Lorentz1D

class astropy.modeling.functional_models.Lorentz1D(amplitude=1, x_0=0, fwhm=1, **kwargs)

Bases: astropy.modeling.Fittable1DModel

One dimensional Lorentzian model.

Parameters

amplitudefloat

Peak value

x_0float

Position of the peak

fwhmfloat

Full width at half maximum (FWHM)

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, RickerWavelet1D

Notes

Model formula:

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

where \(\gamma\) is half of given FWHM.

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()

(png, svg, pdf)

Attributes Summary

amplitude
fwhm
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, 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 = Parameter('amplitude', value=1.0)

fwhm = Parameter('fwhm', value=1.0)

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', 'fwhm')

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

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