# -*- coding: utf-8 -*-
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# Copyright (C) Laboratory of Imaging technologies,
# Faculty of Electrical Engineering,
# University of Ljubljana.
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# This file is part of PyXOpto.
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import os.path
import numpy as np
from .pfmapbase import PfMap2DBase
from ..gk import Gk
from xopto import DATA_PATH
[docs]class GkMap(PfMap2DBase):
DEFAULT_MAP_FILE = 'gk_map.npz'
XLABEL = '$g_{gk}$'
YLABEL = '$\\alpha_{gk}$'
PLOTSCALEFACTORX = 1.0
PLOTSCALEFACTORY = 1.0
[docs] @classmethod
def precalculate(cls, n: int = 100, filename: str = None,
verbose: bool = True):
'''
Precalculate the Gk scattering phase function lookup table.
Parameters
----------
n: int
Number of steps along the scattering phase function parameters.
filename: str
Output file or None to save as the default lookup table.
verbose: bool
Turn on verbose progress report.
'''
if verbose:
print('Creating Gk map:')
gkmap = GkMap(ggk=np.linspace(0.0, 0.98, n),
a=np.linspace(-0.5, 10.0, n),
ng=15)
if filename is None:
filename = cls.default_data_file()
gkmap.save(filename=filename)
def __init__(self, ggk: np.ndarray = None, a: np.ndarray = None, ng:
int = 15, filename: str = None, ncostheta: int = None):
'''
Prepares maps of the first ng Legendre moments of the
Gegenbauer Kernel (GK) scattering phase function, over the specified
range of the GK parameters gg and a. If ng >= 2, a map of
gamma is prepared and if ng >= 3 maps of delta and sigma are
prepared as well. The maps are used to obtain an initial estimate
when calculating the GK scattering phase function parameters
from given Legendre moments, gamma and/or delta.
Parameters
----------
ggk: np.ndarray vector
A Vector of equally spaced values defining the grid density of
the gg parameter of the GK scattering phase function.
a: np.ndarray vector
A Vector of equally spaced values defining the grid density of
the a parameter of the GK scattering phase function.
ng: int
Maps are created for the first ng Legendre moments. If ng >= 2,
a map of gamma is prepared and if g >= 3 maps of delta and sigma
are prepared as well.
filename: str
File with saved data. The values of all the other parameters are
ignored and restored from the file.
ncostheta: int
Number of nodes used to compute the Legendre moments. Use a
large number (> 1000) for accurate results. If None, adaptive
step integration is used, which is accurate but can become slow.
Note
----
The value of parameter ng should be >> 3 to accurately
estimate the value of parameter sigma.
Examples
--------
Prepares maps of gamma and delta, and estimates the GK parameters
given a) g and gamma are known b) gamma and delta are known.
>>> import numpy as np
>>>
>>> m = GkMap(np.linspace(0.0, 0.98, 100), np.linspace(-0.5, 5.0, 100), ng=3)
>>> ggk, a = m.invgammadelta(gamma=2.2, delta=3.5)
>>> print('gamma=2.2, delta=3.5 ==>', 'ggk:', ggk, 'a:', a)
>>> ggk, a = m.invgamma(g=0.8, gamma=2.2)
>>> print('g=0.8, gamma=2.2 ==>', 'ggk:', ggk, 'a:', a)
>>>
Load maps from the default file included in the data/pf folder.
>>> m = GkMap.fromfile()
>>> ggk, a = m.invgammadelta(gamma=2.2, delta=3.5)
>>> print('gamma=2.2, delta=3.5 ==>', 'ggk:', ggk, 'a:', a)
>>> ggk, a = m.invgamma(g=0.8, gamma=2.2)
>>> print('g=0.8, gamma=2.2 ==>', 'ggk:', ggk, 'a:', a)
>>>
'''
if ggk is None:
ggk = np.linspace(0.0, 0.98, 100)
if a is None:
a = np.linspace(-0.5, 10.0, 100)
super().__init__(param1=ggk, param2=a, ng=ng,
pf=Gk, filename=filename, ncostheta=ncostheta)
[docs] def ggk(self) -> np.ndarray:
'''
Returns a vector of points defining the grid of gg GK parameter
'''
return self.param1()
[docs] def a(self) -> np.ndarray:
'''
Returns a vector of points defining the grid of parameter a of the GK
scattering phase function.
'''
return self.param2()
[docs] def ggk_grid(self) -> np.ndarray:
'''
Returns a 2D map (meshgrid) of the first parameter ggk of the GK
scattering phase function input parameter.
'''
return self.grid1()
[docs] def a_grid(self) -> np.ndarray:
'''
Returns a 2D map (meshgrid) of the second parameter a of the GK
scattering phase function input parameter.
'''
return self.grid2()