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, optional
A dictionary
{parameter_name: boolean}
of parameters to not be varied during fitting. True means the parameter is held fixed. Alternatively thefixed
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 thetied
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, themin
andmax
properties of a parameter may be used.- eqcons : list, optional
A list of functions of length
n
such thateqcons[j](x0,*args) == 0.0
in a successfully optimized problem.- ineqcons : list, optional
A list of functions of length
n
such thatieqcons[j](x0,*args) >= 0.0
is a successfully optimized problem.
See also
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()
()
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] [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