MexicanHat2D

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

Bases: astropy.modeling.Fittable2DModel

Two dimensional symmetric Mexican Hat model.

Parameters:

amplitude : float

Amplitude

x_0 : float

x position of the peak

y_0 : float

y position of the peak

sigma : float

Width of the Mexican hat

Other Parameters:  

fixed : a dict

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.

tied : dict

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.

bounds : dict

A dictionary {parameter_name: boolean} of lower and upper bounds of parameters. Keys are parameter names. Values are a list of length 2 giving the desired range for the parameter. Alternatively the min and max properties of a parameter may be used.

eqcons : list

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

ineqcons : list

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

See also

MexicanHat1D, Gaussian2D

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
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

input_units

param_names = ('amplitude', 'x_0', 'y_0', 'sigma')

sigma

x_0

y_0

Methods Documentation

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

Two dimensional Mexican Hat model function