# Polynomial2D¶

class astropy.modeling.polynomial.Polynomial2D(degree, x_domain=[-1, 1], y_domain=[-1, 1], x_window=[-1, 1], y_window=[-1, 1], n_models=None, model_set_axis=None, name=None, meta=None, **params)[source] [edit on github]

2D Polynomial model.

Represents a general polynomial of degree n:

$P(x,y) = c_{00} + c_{10}x + ...+ c_{n0}x^n + c_{01}y + ...+ c_{0n}y^n + c_{11}xy + c_{12}xy^2 + ... + c_{1(n-1)}xy^{n-1}+ ... + c_{(n-1)1}x^{n-1}y$
Parameters: Other Parameters: degree : int highest power of the polynomial, the number of terms is degree+1 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.

Attributes Summary

 input_units This property is used to indicate what units or sets of units the evaluate method expects, and returns a dictionary mapping inputs to units (or None if any units are accepted). inputs outputs

Methods Summary

 __call__(x, y[, model_set_axis, …]) Evaluate this model using the given input(s) and the parameter values that were specified when the model was instantiated. evaluate(x, y, *coeffs) Evaluate the model on some input variables. fit_deriv(x, y, *params) Computes the Vandermonde matrix. invlex_coeff(coeffs) multivariate_horner(x, y, coeffs) Multivariate Horner’s scheme prepare_inputs(x, y, **kwargs) This method is used in __call__ to ensure that all the inputs to the model can be broadcast into compatible shapes (if one or both of them are input as arrays), particularly if there are more than one parameter sets.

Attributes Documentation

input_units

This property is used to indicate what units or sets of units the evaluate method expects, and returns a dictionary mapping inputs to units (or None if any units are accepted).

Model sub-classes can also use function annotations in evaluate to indicate valid input units, in which case this property should not be overridden since it will return the input units based on the annotations.

inputs = ('x', 'y')
outputs = ('z',)

Methods Documentation

__call__(x, y, model_set_axis=None, with_bounding_box=False, fill_value=nan, equivalencies=None) [edit on github]

Evaluate this model using the given input(s) and the parameter values that were specified when the model was instantiated.

evaluate(x, y, *coeffs)[source] [edit on github]

Evaluate the model on some input variables.

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

Computes the Vandermonde matrix.

Parameters: x : ndarray input y : ndarray input params : throw away parameter parameter list returned by non-linear fitters result : ndarray The Vandermonde matrix
invlex_coeff(coeffs)[source] [edit on github]
multivariate_horner(x, y, coeffs)[source] [edit on github]

Multivariate Horner’s scheme

Parameters: x, y : array coeffs : array of coefficients in inverse lexical order
prepare_inputs(x, y, **kwargs)[source] [edit on github]

This method is used in __call__ to ensure that all the inputs to the model can be broadcast into compatible shapes (if one or both of them are input as arrays), particularly if there are more than one parameter sets. This also makes sure that (if applicable) the units of the input will be compatible with the evaluate method.