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, name=None, meta=None, **params)[source]¶ Bases:
astropy.modeling.polynomial.OrthoPolynomialBase
Bivariate Chebyshev series..
It is defined as
\[P_{nm}(x,y) = \sum_{n,m=0}^{n=d,m=d}C_{nm} T_n(x ) T_m(y)\]where
T_n(x)
andT_m(y)
are Chebyshev polynomials of the first kind.Parameters:  x_degree : int
degree in x
 y_degree : int
degree in y
 x_domain : list or None, optional
domain of the x independent variable
 y_domain : list or None, optional
domain of the y independent variable
 x_window : list or None, optional
range of the x independent variable
 y_window : list or None, optional
range of the y independent variable
 **params : dict
keyword: value pairs, representing parameter_name: value
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.
Notes
This model does not support the use of units/quantities, because each term in the sum of Chebyshev polynomials is a polynomial in x and/or y  since the coefficients within each Chebyshev polynomial are fixed, we can’t use quantities for x and/or y since the units would not be compatible. For example, the third Chebyshev polynomial (T2) is 2x^21, but if x was specified with units, 2x^2 and 1 would have incompatible units.
Methods Summary
fit_deriv
(x, y, *params)Derivatives with respect to the coefficients. Methods Documentation

fit_deriv
(x, y, *params)[source]¶ 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 nonlinear fitters
Returns:  result : ndarray
The Vandermonde matrix