Hello everybody, I have to compute something in this form: x = prod(a:b) / prod(c:d), where: a < c and b < d and obviously: a < b and c < d I cannot make assumptions on the relative position of c,b and a,d. The problem is that a,b,c,d are large and the products are huge (R return Inf). Their ratio is less than 1 but significantly higher than 0: it is a non-tiny probability. I need to find a way to simplify this ratio. The only way to solve this that I see is to decompose into prime factors all the numbers in the numerator and the denominator and to remove the ones in common Do you know a better way to do this ? Thank you, Alberto
Ratio of huge products
4 messages · Alberto Magni, R. Michael Weylandt, Peter Langfelder +1 more
Use logs? Michael On Thu, Dec 15, 2011 at 1:35 PM, Alberto Magni
<alberto.magni86 at gmail.com> wrote:
Hello everybody, I have to compute something in this form: x = prod(a:b) / prod(c:d), ? ?where: a < c and b < d and obviously: a < b and c < d I cannot make assumptions on the relative position of c,b and a,d. The problem is that a,b,c,d are large and the products are huge (R return Inf). Their ratio is less than 1 but significantly higher than 0: it is a non-tiny probability. I need to find a way to simplify this ratio. The only way to solve this that I see is to decompose into prime factors all the numbers in the numerator and the denominator and to remove the ones in common Do you know a better way to do this ? Thank you, Alberto
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On Thu, Dec 15, 2011 at 10:35 AM, Alberto Magni
<alberto.magni86 at gmail.com> wrote:
Hello everybody, I have to compute something in this form: x = prod(a:b) / prod(c:d), ? ?where: a < c and b < d and obviously: a < b and c < d I cannot make assumptions on the relative position of c,b and a,d. The problem is that a,b,c,d are large and the products are huge (R return Inf). Their ratio is less than 1 but significantly higher than 0: it is a non-tiny probability. I need to find a way to simplify this ratio. The only way to solve this that I see is to decompose into prime factors all the numbers in the numerator and the denominator and to remove the ones in common Do you know a better way to do this ?
Yes, exp( sum(log(a:c))-sum(log(b:d)) ), which is mathematically exactly equivalent, unless I made a typo. Remeber that log of a product is a sum of the logs of the arguments. Peter.
On Dec 15, 2011, at 1:35 PM, Alberto Magni wrote:
Hello everybody, I have to compute something in this form: x = prod(a:b) / prod(c:d), where: a < c and b < d and obviously: a < b and c < d I cannot make assumptions on the relative position of c,b and a,d. The problem is that a,b,c,d are large and the products are huge (R return Inf).
Well, R does have some limitations.
Their ratio is less than 1 but significantly higher than 0: it is a non-tiny probability. I need to find a way to simplify this ratio.
x <- exp( sum(log(a:b)) -sum(log(c:d)) )
The only way to solve this that I see is to decompose into prime factors all the numbers in the numerator and the denominator and to remove the ones in common
Ewww. That does sound painful.
David Winsemius, MD West Hartford, CT