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non central chi squared

The non-central \( \chi^2 \) distribution.

NonCentralChiSquared(*args, **kwargs)

Bases: PolynomialApproximationTransformer

Polynomial approximation to the inverse CDF of the non-central \( \chi^2 \) distribution.

Source code in src/pyarv/non_central_chi_squared/__init__.py 
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def __init__(self, *args, **kwargs):
    super().__init__(*args, **kwargs)
    self.cached_tables = {}

approximation(*args, order, non_centralities, degrees_of_freedom, **kwargs)

Specialism extending PolynomialApproximationTransformer.transform.

Parameters:

Name Type Description Default
non_centralities Array

The non-centralities, positive (zero values correspond to the central \( \chi^2 \) distribution).

 required
degrees_of_freedom float

The degrees of freedom, strictly positive, assumed to be fixed for all values.

 required
Source code in src/pyarv/non_central_chi_squared/__init__.py 
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def approximation(self,
                  *args,
                  order,
                  non_centralities: Array,
                  degrees_of_freedom: float,
                  **kwargs
                  ):
    r"""
    Specialism extending `PolynomialApproximationTransformer.transform`.

    Parameters
    ----------
    non_centralities:
        The non-centralities, positive (zero values correspond to the central \( \chi^2 \) distribution).
    degrees_of_freedom:
        The degrees of freedom, strictly positive, assumed to be fixed for all values.    
    """
    approximations = {1: linear}
    if self.order not in approximations.keys():
        raise NotImplementedError(f"We have not yet implemented interfaced for higher order approximations. Currently we only support orders: {approximations.keys()}")
    polynomial_coefficients = None
    if self.try_cached_table:
        try:
            polynomial_coefficients = self.cached_tables[degrees_of_freedom]
        except KeyError:
            logging.info(f"There were no cached coefficients for {degrees_of_freedom = }")
    if polynomial_coefficients is None:
        logging.info(f"Generating coefficients for {degrees_of_freedom = }")
        polynomial_coefficients = generate_non_central_chi_squared_coefficients(n_intervals=16,
                                                                                n_interpolation_functions=16,
                                                                                n_polynomial_orders=self.order+1,
                                                                                dof=degrees_of_freedom,
                                                                                dtype=np.float32
                                                                                )
    assert polynomial_coefficients is not None
    if self.cache_table:
        logging.info(f"Caching the coefficients for {degrees_of_freedom = }")
        self.cached_tables[degrees_of_freedom] = polynomial_coefficients
    approximations[self.order](*args,
                               non_centralities=non_centralities,
                               degrees_of_freedom=degrees_of_freedom,
                               polynomial_coefficients=polynomial_coefficients,
                               **kwargs)