[AstroPy] Info LevMarLSQFitter

Wed May 13 12:59:09 EDT 2020

Hi Peter,

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”.)

The thing is that if the model were linear in its parameters, then the
problem would be convex, and LM would find the global unique optimum
no matter the initial point. But if that were the case, I'd advise other
methods to get that solution.

Best,
Zé

On Wed, May 13, 2020 at 10:42 PM Paul Barrett <pebarrett at gmail.com> wrote:

> Personally, I would suggest ditching the Levenberg-Marquardt and Simplex
> algorithms and using an interior point method, which is more versatile and
> robust in finding the global minimum. Interior point methods more easily
> handle constraints and provide better convergence information. cvxopt is a
> nice Python package for second order problems, which appears to be your
> problem. However, if your problem is nonconvex, i.e., has local minima,
> then you might want to consider using a branch-and-bound algorithm, which
> will find the global minimum, although the algorithm is not as efficient.
> The algorithm also works with integer parameters, which are inherently
> nonconvex.
>
> Cheers,
> Paul
>
>
>
> On Tue, May 12, 2020 at 8:36 AM Peter Erwin <peter.erwin at gmail.com> wrote:
>
>> 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
>> >
>> >
>> > _______________________________________________
>> > AstroPy mailing list
>> > AstroPy at python.org
>> > https://mail.python.org/mailman/listinfo/astropy
>> >
>> >
>> > --
>> > Zé Vinícius
>> > https://mirca.github.io
>> > _______________________________________________
>> > AstroPy mailing list
>> > AstroPy at python.org
>> > https://mail.python.org/mailman/listinfo/astropy
>>
>> =============================================================
>> 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
>>
>>
>>
>>
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-- 
Zé Vinícius
https://mirca.github.io
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