# Find maximum of a function.

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ektor on 17 Aug 2015
Commented: JMP Phillips on 20 Aug 2015
Dear all,
I have the following code that aims at maximixing LL_all with respect to "gidraw" which is scalar.
%the data
n=1;
Xfi=[ -1.4+randn(n,1) 0.5+0.6*randn(n,1)];
beta=[3 2 ]';
yi=randn(n) ;
gidraw=0.5;
lam=Xfi*beta + gidraw;
int=yi.*lam-exp(lam);
int=sum(int);
%the function
LL_all = -(log(normpdf(gidraw,2,sqrt(0.5)))+int);
So, my question is what is the maximum of LL_all? That is, how can I find the maximum of this function? Also can I calculate the Hessian matrix(which is a scalar more precisely) of this function?
ektor on 19 Aug 2015
Edited: ektor on 19 Aug 2015
Hi Walter, I made a small modification in the above code to make things easier. n=10 now becomes n=1. Yes, this is what is desired. Basically I want to find the posterior mode of LL_all.

JMP Phillips on 19 Aug 2015
If gidraw is a scalar, your problem doesn't make sense, as LL_all is just a number. If gidraw is vector, the maximum of -[log(normpdf) + int] is +Inf.
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JMP Phillips on 20 Aug 2015
still confused sorry, your code just returns a number. Don't you need to specify a range of inputs for the distribution, so that you can find the maximum within the range? In your equation for LL_all, which is the vector input, is it Int?