incomplete gamma function calculation

Hi,

I have this equation:

gamma(5,x) = 2

how I can find the value of x?

Thanks

[José-Luis]

Matlab's gamma function only accepts one input argument.

[Jamal Ahmad]

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.

Answer 1

[Sean de Wolski]

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

[Jamal Ahmad]

you are right, I tried to write the equation simply. the actual value is 10^-4

thanks again.

[Sean de Wolski]

see More

[Jamal Ahmad]

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]

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]

optimoptions is new in R2013a. If you're using an older release, use optimset which has a slightly different syntax.

[Jamal Ahmad]

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]

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

Answer 2

[Walter Roberson]

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

[Jamal Ahmad]

sure, but how

Answer 3

[Matt J]

 xv =  fzero(@(z) gammainc(5,z.^2)- 2 , sqrt(xguess)).^2;