <- system.file("example.generate.R",package="RGENERATEPREC")
#' ## The corrent file path is given by 'scriptfile' variable:
#' print(scriptfile)
#' ## To run the example file, launch the file with 'source' command (uncomment the following line)
#' #source(scriptfile)
#'
#' ## ALTERNATIVELY you can run the following lines:
#'
#'
#'
#' data(trentino)
#'
#' year_min <- 1961
#' year_max <- 1990
#'
#' origin <- paste(year_min,1,1,sep="-")
#' end <- paste(year_max,12,31,sep="-")
#'
#' period <- PRECIPITATION$year>=year_min & PRECIPITATION$year<=year_max
#' period_temp <- TEMPERATURE_MAX$year>=year_min & TEMPERATURE_MAX$year<=year_max
#'
#' prec_mes <- PRECIPITATION[period,]
#' Tx_mes <- TEMPERATURE_MAX[period_temp,]
#' Tn_mes <- TEMPERATURE_MIN[period_temp,]
## removing nonworking stations (e.g. time series with NA)
#' accepted <- array(TRUE,length(names(prec_mes)))
#' names(accepted) <- names(prec_mes)
#' for (it in names(prec_mes)) {
#' acc <- TRUE
#' acc <- (length(which(!is.na(Tx_mes[,it])))==length(Tx_mes[,it]))
#' acc <- (length(which(!is.na(Tn_mes[,it])))==length(Tn_mes[,it])) & acc
#' accepted[it] <- (length(which(!is.na(prec_mes[,it])))==length(prec_mes[,it])) & acc
#'
#' }
#'
#' valmin <- 1.0
###station <- names(PRECIPITATION)[!(names(PRECIPITATION) %in% c("day","month","year"))]
#' prec_mes <- prec_mes[,accepted]
#'
#'
#'
#' Tx_mes <- Tx_mes[,accepted]
#' Tn_mes <- Tn_mes[,accepted]
#' prec_occurrence_mes <- prec_mes>=valmin
#'
#' station <- names(prec_mes)[!(names(prec_mes) %in% c("day","month","year"))]
#' it <- station[2]
#' vect <- Tx_mes[,it]-Tn_mes[,it]
#' months <- factor(prec_mes$month)
#'
#'
#' \donttest{
#' model <-
#' PrecipitationOccurrenceModel(x=prec_mes[,it],exogen=vect,
#' monthly.factor=months,valmin=valmin)
#'
#' obs <- prec_mes[,it]>=valmin
#'
#' gen <- generate(model,exogen=vect,monthly.factor=months,n=length(months))
#' }
#'
#' ## Only 10 generated realizations!!
#' gen10 <- generate(model,exogen=vect,monthly.factor=months,n=10)
#'
#'
#' ### MultiSite Generation
#'
#'
#' station <- station[1:2]
#' exogen <- Tx_mes[,station]-Tn_mes[,station]
#'
#' months <- factor(prec_mes$month)
#'
#'
#' \donttest{
#'
#' model_multisite <-
#' PrecipitationOccurrenceMultiSiteModel(x=prec_mes[,station],
#' exogen=exogen,origin=origin,multisite_type="wilks")
#'
#'
#' ## LOGIT-type Model
#' model_multisite_logit <-
#' PrecipitationOccurrenceMultiSiteModel(x=prec_mes,exogen=exogen,
#' origin=origin,multisite_type="logit",station=station)
#'
#'
#' obs_multisite <- prec_mes[,station]>=valmin
#'
#' gen_multisite <- generate(model_multisite,exogen=exogen,origin=origin,end=end)
#'
#' gen_multisite_logit <- generate(model_multisite_logit,exogen=exogen,origin=origin,end=end)
#' }
generate.PrecipitationOccurrenceModel <- function(x,newdata=NULL,previous=NULL,n=30,random=runif(n,min=0,max=1),exogen=NULL,monthly.factor=NULL,...) {
p <- x$p
if (p<1) previous <- NULL
if (!is.null(exogen)) newdata <- as.data.frame(exogen)
if (is.null(newdata) & is.null(monthly.factor)) {
newdata <- x$predictor
} else if (is.null(newdata)) {
newdata <- as.data.frame(array(NA,c(length(monthly.factor),0)))
}
if (!is.null(monthly.factor)) newdata$month <- factor(monthly.factor)
if (nrow(newdata)<n) {
warning("Warning: n is reduced, insufficient numbers of predictors!")
