Weighted nonlinear curve fitting

I have the following code that do non-linear curve fiting. However i want to do weighted curve fitting so that it fits well when the value of x is above 45.

      clear all
      clc
      x = [36.78 ,37.53 ,38.28 ,39.06 ,39.85 ,40.65 ,41.47 ,42.31,43.17 ,44.04 ,44.93 ,45.84 ,46.76 ,46.89 ,47.30 ,48.20 ];
      y = [0.01 ,0.0152 ,0.023 ,0.035,0.0536 ,0.081 ,0.12 ,0.1891 ,0.287 ,0.438 ,0.66 ,1.01494 ,1.544 ,2.35,3.578 ,5.445 ];
      f=0:0.2:3;
      fun = @(params) [x - exp((params(2)-1)*f-1)/(params(2)-1)^2, log(y) - log(params(1)) - (params(2)+1)*f];
  lb = [1e-10,-1+1e-10];                      % Set lower bounds 
  ub = [inf,inf];                             % Set upper bounds
  params0 = [0.001,1.7];                      % Set initial point.
  options.Algorithm = 'levenberg-marquardt';
  params = lsqnonlin(fun,params0,lb,ub,options)
  figure(1)
  plot(x,y,'ko',exp((params(2)-1)*f-1)/(params(2)-1)^2,params(1)*exp((params(2)+1)*f),'b-')
  legend('Data','Best fit')
  grid on

I tried this

W = [1 1 1 1 1 1 1 1 1 1 1 5 5 5 5 5]';
params = lsqnonlin(fun,params0,lb,ub,'Weights',W);

But it didnt work. Any help will be appreciated.

Thanks

[Torsten]

Look at the definition of "fun" when you use nlinfit - it's different from "fun" in lsqnonlin.

Best wishes

Torsten.

[friet]

Thanks!

But i have two equations and the writing the model function with nlinfit is becomming difficult for me. Can you please suggest sth for me plz!

f=0:0.2:3;
y=teta*exp((a+1)*f);
x=exp((a-1)*f-1)/(a-1)^2;

These are my two functions. If i would be using "lsqnonlin, i might do like below.

fun = @(params) [x - exp((params(2)-1)*f-1)/(params(2)-1)^2, log(y) - log(params(1)) - (params(2)+1)*f];
params = lsqnonlin(fun,params0,lb,ub,options)

But with nlinfit, i cant

Thanks

[Torsten]

Since you have a (1x32) vector to be fitted ([x,y]), your vector of weights also must have 32 entries.

I think after this change you will be able to use lsqnonlin for your purpose.

Best wishes

Torsten.

[friet]

it is not working. Can you please have a look at my code

clear all
    clc
    x = [36.78 ,37.53 ,38.28 ,39.06 ,39.85 ,40.65 ,41.47 ,42.31,43.17 ,44.04 ,44.93 ,45.84 ,46.76 ,46.89 ,47.30 ,48.20 ];
    y = [0.01 ,0.0152 ,0.023 ,0.035,0.0536 ,0.081 ,0.12 ,0.1891 ,0.287 ,0.438 ,0.66 ,1.01494 ,1.544 ,2.35,3.578 ,5.445 ];
    f=0:0.2:3;
    w=ones(1,32);

      fun = @(params) [x - exp((params(2)-1)*f-1)/(params(2)-1)^2, log(y) - log(params(1)) - (params(2)+1)*f];
  lb = [1e-10,-1+1e-10];                      % Set lower bounds 
  ub = [inf,inf];                             % Set upper bounds
  params0 = [0.001,1.7];                      % Set initial point.
  options.Algorithm = 'levenberg-marquardt';

params = lsqnonlin(fun,params0,lb,ub,options,'Weight',w)
figure(1)
plot(x,y,'ko',exp((params(2)-1)*f-1)/(params(2)-1)^2,params(1)*exp((params(2)+1)*f),'b-')
legend('Data','Best fit')
grid on