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]¶ 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)
andH_m(y)
are Hermite polynomials.For explanation of
x_domain
,y_domain
,x_window
andy_window
see Notes regarding usage of domain and window. Parameters
 x_degreeint
degree in x
 y_degreeint
degree in y
 x_domainlist or None, optional
domain of the x independent variable
 y_domainlist or None, optional
domain of the y independent variable
 x_windowlist or None, optional
range of the x independent variable
 y_windowlist or None, optional
range of the y independent variable
 **paramsdict
keyword: value pairs, representing parameter_name: value
 Other Parameters
 fixeda 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. tieddict, 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. boundsdict, 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. eqconslist, optional
A list of functions of length
n
such thateqcons[j](x0,*args) == 0.0
in a successfully optimized problem. ineqconslist, 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 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^22, but if x was specified with units, 4x^2 and 2 would have incompatible units.
Methods Summary
fit_deriv
(self, x, y, \*params)Derivatives with respect to the coefficients.
Methods Documentation

fit_deriv
(self, 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
 xndarray
input
 yndarray
input
 paramsthrow away parameter
parameter list returned by nonlinear fitters
 Returns
 resultndarray
The Vandermonde matrix