def solve(self, lensing_obj, source_plane_coordinate):
coordinates_list = self.grid_peaks_from(
lensing_obj=lensing_obj,
grid=self.grid,
source_plane_coordinate=source_plane_coordinate,
)
coordinates_list = self.grid_with_coordinates_from_mass_profile_centre_removed(
lensing_obj=lensing_obj, grid=coordinates_list)
coordinates_list = self.grid_with_points_below_magnification_threshold_removed(
lensing_obj=lensing_obj, grid=coordinates_list)
if not self.use_upscaling:
return grid_2d_irregular.Grid2DIrregular(grid=coordinates_list)
pixel_scale = self.grid.pixel_scale
while pixel_scale > self.pixel_scale_precision:
refined_coordinates_list = []
for coordinate in coordinates_list:
refined_coordinates = self.refined_coordinates_from_coordinate(
coordinate=coordinate,
pixel_scale=pixel_scale,
lensing_obj=lensing_obj,
source_plane_coordinate=source_plane_coordinate,
)
if refined_coordinates is not None:
refined_coordinates_list += refined_coordinates
refined_coordinates_list = grid_remove_duplicates(
grid=np.asarray(refined_coordinates_list))
pixel_scale = pixel_scale / self.upscale_factor
coordinates_list = refined_coordinates_list
coordinates_list = self.grid_within_distance_of_source_plane_centre(
lensing_obj=lensing_obj,
grid=grid_2d_irregular.Grid2DIrregularUniform(
grid=coordinates_list,
pixel_scales=(pixel_scale, pixel_scale)),
source_plane_coordinate=source_plane_coordinate,
distance=self.distance_from_source_centre,
)
coordinates_list = self.grid_with_points_below_magnification_threshold_removed(
lensing_obj=lensing_obj, grid=coordinates_list)
return grid_2d_irregular.Grid2DIrregular(grid=coordinates_list)
def grid_buffed_and_upscaled_around_coordinate_from(
self, coordinate, pixel_scales, buffer, upscale_factor):
"""
For an input (y,x) Catersian coordinate create a buffed and upscaled square grid of (y,x) coordinates where:
- The new grid of coordinates are buffed. For example, if buffer=1, the new grid will correspond to a 3x3 grid
of coordinates centred on the input (y,x) value with spacings defined by the input pixel_scales.
- The new grid is upscaled. For example, if upscale=2, the new grid will be at x2 the resolution of the input
pixel_scale.
Buffing and upscaling work together, so a buffer=2 and upscale=2 will produce a new 6x6 grid centred around the
input coordinate.
The `PositionFinder` works by locating pixels that trace closer to the source galaxy than neighboring pixels
and iteratively refining the grid to find pixels that trace close at higher and higher resolutions. This
function is core to producing these upscaled grids.
Parameters
----------
coordinate : (float, float)
The (y,x) Cartesian coordinates aroun which the buffed and upscaled grid is created.
pixel_scales : (float, float)
The pixel-scale resolution of the buffed and upscaled grid that is formed around the input coordinate. If
upscale > 1, the pixel_scales are reduced to pixel_scale / upscale_factor.
buffer : int
The number of pixels around the central (y,x) coordinate that the grid is computed on, i.e. how much it is
buffed. A buffer of 1 puts 1 pixel in every direction around the (y,x) coordinate, creating a 3x3 grid. A
buffer=2 places two pixels around it in every direction, creating a 5x5 grid. And so on.
upscale_factor : int
The factor by which the resolution of the grid is increased relative to the input pixel-scales.
"""
if self.use_upscaling:
upscale_factor = upscale_factor
else:
upscale_factor = 1
grid_buffed = grid_buffed_around_coordinate_from(
coordinate=coordinate,
pixel_scales=pixel_scales,
buffer=buffer,
upscale_factor=upscale_factor,
)
return grid_2d_irregular.Grid2DIrregularUniform(
grid=grid_buffed,
pixel_scales=(
pixel_scales[0] / upscale_factor,
pixel_scales[1] / upscale_factor,
),
)
def grid_with_points_below_magnification_threshold_removed(
self, lensing_obj, grid):
magnifications = np.abs(
lensing_obj.magnification_via_hessian_from_grid(
grid=grid, buffer=grid.pixel_scale))
grid_mag = []
for index, magnification in enumerate(magnifications):
if magnification > self.magnification_threshold:
grid_mag.append(grid[index, :])
return grid_2d_irregular.Grid2DIrregularUniform(
grid=grid_mag, pixel_scales=grid.pixel_scales)
def grid_within_distance_of_source_plane_centre(self, deflection_func,
source_plane_coordinate,
grid, distance):
"""
For an input grid of (y,x) coordinates, remove all coordinates that do not trace within a threshold distance
of the source-plane centre. This is performed by:
1) Computing the deflection angle of every (y,x) coordinate on the grid using the input lensing object.
