eppaurora.electrons._fang_f_y() - Code Metrics - Inspection of "protons: Use more sophisticated `polyval`" - st-bender/pyeppaurora - Measure and Improve Code Quality continuously with Scrutinizer

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eppaurora.electrons._fang_f_y() A

↳ Parent: eppaurora.electrons

Complexity

Conditions

Size

Total Lines	10
Code Lines	5

Duplication

Lines	10
Ratio	100 %

Importance

Changes

Metric	Value
eloc	5
dl	10
loc	10
rs	10
c	0
b	0
f	0
cc	1
nop	2

# coding: utf-8
# Copyright (c) 2020 Stefan Bender
#
# This file is part of pyeppaurora.
# pyeppaurora is free software: you can redistribute it or modify
# it under the terms of the GNU General Public License as published
# by the Free Software Foundation, version 2.
# See accompanying LICENSE file or http://www.gnu.org/licenses/gpl-2.0.html.
"""Atmospheric ionization rate parametrizations

Includes the atmospheric ionization rate parametrizations for auroral
and medium-energy electron precipitation, 100 eV--1 MeV [1]_, [2]_, and [3]_.

.. [1] Roble and Ridley, Ann. Geophys., 5A(6), 369--382, 1987
.. [2] Fang et al., J. Geophys. Res., 113, A09311, 2008
.. [3] Fang et al., Geophys. Res. Lett., 37, L22106, 2010
"""

import numpy as np
from numpy.polynomial.polynomial import polyval

__all__ = [
	"rr1987",
	"rr1987_mod",
	"fang2008",
	"fang2010_mono",
	"fang2010_spec_int",
	"fang2010_maxw_int",
	"maxwell_general",
	"maxwell_pflux",
]

POLY_F2008 = [
	[ 3.49979e-1, -6.18200e-2, -4.08124e-2,  1.65414e-2],
	[ 5.85425e-1, -5.00793e-2,  5.69309e-2, -4.02491e-3],
	[ 1.69692e-1, -2.58981e-2,  1.96822e-2,  1.20505e-3],
	[-1.22271e-1, -1.15532e-2,  5.37951e-6,  1.20189e-3],
	[ 1.57018,     2.87896e-1, -4.14857e-1,  5.18158e-2],
	[ 8.83195e-1,  4.31402e-2, -8.33599e-2,  1.02515e-2],
	[ 1.90953,    -4.74704e-2, -1.80200e-1,  2.46652e-2],
	[-1.29566,    -2.10952e-1,  2.73106e-1, -2.92752e-2]
]

POLY_F2010 = [
	[ 1.24616E+0,  1.45903E+0, -2.42269E-1,  5.95459E-2],
	[ 2.23976E+0, -4.22918E-7,  1.36458E-2,  2.53332E-3],
	[ 1.41754E+0,  1.44597E-1,  1.70433E-2,  6.39717E-4],
	[ 2.48775E-1, -1.50890E-1,  6.30894E-9,  1.23707E-3],
	[-4.65119E-1, -1.05081E-1, -8.95701E-2,  1.22450E-2],
	[ 3.86019E-1,  1.75430E-3, -7.42960E-4,  4.60881E-4],
	[-6.45454E-1,  8.49555E-4, -4.28581E-2, -2.99302E-3],
	[ 9.48930E-1,  1.97385E-1, -2.50660E-3, -2.06938E-3]
]


def rr1987(energy, flux, scale_height, rho):

	"""Atmospheric electron energy dissipation Roble and Ridley, 1987 [#]_

	Equations (typo corrected) taken from Fang et al., 2008.

	Parameters
	----------
	energy: array_like (M,...)
		Characteristic energy E_0 [keV] of the Maxwellian distribution.
	flux: array_like (M,...)
		Integrated energy flux Q_0 [keV / cm² / s¹]
	scale_height: array_like (N,...)
		The atmospheric scale heights [cm].
	rho: array_like (N,...)
		The atmospheric mass density [g / cm³]

	Returns
	-------
	en_diss: array_like (M,N)
		The dissipated energy profiles [keV].

