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plot_GrowthCurve.R
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#' @title Fit and plot a dose-response curve for luminescence data (Lx/Tx against dose)
#'
#' @description
#'
#' A dose-response curve is produced for luminescence measurements using a
#' regenerative or additive protocol. The function supports interpolation and
#' extrapolation to calculate the equivalent dose.
#'
#' @details
#'
#' **Fitting methods**
#'
#' For all options (except for the `LIN`, `QDR` and the `EXP OR LIN`),
#' the [minpack.lm::nlsLM] function with the `LM` (Levenberg-Marquardt algorithm)
#' algorithm is used. Note: For historical reasons for the Monte Carlo
#' simulations partly the function [nls] using the `port` algorithm.
#'
#' The solution is found by transforming the function or using [uniroot].
#'
#' `LIN`: fits a linear function to the data using
#' [lm]: \deqn{y = mx + n}
#'
#' `QDR`: fits a linear function to the data using
#' [lm]: \deqn{y = a + bx + cx^2}
#'
#' `EXP`: tries to fit a function of the form
#' \deqn{y = a(1 - exp(-\frac{(x+c)}{b}))}
#' Parameters b and c are approximated by a linear fit using [lm]. Note: b = D0
#'
#' `EXP OR LIN`: works for some cases where an `EXP` fit fails.
#' If the `EXP` fit fails, a `LIN` fit is done instead.
#'
#' `EXP+LIN`: tries to fit an exponential plus linear function of the
#' form:
#' \deqn{y = a(1-exp(-\frac{x+c}{b}) + (gx))}
#' The \eqn{D_e} is calculated by iteration.
#'
#' **Note:** In the context of luminescence dating, this
#' function has no physical meaning. Therefore, no D0 value is returned.
#'
#' `EXP+EXP`: tries to fit a double exponential function of the form
#' \deqn{y = (a_1 (1-exp(-\frac{x}{b_1}))) + (a_2 (1 - exp(-\frac{x}{b_2})))}
#' This fitting procedure is not robust against wrong start parameters and
#' should be further improved.
#'
#' `GOK`: tries to fit the general-order kinetics function after
#' Guralnik et al. (2015) of the form of
#'
#' \deqn{y = a (d - (1 + (\frac{1}{b}) x c)^{(-1/c)})}
#'
#' where **c > 0** is a kinetic order modifier
#' (not to be confused with **c** in `EXP` or `EXP+LIN`!).
#'
#' `LambertW`: tries to fit a dose-response curve based on the Lambert W function
#' according to Pagonis et al. (2020). The function has the form
#'
#' \deqn{y ~ (1 + (W((R - 1) * exp(R - 1 - ((x + D_{int}) / D_{c}))) / (1 - R))) * N}
#'
#' with \eqn{W} the Lambert W function, calculated using the package [lamW::lambertW0],
#' \eqn{R} the dimensionless retrapping ratio, \eqn{N} the total concentration
#' of trappings states in cm^-3 and \eqn{D_{c} = N/R} a constant. \eqn{D_{int}} is
#' the offset on the x-axis. Please not that finding the root in `mode = "extrapolation"`
#' is a non-easy task due to the shape of the function and the results might be
#' unexpected.
#'
#' **Fit weighting**
#'
#' If the option `fit.weights = TRUE` is chosen, weights are calculated using
#' provided signal errors (Lx/Tx error):
#' \deqn{fit.weights = \frac{\frac{1}{error}}{\Sigma{\frac{1}{error}}}}
#'
#' **Error estimation using Monte Carlo simulation**
#'
#' Error estimation is done using a parametric bootstrapping approach. A set of
#' `Lx/Tx` values is constructed by randomly drawing curve data sampled from normal
#' distributions. The normal distribution is defined by the input values (`mean
#' = value`, `sd = value.error`). Then, a dose-response curve fit is attempted for each
#' dataset resulting in a new distribution of single `De` values. The standard
#' deviation of this distribution is becomes then the error of the `De`. With increasing
#' iterations, the error value becomes more stable. However, naturally the error
#' will not decrease with more MC runs.
#'
#' Alternatively, the function returns highest probability density interval
#' estimates as output, users may find more useful under certain circumstances.
#'
#' **Note:** It may take some calculation time with increasing MC runs,
#' especially for the composed functions (`EXP+LIN` and `EXP+EXP`).\cr
#' Each error estimation is done with the function of the chosen fitting method.
