def test__stochastic_log_evidences_for_instance(self, masked_imaging_7x7):
lens_hyper_image = al.Array2D.ones(shape_native=(3, 3),
pixel_scales=0.1)
lens_hyper_image[4] = 10.0
source_hyper_image = al.Array2D.ones(shape_native=(3, 3),
pixel_scales=0.1)
source_hyper_image[4] = 10.0
hyper_model_image = al.Array2D.full(fill_value=0.5,
shape_native=(3, 3),
pixel_scales=0.1)
hyper_galaxy_image_path_dict = {
("galaxies", "lens"): lens_hyper_image,
("galaxies", "source"): source_hyper_image,
}
result = mock.MockResult(
hyper_galaxy_image_path_dict=hyper_galaxy_image_path_dict,
hyper_model_image=hyper_model_image,
)
galaxies = af.ModelInstance()
galaxies.lens = al.Galaxy(
redshift=0.5, mass=al.mp.SphIsothermal(einstein_radius=1.0))
galaxies.source = al.Galaxy(
redshift=1.0,
pixelization=al.pix.VoronoiMagnification(shape=(3, 3)),
regularization=al.reg.Constant(),
)
instance = af.ModelInstance()
instance.galaxies = galaxies
analysis = al.AnalysisImaging(dataset=masked_imaging_7x7,
hyper_result=result)
stochastic_log_evidences = analysis.stochastic_log_evidences_for_instance(
instance=instance)
assert stochastic_log_evidences is None
galaxies.source = al.Galaxy(
redshift=1.0,
pixelization=al.pix.VoronoiBrightnessImage(pixels=9),
regularization=al.reg.Constant(),
)
instance = af.ModelInstance()
instance.galaxies = galaxies
analysis = al.AnalysisImaging(dataset=masked_imaging_7x7,
hyper_result=result)
stochastic_log_evidences = analysis.stochastic_log_evidences_for_instance(
instance=instance)
assert stochastic_log_evidences[0] != stochastic_log_evidences[1]
def test__use_border__determines_if_border_pixel_relocation_is_used(
self, masked_imaging_7x7
):
model = af.Collection(
galaxies=af.Collection(
lens=al.Galaxy(
redshift=0.5, mass=al.mp.SphIsothermal(einstein_radius=100.0)
),
source=al.Galaxy(
redshift=1.0,
pixelization=al.pix.Rectangular(shape=(3, 3)),
regularization=al.reg.Constant(coefficient=1.0),
),
)
)
masked_imaging_7x7 = masked_imaging_7x7.apply_settings(
settings=al.SettingsImaging(sub_size_inversion=2)
)
analysis = al.AnalysisImaging(
dataset=masked_imaging_7x7,
settings_pixelization=al.SettingsPixelization(use_border=True),
)
analysis.dataset.grid_inversion[4] = np.array([[500.0, 0.0]])
instance = model.instance_from_unit_vector([])
tracer = analysis.tracer_for_instance(instance=instance)
fit = analysis.fit_imaging_for_tracer(
tracer=tracer, hyper_image_sky=None, hyper_background_noise=None
)
assert fit.inversion.linear_obj_list[0].source_grid_slim[4][0] == pytest.approx(
97.19584, 1.0e-2
)
assert fit.inversion.linear_obj_list[0].source_grid_slim[4][1] == pytest.approx(
-3.699999, 1.0e-2
)
analysis = al.AnalysisImaging(
dataset=masked_imaging_7x7,
settings_pixelization=al.SettingsPixelization(use_border=False),
)
analysis.dataset.grid_inversion[4] = np.array([300.0, 0.0])
instance = model.instance_from_unit_vector([])
tracer = analysis.tracer_for_instance(instance=instance)
fit = analysis.fit_imaging_for_tracer(
tracer=tracer, hyper_image_sky=None, hyper_background_noise=None
)
assert fit.inversion.linear_obj_list[0].source_grid_slim[4][0] == pytest.approx(
200.0, 1.0e-4
)
def test__results_include_positions__available_as_property(
self, analysis_imaging_7x7, masked_imaging_7x7,
samples_with_result):
result = res.ResultDataset(
samples=samples_with_result,
analysis=analysis_imaging_7x7,
model=None,
search=None,
)
assert result.positions == None
analysis = al.AnalysisImaging(
dataset=masked_imaging_7x7,
