######################################################################
# MARKOV CHAIN SIMULATION EXAMPLE
# p <- matrix(c(1/3,1/5,2/3,4/5),nrow=2)
# p
#          [,1]      [,2]
# [1,] 0.3333333 0.6666667
# [2,] 0.2000000 0.8000000
# runs <- generateMarkovChain(1,p,100)
# runs
#  [1] 1 2 1 1 1 2 2 2 1 1 1 2 1 2 2 2 2 2 2 2 2 2 2 1 1 1 2 2 1 1 2 1 2 1 1
2 2 2
#  [39] 1 2 1 2 2 2 2 2 1 2 2 2 1 1 2 1 1 2 2 1 2 1 1 2 2 2 1 2 1 2 2 2 2 2
1 1 2 2
#  [77] 2 2 2 1 2 1 2 2 2 1 1 2 2 2 1 2 1 1 1 2 1 2 2 2
######################################################################

#######################################################
#  Given an n x n transition matrix and an initial state in the set
# {1,2,..n}, simulate a markov chain to get the next state
#######################################################
nextState <- function(transitionMatrix, state)
{
  sample(dim(transitionMatrix)[2], size = 1, prob =
transitionMatrix[state,])
}


#######################################################
#  Given an n x n transition matrix and an initial state in the set   #
#  {1,2,..n},
#
#  run a simulation of a markov chain "numRun" times                 #
#######################################################
generateMarkovChain <- function(initialState, transitionMatrix ,numRuns)
{
   states = rep(initialState, numRuns)
   for(i in 2:numRuns)
   {
      states[i] = nextState(transitionMatrix, states[i - 1])
  }
  states
}