#'
#' **Subtitle information**
#'
#' To avoid plotting the subtitle information, provide an empty user `mtext`
#' `mtext = ""`. To plot any other subtitle text, use `mtext`.
#'
#' @param sample [data.frame] (**required**):
#' data frame with three columns for `x = Dose`,`y = LxTx`,`z = LxTx.Error`, `y1 = TnTx`.
#' The column for the test dose response is optional, but requires `'TnTx'` as
#' column name if used. For exponential fits at least three dose points
#' (including the natural) should be provided.
#'
#' @param mode [character] (*with default*):
#' selects calculation mode of the function.
#' - `"interpolation"` (default) calculates the De by interpolation,
#' - `"extrapolation"` calculates the equivalent dose by extrapolation (useful for MAAD measurements) and
#' - `"alternate"` calculates no equivalent dose and just fits the data points.
#'
#' Please note that for option `"regenerative"` the first point is considered
#' as natural dose
#'
#' @param fit.method [character] (*with default*):
#' function used for fitting. Possible options are:
#' - `LIN`,
#' - `QDR`,
#' - `EXP`,
#' - `EXP OR LIN`,
#' - `EXP+LIN`,
#' - `EXP+EXP`,
#' - `GOK`,
#' - `LambertW`
#'
#' See details.
#'
#' @param fit.force_through_origin [logical] (*with default*)
#' allow to force the fitted function through the origin.
#' For `method = "EXP+EXP"` the function will be fixed through
#' the origin in either case, so this option will have no effect.
#'
#' @param fit.weights [logical] (*with default*):
#' option whether the fitting is done with or without weights. See details.
#'
#' @param fit.includingRepeatedRegPoints [logical] (*with default*):
#' includes repeated points for fitting (`TRUE`/`FALSE`).
#'
#' @param fit.NumberRegPoints [integer] (*optional*):
#' set number of regeneration points manually. By default the number of all (!)
#' regeneration points is used automatically.
#'
#' @param fit.NumberRegPointsReal [integer] (*optional*):
#' if the number of regeneration points is provided manually, the value of the
#' real, regeneration points = all points (repeated points) including reg 0,
#' has to be inserted.
#'
#' @param fit.bounds [logical] (*with default*):
#' set lower fit bounds for all fitting parameters to 0. Limited for the use
#' with the fit methods `EXP`, `EXP+LIN`, `EXP OR LIN`, `GOK`, `LambertW`
#' Argument to be inserted for experimental application only!
#'
#' @param NumberIterations.MC [integer] (*with default*):
#' number of Monte Carlo simulations for error estimation. See details.
#'
#' @param output.plot [logical] (*with default*):
#' plot output (`TRUE/FALSE`).
#'
#' @param output.plotExtended [logical] (*with default*):
#' If' `TRUE`, 3 plots on one plot area are provided:
#' 1. growth curve,
#' 2. histogram from Monte Carlo error simulation and
#' 3. a test dose response plot.
#'
#' If `FALSE`, just the growth curve will be plotted.
#' **Requires:** `output.plot = TRUE`.
#'
#' @param output.plotExtended.single [logical] (*with default*):
#' single plot output (`TRUE/FALSE`) to allow for plotting the results in
#' single plot windows. Requires `output.plot = TRUE` and
#' `output.plotExtended = TRUE`.
#'
#' @param cex.global [numeric] (*with default*):
#' global scaling factor.
#'
#' @param txtProgressBar [logical] (*with default*):
#' enables or disables `txtProgressBar`. If `verbose = FALSE` also no
#' `txtProgressBar` is shown.
#'
#' @param verbose [logical] (*with default*):
#' enables or disables terminal feedback.
#'
#' @param ... Further arguments and graphical parameters to be passed. Note:
#' Standard arguments will only be passed to the growth curve plot. Supported:
#' `xlim`, `ylim`, `main`, `xlab`, `ylab`
#'
#' @return
#' Along with a plot (so far wanted) an `RLum.Results` object is returned containing,
#' the slot `data` contains the following elements:
#'
#' \tabular{lll}{
#' **DATA.OBJECT** \tab **TYPE** \tab **DESCRIPTION** \cr
#' `..$De` : \tab `data.frame` \tab Table with De values \cr
#' `..$De.MC` : \tab `numeric` \tab Table with De values from MC runs \cr
#' `..$Fit` : \tab [nls] or [lm] \tab object from the fitting for `EXP`, `EXP+LIN` and `EXP+EXP`.
