Ellipse2D

class astropy.modeling.functional_models.Ellipse2D(amplitude=1, x_0=0, y_0=0, a=1, b=1, theta=0, **kwargs)

Bases: astropy.modeling.Fittable2DModel

A 2D Ellipse model.

Parameters:

amplitude : float

Value of the ellipse.

x_0 : float

x position of the center of the disk.

y_0 : float

y position of the center of the disk.

a : float

The length of the semimajor axis.

b : float

The length of the semiminor axis.

theta : float

The rotation angle in radians of the semimajor axis. The rotation angle increases counterclockwise from the positive x axis.

Other Parameters:  

fixed : a dict, optional

A dictionary {parameter_name: boolean} of parameters to not be varied during fitting. True means the parameter is held fixed. Alternatively the fixed property of a parameter may be used.

tied : dict, optional

A dictionary {parameter_name: callable} of parameters which are linked to some other parameter. The dictionary values are callables providing the linking relationship. Alternatively the tied property of a parameter may be used.

bounds : dict, optional

A dictionary {parameter_name: value} of lower and upper bounds of parameters. Keys are parameter names. Values are a list or a tuple of length 2 giving the desired range for the parameter. Alternatively, the min and max properties of a parameter may be used.

eqcons : list, optional

A list of functions of length n such that eqcons[j](x0,*args) == 0.0 in a successfully optimized problem.

ineqcons : list, optional

A list of functions of length n such that ieqcons[j](x0,*args) >= 0.0 is a successfully optimized problem.

See also

Disk2D, Box2D

Notes

Model formula:

\[\begin{split}f(x, y) = \left \{ \begin{array}{ll} \mathrm{amplitude} & : \left[\frac{(x - x_0) \cos \theta + (y - y_0) \sin \theta}{a}\right]^2 + \left[\frac{-(x - x_0) \sin \theta + (y - y_0) \cos \theta}{b}\right]^2 \leq 1 \\ 0 & : \mathrm{otherwise} \end{array} \right.\end{split}\]

Examples

import numpy as np
from astropy.modeling.models import Ellipse2D
from astropy.coordinates import Angle
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
x0, y0 = 25, 25
a, b = 20, 10
theta = Angle(30, 'deg')
e = Ellipse2D(amplitude=100., x_0=x0, y_0=y0, a=a, b=b,
              theta=theta.radian)
y, x = np.mgrid[0:50, 0:50]
fig, ax = plt.subplots(1, 1)
ax.imshow(e(x, y), origin='lower', interpolation='none', cmap='Greys_r')
e2 = mpatches.Ellipse((x0, y0), 2*a, 2*b, theta.degree, edgecolor='red',
                      facecolor='none')
ax.add_patch(e2)
plt.show()

(png, svg, pdf)

Attributes Summary

a
amplitude
b
input_units	This property is used to indicate what units or sets of units the evaluate method expects, and returns a dictionary mapping inputs to units (or None if any units are accepted).
param_names
theta
x_0
y_0

Methods Summary

evaluate(x, y, amplitude, x_0, y_0, a, b, theta)

Two dimensional Ellipse model function.

Attributes Documentation

a = Parameter('a', value=1.0)

amplitude = Parameter('amplitude', value=1.0)

b = Parameter('b', value=1.0)

input_units

This property is used to indicate what units or sets of units the evaluate method expects, and returns a dictionary mapping inputs to units (or None if any units are accepted).

Model sub-classes can also use function annotations in evaluate to indicate valid input units, in which case this property should not be overridden since it will return the input units based on the annotations.

param_names = ('amplitude', 'x_0', 'y_0', 'a', 'b', 'theta')

theta = Parameter('theta', value=0.0)

x_0 = Parameter('x_0', value=0.0)

y_0 = Parameter('y_0', value=0.0)

Methods Documentation

static evaluate(x, y, amplitude, x_0, y_0, a, b, theta)

Two dimensional Ellipse model function.