positions=al.Grid2DIrregular([[(1.0, 1.0)]]),
settings_lens=al.SettingsLens(positions_threshold=1.0),
)
result = res.ResultDataset(samples=samples_with_result,
analysis=analysis,
model=None,
search=None)
assert (result.positions[0] == np.array([1.0, 1.0])).all()
def test__sets_up_hyper_galaxy_images__froms(self, masked_imaging_7x7):
hyper_galaxy_image_path_dict = {
("galaxies", "lens"):
al.Array2D.ones(shape_native=(3, 3), pixel_scales=1.0),
("galaxies", "source"):
al.Array2D.full(fill_value=2.0,
shape_native=(3, 3),
pixel_scales=1.0),
}
result = mock.MockResult(
hyper_galaxy_image_path_dict=hyper_galaxy_image_path_dict,
hyper_model_image=al.Array2D.full(fill_value=3.0,
shape_native=(3, 3),
pixel_scales=1.0),
)
analysis = al.AnalysisImaging(dataset=masked_imaging_7x7,
hyper_dataset_result=result)
assert (analysis.hyper_galaxy_image_path_dict[(
"galaxies", "lens")].native == np.ones((3, 3))).all()
assert (analysis.hyper_galaxy_image_path_dict[(
"galaxies", "source")].native == 2.0 * np.ones((3, 3))).all()
assert (analysis.hyper_model_image.native == 3.0 * np.ones(
(3, 3))).all()
def test__figure_of_merit__includes_hyper_image_and_noise__matches_fit(
self, masked_imaging_7x7):
hyper_image_sky = al.hyper_data.HyperImageSky(sky_scale=1.0)
hyper_background_noise = al.hyper_data.HyperBackgroundNoise(
noise_scale=1.0)
lens_galaxy = al.Galaxy(redshift=0.5,
light=al.lp.EllSersic(intensity=0.1))
model = af.Collection(
hyper_image_sky=hyper_image_sky,
hyper_background_noise=hyper_background_noise,
galaxies=af.Collection(lens=lens_galaxy),
)
analysis = al.AnalysisImaging(dataset=masked_imaging_7x7)
instance = model.instance_from_unit_vector([])
analysis_log_likelihood = analysis.log_likelihood_function(
instance=instance)
tracer = analysis.tracer_for_instance(instance=instance)
fit = al.FitImaging(
dataset=masked_imaging_7x7,
tracer=tracer,
hyper_image_sky=hyper_image_sky,
hyper_background_noise=hyper_background_noise,
)
assert fit.log_likelihood == analysis_log_likelihood
def test__tracer_all_above_weight_gen(self, masked_imaging_7x7, samples,
model):
path_prefix = "aggregator_tracer_gen"
database_file = path.join(conf.instance.output_path, "tracer.sqlite")
result_path = path.join(conf.instance.output_path, path_prefix)
clean(database_file=database_file, result_path=result_path)
search = mock.MockSearch(samples=samples,
result=mock.MockResult(model=model,
samples=samples))
search.paths = af.DirectoryPaths(path_prefix=path_prefix)
analysis = al.AnalysisImaging(dataset=masked_imaging_7x7)
search.fit(model=model, analysis=analysis)
agg = af.Aggregator.from_database(filename=database_file)
agg.add_directory(directory=result_path)
tracer_agg = al.agg.TracerAgg(aggregator=agg)
tracer_pdf_gen = tracer_agg.all_above_weight_gen(minimum_weight=-1.0)
weight_pdf_gen = tracer_agg.weights_above_gen(minimum_weight=-1.0)
i = 0
for (tracer_gen, weight_gen) in zip(tracer_pdf_gen, weight_pdf_gen):
for tracer in tracer_gen:
i += 1
if i == 1:
assert tracer.galaxies[0].redshift == 0.5
assert tracer.galaxies[0].light.centre == (1.0, 1.0)
assert tracer.galaxies[1].redshift == 1.0
if i == 2:
assert tracer.galaxies[0].redshift == 0.5
assert tracer.galaxies[0].light.centre == (10.0, 10.0)
assert tracer.galaxies[1].redshift == 1.0
for weight in weight_gen:
if i == 0:
assert weight == 0.0
if i == 1:
assert weight == 1.0
assert i == 2
clean(database_file=database_file, result_path=result_path)
def test__uses_hyper_fit_correctly(self, masked_imaging_7x7):
galaxies = af.ModelInstance()
