def test__1x2_image__1x2_visibilities__simple_fourier_transform(self):
# The image plane image generated by the galaxy is [1.0, 1.0]
# Thus the chi squared is 4.0**2.0 + 3.0**2.0 = 25.0
uv_wavelengths = np.array([[0.0, 0.0]])
real_space_mask = al.Mask2D.manual(
mask=np.array([
[True, True, True, True],
[True, False, False, True],
[True, True, True, True],
]),
pixel_scales=1.0,
)
interferometer = al.Interferometer(
visibilities=al.Visibilities.full(fill_value=5.0,
shape_slim=(1, )),
noise_map=al.Visibilities.ones(shape_slim=(1, )),
uv_wavelengths=uv_wavelengths,
real_space_mask=real_space_mask,
settings=al.SettingsInterferometer(
sub_size=1, transformer_class=al.TransformerDFT),
)
interferometer.visibilities[0] = 5.0 + 4.0j
# Setup as a ray trace instance, using a light profile for the lens
g0 = al.Galaxy(redshift=0.5,
light_profile=MockLightProfile(value=1.0, size=2))
tracer = al.Tracer.from_galaxies(galaxies=[g0])
fit = al.FitInterferometer(interferometer=interferometer,
tracer=tracer)
assert (fit.visibilities.slim == np.array([5.0 + 4.0j])).all()
assert (fit.noise_map.slim == np.array([1.0 + 1.0j])).all()
assert (fit.model_visibilities.slim == np.array([2.0 + 0.0j])).all()
assert (fit.residual_map.slim == np.array([3.0 + 4.0j])).all()
assert (fit.normalized_residual_map.slim == np.array([3.0 + 4.0j
])).all()
assert (fit.chi_squared_map.slim == np.array([9.0 + 16.0j])).all()
assert fit.chi_squared == 25.0
assert fit.noise_normalization == (2.0 * np.log(2 * np.pi * 1.0**2.0))
assert fit.log_likelihood == -0.5 * (
25.0 + 2.0 * np.log(2 * np.pi * 1.0**2.0))
def test__simulate_interferometer_data_and_fit__known_likelihood():
mask = al.Mask2D.circular(radius=3.0,
shape_native=(31, 31),
pixel_scales=0.2,
sub_size=1)
grid = al.Grid2D.from_mask(mask=mask)
lens_galaxy = al.Galaxy(
redshift=0.5,
light=al.lp.EllSersic(centre=(0.1, 0.1), intensity=0.1),
mass=al.mp.EllIsothermal(centre=(0.1, 0.1), einstein_radius=1.8),
)
source_galaxy_0 = al.Galaxy(
redshift=1.0,
pixelization=al.pix.Rectangular(shape=(16, 16)),
regularization=al.reg.Constant(coefficient=(1.0)),
)
source_galaxy_1 = al.Galaxy(
redshift=2.0,
pixelization=al.pix.Rectangular(shape=(16, 16)),
regularization=al.reg.Constant(coefficient=(1.0)),
)
tracer = al.Tracer.from_galaxies(
galaxies=[lens_galaxy, source_galaxy_0, source_galaxy_1])
simulator = al.SimulatorInterferometer(
uv_wavelengths=np.ones(shape=(7, 2)),
transformer_class=al.TransformerDFT,
exposure_time=300.0,
noise_seed=1,
)
interferometer = simulator.via_tracer_from(tracer=tracer, grid=grid)
interferometer = interferometer.apply_settings(
settings=al.SettingsInterferometer(
transformer_class=al.TransformerDFT))
fit = al.FitInterferometer(
dataset=interferometer,
tracer=tracer,
settings_inversion=al.SettingsInversion(use_w_tilde=False),
)
assert fit.figure_of_merit == pytest.approx(-5.433894158056919, 1.0e-2)
def test__hyper_background_changes_background_sky__reflected_in_likelihood(
self, ):
uv_wavelengths = np.array([[1.0, 0.0], [1.0, 1.0], [2.0, 2.0]])
real_space_mask = al.Mask2D.manual(
mask=np.array([
[True, True, True, True, True],
[True, False, False, False, True],
[True, True, True, True, True],
]),
pixel_scales=1.0,
)
interferometer = al.Interferometer(
visibilities=al.Visibilities.full(fill_value=5.0,
shape_slim=(3, )),
noise_map=al.Visibilities.full(fill_value=2.0, shape_slim=(3, )),
uv_wavelengths=uv_wavelengths,
real_space_mask=real_space_mask,
settings=al.SettingsInterferometer(sub_size=1),
)
# Setup as a ray trace instance, using a light profile for the lens
g0 = al.Galaxy(redshift=0.5,
light_profile=MockLightProfile(value=1.0, size=2))
tracer = al.Tracer.from_galaxies(galaxies=[g0])
