CODEWITHSUNDEEP
rvectorization
ECII
ECII

Reputation: 10629

Vectorizing a simulation

Trying to wrap my mind arround vectorizing, trying to make some simulations faster I found this very basic epidemic simulation. The code is from the book http://www.amazon.com/Introduction-Scientific-Programming-Simulation-Using/dp/1420068725/ref=sr_1_1?ie=UTF8&qid=1338069156&sr=8-1

#program spuRs/resources/scripts/SIRsim.r

SIRsim <- function(a, b, N, T) {
  # Simulate an SIR epidemic
  # a is infection rate, b is removal rate
  # N initial susceptibles, 1 initial infected, simulation length T
  # returns a matrix size (T+1)*3 with columns S, I, R respectively
  S <- rep(0, T+1)
  I <- rep(0, T+1)
  R <- rep(0, T+1)
  S[1] <- N
  I[1] <- 1
  R[1] <- 0
  for (i in 1:T) {
    S[i+1] <- rbinom(1, S[i], (1 - a)^I[i])
    R[i+1] <- R[i] + rbinom(1, I[i], b)
    I[i+1] <- N + 1 - R[i+1] - S[i+1]
  }
  return(matrix(c(S, I, R), ncol = 3))
}

The core of the simulation is the for loop. My question, is since the code produces the S[i+1] and R[i+1] values from the S[i] and R[i] values, is it possible to vectorize it with an apply function?

Many thanks

Upvotes: 2

Views: 653

Answers (1)

Martin Morgan
Martin Morgan

Reputation: 46866

It's hard to 'vectorize' iterative calculations, but this is a simulation and simulations are likely to be run many times. So write this to do all the the simulations at the same time by adding an argument M (number of simulations to perform), allocating an M x (T + 1) matrix, and then filling in successive columns (times) of each simulation. The changes seem to be remarkably straight-forward (so I've probably made a mistake; I'm particularly concerned about the use of vectors in the second and third arguments to rbinom, though this is consistent with the documentation).

SIRsim <- function(a, b, N, T, M) {
    ## Simulate an SIR epidemic
    ## a is infection rate, b is removal rate
    ## N initial susceptibles, 1 initial infected, simulation length T
    ## M is the number of simulations to run
    ## returns a list of S, I, R matricies, each M simulation
    ## across T + 1 time points
    S <- I <- R <- matrix(0, M, T + 1)
    S[,1] <- N
    I[,1] <- 1
    for (i in seq_along(T)) {
        S[,i+1] <- rbinom(M, S[,i], (1 - a)^I[,i])
        R[,i+1] <- R[,i] + rbinom(M, I[,i], b)
        I[,i+1] <- N + 1 - R[,i+1] - S[,i+1]
    }
    list(S=S, I=I, R=R)
}

Upvotes: 5

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