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+#' Single First-Order kinetics
+#'
+#' Function describing exponential decline from a defined starting value.
+#'
+#' @family parent solutions
+#' @param t Time.
+#' @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 
+#' 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,
+#'   Version 1.1, 18 December 2014
+#'   \url{http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics}
+#' @examples
+#'
+#'   \dontrun{plot(function(x) SFO.solution(x, 100, 3), 0, 2)}
+#'
+#' @export
+SFO.solution <- function(t, parent_0, k)
+{
+	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 
+#' @param alpha Shape parameter determined by coefficient of variation of rate
+#'   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 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}
+#' 
+#'   Gustafson DI and Holden LR (1990) Nonlinear pesticide dissipation in soil:
+#'   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
+}
+
+#' 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 
+#' @param k__iore Rate constant. Note that this depends on the concentration
+#'   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.
+#' @references NAFTA Technical Working Group on Pesticides (not dated) Guidance
+#'   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$par, 
+#'                      row.names = paste("model par", 1:4)))
+#'     print(rbind(fomc = endpoints(fit.fomc)$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))
+}
+
+#' 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 
+#' @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.
+#' @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)
+}
+
+#' Hockey-Stick kinetics
+#' 
+#' Function describing two exponential decline functions with a break point
+#' between them.
+#' 
+#' @family parent solutions
+#' @inherit HS.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}.
+#' @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)))
+}
+
+#' 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 HS.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.
+#' @return The value of the response variable, which is the sum of free and
+#'   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)
+  b1 = 0.5 * (k_12 + k_21 + k_1output) + sqrt_exp
+  b2 = 0.5 * (k_12 + k_21 + k_1output) - sqrt_exp
+
+  parent = parent_0 *
+        (((k_12 + k_21 - b1)/(b2 - b1)) * exp(-b1 * t) +
+        ((k_12 + k_21 - b2)/(b1 - b2)) * exp(-b2 * t))
+}
+
+#' 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 
+#' @param kmax Maximum rate constant.
+#' @param k0 Minumum 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}.
+#' @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),
+#'        xlab = "Time", ylab = "Residue")
+#'   plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.4),
+#'        from = 0, to = 100, add = TRUE, lty = 2, col = 2)
+#'   plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.8),
+#'        from = 0, to = 100, add = TRUE, lty = 3, col = 3)
+#'   plot(function(x) logistic.solution(x, 100, 0.08, 0.001, 0.2),
+#'        from = 0, to = 100, add = TRUE, lty = 4, col = 4)
+#'   plot(function(x) logistic.solution(x, 100, 0.08, 0.08, 0.2),
+#'        from = 0, to = 100, add = TRUE, lty = 5, col = 5)
+#'   legend("topright", inset = 0.05,
+#'          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,
+#'     parms_logistic, c(parent = 100),
+#'     sampling_times)
+#'   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)
+}