#' Function to set up a kinetic model with one or more state variables
#'
#' This function is usually called using a call to [mkinsub()] for each observed
#' variable, specifying the corresponding submodel as well as outgoing pathways
#' (see examples).
#'
#' For the definition of model types and their parameters, the equations given
#' in the FOCUS and NAFTA guidance documents are used.
#'
#' For kinetic models with more than one observed variable, a symbolic solution
#' of the system of differential equations is included in the resulting
#' mkinmod object in some cases, speeding up the solution.
#'
#' If a C compiler is found by [pkgbuild::has_compiler()] and there
#' is more than one observed variable in the specification, C code is generated
#' for evaluating the differential equations, compiled using
#' [inline::cfunction()] and added to the resulting mkinmod object.
#'
#' @param ... For each observed variable, a list as obtained by [mkinsub()]
#' has to be specified as an argument (see examples). Currently, single
#' first order kinetics "SFO", indeterminate order rate equation kinetics
#' "IORE", or single first order with reversible binding "SFORB" are
#' implemented for all variables, while "FOMC", "DFOP", "HS" and "logistic"
#' can additionally be chosen for the first variable which is assumed to be
#' the source compartment.
#' Additionally, [mkinsub()] has an argument \code{to}, specifying names of
#' variables to which a transfer is to be assumed in the model.
#' If the argument \code{use_of_ff} is set to "min"
#' (default) and the model for the compartment is "SFO" or "SFORB", an
#' additional [mkinsub()] argument can be \code{sink = FALSE}, effectively
#' fixing the flux to sink to zero.
#' @param use_of_ff Specification of the use of formation fractions in the
#' model equations and, if applicable, the coefficient matrix. If "min", a
#' minimum use of formation fractions is made in order to avoid fitting the
#' product of formation fractions and rate constants. If "max", formation
#' fractions are always used.
#' @param speclist The specification of the observed variables and their
#' submodel types and pathways can be given as a single list using this
#' argument. Default is NULL.
#' @param quiet Should messages be suppressed?
#' @param verbose If \code{TRUE}, passed to [inline::cfunction()] if
#' applicable to give detailed information about the C function being built.
#' @importFrom methods signature
#' @importFrom pkgbuild has_compiler
#' @importFrom inline cfunction
#' @return A list of class \code{mkinmod} for use with [mkinfit()],
#' containing, among others,
#' \item{diffs}{
#' A vector of string representations of differential equations, one for
#' each modelling variable.
#' }
#' \item{map}{
#' A list containing named character vectors for each observed variable,
#' specifying the modelling variables by which it is represented.
#' }
#' \item{use_of_ff}{
#' The content of \code{use_of_ff} is passed on in this list component.
#' }
#' \item{deg_func}{
#' If generated, a function containing the solution of the degradation
#' model.
#' }
#' \item{coefmat}{
#' The coefficient matrix, if the system of differential equations can be
#' represented by one.
#' }
#' \item{cf}{
#' If generated, a compiled function calculating the derivatives as
#' returned by cfunction.
#' }
#' @note The IORE submodel is not well tested for metabolites. When using this
#' model for metabolites, you may want to read the note in the help
#' page to [mkinfit].
#' @author Johannes Ranke
#' @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}
#'
#' NAFTA Technical Working Group on Pesticides (not dated) Guidance for
#' Evaluating and Calculating Degradation Kinetics in Environmental Media
#' @examples
#'
#' # Specify the SFO model (this is not needed any more, as we can now mkinfit("SFO", ...)