#' In case of a resulting linear fit when using `LIN`, `QDR` or `EXP OR LIN` \cr
#' `..$Formula` : \tab [expression] \tab Fitting formula as R expression \cr
#' `..$call` : \tab `call` \tab The original function call\cr
#' }
#'
#' @section Function version: 1.11.13
#'
#' @author
#' Sebastian Kreutzer, Institute of Geography, Heidelberg University (Germany)\cr
#' Michael Dietze, GFZ Potsdam (Germany)
#'
#' @references
#'
#' Berger, G.W., Huntley, D.J., 1989. Test data for exponential fits. Ancient TL 7, 43-46.
#'
#' Guralnik, B., Li, B., Jain, M., Chen, R., Paris, R.B., Murray, A.S., Li, S.-H., Pagonis, P.,
#' Herman, F., 2015. Radiation-induced growth and isothermal decay of infrared-stimulated luminescence
#' from feldspar. Radiation Measurements 81, 224-231.
#'
#' Pagonis, V., Kitis, G., Chen, R., 2020. A new analytical equation for the dose response of dosimetric materials,
#' based on the Lambert W function. Journal of Luminescence 225, 117333. \doi{10.1016/j.jlumin.2020.117333}
#'
#' @seealso [nls], [RLum.Results-class], [get_RLum], [minpack.lm::nlsLM],
#' [lm], [uniroot], [lamW::lambertW0]
#'
#' @examples
#'
#' ##(1) plot growth curve for a dummy data.set and show De value
#' data(ExampleData.LxTxData, envir = environment())
#' temp <- plot_GrowthCurve(LxTxData)
#' get_RLum(temp)
#'
#' ##(1b) horizontal plot arrangement
#' layout(mat = matrix(c(1,1,2,3), ncol = 2))
#' plot_GrowthCurve(LxTxData, output.plotExtended.single = TRUE)
#'
#' ##(1c) to access the fitting value try
#' get_RLum(temp, data.object = "Fit")
#'
#' ##(2) plot the growth curve only - uncomment to use
#' ##pdf(file = "~/Desktop/Growth_Curve_Dummy.pdf", paper = "special")
#' plot_GrowthCurve(LxTxData)
#' ##dev.off()
#'
#' ##(3) plot growth curve with pdf output - uncomment to use, single output
#' ##pdf(file = "~/Desktop/Growth_Curve_Dummy.pdf", paper = "special")
#' plot_GrowthCurve(LxTxData, output.plotExtended.single = TRUE)
#' ##dev.off()
#'
#' ##(4) plot resulting function for given interval x
#' x <- seq(1,10000, by = 100)
#' plot(
#' x = x,
#' y = eval(temp$Formula),
#' type = "l"
#' )
#'
#' ##(5) plot using the 'extrapolation' mode
#' LxTxData[1,2:3] <- c(0.5, 0.001)
#' print(plot_GrowthCurve(LxTxData,mode = "extrapolation"))
#'
#' ##(6) plot using the 'alternate' mode
#' LxTxData[1,2:3] <- c(0.5, 0.001)
#' print(plot_GrowthCurve(LxTxData,mode = "alternate"))
#'
#' ##(7) import and fit test data set by Berger & Huntley 1989
#' QNL84_2_unbleached <-
#' read.table(system.file("extdata/QNL84_2_unbleached.txt", package = "Luminescence"))
#'
#' results <- plot_GrowthCurve(
#' QNL84_2_unbleached,
#' mode = "extrapolation",
#' plot = FALSE,
#' verbose = FALSE)
#'
#' #calculate confidence interval for the parameters
#' #as alternative error estimation
#' confint(results$Fit, level = 0.68)
#'
#'
#' \dontrun{
#' QNL84_2_bleached <-
#' read.table(system.file("extdata/QNL84_2_bleached.txt", package = "Luminescence"))
#' STRB87_1_unbleached <-
#' read.table(system.file("extdata/STRB87_1_unbleached.txt", package = "Luminescence"))
#' STRB87_1_bleached <-
#' read.table(system.file("extdata/STRB87_1_bleached.txt", package = "Luminescence"))
#'
#' print(
#' plot_GrowthCurve(
#' QNL84_2_bleached,
#' mode = "alternate",
#' plot = FALSE,
#' verbose = FALSE)$Fit)
#'
#' print(
#' plot_GrowthCurve(
#' STRB87_1_unbleached,
#' mode = "alternate",
#' plot = FALSE,
#' verbose = FALSE)$Fit)
#'
#' print(
#' plot_GrowthCurve(
#' STRB87_1_bleached,
#' mode = "alternate",
#' plot = FALSE,
#' verbose = FALSE)$Fit)
#' }
#'
#' @md
#' @export
plot_GrowthCurve <- function(
sample,
mode = "interpolation",
fit.method = "EXP",
fit.force_through_origin = FALSE,
fit.weights = TRUE,
fit.includingRepeatedRegPoints = TRUE,
fit.NumberRegPoints = NULL,
fit.NumberRegPointsReal = NULL,
fit.bounds = TRUE,
NumberIterations.MC = 100,
output.plot = TRUE,
output.plotExtended = TRUE,
output.plotExtended.single = FALSE,
cex.global = 1,
txtProgressBar = TRUE,
verbose = TRUE,
...
