# A numerical calculation problem leading to Inf or NaN in matlab

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Hancheng Zhu on 20 Jul 2024 at 15:02
Commented: David Goodmanson on 21 Jul 2024 at 20:46
I want to calculate the exact value of , where and λ is a very large positive number. Obviously, we have the bound ,and therefore .
However, in reality, for example, if , due to the large λ, we have and the matlab will treat it as 0 and .
On the other hand, if , due to the large λ, we have a very large and matlab will treat the sum as Inf and . So how to avoid the above two cases and get the exact value of F in matlab?
David Goodmanson on 21 Jul 2024 at 20:46
Hi HZ,
(1/lam) log( (x1^lam)*(1 + (x2/x1)^lam + (xn/x1)^lam) )
= log(x1) + (1/lam)*log(1 + (x2/x1)^lam + (xn/x1)^lam))

Torsten on 20 Jul 2024 at 15:35
Moved: Torsten on 20 Jul 2024 at 15:35
log2(norm(x,lambda))
does not work ?
##### 3 CommentsShow 1 older commentHide 1 older comment
Walter Roberson on 21 Jul 2024 at 4:34
Use the Symbolic Toolbox
Torsten on 21 Jul 2024 at 14:59
Edited: Torsten on 21 Jul 2024 at 15:01
Maybe rewriting the expression as
1 / (1 + (x2/x1)^lambda + ... + (xn/x1)^lambda)*u1 +
(x2/x1)^lambda / (1 + (x2/x1)^lambda + ... + (xn/x1)^lambda)*u2 +
(x3/x1)^lambda / (1 + (x2/x1)^lambda + ... + (xn/x1)^lambda)*u3 +
...
(xn/x1)^lambda / (1 + (x2/x1)^lambda + ... + (xn/x1)^lambda)*un
can help.
If not, please give an example for x, u and lambda where the computation fails.

Walter Roberson on 20 Jul 2024 at 21:18
If you need the exact value, calculate using the Symbolic Toolbox.
However, it is questionable what meaning to assign to the exact value of log2 of an expression. It is highly likely that log2 will be an transcendental number -- something that you cannot calculate the exact decimal representation for.

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