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
 degreeint
degree of the series
 domaintuple or None, optional
 windowtuple or None, optional
If None, it is set to (1, 1) Fitters will remap the domain to this 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.
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
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¶

n_outputs
= 1¶
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.

fit_deriv
(x, *params)[source]¶ Computes the Vandermonde matrix.
 Parameters
 xndarray
input
 paramsthrow away parameter
parameter list returned by nonlinear fitters
 Returns
 resultndarray
The Vandermonde matrix

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.