#' @title Analyse fading measurements and returns the fading rate per decade (g-value)
#'
#' @description
#' The function analyses fading measurements and returns a fading rate
#' including an error estimation. The function is not limited to standard
#' fading measurements, as can be seen, e.g., Huntley and Lamothe (2001).
#' Additionally, the density of recombination centres (rho') is estimated after
#' Kars et al. (2008).
#'
#' @details
#' All provided output corresponds to the \eqn{tc} value obtained by this
#' analysis. Additionally, the g-value normalised to 2-days is provided in the
#' output object. The output of this function can be passed to the function
#' [Luminescence::calc_FadingCorr].
#'
#' **Fitting and error estimation**
#'
#' For the fitting the function [stats::lm] is used without applying weights. For the
#' error estimation all input values, except `tc`, as the precision can be considered as sufficiently
#' high enough with regard to the underlying problem, are sampled assuming a normal distribution
#' for each value with the value as the mean and the provided uncertainty as standard deviation.
#'
#' **The options for `t_star`**
#'
#' \itemize{
#'  \item `t_star = "half"` (the default) The calculation follows the simplified
#'  version in Auclair et al. (2003), which reads
#'  \deqn{t_{star} := t_1 + (t_2 - t_1)/2}
#'  \item `t_star = "half_complex"` This option applies the complex function shown in Auclair et al. (2003),
#'  which is derived from Aitken (1985) appendix F, equations 9 and 11.
#'  It reads \deqn{t_{star} = t0 * 10^[(t_2 \log(t_2/t_0) - t_1 \log(t_1/t_0) - 0.43(t_2 - t_1))/(t_2 - t_1)]}
#'  where 0.43 = \eqn{1/\ln(10)}. t0, which is an arbitrary constant, is set to 1.
#'  Please note that the equation in Auclair et al. (2003) is incorrect
#'  insofar that it reads \eqn{10\exp(...)}, where the base should be 10 and not the Euler's number.
#'  Here we use the correct version (base 10).
#'  \item `t_star = "end"` This option uses the simplest possible form for `t_star` which is the time since
#'  irradiation without taking into account any addition parameter and it equals t1 in Auclair et al. (2003)
#'  \item `t_star = <function>` This last option allows you to provide an R function object that works on t1 and
#'  gives you all possible freedom. For instance, you may want to define the following
#'  function `fun <- function(x) {x^2}`, this would square all values of t1, because internally
#'  it calls `fun(t1)`. The name of the function does not matter.
#' }
#'
#' **Density of recombination centres**
#'
#' The density of recombination centres, expressed by the dimensionless variable rho', is estimated
#' by fitting equation 5 in Kars et al. (2008) to the data. For the fitting the function
#' [stats::nls] is used without applying weights. For the error estimation the same
#' procedure as for the g-value is applied (see above).
#'
#' **Multiple aliquots & Lx/Tx normalisation**
#'
#' Be aware that this function will always normalise all \eqn{\frac{L_x}{T_x}}
#' values by the \eqn{\frac{L_x}{T_x}} value of the prompt measurement of the
#' first aliquot. This implicitly assumes that there are no systematic
#' inter-aliquot variations in the \eqn{\frac{L_x}{T_x}} values.
#' If deemed necessary to normalise the \eqn{\frac{L_x}{T_x}} values  of each
#' aliquot by its individual prompt measurement please do so **before** running
#' [Luminescence::analyse_FadingMeasurement] and provide the already normalised values for
#' `object` instead.
#'
#' **Shine-down curve plots**
#' Please note that the shine-down curve plots are for information only. As such
#' a maximum of five pause steps are plotted to avoid graphically overloaded plots.
#' However, *all* pause times are taken into consideration for the analysis.
#'
#' @param object [Luminescence::RLum.Analysis-class], [data.frame] or [list] (**required**):
#' input object with the measurement data. Alternatively, a [list] containing
#' [Luminescence::RLum.Analysis-class] objects or a [data.frame] with three columns
#' (x = LxTx, y = LxTx error, z = time since irradiation) can be provided.
#' Can also be a wide table, i.e. a [data.frame] with a number of columns
#' divisible by 3 and where each triplet has the before mentioned column
#' structure.
#'
#' **Note:** The input object should solely consists of the curve needed
#' for the data analysis, i.e. only IRSL curves representing Lx (and Tx). If
#' the object originated from an XSYG file, also the irradiation steps must
#' be preserved in the input object.
#'
#' If data from multiple aliquots are provided, please see the details below
#' with regard to Lx/Tx normalisation. **Note:** The function assumes that all your
#' measurements are related to one (comparable) sample. If you have to treat
#' independent samples, you have use this function in a loop.
#'
#' @param structure [character] (*with default*):
#' the structure of the measurement data, one of `'Lx'` or `c('Lx','Tx')`.
#'
#' @param signal_integral [vector] (**required**):
#' vector with channels for the signal integral (e.g., `1:10`). It is not