hyper_background_noise = al.hyper_data.HyperBackgroundNoise(
noise_scale=1.0)
fit = al.FitInterferometer(
interferometer=interferometer,
tracer=tracer,
hyper_background_noise=hyper_background_noise,
)
assert (fit.visibilities.slim == (1.0 + 1.0j) *
np.full(fill_value=5.0, shape=(3, ))).all()
assert (fit.noise_map.slim == (1.0 + 1.0j) *
np.full(fill_value=3.0, shape=(3, ))).all()
def print_fit_time_from(interferometer,
transformer_class,
use_w_tilde,
use_linear_operators,
repeats=1):
settings_interferometer = al.SettingsInterferometer(
transformer_class=transformer_class)
interferometer = interferometer.apply_settings(
settings=settings_interferometer)
"""
__Numba Caching__
Call FitImaging once to get all numba functions initialized.
"""
fit = al.FitInterferometer(
dataset=interferometer,
tracer=tracer,
settings_inversion=al.SettingsInversion(
use_w_tilde=use_w_tilde,
use_linear_operators=use_linear_operators),
)
print(fit.figure_of_merit)
"""
__Fit Time__
Time FitImaging by itself, to compare to profiling dict call.
"""
start = time.time()
for i in range(repeats):
fit = al.FitInterferometer(
dataset=interferometer,
tracer=tracer,
settings_inversion=al.SettingsInversion(
use_w_tilde=use_w_tilde,
use_linear_operators=use_linear_operators),
)
fit.figure_of_merit
fit_time = (time.time() - start) / repeats
print(f"Fit Time = {fit_time} \n")
"""
real_space_mask = al.Mask2D.circular(
shape_native=(151, 151), pixel_scales=0.05, radius=3.0
)
dataset_name = "mass_sie__source_sersic_x2"
dataset_path = path.join("dataset", "interferometer", dataset_name)
interferometer = al.Interferometer.from_fits(
visibilities_path=path.join(dataset_path, "visibilities.fits"),
noise_map_path=path.join(dataset_path, "noise_map.fits"),
uv_wavelengths_path=path.join(dataset_path, "uv_wavelengths.fits"),
real_space_mask=real_space_mask,
)
interferometer = interferometer.apply_settings(
settings=al.SettingsInterferometer(transformer_class=al.TransformerDFT)
)
"""
__Inversion Settings (Run Times)__
The run times of an interferometer `Inversion` depend significantly on the following settings:
- `transformer_class`: whether a discrete Fourier transform (`TransformerDFT`) or non-uniform fast Fourier Transform
(`TransformerNUFFT) is used to map the inversion's image from real-space to Fourier space.
- `use_linear_operators`: whether the linear operator formalism or matrix formalism is used for the linear algebra.
The optimal settings depend on the number of visibilities in the dataset:
- For N_visibilities < 1000: `transformer_class=TransformerDFT` and `use_linear_operators=False` gives the fastest
"""
real_space_mask = al.Mask2D.circular(shape_native=(151, 151),
pixel_scales=0.05,
radius=3.0)
dataset_name = "mass_sie__subhalo_nfw__source_sersic_x2"
dataset_path = path.join("dataset", "interferometer", dataset_name)
interferometer = al.Interferometer.from_fits(
visibilities_path=path.join(dataset_path, "visibilities.fits"),
noise_map_path=path.join(dataset_path, "noise_map.fits"),
uv_wavelengths_path=path.join(dataset_path, "uv_wavelengths.fits"),
real_space_mask=real_space_mask,
)
interferometer = interferometer.apply_settings(
settings=al.SettingsInterferometer(transformer_class=al.TransformerNUFFT))
interferometer_plotter = aplt.InterferometerPlotter(
interferometer=interferometer)
interferometer_plotter.subplot_interferometer()
interferometer_plotter.subplot_dirty_images()
"""
__Paths__
The path the results of all chained searches are output:
"""
path_prefix = path.join("interferometer", "slam")
"""
__Redshifts__
The redshifts of the lens and source galaxies, which are used to perform unit converions of the model and data (e.g.
