Polynomial2D#
- class astropy.modeling.polynomial.Polynomial2D(degree, x_domain=None, y_domain=None, x_window=None, y_window=None, n_models=None, model_set_axis=None, name=None, meta=None, **params)[source]#
Bases:
PolynomialModel
2D Polynomial model.
Represents a general polynomial of degree n:
\[P(x,y) = c_{00} + c_{10}x + ...+ c_{n0}x^n + c_{01}y + ...+ c_{0n}y^n + c_{11}xy + c_{12}xy^2 + ... + c_{1(n-1)}xy^{n-1}+ ... + c_{(n-1)1}x^{n-1}y\]For explanation of
x_domain
,y_domain
,x_window
andy_window
see Notes regarding usage of domain and window.- Parameters:
- degree
int
Polynomial degree: largest sum of exponents (\(i + j\)) of variables in each monomial term of the form \(x^i y^j\). The number of terms in a 2D polynomial of degree
n
is given by binomial coefficient \(C(n + 2, 2) = (n + 2)! / (2!\,n!) = (n + 1)(n + 2) / 2\).- x_domain
tuple
orNone
, optional domain of the x independent variable If None, it is set to (-1, 1)
- y_domain
tuple
orNone
, optional domain of the y independent variable If None, it is set to (-1, 1)
- x_window
tuple
orNone
, optional range of the x independent variable If None, it is set to (-1, 1) Fitters will remap the x_domain to x_window
- y_window
tuple
orNone
, optional range of the y independent variable If None, it is set to (-1, 1) Fitters will remap the y_domain to y_window
- **params
dict
keyword: value pairs, representing parameter_name: value
- degree
- Other Parameters:
- fixed
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.
- fixed
Attributes Summary
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).The number of inputs.
The number of outputs.
Methods Summary
__call__
(*inputs[, 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#
- n_inputs = 2#
The number of inputs.
- n_outputs = 1#
The number of outputs.
- x_domain#
- x_window#
- y_domain#
- y_window#
Methods Documentation
- __call__(*inputs, model_set_axis=None, with_bounding_box=False, fill_value=nan, equivalencies=None, inputs_map=None, **new_inputs)#
Evaluate this model using the given input(s) and the parameter values that were specified when the model was instantiated.
- prepare_inputs(x, y, **kwargs)[source]#
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.