# Copyright (C) 2010-2015 Johannes Ranke
# Portions of this code are copyright (C) 2013 Eurofins Regulatory AG
# Contact: jranke@uni-bremen.de
# The summary function is an adapted and extended version of summary.modFit
# from the FME package, v 1.1 by Soetart and Petzoldt, which was in turn
# inspired by summary.nls.lm
# This file is part of the R package mkin
# mkin is free software: you can redistribute it and/or modify it under the
# terms of the GNU General Public License as published by the Free Software
# Foundation, either version 3 of the License, or (at your option) any later
# version.
# This program is distributed in the hope that it will be useful, but WITHOUT
# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
# FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
# details.
# You should have received a copy of the GNU General Public License along with
# this program. If not, see <http://www.gnu.org/licenses/>
if(getRversion() >= '2.15.1') utils::globalVariables(c("name", "value"))
mkinfit <- function(mkinmod, observed,
parms.ini = "auto",
state.ini = "auto",
fixed_parms = NULL,
fixed_initials = names(mkinmod$diffs)[-1],
solution_type = c("auto", "analytical", "eigen", "deSolve", "odeintr"),
method.ode = "lsoda",
method.modFit = c("Port", "Marq", "SANN", "Nelder-Mead", "BFGS", "CG", "L-BFGS-B"),
maxit.modFit = "auto",
control.modFit = list(),
transform_rates = TRUE,
transform_fractions = TRUE,
plot = FALSE, quiet = FALSE,
err = NULL, weight = "none", scaleVar = FALSE,
atol = 1e-8, rtol = 1e-10, n.outtimes = 100,
reweight.method = NULL,
reweight.tol = 1e-8, reweight.max.iter = 10,
trace_parms = FALSE,
...)
{
# Check mkinmod and generate a model for the variable whith the highest value
# if a suitable string is given
parent_models_available = c("SFO", "FOMC", "DFOP", "HS", "SFORB", "IORE")
if (class(mkinmod) != "mkinmod") {
presumed_parent_name = observed[which.max(observed$value), "name"]
if (mkinmod[[1]] %in% parent_models_available) {
speclist <- list(list(type = mkinmod, sink = TRUE))
names(speclist) <- presumed_parent_name
mkinmod <- mkinmod(speclist = speclist)
} else {
stop("Argument mkinmod must be of class mkinmod or a string containing one of\n ",
paste(parent_models_available, collapse = ", "))
}
}
# Check optimisation method and set maximum number of iterations if specified
method.modFit = match.arg(method.modFit)
if (maxit.modFit != "auto") {
if (method.modFit == "Marq") control.modFit$maxiter = maxit.modFit
if (method.modFit == "Port") {
control.modFit$iter.max = maxit.modFit
control.modFit$eval.max = maxit.modFit
}
if (method.modFit %in% c("SANN", "Nelder-Mead", "BFGS", "CG", "L-BFGS-B")) {
control.modFit$maxit = maxit.modFit
}
}
# Get the names of the state variables in the model
mod_vars <- names(mkinmod$diffs)
# Get the names of observed variables
obs_vars <- names(mkinmod$spec)
# Subset observed data with names of observed data in the model
observed <- subset(observed, name %in% obs_vars)
# Define starting values for parameters where not specified by the user
if (parms.ini[[1]] == "auto") parms.ini = vector()
# Prevent inital parameter specifications that are not in the model
wrongpar.names <- setdiff(names(parms.ini), mkinmod$parms)
if (length(wrongpar.names) > 0) {
stop("Initial parameter(s) ", paste(wrongpar.names, collapse = ", "),
" not used in the model")
}
# Warn that the sum of formation fractions may exceed one if they are not
# fitted in the transformed way
if (mkinmod$use_of_ff == "max" & transform_fractions == FALSE) {
warning("The sum of formation fractions may exceed one if you do not use ",
"transform_fractions = TRUE." )
for (box in mod_vars) {
# Stop if formation fractions are not transformed and we have no sink
if (mkinmod$spec[[box]]$sink == FALSE) {
stop("If formation fractions are not transformed during the fitting, ",
"it is not supported to turn off pathways to sink.\n ",
"Consider turning on the transformation of formation fractions or ",
"setting up a model with use_of_ff = 'min'.\n")
}
}
}
# Do not allow fixing formation fractions if we are using the ilr transformation,
# this is not supported
if (transform_fractions == TRUE && length(fixed_parms) > 0) {
if (grepl("^f_", fixed_parms)) {
stop("Fixing formation fractions is not supported when using the ilr ",
"transformation.")
