Solving a non linear least square of a sum function with two unknowns

Question

Zehra Ese 2019-12-18

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/497297-solving-a-non-linear-least-square-of-a-sum-function-with-two-unknowns

编辑： Matt J 2019-12-19

Hello,

i have a Chi-Square merit function with two unknown k1 and k2. Unfortunately, I don't know exactly which syntax to use to minimize this function in order to determine k1 and k2.

are known, each a vector with 1 column and 17 rows.

are constant values.

Unfortunately, I am also relatively new with Matlab. I would be very happy about a step by step explanation. I have already found out that lsqnonlin can be used as a solver.

I appreciate your help. Thank you.

2 个评论
显示无隐藏无

Star Strider 2019-12-18

Note that lsqnonlin fits a function to data.

Do you have a matching vector for

?

Zehra Ese 2019-12-19

Hi,

you're right, I didn't give enough information. Yes its correct I want to fit a function to data. We have given xdata and ydata. g vector contains all measured values. The first term in parantheses is the function we want to fit to the data. I would like to determine

and

, while minimizing this Chi-square funktion. All the other coefficients are known, as explained before.

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Matt J 2019-12-18

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/497297-solving-a-non-linear-least-square-of-a-sum-function-with-two-unknowns#answer_407003

编辑：Matt J 2019-12-19

在 MATLAB Online 中打开

It would look like this,

kInitial = __________; %initial guess of k
kOptimal = lsqnonlin(@(k) residual(k,am,bm,cm,g,ch,bh,ah) , kInitial);  %do the optimization
function r=residual(k,am,bm,cm,g,ch,bh,ah)
   k1=k(1); %extract k(i) into separate variables, for convenience
   k2=k(2);
   
   numerator=cm+bm*k2+am*k1;  %calculate numerator expression for all m
   denominator=ch+bh*k2+ah*k1; %calculate demonator expression for all m
   r=numerator./denominator - g; %calculate the vector of residuals, for all m
end