#' required if a `data.frame` with `LxTx` values is provided.
#'
#' @param background_integral [vector] (**required**):
#' vector with channels for the background integral (e.g., `90:100`). It is not
#' required if a `data.frame` with `LxTx` values is provided.
#'
#' @param integral_input [character] (*with default*):
#' input type for `signal_integral`, one of `"channel"` (default) or
#' `"measurement"`. If set to `"measurement"`, the best matching channels
#' corresponding to the given time range (in seconds) are selected.
#'
#' @param t_star [character], [function] (*with default*):
#' method for calculating the time elapsed since irradiation if input is
#' **not** a `data.frame`. Options are: `'half'` (the default), `'half_complex`,
#' which uses the long equation in Auclair et al. 2003, and `'end'`, which
#' takes the time between irradiation and the measurement step.
#' Alternatively, `t_star` can be a function with one parameter which works on `t1`.
#' For more information see details. \cr
#'
#' *`t_star` has no effect if the input is a [data.frame], because this input comes
#' without irradiation times.*
#'
#' @param n.MC [integer] (*with default*):
#' number for Monte Carlo runs for the error estimation.
#'
#' @param verbose [logical] (*with default*):
#' enable/disable output to the terminal.
#'
#' @param plot [logical] (*with default*):
#' enable/disable the plot output.
#'
#' @param plot_singlePanels [logical] or [numeric] (*with default*):
#' enable/disable single plot mode, i.e. one plot window per plot.
#' Alternatively a vector specifying the plot to be drawn, e.g.,
#' `plot_singlePanels = c(3,4)` draws only the last two plots in separate
#' windows.
#'
#' @param ... further arguments that can be passed to internally used functions.
#' Supported arguments: `xlab`, `log`, `mtext`, `plot.trend` (enable/disable
#' trend blue line), and `xlim` for the two first curve plots, and `ylim` for
#' the fading curve plot. For further plot customization please use the
#' numerical output of the functions for own plots.
#'
#' @return
#' An [Luminescence::RLum.Results-class] object is returned:
#'
#' Slot: **@data**
#'
#' \tabular{lll}{
#'  **OBJECT** \tab **TYPE** \tab **COMMENT**\cr
#' `fading_results` \tab `data.frame` \tab results of the fading measurement in a table \cr
#' `fit` \tab `lm` \tab object returned by the used linear fitting function [stats::lm]\cr
#' `rho_prime` \tab `data.frame` \tab results of rho' estimation after Kars et al. (2008) \cr
#' `LxTx_table` \tab `data.frame` \tab Lx/Tx table, if curve data had been provided \cr
#' `irr.times` \tab `integer` \tab vector with the irradiation times in seconds \cr
#' }
#'
#' Slot: **@info**
#'
#' \tabular{lll}{
#' **OBJECT** \tab `TYPE` \tab `COMMENT`\cr
#' `call` \tab `call` \tab the original function call\cr
#' }
#'
#' @section Function version: 0.1.27
#'
#' @author Sebastian Kreutzer, F2.1 Geophysical Parametrisation/Regionalisation, LIAG - Institute for Applied Geophysics (Germany) \cr
#' Christoph Burow, University of Cologne (Germany)
#'
#' @keywords datagen
#'
#' @references
#'
#' Aitken, M.J., 1985. Thermoluminescence dating, Studies in archaeological science.
#' Academic Press, London, Orlando.
#'
#' Auclair, M., Lamothe, M., Huot, S., 2003. Measurement of anomalous fading for feldspar IRSL using
#' SAR. Radiation Measurements 37, 487-492. \doi{10.1016/S1350-4487(03)00018-0}
#'
#' Huntley, D.J., Lamothe, M., 2001. Ubiquity of anomalous fading in K-feldspars and the measurement
#' and correction for it in optical dating. Canadian Journal of Earth Sciences 38,
#' 1093-1106. doi: `10.1139/cjes-38-7-1093`
#'
#' Kars, R.H., Wallinga, J., Cohen, K.M., 2008. A new approach towards anomalous
#' fading correction for feldspar  IRSL dating-tests on samples in field saturation.
#' Radiation Measurements 43, 786-790. \doi{10.1016/j.radmeas.2008.01.021}
#'
#' @seealso [Luminescence::calc_OSLLxTxRatio], [Luminescence::read_BIN2R],
#' [Luminescence::read_XSYG2R],
#' [Luminescence::extract_IrradiationTimes], [Luminescence::calc_FadingCorr]
#'
#' @examples
#'
#' ## load example data (sample UNIL/NB123, see ?ExampleData.Fading)
#' data("ExampleData.Fading", envir = environment())
#'
#' ##(1) get fading measurement data (here a three column data.frame)
#' fading_data <- ExampleData.Fading$fading.data$IR50
#'
#' ##(2) run analysis
#' g_value <- analyse_FadingMeasurement(
#' fading_data,
#' plot = TRUE,
#' verbose = TRUE,
#' n.MC = 10)
#'
#' ##(3) this can be further used in the function
#' ## to correct the age according to Huntley & Lamothe, 2001
#' results <- calc_FadingCorr(
#' age.faded = c(100,2),
#' g_value = g_value,
#' n.MC = 10)
#'
#' @export
analyse_FadingMeasurement <- function(
  object,
  structure = c("Lx", "Tx"),
  signal_integral = NULL,
  background_integral = NULL,
  integral_input = c("channel", "measurement"),
  t_star = c("half", "half_complex", "end"),
  n.MC = 100,
  verbose = TRUE,
  plot = TRUE,
  plot_singlePanels = FALSE,
  ...
) {
  .set_function_name("analyse_FadingMeasurement")
  on.exit(.unset_function_name(), add = TRUE)

