Moffat1D

class astropy.modeling.functional_models.Moffat1D(amplitude=1, x_0=0, gamma=1, alpha=1, **kwargs)[source] [edit on github]

Bases: astropy.modeling.Fittable1DModel

One dimensional Moffat model.

Parameters:

amplitude : float

Amplitude of the model.

x_0 : float

x position of the maximum of the Moffat model.

gamma : float

Core width of the Moffat model.

alpha : float

Power index of the Moffat model.

Other Parameters:
 

fixed : a dict

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

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

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

eqcons : list

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

ineqcons : list

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

See also

Gaussian1D, Box1D

Notes

Model formula:

\[f(x) = A \left(1 + \frac{\left(x - x_{0}\right)^{2}}{\gamma^{2}}\right)^{- \alpha}\]

Examples

import numpy as np
import matplotlib.pyplot as plt

from astropy.modeling.models import Moffat1D

plt.figure()
s1 = Moffat1D()
r = np.arange(-5, 5, .01)

for factor in range(1, 4):
    s1.amplitude = factor
    s1.width = factor
    plt.plot(r, s1(r), color=str(0.25 * factor), lw=2)

plt.axis([-5, 5, -1, 4])
plt.show()

(png, svg, pdf)

../_images/astropy-modeling-functional_models-Moffat1D-1.png

Attributes Summary

alpha
amplitude
fwhm Moffat full width at half maximum.
gamma
input_units
param_names
x_0

Methods Summary

evaluate(x, amplitude, x_0, gamma, alpha) One dimensional Moffat model function
fit_deriv(x, amplitude, x_0, gamma, alpha) One dimensional Moffat model derivative with respect to parameters

Attributes Documentation

alpha
amplitude
fwhm

Moffat full width at half maximum. Derivation of the formula is available in this notebook by Yoonsoo Bach.

gamma
input_units
param_names = ('amplitude', 'x_0', 'gamma', 'alpha')
x_0

Methods Documentation

static evaluate(x, amplitude, x_0, gamma, alpha)[source] [edit on github]

One dimensional Moffat model function

static fit_deriv(x, amplitude, x_0, gamma, alpha)[source] [edit on github]

One dimensional Moffat model derivative with respect to parameters