进行更高效的蒙特卡罗模拟

Question

所以,我编写了这个代码,它应该有效地估计定义为h(x)的函数曲线下的面积.我的问题是我需要能够将区域估计到小数点后6位,但我在estimateN中定义的算法似乎对我的机器来说太重了.基本上问题是如何使以下代码更有效？有没有办法摆脱那个循环？

h = function(x) {
    return(1+(x^9)+(x^3))
}
estimateN = function(n) {
    count = 0
    k = 1
    xpoints = runif(n, 0, 1)
    ypoints = runif(n, 0, 3)
    while(k <= n){
    if(ypoints[k]<=h(xpoints[k]))
        count = count+1
    k = k+1
    }
    #because of the range that im using for y
    return(3*(count/n))
}
#uses the fact that err<=1/sqrt(n) to determine size of dataset
estimate_to = function(i) {
    n = (10^i)^2
    print(paste(n, " repetitions: ", estimateN(n)))
}

estimate_to(6)

Answer 1

替换此代码:

count = 0
k = 1
while(k <= n){
if(ypoints[k]<=h(xpoints[k]))
    count = count+1
k = k+1
}

有了这条线:

count <- sum(ypoints <= h(xpoints))