eppaurora.spectra.pflux_pow() - Code Metrics - Inspection of "Test spectra normalization" - st-bender/pyeppaurora - Measure and Improve Code Quality continuously with Scrutinizer

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created 2020-09-25 10:12 UTC

eppaurora.spectra.pflux_pow() A

↳ Parent: eppaurora.spectra

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# 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.
"""Particle precipitation spectra

Includes variants describing a normalized particle flux,
as well as variants describing a normalized energy flux.
"""

import numpy as np

__all__ = [
	"exp_general",
	"gaussian_general",
	"maxwell_general",
	"pow_general",
	"pflux_exp",
	"pflux_gaussian",
	"pflux_maxwell",
	"pflux_pow",
]


# General normalized spectra, standard distributions
def exp_general(en, en_0=10.):
	r"""Exponential number flux spectrum as in Aksnes et al., 2006 [0]

	Defined according to Aksnes et al., JGR 2006, Eq. (1),
	normalized to unit number flux, i.e.
	:math:`\int_0^\infty \phi(E) \text{d}E = 1`.

	Parameters
	----------
	en: float or array_like (N,)
		Energy in [keV]
	en_0: float, optional
		Characteristic energy in [keV] of the distribution.
		Default: 10 keV

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


def gaussian_general(en, en_0=10., w=1.):
	r"""Gaussian number flux spectrum as in Fang2008 [1]

	Standard normal distribution with mu = en_0 and sigma = w / sqrt(2)
	for use in Fang et al., JGR 2008, Eq. (1).
	Almost normalized to unit number flux, i.e.
	:math:`\int_0^\infty \phi(E) \text{d}E = 1`
	(ignoring the negative tail).

	Parameters
	----------
	en: float or array_like (N,)
		Energy in [keV]
	en_0: float, optional
		Characteristic energy in [keV], i.e. mode of the distribution.
		Default: 10 keV
	w: float, optional
		Width of the Gaussian distribution, in [keV].

	Returns
	-------
	phi: float or array_like (N,)
		Normalized differential hemispherical number flux at `en` in [keV-1 cm-2 s-1]
		([keV] or scaled by 1 keV-2 cm-2 s-1, e.g.).
	"""
	return 1. / np.sqrt(np.pi * w**2) * np.exp(-(en - en_0)**2 / w**2)


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

	Defined in Fang et al., JGR 2008, Eq. (1),
	normalized to :math:`\int_0^\infty \phi(E) \text{d}E = 1`.

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

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


def pow_general(en, en_0=10., gamma=-3., het=True):

	r"""Power-law number flux spectrum as in Strickland1993 [3]

	Defined e.g. in Strickland et al., 1993,
	normalized to unit particle flux:
	:math:`\int_{E_0}^\infty \phi(E) \text{d}E = 1`
	for the high-energy tail version, and
	:math:`\int_0^{E_0} \phi(E) \text{d}E = 1`
	for the low-energy tail version.

	Parameters
	----------
	en: float or array_like (N,)
		Energy in [keV]
	en_0: float, optional
		Characteristic energy in [keV], i.e. mode of the distribution.
		Default: 10 keV
	gamma: float, optional
		Exponent of the power-law distribution, in [keV].
	het: bool, optional
		Return a high-energy tail (het, default: true) for en > en_0,
		or low-energy tail (false) for en < en_0.
		Adjusts the normalization accordingly.

	Returns
	-------
	phi: float or array_like (N,)
		Normalized differential hemispherical number flux at `en` in [keV-1 cm-2 s-1]
		([keV] or scaled by 1 keV-2 cm-2 s-1, e.g.).
	"""
	spec = (gamma + 1) / en_0 * (en / en_0)**gamma
	if het:
		spec[en < en_0] = 0.
		return -spec
	spec[en > en_0] = 0.
	return spec


def pflux_exp(en, en_0=10.):
	r"""Exponential particle flux spectrum

	Normalized to unit energy flux:
	:math:`\int_0^\infty \phi(E) E \text{d}E = 1`.

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

	Returns
	-------
	phi: float or array_like (N,)
		Hemispherical differential particle flux at `en` in [keV-1 cm-2 s-1]
		([kev-2] scaled by unit energy flux).
	"""
	return exp_general(en, en_0=en_0) / en_0


def pflux_gaussian(en, en_0=10., w=1):
	r"""Gaussian particle flux spectrum

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

	Normalized to :math:`\int_0^\infty \phi(E) E \text{d}E = 1`.
	(ignoring the negative tail).
	Parameters
	----------
	en: float or array_like (N,)
		Energy in [keV]
	en_0: float, optional
		Characteristic energy in [keV], i.e. mode of the distribution.
		Default: 10 keV.

	Returns
	-------
	phi: float or array_like (N,)
		Hemispherical differential particle flux at `en` in [keV-1 cm-2 s-1]
		([kev-2] scaled by unit energy flux).
	"""
	return gaussian_general(en, en_0=en_0, w=w) / en_0


def pflux_maxwell(en, en_0=10.):
	r"""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.