def test__simulate_interferometer_data_and_fit__chi_squared_is_0__noise_normalization_correct(
):
grid = al.Grid2D.uniform(shape_native=(51, 51),
pixel_scales=0.1,
sub_size=1)
lens_galaxy = al.Galaxy(
redshift=0.5,
light=al.lp.EllSersic(centre=(0.1, 0.1), intensity=0.1),
mass=al.mp.EllIsothermal(centre=(0.1, 0.1), einstein_radius=1.0),
)
source_galaxy = al.Galaxy(redshift=1.0,
light=al.lp.EllExponential(centre=(0.1, 0.1),
intensity=0.5))
tracer = al.Tracer.from_galaxies(galaxies=[lens_galaxy, source_galaxy])
simulator = al.SimulatorInterferometer(
uv_wavelengths=np.ones(shape=(7, 2)),
transformer_class=al.TransformerDFT,
exposure_time=300.0,
noise_if_add_noise_false=1.0,
noise_sigma=None,
)
interferometer = simulator.from_tracer_and_grid(tracer=tracer, grid=grid)
file_path = path.join(
"{}".format(path.dirname(path.realpath(__file__))),
"data_temp",
"simulate_and_fit",
)
try:
shutil.rmtree(file_path)
except FileNotFoundError:
pass
if path.exists(file_path) is False:
os.makedirs(file_path)
interferometer.output_to_fits(
visibilities_path=path.join(file_path, "visibilities.fits"),
noise_map_path=path.join(file_path, "noise_map.fits"),
uv_wavelengths_path=path.join(file_path, "uv_wavelengths.fits"),
)
real_space_mask = al.Mask2D.unmasked(shape_native=(51, 51),
pixel_scales=0.1,
sub_size=2)
interferometer = al.Interferometer.from_fits(
visibilities_path=path.join(file_path, "visibilities.fits"),
noise_map_path=path.join(file_path, "noise_map.fits"),
uv_wavelengths_path=path.join(file_path, "uv_wavelengths.fits"),
real_space_mask=real_space_mask,
)
interferometer = interferometer.apply_settings(
settings=al.SettingsInterferometer(
transformer_class=al.TransformerDFT))
tracer = al.Tracer.from_galaxies(galaxies=[lens_galaxy, source_galaxy])
fit = al.FitInterferometer(
interferometer=interferometer,
tracer=tracer,
settings_pixelization=al.SettingsPixelization(use_border=False),
)
assert fit.chi_squared == pytest.approx(0.0)
pix = al.pix.Rectangular(shape=(7, 7))
reg = al.reg.Constant(coefficient=0.0001)
lens_galaxy = al.Galaxy(
redshift=0.5,
light=al.lp.EllSersic(centre=(0.1, 0.1), intensity=0.1),
mass=al.mp.EllIsothermal(centre=(0.1, 0.1), einstein_radius=1.0),
)
source_galaxy = al.Galaxy(redshift=1.0,
pixelization=pix,
regularization=reg)
tracer = al.Tracer.from_galaxies(galaxies=[lens_galaxy, source_galaxy])
fit = al.FitInterferometer(
interferometer=interferometer,
tracer=tracer,
settings_pixelization=al.SettingsPixelization(use_border=False),
)
assert abs(fit.chi_squared) < 1.0e-4
file_path = path.join("{}".format(path.dirname(path.realpath(__file__))),
"data_temp")
if path.exists(file_path) is True:
shutil.rmtree(file_path)
def test__simulate_interferometer_data_and_fit__linear_light_profiles_and_pixelization(
):
grid = al.Grid2D.uniform(shape_native=(51, 51),
pixel_scales=0.1,
sub_size=1)
lens_galaxy = al.Galaxy(
redshift=0.5,
light=al.lp.EllSersic(centre=(0.1, 0.1), intensity=100.0),
mass=al.mp.EllIsothermal(centre=(0.1, 0.1), einstein_radius=1.0),
)
