如何在R中编写双重递归函数

Question

I want tot write a program in R to compute a value, the program is below .

     options( expressions = 5e5 )
     P_n_m=function(r,n,m) {
       if(r >0 & n==1 & m==0 | r >=0 & n==0 & m==1) return(1)
       else if(r >= 0 & n >= 0 | r >= 0 & m >= 0){ 
         return(n/(n+m)*P_n_m(r-n-m,n-1,m)+m/(n+m)*P_n_m(r,n,m-1))
       }
       else return(0)
     }

But it always give me error. I also try to adjust system setting, but it still didn't work. I want to compute P_n_m(49,7,7), and I don't know which part in program is wrong. Can any one help me to solve this problem?

Answer 1

Your function has an infinite recursion in it.

When you compute P_n_m(r,n,m) , you must compute both P_n_m(rnm,n-1,m) and P_n_m(r,n,m-1) . Notice that the second term only reduces m but leaves r and n unchanged. That causes the infinite recursion.

Let's track your example, P_n_m(49,7,7). It will have to compute (among other things)
P_n_m(49,7,6) which has to compute
P_n_m(49,7,5) which has to compute
P_n_m(49,7,4) which has to compute
P_n_m(49,7,3) which has to compute
P_n_m(49,7,2) which has to compute
P_n_m(49,7,1) we have m==1 but not n==0, both r & n > 0 so we need
P_n_m(49,7,0) we have m==0 but not n==1, both r & n > 0 so we need
P_n_m(49,7,-1) and now we need
P_n_m(49,7,m) down to negative infinity.

You need to rethink the definition of your function.