A numerical calculation problem leading to Inf or NaN in matlab
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I want to calculate the exact value of
, where
and λ is a very large positive number. Obviously, we have the bound
,and therefore
.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1738476/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1738481/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1738486/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1738491/image.png)
However, in reality, for example, if
, due to the large λ, we have
and the matlab will treat it as 0 and
.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1738496/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1738501/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1738506/image.png)
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?
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1738511/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1738516/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1738521/image.png)
1 Comment
David Goodmanson
on 21 Jul 2024
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))
Answers (2)
Torsten
on 20 Jul 2024
Moved: Torsten
on 20 Jul 2024
log2(norm(x,lambda))
does not work ?
3 Comments
Torsten
on 21 Jul 2024
Edited: Torsten
on 21 Jul 2024
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
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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