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

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)?

Thank you in advance

[John D'Errico]

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]

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.

Answer 1

[Sargondjani]

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])

[3Nz0]

Thank you for the help. The problem is I reach just one value for g and t.

I made an mfile in which:

%n=3
y1=@(B,x)B(1,1).*exp(-x/B(1,2));
y2=@(B,x)B(2,1).*exp(-x/B(2,2));
y3=@(B,x)B(3,1).*exp(-x/B(3,2));
y=@(B,x)y1(B,x)+y2(B,x)+y3(B,x); %sum()
B0=rand(2,2) %starting values
ObjFunc=@(B) sum(((y_exp-y(B,x))^2)/y_exp^2);
[B_est, SSE] = fminsearch(ObjFunc, B0)

Basically I manually build the sum. However, when "n" is different I need to cut\add some pieces in the sum.

I'd like to make this in automatic way.

[Sargondjani]

Ok, i see your point now.

One way to do it, would be to define a function with a loop over n:

function y_sum = fun_y_sum(x,B)

y_sum = 0;

for ii = 1:size(B,1)

y_sum = y_sum + B(ii,1)*exp(-x/B(ii,2));

end

end

[3Nz0]

Many thanks for your help.

So, this should be the final script:

x_exp=rand(10,1);
y_exp=rand(10,1);
n=input('insert n: ')
B=ones(n,2);

B0=rand(n,2); %starting values
ObjFunc=@(B) sum(((y_exp-fun_y_sum(x_exp,B)).^2)./y_exp.^2);
[B_est, SSE] = fminsearch(ObjFunc, B0)

function y_sum = fun_y_sum(x,B)
y_sum = 0;
for ii = 1:size(B,1)
    y_sum = y_sum + B(ii,1)*exp(-x/B(ii,2));
end
end

[Sargondjani]

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]

I don't know, in the old script B was a matrix in fminsearch().

Again, many thanks for your help