}
}
# Set initial parameter values, including a small increment (salt)
# to avoid linear dependencies (singular matrix) in Eigenvalue based solutions
k_salt = 0
defaultpar.names <- setdiff(mkinmod$parms, names(parms.ini))
for (parmname in defaultpar.names) {
# Default values for rate constants, depending on the parameterisation
if (grepl("^k", parmname)) {
parms.ini[parmname] = 0.1 + k_salt
k_salt = k_salt + 1e-4
}
# Default values for rate constants for reversible binding
if (grepl("free_bound$", parmname)) parms.ini[parmname] = 0.1
if (grepl("bound_free$", parmname)) parms.ini[parmname] = 0.02
# Default values for IORE exponents
if (grepl("^N", parmname)) parms.ini[parmname] = 1
# Default values for the FOMC, DFOP and HS models
if (parmname == "alpha") parms.ini[parmname] = 1
if (parmname == "beta") parms.ini[parmname] = 10
if (parmname == "k1") parms.ini[parmname] = 0.1
if (parmname == "k2") parms.ini[parmname] = 0.01
if (parmname == "tb") parms.ini[parmname] = 5
if (parmname == "g") parms.ini[parmname] = 0.5
}
# Default values for formation fractions in case they are present
for (box in mod_vars) {
f_names <- mkinmod$parms[grep(paste0("^f_", box), mkinmod$parms)]
if (length(f_names) > 0) {
# We need to differentiate between default and specified fractions
# and set the unspecified to 1 - sum(specified)/n_unspecified
f_default_names <- intersect(f_names, defaultpar.names)
f_specified_names <- setdiff(f_names, defaultpar.names)
sum_f_specified = sum(parms.ini[f_specified_names])
if (sum_f_specified > 1) {
stop("Starting values for the formation fractions originating from ",
box, " sum up to more than 1.")
}
if (mkinmod$spec[[box]]$sink) n_unspecified = length(f_default_names) + 1
else {
n_unspecified = length(f_default_names)
}
parms.ini[f_default_names] <- (1 - sum_f_specified) / n_unspecified
}
}
# Set default for state.ini if appropriate
parent_name = names(mkinmod$spec)[[1]]
if (state.ini[1] == "auto") {
parent_time_0 = subset(observed, time == 0 & name == parent_name)$value
parent_time_0_mean = mean(parent_time_0, na.rm = TRUE)
if (is.na(parent_time_0_mean)) {
state.ini = c(100, rep(0, length(mkinmod$diffs) - 1))
} else {
state.ini = c(parent_time_0_mean, rep(0, length(mkinmod$diffs) - 1))
}
}
# Name the inital state variable values if they are not named yet
if(is.null(names(state.ini))) names(state.ini) <- mod_vars
# Transform initial parameter values for fitting
transparms.ini <- transform_odeparms(parms.ini, mkinmod,
transform_rates = transform_rates,
transform_fractions = transform_fractions)
# Parameters to be optimised:
# Kinetic parameters in parms.ini whose names are not in fixed_parms
parms.fixed <- parms.ini[fixed_parms]
parms.optim <- parms.ini[setdiff(names(parms.ini), fixed_parms)]
transparms.fixed <- transform_odeparms(parms.fixed, mkinmod,
transform_rates = transform_rates,
transform_fractions = transform_fractions)
transparms.optim <- transform_odeparms(parms.optim, mkinmod,
transform_rates = transform_rates,
transform_fractions = transform_fractions)
# Inital state variables in state.ini whose names are not in fixed_initials
state.ini.fixed <- state.ini[fixed_initials]
state.ini.optim <- state.ini[setdiff(names(state.ini), fixed_initials)]
# Preserve names of state variables before renaming initial state variable
# parameters
state.ini.optim.boxnames <- names(state.ini.optim)
state.ini.fixed.boxnames <- names(state.ini.fixed)
if(length(state.ini.optim) > 0) {
names(state.ini.optim) <- paste(names(state.ini.optim), "0", sep="_")
}
if(length(state.ini.fixed) > 0) {
names(state.ini.fixed) <- paste(names(state.ini.fixed), "0", sep="_")
}
# Decide if the solution of the model can be based on a simple analytical
# formula, the spectral decomposition of the matrix (fundamental system)
# or a numeric ode solver from the deSolve package
# Prefer odeintr if a compiled model is present
solution_type = match.arg(solution_type)
if (solution_type == "analytical" && length(mkinmod$spec) > 1)
stop("Analytical solution not implemented for models with metabolites.")
