MexicanHat2D

class astropy.modeling.functional_models.MexicanHat2D(amplitude=1, x_0=0, y_0=0, sigma=1, **kwargs)[source]

Bases: astropy.modeling.Fittable2DModel

Two dimensional symmetric Mexican Hat model.

Parameters
amplitudefloat

Amplitude

x_0float

x position of the peak

y_0float

y position of the peak

sigmafloat

Width of the Mexican hat

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.

Notes

Model formula:

\[f(x, y) = A \left(1 - \frac{\left(x - x_{0}\right)^{2} + \left(y - y_{0}\right)^{2}}{\sigma^{2}}\right) e^{\frac{- \left(x - x_{0}\right)^{2} - \left(y - y_{0}\right)^{2}}{2 \sigma^{2}}}\]

Attributes Summary

amplitude

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

sigma

x_0

y_0

Methods Summary

evaluate(x, y, amplitude, x_0, y_0, sigma)

Two dimensional Mexican Hat model function

Attributes Documentation

amplitude = Parameter('amplitude', 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', 'y_0', 'sigma')
sigma = Parameter('sigma', value=1.0)
x_0 = Parameter('x_0', value=0.0)
y_0 = Parameter('y_0', value=0.0)

Methods Documentation

static evaluate(x, y, amplitude, x_0, y_0, sigma)[source]

Two dimensional Mexican Hat model function