Re: lsqnonlin and nonlin_residmin

[Olaf Till]

On Sun, May 31, 2015 at 02:51:40PM +0100, Asma Afzal wrote:
> Hi Olaf,
> 
> > Done, you can check it out from the repository. 'outp' returned by
> > __nonlin_residmin__.m and nonlin_residmin.m/nonlin_curvefit.m now
> > contains a field lambda which should be identical to what Matlabs
> > functions return, so you can just copy this field.
> 
> Thank you for this. My only confusion is that the values of lambda for
> Matlab and Octave and are generally different. For eg.
> 
> t = [0 .3 .8 1.1 1.6 2.3]';
> y = [.82 .72 .63 .60 .55 .50]';
> yhat = @(c,t) c(1) + c(2)*exp(-t);
> x0=[1;1];
> lb=[0.2;0.6];
> 
> lsqnonlin(@(c)yhat(c,t)-y,[1 1],lb) returns c=[0.3541 0.6000], flag=1
> and lambda.lower =  [0;0.1506] for default settings.
> In octave, we get same value of c but cvg= 3 and lambda.lower= [0;
> 7.61] for default settings. Decreasing TolFun still does not change
> cvg but reduces lambda.lower to [0;0.81] for TolFun= 1e-10 and then
> increases it to [0;0.186] for TolFun=1e-20 onward.
> 
> Is it because of a different backend? I tried some other examples too
> but I'm not getting lambda consistent with Matlab.

Lambda depends among others on the way the Hessian is approximated (or
an equivalent calculation is done) by the solver. So lambda can be
different even for the same parameters in the same algorithm (in
particular __lm_svd__) if the previous course of optimization was
different. It's no use trying to get the same lambda as Matlab with a
different algorithm.

Olaf

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