A numerical calculation problem leading to Inf or NaN in matlab

Question

Hancheng Zhu 2024-7-20，15:02

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2138996-a-numerical-calculation-problem-leading-to-inf-or-nan-in-matlab

评论： David Goodmanson 2024-7-21，20:46

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?

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

David Goodmanson about 23 hours 前

在 MATLAB Online 中打开

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))

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Torsten 2024-7-20，15:35

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2138996-a-numerical-calculation-problem-leading-to-inf-or-nan-in-matlab#answer_1488396

移动：Torsten 2024-7-20，15:35

在 MATLAB Online 中打开

log2(norm(x,lambda))

does not work ?

3 个评论
显示 1更早的评论隐藏 1更早的评论

Walter Roberson 2024-7-21，4:34

Use the Symbolic Toolbox

Torsten 2024-7-21，14:59

编辑：Torsten 2024-7-21，15:01

在 MATLAB Online 中打开

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.

请先登录，再进行评论。

Answer 2

Walter Roberson 2024-7-20，21:18

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2138996-a-numerical-calculation-problem-leading-to-inf-or-nan-in-matlab#answer_1488456

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.