galaxies.lens = al.Galaxy(redshift=0.5,
light=al.lp.EllSersic(intensity=1.0),
mass=al.mp.SphIsothermal)
galaxies.source = al.Galaxy(redshift=1.0, light=al.lp.EllSersic())
instance = af.ModelInstance()
instance.galaxies = galaxies
lens_hyper_image = al.Array2D.ones(shape_native=(3, 3),
pixel_scales=0.1)
lens_hyper_image[4] = 10.0
hyper_model_image = al.Array2D.full(fill_value=0.5,
shape_native=(3, 3),
pixel_scales=0.1)
hyper_galaxy_image_path_dict = {("galaxies", "lens"): lens_hyper_image}
result = mock.MockResult(
hyper_galaxy_image_path_dict=hyper_galaxy_image_path_dict,
hyper_model_image=hyper_model_image,
)
analysis = al.AnalysisImaging(dataset=masked_imaging_7x7,
hyper_dataset_result=result)
hyper_galaxy = al.HyperGalaxy(contribution_factor=1.0,
noise_factor=1.0,
noise_power=1.0)
instance.galaxies.lens.hyper_galaxy = hyper_galaxy
analysis_log_likelihood = analysis.log_likelihood_function(
instance=instance)
g0 = al.Galaxy(
redshift=0.5,
light_profile=instance.galaxies.lens.light,
mass_profile=instance.galaxies.lens.mass,
hyper_galaxy=hyper_galaxy,
hyper_model_image=hyper_model_image,
hyper_galaxy_image=lens_hyper_image,
hyper_minimum_value=0.0,
)
g1 = al.Galaxy(redshift=1.0,
light_profile=instance.galaxies.source.light)
tracer = al.Tracer.from_galaxies(galaxies=[g0, g1])
fit = al.FitImaging(dataset=masked_imaging_7x7, tracer=tracer)
assert (fit.tracer.galaxies[0].hyper_galaxy_image == lens_hyper_image
).all()
assert analysis_log_likelihood == fit.log_likelihood
def test__analysis_no_positions__removes_positions_and_threshold(
self, masked_imaging_7x7):
analysis = al.AnalysisImaging(
dataset=masked_imaging_7x7,
positions=al.Grid2DIrregular([(1.0, 100.0), (200.0, 2.0)]),
settings_lens=al.SettingsLens(positions_threshold=0.01),
)
assert analysis.no_positions.positions == None
assert analysis.no_positions.settings_lens.positions_threshold == None
def test__positions__likelihood_overwrites__changes_likelihood(
masked_imaging_7x7):
lens = al.Galaxy(redshift=0.5, mass=al.mp.SphIsothermal())
source = al.Galaxy(redshift=1.0, light=al.lp.SphSersic())
model = af.Collection(galaxies=af.Collection(lens=lens, source=source))
instance = model.instance_from_unit_vector([])
analysis = al.AnalysisImaging(dataset=masked_imaging_7x7)
analysis_log_likelihood = analysis.log_likelihood_function(
instance=instance)
tracer = analysis.tracer_via_instance_from(instance=instance)
fit = al.FitImaging(dataset=masked_imaging_7x7, tracer=tracer)
assert fit.log_likelihood == pytest.approx(analysis_log_likelihood, 1.0e-4)
assert analysis_log_likelihood == pytest.approx(-6258.043397009, 1.0e-4)
positions_likelihood = al.PositionsLHPenalty(positions=al.Grid2DIrregular([
(1.0, 100.0), (200.0, 2.0)
]),
threshold=0.01)
analysis = al.AnalysisImaging(dataset=masked_imaging_7x7,
positions_likelihood=positions_likelihood)
analysis_log_likelihood = analysis.log_likelihood_function(
instance=instance)
log_likelihood_penalty_base = positions_likelihood.log_likelihood_penalty_base_from(
dataset=masked_imaging_7x7)
log_likelihood_penalty = positions_likelihood.log_likelihood_penalty_from(
tracer=tracer)
assert analysis_log_likelihood == pytest.approx(
log_likelihood_penalty_base - log_likelihood_penalty, 1.0e-4)
assert analysis_log_likelihood == pytest.approx(-22048700558.9052, 1.0e-4)
def test__make_result__result_imaging_is_returned(self,
masked_imaging_7x7):
model = af.Collection(galaxies=af.Collection(galaxy_0=al.Galaxy(
redshift=0.5)))
