Gaussian1D

class astropy.modeling.functional_models.Gaussian1D(amplitude=1, mean=0, stddev=1, **kwargs)

Bases: Fittable1DModel

One dimensional Gaussian model.

Parameters:

amplitudepython:float or Quantity.

Amplitude (peak value) of the Gaussian - for a normalized profile (integrating to 1), set amplitude = 1 / (stddev * np.sqrt(2 * np.pi))

meanpython:float or Quantity.

Mean of the Gaussian.

stddevpython:float or Quantity.

Standard deviation of the Gaussian with FWHM = 2 * stddev * np.sqrt(2 * np.log(2)).

Other Parameters:

fixeda python: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.

tiedpython: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 the tied property of a parameter may be used.

boundspython: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, the min and max properties of a parameter may be used.

eqconspython:list, optional

A list of functions of length n such that eqcons[j](x0,*args) == 0.0 in a successfully optimized problem.

ineqconspython:list, optional

A list of functions of length n such that ieqcons[j](x0,*args) >= 0.0 is a successfully optimized problem.

See also

Gaussian2D, Box1D, Moffat1D, Lorentz1D

Notes

Either all or none of input x, mean and stddev must be provided consistently with compatible units or as unitless numbers.

Model formula:

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

Examples

>>> from astropy.modeling import models
>>> def tie_center(model):
...         mean = 50 * model.stddev
...         return mean
>>> tied_parameters = {'mean': tie_center}

Specify that ‘mean’ is a tied parameter in one of two ways:

>>> g1 = models.Gaussian1D(amplitude=10, mean=5, stddev=.3,
...                             tied=tied_parameters)

or

>>> g1 = models.Gaussian1D(amplitude=10, mean=5, stddev=.3)
>>> g1.mean.tied
False
>>> g1.mean.tied = tie_center
>>> g1.mean.tied
<function tie_center at 0x...>

Fixed parameters:

>>> g1 = models.Gaussian1D(amplitude=10, mean=5, stddev=.3,
...                        fixed={'stddev': True})
>>> g1.stddev.fixed
True

or

>>> g1 = models.Gaussian1D(amplitude=10, mean=5, stddev=.3)
>>> g1.stddev.fixed
False
>>> g1.stddev.fixed = True
>>> g1.stddev.fixed
True

import numpy as np
import matplotlib.pyplot as plt

from astropy.modeling.models import Gaussian1D

plt.figure()
s1 = Gaussian1D()
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	Gaussian full width at half maximum.
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).
mean
param_names	Names of the parameters that describe models of this type.
stddev

Methods Summary

evaluate(x, amplitude, mean, stddev)	Gaussian1D model function.
fit_deriv(x, amplitude, mean, stddev)	Gaussian1D model function derivatives.

Attributes Documentation

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

fwhm

Gaussian full width at half maximum.

input_units

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

param_names = ('amplitude', 'mean', 'stddev')

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.

stddev = Parameter('stddev', value=1.0, bounds=(1.1754943508222875e-38, None))

Methods Documentation

static evaluate(x, amplitude, mean, stddev)

Gaussian1D model function.

static fit_deriv(x, amplitude, mean, stddev)

Gaussian1D model function derivatives.