	References
	----------

	.. [#] Roble and Ridley, Ann. Geophys., 5A(6), 369--382, 1987
	"""
	_c1 = 2.11685
	_c2 = 2.97035
	_c3 = 2.09710
	_c4 = 0.74054
	_c5 = 0.58795
	_c6 = 1.72746
	_c7 = 1.37459
	_c8 = 0.93296

	beta = (rho * scale_height / (4 * 1e-6))**(1 / 1.65)  # RR 1987, p. 371
	y = beta / energy  # Corrected in Fang et al. 2008 (4)
	f_y = (_c1 * (y**_c2) * np.exp(-_c3 * (y**_c4)) +
		_c5 * (y**_c6) * np.exp(-_c7 * (y**_c8)))
	# Corrected in Fang et al. 2008 (2)
	en_diss = 0.5 * flux / scale_height * f_y
	return en_diss


def rr1987_mod(energy, flux, scale_height, rho):

	"""Atmospheric electron energy dissipation Roble and Ridley, 1987 [#]_

	Equations (typo corrected) taken from Fang et al., 2008.
	Modified polynomial values to get closer to Fang et al., 2008,
	origin unknown.

	Parameters
	----------
	energy: array_like (M,...)
		Characteristic energy E_0 [keV] of the Maxwellian distribution.
	flux: array_like (M,...)
		Integrated energy flux Q_0 [keV / cm² / s¹]
	scale_height: array_like (N,...)
		The atmospheric scale heights [cm].
	rho: array_like (N,...)
		The atmospheric mass density [g / cm³]

	Returns
	-------
	en_diss: array_like (M,N)
		The dissipated energy profiles [keV].

	References
	----------

	.. [#] Roble and Ridley, Ann. Geophys., 5A(6), 369--382, 1987
	"""
	# Modified polynomial, origin unknown
	_c1 = 3.233
	_c2 = 2.56588
	_c3 = 2.2541
	_c4 = 0.7297198
	_c5 = 1.106907
	_c6 = 1.71349
	_c7 = 1.8835444
	_c8 = 0.86472135

	# Fang et al., 2008, Eq. (4)
	y = (rho * scale_height / (4.6 * 1e-6))**(1 / 1.65) / energy
	f_y = (_c1 * (y**_c2) * np.exp(-_c3 * (y**_c4)) +
		_c5 * (y**_c6) * np.exp(-_c7 * (y**_c8)))
	# energy dissipated [keV]
	en_diss = 0.5 * flux / scale_height * f_y
	return en_diss


def _fang_f_y(_c, _y):

	"""Polynomial evaluation helper

	Fang et al., 2008, Eq. (6), Fang et al., 2010 Eq. (4)
	"""
	ret = (
		_c[0] * (_y**_c[1]) * np.exp(-_c[2] * (_y**_c[3])) +
		_c[4] * (_y**_c[5]) * np.exp(-_c[6] * (_y**_c[7]))
	)
	return ret


def fang2008(energy, flux, scale_height, rho, pij=POLY_F2008):

	"""Atmospheric electron energy dissipation from Fang et al., 2008

	Ionization profile parametrization as derived in Fang et al., 2008 [#]_.

	Parameters
	----------
	energy: array_like (M,...)
		Characteristic energy E_0 [keV] of the Maxwellian distribution.
	flux: array_like (M,...)
		Integrated energy flux Q_0 [keV / cm² / s¹]
	scale_height: array_like (N,...)
		The atmospheric scale height(s) [cm].
	rho: array_like (N,...)
		The atmospheric densities [g / cm³], corresponding to the scale heights.

	Returns
	-------
	en_diss: array_like (M,N)
		The dissipated energy profiles [keV].

	References
	----------

	.. [#] Fang et al., J. Geophys. Res., 113, A09311, 2008, doi: 10.1029/2008JA013384
	"""
	pij = np.asarray(pij)
	# Fang et al., 2008, Eq. (7)
	_cs = np.exp(polyval(np.log(energy), pij.T))
	# Fang et al., 2008, Eq. (4)
	y = (rho * scale_height / (4e-6))**(1 / 1.65) / energy
	f_y = _fang_f_y(_cs, y)
	# Fang et al., 2008, Eq. (2)
	en_diss = 0.5 * f_y * flux / scale_height
	return en_diss


def fang2010_mono(energy, flux, scale_height, rho, pij=POLY_F2010):

	r"""Atmospheric electron energy dissipation from Fang et al., 2010

	Parametrization for mono-energetic electrons [#]_.