if (solution_type == "eigen" && !is.matrix(mkinmod$coefmat))
stop("Eigenvalue based solution not possible, coefficient matrix not present.")
if (solution_type == "auto") {
if (length(mkinmod$spec) == 1) {
solution_type = "analytical"
} else {
if (!is.null(mkinmod$e$m)) {
solution_type = "odeintr"
if (!missing(atol) | !missing(rtol)) {
message("When fitting with solution type odeintr, atol and rtol can only be set in the call to mkinmod()")
}
} else {
if (is.matrix(mkinmod$coefmat)) {
solution_type = "eigen"
if (max(observed$value, na.rm = TRUE) < 0.1) {
stop("The combination of small observed values (all < 0.1) and solution_type = eigen is error-prone")
}
} else {
solution_type = "deSolve"
}
}
}
}
cost.old <- 1e100 # The first model cost should be smaller than this value
calls <- 0 # Counter for number of model solutions
out_predicted <- NA
# Define the model cost function
cost <- function(P)
{
assign("calls", calls+1, inherits=TRUE) # Increase the model solution counter
# Trace parameter values if requested
if(trace_parms) cat(P, "\n")
# Time points at which observed data are available
# Make sure we include time 0, so initial values for state variables are for time 0
outtimes = sort(unique(c(observed$time, seq(min(observed$time),
max(observed$time),
length.out = n.outtimes))))
if(length(state.ini.optim) > 0) {
odeini <- c(P[1:length(state.ini.optim)], state.ini.fixed)
names(odeini) <- c(state.ini.optim.boxnames, state.ini.fixed.boxnames)
} else {
odeini <- state.ini.fixed
names(odeini) <- state.ini.fixed.boxnames
}
odeparms <- c(P[(length(state.ini.optim) + 1):length(P)], transparms.fixed)
parms <- backtransform_odeparms(odeparms, mkinmod,
transform_rates = transform_rates,
transform_fractions = transform_fractions)
# Solve the system with current transformed parameter values
out <- mkinpredict(mkinmod, parms,
odeini, outtimes,
solution_type = solution_type,
method.ode = method.ode,
atol.deSolve = atol, rtol.deSolve = rtol, ...)
assign("out_predicted", out, inherits=TRUE)
mC <- modCost(out, observed, y = "value",
err = err, weight = weight, scaleVar = scaleVar)
# Report and/or plot if the model is improved
if (mC$model < cost.old) {
if(!quiet) cat("Model cost at call ", calls, ": ", mC$model, "\n")
# Plot the data and current model output if requested
if(plot) {
outtimes_plot = seq(min(observed$time), max(observed$time), length.out=100)
out_plot <- mkinpredict(mkinmod, parms,
odeini, outtimes_plot,
solution_type = solution_type,
method.ode = method.ode,
atol.deSolve = atol, rtol.deSolve = rtol, ...)
plot(0, type="n",
xlim = range(observed$time), ylim = c(0, max(observed$value, na.rm=TRUE)),
xlab = "Time", ylab = "Observed")
col_obs <- pch_obs <- 1:length(obs_vars)
lty_obs <- rep(1, length(obs_vars))
names(col_obs) <- names(pch_obs) <- names(lty_obs) <- obs_vars
for (obs_var in obs_vars) {
points(subset(observed, name == obs_var, c(time, value)),
pch = pch_obs[obs_var], col = col_obs[obs_var])
}
matlines(out_plot$time, out_plot[-1], col = col_obs, lty = lty_obs)
legend("topright", inset=c(0.05, 0.05), legend=obs_vars,
col=col_obs, pch=pch_obs, lty=1:length(pch_obs))
}
assign("cost.old", mC$model, inherits=TRUE)
}
return(mC)
}
lower <- rep(-Inf, length(c(state.ini.optim, transparms.optim)))
upper <- rep(Inf, length(c(state.ini.optim, transparms.optim)))
names(lower) <- names(upper) <- c(names(state.ini.optim), names(transparms.optim))
if (!transform_rates) {
index_k <- grep("^k_", names(lower))
lower[index_k] <- 0
index_k__iore <- grep("^k__iore_", names(lower))
lower[index_k__iore] <- 0
other_rate_parms <- intersect(c("alpha", "beta", "k1", "k2", "tb"), names(lower))
lower[other_rate_parms] <- 0
}
if (!transform_fractions) {
index_f <- grep("^f_", names(upper))
lower[index_f] <- 0
upper[index_f] <- 1
other_fraction_parms <- intersect(c("g"), names(upper))
lower[other_fraction_parms] <- 0
upper[other_fraction_parms] <- 1
}
# Do the fit and take the time
fit_time <- system.time({
fit <- modFit(cost, c(state.ini.optim, transparms.optim),
method = method.modFit, control = control.modFit,
lower = lower, upper = upper, ...)
