如何在ode求解器中添加具有矩阵数据的事件

Question

我有一个在交互网络上运行的微分方程模型。 节点连接到食物，并可以以取决于食物大小的速率获取食物（请参阅第一段代码）。

changes <- function(t, state_a, parameters){
      with(as.list(c(state_a, parameters)),{
        r <- rowSums(n_mat * food)
        dN <- matrix(r * state_a,3,1)
        list(c(dN))
      })
    }

food <- c(0,0.2,0.5)
n_vec <- c(0,0,1,1,0,0,0,1,0)
n_mat <- matrix(n_vec, 3 ,3)
times <- seq(0, 10, by = 1) 
state_a <- runif(3, 0, 1000)
parameters <- c(n_mat, food)
out <- ode (y  = state_a, 
            times = times, 
            func = changes, parms = parameters)

但是，我希望能够随着时间的推移改变食物的大小，而微分方程正在运行。 例如，如果食物看起来像下面的代码（其中每一行是一个时间点，每一列是一种食物来源）。 使用ode求解器中的事件似乎可以实现这一点，但是当我有一个要更改的参数矩阵而不是单个参数时，我不知道该怎么做。 有什么好方法吗？

food <- rep(c(0,0.6,0.1,0.4,0.2,0.1,0.2), 6)
food <- matrix(food[1:30],10,3)
colnames(food) <- 1:3
rownames(food) <- 1:10

以下是仅更改单个参数的ode事件的工作示例：

derivs <- function(t, var, parms) {
  list(dvar = rep(0, 2))
}

yini <- c(v1 = 1, v2 = 2)
times <- seq(0, 10, by = 0.1)

eventdat <- data.frame(var = c("v1", "v2", "v2", "v1"),
                       time = c(1, 1, 5, 9) ,
                       value = c(1, 2, 3, 4),
                       method = c("add", "mult", "rep", "add"))
eventdat

out <- vode(func = derivs, y = yini, times = times, parms = NULL,
            events = list(data = eventdat))

新的但不起作用的代码：

calc_food_mat <- function(t, food_df){
  return(food_df[which(food_df$time == floor(t)),2] + ((food_df[which(food_df$time == ceiling(t)),2] - food_df[which(food_df$time == floor(t)),2]) * (t - floor(t))))
}
changes <- function(t, state_a, parameters){
  with(as.list(c(t, state_a, parameters)),{
    food <- calc_food_mat(t, food_df)
    r <- rowSums((n_mat * food)[drop = FALSE])
    dN <- r * state_a
    list(c(dN))
  })
}

seasonl <- 40
foodsize <- 4000
foods <- 3
food_seq <- append(seq(foodsize/5, foodsize, foodsize/5), rev(seq(foodsize/5, foodsize, foodsize/5)))
start <- round(runif(foods, -0.5, seasonl - length(food_seq) + 0.5))
food_mat <- matrix(0, foods, seasonl)
for (i in 1:length(start)){
  food_mat[i,(start[i]+1):(start[i]+length(food_seq))] <- food_seq
}
food_mat <- data.frame(food_mat)
colnames(food_mat) <- 1:seasonl
rownames(food_mat) <- 1:foods
food_df <- food_mat %>%
  gather (key = time, value = resources)
n_vec <- c(0,0,1,1,0,0,0,1,0)
n_mat <- matrix(n_vec, 3 ,3)
times <- seq(0, 40, by = 1) 
state_a <- runif(3, 0, 1000)
parameters <- c(n_mat, food_df)
out <- ode (y  = state_a, 
            times = times, 
            func = changes, parms = parameters)