Simulating random walk on the n-cycle in R

Question

I have been trying to implement a random walk on the n-cycle algorithm in R.

By n-cycle I mean the set of integers Zn, or modulo n. Basically, it’s example 5.3.1 from the book “Markov chains and mixing time”, by Levin, Peres and Wilmer. The intention is as follows: consider two chains modeling the movement of two particles X and Y on Zn with starting points X1 and Y1. By the flip of a fair coin we decide which particle will move (the particles cannot move simultaneously unless they have coupled); the direction is decided by another flip of fair coin. Once the two particle collide, they move together hereafter. It is part of a study project to implement a CFTP algorithm, so the length of the chains should have a pre-defined value, say T.

The code does not run and an error message appears. The error is “object ‘res’ not found”. However, I had previously defined “res” as a list to store the output of the function. Why does this happen and how could it be fixed?

I have two scripts: in the first one the code is split in smaller helper functions; the second one may be messier, as I tried to put all the helper functions within one single function. Any help will be much appreciated.

This one is script 2.

# X1 - initial state of chain X
# Y1 - initial state of chain Y
# T - "length" of a chain, number of steps the chains will run for. 
# n - length of the n-cycle, i.e., Zn. 

Main_Function <- function (X1 = 8, Y1 = 4 , T = 20, n = 6){ 
  X <- rep( X1, T) %% n         # X, Y and res will store the results
  Y <- rep( Y1, T) %% n         
  res <- list(X,Y)              # Here I defined the object res. Later on R encounters an error "object 'res' not found".  
  ps <- TakeOneStep()           # TakeOneStep is a function defined below
  return(ps)
}

TakeOneStep <- function(){
  incr_same <- sample(c(-1, 0, 1), size = 1, prob = c(1/4, 1/2, 1/4))           #direction of the particles after they have coupled
  incr_dif <- sample(c(-1,1), size = 1, prob = c(1/2, 1/2))             # direction of the particles before coupling occurred.  
  choice <- runif(T)                                                    # determines which chain moves, before coupling occurred. 
  for(t in 2:T){
    if(res[[1]][t-1]%%n == res[[2]][t-1]%%n){
      res[[1]][t] <- (res[[1]][t-1] + incr_same) %% n
      res[[2]][t] <- (res[[2]][t-1] + incr_same) %% n
    }else{ if(choice[t] < 0.5) {
            res[[1]][t] <- (res[[1]][t-1] + incr_dif) %% n
            }else{res[[2]][t] <- (res[[2]][t-1] + incr_dif)%%n}
      }
  }
  return(res)
}

Reduce your code to create a minimal [reproducible example](http://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example) and include it in the question itself. Links to other sites are discouraged. Note that variables defined in functions are not directly available to child functions. They should be passed as parameters and functions should return updated values. There is no in-place modification. — MrFlick, Jun 10 '16 at 20:52
Try these changes: `ps <- TakeOneStep(res)` and `TakeOneStep <- function(res)` — R. Schifini, Jun 11 '16 at 14:05
Thank you! It worked, but I also had to add `ps <- TakeOneStep(res, n, T)` and `TakeOneStep <- function(res, n, T)`, because the same error appeared with objects `n` ant `T`. — KirkLand, Jun 11 '16 at 15:05

Simulating random walk on the n-cycle in R

0 Answers0