Re: Custom jacobian (dfdp) in nonlin_curvefit - calling parameters?

[Pavel Hofman]

Dne 18. 11. 19 v 18:39 Olaf Till napsal(a):
> 'dfdp'
>       Function computing the Jacobian of the residuals with respect to
>       the parameters, assuming residuals are reshaped to a column vector.
>
> So for calculating the Jacobian, assume that the array returned by 'f'
> is reshaped to a column vector (as with array(:)). So the Jacobian is
> 2D.
>
> (The differences between nonlin_curvefit and nonlin_residmin do not
> affect this.)

Now my f returns one vector column (first half output of the first 
function, the second half output of the second function).

The default dfdp of minimum differences works perfect. The sum of errors 
is 1e-17 in about 7 iterations.

sum((y - model_values).^2) with 2000 values.


My dfdp is IMO correct now, I checked several times. Yet I never get 
more than 3 iterations, with the sum of errors about 1e-10 which is too 
inprecise for my case.

I configured:

settings = optimset ('dfdp', fDfdp, 'TolFun', 1e-17, 'TolX', 1e-17, 
'Display', "iter");


No change, always only 2 - 3 iteration. I am listing dfdp output before 
leaving the function and values in the four columns of dfdp output make 
sense.

Please could the real-finite differences DFDP do someting significantly 
different than a custom dfdp in terms of settings and tolerances? I did 
not see anything in __nonlin_residmin__ nor in __lm_svd__ when stepping 
through the code in debugger.

My custom dfdp worked great for values of <0, 1>. But when I am fitting 
to values < 1e-7 (incl. p values), the custom dfdp is significantly 
worse than the finite differences. All calculations performed in double.

I can stay with the finite differences, but wanted to try if a custom 
dfdp would further improve the precision since even tiny imprecisions 
are important in my project.

I very much appreciate any recommendation for further troubleshooting.

Regards,

Pavel.