source_galaxy = al.Galaxy(
redshift=1.0,
bulge=al.lp.EllSersic(intensity=0.1, sersic_index=1.0),
disk=al.lp.EllSersic(intensity=0.2, sersic_index=4.0),
)
tracer = al.Tracer.from_galaxies(galaxies=[lens_galaxy, source_galaxy])
simulator = al.SimulatorInterferometer(
uv_wavelengths=np.array([
[0.04, 200.0, 0.3, 400000.0, 60000000.0],
[0.00003, 500.0, 600000.0, 0.1, 75555555],
]),
transformer_class=al.TransformerDFT,
exposure_time=300.0,
noise_if_add_noise_false=1.0,
noise_sigma=None,
)
interferometer = simulator.via_tracer_from(tracer=tracer, grid=grid)
interferometer = interferometer.apply_settings(
settings=al.SettingsInterferometer(grid_class=al.Grid2D,
transformer_class=al.TransformerDFT,
sub_size=1))
lens_galaxy_linear = al.Galaxy(
redshift=0.5,
light=al.lp_linear.EllSersic(centre=(0.1, 0.1)),
mass=al.mp.EllIsothermal(centre=(0.1, 0.1), einstein_radius=1.0),
)
source_galaxy_pix = al.Galaxy(
redshift=1.0,
pixelization=al.pix.Rectangular(shape=(3, 3)),
regularization=al.reg.Constant(coefficient=0.01),
)
tracer_linear = al.Tracer.from_galaxies(
galaxies=[lens_galaxy_linear, source_galaxy_pix])
fit_linear = al.FitInterferometer(
dataset=interferometer,
tracer=tracer_linear,
settings_pixelization=al.SettingsPixelization(use_border=False),
settings_inversion=al.SettingsInversion(use_w_tilde=False),
)
assert fit_linear.inversion.reconstruction == pytest.approx(
np.array([
1.00338472e02,
9.55074606e-02,
9.24767167e-02,
9.45392540e-02,
1.41969109e-01,
1.41828976e-01,
1.41521130e-01,
1.84257307e-01,
1.85507562e-01,
1.83726575e-01,
]),
1.0e-2,
)
assert fit_linear.figure_of_merit == pytest.approx(-29.20551989, 1.0e-4)
lens_galaxy_image = lens_galaxy.image_2d_from(grid=interferometer.grid)
assert fit_linear.galaxy_model_image_dict[
lens_galaxy_linear] == pytest.approx(lens_galaxy_image, 1.0e-2)
traced_grid_2d_list = tracer.traced_grid_2d_list_from(
grid=interferometer.grid)
source_galaxy_image = source_galaxy.image_2d_from(
grid=traced_grid_2d_list[1])
def test__simulate_interferometer_data_and_fit__linear_light_profiles_agree_with_standard_light_profiles(
):
grid = al.Grid2D.uniform(shape_native=(51, 51),
pixel_scales=0.1,
sub_size=1)
lens_galaxy = al.Galaxy(
redshift=0.5,
light=al.lp.EllSersic(centre=(0.1, 0.1), intensity=0.1),
mass=al.mp.EllIsothermal(centre=(0.1, 0.1), einstein_radius=1.0),
)
source_galaxy = al.Galaxy(
redshift=1.0,
bulge=al.lp.EllSersic(intensity=0.1, sersic_index=1.0),
disk=al.lp.EllSersic(intensity=0.2, sersic_index=4.0),
)
tracer = al.Tracer.from_galaxies(galaxies=[lens_galaxy, source_galaxy])
simulator = al.SimulatorInterferometer(
uv_wavelengths=np.array([
[0.04, 200.0, 0.3, 400000.0, 60000000.0],
[0.00003, 500.0, 600000.0, 0.1, 75555555],
]),
transformer_class=al.TransformerDFT,
exposure_time=300.0,
noise_if_add_noise_false=1.0,
noise_sigma=None,
)
interferometer = simulator.via_tracer_from(tracer=tracer, grid=grid)
interferometer = interferometer.apply_settings(
settings=al.SettingsInterferometer(grid_class=al.Grid2D,
transformer_class=al.TransformerDFT,
