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#' @title Model dose rate evolution in carbonate-rich samples
#'
#' @description This function models the dose rate evolution in carbonate enrich environments. For the
#' calculation internal functions are called.
#'
#' @details This function is the starting point for the dose rate modelling for carbonat enrich
#' environments. It provides basically the same functionality as the original version of 'Carb', i.e.
#' you should be also aware of the limitations of this modelling approach. In particular: The model
#' assumes a linear carbonate mass increase due to post-depositional processes. Please read the
#' references cited blow.\cr
#'
#' **Uncertainty estimation**
#'
#' For estimating the uncertainties, Monte-Carloe (MC) simulation runs are used. For very
#' small values (close to 0) this can, however, lead to edge effects (similar in 'Carb') since
#' values below 0 are set to 0.
#'
#' @param data [data.frame] (**required**): input data following the structure given
#' in the example data set `data(Example_Data)`. The input [data.frame] should have at least
#' one row (i.e. values for one sample). For multiple rows the function is automatically re-called.
#'
#' @param length_step [numeric] (with default): step length used for the calculation
#'
#' @param max_time [numeric] (with default): maximum temporal search range
#'
#' @param n.MC [numeric] (with default): number of Monte Carlo runs used for the error calculation
#'
#' @param method_control (*optional*): additional arguments that can be provided to the control the
#' the modelling. See details for further information.
#'
#' @param txtProgressBar [logical] (with default): enables/disables the `txtProgressBar` for the MC runs
#'
#' @param verbose [logical] (with default): enables/disables verbose mode
#'
#' @param plot [logical] (with default): enables/disables plot output
#'
#' @param ... further arguments passed to the underyling plot functions, see also details for further information. Supported standard arguments are `mfrow`, `xlim`, `xlab`.
#'
#' @return The function returns numerical and graphical output
#'
#' -----------------------------------\cr
#' `[ NUMERICAL OUTPUT ]`\cr
#' -----------------------------------\cr
#' * A [data.frame] which is the combination of the input and values calculated by this function.
#'
#' -----------------------------------\cr
#' `[ GRAPHICAL OUTPUT ]`\cr
#' -----------------------------------\cr
#'
#' **Upper plot:** Dose rate evolution over time backwards. The solid black line is the calculation
#' output, the grey shaded area indicates the 2-sigma error margins. The dashed blue line is an indicator
#' of the quality of the error estimations based on Monte Carlo (MC) runs.The closer it follows the
#' black line, the more reliable are the given error margins. \cr
#'
#' **Lower plot:** Totally absorbed dose over time. The plot is an representation of the 'new'
#' age based on the carbonat modelling.
#'
#'
#' @examples
#' ##load example data
#' data("Example_Data", envir = environment())
#'
#' ##run the function for one sample from
#' ##the dataset
#' model_DoseRate(
#' data = Example_Data[14,],
#' n.MC = 2,
#' txtProgressBar = FALSE
#' )
#'
#'
#' @author Sebastian Kreutzer, IRAMAT-CRP2A, UMR 5060, Université Bordeaux Montagine (France); based
#' on 'MATLAB' code given in file Carb_2007a.m of *Carb*
#'
#' @section Function version: 0.1.0
#'
#' @references
#' Mauz, B., Hoffmann, D., 2014. What to do when carbonate replaced water: Carb, the model for estimating the
#' dose rate of carbonate-rich samples. Ancient TL 32, 24–32. \url{http://ancienttl.org/ATL_32-2_2014/ATL_32-2_Mauz_p24-32.pdf}
#'
#' Nathan, R.P., Mauz, B., 2008. On the dose-rate estimate of carbonate-rich sediments for trapped charge dating.
#' Radiation Measurements 43, 14–25. \doi{10.1016/j.radmeas.2007.12.012} \cr
#'
#' **Further reading**
#'
#' Nathan, R.P., 2010. Numerical modelling of environmental dose rate and its application to trapped-charge dating.
#' DPhil thesis, St Hugh’s College, Oxford. \url{https://ora.ox.ac.uk/objects/ora:6421}
#'
#' @keywords dplot manip
#' @md
#' @export
model_DoseRate <- function(
data,
length_step = 1L,
max_time = 500L,
n.MC = 100,
method_control = list(),
txtProgressBar = TRUE,
verbose = TRUE,
plot = TRUE,
...
