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-rw-r--r--R/parent_solutions.R128
1 files changed, 64 insertions, 64 deletions
diff --git a/R/parent_solutions.R b/R/parent_solutions.R
index 04226b73..f11cbff9 100644
--- a/R/parent_solutions.R
+++ b/R/parent_solutions.R
@@ -7,7 +7,7 @@
#' @param parent_0 Starting value for the response variable at time zero.
#' @param k Kinetic rate constant.
#' @return The value of the response variable at time \code{t}.
-#' @references
+#' @references
#' FOCUS (2006) \dQuote{Guidance Document on Estimating Persistence
#' and Degradation Kinetics from Environmental Fate Studies on Pesticides in
#' EU Registration} Report of the FOCUS Work Group on Degradation Kinetics,
@@ -25,33 +25,33 @@
#' @export
SFO.solution <- function(t, parent_0, k)
{
- parent = parent_0 * exp(-k * t)
+ parent = parent_0 * exp(-k * t)
}
#' First-Order Multi-Compartment kinetics
-#'
+#'
#' Function describing exponential decline from a defined starting value, with
#' a decreasing rate constant.
-#'
+#'
#' The form given here differs slightly from the original reference by
#' Gustafson and Holden (1990). The parameter \code{beta} corresponds to 1/beta
#' in the original equation.
-#'
+#'
#' @family parent solutions
-#' @inherit SFO.solution
+#' @inherit SFO.solution
#' @param alpha Shape parameter determined by coefficient of variation of rate
-#' constant values.
+#' constant values.
#' @param beta Location parameter.
#' @note The solution of the FOMC kinetic model reduces to the
-#' \code{\link{SFO.solution}} for large values of \code{alpha} and
-#' \code{beta} with \eqn{k = \frac{\beta}{\alpha}}{k = beta/alpha}.
-#' @references
+#' \code{\link{SFO.solution}} for large values of \code{alpha} and \code{beta}
+#' with \eqn{k = \frac{\beta}{\alpha}}{k = beta/alpha}.
+#' @references
#' FOCUS (2006) \dQuote{Guidance Document on Estimating Persistence
#' and Degradation Kinetics from Environmental Fate Studies on Pesticides in
#' EU Registration} Report of the FOCUS Work Group on Degradation Kinetics,
#' EC Document Reference Sanco/10058/2005 version 2.0, 434 pp,
#' \url{http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics}
-#'
+#'
#' FOCUS (2014) \dQuote{Generic guidance for Estimating Persistence
#' and Degradation Kinetics from Environmental Fate Studies on Pesticides in
#' EU Registration} Report of the FOCUS Work Group on Degradation Kinetics,
@@ -62,119 +62,119 @@ SFO.solution <- function(t, parent_0, k)
#' A new model based on spatial variability. \emph{Environmental Science and
#' Technology} \bold{24}, 1032-1038
#' @examples
-#'
+#'
#' plot(function(x) FOMC.solution(x, 100, 10, 2), 0, 2, ylim = c(0, 100))
-#'
+#'
#' @export
FOMC.solution <- function(t, parent_0, alpha, beta)
{
- parent = parent_0 / (t/beta + 1)^alpha
+ parent = parent_0 / (t/beta + 1)^alpha
}
#' Indeterminate order rate equation kinetics
-#'
+#'
#' Function describing exponential decline from a defined starting value, with
#' a concentration dependent rate constant.
-#'
+#'
#' @family parent solutions
-#' @inherit SFO.solution
+#' @inherit SFO.solution
#' @param k__iore Rate constant. Note that this depends on the concentration
-#' units used.
+#' units used.
#' @param N Exponent describing the nonlinearity of the rate equation
#' @note The solution of the IORE kinetic model reduces to the
-#' \code{\link{SFO.solution}} if N = 1. The parameters of the IORE model can
-#' be transformed to equivalent parameters of the FOMC mode - see the NAFTA
-#' guidance for details.
