Gaussian1D¶
-
class
astropy.modeling.functional_models.
Gaussian1D
(amplitude=1, mean=0, stddev=1, **kwargs)[source]¶ Bases:
astropy.modeling.Fittable1DModel
One dimensional Gaussian model.
- Parameters
- amplitudefloat
Amplitude of the Gaussian.
- meanfloat
Mean of the Gaussian.
- stddevfloat
Standard deviation of the Gaussian.
- 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 thefixed
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 thetied
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, themin
andmax
properties of a parameter may be used.- eqconslist, optional
A list of functions of length
n
such thateqcons[j](x0,*args) == 0.0
in a successfully optimized problem.- ineqconslist, optional
A list of functions of length
n
such thatieqcons[j](x0,*args) >= 0.0
is a successfully optimized problem.
See also
Notes
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()
Attributes Summary
Gaussian 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, 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