# how to use lsqnonlin to solve conditional equation

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cheng li on 5 Sep 2021
Commented: cheng li on 8 Sep 2021
i would like to input the following equation in matlab and use lsqnonlin to find the C0, Cinfi1, k1, t2start, Cinfi2 and k2 that can fit an obriginal data?
Are there anyone knowning how to do that?

Fabio Freschi on 7 Sep 2021
Edited: Fabio Freschi on 7 Sep 2021
The following code should be self explainatory. In the opposite case, simply ask
clear all, close all
% some dummy params values
C0 = 2;
Cinf1 = 10;
k1 = 2;
t2start = 3;
Cinf2 = 8;
k2 = 3;
% t vector
tData = linspace(0,10,50);
% data + noise
rng(0); % for reproducibility
yData = C0+Cinf1*(1-exp(-k1*tData))+(tData >= t2start).*(Cinf2*(1-exp(-k2*(tData-t2start))))+0.3*randn(size(tData));
% anonymous function for fitting (function-data) that must be minimized
% using least squares
% x(1) = C0
% x(2) = Cinf1
% x(3) = k1
% x(4) = t2start
% x(5) = Cinf2
% x(6) = k2
C = @(x)x(1)+x(2)*(1-exp(-x(3)*tData))+(tData >= x(4)).*(x(5)*(1-exp(-x(6)*(tData-x(4)))))-yData;
% initial values (experience may help here)
x0 = [1 1 1 1 1 1];
% fitting
x = lsqnonlin(C,x0);
Local minimum possible. lsqnonlin stopped because the final change in the sum of squares relative to its initial value is less than the value of the function tolerance.
% plot
figure, hold on
plot(tData,yData,'o');
% reconstruction of the best fit from the anonymous function
plot(tData,C(x)+yData);
legend('data','best fit');
cheng li on 8 Sep 2021
thank you so much