MATLAB: Lsqnonlin and true parameters value

lsqnonlin - true parameter valuesMATLAB

Hi,
I'm trying to calculate true values of parameters and get an information about how good the found parameters are. For this I want to use lsqnonlin, while finding the parameters in my ODE. I wonder how to get:
a) least-squares optimal estimate of the parameter values;
b) Chi squared error;
c) asymptotic standard error of the parameters;
d) asymptotic standard error of the result of the simulation;
e) correlation matrix of the parameters;
f) convergence history;
g) R-squared coeeficient of multiple determination;
while using lsqnonlin. Any suggestions will be appreciated. Thanks in advance, Malgosia

Best Answer

I can help you with a) and f), but for the rest you will have to look elsewhere.
The examples Fit ODE, Problem-Based and Fit an Ordinary Differential Equation (ODE) show two ways of finding a fit to an ODE" problem-based or solver-based. To look at the convergence history, set the Display option to 'iter' before you call solve in the first example or lsqcurvefit in the second:
opts = optimoptions('lsqnonlin','Display','iter');
[rsol,sumsq] = solve(prob,r0,'Options',opts) % first case
% or
opts = optimoptions('lsqcurvefit','Display','iter');
[xbest,resnorm,residual] = lsqcurvefit(@fitlorenzfn,x0,tspan,a,lb,ub,opts);
The values in rsol or xbest are tthe least-squares parameter values. sumsq or resnorm are the resulting sum of squared residuals.
Good luck,
Alan Weiss
MATLAB mathematical toolbox documentation
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