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:
astropy.modeling.polynomial.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
- degreeint
highest power of the polynomial, the number of terms is degree+1
- x_domaintuple or None, optional
domain of the x independent variable If None, it is set to (-1, 1)
- y_domaintuple or None, optional
domain of the y independent variable If None, it is set to (-1, 1)
- x_windowtuple or None, 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_windowtuple or None, optional
range of the y independent variable If None, it is set to (-1, 1) Fitters will remap the y_domain to y_window
- **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.
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).Methods Summary
__call__
(self, *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
(self, x, y, *coeffs)Evaluate the model on some input variables.
fit_deriv
(self, x, y, *params)Computes the Vandermonde matrix.
invlex_coeff
(self, coeffs)multivariate_horner
(self, x, y, coeffs)Multivariate Horner’s scheme
prepare_inputs
(self, 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.
-
n_inputs
= 2¶
-
n_outputs
= 1¶
-
x_domain
¶
-
x_window
¶
-
y_domain
¶
-
y_window
¶
Methods Documentation
-
__call__
(self, *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.
-
fit_deriv
(self, x, y, *params)[source]¶ Computes the Vandermonde matrix.
- Parameters
- xndarray
input
- yndarray
input
- paramsthrow away parameter
parameter list returned by non-linear fitters
- Returns
- resultndarray
The Vandermonde matrix
-
multivariate_horner
(self, x, y, coeffs)[source]¶ Multivariate Horner’s scheme
- Parameters
- x, yarray
- coeffsarray of coefficients in inverse lexical order
-
prepare_inputs
(self, 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.