# Copyright (C) 2017  Johannes Ranke

# Contact: jranke@uni-bremen.de
# This file is part of the R package pfm

# This program 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/>

#' Create a time series of decline data
#'
#' The time series starts with the amount specified for the first application.
#' This does not create objects of type \code{\link{ts}}.
#'
#' @param x When numeric, this is the half-life to be used for an exponential
#' decline. If x is an mkinfit object, the decline is calculated from this object
#' @param t_end End of the time series
#' @param res Resolution of the time series
#' @param ... Further arguments passed to methods
#' @importFrom stats filter frequency time ts
#' @export
#' @examples
#' # Only use a half-life
#' pred_0 <- one_box(10)
#' plot(pred_0)
#'
#' # Use a fitted mkinfit model
#' require(mkin)
#' fit <- mkinfit("FOMC", FOCUS_2006_C)
#' pred_1 <- one_box(fit)
#' plot(pred_1)
#'
#' # Use a model with more than one observed variable
#' m_2 <- mkinmod(parent = mkinsub("SFO", "m1"), m1 = mkinsub("SFO"))
#' fit_2 <- mkinfit(m_2, FOCUS_2006_D)
#' pred_2 <- one_box(fit_2)
#' plot(pred_2)
one_box <- function(x,
  t_end = 100, res = 0.01, ...)
{
  UseMethod("one_box")
}

#' @rdname one_box
#' @export
one_box.numeric <- function(x,
  t_end = 100, res = 0.01, ...)
{
  half_life = x
  k = log(2)/half_life
  t_out <- seq(0, t_end, by = res)
  raw <- matrix(exp( - k * t_out), ncol = 1)
  dimnames(raw) <- list(NULL, "parent")
  result <- ts(raw, 0, t_end, frequency = 1/res)
  class(result) <- c("one_box", "ts")
  return(result)
}

#' @rdname one_box
#' @importFrom mkin mkinpredict
#' @export
one_box.mkinfit <- function(x, t_end = 100, res = 0.01, ...) {
  fit <- x
  t_out = seq(0, t_end, by = res)
  odeini <- c(1, rep(0, length(fit$mkinmod$spec) - 1))
  names(odeini) <- names(fit$mkinmod$spec)
  if (length(fit$mkinmod$spec) == 1) solution_type = "analytical"
  else solution_type = "deSolve"

  tmp <- mkinpredict(fit$mkinmod, odeparms = fit$bparms.ode, odeini = odeini,
    outtimes = t_out, solution_type = solution_type)[-1]
  result <- ts(tmp, 0, t_end, frequency = 1/res)
  class(result) <- c("one_box", "ts")
  return(result)
}

#' Plot time series of decline data
#' 
#' @param x The object of type \code{\link{one_box}} to be plotted
#' @param xlim Limits for the x axis
#' @param ylim Limits for the y axis
#' @param xlab Label for the x axis
#' @param ylab Label for the y axis
#' @param max_twa If a numeric value is given, the maximum time weighted
#'   average concentration(s) is/are shown in the graph.
#' @param max_twa_var Variable for which the maximum time weighted average should
#'   be shown if max_twa is not NULL.
#' @param ... Further arguments passed to methods
#' @importFrom stats plot.ts
#' @export
#' @examples
#' plot(sawtooth(one_box(10), 3, 7), max_twa = 21)
plot.one_box <- function(x, 
                         xlim = range(time(x)), ylim = c(0, max(x)),
                         xlab = "Time", ylab = "Fraction of initial",
                         max_twa = NULL, max_twa_var = dimnames(x)[[2]][1], ...)
{
  obs_vars <- dimnames(x)[[2]]
  plot.ts(x, plot.type = "single", xlab = xlab, ylab = ylab,
          lty = 1:length(obs_vars), col = 1:length(obs_vars),
          las = 1, xlim = xlim, ylim = ylim)
  if (!is.null(max_twa)) {
    x_twa <- max_twa(x, window = max_twa)
    value <- x_twa$max[max_twa_var]
    rect(x_twa$window_start[max_twa_var], 0, 
         x_twa$window_end[max_twa_var], value, col = "grey")
    text(x_twa$window_end[max_twa_var], value, paste("Maximum:", signif(value, 3)), pos = 4)
    # Plot a second time to cover the grey rectangle
    matlines(time(x), as.matrix(x), lty = 1:length(obs_vars), col = 1:length(obs_vars))
  }
}