# Reiterate the fit until convergence of the variance components (IRLS)
# if requested by the user
weight.ini = weight
if (!is.null(err)) weight.ini = "manual"
if (!is.null(reweight.method)) {
if (reweight.method != "obs") stop("Only reweighting method 'obs' is implemented")
if(!quiet) {
cat("IRLS based on variance estimates for each observed variable\n")
}
if (!quiet) {
cat("Initial variance estimates are:\n")
print(signif(fit$var_ms_unweighted, 8))
}
reweight.diff = 1
n.iter <- 0
if (!is.null(err)) observed$err.ini <- observed[[err]]
err = "err.irls"
while (reweight.diff > reweight.tol & n.iter < reweight.max.iter) {
n.iter <- n.iter + 1
sigma.old <- sqrt(fit$var_ms_unweighted)
observed[err] <- sqrt(fit$var_ms_unweighted)[as.character(observed$name)]
fit <- modFit(cost, fit$par, method = method.modFit,
control = control.modFit, lower = lower, upper = upper, ...)
reweight.diff = sum((sqrt(fit$var_ms_unweighted) - sigma.old)^2)
if (!quiet) {
cat("Iteration", n.iter, "yields variance estimates:\n")
print(signif(fit$var_ms_unweighted, 8))
cat("Sum of squared differences to last variance estimates:",
signif(reweight.diff, 2), "\n")
}
}
}
})
# Check for convergence
if (method.modFit == "Marq") {
if (!fit$info %in% c(1, 2, 3)) {
fit$warning = paste0("Optimisation by method ", method.modFit,
" did not converge.\n",
"The message returned by nls.lm is:\n",
fit$message)
warning(fit$warning)
}
else {
if(!quiet) cat("Optimisation by method", method.modFit, "successfully terminated.\n")
}
}
if (method.modFit %in% c("Port", "SANN", "Nelder-Mead", "BFGS", "CG", "L-BFGS-B")) {
if (fit$convergence != 0) {
fit$warning = paste0("Optimisation by method ", method.modFit,
" did not converge.\n",
"Convergence code is ", fit$convergence,
ifelse(is.null(fit$message), "",
paste0("\nMessage is ", fit$message)))
warning(fit$warning)
} else {
if(!quiet) cat("Optimisation by method", method.modFit, "successfully terminated.\n")
}
}
# Return number of iterations for SANN method
if (method.modFit == "SANN") {
fit$iter = maxit.modFit
if(!quiet) cat("Termination of the SANN algorithm does not imply convergence.\n")
}
# We need to return some more data for summary and plotting
fit$solution_type <- solution_type
fit$transform_rates <- transform_rates
fit$transform_fractions <- transform_fractions
fit$method.modFit <- method.modFit
fit$maxit.modFit <- maxit.modFit
fit$calls <- calls
fit$time <- fit_time
# We also need the model for summary and plotting
fit$mkinmod <- mkinmod
# We need data and predictions for summary and plotting
fit$observed <- observed
fit$obs_vars <- obs_vars
fit$predicted <- mkin_wide_to_long(out_predicted, time = "time")
# Backtransform parameters
bparms.optim = backtransform_odeparms(fit$par, fit$mkinmod,
transform_rates = transform_rates,
transform_fractions = transform_fractions)
