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Chebyshev2D

class astropy.modeling.polynomial.Chebyshev2D(x_degree, y_degree, x_domain=None, x_window=[-1, 1], y_domain=None, y_window=[-1, 1], n_models=None, model_set_axis=None, **params)[source] [edit on github]

Bases: astropy.modeling.polynomial.OrthoPolynomialBase

2D Chebyshev polynomial of the 1st kind.

It is defined as

P_{n_m}(x,y) = \sum C_{n_m} T_n(x) T_m(y)

Parameters:

x_degree : int

degree in x

y_degree : int

degree in y

x_domain : list or None

domain of the x independent variable

y_domain : list or None

domain of the y independent variable

x_window : list or None

range of the x independent variable

y_window : list or None

range of the y independent variable

param_dim : int

number of parameter sets

**params : dict

keyword: value pairs, representing parameter_name: value
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.

Attributes Summary

input_names list() -> new empty list

Methods Summary

fit_deriv(x, y, *params) Derivatives with respect to the coefficients.

Attributes Documentation

input_names = []

Methods Documentation

fit_deriv(x, y, *params)[source] [edit on github]

Derivatives with respect to the coefficients.

This is an array with Chebyshev polynomials:

T_{x_0}T_{y_0}, T_{x_1}T_{y_0}...T_{x_n}T_{y_0}...T_{x_n}T_{y_m}

Parameters:

x : ndarray

input

y : ndarray

input

params : throw away parameter

parameter list returned by non-linear fitters
Returns:

result : ndarray

The Vandermonde matrix

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