search = mock.MockSearch(name="test_search")
analysis = al.AnalysisImaging(dataset=masked_imaging_7x7)
result = search.fit(model=model, analysis=analysis)
assert isinstance(result, res.ResultImaging)
def test__modify_before_fit__inversion_no_positions_likelihood__raises_exception(
masked_imaging_7x7):
lens = al.Galaxy(redshift=0.5, mass=al.mp.SphIsothermal())
source = al.Galaxy(redshift=1.0,
pixelization=al.pix.Rectangular,
regularization=al.reg.Constant())
model = af.Collection(galaxies=af.Collection(lens=lens, source=source))
analysis = al.AnalysisImaging(dataset=masked_imaging_7x7)
with pytest.raises(exc.AnalysisException):
analysis.modify_before_fit(paths=af.DirectoryPaths(), model=model)
positions_likelihood = al.PositionsLHPenalty(positions=al.Grid2DIrregular([
(1.0, 100.0), (200.0, 2.0)
]),
threshold=0.01)
analysis = al.AnalysisImaging(dataset=masked_imaging_7x7,
positions_likelihood=positions_likelihood)
analysis.modify_before_fit(paths=af.DirectoryPaths(), model=model)
def test__fit_imaging_all_above_weight_gen(masked_imaging_7x7, samples, model):
path_prefix = "aggregator_fit_imaging_gen"
database_file = path.join(conf.instance.output_path, "fit_imaging.sqlite")
result_path = path.join(conf.instance.output_path, path_prefix)
clean(database_file=database_file, result_path=result_path)
search = al.m.MockSearch(samples=samples,
result=al.m.MockResult(model=model,
samples=samples))
search.paths = af.DirectoryPaths(path_prefix=path_prefix)
analysis = al.AnalysisImaging(dataset=masked_imaging_7x7)
search.fit(model=model, analysis=analysis)
agg = af.Aggregator.from_database(filename=database_file)
agg.add_directory(directory=result_path)
fit_imaging_agg = al.agg.FitImagingAgg(aggregator=agg)
fit_imaging_pdf_gen = fit_imaging_agg.all_above_weight_gen_from(
minimum_weight=-1.0)
i = 0
for fit_imaging_gen in fit_imaging_pdf_gen:
for fit_imaging in fit_imaging_gen:
i += 1
if i == 1:
assert fit_imaging.tracer.galaxies[0].redshift == 0.5
assert fit_imaging.tracer.galaxies[0].light.centre == (1.0,
1.0)
assert fit_imaging.tracer.galaxies[1].redshift == 1.0
if i == 2:
assert fit_imaging.tracer.galaxies[0].redshift == 0.5
assert fit_imaging.tracer.galaxies[0].light.centre == (10.0,
10.0)
assert fit_imaging.tracer.galaxies[1].redshift == 1.0
assert i == 2
clean(database_file=database_file, result_path=result_path)
def test__figure_of_merit__matches_correct_fit_given_galaxy_profiles(
masked_imaging_7x7):
lens = al.Galaxy(redshift=0.5, light=al.lp.EllSersic(intensity=0.1))
model = af.Collection(galaxies=af.Collection(lens=lens))
analysis = al.AnalysisImaging(dataset=masked_imaging_7x7)
instance = model.instance_from_unit_vector([])
analysis_log_likelihood = analysis.log_likelihood_function(
instance=instance)
tracer = analysis.tracer_via_instance_from(instance=instance)
fit = al.FitImaging(dataset=masked_imaging_7x7, tracer=tracer)
assert fit.log_likelihood == analysis_log_likelihood
def test__positions__resample__raises_exception(masked_imaging_7x7):
model = af.Collection(galaxies=af.Collection(
lens=al.Galaxy(redshift=0.5, mass=al.mp.SphIsothermal()),
source=al.Galaxy(redshift=1.0),
))
positions_likelihood = al.PositionsLHResample(positions=al.Grid2DIrregular(
[(1.0, 100.0), (200.0, 2.0)]),
threshold=0.01)
analysis = al.AnalysisImaging(dataset=masked_imaging_7x7,
positions_likelihood=positions_likelihood)
instance = model.instance_from_unit_vector([])
with pytest.raises(exc.RayTracingException):
analysis.log_likelihood_function(instance=instance)
