Is it possible to create a general function where the user can specify the number of variables between each execution? The variables would have the same relation between themselves and their neighbours e.g. x2 would have the same relation with x1 and x3 as x3 would with x2 and x4 and so forth. The aim is to refine the partition without having to hard code the function.
It would help a lot if the function was symbolic since I need to differentiate it, I need the Hessian, but the function also has to be able to be evaluated with fminunc, I need to find the values of the variables,x, which give the function its maximum.
I have included a sample of the code to give you an idea, I would like to be able to extend it to an arbitrary high xN.
function q=defOrnUhl(x0,xT,t0,T,theta)
m=10;
deltaT=(T-t0)/m;
theta=theta;
x0=x0;
xT=xT;
vpaPi=vpa(pi);
syms x1 x2 x3 x4 x5 x6 x7 x8 x9
q=symfun((-1/2*log(2*vpaPi*deltaT)-1/2*(((x1-(1-theta*deltaT)*x0))^2)/deltaT...
-1/2*log(2*vpaPi*deltaT)-1/2*(((x2-(1-theta*deltaT)*x1))^2)/deltaT...
-1/2*log(2*vpaPi*deltaT)-1/2*(((x3-(1-theta*deltaT)*x2))^2)/deltaT...
-1/2*log(2*vpaPi*deltaT)-1/2*(((x4-(1-theta*deltaT)*x3))^2)/deltaT...
-1/2*log(2*vpaPi*deltaT)-1/2*(((x5-(1-theta*deltaT)*x4))^2)/deltaT...
-1/2*log(2*vpaPi*deltaT)-1/2*(((x6-(1-theta*deltaT)*x5))^2)/deltaT...
-1/2*log(2*vpaPi*deltaT)-1/2*(((x7-(1-theta*deltaT)*x6))^2)/deltaT...
-1/2*log(2*vpaPi*deltaT)-1/2*(((x8-(1-theta*deltaT)*x7))^2)/deltaT...
-1/2*log(2*vpaPi*deltaT)-1/2*(((x9-(1-theta*deltaT)*x8))^2)/deltaT...
-1/2*log(2*vpaPi*deltaT)-1/2*(((xT-(1-theta*deltaT)*x9))^2)/deltaT), [x1 x2 x3 x4 x5 x6 x7 x8 x9]);
end