#' Create decline time series for multiple applications
#'
#' If the number of application cycles \code{n} is greater than 1, the
#' application pattern specified in \code{applications} is repeated \code{n}
#' times, with an interval \code{i}.
#' @param x A \code{\link{one_box}} object
#' @param n The number of applications. If \code{applications} is specified, \code{n} is not used
#' @param i The interval between applications. If \code{applications} is specified, \code{i} 
#'   is not used
#' @param applications A data frame holding the application times in the first column and
#'   the corresponding amounts applied in the second column for each application cycle.
#'   If \code{n} is one, the application pattern specified here is used only once.
#' @export
#' @examples
#' applications = data.frame(time = seq(0, 14, by = 7), amount = c(1, 2, 3))
#' pred <- one_box(10)
#' plot(sawtooth(pred, applications = applications))
#'
#' m_2 <- mkinmod(parent = mkinsub("SFO", "m1"), m1 = mkinsub("SFO"))
#' fit_2 <- mkinfit(m_2, FOCUS_2006_D)
#' pred_2 <- one_box(fit_2)
#' pred_2_saw <- sawtooth(pred_2, 2, 7)
#' plot(pred_2_saw, max_twa = 21, max_twa_var = "m1")
#'
#' max_twa(pred_2_saw)
sawtooth <- function(x, n = 1, i = 365, 
                     applications = data.frame(time = seq(0, 0 + n * i, length.out = n), 
                                               amount = 1))
{
  n_obs = ncol(as.matrix(x))
  t_end = max(time(x))
  freq = frequency(x)
  empty <- ts(matrix(0, nrow = t_end * freq, ncol = n_obs), 0, t_end, freq)
  result <- empty
  for (i_app in 1:nrow(applications)) {
    t_app <- applications[i_app, "time"]
    amount_app <- applications[i_app, "amount"]
    if (t_app == 0) {
      result <- result + x * amount_app
    } else {
      lag_phase <- as.matrix(empty)[1:(t_app * freq), , drop = FALSE]
      app_phase <- amount_app * as.matrix(x)[1:((t_end - t_app) * freq + 1), , drop = FALSE]
      app_ts <- ts(rbind(lag_phase, app_phase), 0, t_end, frequency = freq)
      result <- result + app_ts
    }
  }
  class(result) = c("one_box", "ts")
  dimnames(result) <- dimnames(x)
  return(result)
}

#' Calculate a time weighted average concentration
#'
#' The moving average is built only using the values in the past, so
#' the earliest possible time for the maximum in the time series returned
#' is after one window has passed.
#'
#' @param x An object of type \code{\link{one_box}}
#' @param window The size of the moving window
#' @seealso max_twa
#' @export
#' @examples
#' pred <- sawtooth(one_box(10),
#'   applications = data.frame(time = c(0, 7), amount = c(1, 1)))
#' max_twa(pred)
twa <- function(x, window = 21) UseMethod("twa")

#' @rdname twa
#' @export
twa.one_box <- function(x, window = 21)
{
  resolution = 1/frequency(x)
  n_filter = window/resolution
  result = filter(x, rep(1/n_filter, n_filter), method = "convolution", sides = 1)
  class(result) = c("one_box", "ts")
  dimnames(result) <- dimnames(x)
  return(result)
}

#' The maximum time weighted average concentration for a moving window
#' 
#' @seealso twa
#' @inheritParams twa
#' @export
max_twa <- function(x, window = 21) UseMethod("max_twa")

#' @export
max_twa.one_box <- function(x, window = 21)
{
  freq = frequency(x)

  twa_ts <- twa(x, window = window)
  window_end <- apply(twa_ts, 2, which.max) / freq
  result <- list()
  result$max <- apply(twa_ts, 2, max, na.rm = TRUE)
  result$window_start <- window_end - window
  result$window_end <- window_end
  return(result)
}