Non-linear curve fitting

I apologize in advance if there there are similar cases of this question already getting answered, I tried following along but had trouble applying the given solutions to my own issue and would really appreciate a step-by-step solution.

I have a case where I've gathered experimental data, x and y where both x and y are vectors and im trying to fit it to the equation y = c1 + (c2*x)/(1 + c3*x)

I need to find a way to solve for c1, c2, and c3. Any help would be tremendously appreciated

[Stephan]

please provide the code you have tried so far.

Answer 1

[Star Strider]

You need to define your model function as a function, then use some optimization function to fit the parameters.

Example:

yfcn = @(c1,c2,c3,x) c1 + (c2.*x)./(1 + c3.*x);                             % Model Function (Objective Function)

x = rand(10,1);                                                             % Create Data
y = rand(10,1);                                                             % Create Data

[B,fval] = fminsearch(@(b) norm(y - yfcn(b(1),b(2),b(3),x)), [1; 2; 1]);    % Estimate Parameters
C1 = B(1)
C2 = B(2)
C3 = B(3)

There are many other functions you can use to estimate the parameters, including fmincon, fminunc, nlinfit, lsqcurvefit, and ga, as well as many others. See the documentation for the various functions (including norm here) to understand how to use them.

Answer 2

[Matt J]

fminspleas would be good for this (Download Here)

c3_guess =  ____; %As good a guess as you know of c3

flist={1,@(c3,x)x./(1+c3.*x)};

[c3,c12]=fminspleas(flist,c3_guess);

c=[c12,c3];