sub_size=1))
fit = al.FitInterferometer(
dataset=interferometer,
tracer=tracer,
settings_pixelization=al.SettingsPixelization(use_border=False),
settings_inversion=al.SettingsInversion(use_w_tilde=False),
)
lens_galaxy_linear = al.Galaxy(
redshift=0.5,
light=al.lp_linear.EllSersic(centre=(0.1, 0.1)),
mass=al.mp.EllIsothermal(centre=(0.1, 0.1), einstein_radius=1.0),
)
source_galaxy_linear = al.Galaxy(
redshift=1.0,
bulge=al.lp_linear.EllSersic(sersic_index=1.0),
disk=al.lp_linear.EllSersic(sersic_index=4.0),
)
tracer_linear = al.Tracer.from_galaxies(
galaxies=[lens_galaxy_linear, source_galaxy_linear])
fit_linear = al.FitInterferometer(
dataset=interferometer,
tracer=tracer_linear,
settings_pixelization=al.SettingsPixelization(use_border=False),
settings_inversion=al.SettingsInversion(use_w_tilde=False),
)
assert fit_linear.inversion.reconstruction == pytest.approx(
np.array([0.1, 0.1, 0.2]), 1.0e-4)
assert fit_linear.linear_light_profile_intensity_dict[
lens_galaxy_linear.light] == pytest.approx(0.1, 1.0e-2)
assert fit_linear.linear_light_profile_intensity_dict[
source_galaxy_linear.bulge] == pytest.approx(0.1, 1.0e-2)
assert fit_linear.linear_light_profile_intensity_dict[
source_galaxy_linear.disk] == pytest.approx(0.2, 1.0e-2)
assert fit.log_likelihood == fit_linear.log_likelihood
lens_galaxy_image = lens_galaxy.image_2d_from(grid=interferometer.grid)
assert fit_linear.galaxy_model_image_dict[
lens_galaxy_linear] == pytest.approx(lens_galaxy_image, 1.0e-4)
traced_grid_2d_list = tracer.traced_grid_2d_list_from(
grid=interferometer.grid)
source_galaxy_image = source_galaxy.image_2d_from(
grid=traced_grid_2d_list[1])
assert fit_linear.galaxy_model_image_dict[
source_galaxy_linear] == pytest.approx(source_galaxy_image, 1.0e-4)
lens_galaxy_visibilities = lens_galaxy.visibilities_via_transformer_from(
grid=interferometer.grid, transformer=interferometer.transformer)
assert fit_linear.galaxy_model_visibilities_dict[
lens_galaxy_linear] == pytest.approx(lens_galaxy_visibilities, 1.0e-4)
source_galaxy_visibilities = source_galaxy.visibilities_via_transformer_from(
grid=traced_grid_2d_list[1], transformer=interferometer.transformer)
assert fit_linear.galaxy_model_visibilities_dict[
source_galaxy_linear] == pytest.approx(source_galaxy_visibilities,
1.0e-4)
transformer_class = al.TransformerDFT
"""
However, the direct Fourier transform is inefficient. For ~10 million visibilities, it requires **thousands of seconds**
to perform a single transform. To model a lens, we'll perform tens of thousands of transforms, making this approach
unfeasible for high quality ALMA and radio datasets.
For this reason, **PyAutoLens** supports the non-uniform fast fourier transform algorithm
**PyNUFFT** (https://github.com/jyhmiinlin/pynufft), which is significantly faster, being able too perform a Fourier
transform of ~10 million in less than a second!
"""
transformer_class = al.TransformerNUFFT
"""
The use this transformer in a fit, we use the `apply_settings` method.
