Fitting different datasets simultaneously, using models with parameters tied across models

Given two models called a with parameters a1, a2 and b with parameters b1, b2, I want to do a joint fit, of a evaluated on data1 (in my example that data is a two-dimensional image) and b evaluated on data2 (in my example a different image which happens to have the same dimensionality, but in the general case, that could be different), such that parameters a1 and b1 are tied through some arbitrary python function (in my example: the identity function, a1 = b1).

I’ll describe my specific use case in mode detail. In this case, I deal with PSF fitting, but note that this is outside of the scope of current photutils and the modeling problem is more general. I can give examples for fitting spectra or SEDs, too, I just happened to come upon this problem by working with images right now, that’s why I describe this example here: I have two images. They show the same object on the same WCS, but that object has different fluxes (duh, it’s in different bands). Unfortunately, there are a lot of unususable pixles in both images (saturated from a near-by object). Thus, I’d like to fit a psf (let’s call the models psf1 and psf2) to both images at the same time and require that x, y are the same, but the flux is different. So, I have two models, evaluated on two different datasets (psf_621_copy on image1 with parameters x, y, amplitude_1 and psf_845_copy evaluated on image2 with parameters x, y, flux2). I want to minimize the combined fit statistic. Is there a reasonable way to make that happen with astropy now or do I have to wait for #8769? Maybe something like psf1 | psf2 evaluated on data that is a list with two elements (image 1 and amplitude2). But then, how do I couple x and y? Seems that a problem like this is not unique to me, but I don’t find a way to express it well in the current astropy modelling paradigm.

I’m not asking for help with a specific problem, I’m describing the use case here for a feature request. If that’s already possible in the current version, an example in the docs might be enough.

For reference, I’ll paste below how I address this problem with a custom model, but I feel that there should be (and maybe is already?) a way to make that work by using operations on models as opposed to coding up a user model:

@custom_model
def twobandpsf(xy, x_0=0., y_0=0., amplitude1=1, amplitude2=1.):
    psf_621_copy.x_0_2 = x_0
    psf_621_copy.y_0_2 = y_0
    psf_621_copy.amplitude_3 = amplitude1
    psf_845_copy.x_0_2 = x_0
    psf_845_copy.y_0_2 = y_0
    psf_845_copy.amplitude_3 = amplitude2
    return np.stack([psf_621_copy(xy[0], xy[1]), psf_845_copy(xy[0], xy[1])])
@custom_model

[karllark]

Not fully. Tying parameters between models using a python function is not supported by JointFitter at this time.

[pllim]

tl;dr – Does #12720 completely resolve this issue?