){
# Self-call -----------------------------------------------------------------------------------
##we keep it as simple as possible, only a data.frame is allowed, all subsequent tests
##are handed over to the code below
if(class(data) == "data.frame" &&
nrow(data) > 1) {
##split input in a list
data_list <- split(data, f = 1:nrow(data))
##get provided arguments
##by using this option we do not have to double check in future whether we missed arguments
args <- as.list(match.call())
##remove first (the function name) and 'data'
args[[1]] <- NULL
args$data <- NULL
##run function
results_list <- lapply(data_list, function(x){
temp <- try(do.call(model_DoseRate, c(list(data = x),args)))
if(class(temp) == "try-error"){
try(stop(paste0("[model_DoseRate()] Calculation for sample ", x[[1]], " failed. NULL returned!"),
call. = FALSE))
return(NULL)
}else{
return(temp)
}
})
##remove NULL elements from failed attempts
results_list <- results_list[!sapply(results_list, is.null)]
##combine into one single data.frame
results <- do.call(rbind, results_list)
##return
return(results)
}
# Integrity tests -----------------------------------------------------------------------------
##NOTE: The integrity tests are done mainly here and not in the function '.calc_DoseRate' to
##avoid additional overhead
##checks for data
if (class(data) != "data.frame")
stop("[model_DoseRate()] 'data' is not a 'data.frame'", call. = FALSE)
if (nrow(data) == 0)
stop("[model_DoseRate()] 'data' is empty!", call. = FALSE)
##remove NA values
if (any(is.na(data))) {
data <- na.exclude(data)
warning("[model_DoseRate()] 'data' contained NA values; removed.",
call. = FALSE)
##re-check; maybe it is empty
if (nrow(data) == 0)
stop("[model_DoseRate()] 'data' is empty!", call. = FALSE)
}
##Now check against the example data
Example_Data <- NULL
data("Example_Data", envir = environment())
##check columns
if (ncol(Example_Data) != ncol(data) &&
!all(colnames(Example_Data) == colnames(data))) {
stop(
"[model_DoseRate()] The column names of your input data.frame do not match the requirements.
Please check the example dataset via 'data(head(Example_Data))' to see how it should look like!",
call. = FALSE
)
}
##remove example data
rm(Example_Data)
##check n.MC
if(is.null(n.MC) || n.MC[1] <= 1){
n.MC <- 1
txtProgressBar <- FALSE
}
# Rewrite variables names to match the MATLAB code --------------------------------------------
ERROR <- n.MC[1]
STEP1 <- length_step[1]
# Prepare data --------------------------------------------------------------------------------
##load reference data here; we do not provide the option to the user to add it here
Reference_Data <- NULL
data("Reference_Data", envir = environment())
ref <- Reference_Data
rm(Reference_Data)
##minimise potential user problems
max_time <- max_time[1]
##method control
method_control_default <- list(
trace = FALSE,
lower = 0,
upper = max_time
)
method_control <- modifyList(x = method_control_default, val = method_control)
# Run optimisation ----------------------------------------------------------------------------
##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++
##AGE
##find minimum
DATE <- nlminb(
start = STEP1,
objective = .calc_DoseRate,
control = list(
trace = method_control$trace),
lower = method_control$lower,
upper = method_control$upper,
data = data,
ref = ref,
length_step = STEP1,
mode_optim = TRUE
)
##calculate values with minimum value
DATE <- .calc_DoseRate(
x = DATE$par,
data = data,
ref = ref,
length_step = STEP1,
max_time = max_time
)
##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++
##UNCERTAINTIES
##ceate needed objects according to MATLAB code
DE_ <- numeric(ERROR)
DR_ <- matrix(0, nrow = DATE[["LEN"]], ncol = ERROR)
DRA_ <- matrix(0, nrow = DATE[["LEN"]], ncol = ERROR)
CUMDR_ <- matrix(0, nrow = DATE[["LEN"]], ncol = ERROR)
AGE_ <- numeric(ERROR)
AGEA_ <- numeric(ERROR)
##create variables we want to use (we do not do this in the loop as in MATLAB)
##TODO: We should evtl. set all values below 0 as NA and remove such lines; this might
##be better than setting it to 0. However, for the moment this is precisely what Carb did before
