[AstroPy] Info LevMarLSQFitter

[Peter Erwin]

Hi Zé,

As an aside, the fact that the Sersic2D model is nonlinear in its parameters is formally
irrelevant, since Levernberg-Marquardt is by design a *non-linear least-squares* algorithm.
(Levenberg’s original 1944 paper describing the algorithm was titled "A Method for the Solution 
of Certain Non-Linear Problems in Least Squares”.)

In practice, I find that Levenberg-Marquardt *usually* finds the global minimum
in galaxy image-fitting problems (e.g., I get the same solution when running Imfit
with Levenberg-Marquardt or with the Differential Evolution algorithm, which
doesn’t use initial values), though there *are* cases where L-M does get trapped in
local minima. (The fact that Diana says she “always” gets a different result for 
different starting parameters maybe suggests something else is the problem.)


Diana — have you tried using an alternate fitting algorithm, such as the SimplexLSQFitter
class? (Simplex fitters tend to be less likely to be trapped by local minima than
Levenberg-Marquardt, though they’re usually significantly slower.)


cheers,

Peter [Erwin]

> On May 12, 2020, at 11:17 AM, Zé Vinícius <jvmirca at gmail.com> wrote:
> 
> Hi Diana,
> 
> From my understanding, LevMarLSQFitter uses the least-squares function as the objective to be minimized using the Levenberg-Marquardt algorithm.
> 
> Because Sersic2D is a non-linear model on the parameters to be fitted, the problem is most likely non-convex, which means that Levenberg-Marquardt only guarantees to find a local solution, which will depend on the initial value for those parameters.
> 
> Best,
> Zé
> 
> On Tue, May 12, 2020 at 4:53 PM Diana Scognamiglio <dianasco at astro.uni-bonn.de> wrote:
> Dear Astropy Staff,
> 
> I am Diana Scognamiglio and I have some problems to deep understand how LevMarLSQFitter works.
> 
> I am trying to fit a mock Sersic galaxy using the LevMarLSQFitter classe, coding these lines:
> 
>  
>  
> ini_mod =
> EllipSersic2D(flux=ini_flux, r_eff=ini_r_eff, n=ini_n, x_0=stampsize/2.0, y_0=stampsize/2.0, g1=0.0, g2=0.0)
> 
> fitter = fitting.LevMarLSQFitter()
> 
> fit_mod = fitter(ini_mod, x_array, y_array, stamp, weights=weights, maxiter = 1000, acc=1.0e-7, epsilon=1.0e-6,
> estimate_jacobian=False)  
> 
>  
> I have figured out that if I change the initial parameters in ini_mod (i.e., ini_flux, ini_r_eff, etc), I counterintuitively obtain always a different result although the galaxy I am fitting is the same. How does the fit depend on those initial parameters?
> 
> Please, can you help me with this issue?
> 
> Thank you in advance.
> 
> I wait for hearing from you.
> 
> Best regards,
> 
> Diana Scognamiglio
> 
>  
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> 
> -- 
> Zé Vinícius
> https://mirca.github.io
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=============================================================
Peter Erwin                   Max-Planck-Insitute for Extraterrestrial 
erwin at mpe.mpg.de              Physics, Giessenbachstrasse
tel. +49 (0)176 2481 7713     85748 Garching, Germany
fax  +49 (0)89 30000 3495     https://www.mpe.mpg.de/~erwin