) {
##1. Check input variable
switch(
class(sample)[1],
data.frame = sample,
matrix = sample <- as.data.frame(sample),
list = sample <- as.data.frame(sample),
stop(
"[plot_GrowthCurve()] Argument 'sample' needs to be of type 'data.frame'!",
call. = FALSE)
)
##2. Check supported fit methods
fit.method_supported <- c("LIN", "QDR", "EXP", "EXP OR LIN", "EXP+LIN", "EXP+EXP", "GOK", "LambertW")
if (!fit.method[1] %in% fit.method_supported) {
stop(paste0(
"[plot_GrowthCurve()] Fit method not supported, supported methods are: ",
paste(fit.method_supported, collapse = ", ")
),
call. = FALSE)
}
##2. check if sample contains a least three rows
if(length(sample[[1]]) < 3 && fit.method != "LIN")
stop("\n [plot_GrowthCurve()] At least three regeneration points are required!", call. = FALSE)
##2.1 check column numbers; we assume that in this particular case no error value
##was provided, e.g., set all errors to 0
if(ncol(sample) == 2)
sample <- cbind(sample, 0)
##2.2 check for inf data in the data.frame
if(any(is.infinite(unlist(sample)))){
#https://stackoverflow.com/questions/12188509/cleaning-inf-values-from-an-r-dataframe
#This is slow, but it does not break with previous code
sample <- do.call(data.frame, lapply(sample, function(x) replace(x, is.infinite(x),NA)))
.throw_warning("Inf values found, replaced by NA")
}
##2.3 check whether the dose value is equal all the time
if(sum(abs(diff(sample[[1]])), na.rm = TRUE) == 0){
message("[plot_GrowthCurve()] Error: All points have the same dose, ",
"NULL returned")
return(NULL)
}
## count and exclude NA values and print result
if (sum(!complete.cases(sample)) > 0)
.throw_warning(sum(!complete.cases(sample)),
" NA values removed")
## exclude NA
sample <- na.exclude(sample)
## Check if anything is left after removal
if (nrow(sample) == 0) {
message("[plot_GrowthCurve()] Error: After NA removal, nothing is left ",
"from the data set, NULL returned")
return(NULL)
}
##3. verbose mode
if(!verbose)
txtProgressBar <- FALSE
##remove rownames from data.frame, as this could causes errors for the reg point calculation
rownames(sample) <- NULL
##zero values in the data.frame are not allowed for the y-column
if(length(sample[sample[,2]==0,2])>0){
warning(
paste("[plot_GrowthCurve()]",
length(sample[sample[,2]==0,2]), "values with 0 for Lx/Tx detected; replaced by ",
.Machine$double.eps),
call. = FALSE)
sample[sample[, 2] == 0, 2] <- .Machine$double.eps
}
##1. INPUT
#1.0.1 calculate number of reg points if not set
if(is.null(fit.NumberRegPoints))
fit.NumberRegPoints <- length(sample[-1,1])
if(is.null(fit.NumberRegPointsReal)){
fit.RegPointsReal <- which(!duplicated(sample[,1]) | sample[,1] != 0)
fit.NumberRegPointsReal <- length(fit.RegPointsReal)
}
#1.1 Produce data.frame from input values, two options for different modes
if(mode[1] == "interpolation"){
xy <- data.frame(x=sample[2:(fit.NumberRegPoints+1),1],y=sample[2:(fit.NumberRegPoints+1),2])
y.Error <- sample[2:(fit.NumberRegPoints+1),3]
} else if (mode[1] == "extrapolation" || mode[1] == "alternate") {
xy <- data.frame(
x = sample[1:(fit.NumberRegPoints+1),1],
y = sample[1:(fit.NumberRegPoints+1),2])
y.Error <- sample[1:(fit.NumberRegPoints+1),3]
}else{
stop("[plot_GrowthCurve()] Unknown input for argument 'mode'", call. = FALSE)
}
##1.1.1 produce weights for weighted fitting
if(fit.weights){
