Lorentz1D

class astropy.modeling.functional_models.Lorentz1D

Bases: astropy.modeling.Fittable1DModel

One dimensional Lorentzian model.

Parameters:

amplitude : float

Peak value

x_0 : float

Position of the peak

fwhm : float

Full width at half maximum

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, MexicanHat1D

Notes

Model formula:

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

Examples

import numpy as np
import matplotlib.pyplot as plt

from astropy.modeling.models import Lorentz1D

plt.figure()
s1 = Lorentz1D()
r = np.arange(-5, 5, .01)

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

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

(Source code, png, hires.png, pdf)

Attributes Summary

amplitude
fwhm
param_names
x_0

Methods Summary

evaluate(x, amplitude, x_0, fwhm)	One dimensional Lorentzian model function
fit_deriv(x, amplitude, x_0, fwhm)	One dimensional Lorentzian model derivative with respect to parameters

Attributes Documentation

amplitude

fwhm

param_names = ('amplitude', 'x_0', 'fwhm')

x_0

Methods Documentation

static evaluate(x, amplitude, x_0, fwhm)

One dimensional Lorentzian model function

static fit_deriv(x, amplitude, x_0, fwhm)

One dimensional Lorentzian model derivative with respect to parameters