	Normalized to :math:`\int_0^\infty \phi(E) E \text{d}E = 1`.

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

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


def pflux_pow(en, en_0=10., gamma=-3., het=True):
	r"""Power-law particle flux spectrum

	Defined e.g. in Strickland et al., 1993.
	Normalized to :math:`\int_{E_0}^\infty \phi(E) E \text{d}E = 1`
	for the high-energy tail version, and to
	:math:`\int_0^{E_0} \phi(E) E \text{d}E = 1`
	for the low-energy tail version.

	Parameters
	----------
	en: float or array_like (N,)
		Energy in [keV]
	en_0: float, optional
		Characteristic energy in [keV], i.e. mode of the distribution.
		Default: 10 keV
	gamma: float, optional
		Exponent of the power-law distribution, in [keV].
	het: bool, optional (default True)
		Return a high-energy tail (true) for en > en_0,
		or low-energy tail (false) for en < en_0.
		Adjusts the normalization accordingly.

	Returns
	-------
	phi: float or array_like (N,)
		Hemispherical differential particle flux at `en` in [keV-1 cm-2 s-1]
		([kev-2] scaled by unit energy flux).
	"""
	return (gamma + 2) / (gamma + 1) / en_0 * pow_general(en, en_0=en_0, gamma=gamma, het=het)