  integral_input <- .validate_args(integral_input, c("channel", "measurement"))

  ## deprecated arguments
  extraArgs <- list(...)
  if (any(grepl("[signal|background]\\.integral", names(extraArgs)))) {
    .deprecated(old = c("signal.integral", "background.integral"),
                new = c("signal_integral", "background_integral"),
                since = "1.2.0")
    if (integral_input != "channel") {
      .throw_error("'integral_input' is not supported with old argument names")
    }
    signal_integral <- extraArgs$signal.integral
    background_integral <- extraArgs$background.integral
  }

  ## Integrity checks -------------------------------------------------------
  .validate_class(object, c("RLum.Analysis", "data.frame", "list"))
  .validate_class(structure, "character")
  ## signal_integral and background_integral are validated in calc_OSLLxTxRatio()
  .validate_class(plot_singlePanels, c("logical", "integer", "numeric"))
  .validate_positive_scalar(n.MC, int = TRUE)

  if (inherits(object, "list")) {
    wrong.class <- !sapply(object, inherits, "RLum.Analysis")
    if (any(wrong.class)) {
      .throw_warning(sum(wrong.class), " unsupported records removed")

      ## remove unwanted stuff
      object <- object[!wrong.class]
      if (length(object) == 0) {
        .throw_error("No valid records in 'object' left")
      }
    }
  } else if (inherits(object, "RLum.Analysis")) {
    object <- list(object)

  } else if(inherits(object,"data.frame")){
    .validate_not_empty(object)
    if (ncol(object) %% 3 != 0) {
      .throw_error("When 'object' is a data.frame, the number of columns ",
                   "must be a multiple of 3")
    }
    colnames(object) <- NULL
    object <- do.call(rbind,
                      lapply(seq(1, ncol(object), 3), function(col) {
                        object[, col + 0:2]
                      }))
      object <- object[stats::complete.cases(object), ]
      if (nrow(object) == 0)
        .throw_error("After NA removal, nothing is left from the data set")

    ##set table and object
    LxTx_table <- data.frame(LxTx = object[[1]], LxTx.Error = object[[2]])
    irradiation_times <- TIMESINCEIRR <- object[[3]]
    if (any(irradiation_times < 0)) {
      .throw_error("'object' cannot contain negative irradiation times")
    }
    object <- NULL
  }

  if (!inherits(t_star, "function")) {
    t_star <- .validate_args(t_star, c("half", "half_complex", "end"),
                             extra = "a function")
  }

  # Prepare data --------------------------------------------------------------------------------
  if(!is.null(object)){
    if (!(length(structure) == 1 && structure == "Lx" ||
          length(structure) == 2 && all(structure == c("Lx", "Tx")))) {
      .throw_message("'structure' can only be 'Lx' or c('Lx', 'Tx'), ",
                     "NULL returned")
      return(NULL)
    }

    ## support read_XSYG2R()
    originator <- unique(unlist(lapply(object, slot, name = "originator")))
    if (length(originator) != 1 ||
        !originator %in% c("read_XSYG2R", "read_BIN2R",
                           "Risoe.BINfileData2RLum.Analysis"))  {
      .throw_message("Unknown or unsupported originator, NULL returned")
      return(NULL)
    }

    if (originator == "read_XSYG2R") {
      ## extract irradiation times
      irradiation_times <- extract_IrradiationTimes(object)

      ## get TIMESINCEIRR
      TIMESINCEIRR <- unlist(lapply(irradiation_times, function(x) {
        x@data$irr.times[["TIMESINCEIRR"]][!grepl(pattern = "irradiation",
                                             x = x@data$irr.times[["STEP"]],
                                             fixed = TRUE)]
      }))
      if (all(TIMESINCEIRR < 0)) {
        .throw_error("No irradiation times could be retrieved, check that ",
                     "'object' contains irradiation steps")
      }

      ## get irradiation times
      irradiation_times <- unlist(lapply(irradiation_times, function(x) {
          x@data$irr.times[["IRR_TIME"]][!grepl(pattern = "irradiation",
                                           x = x@data$irr.times[["STEP"]],
                                           fixed = TRUE)]
      }))

      ##clean object by removing the irradiation step ... and yes, we drop!
      object_clean <- unlist(get_RLum(object, curveType = "measured"))

      ## if we are left with fewer curves than expected we cannot proceed
      if (length(object_clean) < length(structure)) {
        .throw_message("After irradiation step removal not enough curves ",
                       "are left from the data set, NULL returned")
        return(NULL)
      }

      ##support read_BIN2R()
    } else if (originator %in% c("read_BIN2R", "Risoe.BINfileData2RLum.Analysis")) {

      ##assign object, unlist and drop it
      object_clean <- unlist(get_RLum(object))
      bin.version <- object_clean[[1]]@info$VERSION
      if (as.integer(bin.version) < 5) {
        .throw_error("BIN-file has version ", bin.version,
                     ", but only versions from 05 on are supported")
      }

