Legendre1D¶

class
astropy.modeling.polynomial.
Legendre1D
(degree, domain=None, window=None, n_models=None, model_set_axis=None, name=None, meta=None, **params)[source]¶ Bases:
astropy.modeling.polynomial._PolyDomainWindow1D
Univariate Legendre series.
It is defined as:
\[P(x) = \sum_{i=0}^{i=n}C_{i} * L_{i}(x)\]where
L_i(x)
is the corresponding Legendre polynomial.For explanation of
domain
, andwindow
see Notes regarding usage of domain and window. Parameters
 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 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
Notes
This model does not support the use of units/quantities, because each term in the sum of Legendre polynomials is a polynomial in x  since the coefficients within each Legendre polynomial are fixed, we can’t use quantities for x since the units would not be compatible. For example, the third Legendre polynomial (P2) is 1.5x^20.5, but if x was specified with units, 1.5x^2 and 0.5 would have incompatible units.
Attributes Summary
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.
clenshaw
(x, coeffs)evaluate
(x, *coeffs)Evaluate the model on some input variables.
fit_deriv
(x, *params)Computes the Vandermonde matrix.
prepare_inputs
(x, **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

n_inputs
= 1¶ The number of inputs.

n_outputs
= 1¶ The number of outputs.
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, **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.