bparms.fixed = c(state.ini.fixed, parms.fixed)
bparms.all = c(bparms.optim, parms.fixed)
# Collect initial parameter values in three dataframes
fit$start <- data.frame(value = c(state.ini.optim,
parms.optim))
fit$start$type = c(rep("state", length(state.ini.optim)),
rep("deparm", length(parms.optim)))
fit$start_transformed = data.frame(
value = c(state.ini.optim, transparms.optim),
lower = lower,
upper = upper)
fit$fixed <- data.frame(value = c(state.ini.fixed, parms.fixed))
fit$fixed$type = c(rep("state", length(state.ini.fixed)),
rep("deparm", length(parms.fixed)))
# Collect observed, predicted, residuals and weighting
data <- merge(fit$observed, fit$predicted, by = c("time", "name"))
data$name <- ordered(data$name, levels = obs_vars)
data <- data[order(data$name, data$time), ]
fit$data <- data.frame(time = data$time,
variable = data$name,
observed = data$value.x,
predicted = data$value.y)
fit$data$residual <- fit$data$observed - fit$data$predicted
if (!is.null(data$err.ini)) fit$data$err.ini <- data$err.ini
if (!is.null(err)) fit$data[[err]] <- data[[err]]
fit$atol <- atol
fit$rtol <- rtol
fit$weight.ini <- weight.ini
fit$reweight.method <- reweight.method
fit$reweight.tol <- reweight.tol
fit$reweight.max.iter <- reweight.max.iter
# Return different sets of backtransformed parameters for summary and plotting
fit$bparms.optim <- bparms.optim
fit$bparms.fixed <- bparms.fixed
# Return ode and state parameters for further fitting
fit$bparms.ode <- bparms.all[mkinmod$parms]
fit$bparms.state <- c(bparms.all[setdiff(names(bparms.all), names(fit$bparms.ode))],
state.ini.fixed)
names(fit$bparms.state) <- gsub("_0$", "", names(fit$bparms.state))
fit$date <- date()
class(fit) <- c("mkinfit", "modFit")
return(fit)
}
summary.mkinfit <- function(object, data = TRUE, distimes = TRUE, alpha = 0.05, ...) {
param <- object$par
pnames <- names(param)
bpnames <- names(object$bparms.optim)
p <- length(param)
mod_vars <- names(object$mkinmod$diffs)
covar <- try(solve(0.5*object$hessian), silent = TRUE) # unscaled covariance
rdf <- object$df.residual
resvar <- object$ssr / rdf
if (!is.numeric(covar)) {
covar <- NULL
se <- lci <- uci <- tval <- pval1 <- pval2 <- rep(NA, p)
} else {
rownames(covar) <- colnames(covar) <- pnames
se <- sqrt(diag(covar) * resvar)
lci <- param + qt(alpha/2, rdf) * se
uci <- param + qt(1-alpha/2, rdf) * se
tval <- param/se
pval1 <- 2 * pt(abs(tval), rdf, lower.tail = FALSE)
pval2 <- pt(abs(tval), rdf, lower.tail = FALSE)
}
names(se) <- pnames
modVariance <- object$ssr / length(object$residuals)
param <- cbind(param, se, lci, uci, tval, pval1, pval2)
dimnames(param) <- list(pnames, c("Estimate", "Std. Error", "Lower", "Upper",
"t value", "Pr(>|t|)", "Pr(>t)"))
bparam <- cbind(Estimate = object$bparms.optim, Lower = NA, Upper = NA)
