First automatic generation of an nlme model

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+#' Estimation of parameter distributions from mmkin row objects
+#'
+#' This function sets up and attempts to fit a mixed effects model to
+#' an mmkin row object which is essentially a list of mkinfit objects
+#' that have been obtained by fitting the same model to a list of
+#' datasets.
+#'
+#' @param object An mmkin row object containing several fits of the same model to different datasets
+#' @param ... Additional arguments passed to \code{\link{nlme}}
+#' @importFrom nlme nlme
+#' @return A fitted object of class 'memkin'
+#' @examples
+#' sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
+#' m_SFO <- mkinmod(parent = mkinsub("SFO"))
+#' d_SFO_1 <- mkinpredict(m_SFO,
+#'   c(k_parent_sink = 0.1),
+#'   c(parent = 98), sampling_times)
+#' d_SFO_1_long <- mkin_wide_to_long(d_SFO_1, time = "time")
+#' d_SFO_2 <- mkinpredict(m_SFO,
+#'   c(k_parent_sink = 0.05),
+#'   c(parent = 102), sampling_times)
+#' d_SFO_2_long <- mkin_wide_to_long(d_SFO_2, time = "time")
+#' d_SFO_3 <- mkinpredict(m_SFO,
+#'   c(k_parent_sink = 0.02),
+#'   c(parent = 103), sampling_times)
+#' d_SFO_3_long <- mkin_wide_to_long(d_SFO_3, time = "time")
+#'
+#' d1 <- add_err(d_SFO_1, function(value) 3, n = 1)
+#' d2 <- add_err(d_SFO_2, function(value) 2, n = 1)
+#' d3 <- add_err(d_SFO_3, function(value) 4, n = 1)
+#' ds <- c(d1 = d1, d2 = d2, d3 = d3)
+#'
+#' f <- mmkin("SFO", ds)
+#' x <- memkin(f)
+#'
+#' @export
+memkin <- function(object, ...) {
+  if (nrow(object) > 1) stop("Only row objects allowed")
+  ds_names <- colnames(object)
+
+  p_mat_start_trans <- sapply(object, parms, transformed = TRUE)
+  colnames(p_mat_start_trans) <- ds_names
+
+  p_names_mean_function <- setdiff(rownames(p_mat_start_trans), names(object[[1]]$errparms))
+  p_start_mean_function <- apply(p_mat_start_trans[p_names_mean_function, ], 1, mean)
+
+  ds_list <- lapply(object, function(x) x$data[c("time", "variable", "observed")])
+  names(ds_list) <- ds_names
+  ds_nlme <- purrr::map_dfr(ds_list, function(x) x, .id = "ds")
+  ds_nlme_grouped <- groupedData(observed ~ time | ds, ds_nlme)
+
+  mkin_model <- object[[1]]$mkinmod
+
+  # Inspired by https://stackoverflow.com/a/12983961/3805440
+  # and https://stackoverflow.com/a/26280789/3805440
+  model_function_alist <- replicate(length(p_names_mean_function) + 2, substitute())
+  names(model_function_alist) <- c("name", "time", p_names_mean_function)
+
+
+
+  model_function_body <- quote({
+    arg_frame <- as.data.frame(as.list((environment())))
+    res <- parent_0 * exp( - exp(log_k_parent_sink) * time)
+    dump(c("arg_frame", "res"), file = "out_1.txt", append = TRUE)
+    return(res)
+  })
+  model_function <- as.function(c(model_function_alist, model_function_body))
+  f_nlme <- eval(parse(text = nlme_call_text))
+
+  model_function_body <- quote({
+    arg_frame <- as.data.frame(as.list((environment())))
+
+    res_frame <- arg_frame[1:2]
+
+    parm_frame <- arg_frame[-(1:2)]
+    parms_unique <- unique(parm_frame)
+
+    n_unique <- nrow(parms_unique)
+
+    times_ds <- list()
+    names_ds <- list()
+    for (i in 1:n_unique) {
+      times_ds[[i]] <-
+        arg_frame[which(arg_frame[[3]] == parms_unique[i, 1]), "time"]
+      names_ds[[i]] <-
+        arg_frame[which(arg_frame[[3]] == parms_unique[i, 1]), "name"]
+    }
+
+    res_list <- lapply(1:n_unique, function(x) {
+      parms <- unlist(parms_unique[x, , drop = TRUE])
+      odeini_parm_names <- grep('_0$', names(parms), value = TRUE)
+      odeparm_names <- setdiff(names(parms), odeini_parm_names)
+      odeini <- parms[odeini_parm_names]
+      names(odeini) <- gsub('_0$', '', odeini_parm_names)
+      odeparms <- backtransform_odeparms(parms[odeparm_names], mkin_model) # TBD rates/fractions
+      out_wide <- mkinpredict(mkin_model, odeparms = odeparms,
+        solution_type = "analytical",
+        odeini = odeini, outtimes = unique(times_ds[[x]]))
+      out_array <- out_wide[, -1, drop = FALSE]
+      rownames(out_array) <- as.character(unique(times_ds[[x]]))
+      out_times <- as.character(times_ds[[x]])
+      out_names <- names_ds[[x]]
+      out_values <- mapply(function(times, names) out_array[times, names],
+        out_times, out_names)
+      return(as.numeric(out_values))
+    })
+    res <- unlist(res_list)
+    #dump(c("arg_frame", "res"), file = "out_2.txt", append = TRUE)
+    return(res)
+  })
+  model_function <- as.function(c(model_function_alist, model_function_body))
+  debug(model_function)
+  f_nlme <- eval(parse(text = nlme_call_text))
+
+  undebug(model_function)
+
+  model_function(c(0, 0, 100), parent_0 = 100, log_k_parent_sink = log(0.1))
+
+  nlme_call_text <- paste0(
+    "nlme(observed ~ model_function(variable, time, ",
+      paste(p_names_mean_function, collapse = ", "), "),\n",
+    "  data = ds_nlme_grouped,\n",
+    "  fixed = ", paste(p_names_mean_function, collapse = " + "), " ~ 1,\n",
+    "  random = pdDiag(", paste(p_names_mean_function, collapse = " + "), " ~ 1),\n",
+    #"  start = c(parent_0 = 100, log_k_parent_sink = log(0.1)), verbose = TRUE)\n")
+    #"  start = p_start_mean_function)\n")
+    "  start = p_start_mean_function, verbose = TRUE)\n")
+  cat(nlme_call_text)
+
+  f_nlme <- eval(parse(text = nlme_call_text))
+
+  return(f_nlme)
+}