DE <- data[["DE"]] + rnorm(n.MC) * data[["DE_X"]]
DE[DE < 0] <- 0
COSMIC <- data[["COSMIC"]] + rnorm(n.MC) * data[["COSMIC_X"]]
COSMIC[COSMIC < 0] <- 0
INTERNAL <- data[["INTERNAL"]] + rnorm(n.MC) * data[["INTERNAL_X"]]
INTERNAL[INTERNAL < 0] <- 0
ONSET <- round(data[["ONSET"]] + rnorm(n.MC) * data[["ONSET_X"]],0)
ONSET[ONSET < 0] <- 0
ONSET[ONSET > max_time] <- max_time
FINISH <- round(data[["FINISH"]] + rnorm(n.MC) * data[["FINISH_X"]],0)
FINISH[FINISH < 0] <- 0
FINISH[FINISH > ONSET] <- ONSET[FINISH > ONSET]
DIAM <- data[["DIAM"]] + rnorm(n.MC) * data[["DIAM_X"]]
DIAM[DIAM < 0] <- 0
CC <- data[["CC"]] + rnorm(n.MC) * data[["CC_X"]]
CC[CC < 1e-03] <- 1e-03
WCF <- data[["WCF"]] + rnorm(n.MC) * data[["WCF_X"]]
WCF[WCF < 1e-03] <- 1e-03
WCI <- data[["WCI"]] + rnorm(n.MC) * data[["WCI_X"]]
WCI[WCI < 1e-03] <- 1e-03
K <- data[["K"]] + rnorm(n.MC) * data[["K_X"]]
K[K < 0] <- 0
U <- data[["U"]] + rnorm(n.MC) * data[["U_X"]]
U[U < 0] <- 0
T <- data[["T"]] + rnorm(n.MC) * data[["T_X"]]
T[T < 0] <- 0
# K <- KA * (1 + CC / 100)
# U <- UA * (1 + CC / 100)
# T <- TA * (1 + CC / 100)
##now combine everything in a data.frame, not efficient but we want to stick as close
##as possible with the MATLAB code (the order does not matter)
data_MC <- cbind(K, T, U,
U238 = rep(data[["U238"]],n.MC),
U234_U238 = rep(data[["U234_U238"]],n.MC),
WCI, WCF, CC, DIAM, COSMIC, INTERNAL, ONSET, FINISH, DE
)
rm(K,T,U,WCI,WCF, CC, DIAM, COSMIC, INTERNAL, ONSET, FINISH, DE)
##set txtprogressbar
if(verbose && txtProgressBar)
pb <- txtProgressBar(min = 1, max = n.MC, style = 3)
##start loop
for(i in 1:n.MC){
DATE_MC <- suppressWarnings(nlminb(
start = STEP1,
objective = .calc_DoseRate,
control = list(
trace = FALSE),
lower = method_control$lower,
upper = method_control$upper,
data = data_MC[i,],
ref = ref,
length_step = STEP1,
mode_optim = TRUE
))
##calculate values with minium value
DATE_MC <-
.calc_DoseRate(
x = DATE_MC$par,
data = data_MC[i,],
ref = ref,
length_step = STEP1,
max_time = max_time
)
##fill variables
DE_[i] <- data_MC[i,"DE"]
DR_[,i] <- DATE_MC$DR
DRA_[,i] <- DATE_MC$DRA
CUMDR_[,i] <- DATE_MC$CUMDR
AGE_[i] <- DATE_MC$AGE
AGEA_[i] <- DATE_MC$AGEA
##update progressbar
if(verbose && txtProgressBar) setTxtProgressBar(pb,i)
}
##close pb
if(verbose && txtProgressBar) close(pb)
# Extract final values ------------------------------------------------------------------------
##extract all values we want to return in the terimal and in the results data.frame
data_results <- round(data.frame(
AGE_CONV = DATE$AGEA,
AGE_CONV_X = sd(AGEA_),
AGE = DATE$AGE,
AGE_X = sd(AGE_),
DR_CONV = DATE$DRA[1],
DR_CONV_X = sd(DRA_),
DR_ONSET = rowMeans(DR_)[nrow(DR_)],
DR_ONSET_X = sd(DR_[nrow(DR_),1:n.MC]),
DR_FINAL = rowMeans(DR_)[1],
DR_FINAL_X = sd(DR_[1,1:n.MC]),
n.MC = as.integer(n.MC[1])
),3)
# Terminal output -----------------------------------------------------------------------------
if(verbose){
cat("\n[model_DoseRate()]\n\n")
cat(" Sample ID:\t\t", data[["SAMP_NAME"]], "\n")
cat(" Equivalent dose:\t", round(data[["DE"]],2), " \u00b1 ", round(data[["DE_X"]],2), "Gy\n")
cat(" Diameter:\t\t", data[["DIAM"]], "\u00b5m \n")
cat(" MC runs error estim.:\t", n.MC," \n")
cat(" ------------------------------------------------ \n")
cat(" Age (conv.):\t\t",data_results[["AGE_CONV"]], " \u00b1 ",
data_results[["AGE_CONV_X"]], " ka\n")
cat(" Age (new):\t\t", data_results[["AGE"]],
" \u00b1 ", data_results[["AGE_X"]], " ka\n\n")
cat(" Dose rate (conv.):\t",data_results[["DR_CONV"]], " \u00b1 ",
data_results[["DR_CONV_X"]], " Gy/ka\n")
cat(" Dose rate (onset):\t",data_results[["DR_ONSET"]], " \u00b1 ",
data_results[["DR_ONSET_X"]], " Gy/ka\n")
cat(" Dose rate (final):\t", data_results[["DR_FINAL"]], " \u00b1 ",
data_results[["DR_FINAL_X"]], " Gy/ka\n")
cat(" ------------------------------------------------ \n")
}
# Plotting ------------------------------------------------------------------------------------
if(plot){
##set plot settings
plot_settings <- modifyList(x = list(
mfrow = c(2,1),
xlim = c(0, max(c(DATE[["AGE"]], DATE[["AGEA"]])) * 1.1),
xlab = "Time [ka]"
),
val = list(...))
##par settings; including restoring them
par.default <- list(mfrow = par()$mfrow)
on.exit(do.call(par, args = par.default))
par(mfrow = plot_settings$mfrow)
##calculate some variables needed later
DR_rowMeans <- rowMeans(DR_)
DR_rowSds <- matrixStats::rowSds(DR_)
CUMDR_rowMeans <- rowMeans(CUMDR_)
CUMDR_rowSds <- matrixStats::rowSds(CUMDR_)
## =============================================================================================
##(A) dose rate plot
plot(
NA,
NA,
xlim = plot_settings$xlim,
ylim = if(n.MC > 2){
range(c(DR_rowMeans - DR_rowSds, DR_rowMeans + DR_rowSds))
}else{
range(DR_rowMeans)
},
xlab = plot_settings$xlab,
ylab = "Dose rate [Gy/ka]",
main = data[["SAMP_NAME"]]
)
##error polygon
polygon(
x = c(0:max_time, max_time:0),
y = c(
DR_rowMeans + DR_rowSds,
rev(DR_rowMeans - DR_rowSds)),
col = rgb(0, 0, 0, .1),
border = NA
)
##add center line
lines(x = 0:max_time, y = DATE[["DR"]], lwd = 1)
##set mean line (give a good indication whether the n.MC runs had been enough)
lines(x = 0:max_time, y = rowMeans(DR_), lwd = 1, lty = 2, col = "blue")
## =============================================================================================
##(B) accummulated dose and age
plot(
NA,
NA,
xlim = plot_settings$xlim,
ylim = c(0, data[["DE"]] * 1.2),
xlab = plot_settings$xlab,
ylab = "Absorbed dose [Gy]",
main = data[["SAMP_NAME"]],
sub = paste0("(n.MC = ",n.MC,")")
)
##add error polygon
polygon(
x = c(0:max_time, max_time:0),
y = c(
CUMDR_rowMeans + CUMDR_rowSds,
rev(CUMDR_rowMeans - CUMDR_rowSds)),
col = rgb(0, 0, 0, .1),
border = NA
)
##lines showing the De distribution used for MC runs
density_De_y <- seq(0, data[["DE"]] * 1.2, length.out = 100)
density_De_x <- (1 / sqrt(2 * pi * data[["DE_X"]]^2)) *
exp(-(density_De_y - data[["DE"]])^2 / 2 * data[["DE_X"]]^2)
##this looks weird, otherwise the plot is not really right and we have overplotting
##issues
density_De_x <- (density_De_x * -par()$usr[1])/ max(density_De_x) + par()$usr[1]
density_De_x[which.min(density_De_x)] <- min(density_De_x)
density_De_x[density_De_x <= par()$usr[1]] <- par()$usr[1] - 0.2
lines(x = density_De_x, density_De_y, col = "red")
##centre lines horizontal (De)
lines(
x = c(0, DATE[["AGE"]]),
y = rep(data[["DE"]], 2),
col = "red",
lty = 2
)
##center lines vertical (age)
lines(x = rep(DATE[["AGE"]], 2),
y = c(0, data[["DE"]]),
col = "red",
lty = 2)
##add density (two times, 1st density lines, then colour)
if(n.MC > 1){
temp_density <- density(AGE_)
polygon(
x = c(temp_density$x, rev(temp_density$x)),
y = c((temp_density$y * data[["DE"]]) / max(temp_density$y), rep(0,length(temp_density$x))),
lty = 1,
density = 10,
col = "grey"
)
polygon(
x = c(temp_density$x, rev(temp_density$x)),
y = c((temp_density$y * data[["DE"]]) / max(temp_density$y), rep(0,length(temp_density$x))),
lty = 0,
col = rgb(1,0,0,.2)
)
}
##add lines of absorbed dose
lines(x = 0:max_time, y = DATE[["CUMDR"]])
##add central point
points(x = DATE[["AGE"]], y = data[["DE"]], cex = 1.4, pch = 21, col = "red", bg = "grey")
##add mtext
mtext(side = 3, text = paste0("Age: ", round(DATE$AGE,2), " \u00b1 ", round(sd(AGE_),2), " ka"))
}#end plot
# Return value --------------------------------------------------------------------------------
##the return value is the input data.frame + added lines
results <- cbind(
data,
data_results,
stringsAsFactors = FALSE
)
##add attributes to data.frame
attr(results, which = "package") <- "RCarb"
##return
return(results)
}
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