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import numpy as np
from .pfbase import PfBase
[docs]class Pc(PfBase):
def __init__(self, n: float):
'''
Power of cosines scattering phase function constructor.
.. math::
p(\\cos(\\theta)) = \\frac{(n + 1)}/{2^{(n + 1)}} (1 + \\cos(\\theta))^n
Parameters
----------
n: float
Parameter of the power of cosine scattering phase function.
Examples
--------
Power of cosines scattering phase function.
n = {0.1, 0.5, 1.0, 2.0, 5.0, 10.0}.
>>> import numpy as np
>>> from matplotlib import pyplot as pp
>>>
>>> cos_theta = np.linspace(-1.0, 1.0, 1000)
>>>
>>> pp.figure()
>>> for n in [0.1, 0.5, 1.0, 2.0, 5.0, 10.0]:
>>> pp.semilogy(cos_theta, Pc(n)(cos_theta), label='n={}'.format(n))
>>> pp.legend()
'''
super().__init__()
self._n = float(n)
self._k = (n + 1.0)/(2**(n + 1))
self._gs = np.zeros((20 + 1,))
self._gs[0] = 1.0
self._gs[1] = self._n/(self._n + 2.0)
for moment in range(2, 20 + 1):
self._gs[moment] = self._gs[moment - 1]*(self._n - moment + 1)/\
(self._n + moment + 1)
self._gs = np.abs(np.maximum(self._gs, 0.0))
def __call__(self, costheta: float or np.ndarray) -> float or np.ndarray:
'''
Call method of the Gegenbauer kernel scattering phase function.
Parameters
----------
costheta: float or np.ndarray
Scattering angle cosines at which the scattering phase function
is evaluated.
Returns
-------
f: float or np.ndarray
Scattering phase function at the specified scattering angle cosines.
'''
return self._k*(1.0 + costheta)**self._n
[docs] def g(self, n: int) -> float:
'''
Overloads the :py:meth:`PfBase.g` method of the base class with
an analytical solution.
'''
if n < self._gs.size:
g = float(self._gs[n])
else:
g = np.prod(np.arange(self._n, self._n - n + 2))/ \
np.prod(np.arange(self._n + 2, self._n + n + 2))
g = abs(max(float(g), 0.0))
return g
[docs] def gs(self, last: int) -> np.ndarray:
'''
Overloads the py:meth:PfBase.gs method of the base class with
an analytical solution.
'''
gs = np.zeros((last + 1,))
if last + 1 < self._gs.size:
gs[:last + 1] = self._gs[:last + 1]
else:
gs[:self._gs.size] = self._gs
for moment in range(self._gs.size, last):
g = gs[moment - 1]*(self._n - moment + 1)/ \
(self._n + moment + 1)
gs[moment] = abs(max(g, 0.0))
return gs
[docs] def fastg(self, n: int, **kwargs) -> float:
'''
Overloads the py:meth:PfBase.fastg method of the base class with
an analytical solution.
'''
return self.g(n)
[docs] def fastgs(self, last: int, **kwargs) -> np.ndarray:
'''
Overloads the py:meth:PfBase.fastgs method of the base class with
an analytical solution.
'''
return self.gs(last)
def __repr__(self):
return 'Pc({})'.format(self._n)