fit.weights <- 1 / abs(y.Error) / sum(1 / abs(y.Error))
if(any(is.na(fit.weights))){
fit.weights <- rep(1, length(y.Error))
warning(
"[plot_GrowthCurve()] 'fit.weights' ignored since the error column is invalid or 0.",
call. = FALSE)
}
}else{
fit.weights <- rep(1, length(y.Error))
}
#1.2 Prepare data sets regeneration points for MC Simulation
if (mode[1] == "interpolation") {
data.MC <- t(vapply(
X = seq(2, fit.NumberRegPoints + 1, by = 1),
FUN = function(x) {
sample(rnorm(
n = 10000,
mean = sample[x, 2],
sd = abs(sample[x, 3])
),
size = NumberIterations.MC,
replace = TRUE)
},
FUN.VALUE = vector("numeric", length = NumberIterations.MC)
))
#1.3 Do the same for the natural signal
data.MC.De <- numeric(NumberIterations.MC)
data.MC.De <-
sample(rnorm(10000, mean = sample[1, 2], sd = abs(sample[1, 3])),
NumberIterations.MC,
replace = TRUE)
}else{
data.MC <- t(vapply(
X = seq(1, fit.NumberRegPoints + 1, by = 1),
FUN = function(x) {
sample(rnorm(
n = 10000,
mean = sample[x, 2],
sd = abs(sample[x, 3])
),
size = NumberIterations.MC,
replace = TRUE)
},
FUN.VALUE = vector("numeric", length = NumberIterations.MC)
))
}
#1.3 set x.natural
x.natural <- vector("numeric", length = NumberIterations.MC)
x.natural <- NA
##1.4 set initialise variables
De <- De.Error <- D01 <- R <- Dc <- N <- NA
# FITTING ----------------------------------------------------------------------
##3. Fitting values with nonlinear least-squares estimation of the parameters
## set functions for fitting
## REMINDER: DO NOT ADD {} brackets, otherwise the formula construction will not
## work
## get current environment, we need that later
currn_env <- environment()
## Define functions ---------
### EXP -------
fit.functionEXP <- function(a,b,c,x) a*(1-exp(-(x+c)/b))
### EXP+LIN -----------
fit.functionEXPLIN <- function(a,b,c,g,x) a*(1-exp(-(x+c)/b)+(g*x))
### EXP+EXP ----------
fit.functionEXPEXP <- function(a1,a2,b1,b2,x) (a1*(1-exp(-(x)/b1)))+(a2*(1-exp(-(x)/b2)))
### GOK ----------------
fit.functionGOK <- function(a,b,c,d,x) a*(d-(1+(1/b)*x*c)^(-1/c))
### Lambert W -------------
fit.functionLambertW <- function(R, Dc, N, Dint, x) (1 + (lamW::lambertW0((R - 1) * exp(R - 1 - ((x + Dint) / Dc ))) / (1 - R))) * N
##input data for fitting; exclude repeated RegPoints
if (!fit.includingRepeatedRegPoints[1]) {
data <-
data.frame(x = xy[[1]][!duplicated(xy[[1]])], y = xy[[2]][!duplicated(xy[[1]])])
fit.weights <- fit.weights[!duplicated(xy[[1]])]
data.MC <- data.MC[!duplicated(xy[[1]]),,drop = FALSE]
y.Error <- y.Error[!duplicated(xy[[1]])]
xy <- xy[!duplicated(xy[[1]]),,drop = FALSE]
}else{
data <- data.frame(xy)
}
## for unknown reasons with only two points the nls() function is trapped in
## an endless mode, therefore the minimum length for data is 3
## (2016-05-17)
if(any(fit.method %in% c("EXP", "EXP+LIN", "EXP+EXP", "EXP OR LIN")) && length(data[,1])<=2) {
##set to LIN
fit.method <- "LIN"
warning("[plot_GrowthCurve()] Fitting using an exponential term requires at
least 3 dose points! fit.method set to 'LIN'", call. = FALSE)
if(verbose)
message("[plot_GrowthCurve()] fit.method set to 'LIN', see warnings()")
}
##START PARAMETER ESTIMATION
##general setting of start parameters for fitting
##a - estimation for a a the maximum of the y-values (Lx/Tx)
a <- max(data[,2])
##b - get start parameters from a linear fit of the log(y) data
