Gaussian1D¶
-
class
astropy.modeling.functional_models.
Gaussian1D
(amplitude=1, mean=0, stddev=1, **kwargs)[source] [edit on github]¶ Bases:
astropy.modeling.Fittable1DModel
One dimensional Gaussian model.
Parameters: - amplitude : float
Amplitude of the Gaussian.
- mean : float
Mean of the Gaussian.
- stddev : float
Standard deviation of the Gaussian.
Other Parameters: - fixed : a 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.- tied : 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 thetied
property of a parameter may be used.- bounds : 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, themin
andmax
properties of a parameter may be used.- eqcons : list, optional
A list of functions of length
n
such thateqcons[j](x0,*args) == 0.0
in a successfully optimized problem.- ineqcons : list, 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
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
stddev
Methods Summary
evaluate
(x, amplitude, mean, stddev)Gaussian1D model function. fit_deriv
(x, amplitude, mean, stddev)Gaussian1D model function derivatives. Attributes Documentation
-
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).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.
-
mean
¶
-
param_names
= ('amplitude', 'mean', 'stddev')¶
-
stddev
¶
Methods Documentation
-
static
evaluate
(x, amplitude, mean, stddev)[source] [edit on github]¶ Gaussian1D model function.
-
static
fit_deriv
(x, amplitude, mean, stddev)[source] [edit on github]¶ Gaussian1D model function derivatives.