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import numpy as np
from .pfbase import PfBase
[docs]class Rayleigh(PfBase):
def __init__(self, gamma: float):
'''
Rayleigh scattering phase function constructor.
Parameters
----------
gamma: float
Molecular anisotropy. Scattering is isotropic for gamma = 0.
Examples
--------
Rayleigh scattering phase function for gamma [0.0, 0.1, 0.2, 0.5, 1.0].
>>> import numpy as np
>>> from matplotlib import pyplot as pp
>>>
>>> cos_theta = np.linspace(-1.0, 1.0, 1000)
>>>
>>> pp.figure()
>>> for gamma in [0.0, 0.1, 0.2, 0.5, 1.0]:
>>> pp.semilogy(cos_theta, Rayleigh(gamma)(cos_theta), label='gamma={}'.format(gamma))
>>> pp.legend()
'''
super().__init__()
self._gamma = float(gamma)
self._gs_data = np.array((1.0, 0.0, super().g(2)))
[docs] def g(self, n: int) -> float:
'''
Overloads the :py:meth:`PfBase.g` method of the base class with
an analytical solution.
'''
if n <= 2:
return self._gs_data[n]
else:
return 0
[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,))
last = int(last)
gs[:min(3, last)] = self._gs_data[:min(3, last)]
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 __call__(self, costheta: float or np.ndarray) -> float or np.ndarray:
'''
Call method of the Rayleigh scattering phase function object.
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 (3.0/8.0)*((1.0 + 3.0*self._gamma) + \
(1.0 - self._gamma)*costheta*costheta)/(1.0 + 2.0*self._gamma)
def __repr__(self):
return 'Rayleigh({})'.format(self._gamma)