Moffat2D#
- class astropy.modeling.functional_models.Moffat2D(amplitude=1, x_0=0, y_0=0, gamma=1, alpha=1, **kwargs)[source]#
Bases:
Fittable2DModel
Two dimensional Moffat model.
- Parameters:
- Other Parameters:
- fixed
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.
- fixed
See also
Notes
Model formula:
\[f(x, y) = A \left(1 + \frac{\left(x - x_{0}\right)^{2} + \left(y - y_{0}\right)^{2}}{\gamma^{2}}\right)^{- \alpha}\]Attributes Summary
Moffat 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, y, amplitude, x_0, y_0, gamma, alpha)Two dimensional Moffat model function.
fit_deriv
(x, y, amplitude, x_0, y_0, gamma, ...)Two dimensional Moffat model derivative with respect to parameters.
Attributes Documentation
- alpha = Parameter('alpha', value=1.0)#
- amplitude = Parameter('amplitude', value=1.0)#
- fwhm#
Moffat full width at half maximum. Derivation of the formula is available in this notebook by Yoonsoo Bach.
- gamma = Parameter('gamma', value=1.0)#
- input_units#
- param_names = ('amplitude', 'x_0', 'y_0', 'gamma', 'alpha')#
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.
- x_0 = Parameter('x_0', value=0.0)#
- y_0 = Parameter('y_0', value=0.0)#
Methods Documentation