incomplete gamma function calculation

2013 5 24
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Hi,
I have this equation:
gamma(5,x) = 2
how I can find the value of x?
Thanks

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José-Luis
José-Luis 2013-5-24
Matlab's gamma function only accepts one input argument.
Jamal Ahmad
Jamal Ahmad 2013-5-24
this is incomplete gamma function, in matlab we can write as the following:
gammainc(a,x)
a = 5 and the result of the above function is 2 I need the value of x.

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Sean de Wolski
Sean de Wolski 2013-5-24
编辑：Sean de Wolski 2013-5-24

0 个投票

I don't believe that's possible:
gammainc(5,0)
gammainc(5,1000);
it never goes near two.
More
options = optimoptions(@fminunc,'tolfun',10^-10,'tolx',10^-12);
xv = fminunc(@(x)(gammainc(5,x)-(10^-4)).^2,4,options)
%xv =15.6926
gammainc(5,xv)
% ans =
% 1.0004e-04

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Jamal Ahmad
Jamal Ahmad 2013-5-24
you are right, I tried to write the equation simply. the actual value is 10^-4
thanks again.
Jamal Ahmad
Jamal Ahmad 2013-5-24
I receive this error:
Undefined function 'optimoptions' for input arguments of type 'function_handle'.
Error in Untitled2 (line 2) options = optimoptions(@fminunc,'tolfun',10^-10,'tolx',10^-12);
Walter Roberson
Walter Roberson 2013-5-24
There are different meanings for "incomplete gamma function". The more obvious one has to do with upper or lower tail, but MATLAB also defines the upper-tail version differently than some other systems such as Maple do. Where MATLAB defines the upper tail as 1 - gammainc(a,x), MAPLE uses gamma(a) in place of 1, creating the "complementary upper gamma function". And in that usage of "incomplete gamma" there is a solution, at approximately 8.307413412
Sean de Wolski
Sean de Wolski 2013-5-24
optimoptions is new in R2013a. If you're using an older release, use optimset which has a slightly different syntax.
Jamal Ahmad
Jamal Ahmad 2013-5-24
Thank you very much. I use R2012a. Now it works.
options = optimset('tolfun',10^-10,'tolx',10^-12); xv = fminunc(@(x)(gammainc(5,x)-(10^-4)).^2,4,options) gammainc(5,xv)
Jamal Ahmad
Jamal Ahmad 2013-5-24
now I have this warning:
Warning: Gradient must be provided for trust-region algorithm; using line-search algorithm instead. > In fminunc at 367 In test_2 at 12

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Walter Roberson
Walter Roberson 2013-5-24

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It appears to me that you will need to proceed numerically.

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