autogalaxy.profiles.geometry_profiles.EllProfile#
- class EllProfile[source]#
Bases:
SphProfile
An elliptical profile, which describes the geometry of profiles defined by an ellipse.
The elliptical components (ell_comps) of this profile are used to define the axis_ratio (q) and angle (phi) :
- Math
phi = (180/pi) * arctan2(e_y / e_x) / 2
- Math
f = sqrt(e_y^2 + e_x^2)
- Math
q = (1 - f) / (1 + f)
Where:
e_y = y elliptical component = ell_comps[0] e_x = x elliptical component = ell_comps[1] q = axis_ratio (major_axis / minor_axis)
This means that given an axis-ratio and angle the elliptical components can be computed as:
- Math
f = (1 - q) / (1 + q)
- Math
e_y = f * sin(2*phi)
- Math
e_x = f * cos(2*phi)
For an input (y,x) grid of Cartesian coordinates this is used to compute the elliptical coordinates of a profile:
\[\xi = q^{0.5} * ((y-y_c^2 + x-x_c^2 / q^2)^{0.5}\]Where:
y_c = profile y centre = centre[0] x_c = profile x centre = centre[1]
The majority of elliptical profiles use xi to compute their image.
- Parameters
Methods
The angle between each angle theta on the grid and the profile, in radians.
Convert a grid of (y,x) coordinates to an eccentric radius: :math: axis_ratio^0.5 (x^2 + (y^2/q))^0.5
Convert a grid of (y,x) coordinates to their elliptical radii values: :math: (x^2 + (y^2/q))^0.5
has
Does this instance have an attribute which is of type cls?
radial_grid_from
Convert a grid of (y, x) coordinates, to their radial distances from the profile centre (e.g.
Rotate a grid of (y,x) coordinates which have been transformed to the elliptical reference frame of a profile back to the original unrotated coordinate grid reference frame.
Transform a grid of (y,x) coordinates from the reference frame of the profile to the original observer reference frame.
Transform a grid of (y,x) coordinates to the reference frame of the profile.
Attributes
The position angle in degrees of the major-axis of the ellipse defined by profile, defined counter clockwise from the positive x-axis (0.0 > angle > 180.0).
The position angle in radians of the major-axis of the ellipse defined by profile, defined counter clockwise from the positive x-axis (0.0 > angle > 2pi).
The ratio of the minor-axis to major-axis (b/a) of the ellipse defined by profile (0.0 > q > 1.0).
- property axis_ratio: float#
The ratio of the minor-axis to major-axis (b/a) of the ellipse defined by profile (0.0 > q > 1.0).
- Return type
- property angle: float#
The position angle in degrees of the major-axis of the ellipse defined by profile, defined counter clockwise from the positive x-axis (0.0 > angle > 180.0).
- Return type
- property angle_radians: float#
The position angle in radians of the major-axis of the ellipse defined by profile, defined counter clockwise from the positive x-axis (0.0 > angle > 2pi).
- Return type
- angle_to_profile_grid_from(grid_angles)[source]#
The angle between each angle theta on the grid and the profile, in radians.
- Parameters
grid_angles – The angle theta counter-clockwise from the positive x-axis to each coordinate in radians.
- rotated_grid_from_reference_frame_from(grid)[source]#
Rotate a grid of (y,x) coordinates which have been transformed to the elliptical reference frame of a profile back to the original unrotated coordinate grid reference frame.
Note that unlike the method transformed_from_reference_frame_grid_from the coordinates are not translated back to the profile’s original centre.
This routine is used after computing deflection angles in the reference frame of the profile, so that the deflection angles can be re-rotated to the frame of the original coordinates before performing ray-tracing.
- Parameters
grid – The (y, x) coordinates in the reference frame of an elliptical profile.
- elliptical_radii_grid_from(grid)[source]#
Convert a grid of (y,x) coordinates to their elliptical radii values: :math: (x^2 + (y^2/q))^0.5
If the coordinates have not been transformed to the profile’s geometry (e.g. translated to the profile centre), this is performed automatically.
- Parameters
grid (
Union
[ndarray
,Grid2D
,Grid2DIterate
,Grid2DIrregular
]) – The (y, x) coordinates in the reference frame of the elliptical profile.- Return type
ndarray
- eccentric_radii_grid_from(grid)[source]#
Convert a grid of (y,x) coordinates to an eccentric radius: :math: axis_ratio^0.5 (x^2 + (y^2/q))^0.5
This is used in certain light profiles define their half-light radii as a circular radius.
If the coordinates have not been transformed to the profile’s geometry (e.g. translated to the profile centre), this is performed automatically.
- Parameters
grid (
Union
[ndarray
,Grid2D
,Grid2DIterate
,Grid2DIrregular
]) – The (y, x) coordinates in the reference frame of the elliptical profile.- Return type
ndarray
- transformed_to_reference_frame_grid_from(grid)[source]#
Transform a grid of (y,x) coordinates to the reference frame of the profile.
This includes a translation to the profile’s centre and a rotation using its angle.
- Parameters
grid (
Union
[ndarray
,Grid2D
,Grid2DIterate
,Grid2DIrregular
]) – The (y, x) coordinates in the original reference frame of the grid.- Return type
Grid2DTransformedNumpy
- transformed_from_reference_frame_grid_from(grid)[source]#
Transform a grid of (y,x) coordinates from the reference frame of the profile to the original observer reference frame.
This includes a translation from the profile’s centre and a rotation using its angle.
- Parameters
grid (
Union
[ndarray
,Grid2D
,Grid2DIterate
,Grid2DIrregular
]) – The (y, x) coordinates in the reference frame of the profile.- Return type
Union
[ndarray
,Grid2D
,Grid2DIterate
,Grid2DIrregular
]