+#' \code{\link{SFO.solution}} if N = 1. The parameters of the IORE model can
+#' be transformed to equivalent parameters of the FOMC mode - see the NAFTA
+#' guidance for details.
#' @references NAFTA Technical Working Group on Pesticides (not dated) Guidance
-#' for Evaluating and Calculating Degradation Kinetics in Environmental Media
+#' for Evaluating and Calculating Degradation Kinetics in Environmental Media
#' @examples
-#'
+#'
#' plot(function(x) IORE.solution(x, 100, 0.2, 1.3), 0, 2, ylim = c(0, 100))
#' \dontrun{
#' fit.fomc <- mkinfit("FOMC", FOCUS_2006_C, quiet = TRUE)
#' fit.iore <- mkinfit("IORE", FOCUS_2006_C, quiet = TRUE)
#' fit.iore.deS <- mkinfit("IORE", FOCUS_2006_C, solution_type = "deSolve", quiet = TRUE)
-#'
-#' print(data.frame(fit.fomc$par, fit.iore$par, fit.iore.deS$par,
+#'
+#' print(data.frame(fit.fomc$par, fit.iore$par, fit.iore.deS$par,
#' row.names = paste("model par", 1:4)))
-#' print(rbind(fomc = endpoints(fit.fomc)$distimes, iore = endpoints(fit.iore)$distimes,
+#' print(rbind(fomc = endpoints(fit.fomc)$distimes, iore = endpoints(fit.iore)$distimes,
#' iore.deS = endpoints(fit.iore)$distimes))
#' }
-#'
+#'
#' @export
IORE.solution <- function(t, parent_0, k__iore, N)
{
- parent = (parent_0^(1 - N) - (1 - N) * k__iore * t)^(1/(1 - N))
+ parent = (parent_0^(1 - N) - (1 - N) * k__iore * t)^(1/(1 - N))
}
#' Double First-Order in Parallel kinetics
-#'
+#'
#' Function describing decline from a defined starting value using the sum of
#' two exponential decline functions.
-#'
+#'
#' @family parent solutions
-#' @inherit SFO.solution
+#' @inherit SFO.solution
#' @param t Time.
#' @param k1 First kinetic constant.
#' @param k2 Second kinetic constant.
#' @param g Fraction of the starting value declining according to the first
-#' kinetic constant.
+#' kinetic constant.
#' @examples
-#'
+#'
#' plot(function(x) DFOP.solution(x, 100, 5, 0.5, 0.3), 0, 4, ylim = c(0,100))
-#'
+#'
#' @export
DFOP.solution <- function(t, parent_0, k1, k2, g)
{
- parent = g * parent_0 * exp(-k1 * t) +
- (1 - g) * parent_0 * exp(-k2 * t)
+ parent = g * parent_0 * exp(-k1 * t) +
+ (1 - g) * parent_0 * exp(-k2 * t)
}
#' Hockey-Stick kinetics
-#'
+#'
#' Function describing two exponential decline functions with a break point
#' between them.
-#'
+#'
#' @family parent solutions
-#' @inherit DFOP.solution
+#' @inherit DFOP.solution
#' @param tb Break point. Before this time, exponential decline according to
-#' \code{k1} is calculated, after this time, exponential decline proceeds
-#' according to \code{k2}.
+#' \code{k1} is calculated, after this time, exponential decline proceeds
+#' according to \code{k2}.
#' @examples
-#'
+#'
#' plot(function(x) HS.solution(x, 100, 2, 0.3, 0.5), 0, 2, ylim=c(0,100))
-#'
+#'
#' @export
HS.solution <- function(t, parent_0, k1, k2, tb)
{
- parent = ifelse(t <= tb,
- parent_0 * exp(-k1 * t),
- parent_0 * exp(-k1 * tb) * exp(-k2 * (t - tb)))
+ parent = ifelse(t <= tb,
+ parent_0 * exp(-k1 * t),
+ parent_0 * exp(-k1 * tb) * exp(-k2 * (t - tb)))
}
#' Single First-Order Reversible Binding kinetics
-#'
+#'
#' Function describing the solution of the differential equations describing
#' the kinetic model with first-order terms for a two-way transfer from a free
#' to a bound fraction, and a first-order degradation term for the free
#' fraction. The initial condition is a defined amount in the free fraction
#' and no substance in the bound fraction.