## (suppress the warning in case one parameter is negative)
fit.lm <- try(lm(suppressWarnings(log(data$y))~data$x))
b <- 1
if (!inherits(fit.lm, "try-error"))
b <- as.numeric(1/fit.lm$coefficients[2])
##c - get start parameters from a linear fit - offset on x-axis
fit.lm<-lm(data$y~data$x)
c <- as.numeric(abs(fit.lm$coefficients[1]/fit.lm$coefficients[2]))
#take slope from x - y scaling
g <- max(data[,2]/max(data[,1]))
#set D01 and D02 (in case of EXp+EXP)
D01 <- NA
D01.ERROR <- NA
D02 <- NA
D02.ERROR <- NA
##--------------------------------------------------------------------------##
##to be a little bit more flexible the start parameters varries within a normal distribution
##draw 50 start values from a normal distribution a start values
if (fit.method != "LIN") {
a.MC <- suppressWarnings(rnorm(50, mean = a, sd = a / 100))
if (!is.na(b)) {
b.MC <- suppressWarnings(rnorm(50, mean = b, sd = b / 100))
}
c.MC <- suppressWarnings(rnorm(50, mean = c, sd = c / 100))
g.MC <- suppressWarnings(rnorm(50, mean = g, sd = g / 1))
##set start vector (to avoid errors within the loop)
a.start <- NA
b.start <- NA
c.start <- NA
g.start <- NA
}
# QDR ------------------------------------------------------------------------
if (fit.method == "QDR"){
##Do fitting with option to force curve through the origin
if(fit.force_through_origin){
##linear fitting ... polynomial
fit <- lm(data$y ~ 0 + I(data$x) + I(data$x^2), weights = fit.weights)
##give function for uniroot
De.fs <- function(x, y) {
0 + coef(fit)[1] * x + coef(fit)[2] * x ^ 2 - y
}
}else{
##linear fitting ... polynomial
fit <- lm(data$y ~ I(data$x) + I(data$x^2), weights = fit.weights)
##give function for uniroot
De.fs <- function(x, y) {
coef(fit)[1] + coef(fit)[2] * x + coef(fit)[3] * x ^ 2 - y
}
}
##solve and get De
De <- NA
if (mode == "interpolation") {
De.uniroot <- try(uniroot(De.fs,
y = sample[1, 2],
lower = 0,
upper = max(sample[, 1]) * 1.5), silent = TRUE)
if (!inherits(De.uniroot, "try-error")) {
De <- De.uniroot$root
if (verbose) {
if (mode != "alternate") {
writeLines(paste0("[plot_GrowthCurve()] Fit: ", fit.method,
" (", mode,") ", "| De = ", round(De,2)))
}
}
} else{
if (verbose)
writeLines("[plot_GrowthCurve()] no solution found for QDR fit")
}
}else if (mode == "extrapolation"){
De.uniroot <- try(uniroot(De.fs,
y = 0,
lower = -1e06,
upper = max(sample[, 1]) * 1.5), silent = TRUE)
if (!inherits(De.uniroot, "try-error")) {
De <- De.uniroot$root
if (verbose) {
if (mode != "alternate") {
writeLines(paste0("[plot_GrowthCurve()] Fit: ", fit.method,
" (", mode,") ", "| De = ", round(abs(De), 2)))
}
}
} else{
if (verbose)
writeLines("[plot_GrowthCurve()] no solution found for QDR fit")
}
}
##set progressbar
if(txtProgressBar){
cat("\n\t Run Monte Carlo loops for error estimation of the QDR fit\n")
pb<-txtProgressBar(min=0,max=NumberIterations.MC, char="=", style=3)
}
#start loop for Monte Carlo Error estimation
fit.MC <- sapply(1:NumberIterations.MC, function(i){
data <- data.frame(x = xy$x, y = data.MC[,i])
if(fit.force_through_origin){
##linear fitting ... polynomial
fit.MC <- lm(data$y ~ 0 + I(data$x) + I(data$x^2), weights = fit.weights)
##give function for uniroot
De.fs.MC <- function(x, y) {
0 + coef(fit.MC)[1] * x + coef(fit.MC)[2] * x ^ 2 - y
0 + coef(fit.MC)[1] * x + coef(fit.MC)[2] * x ^ 2 - y
}
}else{
##linear fitting ... polynomial