def test__positions_do_not_trace_within_threshold__raises_exception(
self, masked_imaging_7x7):
model = af.Collection(galaxies=af.Collection(
lens=al.Galaxy(redshift=0.5, mass=al.mp.SphIsothermal()),
source=al.Galaxy(redshift=1.0),
))
analysis = al.AnalysisImaging(
dataset=masked_imaging_7x7,
positions=al.Grid2DIrregular([(1.0, 100.0), (200.0, 2.0)]),
settings_lens=al.SettingsLens(positions_threshold=0.01),
)
instance = model.instance_from_unit_vector([])
with pytest.raises(exc.RayTracingException):
analysis.log_likelihood_function(instance=instance)
def test__profile_log_likelihood_function(masked_imaging_7x7):
lens = al.Galaxy(redshift=0.5, light=al.lp.EllSersic(intensity=0.1))
source = al.Galaxy(
redshift=1.0,
regularization=al.reg.Constant(coefficient=1.0),
pixelization=al.pix.Rectangular(shape=(3, 3)),
)
model = af.Collection(galaxies=af.Collection(lens=lens, source=source))
instance = model.instance_from_unit_vector([])
analysis = al.AnalysisImaging(dataset=masked_imaging_7x7)
profiling_dict = analysis.profile_log_likelihood_function(
instance=instance)
assert "regularization_term_0" in profiling_dict
assert "log_det_regularization_matrix_term_0" in profiling_dict
def test__tracer_randomly_drawn_via_pdf_gen_from(masked_imaging_7x7, samples,
model):
path_prefix = "aggregator_tracer_gen"
database_file = path.join(conf.instance.output_path, "tracer.sqlite")
result_path = path.join(conf.instance.output_path, path_prefix)
clean(database_file=database_file, result_path=result_path)
search = al.m.MockSearch(samples=samples,
result=al.m.MockResult(model=model,
samples=samples))
search.paths = af.DirectoryPaths(path_prefix=path_prefix)
analysis = al.AnalysisImaging(dataset=masked_imaging_7x7)
search.fit(model=model, analysis=analysis)
agg = af.Aggregator.from_database(filename=database_file)
agg.add_directory(directory=result_path)
tracer_agg = al.agg.TracerAgg(aggregator=agg)
tracer_pdf_gen = tracer_agg.randomly_drawn_via_pdf_gen_from(
total_samples=2)
i = 0
for tracer_gen in tracer_pdf_gen:
for tracer in tracer_gen:
i += 1
assert tracer.galaxies[0].redshift == 0.5
assert tracer.galaxies[0].light.centre == (10.0, 10.0)
assert tracer.galaxies[1].redshift == 1.0
assert i == 2
clean(database_file=database_file, result_path=result_path)
def test__make_result__result_imaging_is_returned(masked_imaging_7x7):
model = af.Collection(galaxies=af.Collection(galaxy_0=al.Galaxy(
redshift=0.5)))
instance = model.instance_from_prior_medians()
samples = al.m.MockSamples(max_log_likelihood_instance=instance)
search = al.m.MockSearch(name="test_search", samples=samples)
analysis = al.AnalysisImaging(dataset=masked_imaging_7x7)
def modify_after_fit(paths: af.DirectoryPaths,
model: af.AbstractPriorModel, result: af.Result):
pass
analysis.modify_after_fit = modify_after_fit
result = search.fit(model=model, analysis=analysis)
assert isinstance(result, ResultImaging)
def test__check_preloads(self, masked_imaging_7x7):
conf.instance["general"]["test"]["check_preloads"] = True
lens_galaxy = al.Galaxy(redshift=0.5, light=al.lp.EllSersic(intensity=0.1))
model = af.Collection(galaxies=af.Collection(lens=lens_galaxy))
analysis = al.AnalysisImaging(dataset=masked_imaging_7x7)
instance = model.instance_from_unit_vector([])
tracer = analysis.tracer_for_instance(instance=instance)
fit = al.FitImaging(dataset=masked_imaging_7x7, tracer=tracer)
analysis.preloads.check_via_fit(fit=fit)
analysis.preloads.blurred_image = fit.blurred_image
