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- Legendre1D

# Legendre1D

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

  Bases: `_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`, and `window` see Notes regarding usage of domain and window.

  Parameters:
    degree `python:int`

      degree of the series

    domain `python:tuple` or `python:None`, optional
    window `python:tuple` or `python:None`, optional

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

    **params `python:dict`

      keyword: value pairs, representing parameter_name: value

  Other Parameters:
    fixed `a` `python: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 `python: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 `python: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 `python:list`, optional

      A list of functions of length `n` such that `eqcons[j](x0,*args) == 0.0` in a successfully optimized problem.

    ineqcons `python: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

  `n_inputs` | The number of inputs.
  `n_outputs` | 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.

  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 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.