Lorentz2D#

class astropy.modeling.functional_models.Lorentz2D(amplitude=1, x_0=0, y_0=0, fwhm=1, **kwargs)[source]#

Bases: Fittable2DModel

Two-dimensional Lorentzian model.

Parameters:

amplitudefloat or Quantity.: Peak value.
x_0float or Quantity.: Position of the peak in x.
y_0float or Quantity.: Position of the peak in y.
fwhmfloat or Quantity.: Full width at half maximum (FWHM).

See also

Lorentz1D, Gaussian2D, Moffat2D

Notes

The x, y, x_0, y_0, and fwhm inputs must have compatible units or as unitless numbers.

Model formula:

\[f(x, y) = \frac{A \gamma^{2}}{\gamma^{2} + \left(x - x_{0}\right)^2 + \left(y - y_{0}\right)^{2}}\]

where \(\gamma\) is the half width at half maximum (HWHM), which is half the FWHM.

The area under the Lorentz2D profile is infinite, therefore this model profile cannot be normalized to sum to 1.

Examples

import numpy as np
import matplotlib.pyplot as plt

from astropy.modeling.models import Lorentz2D

plt.figure()
model = Lorentz2D(x_0=12, y_0=12, fwhm=3)
yy, xx = np.mgrid[:25, :25]
data = model(xx, yy)

plt.imshow(data)
plt.show()

(png, svg, pdf)

../_images/astropy-modeling-functional_models-Lorentz2D-1.png

Attributes Summary

`amplitude`
`fwhm`
`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.
`x_0`
`y_0`

Methods Summary

`evaluate`(x, y, amplitude, x_0, y_0, fwhm)	Two dimensional Lorentzian model function.
`fit_deriv`(x, y, amplitude, x_0, y_0, fwhm)	Two dimensional Lorentzian model derivative with respect to parameters.

Attributes Documentation

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

fwhm = Parameter('fwhm', value=1.0)#

input_units#

param_names = ('amplitude', 'x_0', 'y_0', 'fwhm')#

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.

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, fwhm)[source]#: Two dimensional Lorentzian model function.

static fit_deriv(x, y, amplitude, x_0, y_0, fwhm)[source]#: Two dimensional Lorentzian model derivative with respect to parameters.