#' SFO <- mkinmod(parent = mkinsub("SFO"))
#'
#' # One parent compound, one metabolite, both single first order
#' SFO_SFO <- mkinmod(
#' parent = mkinsub("SFO", "m1"),
#' m1 = mkinsub("SFO"))
#'
#' \dontrun{
#' # The above model used to be specified like this, before the advent of mkinsub()
#' SFO_SFO <- mkinmod(
#' parent = list(type = "SFO", to = "m1"),
#' m1 = list(type = "SFO"))
#'
#' # Show details of creating the C function
#' SFO_SFO <- mkinmod(
#' parent = mkinsub("SFO", "m1"),
#' m1 = mkinsub("SFO"), verbose = TRUE)
#'
#' # The symbolic solution which is available in this case is not
#' # made for human reading but for speed of computation
#' SFO_SFO$deg_func
#'
#' # If we have several parallel metabolites
#' # (compare tests/testthat/test_synthetic_data_for_UBA_2014.R)
#' m_synth_DFOP_par <- mkinmod(
#' parent = mkinsub("DFOP", c("M1", "M2")),
#' M1 = mkinsub("SFO"),
#' M2 = mkinsub("SFO"),
#' use_of_ff = "max", quiet = TRUE)
#'
#' fit_DFOP_par_c <- mkinfit(m_synth_DFOP_par,
#' synthetic_data_for_UBA_2014[[12]]$data,
#' quiet = TRUE)
#' }
#'
#' @export mkinmod
mkinmod <- function(..., use_of_ff = "max", speclist = NULL, quiet = FALSE, verbose = FALSE)
{
if (is.null(speclist)) spec <- list(...)
else spec <- speclist
obs_vars <- names(spec)
# Check if any of the names of the observed variables contains any other
for (obs_var in obs_vars) {
if (length(grep(obs_var, obs_vars)) > 1) stop("Sorry, variable names can not contain each other")
if (grepl("_to_", obs_var)) stop("Sorry, names of observed variables can not contain _to_")
if (obs_var == "sink") stop("Naming a compound 'sink' is not supported")
}
if (!use_of_ff %in% c("min", "max"))
stop("The use of formation fractions 'use_of_ff' can only be 'min' or 'max'")
parms <- vector()
# }}}
# Do not return a coefficient matrix mat when FOMC, IORE, DFOP, HS or logistic is used for the parent {{{
if(spec[[1]]$type %in% c("FOMC", "IORE", "DFOP", "HS", "logistic")) {
mat = FALSE
} else mat = TRUE
#}}}
# Establish a list of differential equations as well as a map from observed {{{
# compartments to differential equations
diffs <- vector()
map <- list()
for (varname in obs_vars)
{
# Check the type component of the compartment specification {{{
if(is.null(spec[[varname]]$type)) stop(
"Every part of the model specification must be a list containing a type component")
if(!spec[[varname]]$type %in% c("SFO", "FOMC", "IORE", "DFOP", "HS", "SFORB", "logistic")) stop(
"Available types are SFO, FOMC, IORE, DFOP, HS, SFORB and logistic only")
if(spec[[varname]]$type %in% c("FOMC", "DFOP", "HS", "logistic") & match(varname, obs_vars) != 1) {
stop(paste("Types FOMC, DFOP, HS and logistic are only implemented for the first compartment,",
"which is assumed to be the source compartment"))
}
#}}}
# New (sub)compartments (boxes) needed for the model type {{{
new_boxes <- switch(spec[[varname]]$type,
SFO = varname,
FOMC = varname,
IORE = varname,
DFOP = varname,
HS = varname,
logistic = varname,
SFORB = paste(varname, c("free", "bound"), sep = "_")
)
map[[varname]] <- new_boxes
names(map[[varname]]) <- rep(spec[[varname]]$type, length(new_boxes)) #}}}
# Start a new differential equation for each new box {{{
new_diffs <- paste("d_", new_boxes, " =", sep = "")
names(new_diffs) <- new_boxes
diffs <- c(diffs, new_diffs) #}}}
} #}}}
# Create content of differential equations and build parameter list {{{
for (varname in obs_vars)
{
# Get the name of the box(es) we are working on for the decline term(s)
box_1 = map[[varname]][[1]] # This is the only box unless type is SFORB