2) Ray tracing these coordinates to the source-plane.
3) Computing their distance to the centre of the source in the source-plane.
4) Removing all coordinates that are not within the input distance of the centre.
This algorithm is optionally used in the _PositionFiner_. It may be required to remove solutions that are
genuine 'peaks' that tracer closer to a source than their 8 neighboring pixels, but which do not truly
trace to the centre of the source-centre.
Parameters
----------
lensing_obj : autogalaxy.LensingObject
An object which has a deflection_from_grid method for performing lensing calculations, for example a
`MassProfile`, _Galaxy_, `Plane` or `Tracer`.
grid : autoarray.Grid2DIrregularUniform or ndarray
A grid of (y,x) Cartesian coordinates for which the 'peak' values that trace closer to the source than
their neighbors are found.
source_plane_coordinate : (y,x)
The (y,x) coordinate in the source-plane pixels that the distance of traced grid coordinates are computed
for.
distance : float
The distance within which a grid coordinate must trace to the source-plane centre to be retained.
"""
if distance is None:
return grid
deflections = deflection_func(grid=grid)
source_plane_grid = grid.grid_from_deflection_grid(
deflection_grid=deflections)
source_plane_distances = source_plane_grid.distances_from_coordinate(
coordinate=source_plane_coordinate)
grid_within_distance_of_centre = grid_within_distance(
distances_1d=source_plane_distances,
grid_slim=grid,
within_distance=distance,
)
return grid_2d_irregular.Grid2DIrregularUniform(
grid=grid_within_distance_of_centre,
pixel_scales=grid.pixel_scales)
def grid_peaks_from(self, deflections_func, grid, source_plane_coordinate):
"""
Find the 'peaks' of a grid of coordinates, where a peak corresponds to a (y,x) coordinate on the grid which
traces closer to the input (y,x) source-plane coordinate than any of its 8 adjacent neighbors. This is
performed by:
1) Computing the deflection angle of every (y,x) coordinate on the grid using the input lensing object.
2) Ray tracing these coordinates to the source-plane.
3) Computing their distance to the centre of the source in the source-plane.
4) Finding pixels whose source-plane distance is lower than all 8 neighboring pixels.
The `PositionFinder` works by locating pixels that trace closer to the source galaxy than neighboring pixels
and iteratively refining the grid to find pixels that trace close at higher and higher resolutions. This
function is core to finding pixelsl that meet this criteria.
Parameters
----------
lensing_obj : autogalaxy.LensingObject
An object which has a deflection_from_grid method for performing lensing calculations, for example a
`MassProfile`, _Galaxy_, `Plane` or `Tracer`.
grid : autoarray.Grid2DIrregularUniform or ndarray
A grid of (y,x) Cartesian coordinates for which the 'peak' values that trace closer to the source than
their neighbors are found.
source_plane_coordinate : (y,x)
The (y,x) coordinate in the source-plane pixels that the distance of traced grid coordinates are computed
for.
"""
deflections = deflections_func(grid=grid)
source_plane_grid = grid.grid_from_deflection_grid(
deflection_grid=deflections)
source_plane_distances = source_plane_grid.distances_from_coordinate(
coordinate=source_plane_coordinate)
neighbors, has_neighbors = grid_square_neighbors_1d_from(
shape_slim=grid.shape[0])
grid_peaks = grid_peaks_from(
distance_1d=source_plane_distances,
grid_slim=grid,
neighbors=neighbors.astype("int"),
has_neighbors=has_neighbors,
)
return grid_2d_irregular.Grid2DIrregularUniform(
grid=grid_peaks, pixel_scales=grid.pixel_scales)
def grid_with_coordinates_from_mass_profile_centre_removed(
self, lensing_obj, grid):
"""Remove all coordinates from a grid which are within the distance_from_mass_profile_centre attribute of any
mass profile of the lensing object.