	Parameters
	----------
	energy: array_like (M,...)
		Energy E_0 of the mono-energetic electron beam [keV].
	flux: array_like (M,...)
		Energy flux Q_0 of the mono-energetic electron beam [keV / cm² / s¹].
	scale_height: array_like (N,...)
		The atmospheric scale heights [cm].
	rho: array_like (N,...)
		The atmospheric mass densities [g / cm³], corresponding to the scale heights.

	Returns
	-------
	en_diss: array_like (M,N)
		The dissipated energy profiles [keV].

	References
	----------

	.. [#] Fang et al., Geophys. Res. Lett., 37, L22106, 2010, doi: 10.1029/2010GL045406
	"""
	pij = np.asarray(pij)
	# Fang et al., 2010, Eq. (5)
	_cs = np.exp(polyval(np.log(energy), pij.T))
	# Fang et al., 2010, Eq. (1)
	y = 2. / energy * (rho * scale_height / (6e-6))**(0.7)
	f_y = _fang_f_y(_cs, y)
	# Fang et al., 2008, Eq. (2)
	en_diss = f_y * flux / scale_height
	return en_diss


def fang2010_spec_int(ens, dfluxes, scale_height, rho, pij=POLY_F2010, axis=-1):

	r"""Integrate over a given energy spectrum

	Integrates over the mono-energetic parametrization `q` from Fang et al., 2010
	using the given differential particle spectrum `phi`:

	:math:`\int_\text{spec} \phi(E) q(E, Q) E \text{d}E`

	Parameters
	----------
	ens: array_like (M,...)
		Central (bin) energies of the spectrum
	dfluxes: array_like (M,...)
		Differential particle fluxes in the given bins
	scale_height: array_like (N,...)
		The atmospheric scale heights
	rho: array_like (N,...)
		The atmospheric densities, corresponding to the
		scale heights.

	Returns
	-------
	en_diss: array_like (N)
		The dissipated energy profiles [keV].

	See Also
	--------
	fang2010_mono
	"""
	ediss_f10 = fang2010_mono(
		ens[None, None, :],
		dfluxes,
		scale_height[..., None],
		rho[..., None],
		pij=pij,
	)
	return np.trapz(ediss_f10 * ens, ens, axis=axis)


def fang2010_maxw_int(energy, flux, scale_height, rho, bounds=(0.1, 300.), nstep=128, pij=POLY_F2010):

	"""Integrate Fang et al., 2010 over a Maxwellian spectrum

	Integrates the mono-energetic parametrization from Fang et al., 2010 [#]_
	over a Maxwellian spectrum with characteristic energy `energy` and
	total energy flux `flux`.

	Parameters
	----------
	energy: array_like (M,...)
		Characteristic energy E_0 [keV] of the Maxwellian distribution.
	flux: array_like (M,...)
		Integrated energy flux Q_0 [keV / cm² / s¹]
	scale_height: array_like (N,...)
		The atmospheric scale heights [cm].
	rho: array_like (N,...)
		The atmospheric mass density [g / cm³]
	bounds: tuple, optional
		(min, max) [keV] of the integration range to integrate the Maxwellian.
		Make sure that this is appropriate to encompass the spectrum.
		Default: (0.1, 300.)
	nsteps: int, optional
		Number of integration steps, default: 128.

	Returns
	-------
	en_diss: array_like (M,N)
		The dissipated energy profiles [keV].

	See Also
	--------
	fang2010_mono, fang2010_spec_int, maxwell_pflux
	"""
	bounds_l10 = np.log10(bounds)
	ens = np.logspace(*bounds_l10, num=nstep)
	dflux = flux * maxwell_pflux(ens[:, None], energy)
	return fang2010_spec_int(ens, dflux.T, scale_height, rho, pij=pij, axis=-1)


def maxwell_general(en, en_0=10.):
	"""Maxwell number flux spectrum as in Fang2008 [1]

	Defined in Fang et al., JGR 2008, Eq. (1).

