def deflections_2d_from_grid(self, grid):
"""
Calculate the deflection angles at a given set of arc-second gridded coordinates.
Following Eq. (15) and (16), but the parameters are slightly different.
Parameters
----------
grid : aa.Grid2D
The grid of (y,x) arc-second coordinates the deflection angles are computed on.
"""
factor = (2.0 * self.mass_to_light_ratio * self.intensity /
(1 + self.axis_ratio) * self.axis_ratio /
np.sqrt(1.0 - self.axis_ratio**2.0))
core_radius_0 = np.sqrt(
(4.0 * self.core_radius_0**2.0) / (1.0 + self.axis_ratio)**2)
core_radius_1 = np.sqrt(
(4.0 * self.core_radius_1**2.0) / (1.0 + self.axis_ratio)**2)
psi0 = psi_from(grid=grid,
axis_ratio=self.axis_ratio,
core_radius=core_radius_0)
psi1 = psi_from(grid=grid,
axis_ratio=self.axis_ratio,
core_radius=core_radius_1)
deflection_y0 = np.arctanh(
np.divide(
np.multiply(np.sqrt(1.0 - self.axis_ratio**2.0), grid[:, 0]),
np.add(psi0, self.axis_ratio**2.0 * core_radius_0),
))
deflection_x0 = np.arctan(
np.divide(
np.multiply(np.sqrt(1.0 - self.axis_ratio**2.0), grid[:, 1]),
np.add(psi0, core_radius_0),
))
deflection_y1 = np.arctanh(
np.divide(
np.multiply(np.sqrt(1.0 - self.axis_ratio**2.0), grid[:, 0]),
np.add(psi1, self.axis_ratio**2.0 * core_radius_1),
))
deflection_x1 = np.arctan(
np.divide(
np.multiply(np.sqrt(1.0 - self.axis_ratio**2.0), grid[:, 1]),
np.add(psi1, core_radius_1),
))
deflection_y = np.subtract(deflection_y0, deflection_y1)
deflection_x = np.subtract(deflection_x0, deflection_x1)
return self.rotate_grid_from_reference_frame(
np.multiply(factor,
np.vstack((deflection_y, deflection_x)).T))
def deflections_2d_from_grid(self, grid):
"""
Calculate the deflection angles on a grid of (y,x) arc-second coordinates.
For coordinates (0.0, 0.0) the analytic calculation of the deflection angle gives a NaN. Therefore, \
coordinates at (0.0, 0.0) are shifted slightly to (1.0e-8, 1.0e-8).
Parameters
----------
grid : aa.Grid2D
The grid of (y,x) arc-second coordinates the deflection angles are computed on.
"""
factor = (2.0 * self.einstein_radius_rescaled * self.axis_ratio /
np.sqrt(1 - self.axis_ratio**2))
psi = psi_from(grid=grid, axis_ratio=self.axis_ratio, core_radius=0.0)
deflection_y = np.arctanh(
np.divide(np.multiply(np.sqrt(1 - self.axis_ratio**2), grid[:, 0]),
psi))
deflection_x = np.arctan(
np.divide(np.multiply(np.sqrt(1 - self.axis_ratio**2), grid[:, 1]),
psi))
return self.rotate_grid_from_reference_frame(
grid=np.multiply(factor,
np.vstack((deflection_y, deflection_x)).T))