Legendre1D

class astropy.modeling.polynomial.Legendre1D(degree, domain=None, window=[-1, 1], n_models=None, model_set_axis=None, name=None, meta=None, **params)

Bases: astropy.modeling.polynomial.PolynomialModel

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.

Parameters:

degree : int

degree of the series

domain : list or None, optional

window : list or None, optional

If None, it is set to [-1,1] Fitters will remap the domain to this window

**params : dict

keyword: value pairs, representing parameter_name: value

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 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.

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^2-0.5, but if x was specified with units, 1.5x^2 and -0.5 would have incompatible units.

Attributes Summary

inputs
outputs

Methods Summary

__call__(x[, 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

inputs = ('x',)

outputs = ('y',)

Methods Documentation

__call__(x, model_set_axis=None, with_bounding_box=False, fill_value=nan, equivalencies=None)

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

static clenshaw(x, coeffs)

evaluate(x, *coeffs)

Evaluate the model on some input variables.

fit_deriv(x, *params)

Computes the Vandermonde matrix.

Parameters:

x : ndarray

input

params : throw away parameter

parameter list returned by non-linear fitters

Returns:

result : ndarray

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. This also makes sure that (if applicable) the units of the input will be compatible with the evaluate method.