	Parameters
	----------
	en: float
		Energy in [keV]
	en_0: float, optional
		Characteristic energy in [keV], i.e. mode of the distribution.
		Default: 10 keV

	Returns
	-------
	phi: float
		Differential hemispherical number flux in [keV-1 cm-2 s-1]
		([keV] or scaled by 1 keV-2 cm-2 s-1, e.g. ).
	"""
	return en * np.exp(-en / en_0)


def maxwell_pflux(en, en_0=10.):
	"""Maxwell particle flux spectrum as in Fang2008 [1]

	Defined in Fang et al., JGR 2008, Eq. (1).
	The total precipitating energy flux is fixed to 1 keV cm-2 s-1,
	multiply by Q_0 [keV cm-2 s-1] to scale the particle flux.

	Parameters
	----------
	en: float
		Energy in [keV]
	en_0: float, optional
		Characteristic energy in [keV], i.e. mode of the distribution.
		Default: 10 keV.

	Returns
	-------
	phi: float
		Hemispherical differential particle flux in [keV-1 cm-2 s-1]
		([kev-2] scaled by unit energy flux).
	"""
	return 0.5 / en_0**3 * maxwell_general(en, en_0)


1		# coding: utf-8
2		# Copyright (c) 2020 Stefan Bender
3		#
4		# This file is part of pyeppaurora.
5		# pyeppaurora is free software: you can redistribute it or modify
6		# it under the terms of the GNU General Public License as published
7		# by the Free Software Foundation, version 2.
8		# See accompanying LICENSE file or http://www.gnu.org/licenses/gpl-2.0.html.
9		"""Atmospheric ionization rate parametrizations
10
11		Includes the atmospheric ionization rate parametrizations for auroral
12		and medium-energy electron precipitation, 100 eV--1 MeV [1]_, [2]_, and [3]_.
13
14		.. [1] Roble and Ridley, Ann. Geophys., 5A(6), 369--382, 1987
15		.. [2] Fang et al., J. Geophys. Res., 113, A09311, 2008
16		.. [3] Fang et al., Geophys. Res. Lett., 37, L22106, 2010
17		"""
18
19		import numpy as np
20		from numpy.polynomial.polynomial import polyval
21
22		__all__ = [
23		"rr1987",
24		"rr1987_mod",
25		"fang2008",
26		"fang2010_mono",
27		"fang2010_spec_int",
28		"fang2010_maxw_int",
29		"maxwell_general",
30		"maxwell_pflux",
31		]
32
33		POLY_F2008 = [
34		[ 3.49979e-1, -6.18200e-2, -4.08124e-2, 1.65414e-2],
35		[ 5.85425e-1, -5.00793e-2, 5.69309e-2, -4.02491e-3],
36		[ 1.69692e-1, -2.58981e-2, 1.96822e-2, 1.20505e-3],
37		[-1.22271e-1, -1.15532e-2, 5.37951e-6, 1.20189e-3],
38		[ 1.57018, 2.87896e-1, -4.14857e-1, 5.18158e-2],
39		[ 8.83195e-1, 4.31402e-2, -8.33599e-2, 1.02515e-2],
40		[ 1.90953, -4.74704e-2, -1.80200e-1, 2.46652e-2],
41		[-1.29566, -2.10952e-1, 2.73106e-1, -2.92752e-2]
42		]
43
44		POLY_F2010 = [
45		[ 1.24616E+0, 1.45903E+0, -2.42269E-1, 5.95459E-2],
46		[ 2.23976E+0, -4.22918E-7, 1.36458E-2, 2.53332E-3],
47		[ 1.41754E+0, 1.44597E-1, 1.70433E-2, 6.39717E-4],
48		[ 2.48775E-1, -1.50890E-1, 6.30894E-9, 1.23707E-3],
49		[-4.65119E-1, -1.05081E-1, -8.95701E-2, 1.22450E-2],
50		[ 3.86019E-1, 1.75430E-3, -7.42960E-4, 4.60881E-4],
51		[-6.45454E-1, 8.49555E-4, -4.28581E-2, -2.99302E-3],
52		[ 9.48930E-1, 1.97385E-1, -2.50660E-3, -2.06938E-3]
53		]
54
55
56	View Code Duplication	def rr1987(energy, flux, scale_height, rho):
		0 ignored issues – show Duplication introduced 2020-06-06 16:42 UTC by Report Bug Copy Issue Report This code seems to be duplicated in your project. Loading history...
57		"""Atmospheric electron energy dissipation Roble and Ridley, 1987 [#]_
58
59		Equations (typo corrected) taken from Fang et al., 2008.