      ##set TIMESINCEIRR vector
      TIMESINCEIRR <- vapply(object_clean, function(o){
        o@info$TIMESINCEIRR
      }, numeric(1))

      ##check whether we have negative irradiation times, sort out such values
      if(any(TIMESINCEIRR < 0)){
        ##now we have a problem and we first have to make sure that we understand
        ##the data structure and remove also the corresponding values
        if(all(structure == c("Lx", "Tx"))){
          rm_id <- matrix(TIMESINCEIRR, ncol = 2, byrow = TRUE)
          rm_id[apply(rm_id < 0, MARGIN = 1, any),] <- NA
          rm_id <- is.na(as.numeric(t(rm_id)))
        }else{
          rm_id <- TIMESINCEIRR < 0
        }
        object_clean[rm_id] <- NULL
        TIMESINCEIRR <- TIMESINCEIRR[!rm_id]
        rm_records <- sum(rm_id)

        .throw_warning("removed ", rm_records, " records with negative ",
                       "'time since irradiation'")

        ## check if we have removed everything
        if (length(object_clean) == 0) {
          .throw_message("After record removal nothing is left from ",
                         "the data set, NULL returned")
          return(NULL)
        }
      }

      ##set irradiation times
      irradiation_times <- vapply(object_clean, function(o){
        o@info$IRR_TIME
      }, numeric(1))
    }

    ##correct irradiation time for t_star
    ##in accordance with Auclair et al., 2003, p. 488
    ##but here we have no t1 ... this needs to be calculated
    ##set variables
    t1 <- TIMESINCEIRR
    t2 <- TIMESINCEIRR + irradiation_times

    ## set t_star ----
    if (inherits(t_star, "function")) {
      t_star <- t_star(t1)
    } else {
      t_star <- switch(
          t_star,

          ## use the simplified equation in Auclair et al. (2003)
          half = t1 + (t2 - t1) / 2,

          ## use full equation Auclair et al. (2003)
          ## t0 is an arbitrary constant, we are setting that to 1
          half_complex = {
            t0 <- 1
            t_star <- t0 * 10^((t2 * log10(t2/t0) -
                                t1 * log10(t1/t0) -
                                (t2 - t1) * log10(exp(1))) / (t2 - t1))
          },

          ## set t_star to t_1 (so after the end of irradiation)
          end = t1
      )
    }

    ##overwrite TIMESINCEIRR
    TIMESINCEIRR <- pmax(t_star, 1e-6)
    rm(t_star)
    # Calculation ---------------------------------------------------------------------------------
    ##calculate Lx/Tx or ... just Lx, it depends on the pattern ... set IRR_TIME
    if(length(structure) == 2){
      Lx_data <- object_clean[seq(1,length(object_clean), by = 2)]
      Tx_data <- object_clean[seq(2,length(object_clean), by = 2)]

      ## check whether the length of Lx is the length of Tx
      len.Lx <- length(Lx_data)
      len.Tx <- length(Tx_data)
      if (len.Lx != len.Tx) {
        .throw_error("The number of Lx curves (", len.Lx, ") differs from ",
                     "the number of Tx curves (", len.Tx, "), ",
                     "check your data or consider setting `structure = 'Lx'`")
      }

      ##we need only every 2nd irradiation time, the one from the Tx should be the same ... all the time
      TIMESINCEIRR <- TIMESINCEIRR[seq(1,length(TIMESINCEIRR), by = 2)]

      ## check that all Lx/Tx pairs have the same size
      size.mismatch <- vapply(1:len.Lx, function(i) {
        floor(length(Lx_data[[i]])) != floor(length(Tx_data[[i]]))
      }, logical(1))

      ## skip samples with mismatching sizes
      if (any(size.mismatch)) {

        ## terminate if all pairs have mismatching sizes
        if (all(size.mismatch)) {
          .throw_error("No curves left after removing those with different ",
                       "Lx and Tx sizes")
        }

        rm.idx <- which(size.mismatch)
        .throw_warning("Skipped the following samples because Lx and Tx have ",
                       "different sizes: ", .collapse(rm.idx, quote = FALSE))
        Lx_data <- Lx_data[-rm.idx]
        Tx_data <- Tx_data[-rm.idx]
        TIMESINCEIRR <- TIMESINCEIRR[-rm.idx]
      }

    }else if(length(structure) == 1){
      Lx_data <- object_clean
      Tx_data <- NULL
    }

    ##calculate Lx/Tx table
    LxTx_table <- merge_RLum(.warningCatcher(
      calc_OSLLxTxRatio(
        Lx.data = Lx_data,
        Tx.data = Tx_data,
        signal_integral = signal_integral,
        background_integral = background_integral,
        signal_integral_Tx = list(...)$signal_integral_Tx,
        background_integral_Tx = list(...)$background_integral_Tx,
        integral_input = integral_input,
        sigmab = list(...)$sigmab,
        sig0 = list(...)$sig0 %||% formals(calc_OSLLxTxRatio)$sig0,
        background.count.distribution =
          list(...)$background.count.distribution %||%
                   formals(calc_OSLLxTxRatio)$background.count.distribution
      )
    ))$LxTx.table
  }

  ##create unique identifier
  uid <- create_UID()

