Weighted curve fitting with lsqnonlin

Question

friet 2016-2-28

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/270500-weighted-curve-fitting-with-lsqnonlin

回答： Torsten 2016-2-29

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