# Turn on sink if this is not explicitly excluded by the user by
# specifying sink=FALSE
if(is.null(spec[[varname]]$sink)) spec[[varname]]$sink <- TRUE
if(spec[[varname]]$type %in% c("SFO", "IORE", "SFORB")) { # {{{ Add decline term
if (use_of_ff == "min") { # Minimum use of formation fractions
if(spec[[varname]]$type == "IORE" && length(spec[[varname]]$to) > 0) {
stop("Transformation reactions from compounds modelled with IORE\n",
"are only supported with formation fractions (use_of_ff = 'max')")
}
if(spec[[varname]]$sink) {
# If sink is requested, add first-order/IORE sink term
k_compound_sink <- paste("k", box_1, "sink", sep = "_")
if(spec[[varname]]$type == "IORE") {
k_compound_sink <- paste("k__iore", box_1, "sink", sep = "_")
}
parms <- c(parms, k_compound_sink)
decline_term <- paste(k_compound_sink, "*", box_1)
if(spec[[varname]]$type == "IORE") {
N <- paste("N", box_1, sep = "_")
parms <- c(parms, N)
decline_term <- paste0(decline_term, "^", N)
}
} else { # otherwise no decline term needed here
decline_term = "0"
}
} else { # Maximum use of formation fractions
k_compound <- paste("k", box_1, sep = "_")
if(spec[[varname]]$type == "IORE") {
k_compound <- paste("k__iore", box_1, sep = "_")
}
parms <- c(parms, k_compound)
decline_term <- paste(k_compound, "*", box_1)
if(spec[[varname]]$type == "IORE") {
N <- paste("N", box_1, sep = "_")
parms <- c(parms, N)
decline_term <- paste0(decline_term, "^", N)
}
}
} #}}}
if(spec[[varname]]$type == "FOMC") { # {{{ Add FOMC decline term
# From p. 53 of the FOCUS kinetics report, without the power function so it works in C
decline_term <- paste("(alpha/beta) * 1/((time/beta) + 1) *", box_1)
parms <- c(parms, "alpha", "beta")
} #}}}
if(spec[[varname]]$type == "DFOP") { # {{{ Add DFOP decline term
# From p. 57 of the FOCUS kinetics report
decline_term <- paste("((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) *", box_1)
parms <- c(parms, "k1", "k2", "g")
} #}}}
HS_decline <- "ifelse(time <= tb, k1, k2)" # Used below for automatic translation to C
if(spec[[varname]]$type == "HS") { # {{{ Add HS decline term
# From p. 55 of the FOCUS kinetics report
decline_term <- paste(HS_decline, "*", box_1)
parms <- c(parms, "k1", "k2", "tb")
} #}}}
if(spec[[varname]]$type == "logistic") { # {{{ Add logistic decline term
# From p. 67 of the FOCUS kinetics report (2014)
decline_term <- paste("(k0 * kmax)/(k0 + (kmax - k0) * exp(-r * time)) *", box_1)
parms <- c(parms, "kmax", "k0", "r")
} #}}}
# Add origin decline term to box 1 (usually the only box, unless type is SFORB)#{{{
diffs[[box_1]] <- paste(diffs[[box_1]], "-", decline_term)#}}}
if(spec[[varname]]$type == "SFORB") { # {{{ Add SFORB reversible binding terms
box_2 = map[[varname]][[2]]
k_free_bound <- paste("k", varname, "free", "bound", sep = "_")
k_bound_free <- paste("k", varname, "bound", "free", sep = "_")
parms <- c(parms, k_free_bound, k_bound_free)
reversible_binding_term_1 <- paste("-", k_free_bound, "*", box_1, "+",
k_bound_free, "*", box_2)
reversible_binding_term_2 <- paste("+", k_free_bound, "*", box_1, "-",
k_bound_free, "*", box_2)
diffs[[box_1]] <- paste(diffs[[box_1]], reversible_binding_term_1)
diffs[[box_2]] <- paste(diffs[[box_2]], reversible_binding_term_2)
} #}}}
# Transfer between compartments#{{{
to <- spec[[varname]]$to
if(!is.null(to)) {
# Name of box from which transfer takes place
origin_box <- box_1
# Number of targets
n_targets = length(to)
