# Hermite2D¶

class astropy.modeling.polynomial.Hermite2D(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]

Bivariate Hermite series.

It is defined as

$P_{nm}(x,y) = \sum_{n,m=0}^{n=d,m=d}C_{nm} H_n(x) H_m(y)$

where H_n(x) and H_m(y) are Hermite polynomials.

Parameters: Other 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 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 the fixed 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 the tied 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, the min and max properties of a parameter may be used. eqcons : list, optional A list of functions of length n such that eqcons[j](x0,*args) == 0.0 in a successfully optimized problem. ineqcons : list, optional A list of functions of length n such that ieqcons[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 Hermite polynomials is a polynomial in x and/or y - since the coefficients within each Hermite polynomial are fixed, we can’t use quantities for x and/or y since the units would not be compatible. For example, the third Hermite polynomial (H2) is 4x^2-2, but if x was specified with units, 4x^2 and -2 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 Hermite polynomials:

$H_{x_0}H_{y_0}, H_{x_1}H_{y_0}...H_{x_n}H_{y_0}...H_{x_n}H_{y_m}$
Parameters: x : ndarray input y : ndarray input params : throw away parameter parameter list returned by non-linear fitters result : ndarray The Vandermonde matrix