import numpy as np
import openmc
from collections.abc import Iterable
[docs]def legendre_from_expcoef(coef, domain=(-1, 1)):
"""Return a Legendre series object based on expansion coefficients.
Given a list of coefficients from FET tally and a array of down, return
the numpy Legendre object.
Parameters
----------
coef : Iterable of float
A list of coefficients of each term in Legendre polynomials
domain : (2,) List of float
Domain of the Legendre polynomial
Returns
-------
numpy.polynomial.Legendre
A numpy Legendre series class
"""
n = np.arange(len(coef))
c = (2*n + 1) * np.asarray(coef) / (domain[1] - domain[0])
return np.polynomial.Legendre(c, domain)
class Polynomial(object):
"""Abstract Polynomial Class for creating polynomials.
"""
def __init__(self, coef):
self.coef = np.asarray(coef)
[docs]class ZernikeRadial(Polynomial):
"""Create radial only Zernike polynomials given coefficients and domain.
The radial only Zernike polynomials are defined as in
:class:`ZernikeRadialFilter`.
Parameters
----------
coef : Iterable of float
A list of coefficients of each term in radial only Zernike polynomials
radius : float
Domain of Zernike polynomials to be applied on. Default is 1.
r : float
Position to be evaluated, normalized on radius [0,1]
Attributes
----------
order : int
The maximum (even) order of Zernike polynomials.
radius : float
Domain of Zernike polynomials to be applied on. Default is 1.
norm_coef : iterable of float
The list of coefficients of each term in the polynomials after
normailization.
"""
def __init__(self, coef, radius=1):
super().__init__(coef)
self._order = 2 * (len(self.coef) - 1)
self.radius = radius
norm_vec = (2 * np.arange(len(self.coef)) + 1) / (np.pi * radius**2)
self._norm_coef = norm_vec * self.coef
@property
def order(self):
return self._order
def __call__(self, r):
import openmc.lib as lib
if isinstance(r, Iterable):
return [np.sum(self._norm_coef * lib.calc_zn_rad(self.order, r_i))
for r_i in r]
else:
return np.sum(self._norm_coef * lib.calc_zn_rad(self.order, r))