  ##normalise data to prompt measurement
  tc <- min(TIMESINCEIRR)[1]

  ## remove Inf values in LxTx table
  if(any(is.infinite(LxTx_table[["LxTx"]]))){
    rm_id <- which(is.infinite(LxTx_table[["LxTx"]]))
    LxTx_table <- LxTx_table[-rm_id,]
    TIMESINCEIRR <- TIMESINCEIRR[-rm_id]
    rm(rm_id)
  }

  ##normalise
  idx.tc <- which(TIMESINCEIRR == tc)[1]
  if (length(structure) == 2 || is.null(object)){
    LxTx <- LxTx_table[["LxTx"]]
    if (LxTx[idx.tc] <= 0) {
      .throw_error("Normalisation term is not positive, check your input")
    }
    LxTx_NORM <- LxTx / LxTx[idx.tc]
    LxTx_NORM.ERROR <- LxTx_table[["LxTx.Error"]] / LxTx[idx.tc]
  } else {
    LnLx <- LxTx_table[["Net_LnLx"]]
    LxTx_NORM <- LnLx / LnLx[idx.tc]
    LxTx_NORM.ERROR <- LxTx_table[["Net_LnLx.Error"]] / LnLx[idx.tc]
  }

  ## normalise time since irradiation
  TIMESINCEIRR_NORM <- TIMESINCEIRR/tc

  ##add dose and time since irradiation
  LxTx_table <-
    cbind(
      LxTx_table,
      TIMESINCEIRR = TIMESINCEIRR,
      TIMESINCEIRR_NORM = TIMESINCEIRR_NORM,
      TIMESINCEIRR_NORM.LOG = log10(TIMESINCEIRR_NORM),
      LxTx_NORM = LxTx_NORM,
      LxTx_NORM.ERROR = LxTx_NORM.ERROR,
      UID = uid
    )

  # Fitting -------------------------------------------------------------------------------------
  ## prevent that n.MC can become smaller than 2
  n.MC <- max(n.MC, 2)

  ##we need to fit the data to get the g_value

  ##sample for monte carlo runs
  MC_matrix <- suppressWarnings(cbind(LxTx_table[["TIMESINCEIRR_NORM.LOG"]],
                     matrix(rnorm(
                       n = n.MC * nrow(LxTx_table),
                       mean = LxTx_table[["LxTx_NORM"]],
                       sd = abs(LxTx_table[["LxTx_NORM.ERROR"]])
                     ),
                     ncol = n.MC)))

  ##apply the fit
  fit_matrix <- vapply(X = 1:n.MC, FUN = function(x) {
    ##fit
    fit <- try(stats::lm(y ~ x, data = data.frame(
      x = MC_matrix[,1],
      y = MC_matrix[, x + 1]))$coefficients, silent = TRUE)

    if (inherits(fit, "try-error"))
      return(c(NA_real_, NA_real_))
    return(fit)
  }, FUN.VALUE = numeric(2))

  ##calculate g-values from matrix
  g_value.MC <- -fit_matrix[2, ] * 1 / fit_matrix[1, ] * 100

  ##calculate rho prime (Kars et al. 2008; proposed by Georgina E. King)

  ##s value after Huntley (2006) J. Phys. D.
  Hs <- 3e15

  ##sample for monte carlo runs
  MC_matrix_rhop <-  suppressWarnings(matrix(rnorm(
    n = n.MC * nrow(LxTx_table),
    mean = LxTx_table[["LxTx_NORM"]],
    sd = abs(LxTx_table[["LxTx_NORM.ERROR"]])
  ), ncol = n.MC))

  ## calculate rho prime for all MC samples
  fit_vector_rhop <- suppressWarnings(apply(MC_matrix_rhop, MARGIN = 2, FUN = function(x) {
    tryCatch({
      coef(minpack.lm::nlsLM(x ~ c * exp(-rhop * (log(1.8 * Hs * TIMESINCEIRR))^3),
                             start = list(c = x[1], rhop = 10^-5.5),
                             data = LxTx_table))[["rhop"]]
    },
    error = function(e) {
      return(NA)
    })
  }))

  ## discard all NA values produced in MC runs
  fit_vector_rhop <- fit_vector_rhop[!is.na(fit_vector_rhop)]

  .collect_results <- function(val, vals.MC) {
    data.frame(FIT = val,
               MEAN = mean(vals.MC),
               SD = sd(vals.MC),
               Q_0.025 = quantile(vals.MC, probs = 0.025, na.rm = TRUE),
               Q_0.16  = quantile(vals.MC, probs = 0.16,  na.rm = TRUE),
               Q_0.84  = quantile(vals.MC, probs = 0.84,  na.rm = TRUE),
               Q_0.975 = quantile(vals.MC, probs = 0.975, na.rm = TRUE),
               row.names = NULL)
  }

  ## calculate mean and standard deviation of rho prime (in log10 space)
  rhoPrime <- .collect_results(mean(fit_vector_rhop), fit_vector_rhop)

  ## calc g-value -----
  df <- data.frame(x = LxTx_table[["TIMESINCEIRR_NORM.LOG"]],
                   y = LxTx_table[["LxTx_NORM"]])
  fit <- try(stats::lm(y ~ x, data = df), silent = TRUE)
  fit_power <- try(stats::lm(y ~ I(x^3) + I(x^2) + I(x),
                             data = df), silent = TRUE)

