nonlinear fit for a sum function

i want to fit the following function to a given data i have.

%DATA
X=linspace(1,20,100)';
Y=2*exp(0.13*X)+11.2  +  4*exp(0.13*X)+11.2  +  7*exp(0.13*X)+11.2; %consider it as a given data

n=[2 4 7]; %given 
b=[0.1 11]; %initial guess

i used fitnlm as follows:

modelfun=@(b,x) 2.*exp(b(1).*x)+b(2)  +  4.*exp(b(1).*x)+b(2)  +  7.*exp(b(1).*x)+b(2);
beta = fitnlm(X,Y,modelfun,b)

Now, i need help with writing 'modelfun' in a nondirect way because the real problem i have is () ,

and obviously it is not practical to write it directly as above.

Answer 1

[Ameer Hamza]

This is the general way to write this problem

%DATA
X=linspace(1,20,100)';
Y=2*exp(0.13*X)+11.2  +  4*exp(0.13*X)+11.2  +  7*exp(0.13*X)+11.2; %consider it as a given data

n=[2 4 7]; %given 
b=[0.1 11]; %initial guess

m = numel(n);

modelfun = @(b,x) sum(n).*exp(b(1).*x)+m*b(2);
beta = fitnlm(X,Y,modelfun,b)

[Dor Bettran]

Thank you, but i wanted to know if there is a more general way for this.

For example, if i have more complicated function like:

n=[2 4 7]; %given 
m=[11 2 3] %given

[Ameer Hamza]

The solution will change from model to model, for example, for the model in your comment, following will work

modelfun = @(b,x) sum(exp((n-m)/b(1).*x), 2);

This uses some automatic-array expansion trick which might be difficult to understand at the beginning, so for a general solution, you can just write a for-loop.

fun = @(b,x) modelfun(b,x,n,m);
beta = fitnlm(X,Y, fun,b)

function y = modelfun(b,x,n,m)
    y = zeros(size(x));
    for i = 1:numel(n)
        y = y + exp(n(i)-m(i)/b(1).*x);
    end
end

[Dor Bettran]

thank you very much, very helpful!