R：尝试编写等效函数n选择k时出错

Question

I'm taking the class of introduction for R programming.

we were asked to write a function that will be the same as n choose k:

choose(n, k)

we were asked to check if the function works by running n = 200, k = 50.

I wrote the following code:

    select_k <- function(n, k){
  sr <- c(log10(log10((factorial(n-1)/factorial(k-1)*factorial(n-k-2)))*(n/k)))
  return(sr)
}

as select_k is supposed to be the " n choose k".

my function works with values such as: 100 choose 25, but it doesn't work with greater values, like n = 200, k = = 50.

select_k( n = 200, k = 50)
[1] NaN
Warning message:
In factorial(n) : value out of range in 'gammafn'

I have no idea what else can be done to fix that.

Answer 1

This doesn't work for larger n because factorial(n) is too big:

> factorial(199)
[1] Inf
Warning message:
In factorial(199) : value out of range in 'gammafn'

This should return 200, but the computer only sees that you are trying to divide Inf by Inf :

> factorial(200)/factorial(199)
[1] NaN
Warning messages:
1: In factorial(200) : value out of range in 'gammafn'
2: In factorial(199) : value out of range in 'gammafn'

Obviously a lot of the multiplications in "n choose k" cancel out, so you'll need to avoid using regular factorial and only multiply the numbers that don't cancel out ( ?prod might be useful for you). Or (probably better) use the log version lfactorial to avoid running into numbers your computer can't store.

Edit: Added lfactorial recommendation from @MrFlick's comment

Answer 2

Have a look at this {

a <- function(n, k) {
  exp(lgamma(n+1) - lgamma(n - k + 1) - lgamma(k + 1) )
}