  ##for predicting
  fit_predict <-
    try(stats::lm(y ~ x, data = data.frame(y = LxTx_table[["TIMESINCEIRR_NORM.LOG"]],
                                       x = LxTx_table[["LxTx_NORM"]])), silent = TRUE)

  ##calculate final g_value
  ##the 2nd term corrects for the (potential) offset from one
  g_value_fit <- NA
  if (!inherits(fit, "try-error")) {
    g_value_fit <- -fit$coefficient[2] * 1 / fit$coefficient[1] * 100
  }

  ##construct output data.frame
  g_value <- .collect_results(g_value_fit, g_value.MC)

  ##normalise the g-value to 2-days using the equation provided by Sébastien Huot via e-mail
  ##this means the data is extended
  ## calc g2-value days ----
  k0 <- g_value[,c("FIT", "SD")] / 100 / log(10)
  k1 <- k0 / (1 - k0 * log(172800/tc))
  g_value_2days <-  as.numeric(100 * k1 * log(10))
  names(g_value_2days) <- c("G_VALUE_2DAYS", "G_VALUE_2DAYS.ERROR")

  # Approximation -------------------------------------------------------------------------------
  T_0.5.interpolated <- try(approx(x = LxTx_table[["LxTx_NORM"]],
                               y = LxTx_table[["TIMESINCEIRR_NORM"]],
                               ties = mean,
                               xout = 0.5), silent = TRUE)

  if(inherits(T_0.5.interpolated, 'try-error')){
    T_0.5 <- data.frame(
        T_0.5_INTERPOLATED = NA,
        T_0.5_PREDICTED = NA,
        T_0.5_PREDICTED.LOWER = NA,
        T_0.5_PREDICTED.UPPER = NA
    )
  }else{
    ## if the number of observations is less than 3, the number of residual
    ## degrees of freedom is 0, and we would get this warning when computing
    ## the prediction interval:
    ##   In qt((1 - level)/2, df) : NaNs produced
    ## hence, we suppress the warning (#616)
    T_0.5.predict <- suppressWarnings(
        stats::predict.lm(fit_predict, newdata = data.frame(x = 0.5),
                          interval = "predict"))
    T_0.5 <- data.frame(
        T_0.5_INTERPOLATED = T_0.5.interpolated$y,
        T_0.5_PREDICTED = (10 ^ T_0.5.predict[, 1]) * tc,
        T_0.5_PREDICTED.LOWER = (10 ^ T_0.5.predict[, 2]) * tc,
        T_0.5_PREDICTED.UPPER = (10 ^ T_0.5.predict[, 2]) * tc
    )
  }

  ## Plotting ---------------------------------------------------------------
  if(plot) {
    ## deprecated argument
    if ("plot.single" %in% ...names()) {
      plot_singlePanels <- list(...)$plot.single
      .deprecated("plot.single", "plot_singlePanels", since = "1.0.0")
    }

    ## split the plot area into 4 regions if plot_singlePanels = FALSE (default)
    if (is.logical(plot_singlePanels) && !plot_singlePanels[1]) {
      par.default <- .par_defaults()
      on.exit(par(par.default), add = TRUE)
      par(mfrow = c(2, 2))
    }

    ##get package
    col <- get("col", pos = .LuminescenceEnv)

    ##set some plot settings
    plot_settings <- list(
      xlab = "Stimulation time [s]",
      ylim = NULL,
      xlim = NULL,
      log = "",
      mtext = "",
      plot.trend = TRUE
    )

    ##modify on request
    plot_settings <- modifyList(x = plot_settings, val = list(...))

    ##get unique irradiation times ... for plotting
    irradiation_times.unique <- unique(TIMESINCEIRR)

    ##limit to max 5
    if(length(irradiation_times.unique) >= 5){
      irradiation_times.unique <-
        irradiation_times.unique[seq(1, length(irradiation_times.unique),
                                     length.out = 5)]
    }

    ## convert plot_singlePanels to numeric if it was given as logical: this
    ## helps simplifying the checks below
    if (is.logical(plot_singlePanels))
      plot_singlePanels <- 1:4

    ## compute integration limits for plots
    if (!is.null(object)) {
      if (length(structure) == 2) {
        int.limits.lx <- c(object_clean[[1]][range(signal_integral), 1],
                           object_clean[[1]][range(background_integral), 1])
      } else {
        int.limits.lx <- c(range(signal_integral), range(background_integral)) *
          max(as.matrix(object_clean[[1]][, 1])) /
          nrow(as.matrix(object_clean[[1]]))
      }
      if (is.null(list(...)$signal_integral_Tx)) {
        int.limits.tx <- int.limits.lx
      } else {
        int.limits.tx <- c(range(list(...)$signal_integral_Tx),
                           range(list(...)$background_integral_Tx)) *
          max(as.matrix(object_clean[[1]][, 1])) /
          nrow(as.matrix(object_clean[[1]]))
      }
    }