fit.MC <- lm(data$y ~ I(data$x) + I(data$x^2), weights = fit.weights)
##give function for uniroot
De.fs.MC <- function(x, y) {
coef(fit.MC)[1] + coef(fit.MC)[2] * x + coef(fit.MC)[3] * x ^ 2 - y
}
}
De.MC <- NA
if (mode == "interpolation") {
##solve and get De
De.uniroot.MC <- try(uniroot(
De.fs.MC,
y = data.MC.De[i],
lower = 0,
upper = max(sample[, 1]) * 1.5
),
silent = TRUE)
if (!inherits(De.uniroot.MC, "try-error")) {
De.MC <- De.uniroot.MC$root
}
}else if (mode == "extrapolation"){
##solve and get De
De.uniroot.MC <- try(uniroot(
De.fs.MC,
y = 0,
lower = -1e6,
upper = max(sample[, 1]) * 1.5
),
silent = TRUE)
if (!inherits(De.uniroot.MC, "try-error")) {
De.MC <- De.uniroot.MC$root
}
}
##update progress bar
if(txtProgressBar) setTxtProgressBar(pb, i)
return(De.MC)
})
if(txtProgressBar) close(pb)
x.natural<- fit.MC
}
#===========================================================================##
#EXP ---------------
if (fit.method=="EXP" | fit.method=="EXP OR LIN" | fit.method=="LIN"){
if((is.na(a) | is.na(b) | is.na(c)) && fit.method != "LIN"){
message("[plot_GrowthCurve()] Error: Fit could not be applied ",
"for this data set, NULL returned")
return(NULL)
}
if(fit.method != "LIN"){
##FITTING on GIVEN VALUES##
# --use classic R fitting routine to fit the curve
##try to create some start parameters from the input values to make
## the fitting more stable
for(i in 1:50){
a <- a.MC[i]
b <- b.MC[i]
c <- c.MC[i]
fit.initial <- suppressWarnings(try(nls(
formula = .toFormula(fit.functionEXP, env = currn_env),
data = data,
start = c(a = a, b = b, c = c),
trace = FALSE,
algorithm = "port",
lower = c(a = 0, b > 0, c = 0),
nls.control(
maxiter = 100,
warnOnly = TRUE,
minFactor = 1 / 2048
)
),
silent = TRUE
))
if(!inherits(fit.initial, "try-error")){
#get parameters out of it
parameters<-(coef(fit.initial))
b.start[i] <- as.vector((parameters["b"]))
a.start[i] <- as.vector((parameters["a"]))
c.start[i] <- as.vector((parameters["c"]))
}
}
##used median as start parameters for the final fitting
a <- median(na.exclude(a.start))
b <- median(na.exclude(b.start))
c <- median(na.exclude(c.start))
##exception for b: if b is 1 it is likely to b wrong and should be reset
if(!is.na(b) && b == 1)
b <- mean(b.MC)
#FINAL Fit curve on given values
fit <- try(minpack.lm::nlsLM(
formula = .toFormula(fit.functionEXP, env = currn_env),
data = data,
start = list(a = a, b = b,c = 0),
weights = fit.weights,
trace = FALSE,
algorithm = "LM",
lower = if (fit.bounds) {
c(0,0,0)
}else{
c(-Inf,-Inf,-Inf)
},
upper = if (fit.force_through_origin) {
c(Inf, Inf, 0)
}else{
c(Inf, Inf, Inf)
},
control = minpack.lm::nls.lm.control(maxiter = 500)
), silent = TRUE
)
if (inherits(fit, "try-error") & inherits(fit.initial, "try-error")){
if(verbose) writeLines("[plot_GrowthCurve()] try-error for EXP fit")
}else{
##this is to avoid the singular convergence failure due to a perfect fit at the beginning
##this may happen especially for simulated data
if(inherits(fit, "try-error") & !inherits(fit.initial, "try-error")){
fit <- fit.initial
rm(fit.initial)
}
#get parameters out of it
parameters <- (coef(fit))
b <- as.vector((parameters["b"]))
a <- as.vector((parameters["a"]))
c <- as.vector((parameters["c"]))
#calculate De
De <- NA
if(mode == "interpolation"){
De <- suppressWarnings(-c-b*log(1-sample[1,2]/a))
