# Inf and NaN problem

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Hajar on 14 Jan 2015
Commented: Star Strider on 14 Jan 2015
I have to do some computations with very big numbers values, so my matlab code returns "Inf" and "NaN.. I want to know if there is a way to avoid this problem? here is the part of my code that returns Inf and NaN
UtiliteProba(b,l)=exp((UtiliteB(b,l)+UtiliteC(b,l))/T);
proba(b,l)=UtiliteProba(b,l)/constante(1,b);
Actually the "UtiliteProba"= Inf and "proba"=NaN , the "constante" is equal to Inf too..
thank you so much for your help

Iain on 14 Jan 2015
Logarithms are your friends. Here's what I mean maths:
log(UtiliteProba) = (UtiliteB(b,l)+UtiliteC(b,l))/T (values in the range of a few hundred correspond to the maximum values matlab can handle with doubles)
proba = e^(log(UtiliteProba) - log(constante(1,b))
log(proba) = (log(UtiliteProba) - log(constante(1,b))

#### 1 Comment

Hajar on 14 Jan 2015
I forgot to mention that
constante(1,b)=sum(UtiliteProba(b,:))
then
log(proba)=log(utiliteProba)-log(constante)
=log(utiliteProba)-log(sum(utiliteProba))
for log(utiliteProba) it's okay since I can calculate it by using (UtiliteB(b,l)+UtiliteC(b,l))/T , but log(constante) would be log(inf) :s :s

Star Strider on 14 Jan 2015
The only way I can imagine to avoid the Inf and NaN values (assuming none of the arguments ‘UtiliteB’ and ‘UtiliteC’ are either Inf or NaN) is to not take the exponential and keep them as logarithms until you need to actually evaluate them as exponentials:
UtiliteProba(b,l) = ((UtiliteB(b,l)+UtiliteC(b,l))/T);
proba(b,l) = UtiliteProba(b,l) - log(constante(1,b));

Hajar on 14 Jan 2015
actually constante(1,b)=sum(UtiliteProba(b,l)) :s
Star Strider on 14 Jan 2015
â€˜log(constante) would be log(inf)â€™
If â€˜constante = Infâ€™, then none of your calculations using it will produce any useful results.
You need to review your calculation of â€˜constanteâ€™ and see what the problem is with it.