# How to evaluate parameters in sum() of handle functions with fminsearch

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3Nz0 on 24 Oct 2021
Commented: 3Nz0 on 24 Oct 2021
I have some problems with the evaluation of parameters in a sum of handle functions
x_exp and y_exp are known vectors.
I want to evaluate the parameters in the following function:
The idea is to use fminsearch to evaluate g(i) and t(i): ObjFunc=@(g,t)sum((y_exp-y_eq(x))^2/(y_exp^2))
Looking in the community, I tried to use:
x_exp=rand(1,10); %just to define the known vectors
y_exp=rand(1,10);
n=3;
g=rand(1,n);
t=rand(1,n);
syms x i
y_eq = matlabFunction( symsum(g.*exp(-x_eq./t), i, 1, n));
My question is: "How can I evaluate g(i) and t(i)?
John D'Errico on 24 Oct 2021
Edited: John D'Errico on 24 Oct 2021
This is a question I see often, where somene feels they need to introduce symbolic parameters. When there is no reason to use a symbolic expression, DON'T! That you don't know the value of something does not mean it must be symbolic. And, as soon as you make things symbolic, you make MATLAB run MUCH more slowly.
As you can see in the answer you got, no symbolic parameters needed to be created or involved.
3Nz0 on 24 Oct 2021
Sorry, I know it is not necessary to use the symbolic parameters.
I solved the problem but, actually, I really don't know how to make this in an automatic way.
My mfile (posted in the other comment) works fine, but an adaptive mfile depending on "n" should be great.
Thank you.

Sargondjani on 24 Oct 2021
Take a look at this. I hope it helps.
x_exp=rand(1,10); %just to define the known vectors
y_exp=rand(1,10);
n=3;
g=rand(1,n);
t=rand(1,n);
%Create function handle:
fun_eq = @(g,t,x_eq)sum(g*-exp(-x_eq/t));
% Evalute y_eq for g(2) and t(2):
ii = 2;
y_eq = fun_eq(g(ii),t(ii),x_exp);
% Use fminsearch as follows:
%Define the objective
ObjFunc = @(g,t,x_,y_)sum((y_-fun_eq(g,t,x_)).^2./(y_.^2));
% Use x_exp and y_exp as input x_ and y_, and g and t are inputs x(1) and (x2)
[sol] = fminsearch(@(x)ObjFunc(x(1),x(2),x_exp,y_exp),[1,1])
Sargondjani on 24 Oct 2021
Edited: Sargondjani on 24 Oct 2021
There is one thing. I think the argument in fminsearch needs to be a vector. So you would need a transformation. So:
ObjFunc=@(B) sum(((y_exp-fun_y_sum(x_exp,B(1:n),B(n+1:2*n))).^2)./y_exp.^2);
B0=rand(2*n,1);
[B_est, SSE] = fminsearch(ObjFunc, B0)
B_est = [B_est(1:n),B(n+1:2*n)]
with
function y_sum = fun_y_sum(x,B1,B2)
y_sum = 0;
for ii = 1:size(B1,1)
y_sum = y_sum + B1(ii,1)*exp(-x/B2(ii,1));
end
end
3Nz0 on 24 Oct 2021
I don't know, in the old script B was a matrix in fminsearch().
Again, many thanks for your help

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