60
61		Parameters
62		----------
63		energy: array_like (M,...)
64		Characteristic energy E_0 [keV] of the Maxwellian distribution.
65		flux: array_like (M,...)
66		Integrated energy flux Q_0 [keV / cm² / s¹]
67		scale_height: array_like (N,...)
68		The atmospheric scale heights [cm].
69		rho: array_like (N,...)
70		The atmospheric mass density [g / cm³]
71
72		Returns
73		-------
74		en_diss: array_like (M,N)
75		The dissipated energy profiles [keV].
76
77		References
78		----------
79
80		.. [#] Roble and Ridley, Ann. Geophys., 5A(6), 369--382, 1987
81		"""
82		_c1 = 2.11685
83		_c2 = 2.97035
84		_c3 = 2.09710
85		_c4 = 0.74054
86		_c5 = 0.58795
87		_c6 = 1.72746
88		_c7 = 1.37459
89		_c8 = 0.93296
90
91		beta = (rho * scale_height / (4 * 1e-6))**(1 / 1.65) # RR 1987, p. 371
92		y = beta / energy # Corrected in Fang et al. 2008 (4)
93		f_y = (_c1 * (y*_c2) np.exp(-_c3 * (y**_c4)) +
94		_c5 * (y*_c6) np.exp(-_c7 * (y**_c8)))
95		# Corrected in Fang et al. 2008 (2)
96		en_diss = 0.5 * flux / scale_height * f_y
97		return en_diss
98
99
100	View Code Duplication	def rr1987_mod(energy, flux, scale_height, rho):
		0 ignored issues – show Duplication introduced 2020-06-06 16:42 UTC by Report Bug Copy Issue Report This code seems to be duplicated in your project. Loading history...
101		"""Atmospheric electron energy dissipation Roble and Ridley, 1987 [#]_
102
103		Equations (typo corrected) taken from Fang et al., 2008.
104		Modified polynomial values to get closer to Fang et al., 2008,
105		origin unknown.
106
107		Parameters
108		----------
109		energy: array_like (M,...)
110		Characteristic energy E_0 [keV] of the Maxwellian distribution.
111		flux: array_like (M,...)
112		Integrated energy flux Q_0 [keV / cm² / s¹]
113		scale_height: array_like (N,...)
114		The atmospheric scale heights [cm].
115		rho: array_like (N,...)
116		The atmospheric mass density [g / cm³]
117
118		Returns
119		-------
120		en_diss: array_like (M,N)
121		The dissipated energy profiles [keV].
122
123		References
124		----------
125
126		.. [#] Roble and Ridley, Ann. Geophys., 5A(6), 369--382, 1987
127		"""
128		# Modified polynomial, origin unknown
129		_c1 = 3.233
130		_c2 = 2.56588
131		_c3 = 2.2541
132		_c4 = 0.7297198
133		_c5 = 1.106907
134		_c6 = 1.71349
135		_c7 = 1.8835444
136		_c8 = 0.86472135
137
138		# Fang et al., 2008, Eq. (4)
139		y = (rho * scale_height / (4.6 * 1e-6))**(1 / 1.65) / energy
140		f_y = (_c1 * (y*_c2) np.exp(-_c3 * (y**_c4)) +
141		_c5 * (y*_c6) np.exp(-_c7 * (y**_c8)))
142		# energy dissipated [keV]
143		en_diss = 0.5 * flux / scale_height * f_y
144		return en_diss
145
146
147	View Code Duplication	def _fang_f_y(_c, _y):
		0 ignored issues – show Duplication introduced 2020-07-22 20:36 UTC by Report Bug Copy Issue Report This code seems to be duplicated in your project. Loading history...
148		"""Polynomial evaluation helper
149
150		Fang et al., 2008, Eq. (6), Fang et al., 2010 Eq. (4)
151		"""
152		ret = (
153		_c[0] * (_y*_c[1]) np.exp(-_c[2] * (_y**_c[3])) +
154		_c[4] * (_y*_c[5]) np.exp(-_c[6] * (_y**_c[7]))
155		)
156		return ret
157
158
159	View Code Duplication	def fang2008(energy, flux, scale_height, rho, pij=POLY_F2008):
		0 ignored issues – show Duplication introduced 2020-06-06 16:42 UTC by Report Bug Copy Issue Report This code seems to be duplicated in your project. Loading history...
