Creating fun structure in a loop

Hi,

as a bloody beginner i cant figure out on how i could write a loop, which should sum up a specific term in a symbolic way.

I need

fun = @(x)x(1)*(1 - exp(-xdata/x(2))) + x(3)*(1 - exp(-xdata/x(4))) + x(5)*(1 - exp(-xdata/x(6))) + x(7)*(1 - exp(-xdata/x(8))) - ydata;

but i want to write a loop, so that the term

x(1)*(1 - exp(-xdata/x(2)))

is added as often as i want.

I need it for thermal calculation for a changeable amount of RC-terms in the Foster model, which is later tranformed into the Cauer model.

My code in general:

prompt = {'Enter the desired amount of RC-Terms'};
dlgtitle = 'RC-Terms';
definput = {''};
opts.Interpreter = 'tex';
answer = inputdlg(prompt,dlgtitle,[1 40],definput,opts);
amount = str2double(answer{1});
x0= 1:1:2*amount; % starting position for fit algorithm
for i=1:2:2*amount
    x0(1,i)=0.1;
for k=2:2:2*amount
    x0(1,k)=1;
end
end
options = optimoptions(@lsqnonlin,'Algorithm','levenberg-marquardt');
fun= %this is, where the loop should be for a variable amount of Rc terms
x = lsqnonlin(fun,x0,[],[],options);
...

[darova]

I don't understand the question

[LuReb]

I need a function that expands automatically based on the selected number. My default term is

x(1)*exp(-t/x(2))

, physically

R(1)*exp(-t/tau(2))

, which should be concatenated as often as you like depending on the number. The vector x contains different values, speaking always [R1 tau1 R2 tau2 R3 tau3 ...]. Therefore I need for 2 terms:

x(1)*exp(-t/x(2))+x(3)*exp(-t/x(3))

For 3 terms:

x(1)*exp(-t/x(2))+x(3)*exp(-t/x(4))+x(5)*exp(-t/x(6))

and so on.

I hope it is clear now :)

Answer 1

[Rik]

You could do it with a loop, but I would prefer a more direct strategy. Depending on the shape of x0 and t, the sum version will automatically determine the number of terms, unlike the loop version.

t=rand(2,1);
amount = 2;

% starting position for fit algorithm
x0=zeros(1,amount*2);x0(1:2:end)=0.1;x0(2:2:end)=1;

options = optimoptions(@lsqnonlin,'Algorithm','levenberg-marquardt');

fun_loop=@(x) 0;%initialize
for k=1:2:(2*amount)
    fun_loop=@(x) fun_loop(x) + x(k)*exp(-t/x(k+1));
end

fun_sum=@(x)sum( x(1:2:end).*exp(-t./x(2:2:end)) ,2);

x_fit1 = lsqnonlin(fun_loop,x0,[],[],options);
x_fit2 = lsqnonlin(fun_sum,x0,[],[],options);

%if this value is small (0 or at least <1e-15) the 2 methods are equivalent
clc,max(abs(x_fit1-x_fit2))

[LuReb]

perfect, thank you very much!