Sum function handle in a for loop

Hi, Im trying to sum function handle for fitting data with the function fitnlm.

My non-linear-model is:

sigma=2;
mu=[1 2 3 4];
modelfun = @(b,x) b(1) * exp(-(x(:, 1) - mu(1)).^2/sigma.^2) + b(2) * exp(-(x(:, 1) - mu(2)).^2/sigma.^2) ... 
    + b(3) * exp(-(x(:, 1) - mu(3)).^2/sigma.^2) + b(4) * exp(-(x(:, 1) - mu(4)).^2/sigma.^2);

But i want to sum all this expressions in a for loop because in general i do not know the number of gaussian im trying to fit.

I tried things like this:

M = b(1) .* exp(-(x(:, 1) - mu(1)).^2/sigma.^2);
for  k = 2:N
     add = @(b,x) b(k) .* exp(-(x(:, 1) - mu(k)).^2/sigma.^2);
     M = M + add; 
end

and many variants but none of them did work.

I'm sure there are some ways to sum up function handle in for loop but i can't figure out.

Regards

Answer 1

[Sulaymon Eshkabilov]

Hi,

Using symbolics might be an easy solution here:

sigma=2;
syms x 
syms b [1 4]
syms mu [1 4 ]

M =(b(1) .* exp(-(x - mu(1)).^2/sigma.^2));
for k = 2:numel(mu)
    M = M+ b(k) .* exp(-(x - mu(k)).^2/sigma.^2);
end
% Then you can substitte the values of mu, b using subs()

Good luck

[Clément Métayer]

Thx for your answer !!

[Walter Roberson]

After you have the symbolic M then use matlabFunction() to create an anonymous function for use in fitting. Be sure to use the 'vars' option so that the inputs will be in the correct order.

Answer 2

[Walter Roberson]

M = @(b,x) b(1) .* exp(-(x(:, 1) - mu(1)).^2/sigma.^2);
for  k = 2:N
     add = @(b,x) b(k) .* exp(-(x(:, 1) - mu(k)).^2/sigma.^2);
     M = @(b,x) M(b,x) + add(b,x); 
end

At the end if you look at M you will see just

M(b,x) + add(b,x)

so it will look like it did not work.

The result will not be efficient.

You should consider other routes, such as

ROW = @(V) reshape(V,1,[]);
M = @(b,x) sum(ROW(b) .* exp((x(:,1) - ROW(mu)).^2/sigma.^2),2)

This requires that b and mu are the same length. It does not assume that b and mu are row vectors (the code could be made slightly more efficient if you were willing to fix the orientation of b and mu, especially if you knew for sure they were row vectors)

[Clément Métayer]

Thank you for your answer, it helps me. I accepted the other answer just because i can only accept one.

Regards