Difference in MATLAB function evaluation
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According to the properties of gamma function, for any x > 0
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/160284/image.png)
But when I try to use it in MATLAB, it shows a very large error
gamma(150) - 149*gamma(149)
ans =
-1.5240e+247
Can anybody explain the reason for this? I need it for an approximation algorithm I am trying to develop.
Thanks in advance.
1 Comment
Star Strider
on 31 Jan 2017
FWIW, I get similar results for these (in R2016b):
n = 149;
q1 = gamma(n+1) - n*gamma(n);
q2 = gamma(n+1) - factorial(n);
q3 = gamma(n+1) - prod(1:n);
q1 =
-15.2402e+246
q2 =
-819.3656e+243
q3 =
-819.3656e+243
I hope this is a problem with my understanding of the gamma function, and not a problem with its implementation in MATLAB.
Accepted Answer
Honglei Chen
on 31 Jan 2017
For your use case, 150! is a very large number so the numerical precision issue starts to kick in. I'd suggest you to use gammaln instead, for example, you can do
gammaln(150)-(log(149)+gammaln(149))
and the result is indeed 0.
HTH.
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More Answers (1)
Jan
on 31 Jan 2017
Edited: Jan
on 31 Jan 2017
While the absolute error is huge, the relative error is tiny:
(gamma(150) - 149*gamma(149)) / gamma(150)
>> -3.9868e-014
This is the expected error caused by using the IEEE754 double format. This stores about 16 valid digits.
If an approxmation algorithm is sensitive for this difference, it is instable and of limited use.
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