epr_ueb_l_4.Rnw

<<child='epr_ueb_a_4.Rnw'>>=
@
<<echo = FALSE>>=
monte_carlo = function(f, a = 0, b = 5, n, ...) {
  opt = optimize(f, interval = c(a, b), maximum = TRUE)
  
  bot = 0
  top = opt$objective
  rect_area = (b - a)*(top - bot)

  x = runif(n, a, b)
  y = runif(n, bot, top)
  x_eval = sapply(x, f)
  hit = (y <= x_eval) & (x_eval >= 0)
  
  return(rect_area * mean(hit))
}
@

<<eval = FALSE>>=
f = function(x) sqrt(x) * sin(x) * cos(x) + 1

N = 100
library(parallelMap)
parallelStartSocket(1)
res1 = system.time(parallelMap(monte_carlo, n = rep(10^6, N), more.args = list(f = f)))
parallelStop()

parallelStartSocket(4)
res2 = system.time(parallelMap(monte_carlo, n = rep(10^6, N), more.args = list(f = f)))
parallelStop()
res1
res2
@

<<eval = FALSE>>=
library(batchtools)

reg = makeRegistry(file.dir = NA, seed = 1)

batchMap(fun = monte_carlo, n = rep(10^6, 100), more.args = list(f = f))

submitJobs()

getStatus()
res = reduceResultsList()
@