-#'
+#'
#' @family parent solutions
-#' @inherit SFO.solution
+#' @inherit SFO.solution
#' @param k_12 Kinetic constant describing transfer from free to bound.
#' @param k_21 Kinetic constant describing transfer from bound to free.
#' @param k_1output Kinetic constant describing degradation of the free
-#' fraction.
+#' fraction.
#' @return The value of the response variable, which is the sum of free and
-#' bound fractions at time \code{t}.
+#' bound fractions at time \code{t}.
#' @examples
-#'
+#'
#' \dontrun{plot(function(x) SFORB.solution(x, 100, 0.5, 2, 3), 0, 2)}
-#'
+#'
#' @export
SFORB.solution = function(t, parent_0, k_12, k_21, k_1output) {
- sqrt_exp = sqrt(1/4 * (k_12 + k_21 + k_1output)^2 + k_12 * k_21 - (k_12 + k_1output) * k_21)
+ sqrt_exp = sqrt(1/4 * (k_12 + k_21 + k_1output)^2 - k_1output * k_21)
b1 = 0.5 * (k_12 + k_21 + k_1output) + sqrt_exp
b2 = 0.5 * (k_12 + k_21 + k_1output) - sqrt_exp
@@ -184,19 +184,19 @@ SFORB.solution = function(t, parent_0, k_12, k_21, k_1output) {
}
#' Logistic kinetics
-#'
+#'
#' Function describing exponential decline from a defined starting value, with
#' an increasing rate constant, supposedly caused by microbial growth
-#'
+#'
#' @family parent solutions
-#' @inherit SFO.solution
+#' @inherit SFO.solution
#' @param kmax Maximum rate constant.
#' @param k0 Minimum rate constant effective at time zero.
#' @param r Growth rate of the increase in the rate constant.
#' @note The solution of the logistic model reduces to the
-#' \code{\link{SFO.solution}} if \code{k0} is equal to \code{kmax}.
+#' \code{\link{SFO.solution}} if \code{k0} is equal to \code{kmax}.
#' @examples
-#'
+#'
#' # Reproduce the plot on page 57 of FOCUS (2014)
#' plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.2),
#' from = 0, to = 100, ylim = c(0, 100),
@@ -213,10 +213,10 @@ SFORB.solution = function(t, parent_0, k_12, k_21, k_1output) {
#' legend = paste0("k0 = ", c(0.0001, 0.0001, 0.0001, 0.001, 0.08),
#' ", r = ", c(0.2, 0.4, 0.8, 0.2, 0.2)),
#' lty = 1:5, col = 1:5)
-#'
+#'
#' # Fit with synthetic data
#' logistic <- mkinmod(parent = mkinsub("logistic"))
-#'
+#'
#' sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
#' parms_logistic <- c(kmax = 0.08, k0 = 0.0001, r = 0.2)
#' d_logistic <- mkinpredict(logistic,
@@ -225,14 +225,14 @@ SFORB.solution = function(t, parent_0, k_12, k_21, k_1output) {
#' d_2_1 <- add_err(d_logistic,
#' sdfunc = function(x) sigma_twocomp(x, 0.5, 0.07),
#' n = 1, reps = 2, digits = 5, LOD = 0.1, seed = 123456)[[1]]
-#'
+#'
#' m <- mkinfit("logistic", d_2_1, quiet = TRUE)
#' plot_sep(m)
#' summary(m)$bpar
#' endpoints(m)$distimes
-#'
+#'
#' @export
logistic.solution <- function(t, parent_0, kmax, k0, r)
{
- parent = parent_0 * (kmax / (kmax - k0 + k0 * exp (r * t))) ^(kmax/r)
+ parent = parent_0 * (kmax / (kmax - k0 + k0 * exp (r * t))) ^(kmax/r)
}

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