如何在 R 中定义 function 的图形上 plot 几条曲线？

Question

I need to plot a couple of curves on one graph. I've got trajectories of Brownian simulation which I got from the function:

brownian <- function(T,N){
  alpha=0
  sigma=1
  
  delta_t=T/N
  
  t=seq(0,T,by=delta_t)
  #x=c(0,alpha*delta_t+sigma*sqrt(delta_t)*rnorm(N,mean=0,sd=1))
  x=c(0,alpha*delta_t+sqrt(delta_t)*rnorm(N,mean=0,sd=1))
  Xt=cumsum(x)
  plot(t,Xt,type='l',col = rep(1:3, each = 10),xlab="t=[0,T]",ylab = "B(t,ω)")
}

For example for brownian(1,1000) I get:

And for brownian(10,1000) I get:

As you can see I get black graphs. I have to plot these trajectories on one graph (every trajectory should have different color). When it takes several trajectories, it should look like:

Do you have any advices how can I plot these curves on one graph and each curve has different color?

Thanks in advance

Answer 1

You could do this pretty easily by modifying the function and using ggplot() to make the graph. The function below takes ntimes as an argument which specifies the number of times you want to do the simulation. It then uses ggplot() to make the graph. You could adjust the internals of the function to have it produce a different looking plot if you like.

brownian <- function(T,N, ntimes){
  if((length(N) != length(T)) & length(N) != 1){
    stop("N has to be either length of T or 1\n")
  }
  alpha=0
  sigma=1
  if(length(N) == 1 & length(T) > 1)N <- rep(N, length(T))
  dat <- NULL
  for(i in 1:ntimes){
    delta_t=T/N  
    t=seq(0,T,by=delta_t)
    #x=c(0,alpha*delta_t+sigma*sqrt(delta_t)*rnorm(N,mean=0,sd=1))
    x=c(0,alpha*delta_t+sqrt(delta_t)*rnorm(N,mean=0,sd=1))
    Xt=cumsum(x)
    dat <- rbind(dat, data.frame(xt=Xt, t=t, n=i))
  }
  require(ggplot2)
  ggplot(dat, aes(x=t, y=xt, colour=as.factor(n))) + 
    geom_line(show.legend=FALSE) + 
    labs(x="t=[0,T]",y = "B(t,ω)", colour="T") + 
    theme_classic()
}
brownian(10,1000, 5)

Answer 2

Here is a base R solution with matplot . It is ideal for this type of plot, since it computes the x and y axis ranges and plots all lines in one call only. It uses DaveArmstrong's idea of adding an extra argument ntimes . This argument is also used for the color scheme.

brownian <- function(T, N, ntimes){
  alpha <- 0
  sigma <- 1
  delta_t <- T/N
  t <- seq(0, T, by = delta_t)
  #x=c(0,alpha*delta_t+sigma*sqrt(delta_t)*rnorm(N,mean=0,sd=1))
  Xt <- replicate(ntimes,
                  cumsum(c(0, alpha*delta_t+sqrt(delta_t)*rnorm(N, mean = 0, sd = 1)))
  )
  matplot(t, Xt, 
          type = "l", lty = 1, 
          col = seq_len(ntimes),
          xlab = "t=[0,T]", ylab = "B(t,ω)")
}

set.seed(2020)
brownian(1, 1000, 5)