160		"""Atmospheric electron energy dissipation from Fang et al., 2008
161
162		Ionization profile parametrization as derived in Fang et al., 2008 [#]_.
163
164		Parameters
165		----------
166		energy: array_like (M,...)
167		Characteristic energy E_0 [keV] of the Maxwellian distribution.
168		flux: array_like (M,...)
169		Integrated energy flux Q_0 [keV / cm² / s¹]
170		scale_height: array_like (N,...)
171		The atmospheric scale height(s) [cm].
172		rho: array_like (N,...)
173		The atmospheric densities [g / cm³], corresponding to the scale heights.
174
175		Returns
176		-------
177		en_diss: array_like (M,N)
178		The dissipated energy profiles [keV].
179
180		References
181		----------
182
183		.. [#] Fang et al., J. Geophys. Res., 113, A09311, 2008, doi: 10.1029/2008JA013384
184		"""
185		pij = np.asarray(pij)
186		# Fang et al., 2008, Eq. (7)
187		_cs = np.exp(polyval(np.log(energy), pij.T))
188		# Fang et al., 2008, Eq. (4)
189		y = (rho * scale_height / (4e-6))**(1 / 1.65) / energy
190		f_y = _fang_f_y(_cs, y)
191		# Fang et al., 2008, Eq. (2)
192		en_diss = 0.5 * f_y * flux / scale_height
193		return en_diss
194
195
196	View Code Duplication	def fang2010_mono(energy, flux, scale_height, rho, pij=POLY_F2010):
		0 ignored issues – show Duplication introduced 2020-06-06 16:42 UTC by Report Bug Copy Issue Report This code seems to be duplicated in your project. Loading history...
197		r"""Atmospheric electron energy dissipation from Fang et al., 2010
198
199		Parametrization for mono-energetic electrons [#]_.
200
201		Parameters
202		----------
203		energy: array_like (M,...)
204		Energy E_0 of the mono-energetic electron beam [keV].
205		flux: array_like (M,...)
206		Energy flux Q_0 of the mono-energetic electron beam [keV / cm² / s¹].
207		scale_height: array_like (N,...)
208		The atmospheric scale heights [cm].
209		rho: array_like (N,...)
210		The atmospheric mass densities [g / cm³], corresponding to the scale heights.
211
212		Returns
213		-------
214		en_diss: array_like (M,N)
215		The dissipated energy profiles [keV].
216
217		References
218		----------
219
220		.. [#] Fang et al., Geophys. Res. Lett., 37, L22106, 2010, doi: 10.1029/2010GL045406
221		"""
222		pij = np.asarray(pij)
223		# Fang et al., 2010, Eq. (5)
224		_cs = np.exp(polyval(np.log(energy), pij.T))
225		# Fang et al., 2010, Eq. (1)
226		y = 2. / energy * (rho * scale_height / (6e-6))**(0.7)
227		f_y = _fang_f_y(_cs, y)
228		# Fang et al., 2008, Eq. (2)
229		en_diss = f_y * flux / scale_height
230		return en_diss
231
232
233	View Code Duplication	def fang2010_spec_int(ens, dfluxes, scale_height, rho, pij=POLY_F2010, axis=-1):
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234		r"""Integrate over a given energy spectrum
235
236		Integrates over the mono-energetic parametrization `q` from Fang et al., 2010
237		using the given differential particle spectrum `phi`:
238
239		:math:`\int_\text{spec} \phi(E) q(E, Q) E \text{d}E`
240
241		Parameters
242		----------
243		ens: array_like (M,...)
244		Central (bin) energies of the spectrum
245		dfluxes: array_like (M,...)
246		Differential particle fluxes in the given bins
247		scale_height: array_like (N,...)
248		The atmospheric scale heights
249		rho: array_like (N,...)
