Slow code on inhomogeneous poisson process

Question

I am trying to generate times from an inhomogeneous Poisson process having intensity function (lambda_time) as below-

     lambda_time<-function(k,p,a,t){
          k*(p-1)*(a^(p-1))*((t+a)^(-p))
          } 

. My code for generating "n" times between the interval (0,Tmax) is as follows-

   Inhomogeneous<- function(lambda_time,n,k,p,a,tmax,lambdamax=NA){
      if(is.na(lambdamax)){
        lambdamax<-  max(sapply(seq(0,tmax,length.out=2000),lambda_time,k=k,p=p,a=a))
      }
     t<-0
     count<-1
     times<-numeric()
     times[1]<-t
     while(times[length(times)]<tmax && count<=n){
         e<-rexp(1,lambdamax)
         t<-t+e
         v<-runif(1)
         if(t<tmax && v<=(lambda_time(k,p,a,t)/lambdamax)){
            times<-c(times,t)
            count<-count+1
        }
    }
   return(times[-1])

}

. But the code is very slow. I do not understand why? Can anyone tell me? The values of k,p,a will be like 1.8,1.9,0.6 or something like these.

Answer 1

R runs best when variables are vectorized. Your programming style in reminiscent of low-level and assembly languages like C and Fortran, in which vectorization does not offer a significant speed improvement.

There are a few things you could do to reduce the amount of function calls and declarations in your code.

1. Use a for loop and control flow with a break statement.

   for( i in 1:n ){

   ### do math here

   if( times[length(times)] < tmax ) break

   }

2. Pre-declare vectors and have R access them by index (even if you don't use every random number you generate)

   v <- runif( n = n )

   t <- rep(NA, n)

   etc...

   for( i in 1:n ){

   ### do math here

   ### access v as v[i]

   if( times[length(times)] < tmax ) break

   }