analysis.preloads.check_via_fit(fit=fit)
analysis.preloads.blurred_image = fit.blurred_image + 1.0
with pytest.raises(exc.PreloadsException):
analysis.preloads.check_via_fit(fit=fit)
def test__results_include_positions__available_as_property(
analysis_imaging_7x7, masked_imaging_7x7, samples_with_result):
result = res.ResultDataset(samples=samples_with_result,
analysis=analysis_imaging_7x7,
model=None)
assert result.positions == None
positions_likelihood = al.PositionsLHResample(positions=al.Grid2DIrregular(
[(1.0, 100.0), (200.0, 2.0)]),
threshold=1.0)
analysis = al.AnalysisImaging(
dataset=masked_imaging_7x7,
positions_likelihood=positions_likelihood,
settings_lens=al.SettingsLens(threshold=1.0),
)
result = res.ResultDataset(samples=samples_with_result,
analysis=analysis,
model=None)
assert (result.positions[0] == np.array([1.0, 100.0])).all()
galaxies=af.Collection(
lens=af.Model(
al.Galaxy, redshift=0.5, mass=al.mp.EllIsothermal, shear=al.mp.ExternalShear
),
source=af.Model(al.Galaxy, redshift=1.0, bulge=al.lp.EllSersic),
)
)
search = af.DynestyStatic(
path_prefix=path_prefix,
name="search[1]_mass[sie]_source[parametric]",
unique_tag=dataset_name,
nlive=50,
)
analysis = al.AnalysisImaging(dataset=imaging)
result_1 = search.fit(model=model, analysis=analysis)
"""
__Model + Search + Analysis + Model-Fit (Search 2)__
We use the results of search 1 to create the lens model fitted in search 2, where:
- The lens galaxy's total mass distribution is an `EllPowerLaw` with `ExternalShear` [8 parameters: priors
initialized from search 1].
- The source galaxy's light is a bulge+disk using two parametric `EllSersic`'s whose centres are shared
[12 parameters: priors of bulge initialized from search 1].
The number of free parameters and therefore the dimensionality of non-linear parameter space is N=20.
"""
__SOURCE PARAMETRIC PIPELINE (with lens light)__
The SOURCE PARAMETRIC PIPELINE (with lens light) uses three searches to initialize a robust model for the
source galaxy's light, which in this example:
- Uses a parametric `EllSersic` bulge and `EllExponential` disk with centres aligned for the lens
galaxy's light.
- Uses an `EllIsothermal` model for the lens's total mass distribution with an `ExternalShear`.
__Settings__:
- Mass Centre: Fix the mass profile centre to (0.0, 0.0) (this assumption will be relaxed in the MASS TOTAL PIPELINE).
"""
analysis = al.AnalysisImaging(dataset=imaging)
bulge = af.Model(al.lp.EllSersic)
disk = af.Model(al.lp.EllExponential)
bulge.centre = (0.0, 0.0)
disk.centre = (0.0, 0.0)
source_parametric_results = slam.source_parametric.with_lens_light(
path_prefix=path_prefix,
unique_tag=dataset_name,
analysis=analysis,
setup_hyper=setup_hyper,
lens_bulge=bulge,
lens_disk=disk,
mass=af.Model(al.mp.EllIsothermal),
shear=af.Model(al.mp.ExternalShear),
hyper_galaxies_source=False,
hyper_image_sky=al.hyper_data.HyperImageSky,
hyper_background_noise=None,
)
"""
__Model-Fits via Searches 1, 2 & 3__
Searches 1, 2 and 3 initialize the lens model by fitting the lens light, then the lens mass + source, and then all
simultaneously. This is identical to the pipeline `chaining/pipelines/light_parametric__mass_total__source_inversion.py`
We can only use hyper-model once we have a good model for the lens and source galaxies, given that it needs hyper-model
images of both of these components to effectively perform tasks like scaling their noise or adapting a pixelization
or regularization pattern to the source's unlensed morphology.
