# Ellipse2D¶

class astropy.modeling.functional_models.Ellipse2D(amplitude=1, x_0=0, y_0=0, a=1, b=1, theta=0.0, **kwargs)[source]

A 2D Ellipse model.

Parameters
amplitudefloat

Value of the ellipse.

x_0float

x position of the center of the disk.

y_0float

y position of the center of the disk.

afloat

The length of the semimajor axis.

bfloat

The length of the semiminor axis.

thetafloat or Quantity, optional

The rotation angle as an angular quantity (Quantity or Angle) or a value in radians (as a float). The rotation angle increases counterclockwise from the positive x axis.

Other Parameters
fixeda 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.

tieddict, 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.

boundsdict, 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.

eqconslist, optional

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

ineqconslist, optional

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

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,
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')
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 Names of the parameters that describe models of this type. 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
param_names = ('amplitude', 'x_0', 'y_0', 'a', 'b', 'theta')

Names of the parameters that describe models of this type.

The parameters in this tuple are in the same order they should be passed in when initializing a model of a specific type. Some types of models, such as polynomial models, have a different number of parameters depending on some other property of the model, such as the degree.

When defining a custom model class the value of this attribute is automatically set by the Parameter attributes defined in the class body.

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)[source]

Two dimensional Ellipse model function.