250		The atmospheric densities, corresponding to the
251		scale heights.
252
253		Returns
254		-------
255		en_diss: array_like (N)
256		The dissipated energy profiles [keV].
257
258		See Also
259		--------
260		fang2010_mono
261		"""
262		ediss_f10 = fang2010_mono(
263		ens[None, None, :],
264		dfluxes,
265		scale_height[..., None],
266		rho[..., None],
267		pij=pij,
268		)
269		return np.trapz(ediss_f10 * ens, ens, axis=axis)
270
271
272	View Code Duplication	def fang2010_maxw_int(energy, flux, scale_height, rho, bounds=(0.1, 300.), nstep=128, pij=POLY_F2010):
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273		"""Integrate Fang et al., 2010 over a Maxwellian spectrum
274
275		Integrates the mono-energetic parametrization from Fang et al., 2010 [#]_
276		over a Maxwellian spectrum with characteristic energy `energy` and
277		total energy flux `flux`.
278
279		Parameters
280		----------
281		energy: array_like (M,...)
282		Characteristic energy E_0 [keV] of the Maxwellian distribution.
283		flux: array_like (M,...)
284		Integrated energy flux Q_0 [keV / cm² / s¹]
285		scale_height: array_like (N,...)
286		The atmospheric scale heights [cm].
287		rho: array_like (N,...)
288		The atmospheric mass density [g / cm³]
289		bounds: tuple, optional
290		(min, max) [keV] of the integration range to integrate the Maxwellian.
291		Make sure that this is appropriate to encompass the spectrum.
292		Default: (0.1, 300.)
293		nsteps: int, optional
294		Number of integration steps, default: 128.
295
296		Returns
297		-------
298		en_diss: array_like (M,N)
299		The dissipated energy profiles [keV].
300
301		See Also
302		--------
303		fang2010_mono, fang2010_spec_int, maxwell_pflux
304		"""
305		bounds_l10 = np.log10(bounds)
306		ens = np.logspace(*bounds_l10, num=nstep)
307		dflux = flux * maxwell_pflux(ens[:, None], energy)
308		return fang2010_spec_int(ens, dflux.T, scale_height, rho, pij=pij, axis=-1)
309
310
311		def maxwell_general(en, en_0=10.):
312		"""Maxwell number flux spectrum as in Fang2008 [1]
313
314		Defined in Fang et al., JGR 2008, Eq. (1).
315
316		Parameters
317		----------
318		en: float
319		Energy in [keV]
320		en_0: float, optional
321		Characteristic energy in [keV], i.e. mode of the distribution.
322		Default: 10 keV
323
324		Returns
325		-------
326		phi: float
327		Differential hemispherical number flux in [keV-1 cm-2 s-1]
328		([keV] or scaled by 1 keV-2 cm-2 s-1, e.g. ).
329		"""
330		return en * np.exp(-en / en_0)
331
332
333		def maxwell_pflux(en, en_0=10.):
334		"""Maxwell particle flux spectrum as in Fang2008 [1]
335
336		Defined in Fang et al., JGR 2008, Eq. (1).
337		The total precipitating energy flux is fixed to 1 keV cm-2 s-1,
338		multiply by Q_0 [keV cm-2 s-1] to scale the particle flux.
339
340		Parameters
341		----------
342		en: float
343		Energy in [keV]
344		en_0: float, optional
345		Characteristic energy in [keV], i.e. mode of the distribution.
346		Default: 10 keV.
347
348		Returns
349		-------
350		phi: float
351		Hemispherical differential particle flux in [keV-1 cm-2 s-1]
352		([kev-2] scaled by unit energy flux).
353		"""
354		return 0.5 / en_0*3 maxwell_general(en, en_0)
355

st-bender / pyeppaurora

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eppaurora.electrons._fang_f_y() A

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