# source("BMsim2.R") 
# in R under Windows, use 'change dir' to read from the right place

howlong<-system.time(  # let's measure now long it takes
{
n<-1000000

capT<-1 # time horizon; both 't' & 'T' are both reserved 

tvec<-capT*0:n/n
# vectors in R are unit offfset, ie. 1st entry is number 1 (not 0)			
dW<-c(0,rnorm(n,0,sqrt(capT/n))) # rnorm (n,m,sd) simulates n indep. N(m,sd^2)
		
W<-cumsum(dW) # a bulid-in function that caluculates the cumulative sum 
	      #	this is much faster than loops

freq<-1000   # take out every 1000th point in the simulation & plot it

pick<-freq*(0:(n/freq))+1

plot(tvec[pick],W[pick],type='l', xlab="time",ylab="W(time)", main="A Path of Brownian Motion")
}
)

print(c("It took", round(howlong[3],2), " seconds to do ", n , " points (and to plot)"))  # the 3rd coordinate is 'elapsed time', ie. how long it actually takes