Serialising covariance of CompoundSpectralModel with a TemplateSpectralModel

Bug description

The covariance matrix is incorrectly written for a CompoundSpectralModel which is a product of a TemplateSpectralModel and a NormSpectralModel

To Reproduce

Either serialise the diffuse_iem model in the Fermi-LAT tutorial, or

from gammapy.modeling.models import *
t = TemplateSpectralModel(energy=[1,3,9]*u.TeV, 
                        values=[20,30,40]*1 / (u.cm*u.cm*u.MeV*u.s))
p = PowerLawNormSpectralModel()
sk = SkyModel(spectral_model=t*p, name="xx")
Models([sk]).write("test.yaml", overwrite=True)
m1 = Models.read("test.yaml")

This leads to an error

File ~/Gammapy-dev/gammapy/gammapy/modeling/models/core.py:362, in DatasetModels.covariance(self, covariance)
    359 @covariance.setter
    360 def covariance(self, covariance):
    361     self._check_covariance()
--> 362     self._covariance.data = covariance
    364     for model in self._models:
    365         subcovar = self._covariance.get_subcovariance(model.covariance.parameters)

File ~/Gammapy-dev/gammapy/gammapy/modeling/covariance.py:59, in Covariance.data(self, value)
     57 shape = (npars, npars)
     58 if value.shape != shape:
---> 59     raise ValueError(
     60         f"Invalid covariance shape: {value.shape}, expected {shape}"
     61     )
     63 self._data = value

ValueError: Invalid covariance shape: (13, 12), expected (13, 13)

This occurs because the norm parameter is present on both the TemplateSpectralModel and the normed model, and is incorrectly serialised during writing.

Other information

It would be good to sort this before 1.0 Otherwise, Fermi datasets serialisation is difficult.

[registerrier]

Apparently changing to this:

def write_covariance(self, filename, **kwargs):
    """Write covariance to file
    Parameters
    ----------
    filename : str
        Filename
    **kwargs : dict
        Keyword arguments passed to `~astropy.table.Table.write`
    """
    names = self.parameters_unique_names
    table = Table()
    table["Parameters"] = names

    for idx, name in enumerate(names):
        values = self.covariance.data[idx]
        table[str(idx)] = values

    table.write(make_path(filename), **kwargs)

might be working.

We don’t need to have the name repeated on the lines and columns of the Table

[adonath]

Is this safe? It might be useful to have additive models with some correction from norm models, no?

Yes, but handling the hierarchy adds additional complexity. If we’d like to handle arbitrary complex hierarchies we need a recursive solution to generate the unique parameter names…

So we could end up with things like:

['xx.spectral.model1.model2.model1.norm',
 'xx.spectral.model2.model1.model2norm',
 ...]