## account for the fact that we can still calculate a De that is negative
## even it does not make sense
if(!is.na(De) && De < 0)
De <- NA
}else if (mode == "extrapolation"){
De <- suppressWarnings(-c-b*log(1-0/a))
}
#print D01 value
D01 <- b
if (verbose) {
if (mode != "alternate") {
writeLines(paste0(
"[plot_GrowthCurve()] Fit: ",
fit.method,
" (",
mode,
")",
" | De = ",
round(abs(De), digits = 2),
" | D01 = ",
round(D01, 2)
))
}
}
#EXP MC -----
##Monte Carlo Simulation
# --Fit many curves and calculate a new De +/- De_Error
# --take De_Error
#set variables
var.b<-vector(mode="numeric", length=NumberIterations.MC)
var.a<-vector(mode="numeric", length=NumberIterations.MC)
var.c<-vector(mode="numeric", length=NumberIterations.MC)
#start loop
for (i in 1:NumberIterations.MC) {
##set data set
data <- data.frame(x = xy$x,y = data.MC[,i])
fit.MC <- try(minpack.lm::nlsLM(
formula = .toFormula(fit.functionEXP, env = currn_env),
data = data,
start = list(a = a, b = b, c = c),
weights = fit.weights,
trace = FALSE,
algorithm = "LM",
lower = if (fit.bounds) {
c(0,0,0)
}else{
c(-Inf,-Inf,-Inf)
},
upper = if (fit.force_through_origin) {
c(Inf, Inf, 0)
}else{
c(Inf, Inf, Inf)
},
control = minpack.lm::nls.lm.control(maxiter = 500)
), silent = TRUE
)
#get parameters out of it including error handling
if (inherits(fit.MC, "try-error")) {
x.natural[i] <- NA
}else {
#get parameters out
parameters<-coef(fit.MC)
var.b[i]<-as.vector((parameters["b"])) #D0
var.a[i]<-as.vector((parameters["a"])) #Imax
var.c[i]<-as.vector((parameters["c"]))
#calculate x.natural for error calculation
if(mode == "interpolation"){
x.natural[i]<-suppressWarnings(
-var.c[i]-var.b[i]*log(1-data.MC.De[i]/var.a[i]))
}else if(mode == "extrapolation"){
x.natural[i]<-suppressWarnings(
abs(-var.c[i]-var.b[i]*log(1-0/var.a[i])))
}else{
x.natural[i] <- NA
}
}
}#end for loop
##write D01.ERROR
D01.ERROR <- sd(var.b, na.rm = TRUE)
##remove values
rm(var.b, var.a, var.c)
}#endif::try-error fit
}#endif:fit.method!="LIN"
##LIN -----
##two options: just linear fit or LIN fit after the EXP fit failed
#set fit object, if fit object was not set before
if(exists("fit")==FALSE){fit<-NA}
if ((fit.method=="EXP OR LIN" & inherits(fit, "try-error")) |
fit.method=="LIN" | length(data[,1])<2) {
##Do fitting again as just allows fitting through the origin
if(fit.force_through_origin){
fit.lm<-lm(data$y ~ 0 + data$x, weights = fit.weights)
#calculate De
De <- 0
if(mode == "interpolation"){
De <- sample[1,2]/fit.lm$coefficients[1]
}
}else{
fit.lm<-lm(data$y ~ data$x, weights = fit.weights)
#calculate De
if(mode == "interpolation"){
De <- (sample[1,2]-fit.lm$coefficients[1])/fit.lm$coefficients[2]
}else if(mode == "extrapolation"){
De <- (0-fit.lm$coefficients[1])/fit.lm$coefficients[2]
}
}
##remove vector labels
De <- as.numeric(as.character(De))
if (verbose) {
if (mode != "alternate") {
writeLines(paste0(
"[plot_GrowthCurve()] Fit: ",
fit.method,
" (",
mode,
") ",
"| De = ",
round(abs(De), 2)
))
}
}
#start loop for Monte Carlo Error estimation
#LIN MC ---------
for (i in 1:NumberIterations.MC) {
data <- data.frame(x = xy$x, y = data.MC[, i])
if(fit.force_through_origin){
##do fitting
fit.lmMC <- lm(data$y ~ 0 + data$x, weights=fit.weights)
#calculate x.natural
if(mode == "interpolation"){
x.natural[i] <- data.MC.De[i]/fit.lmMC$coefficients[1]
}else if (mode == "extrapolation"){
x.natural[i] <- 0
}
}else{