"""
analysis = al.AnalysisImaging(dataset=imaging)
bulge = af.Model(al.lp.EllSersic)
disk = af.Model(al.lp.EllExponential)
bulge.centre = disk.centre
model = af.Collection(
galaxies=af.Collection(
lens=af.Model(al.Galaxy, redshift=0.5, bulge=bulge, disk=disk)
)
)
search = af.DynestyStatic(
path_prefix=path_prefix,
name="hyper[1]_light[parametric]",
applied is passed into the `AnalysisImaging` object, ensuring that this is the mask the model-fit uses.
"""
model = af.Collection(galaxies=af.Collection(
lens=af.Model(al.Galaxy, redshift=0.5, mass=al.mp.SphIsothermal),
source=af.Model(al.Galaxy, redshift=1.0, bulge=al.lp.SphExponential),
))
search = af.DynestyStatic(
path_prefix=path.join("howtolens", "chapter_2"),
name="tutorial_5_with_custom_mask",
unique_tag=dataset_name,
nlive=40,
number_of_cores=1,
)
analysis = al.AnalysisImaging(dataset=imaging)
search.fit(model=model, analysis=analysis)
"""
__Discussion__
So, we can choose the mask we use in a model-fit. We know that we want the mask to not remove any of the lensed source
galaxy's light, but is this the 'right' mask? What is the 'right' mask? Maybe we want a bigger mask? a smaller mask?
When it comes to choosing a mask, we are essentially balancing two things: computational run-time and accuracy. When we
use a bigger the mask the model-fit will take longer to perform. Why? Because a bigger mask includes more image-pixels
in the analysis, and for every additional image-pixel we have to compute its deflection angles, trace it to the source
plane, fit its light, etc.
If run-time was not a consideration we would always choose a bigger mask, for two reasons:
"""
__SOURCE PARAMETRIC PIPELINE (with lens light)__
The SOURCE PARAMETRIC PIPELINE (with lens light) uses three searches to initialize a robust model for the
source galaxy's light, which in this example:
- Uses a parametric `EllSersic` bulge.
- Uses an `EllIsothermal` model for the lens's total mass distribution with an `ExternalShear`.
__Settings__:
- Mass Centre: Fix the mass profile centre to (0.0, 0.0) (this assumption will be relaxed in the MASS LIGHT DARK
PIPELINE).
"""
analysis = al.AnalysisImaging(dataset=imaging)
bulge = af.Model(al.lp.EllSersic)
bulge.centre = (0.0, 0.0)
source_parametric_results = slam.source_parametric.with_lens_light(
settings_autofit=settings_autofit,
analysis=analysis,
setup_hyper=setup_hyper,
lens_bulge=bulge,
lens_disk=None,
mass=af.Model(al.mp.EllIsothermal),
shear=af.Model(al.mp.ExternalShear),
source_bulge=af.Model(al.lp.EllSersic),
mass_centre=(0.0, 0.0),
redshift_lens=redshift_lens,
"""
We now iterate through the model list, replacing each slope prior with the shared slope prior.
"""
for model in model_list:
model.galaxies.lens.mass.slope = slope_shared_prior
"""
__Analysis__
For each dataset we now create a corresponding `AnalysisImaging` class, as we are used to doing for `Imaging` data.
"""
analysis_list = []
for masked_imaging in masked_imaging_list:
analysis = al.AnalysisImaging(dataset=masked_imaging)
analysis_list.append(analysis)
"""
__Analysis Factors__
Above, we composed a `model_list` consisting of three lens models which each had a shared `slope` prior. We also
loaded three datasets which we intend to fit with each of these lens models, setting up each in an `Analysis` class
that defines how the model is used to fit the data.
We now simply pair each lens model to each `Analysis` class, so that **PyAutoLens** knows that:
- `model_list[0]` fits `masked_imaging_list[0]` via `analysis_list[0]`.
- `model_list[1]` fits `masked_imaging_list[1]` via `analysis_list[1]`.
- `model_list[2]` fits `masked_imaging_list[2]` via `analysis_list[2]`.
To prevent these solutions biasing the model-fit we specify a `position_threshold` of 0.5", which requires that a
mass model traces the four (y,x) coordinates specified by our positions (that correspond to the brightest regions of the
lensed source) within 0.5" of one another in the source-plane, else the mass model is discarded and a new
model is sampled. This removes the unphysical solutions that bias an `Inversion`.
