# [R] how to calculate this natural logarithm

Petr Savicky savicky at praha1.ff.cuni.cz
Fri Jan 7 18:54:50 CET 2011

```On Sat, Jan 08, 2011 at 12:20:59AM +0800, zhaoxing731 wrote:
> Hello
>
> 	I want to calculate natural logarithm of sum of combinations as follow: (R code)
>
> 	{
> 		com_sum=choose(2000000,482)*choose(1000000,118)+choose(2000000,483)*choose(1000000,117)+...+choose(2000000,i)*choose(1000000,600-i)+...+choose(2000000,600)*choose(1000000,0)                  #calculate the sum
> 	   result=log(com_sum)                          	   #calculate the log of the sum
> 	}
>
> 	But every element of the com_sum is Inf, so I can't get the result

The natural logarithm of choose() is lchoose(), so the
natural logarithms of the products above are

i <- 482:600
logx <- lchoose(2000000,i) + lchoose(1000000,600-i)
maxlog <- max(logx)
# [1] 5675.315

The sum of numbers, which have very different magnitudes, may
be approximated by their maximum, so max(logx) is an
approximation of the required logarithm. A more accurate
calculation can be done, for example, as follows

maxlog + log(sum(exp(logx - maxlog)))
# [1] 5675.977

Petr Savicky.

```