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)

Bases: astropy.modeling.polynomial.OrthoPolynomialBase

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:

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 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)

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

Returns:

result : ndarray

The Vandermonde matrix