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		"""Particle precipitation spectra
10
11		Includes variants describing a normalized particle flux,
12		as well as variants describing a normalized energy flux.
13		"""
14
15		import numpy as np
16
17		__all__ = [
18		"exp_general",
19		"gaussian_general",
20		"maxwell_general",
21		"pow_general",
22		"pflux_exp",
23		"pflux_gaussian",
24		"pflux_maxwell",
25		"pflux_pow",
26		]
27
28
29		# General normalized spectra, standard distributions
30		def exp_general(en, en_0=10.):
31		r"""Exponential number flux spectrum as in Aksnes et al., 2006 [0]
32
33		Defined according to Aksnes et al., JGR 2006, Eq. (1),
34		normalized to unit number flux, i.e.
35		:math:`\int_0^\infty \phi(E) \text{d}E = 1`.
36
37		Parameters
38		----------
39		en: float or array_like (N,)
40		Energy in [keV]
41		en_0: float, optional
42		Characteristic energy in [keV] of the distribution.
43		Default: 10 keV
44
45		Returns
46		-------
47		phi: float or array_like (N,)
48		Normalized differential hemispherical number flux at `en` in [keV-1 cm-2 s-1]
49		([keV] or scaled by 1 keV-2 cm-2 s-1, e.g. ).
50		"""
51		return 1. / en_0 * np.exp(-en / en_0)
52
53
54		def gaussian_general(en, en_0=10., w=1.):
55		r"""Gaussian number flux spectrum as in Fang2008 [1]
56
57		Standard normal distribution with mu = en_0 and sigma = w / sqrt(2)
58		for use in Fang et al., JGR 2008, Eq. (1).
59		Almost normalized to unit number flux, i.e.
60		:math:`\int_0^\infty \phi(E) \text{d}E = 1`
61		(ignoring the negative tail).
62
63		Parameters
64		----------
65		en: float or array_like (N,)
66		Energy in [keV]
67		en_0: float, optional
68		Characteristic energy in [keV], i.e. mode of the distribution.
69		Default: 10 keV
70		w: float, optional
71		Width of the Gaussian distribution, in [keV].
72
73		Returns
74		-------
75		phi: float or array_like (N,)
76		Normalized differential hemispherical number flux at `en` in [keV-1 cm-2 s-1]
77		([keV] or scaled by 1 keV-2 cm-2 s-1, e.g.).
78		"""
79		return 1. / np.sqrt(np.pi * w*2) np.exp(-(en - en_0)2 / w2)
80
81
82		def maxwell_general(en, en_0=10.):
83		r"""Maxwell number flux spectrum as in Fang2008 [1]
84
85		Defined in Fang et al., JGR 2008, Eq. (1),
86		normalized to :math:`\int_0^\infty \phi(E) \text{d}E = 1`.
87
88		Parameters
89		----------
90		en: float or array_like (N,)
91		Energy in [keV]
92		en_0: float, optional
93		Characteristic energy in [keV], i.e. mode of the distribution.
94		Default: 10 keV
95
96		Returns
97		-------
98		phi: float or array_like (N,)
99		Normalized differential hemispherical number flux at `en` in [keV-1 cm-2 s-1]
100		([keV] or scaled by 1 keV-2 cm-2 s-1, e.g.).
101		"""
102		return en / en_0*2 np.exp(-en / en_0)
103
104
105	View Code Duplication	def pow_general(en, en_0=10., gamma=-3., het=True):
		0 ignored issues – show Duplication introduced 2020-09-25 10:14 UTC by Report Bug Copy Issue Report This code seems to be duplicated in your project. Loading history...
106		r"""Power-law number flux spectrum as in Strickland1993 [3]
107
108		Defined e.g. in Strickland et al., 1993,
109		normalized to unit particle flux:
110		:math:`\int_{E_0}^\infty \phi(E) \text{d}E = 1`
111		for the high-energy tail version, and
112		:math:`\int_0^{E_0} \phi(E) \text{d}E = 1`
113		for the low-energy tail version.
114
115		Parameters
116		----------
117		en: float or array_like (N,)
118		Energy in [keV]
119		en_0: float, optional
120		Characteristic energy in [keV], i.e. mode of the distribution.
121		Default: 10 keV
122		gamma: float, optional
123		Exponent of the power-law distribution, in [keV].
124		het: bool, optional
125		Return a high-energy tail (het, default: true) for en > en_0,
126		or low-energy tail (false) for en < en_0.
127		Adjusts the normalization accordingly.
128
129		Returns
130		-------
131		phi: float or array_like (N,)
132		Normalized differential hemispherical number flux at `en` in [keV-1 cm-2 s-1]
133		([keV] or scaled by 1 keV-2 cm-2 s-1, e.g.).
134		"""
135		spec = (gamma + 1) / en_0 * (en / en_0)**gamma
136		if het:
137		spec[en < en_0] = 0.
138		return -spec
139		spec[en > en_0] = 0.
140		return spec
141
142
143		def pflux_exp(en, en_0=10.):
144		r"""Exponential particle flux spectrum
145
146		Normalized to unit energy flux:
147		:math:`\int_0^\infty \phi(E) E \text{d}E = 1`.
148
149		Parameters
150		----------
151		en: float or array_like (N,)
152		Energy in [keV]
153		en_0: float, optional
154		Characteristic energy in [keV], i.e. mode of the distribution.
155		Default: 10 keV.
156
157		Returns
158		-------
159		phi: float or array_like (N,)
160		Hemispherical differential particle flux at `en` in [keV-1 cm-2 s-1]
161		([kev-2] scaled by unit energy flux).
162		"""
163		return exp_general(en, en_0=en_0) / en_0
164
165
166		def pflux_gaussian(en, en_0=10., w=1):
167		r"""Gaussian particle flux spectrum
168
169		Defined in Fang et al., JGR 2008, Eq. (1).
170
171		Normalized to :math:`\int_0^\infty \phi(E) E \text{d}E = 1`.
172		(ignoring the negative tail).
173		Parameters
174		----------
175		en: float or array_like (N,)
176		Energy in [keV]
177		en_0: float, optional
178		Characteristic energy in [keV], i.e. mode of the distribution.
179		Default: 10 keV.
180
181		Returns
182		-------
183		phi: float or array_like (N,)
184		Hemispherical differential particle flux at `en` in [keV-1 cm-2 s-1]
185		([kev-2] scaled by unit energy flux).
186		"""
187		return gaussian_general(en, en_0=en_0, w=w) / en_0
188
189
190		def pflux_maxwell(en, en_0=10.):
191		r"""Maxwell particle flux spectrum as in Fang2008 [1]
192
193		Defined in Fang et al., JGR 2008, Eq. (1).
194		The total precipitating energy flux is fixed to 1 keV cm-2 s-1,
195		multiply by Q_0 [keV cm-2 s-1] to scale the particle flux.
196
197		Normalized to :math:`\int_0^\infty \phi(E) E \text{d}E = 1`.
198
199		Parameters
200		----------
201		en: float or array_like (N,)
202		Energy in [keV]
203		en_0: float, optional
204		Characteristic energy in [keV], i.e. mode of the distribution.
205		Default: 10 keV.
206
207		Returns
208		-------
209		phi: float or array_like (N,)
210		Hemispherical differential particle flux at `en` in [keV-1 cm-2 s-1]
211		([kev-2] scaled by unit energy flux).
212		"""
213		return 0.5 / en_0 * maxwell_general(en, en_0)
214
215
216		def pflux_pow(en, en_0=10., gamma=-3., het=True):
217		r"""Power-law particle flux spectrum
218
219		Defined e.g. in Strickland et al., 1993.
220		Normalized to :math:`\int_{E_0}^\infty \phi(E) E \text{d}E = 1`
221		for the high-energy tail version, and to
222		:math:`\int_0^{E_0} \phi(E) E \text{d}E = 1`
223		for the low-energy tail version.
224
225		Parameters
226		----------
227		en: float or array_like (N,)
228		Energy in [keV]
229		en_0: float, optional
230		Characteristic energy in [keV], i.e. mode of the distribution.
231		Default: 10 keV
232		gamma: float, optional
233		Exponent of the power-law distribution, in [keV].
234		het: bool, optional (default True)
235		Return a high-energy tail (true) for en > en_0,
236		or low-energy tail (false) for en < en_0.
237		Adjusts the normalization accordingly.
238
239		Returns
240		-------
241		phi: float or array_like (N,)
242		Hemispherical differential particle flux at `en` in [keV-1 cm-2 s-1]
243		([kev-2] scaled by unit energy flux).
244		"""
245		return (gamma + 2) / (gamma + 1) / en_0 * pow_general(en, en_0=en_0, gamma=gamma, het=het)
246

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eppaurora.spectra.pflux_pow() A

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