Non linear Least square fitting

Question

aditi 2014-11-1

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https://ww2.mathworks.cn/matlabcentral/answers/160867-non-linear-least-square-fitting

回答： Star Strider 2014-11-1

I have a data set with three columns of X, Y and Y_error coordinates... I have to fit a equation

y = a[x^(-1/k) - 37^(-1/k)]

and find a and k along with the error associated with them. Also while fitting we have to consider the 3rd column also i.e the errors with Y coordinate.

So basically I have to do weighted non linear LS fitting and all this without using CFTOOL

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Answer 1

Star Strider 2014-11-1

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https://ww2.mathworks.cn/matlabcentral/answers/160867-non-linear-least-square-fitting#answer_157333

在 MATLAB Online 中打开

This is how I would do it:

% % b(1) = a,   b(2) = k
y = @(b,x) b(1).*[x.^(-1./b(2)) - 37.^(-1./b(2))];
XYE = rand(10,3);                       % X, Y, Error Vectors Matrix — Create Data
X = XYE(:,1);                           % X Data
Y = XYE(:,2);                           % Y Data
W = XYE(:,3);                           % Weight Data
WLSCF = @(b) sum(W.*(Y - y(b,X)).^2);   % Weighted Least Squares Cost Function
B = fminsearch(WLSCF, rand(2,1));