Moffat1D¶

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

Bases: astropy.modeling.Fittable1DModel

One dimensional Moffat model.

Parameters

amplitudefloat: Amplitude of the model.
x_0float: x position of the maximum of the Moffat model.
gammafloat: Core width of the Moffat model.
alphafloat: Power index of the Moffat model.

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.

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()

()

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

Attributes Summary

`alpha`
`amplitude`
`fwhm`	Moffat full width at half maximum.
`gamma`
`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`
`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¶

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', 'gamma', 'alpha')¶

x_0¶

Methods Documentation

static evaluate(x, amplitude, x_0, gamma, alpha)[source]¶: One dimensional Moffat model function

static fit_deriv(x, amplitude, x_0, gamma, alpha)[source]¶: One dimensional Moffat model derivative with respect to parameters

Navigation

Moffat1D¶