"""
interferometer = interferometer.apply_settings(
settings=al.SettingsInterferometer(transformer_class=transformer_class))
"""
__Fitting__
The interferometer can now be used with a `FitInterferometer` object to fit it to a data-set:
"""
fit = al.FitInterferometer(dataset=interferometer, tracer=tracer)
fit_interferometer_plotter = aplt.FitInterferometerPlotter(fit=fit)
fit_interferometer_plotter.subplot_fit_interferometer()
"""
Interferometer data can also be modeled using pixelized source's, which again perform the source reconstruction by
directly fitting the visibilities in the uv-plane. The source reconstruction is visualized in real space:
Computing this source recontruction would be extremely inefficient if **PyAutoLens** used a traditional approach to
linear algebra which explicitly stored in memory the values required to solve for the source fluxes. In fact, for an
def test__3x2_image__2x2_visibilities__use_transformer_for_likelihood(
self):
uv_wavelengths = np.array([[1.0, 0.0], [1.0, 1.0], [2.0, 2.0]])
real_space_mask = al.Mask2D.unmasked(shape_native=(1, 3),
pixel_scales=1.0)
transformer = al.TransformerDFT(uv_wavelengths=uv_wavelengths,
real_space_mask=real_space_mask)
real_space_mask = al.Mask2D.manual(
mask=np.array([
[True, True, True, True, True],
[True, False, False, False, True],
[True, True, True, True, True],
]),
pixel_scales=1.0,
)
interferometer = al.Interferometer(
visibilities=al.Visibilities.full(fill_value=5.0,
shape_slim=(3, )),
noise_map=al.Visibilities.full(fill_value=2.0, shape_slim=(3, )),
uv_wavelengths=uv_wavelengths,
real_space_mask=real_space_mask,
settings=al.SettingsInterferometer(
sub_size=1, transformer_class=al.TransformerDFT),
)
# Setup as a ray trace instance, using a light profile for the lens
g0 = al.Galaxy(redshift=0.5,
light_profile=al.lp.EllSersic(intensity=0.001))
image = g0.image_2d_from_grid(grid=interferometer.grid)
model_visibilities_manual = transformer.visibilities_from_image(
image=image)
tracer = al.Tracer.from_galaxies(galaxies=[g0])
fit = al.FitInterferometer(interferometer=interferometer,
tracer=tracer)
assert (fit.visibilities.slim == np.array(
[5.0 + 5.0j, 5.0 + 5.0j, 5.0 + 5.0j])).all()
assert (fit.noise_map.slim == np.array(
[2.0 + 2.0j, 2.0 + 2.0j, 2.0 + 2.0j])).all()
assert fit.model_visibilities.slim == pytest.approx(
model_visibilities_manual, 1.0e-4)
# moddel visibilities are all [1.94805, 0.0]
assert fit.residual_map.slim == pytest.approx(
np.array([3.0519 + 5.0j, 3.0519 + 5.0j, 3.0519 + 5.0j]), 1.0e-4)
assert fit.normalized_residual_map.slim == pytest.approx(
np.array([
3.0519 / 2.0 + (5.0 / 2.0) * 1.0j,
3.0519 / 2.0 + (5.0 / 2.0) * 1.0j,
3.0519 / 2.0 + (5.0 / 2.0) * 1.0j,
]),
1.0e-4,
)
assert fit.chi_squared_map.slim == pytest.approx(
np.array([
(3.0519 / 2.0)**2.0 + ((5.0 / 2.0)**2.0) * 1.0j,
(3.0519 / 2.0)**2.0 + ((5.0 / 2.0)**2.0) * 1.0j,
(3.0519 / 2.0)**2.0 + ((5.0 / 2.0)**2.0) * 1.0j,
]),
1.0e-4,
)
assert fit.chi_squared == pytest.approx(25.73579, 1.0e-4)
assert fit.noise_normalization == pytest.approx(
(6.0 * np.log(2 * np.pi * 2.0**2.0)), 1.0e-4)
assert fit.log_likelihood == pytest.approx(
-0.5 * (25.73579 + 6.0 * np.log(2 * np.pi * 2.0**2.0)), 1.0e-4)
