Model Cookbook#
The model cookbook provides a concise reference to model composition tools, specifically the Model
and Collection objects.
Examples using different PyAutoGalaxy API’s for model composition are provided, which produce more concise and readable code for different use-cases.
Simple Model#
A simple model we can compose has a galaxy with a Sersic light profile:
bulge = af.Model(ag.lp.Sersic)
galaxy = af.Model(ag.Galaxy, redshift=0.5, bulge=bulge)
model = af.Collection(galaxies=af.Collection(galaxy=galaxy))
The model total_free_parameters tells us the total number of free parameters (which are fitted for via a
non-linear search), which in this case is 7.
print(f"Model Total Free Parameters = {model.total_free_parameters}")
If we print the info attribute of the model we get information on all of the parameters and their priors.
print(model.info)
This gives the following output:
galaxies
galaxy
redshift 0.5
bulge
centre
centre_0 GaussianPrior, mean = 0.0, sigma = 0.3
centre_1 GaussianPrior, mean = 0.0, sigma = 0.3
ell_comps
ell_comps_0 GaussianPrior, mean = 0.0, sigma = 0.5
ell_comps_1 GaussianPrior, mean = 0.0, sigma = 0.5
intensity LogUniformPrior, lower_limit = 1e-06, upper_limit = 1000000.0
effective_radius UniformPrior, lower_limit = 0.0, upper_limit = 30.0
sersic_index UniformPrior, lower_limit = 0.8, upper_limit = 5.0
More Complex Models#
The API above can be easily extended to compose models where each galaxy has multiple light or mass profiles:
bulge = af.Model(ag.lp.Sersic)
disk = af.Model(ag.lp.Exponential)
bar = af.Model(ag.lp.Sersic)
galaxy = af.Model(
ag.Galaxy,
redshift=0.5,
bulge=bulge,
disk=disk,
bar=bar
)
model = af.Collection(galaxies=af.Collection(galaxy=galaxy))
The use of the words bulge, disk and bar above are arbitrary. They can be replaced with any name you like, e.g. bulge_0, bulge_1, star_clump, and the model will still behave in the same way.
The API can also be extended to compose models where there are multiple galaxies:
bulge = af.Model(ag.lp.Sersic)
galaxy_0 = af.Model(
ag.Galaxy,
redshift=0.5,
bulge=bulge,
)
bulge = af.Model(ag.lp.Sersic)
galaxy_1 = af.Model(
ag.Galaxy,
redshift=0.5,
bulge=bulge,
)
model = af.Collection(
galaxies=af.Collection(
galaxy_0=galaxy_0,
galaxy_1=galaxy_1,
)
)
Concise API#
If a light profile is passed directly to the af.Model of a galaxy, it is automatically assigned to be a af.Model component of the galaxy.
This means we can write the model above comprising multiple light profiles more concisely as follows:
galaxy = af.Model(
ag.Galaxy,
redshift=0.5,
bulge=ag.lp.Sersic,
disk=ag.lp.Exponential,
bar=ag.lp.Sersic
)
model = af.Collection(galaxies=af.Collection(galaxy=galaxy))
Prior Customization#
We can customize the priors of the model component individual parameters as follows:
bulge = af.Model(ag.lp.Sersic)
bulge.centre.centre_0 = af.UniformPrior(lower_limit=-0.1, upper_limit=0.1)
bulge.centre.centre_1 = af.UniformPrior(lower_limit=-0.1, upper_limit=0.1)
bulge.intensity = af.LogUniformPrior(lower_limit=1e-4, upper_limit=1e4)
bulge.sersic_index = af.GaussianPrior(mean=4.0, sigma=1.0, lower_limit=1.0, upper_limit=8.0)
galaxy = af.Model(
ag.Galaxy,
redshift=0.5,
bulge=bulge,
)
model = af.Collection(galaxies=af.Collection(galaxy=galaxy))
Model Customization#
We can customize the model parameters in a number of different ways, as shown below:
bulge = af.Model(ag.lp.Sersic)
disk = af.Model(ag.lp.Exponential)
# Parameter Pairing: Pair the centre of the bulge and disk together, reducing
# the complexity of non-linear parameter space by N = 2
bulge.centre = disk.centre
# Parameter Fixing: Fix the sersic_index of the bulge to a value of 4, reducing
# the complexity of non-linear parameter space by N = 1
bulge.sersic_index = 4.0
# Parameter Offsets: Make the bulge intensity parameters the same value as
# the disk but with an offset.
bulge.intensity = disk.intensity + 0.1
galaxy = af.Model(
ag.Galaxy,
redshift=0.5,
bulge=bulge,
disk=disk,
)
model = af.Collection(galaxies=af.Collection(galaxy=galaxy))
# Assert that the effective radius of the bulge is larger than that of the disk.
# (Assertions can only be added at the end of model composition, after all components
# have been bright together in a `Collection`.
model.add_assertion(model.galaxies.bulge.effective_radius > model.galaxies.disk.effective_radius)
# Assert that the bulge effetive radius is below 3.0":
model.add_assertion(model.galaxies.bulge.effective_radius < 3.0)
Available Model Components#
The light profiles, mass profiles and other components that can be used for galaxy modeling are given at the following API documentation pages:
JSon Outputs#
After a model is composed, it can easily be output to a .json file on hard-disk in a readable structure:
import os
import json
model_path = path.join("path", "to", "model", "json")
os.makedirs(model_path, exist_ok=True)
model_file = path.join(model_path, "model.json")
with open(model_file, "w+") as f:
json.dump(model.dict(), f, indent=4)
We can load the model from its .json file.
model = af.Model.from_json(file=model_file)
This means in PyAutoGalaxy one can write a model in a script, save it to hard disk and load it elsewhere, as well as manually customize it in the .json file directory.
Many Profile Models (Advanced)#
Features such as the Multi Gaussian Expansion (MGE) and shapelets compose models consisting of 50 - 500+ light profiles.
The following example notebooks show how to compose and fit these models:
https://github.com/Jammy2211/autogalaxy_workspace/blob/release/notebooks/imaging/modeling/features/multi_gaussian_expansion.ipynb https://github.com/Jammy2211/autogalaxy_workspace/blob/release/notebooks/imaging/modeling/features/shapelets.ipynb
Model Linking (Advanced)#
When performing non-linear search chaining, the inferred model of one phase can be linked to the model.
The following example notebooks show how to compose and fit these models:
Across Datasets (Advanced)#
When fitting multiple datasets, model can be composed where the same model component are used across the datasets but certain parameters are free to vary across the datasets.
The following example notebooks show how to compose and fit these models:
Relations (Advanced)#
We can compose models where the free parameter(s) vary according to a user-specified function (e.g. y = mx +c -> intensity = (m * wavelength) + c across the datasets.
The following example notebooks show how to compose and fit these models:
PyAutoFit API#
PyAutoFit is a general model composition library which offers even more ways to compose models not detailed in this cookbook.
The PyAutoFit model composition cookbooks detail this API in more detail:
https://pyautofit.readthedocs.io/en/latest/cookbooks/model.html https://pyautofit.readthedocs.io/en/latest/cookbooks/multi_level_model.html
Wrap Up#
This cookbook shows how to compose simple models using the af.Model() and af.Collection() objects.