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
- 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.
- fixed
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
Moffat full width at half maximum.
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).Names of the parameters that describe models of this type.
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
= Parameter('alpha', value=1.0)¶
-
amplitude
= Parameter('amplitude', value=1.0)¶
-
fwhm
¶ Moffat full width at half maximum. Derivation of the formula is available in this notebook by Yoonsoo Bach.
-
gamma
= Parameter('gamma', value=1.0)¶
-
input_units
¶
-
param_names
= ('amplitude', 'x_0', 'gamma', 'alpha')¶ 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)¶
Methods Documentation