Hello !
I use the lsqnonlin Matlab function to fit a curve, called f, to my experimental points (coordinates x_i and y_i). Thus, we have to make simple :
[optimum_result,resnorm,residual,exitflag,output,lambda,jacobian] = lsqnonlin( y_i – f(a,x_i) ) where a is my fit parameter.
I'm wondering what is the definition of the jacobian returned by Matlab :
– the square of the Jacobian returned by lsqnonlin = the second derivative of the residual squared (calculated at the optimum, means the best fit parameter found). Here my residual is : y_i – f(a,x_i). it is the definition found here http://www.ligo-wa.caltech.edu/~ehirose/work/andri_matlab_tools/fitting/MatlabJacobianDef.pdf
OR
– the Jacobian returned by lsqnonlin = the derivative of the residual (calculated at the optimum). It is why I have understand reading Matlab help.
If the answer is the derivative of the residual (calculated at the optimum), I have a misunderstanding. In fact, at the optimum, the sum of my residual vector squared have to be minimum. So the sum of my jacobian, a derivative, has to be equal to (or close to) zero. yes or not ? In Matlab it is not equal to zero, it is why I have a misunderstanding.
Thanks.
Best Answer