    ## plot Lx-curves -----
    if (!is.null(object) && 1 %in% plot_singlePanels) {
      records <- object_clean[seq(1, length(object_clean), by = length(structure))]
      plot_RLum(
          set_RLum(class = "RLum.Analysis",
                   records = records),
          combine = length(records) > 1,
          records_max = 10,
          plot_singlePanels = TRUE,
          legend.text = c(paste(round(irradiation_times.unique, 1), "s")),
          xlab = plot_settings$xlab,
          xlim = plot_settings$xlim,
          log = plot_settings$log,
          legend.pos = "outside",
          main = bquote(L[x] ~ "- curve"),
          mtext = plot_settings$mtext
      )
      abline(v = int.limits.lx, lty = 2,
             col = c("green", "green", "red", "red"))
    } else if (1 %in% plot_singlePanels) {
      ## empty Lx plot
      shape::emptyplot()
      text(x = 0.5, y = 0.5,
           labels = expression(paste("No ", L[x], " curves detected")))
    }

    ## plot Tx-curves ----
    if (!is.null(object) && length(structure) == 2 && 2 %in% plot_singlePanels) {
      records <- object_clean[seq(2, length(object_clean), by = 2)]
      plot_RLum(
          set_RLum(class = "RLum.Analysis",
                   records = records),
          combine = length(records) > 1,
          records_max = 10,
          plot_singlePanels = TRUE,
          legend.text = paste(round(irradiation_times.unique, 1), "s"),
          xlab = plot_settings$xlab,
          log = plot_settings$log,
          legend.pos = "outside",
          main = bquote(T[x] ~ "- curve"),
          mtext = plot_settings$mtext
      )
      abline(v = int.limits.tx, lty = 2,
             col = c("green", "green", "red", "red"))
    } else if (2 %in% plot_singlePanels) {
      ## empty Tx plot
      shape::emptyplot()
      text(x = 0.5, y = 0.5,
           labels = expression(paste("No ", T[x], " curves detected")))
    }

    ## plot fading ----
    if (3 %in% plot_singlePanels) {

      if(all(is.na(LxTx_table[["LxTx_NORM"]]))){
        ## FIXME(mcol): this block seems unreachable since 5f63c1f1
        # nocov start
          shape::emptyplot()
          text(x = 0.5, y = 0.5, labels = "All NA values!")
        # nocov end
      }else{
        plot(
          NA,
          NA,
          ylab = "Norm. intensity",
          xaxt = "n",
          xlab = "Time since irradition [s]",
          sub = expression(paste("[", log[10](t / t[c]), "]")),
          ylim = plot_settings$ylim %||% (
            if (max(LxTx_table[["LxTx_NORM"]]) > 1.1) {
              c(0.1, max(LxTx_table[["LxTx_NORM"]]) + max(LxTx_table[["LxTx_NORM.ERROR"]]))
            } else {
              c(0.1, 1.1)
            }
          ),
          xlim = range(LxTx_table[["TIMESINCEIRR_NORM.LOG"]], na.rm = TRUE),
          main = "Signal Fading"
        )

        ##add axis (with an additional formatting to provide a nice log10-axis)
        ##https://stackoverflow.com/questions/6897243/labelling-logarithmic-scale-display-in-r
        x_axis_lab <- seq(0:nchar(floor(max(LxTx_table[["TIMESINCEIRR"]]))))
        x_axis_ticks <- log10((10^x_axis_lab)/tc)

        ## if we have less then two values to show, we fall back to the
        ## old data representation.
        if (length(x_axis_ticks[x_axis_ticks > 0]) > 2) {
          axis(
            side = 1,
            at = x_axis_ticks,
            labels = sapply(x_axis_lab, function(i)
              as.expression(bquote(10 ^ .(i))))
          )
          ##lower axis
          axis(
            side = 1,
            at = x_axis_ticks,
            labels = paste0("[",round(x_axis_ticks,1),"]"),
            cex.axis = 0.7,
            tick = FALSE,
            line = 0.75)

        } else {
          axis(
            side = 1,
            at = axTicks(side = 1),
            labels = suppressWarnings(format((10 ^ (axTicks(side = 1)) * tc),
                                                digits = 1,
                                                decimal.mark = "",
                                                scientific = TRUE)))

          ##lower axis
          axis(
            side = 1,
            at = axTicks(1),
            labels = axTicks(1),
            cex.axis = 0.7,
            tick = FALSE,
            line = 0.75)
        }

        mtext(
          side = 3,
          paste0(
            "g-value: ",
            round(g_value$FIT, digits = 2),
            " \u00b1 ",
            round(g_value$SD, digits = 2),
            " (%/decade) | tc = ",
            format(tc, digits = 4, scientific = TRUE)
          ),
          cex = par()$cex * 0.9
        )

        ##add MC error polygon
        x_range <- range(LxTx_table[["TIMESINCEIRR_NORM.LOG"]], na.rm = TRUE)
          x <- seq(x_range[1], x_range[2], length.out = 50)
          m <- matrixStats::rowRanges(vapply(1:n.MC, function(i){
            fit_matrix[2, i] * x + fit_matrix[1, i]

          }, numeric(length(x))))
          polygon(
            x = c(x, rev(x)),
            y = c(m[, 2], rev(m[, 1])),
            col = rgb(0, 0, 0, 0.2),
            border = NA
          )

