how to use lsqnonlin to solve conditional equation

Question

cheng li 2021-9-5

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1446979-how-to-use-lsqnonlin-to-solve-conditional-equation

评论： cheng li 2021-9-8

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?

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Fabio Freschi 2021-9-7

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1446979-how-to-use-lsqnonlin-to-solve-conditional-equation#answer_782369

编辑：Fabio Freschi 2021-9-7

在 MATLAB Online 中打开

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');