The threshold of 0.5" is large. For an accurate lens model we would anticipate the positions trace within < 0.01" of
one another. However, we only want the threshold to aid the non-linear with the choice of mass model, but not risk
removing genuinely physical models.
Position thresholding is described in more detail in the
script `autolens_workspace/notebooks/imaging/modeling/customize/positions.py`
"""
analysis = al.AnalysisImaging(
dataset=imaging,
positions=positions,
settings_lens=al.SettingsLens(positions_threshold=0.5),
)
"""
__Model-Fit__
We can now begin the model-fit by passing the model and analysis object to the search, which performs a non-linear
search to find which models fit the data with the highest likelihood.
Checkout the output folder for live outputs of the results of the fit, including on-the-fly visualization of the best
fit model!
"""
result = search.fit(model=model, analysis=analysis)
"""
__Result__
bulge.centre = disk.centre
model = af.Collection(
galaxies=af.Collection(
lens=af.Model(al.Galaxy, redshift=0.5, bulge=bulge, disk=disk)
)
)
search = af.DynestyStatic(
path_prefix=path_prefix,
name="search[1]_light[parametric]",
unique_tag=dataset_name,
nlive=50,
)
analysis = al.AnalysisImaging(dataset=imaging)
result_1 = search.fit(model=model, analysis=analysis)
"""
__Model + Search + Analysis + Model-Fit (Search 2)__
We use the results of search 1 to create the lens model fitted in search 2, where:
- The lens galaxy's light and stellar mass is an `EllSersic` bulge and `EllExponential` disk [Parameters
fixed to results of search 1].
- The lens galaxy's dark matter mass distribution is a `EllNFWMCRLudlow` whose centre is aligned with the
`EllSersic` bulge and stellar mass model above [3 parameters].
- The lens mass model also includes an `ExternalShear` [2 parameters].
galaxies=af.Collection(
lens=af.Model(
al.Galaxy, redshift=0.5, mass=al.mp.EllIsothermal, shear=al.mp.ExternalShear
),
source=af.Model(al.Galaxy, redshift=1.0, bulge=al.lp.EllSersic),
)
)
search = af.DynestyStatic(
path_prefix=path.join("howtolens", "chapter_4"),
name="search[1]_mass[sie]_source[parametric]",
unique_tag=dataset_name,
nlive=50,
)
analysis = al.AnalysisImaging(dataset=imaging)
result_1 = search.fit(model=model, analysis=analysis)
"""
__Model + Search + Analysis + Model-Fit (Search 2)__
We use the results of search 1 to create the lens model fitted in search 2, where:
- The lens galaxy's total mass distribution is an `EllIsothermal` and `ExternalShear` [Parameters fixed to
results of search 1].
- The source-galaxy's light uses a `DelaunayMagnification` pixelization [2 parameters].
- This pixelization is regularized using a `Constant` scheme [1 parameter].
hyper_galaxies_lens=True,
hyper_galaxies_source=False,
hyper_image_sky=al.hyper_data.HyperImageSky,
hyper_background_noise=None,
)
"""
__Model-Fits via Searches 1, 2 & 3__
Searches 1, 2 and 3 initialize the lens model by fitting the lens light, then the lens mass + source, and then all
simultaneously. This is identical to the pipeline `chaining/pipelines/light_parametric__mass_total__source_inversion.py`
We can only use hyper-model once we have a good model for the lens and source galaxies, given that it needs hyper-model
images of both of these components to effectively perform tasks like scaling their noise or adapting a pixelization
or regularization pattern to the source's unlensed morphology.
"""
analysis = al.AnalysisImaging(dataset=imaging)
bulge = af.Model(al.lp.EllSersic)
disk = af.Model(al.lp.EllExponential)
bulge.centre = disk.centre
model = af.Collection(galaxies=af.Collection(
lens=af.Model(al.Galaxy, redshift=0.5, bulge=bulge, disk=disk)))
search = af.DynestyStatic(
path_prefix=path.join("howtolens", "chapter_5"),
name="hyper[1]_light[parametric]",
unique_tag=dataset_name,
nlive=50,
)