How to obtain the Jacobian matrix (or co-variance matrix) from a multi- or global-search

Using lsqnonlin for non-linear fitting, you can obtain Jacobian matrix in the output:

[x,resnorm,residual,exitflag,output,lambda,jacobian] = lsqnonlin(___)

I however used multistart with lsqnonlin to avoid local minima. On contrary, the command run which is needed to do a multisearch with lsqnonlin (see here ) dos not provide Jacobian as an output. Any suggestion how can I get it? I need it to determine the confidence intervals for the estimated parameters.

Answer 1

[Matt J]

Once you have the solution xsol using multistart, just run lsqnonin without multistart and with xsol as the initial guess. If xsol was a solution, it should stop in a single iteration (or you can force it to) and the output should be the finite difference Jacobian at that point.

[Mehdi Gh]

Thanks Matt for you answer. Do you know how MATLAB calculates this Jacobian matrix? I mean if I want to calculate it analytically, what I have to do?

[Matt J]

It uses finite difference computations, if you do not provide your own analytical Jacobian computation. To do that, you use the 'SpecifyObjectiveGradient' option, as described here.