How to avoid NaN while evaluating a function

Question

Ruye Wang 2013-5-16

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https://ww2.mathworks.cn/matlabcentral/answers/75967-how-to-avoid-nan-while-evaluating-a-function

The function below is always finite and reaches maximum y=1/4 when x=0. However, when x<0 and abs(x) is large, the numerator exp(-x) may return a NaN, causing the returned value of the function to be NaN as well, although the function should return a very small number (almost zero). What should I do to get the desired answer zero instead of an NaN?

function y=dg(x) y=exp(-x)./(1+exp(-x)).^2 end

Thanks!

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Answer 1

Azzi Abdelmalek 2013-5-16

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https://ww2.mathworks.cn/matlabcentral/answers/75967-how-to-avoid-nan-while-evaluating-a-function#answer_85625

编辑：Azzi Abdelmalek 2013-5-16

在 MATLAB Online 中打开

function y=dg(x)
  y=exp(-x)./(1+exp(-x)).^2
  y(isnan(y))=0

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Answer 2

José-Luis 2013-5-16

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在 MATLAB Online 中打开

If you have the symbolic math tool then you could use variable precision arithmetic. For instance, please try the following snippet:

 myFun = @(x) vpa(exp(-x)./(1+exp(-x)).^2,1000);
 test = myFun(500)

Which should return a value different from zero. The problem you are encountering is due to the finite numerical precision of doubles. If you don't have the toolbox you could look in the file exchange for alternatives that perform the same tasks, for example:

http://www.mathworks.com/matlabcentral/fileexchange/22725-variable-precision-integer-arithmetic