The `PositionFinder` often finds multiple unphyiscal solutions near a mass profile due to the high levels of
demagnification. These are typically not observable in real galaxies and thus may benefit from being removed
from the PositionFiner.
The positions are removed by computing the distance between all grid points and the mass profile centres of
every mass profile in the lensing object.
Parameters
----------
lensing_obj : autogalaxy.LensingObject
An object which has a deflection_from_grid method for performing lensing calculations, for example a
`MassProfile`, _Galaxy_, `Plane` or `Tracer`.
grid : autoarray.Grid2DIrregularUniform or ndarray
A gridd of (y,x) Cartesian coordinates for which their distances to the mass profile centres are computed,
with points within the threshold removed.
"""
if self.distance_from_mass_profile_centre is not None:
pixel_scales = grid.pixel_scales
centres = lensing_obj.extract_attribute(cls=mp.MassProfile,
attr_name="centre")
for centre in centres.in_list:
distances_1d = np.sqrt(
np.square(grid[:, 0] - centre[0]) +
np.square(grid[:, 1] - centre[1]))
grid = grid_outside_distance_mask_from(
distances_1d=distances_1d,
grid_slim=grid,
outside_distance=self.distance_from_mass_profile_centre,
)
return grid_2d_irregular.Grid2DIrregularUniform(
grid=grid, pixel_scales=pixel_scales)
return grid
def solve(self,
lensing_obj,
source_plane_coordinate,
upper_plane_index=None):
if upper_plane_index is None:
deflections_func = lensing_obj.deflections_2d_from_grid
else:
deflections_func = partial(
lensing_obj.deflections_between_planes_from_grid,
plane_i=0,
plane_j=upper_plane_index,
)
coordinates_list = self.grid_peaks_from(
grid=self.grid,
source_plane_coordinate=source_plane_coordinate,
deflections_func=deflections_func,
)
coordinates_list = self.grid_with_coordinates_from_mass_profile_centre_removed(
lensing_obj=lensing_obj, grid=coordinates_list)
coordinates_list = self.grid_with_points_below_magnification_threshold_removed(
lensing_obj=lensing_obj,
deflections_func=deflections_func,
grid=coordinates_list,
)
if not self.use_upscaling:
coordinates_list = self.grid_within_distance_of_source_plane_centre(
deflection_func=deflections_func,
grid=grid_2d_irregular.Grid2DIrregularUniform(
grid=coordinates_list,
pixel_scales=self.grid.pixel_scales),
source_plane_coordinate=source_plane_coordinate,
distance=self.distance_from_source_centre,
)
return grid_2d_irregular.Grid2DIrregular(grid=coordinates_list)
pixel_scale = self.grid.pixel_scale
while pixel_scale > self.pixel_scale_precision:
refined_coordinates_list = []
for coordinate in coordinates_list:
refined_coordinates = self.refined_coordinates_from_coordinate(
deflections_func=deflections_func,
coordinate=coordinate,
pixel_scale=pixel_scale,
source_plane_coordinate=source_plane_coordinate,
)
if refined_coordinates is not None:
refined_coordinates_list += refined_coordinates
refined_coordinates_list = grid_remove_duplicates(
grid=np.asarray(refined_coordinates_list))
pixel_scale = pixel_scale / self.upscale_factor
coordinates_list = refined_coordinates_list
coordinates_list = self.grid_within_distance_of_source_plane_centre(
deflection_func=deflections_func,
grid=grid_2d_irregular.Grid2DIrregularUniform(
grid=coordinates_list,
pixel_scales=(pixel_scale, pixel_scale)),
source_plane_coordinate=source_plane_coordinate,
distance=self.distance_from_source_centre,
)
coordinates_list = self.grid_with_points_below_magnification_threshold_removed(
lensing_obj=lensing_obj,
deflections_func=deflections_func,
grid=coordinates_list,
)
return grid_2d_irregular.Grid2DIrregular(grid=coordinates_list)