# Add transfer terms to listed compartments
for (target in to) {
if (!target %in% obs_vars) stop("You did not specify a submodel for target variable ", target)
target_box <- switch(spec[[target]]$type,
SFO = target,
IORE = target,
SFORB = paste(target, "free", sep = "_"))
if (use_of_ff == "min" && spec[[varname]]$type %in% c("SFO", "SFORB"))
{
k_from_to <- paste("k", origin_box, target_box, sep = "_")
parms <- c(parms, k_from_to)
diffs[[origin_box]] <- paste(diffs[[origin_box]], "-",
k_from_to, "*", origin_box)
diffs[[target_box]] <- paste(diffs[[target_box]], "+",
k_from_to, "*", origin_box)
} else {
# Do not introduce a formation fraction if this is the only target
if (spec[[varname]]$sink == FALSE && n_targets == 1) {
diffs[[target_box]] <- paste(diffs[[target_box]], "+",
decline_term)
} else {
fraction_to_target = paste("f", origin_box, "to", target, sep = "_")
parms <- c(parms, fraction_to_target)
diffs[[target_box]] <- paste(diffs[[target_box]], "+",
fraction_to_target, "*", decline_term)
}
}
}
} #}}}
} #}}}
model <- list(diffs = diffs, parms = parms, map = map, spec = spec, use_of_ff = use_of_ff)
# Create coefficient matrix if possible #{{{
if (mat) {
boxes <- names(diffs)
n <- length(boxes)
m <- matrix(nrow=n, ncol=n, dimnames=list(boxes, boxes))
if (use_of_ff == "min") { # {{{ Minimum use of formation fractions
for (from in boxes) {
for (to in boxes) {
if (from == to) { # diagonal elements
k.candidate = paste("k", from, c(boxes, "sink"), sep = "_")
k.candidate = sub("free.*bound", "free_bound", k.candidate)
k.candidate = sub("bound.*free", "bound_free", k.candidate)
k.effective = intersect(model$parms, k.candidate)
m[from,to] = ifelse(length(k.effective) > 0,
paste("-", k.effective, collapse = " "), "0")
} else { # off-diagonal elements
k.candidate = paste("k", from, to, sep = "_")
if (sub("_free$", "", from) == sub("_bound$", "", to)) {
k.candidate = paste("k", sub("_free$", "_free_bound", from), sep = "_")
}
if (sub("_bound$", "", from) == sub("_free$", "", to)) {
k.candidate = paste("k", sub("_bound$", "_bound_free", from), sep = "_")
}
k.effective = intersect(model$parms, k.candidate)
m[to, from] = ifelse(length(k.effective) > 0,
k.effective, "0")
}
}
} # }}}
} else { # {{{ Use formation fractions where possible
for (from in boxes) {
for (to in boxes) {
if (from == to) { # diagonal elements
k.candidate = paste("k", from, sep = "_")
m[from,to] = ifelse(k.candidate %in% model$parms,
paste("-", k.candidate), "0")
if(grepl("_free", from)) { # add transfer to bound compartment for SFORB
m[from,to] = paste(m[from,to], "-", paste("k", from, "bound", sep = "_"))
}
if(grepl("_bound", from)) { # add backtransfer to free compartment for SFORB
m[from,to] = paste("- k", from, "free", sep = "_")
}
m[from,to] = m[from,to]
} else { # off-diagonal elements
f.candidate = paste("f", from, "to", to, sep = "_")
k.candidate = paste("k", from, to, sep = "_")
k.candidate = sub("free.*bound", "free_bound", k.candidate)
k.candidate = sub("bound.*free", "bound_free", k.candidate)
m[to, from] = ifelse(f.candidate %in% model$parms,
paste(f.candidate, " * k_", from, sep = ""),
ifelse(k.candidate %in% model$parms, k.candidate, "0"))
# Special case: singular pathway and no sink
if (spec[[from]]$sink == FALSE && length(spec[[from]]$to) == 1 && to %in% spec[[from]]$to) {
m[to, from] = paste("k", from, sep = "_")
}
}
}
}
} # }}}
model$coefmat <- m
}#}}}
# Try to create a function compiled from C code if there is more than one observed variable {{{
# and a compiler is available
if (length(obs_vars) > 1 & has_compiler()) {