n <- nrow(newdata)
}
names_n <- names(newdata)
newdata <- as.data.frame(newdata[1:n,])
names(newdata) <- names_n
if (is.null(previous)) {
previous <- rnorm(x$p)>=0
}
out <- array(NA,n)
for (i in 1:n) {
### prob <- 1-predict(x,newdata=newdata[i,],previous=previous,type="response",endogenous=endogenous,...)
##EC 20230123x01 <<- x
##EC 20230123newdata01 <<- newdata[i,]
##EC 20230123previous01 <<- previous
##EC 20230123i01 <<- i
prob <- 1-predict(x,newdata=newdata[i,],previous=previous,type="response",...) ## ec 20141208
out[i] <- random[i]>=prob
previous <- c(out[i],previous[-p])
}
return(out)
}
NULL
#'
#'
#'
#' @export
#' @method generate CCGammaObjectListPerEachMonth
#### @S3method generate CCGammaObjectListPerEachMonth
#' @aliases generate generate.CCGammaObjectListPerEachMonth
#' @rdname generate
#'
generate.CCGammaObjectListPerEachMonth <- function(x,...) {
class(x) <- "list"
out <- generate(x,...)
return(out)
}
NULL
#'
#'
#'
#' @export
#' @method generate PrecipitationOccurrenceMultiSiteModel
#### @S3method generate PrecipitationOccurrenceMultiSiteModel
#' @aliases generate generate.PrecipitationOccurrenceMultiSiteModel
#' @rdname generate
#'
generate.PrecipitationOccurrenceMultiSiteModel <- function(x,exogen,n=NA,origin="1961-1-1",end="1990-1-1",previous=NULL,monthly.factor=NULL,...) {
out <- NULL
## EC 20230123
if (is.null(origin)) origin <- NA
if (is.null(end)) end <- NA
if (!is.na(n) & n>0) {
if (!is.na(origin)) {
end <- as.Date(origin)+lubridate::days(n-1)
} else if (!is.na(end)) {
origin <- as.Date(end)-lubridate::days(n-1)
}
}
if (is.null(monthly.factor)) {
dates <- as.Date(origin):as.Date(end)
months <- adddate(as.data.frame(dates),origin=origin)$month
n <- length(months)
} else {
months <- monthly.factor
n <- length(months)
}
if (x$type=="wilks") {
monthsf <- sprintf("month%02d",months)
gen_wilks <- generate(x$ccgamma,FUN=rnorm,type="covariance",names=x$station,factor.series=monthsf)
for (c in 1:ncol(gen_wilks)) {
gen_wilks[,c] <- pnorm(gen_wilks[,c])
}
if (is.null(exogen)) {
exogen <- lapply(X=x$station,FUN=function(x){ NULL })
names(exogen) <- x$station
}
if (is.null(previous)) {
previous <- lapply(X=x$station,FUN=function(x){ NULL })
names(previous) <- x$station
}
out <- as.data.frame(array(NA,dim(gen_wilks)))
names(out) <- names(gen_wilks)
for (it in x$station) {
# if (is.data.frame(exogen)) {
#
# exogen_loc <- exogen[,it]
#
# } else {
#
# exogen_loc <- exogen[[it]]
# }
if (is.data.frame(exogen)) {
cols <- str_detect(names(exogen),it)
exogen_loc <- exogen[,cols]
} else if (is.list(exogen)) {
exogen_loc <- exogen[[it]]
} else {
exogen_loc <- exogen
}
if (is.data.frame(previous)) {
previous_loc <- previous[,it]
} else {
previous_loc <- previous[[it]]
}
###
###function(x,newdata=NULL,previous=NULL,n=30,random=runif(n,min=0,max=1),exogen=NULL,monthly.factor=NULL,...) {
message(paste("Processing",it))
##EC 20230123 print(exogen_loc)
##EC 20230123print(n)
##EC 20230123exogen_loc00 <<- exogen_loc
##EC 20230123n00 <<- n
##EC 20230123ff00 <<- factor(months)
##EC 20230123xx00 <<- x[[it]]
##EC 20230123it00 <<- it
##EC 20230123random00 <<- gen_wilks[,it]
out[,it] <- generate(x[[it]],previous=previous_loc,exogen=exogen_loc,monthly.factor=factor(months),random=gen_wilks[,it],n=n)
###
}
} else if (x$type=="logit") {
if (is.null(exogen)) {
exogen <- as.data.frame(array(NA,c(n,0)))
}
if (is.null(previous)) {
previous <- as.data.frame(array(rnorm(x$p*x$K)>=0,c(x$p,x$K)))
names(previous) <- x$station
} else {
previous <- previous[,x$station] ## ec 20141204
}
out <- as.data.frame(array(NA,c(n,length(x$station))))
names(out) <- x$station
percs <- seq(from=0,to=100,by=5)
npercs <- trunc(percs/100*n)
for (ncnt in 1:n) {
if (ncnt %in% npercs) {
valprec <- percs[npercs==ncnt]
message <- paste(sprintf("Processing: %0.2f",valprec),"%",sep="")
message(message)
}
out[ncnt,] <- unlist(lapply(X=x[x$station],FUN=generate,previous=previous,endogenous=x$station,exogen=exogen[ncnt,],monthly.factor=factor(months)[ncnt],n=1,...))
previous[-1,] <- previous[-x$p,]
previous[1,] <- out[ncnt,]
}
#### out[,it] <- generate(x[[it]],previous=previous_loc,exogen=exogen,monthly.factor=factor(months),random=gen_wilks[,it],n=n)
}
### out <- NULL
## TO DO
## TO GO ON ....
return(out)
}
ecor/RGENERATEPREC documentation built on Feb. 3, 2023, 10:38 a.m.
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Defines functions generate.PrecipitationOccurrenceMultiSiteModel generate.CCGammaObjectListPerEachMonth generate.PrecipitationOccurrenceModel
Documented in generate.CCGammaObjectListPerEachMonth generate.PrecipitationOccurrenceModel generate.PrecipitationOccurrenceMultiSiteModel
NULL
#' Stochastic Generation of a \code{PrecipitationOccurrenceModel} or \code{PrecipitationOccurrenceMultiSiteModel} model object
#'
#' It is an implentation of \code{\link{generate}} method
#'
#' @param x model returned by \code{\link{PrecipitationOccurrenceModel}} or \code{\link{PrecipitationOccurrenceMultiSiteModel}}
#' @param newdata predictor or exogenous variables. See \code{\link{predict.PrecipitationOccurrenceModel}}
#' @param exogen predictor or exogenous variables
#' @param monthly.factor vector of factors indicating the month of the days
#' @param random vector of random or calculated numbers ranging between 0 and 1
#' @param origin,end character strings (yyyy-dd-mm) indicating the start and/or end date of the daily weather generation.
#' @param n number of generations. See \code{\link{generate}}. Here it is ignored and the number of generations is given by \code{origin},\code{end} or \code{monthly.factor}.
#' @param previous logical vector containing previously occurred states
#' @param ... further arguments
#'
#' @seealso \code{\link{generate}},\code{\link{predict.glm}},\code{\link{PrecipitationOccurrenceModel}},\code{\link{PrecipitationOccurrenceMultiSiteModel}}
#' @export
#' @method generate PrecipitationOccurrenceModel
#### @S3method generate PrecipitationOccurrenceModel
#' @aliases generate generate.PrecipitationOccurrenceModel
#' @rdname generate
#' @importFrom RGENERATE generate
#' @return A vector or a data frame reporting generated time series for each station.
#' @references
#' D.S. Wilks (1998), Multisite Generalization of a Daily Stochastic Precipitation Generation Model, Journal of Hydrology, Volume 210, Issues 1-4, September 1998, Pages 178-191,
#' \url{https://www.sciencedirect.com/science/article/pii/S0022169498001863}
#'
#' Muamaraldin Mhanna and Willy Bauwens (2011) A Stochastic Space-Time Model for the Generation of Daily Rainfall in the Gaza Strip, International Journal of Climatology, Volume 32, Issue 7, pages 1098-1112,
#' \doi{10.1002/joc.2305}, \url{https://rmets.onlinelibrary.wiley.com/doi/abs/10.1002/joc.2305}
#'
#'
#'
#'
#' @examples
#'
#' library(RGENERATEPREC)
#'
#'
#' ## A function example can be found in the following script file:
#' scriptfile <- system.file("example.generate.R",package="RGENERATEPREC")
#' ## The corrent file path is given by 'scriptfile' variable:
#' print(scriptfile)
#' ## To run the example file, launch the file with 'source' command (uncomment the following line)
#' #source(scriptfile)
#'
#' ## ALTERNATIVELY you can run the following lines:
#'
#'
#'
#' data(trentino)
#'
#' year_min <- 1961
#' year_max <- 1990
#'
#' origin <- paste(year_min,1,1,sep="-")
#' end <- paste(year_max,12,31,sep="-")
#'
#' period <- PRECIPITATION$year>=year_min & PRECIPITATION$year<=year_max
#' period_temp <- TEMPERATURE_MAX$year>=year_min & TEMPERATURE_MAX$year<=year_max
#'
#' prec_mes <- PRECIPITATION[period,]
#' Tx_mes <- TEMPERATURE_MAX[period_temp,]
#' Tn_mes <- TEMPERATURE_MIN[period_temp,]
## removing nonworking stations (e.g. time series with NA)
#' accepted <- array(TRUE,length(names(prec_mes)))
#' names(accepted) <- names(prec_mes)
#' for (it in names(prec_mes)) {
#' acc <- TRUE
#' acc <- (length(which(!is.na(Tx_mes[,it])))==length(Tx_mes[,it]))
#' acc <- (length(which(!is.na(Tn_mes[,it])))==length(Tn_mes[,it])) & acc
#' accepted[it] <- (length(which(!is.na(prec_mes[,it])))==length(prec_mes[,it])) & acc
#'
#' }
#'
#' valmin <- 1.0
###station <- names(PRECIPITATION)[!(names(PRECIPITATION) %in% c("day","month","year"))]
#' prec_mes <- prec_mes[,accepted]
#'
#'
#'
#' Tx_mes <- Tx_mes[,accepted]
#' Tn_mes <- Tn_mes[,accepted]
#' prec_occurrence_mes <- prec_mes>=valmin
#'
#' station <- names(prec_mes)[!(names(prec_mes) %in% c("day","month","year"))]
#' it <- station[2]
#' vect <- Tx_mes[,it]-Tn_mes[,it]
#' months <- factor(prec_mes$month)
#'
#'
#' \donttest{
#' model <-
#' PrecipitationOccurrenceModel(x=prec_mes[,it],exogen=vect,
#' monthly.factor=months,valmin=valmin)
#'
#' obs <- prec_mes[,it]>=valmin
#'
#' gen <- generate(model,exogen=vect,monthly.factor=months,n=length(months))
#' }
#'
#' ## Only 10 generated realizations!!
#' gen10 <- generate(model,exogen=vect,monthly.factor=months,n=10)
#'
#'
#' ### MultiSite Generation
#'
#'
#' station <- station[1:2]
#' exogen <- Tx_mes[,station]-Tn_mes[,station]
#'
#' months <- factor(prec_mes$month)
#'
#'
#' \donttest{
#'
#' model_multisite <-
#' PrecipitationOccurrenceMultiSiteModel(x=prec_mes[,station],
#' exogen=exogen,origin=origin,multisite_type="wilks")
#'
#'
#' ## LOGIT-type Model
#' model_multisite_logit <-
#' PrecipitationOccurrenceMultiSiteModel(x=prec_mes,exogen=exogen,
#' origin=origin,multisite_type="logit",station=station)
#'
#'
#' obs_multisite <- prec_mes[,station]>=valmin
#'
#' gen_multisite <- generate(model_multisite,exogen=exogen,origin=origin,end=end)
#'
#' gen_multisite_logit <- generate(model_multisite_logit,exogen=exogen,origin=origin,end=end)
#' }
generate.PrecipitationOccurrenceModel <- function(x,newdata=NULL,previous=NULL,n=30,random=runif(n,min=0,max=1),exogen=NULL,monthly.factor=NULL,...) {
p <- x$p
if (p<1) previous <- NULL
if (!is.null(exogen)) newdata <- as.data.frame(exogen)
if (is.null(newdata) & is.null(monthly.factor)) {
newdata <- x$predictor
} else if (is.null(newdata)) {
newdata <- as.data.frame(array(NA,c(length(monthly.factor),0)))
}
if (!is.null(monthly.factor)) newdata$month <- factor(monthly.factor)
if (nrow(newdata)<n) {
warning("Warning: n is reduced, insufficient numbers of predictors!")
n <- nrow(newdata)
}
names_n <- names(newdata)
newdata <- as.data.frame(newdata[1:n,])
names(newdata) <- names_n
if (is.null(previous)) {
previous <- rnorm(x$p)>=0
}
out <- array(NA,n)
for (i in 1:n) {
### prob <- 1-predict(x,newdata=newdata[i,],previous=previous,type="response",endogenous=endogenous,...)
##EC 20230123x01 <<- x
##EC 20230123newdata01 <<- newdata[i,]
##EC 20230123previous01 <<- previous
##EC 20230123i01 <<- i
prob <- 1-predict(x,newdata=newdata[i,],previous=previous,type="response",...) ## ec 20141208
out[i] <- random[i]>=prob
previous <- c(out[i],previous[-p])
}
return(out)
}
NULL
#'
#'
#'
#' @export
#' @method generate CCGammaObjectListPerEachMonth
#### @S3method generate CCGammaObjectListPerEachMonth
#' @aliases generate generate.CCGammaObjectListPerEachMonth
#' @rdname generate
#'
generate.CCGammaObjectListPerEachMonth <- function(x,...) {
class(x) <- "list"
out <- generate(x,...)
return(out)
}
NULL
#'
#'
#'
#' @export
#' @method generate PrecipitationOccurrenceMultiSiteModel
#### @S3method generate PrecipitationOccurrenceMultiSiteModel
#' @aliases generate generate.PrecipitationOccurrenceMultiSiteModel
#' @rdname generate
#'
generate.PrecipitationOccurrenceMultiSiteModel <- function(x,exogen,n=NA,origin="1961-1-1",end="1990-1-1",previous=NULL,monthly.factor=NULL,...) {
out <- NULL
## EC 20230123
if (is.null(origin)) origin <- NA
if (is.null(end)) end <- NA
if (!is.na(n) & n>0) {
if (!is.na(origin)) {
end <- as.Date(origin)+lubridate::days(n-1)
} else if (!is.na(end)) {
origin <- as.Date(end)-lubridate::days(n-1)
}
}
if (is.null(monthly.factor)) {
dates <- as.Date(origin):as.Date(end)
months <- adddate(as.data.frame(dates),origin=origin)$month
n <- length(months)
} else {
months <- monthly.factor
n <- length(months)
}
if (x$type=="wilks") {
monthsf <- sprintf("month%02d",months)
gen_wilks <- generate(x$ccgamma,FUN=rnorm,type="covariance",names=x$station,factor.series=monthsf)
for (c in 1:ncol(gen_wilks)) {
gen_wilks[,c] <- pnorm(gen_wilks[,c])
}
if (is.null(exogen)) {
exogen <- lapply(X=x$station,FUN=function(x){ NULL })
names(exogen) <- x$station
}
if (is.null(previous)) {
previous <- lapply(X=x$station,FUN=function(x){ NULL })
names(previous) <- x$station
}
out <- as.data.frame(array(NA,dim(gen_wilks)))
names(out) <- names(gen_wilks)
for (it in x$station) {
# if (is.data.frame(exogen)) {
#
# exogen_loc <- exogen[,it]
#
# } else {
#
# exogen_loc <- exogen[[it]]
# }
if (is.data.frame(exogen)) {
cols <- str_detect(names(exogen),it)
exogen_loc <- exogen[,cols]
} else if (is.list(exogen)) {
exogen_loc <- exogen[[it]]
} else {
exogen_loc <- exogen
}
if (is.data.frame(previous)) {
previous_loc <- previous[,it]
} else {
previous_loc <- previous[[it]]
}
###
###function(x,newdata=NULL,previous=NULL,n=30,random=runif(n,min=0,max=1),exogen=NULL,monthly.factor=NULL,...) {
message(paste("Processing",it))
##EC 20230123 print(exogen_loc)
##EC 20230123print(n)
##EC 20230123exogen_loc00 <<- exogen_loc
##EC 20230123n00 <<- n
##EC 20230123ff00 <<- factor(months)
##EC 20230123xx00 <<- x[[it]]
##EC 20230123it00 <<- it
##EC 20230123random00 <<- gen_wilks[,it]
out[,it] <- generate(x[[it]],previous=previous_loc,exogen=exogen_loc,monthly.factor=factor(months),random=gen_wilks[,it],n=n)
###
}
} else if (x$type=="logit") {
if (is.null(exogen)) {
exogen <- as.data.frame(array(NA,c(n,0)))
}
if (is.null(previous)) {
previous <- as.data.frame(array(rnorm(x$p*x$K)>=0,c(x$p,x$K)))
names(previous) <- x$station
} else {
previous <- previous[,x$station] ## ec 20141204
}
out <- as.data.frame(array(NA,c(n,length(x$station))))
names(out) <- x$station
percs <- seq(from=0,to=100,by=5)
npercs <- trunc(percs/100*n)
for (ncnt in 1:n) {
if (ncnt %in% npercs) {
valprec <- percs[npercs==ncnt]
message <- paste(sprintf("Processing: %0.2f",valprec),"%",sep="")
message(message)
}
out[ncnt,] <- unlist(lapply(X=x[x$station],FUN=generate,previous=previous,endogenous=x$station,exogen=exogen[ncnt,],monthly.factor=factor(months)[ncnt],n=1,...))
previous[-1,] <- previous[-x$p,]
previous[1,] <- out[ncnt,]
}
#### out[,it] <- generate(x[[it]],previous=previous_loc,exogen=exogen,monthly.factor=factor(months),random=gen_wilks[,it],n=n)
}
### out <- NULL
## TO DO
## TO GO ON ....
return(out)
}
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