        ##add master curve in red
        curve(
          fit$coefficient[2] * x + fit$coefficient[1],
          col = "red",
          add = TRUE,
          lwd = 1.5
        )

        ##add power law curve
        if(plot_settings$plot.trend) {
          curve(
            x ^ 3 * fit_power$coefficient[2] + x ^ 2 * fit_power$coefficient[3] + x
            * fit_power$coefficient[4] + fit_power$coefficient[1],
            add = TRUE,
            col = "blue",
            lty = 2
          )
        }

        ##add points
        points(x = LxTx_table[["TIMESINCEIRR_NORM.LOG"]],
               y = LxTx_table[["LxTx_NORM"]],
               pch = 21,
               bg = "grey")

        ##error bars
        segments(
          x0 = LxTx_table[["TIMESINCEIRR_NORM.LOG"]],
          x1 = LxTx_table[["TIMESINCEIRR_NORM.LOG"]],
          y0 = LxTx_table[["LxTx_NORM"]] + LxTx_table[["LxTx_NORM.ERROR"]],
          y1 = LxTx_table[["LxTx_NORM"]] - LxTx_table[["LxTx_NORM.ERROR"]],
          col = "grey"
        )

        ##add legend
        legend(
          "bottom",
          legend = c("fit", "fit MC", if(plot_settings$plot.trend) "trend" else NULL),
          col = c("red", "grey", if(plot_settings$plot.trend) "blue" else NULL),
          lty = c(1, 1, if(plot_settings$plot.trend) 2 else NULL),
          bty = "n",
          horiz = TRUE
        )
      }#end if a
    }#

    if (4 %in% plot_singlePanels) {

      if(all(is.na(g_value.MC))){
        shape::emptyplot()
        text(x = 0.5, y = 0.5, labels = "All NA values!")

      }else{
        plot(density(g_value.MC),
             main = "Density: g-values (%/decade)")
        graphics::rug(x = g_value.MC)
        abline(v = c(g_value[["Q_0.16"]], g_value[["Q_0.84"]]),
               lty = 2,
               col = "darkgreen")
        abline(v = c(g_value[["Q_0.025"]], g_value[["Q_0.975"]]),
               lty = 2,
               col = "red")
        legend(
          "topleft",
          legend = c("HPD - 68 %", "HPD - 95 %"),
          lty = 2,
          col = c("darkgreen", "red"),
          bty = "n"
        )
      }
    }
  }

  # Terminal ------------------------------------------------------------------------------------
  if (verbose){
    cat("\n[analyse_FadingMeasurement()]\n")
    cat("\n n.MC:\t", n.MC)
    cat("\n tc:\t", format(tc, digits = 4, scientific = TRUE), "s")
    cat("\n---------------------------------------------------")
    cat("\nT_0.5 interpolated:\t", T_0.5$T_0.5_INTERPOLATED)
    cat("\nT_0.5 predicted:\t", format(T_0.5$T_0.5_PREDICTED, digits = 2, scientific = TRUE))
    cat("\ng-value:\t\t", round(g_value$FIT, digits = 2),
        "\u00b1", round(g_value$SD, digits = 2), "(%/decade)")
    cat("\ng-value (norm. 2 days):\t", round(g_value_2days[1], digits = 2),
        "\u00b1", round(g_value_2days[2], digits = 2), "(%/decade)")
    cat("\n---------------------------------------------------")
    cat("\nrho':\t\t\t", format(rhoPrime$MEAN, digits = 3),
        "\u00b1", format(rhoPrime$SD, digits = 3))
    cat("\nlog10(rho'):\t\t", suppressWarnings(round(log10(rhoPrime$MEAN), 2)),
        "\u00b1", round(rhoPrime$SD / (rhoPrime$MEAN * log(10)), 2))
    cat("\n---------------------------------------------------\n")
  }

  # Return --------------------------------------------------------------------------------------

  ##set data.frame
  if(all(is.na(g_value))){
    fading_results <- data.frame(
      FIT = NA,
      MEAN = NA,
      SD = NA,
      Q_0.025 = NA,
      Q_0.16 = NA,
      Q_0.84 = NA,
      Q_0.975 = NA,
      TC = NA,
      G_VALUE_2DAYS = NA,
      G_VALUE_2DAYS.ERROR = NA,
      T_0.5_INTERPOLATED = NA,
      T_0.5_PREDICTED = NA,
      T_0.5_PREDICTED.LOWER = NA,
      T_0.5_PREDICTED.UPPER =  NA,
      UID = uid,
      stringsAsFactors = FALSE
    )
  }else{
    fading_results <- data.frame(
      g_value,
      TC = tc,
      G_VALUE_2DAYS = g_value_2days[1],
      G_VALUE_2DAYS.ERROR = g_value_2days[2],
      T_0.5,
      UID = uid,
      stringsAsFactors = FALSE
    )
  }

  ##return
  set_RLum(
    class = "RLum.Results",
    data = list(
      fading_results = fading_results,
      fit = fit,
      rho_prime = rhoPrime,
      LxTx_table = LxTx_table,
      irr.times = irradiation_times
    ),
    info = list(call = sys.call())
  )
}