# Translate the R code for the derivatives to C code
diffs.C <- paste(diffs, collapse = ";\n")
diffs.C <- paste0(diffs.C, ";")
# HS
diffs.C <- gsub(HS_decline, "(time <= tb ? k1 : k2)", diffs.C, fixed = TRUE)
for (i in seq_along(diffs)) {
state_var <- names(diffs)[i]
# IORE
if (state_var %in% obs_vars) {
if (spec[[state_var]]$type == "IORE") {
diffs.C <- gsub(paste0(state_var, "^N_", state_var),
paste0("pow(y[", i - 1, "], N_", state_var, ")"),
diffs.C, fixed = TRUE)
}
}
# Replace d_... terms by f[i-1]
# First line
pattern <- paste0("^d_", state_var)
replacement <- paste0("\nf[", i - 1, "]")
diffs.C <- gsub(pattern, replacement, diffs.C)
# Other lines
pattern <- paste0("\\nd_", state_var)
replacement <- paste0("\nf[", i - 1, "]")
diffs.C <- gsub(pattern, replacement, diffs.C)
# Replace names of observed variables by y[i],
# making the implicit assumption that the observed variables only occur after "* "
pattern <- paste0("\\* ", state_var)
replacement <- paste0("* y[", i - 1, "]")
diffs.C <- gsub(pattern, replacement, diffs.C)
}
derivs_sig <- signature(n = "integer", t = "numeric", y = "numeric",
f = "numeric", rpar = "numeric", ipar = "integer")
# Declare the time variable in the body of the function if it is used
derivs_code <- if (spec[[1]]$type %in% c("FOMC", "DFOP", "HS")) {
paste0("double time = *t;\n", diffs.C)
} else {
diffs.C
}
# Define the function initializing the parameters
npar <- length(parms)
initpar_code <- paste0(
"static double parms [", npar, "];\n",
paste0("#define ", parms, " parms[", 0:(npar - 1), "]\n", collapse = ""),
"\n",
"void initpar(void (* odeparms)(int *, double *)) {\n",
" int N = ", npar, ";\n",
" odeparms(&N, parms);\n",
"}\n\n")
# Try to build a shared library
cf <- try(cfunction(list(func = derivs_sig), derivs_code,
otherdefs = initpar_code,
verbose = verbose,
convention = ".C", language = "C"),
silent = TRUE)
if (!inherits(cf, "try-error")) {
if (!quiet) message("Successfully compiled differential equation model from auto-generated C code.")
model$cf <- cf
}
}
# }}}
# Attach a degradation function if an analytical solution is available
model$deg_func <- create_deg_func(spec, use_of_ff)
class(model) <- "mkinmod"
return(model)
}
#' Print mkinmod objects
#'
#' Print mkinmod objects in a way that the user finds his way to get to its
#' components.
#'
#' @param x An \code{\link{mkinmod}} object.
#' @param \dots Not used.
#' @examples
#'
#' m_synth_SFO_lin <- mkinmod(parent = list(type = "SFO", to = "M1"),
#' M1 = list(type = "SFO", to = "M2"),
#' M2 = list(type = "SFO"), use_of_ff = "max")
#'
#' print(m_synth_SFO_lin)
#'
#' @export
print.mkinmod <- function(x, ...) {
cat("<mkinmod> model generated with\n")
cat("Use of formation fractions $use_of_ff:", x$use_of_ff, "\n")
cat("Specification $spec:\n")
for (obs in names(x$spec)) {
cat("$", obs, "\n", sep = "")
spl <- x$spec[[obs]]
cat("$type:", spl$type)
if (!is.null(spl$to) && length(spl$to)) cat("; $to: ", paste(spl$to, collapse = ", "), sep = "")
cat("; $sink: ", spl$sink, sep = "")
if (!is.null(spl$full_name)) if (!is.na(spl$full_name)) cat("; $full_name:", spl$full_name)
cat("\n")
}
if (is.matrix(x$coefmat)) cat("Coefficient matrix $coefmat available\n")
if (!is.null(x$cf)) cat("Compiled model $cf available\n")
cat("Differential equations:\n")
nice_diffs <- gsub("^(d.*) =", "\\1/dt =", x[["diffs"]])
writeLines(strwrap(nice_diffs, exdent = 11))
}
# vim: set foldmethod=marker ts=2 sw=2 expandtab:
