Voigt1D#

class astropy.modeling.functional_models.Voigt1D(x_0=0, amplitude_L=1, fwhm_L=0.6366197723675814, fwhm_G=np.float64(0.6931471805599453), method=None, **kwargs)[source]#

Bases: Fittable1DModel

One dimensional model for the Voigt profile.

Parameters:

x_0float or Quantity: Position of the peak
amplitude_Lfloat or Quantity.: The Lorentzian amplitude (peak of the associated Lorentz function) - for a normalized profile (integrating to 1), set amplitude_L = 2 / (np.pi * fwhm_L)
fwhm_Lfloat or Quantity: The Lorentzian full width at half maximum
fwhm_Gfloat or Quantity.: The Gaussian full width at half maximum
methodstr, optional: Algorithm for computing the complex error function; one of ‘Humlicek2’ (default, fast and generally more accurate than rtol=3.e-5) or ‘Scipy’, alternatively ‘wofz’ (requires scipy, almost as fast and reference in accuracy).

Other Parameters:

fixeddict, 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, Lorentz1D

Notes

The x, x_0, and fwhm_* inputs must have compatible units or be unitless numbers.

Voigt function is calculated as real part of the complex error function computed from either Humlicek’s rational approximations (JQSRT 21:309, 1979; 27:437, 1982) following Schreier 2018 (MNRAS 479, 3068; and hum2zpf16m from his cpfX.py module); or wofz (implementing ‘Faddeeva.cc’).

Examples

import numpy as np
from astropy.modeling.models import Voigt1D
import matplotlib.pyplot as plt

plt.figure()
x = np.arange(0, 10, 0.01)
v1 = Voigt1D(x_0=5, amplitude_L=10, fwhm_L=0.5, fwhm_G=0.9)
plt.plot(x, v1(x))
plt.show()

(png, svg, pdf)

../_images/astropy-modeling-functional_models-Voigt1D-1.png

Attributes Summary

`amplitude_L`
`fwhm_G`
`fwhm_L`
`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.
`sqrt_ln2`
`sqrt_ln2pi`
`sqrt_pi`
`x_0`

Methods Summary

`evaluate`(x, x_0, amplitude_L, fwhm_L, fwhm_G)	One dimensional Voigt function scaled to Lorentz peak amplitude.
`fit_deriv`(x, x_0, amplitude_L, fwhm_L, fwhm_G)	Derivative of the one dimensional Voigt function with respect to parameters.

Attributes Documentation

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

fwhm_G = Parameter('fwhm_G', value=0.6931471805599453)#

fwhm_L = Parameter('fwhm_L', value=0.6366197723675814)#

input_units#

param_names = ('x_0', 'amplitude_L', 'fwhm_L', 'fwhm_G')#

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.

sqrt_ln2 = np.float64(0.8325546111576977)#

sqrt_ln2pi = np.float64(1.475664626635606)#

sqrt_pi = np.float64(1.7724538509055159)#

x_0 = Parameter('x_0', value=0.0)#

Methods Documentation

evaluate(x, x_0, amplitude_L, fwhm_L, fwhm_G)[source]#: One dimensional Voigt function scaled to Lorentz peak amplitude.

fit_deriv(x, x_0, amplitude_L, fwhm_L, fwhm_G)[source]#: Derivative of the one dimensional Voigt function with respect to parameters.