# Transform boundaries of CI for one parameter at a time,
# with the exception of sets of formation fractions (single fractions are OK).
f_names_skip <- character(0)
for (box in mod_vars) { # Figure out sets of fractions to skip
f_names <- grep(paste("^f", box, sep = "_"), pnames, value = TRUE)
n_paths <- length(f_names)
if (n_paths > 1) f_names_skip <- c(f_names_skip, f_names)
}
for (pname in pnames) {
if (!pname %in% f_names_skip) {
par.lower <- param[pname, "Lower"]
par.upper <- param[pname, "Upper"]
names(par.lower) <- names(par.upper) <- pname
bpl <- backtransform_odeparms(par.lower, object$mkinmod,
object$transform_rates,
object$transform_fractions)
bpu <- backtransform_odeparms(par.upper, object$mkinmod,
object$transform_rates,
object$transform_fractions)
bparam[names(bpl), "Lower"] <- bpl
bparam[names(bpu), "Upper"] <- bpu
}
}
ans <- list(
version = as.character(packageVersion("mkin")),
Rversion = paste(R.version$major, R.version$minor, sep="."),
date.fit = object$date,
date.summary = date(),
solution_type = object$solution_type,
method.modFit = object$method.modFit,
warning = object$warning,
use_of_ff = object$mkinmod$use_of_ff,
weight.ini = object$weight.ini,
reweight.method = object$reweight.method,
residuals = object$residuals,
residualVariance = resvar,
sigma = sqrt(resvar),
modVariance = modVariance,
df = c(p, rdf),
cov.unscaled = covar,
cov.scaled = covar * resvar,
info = object$info,
niter = object$iterations,
calls = object$calls,
time = object$time,
stopmess = message,
par = param,
bpar = bparam)
ans$diffs <- object$mkinmod$diffs
if(data) ans$data <- object$data
ans$start <- object$start
ans$start_transformed <- object$start_transformed
ans$fixed <- object$fixed
ans$errmin <- mkinerrmin(object, alpha = 0.05)
ans$bparms.ode <- object$bparms.ode
ep <- endpoints(object)
if (length(ep$ff) != 0)
ans$ff <- ep$ff
if(distimes) ans$distimes <- ep$distimes
if(length(ep$SFORB) != 0) ans$SFORB <- ep$SFORB
class(ans) <- c("summary.mkinfit", "summary.modFit")
return(ans)
}
# Expanded from print.summary.modFit
print.summary.mkinfit <- function(x, digits = max(3, getOption("digits") - 3), ...) {
cat("mkin version: ", x$version, "\n")
cat("R version: ", x$Rversion, "\n")
cat("Date of fit: ", x$date.fit, "\n")
cat("Date of summary:", x$date.summary, "\n")
if (!is.null(x$warning)) cat("\n\nWarning:", x$warning, "\n\n")
cat("\nEquations:\n")
writeLines(strwrap(x[["diffs"]], exdent = 11))
df <- x$df
rdf <- df[2]
cat("\nModel predictions using solution type", x$solution_type, "\n")
cat("\nFitted with method", x$method.modFit,
"using", x$calls, "model solutions performed in", x$time[["elapsed"]], "s\n")
cat("\nWeighting:", x$weight.ini)
if(!is.null(x$reweight.method)) cat(" then iterative reweighting method",
x$reweight.method)
cat("\n")
cat("\nStarting values for parameters to be optimised:\n")
print(x$start)
cat("\nStarting values for the transformed parameters actually optimised:\n")
print(x$start_transformed)
cat("\nFixed parameter values:\n")
if(length(x$fixed$value) == 0) cat("None\n")
else print(x$fixed)
cat("\nOptimised, transformed parameters:\n")
print(signif(x$par, digits = digits))
if (x$calls > 0) {
cat("\nParameter correlation:\n")
if (!is.null(x$cov.unscaled)){
Corr <- cov2cor(x$cov.unscaled)
rownames(Corr) <- colnames(Corr) <- rownames(x$par)
print(Corr, digits = digits, ...)
} else {
cat("Could not estimate covariance matrix; singular system:\n")
}
}
cat("\nResidual standard error:",
format(signif(x$sigma, digits)), "on", rdf, "degrees of freedom\n")
cat("\nBacktransformed parameters:\n")
print(signif(x$bpar, digits = digits))
cat("\nChi2 error levels in percent:\n")
x$errmin$err.min <- 100 * x$errmin$err.min
print(x$errmin, digits=digits,...)
printSFORB <- !is.null(x$SFORB)
if(printSFORB){
cat("\nEstimated Eigenvalues of SFORB model(s):\n")
print(x$SFORB, digits=digits,...)
}
printff <- !is.null(x$ff)
if(printff){
cat("\nResulting formation fractions:\n")
print(data.frame(ff = x$ff), digits=digits,...)
}
printdistimes <- !is.null(x$distimes)
if(printdistimes){
cat("\nEstimated disappearance times:\n")
print(x$distimes, digits=digits,...)
}
printdata <- !is.null(x$data)
if (printdata){
cat("\nData:\n")
print(format(x$data, digits = digits, ...), row.names = FALSE)
}
invisible(x)
}
# vim: set ts=2 sw=2 expandtab:
