from __future__ import division
from past.utils import old_div
import astropy.units as u
from astromodels.functions.function import Function3D, FunctionMeta
import numpy as np
from astromodels.utils.angular_distance import angular_distance_fast
from future.utils import with_metaclass
class Continuous_injection_diffusion_ellipse(with_metaclass(FunctionMeta, Function3D)):
r"""
description :
Positron and electrons diffusing away from the accelerator
latex : $\left(\frac{180^\circ}{\pi}\right)^2 \frac{1.2154}{\sqrt{\pi^3} r_{\rm diff} ({\rm angsep} ({\rm x, y, lon_0, lat_0})+0.06 r_{\rm diff} )} \, {\rm exp}\left(-\frac{{\rm angsep}^2 ({\rm x, y, lon_0, lat_0})}{r_{\rm diff} ^2} \right)$
parameters :
lon0 :
desc : Longitude of the center of the source
initial value : 0.0
min : 0.0
max : 360.0
lat0 :
desc : Latitude of the center of the source
initial value : 0.0
min : -90.0
max : 90.0
rdiff0 :
desc : Projected diffusion radius. The maximum allowed value is used to define the truncation radius.
initial value : 1.0
min : 0
max : 20
delta :
desc : index for the diffusion coefficient
initial value : 0.5
min : 0.3
max : 0.6
fix : yes
b :
desc : b field strength in uG
initial value : 3
min : 1
max : 10.
fix : yes
piv :
desc : Pivot for the diffusion radius
initial value : 2e10
min : 0
fix : yes
piv2 :
desc : Pivot for converting gamma energy to electron energy (always be 1 TeV)
initial value : 1e9
min : 0
fix : yes
incl :
desc : inclination of semimajoraxis to a line of constant latitude
initial value : 0.0
min : -90.0
max : 90.0
fix : yes
elongation :
desc : elongation of the ellipse (b/a)
initial value : 1.
min : 0.1
max : 10.
"""
def _set_units(self, x_unit, y_unit, z_unit, w_unit):
# lon0 and lat0 and rdiff have most probably all units of degrees. However,
# let's set them up here just to save for the possibility of using the
# formula with other units (although it is probably never going to happen)
self.lon0.unit = x_unit
self.lat0.unit = y_unit
self.rdiff0.unit = x_unit
# Delta is of course unitless
self.delta.unit = u.dimensionless_unscaled
self.b.unit = u.dimensionless_unscaled
self.incl.unit = x_unit
self.elongation.unit = u.dimensionless_unscaled
# Piv has the same unit as energy (which is z)
self.piv.unit = z_unit
self.piv2.unit = z_unit
def evaluate(self, x, y, z, lon0, lat0, rdiff0, delta, b, piv, piv2, incl, elongation):
lon, lat = x, y
energy = z
# energy in kev -> TeV.
# NOTE: the use of piv2 is necessary to preserve dimensional correctness: the logarithm can only be taken
# of a dimensionless quantity, so there must be a pivot there.
e_energy_piv2 = 17. * np.power(old_div(energy, piv2), 0.54 + 0.046 * np.log10(old_div(energy, piv2)))
e_piv_piv2 = 17. * np.power(old_div(piv, piv2), 0.54 + 0.046 * np.log10(old_div(piv, piv2)))
try:
rdiff_a = rdiff0 * np.power(old_div(e_energy_piv2, e_piv_piv2), old_div((delta - 1.), 2.)) * \
np.sqrt(b * b / 8. / np.pi * 0.624 + 0.26 * np.power(1. + 0.0107 * e_piv_piv2, -1.5)) / \
np.sqrt(b * b / 8. / np.pi * 0.624 + 0.26 * np.power(1. + 0.0107 * e_energy_piv2, -1.5))
except ValueError:
# This happens when using units, because astropy.units fails with the message:
# "ValueError: Quantities and Units may only be raised to a scalar power"
# Work around the problem with this loop, which is slow but using units is only for testing purposes or
# single calls, so it shouldn't matter too much
rdiff_a = np.array( [(rdiff0 * np.power(old_div(e_energy_piv2, e_piv_piv2), x)).value for x in (delta - 1.) / 2. * np.sqrt(b * b / 8. / np.pi * 0.624 + 0.26 * np.power(1. + 0.0107 * e_piv_piv2, -1.5)) /
np.sqrt(b * b / 8. / np.pi * 0.624 + 0.26 * np.power(1. + 0.0107 * e_energy_piv2, -1.5))]) * rdiff0.unit
rdiff_b = rdiff_a * elongation
pi = np.pi
angsep = angular_distance_fast(lon, lat, lon0, lat0)
ang = np.arctan2(lat - lat0, (lon - lon0) * np.cos(lat0 * np.pi / 180.))
theta = np.arctan2(old_div(np.sin(ang-incl*np.pi/180.),elongation), np.cos(ang-incl*np.pi/180.))
rdiffs_a, thetas = np.meshgrid(rdiff_a, theta)
rdiffs_b, angseps = np.meshgrid(rdiff_b, angsep)
rdiffs = np.sqrt(rdiffs_a ** 2 * np.cos(thetas) ** 2 + rdiffs_b ** 2 * np.sin(thetas) ** 2)
results = np.power(old_div(180.0, pi), 2) * 1.22 / (pi * np.sqrt(pi) * rdiffs_a * np.sqrt(elongation) * (angseps + 0.06 * rdiffs)) * np.exp(old_div(-np.power(angseps, 2), rdiffs ** 2))
return results
def get_boundaries(self):
# Truncate the function at the max of rdiff allowed
maximum_rdiff = self.rdiff0.max_value
min_latitude = max(-90., self.lat0.value - maximum_rdiff)
max_latitude = min(90., self.lat0.value + maximum_rdiff)
max_abs_lat = max(np.absolute(min_latitude), np.absolute(max_latitude))
if max_abs_lat > 89. or old_div(maximum_rdiff, np.cos(max_abs_lat * np.pi / 180.)) >= 180.:
min_longitude = 0.
max_longitude = 360.
else:
min_longitude = self.lon0.value - old_div(maximum_rdiff, np.cos(max_abs_lat * np.pi / 180.))
max_longitude = self.lon0.value + old_div(maximum_rdiff, np.cos(max_abs_lat * np.pi / 180.))
if min_longitude < 0.:
min_longitude += 360.
elif max_longitude > 360.:
max_longitude -= 360.
return (min_longitude, max_longitude), (min_latitude, max_latitude)
def get_total_spatial_integral(self, z=None):
"""
Returns the total integral (for 2D functions) or the integral over the spatial components (for 3D functions).
needs to be implemented in subclasses.
:return: an array of values of the integral (same dimension as z).
"""
if isinstance( z, u.Quantity):
z = z.value
return np.ones_like( z )
class Continuous_injection_diffusion(with_metaclass(FunctionMeta, Function3D)):
r"""
description :
Positron and electrons diffusing away from the accelerator
latex : $\left(\frac{180^\circ}{\pi}\right)^2 \frac{1.2154}{\sqrt{\pi^3} r_{\rm diff} ({\rm angsep} ({\rm x, y, lon_0, lat_0})+0.06 r_{\rm diff} )} \, {\rm exp}\left(-\frac{{\rm angsep}^2 ({\rm x, y, lon_0, lat_0})}{r_{\rm diff} ^2} \right)$
parameters :
lon0 :
desc : Longitude of the center of the source
initial value : 0.0
min : 0.0
max : 360.0
lat0 :
desc : Latitude of the center of the source
initial value : 0.0
min : -90.0
max : 90.0
rdiff0 :
desc : Projected diffusion radius limited by the cooling time. The maximum allowed value is used to define the truncation radius.
initial value : 1.0
min : 0
max : 20
rinj :
desc : Ratio of diffusion radius limited by the injection time over rdiff0. The maximum allowed value is used to define the truncation radius.
initial value : 100.0
min : 0
max : 200
fix : yes
delta :
desc : index for the diffusion coefficient
initial value : 0.5
min : 0.3
max : 0.6
fix : yes
b :
desc : b field strength in uG
initial value : 3
min : 1
max : 10.
fix : yes
piv :
desc : Pivot for the diffusion radius
initial value : 2e10
min : 0
fix : yes
piv2 :
desc : Pivot for converting gamma energy to electron energy (always be 1 TeV)
initial value : 1e9
min : 0
fix : yes
"""
def _set_units(self, x_unit, y_unit, z_unit, w_unit):
# lon0 and lat0 and rdiff have most probably all units of degrees. However,
# let's set them up here just to save for the possibility of using the
# formula with other units (although it is probably never going to happen)
self.lon0.unit = x_unit
self.lat0.unit = y_unit
self.rdiff0.unit = x_unit
self.rinj.unit = u.dimensionless_unscaled
# Delta is of course unitless
self.delta.unit = u.dimensionless_unscaled
self.b.unit = u.dimensionless_unscaled
# Piv has the same unit as energy (which is z)
self.piv.unit = z_unit
self.piv2.unit = z_unit
def evaluate(self, x, y, z, lon0, lat0, rdiff0, rinj, delta, b, piv, piv2):
lon, lat = x, y
energy = z
# energy in kev -> TeV.
# NOTE: the use of piv2 is necessary to preserve dimensional correctness: the logarithm can only be taken
# of a dimensionless quantity, so there must be a pivot there.
e_energy_piv2 = 17. * np.power(old_div(energy, piv2), 0.54 + 0.046 * np.log10(old_div(energy, piv2)))
e_piv_piv2 = 17. * np.power(old_div(piv, piv2), 0.54 + 0.046 * np.log10(old_div(piv, piv2)))
rdiff_c = rdiff0 * np.power(old_div(e_energy_piv2, e_piv_piv2), old_div((delta - 1.), 2.)) * \
np.sqrt(b * b / 8. / np.pi * 0.624 + 0.26 * np.power(1. + 0.0107 * e_piv_piv2, -1.5)) / \
np.sqrt(b * b / 8. / np.pi * 0.624 + 0.26 * np.power(1. + 0.0107 * e_energy_piv2, -1.5))
rdiff_i = rdiff0 * rinj * np.power(old_div(e_energy_piv2, e_piv_piv2), old_div(delta, 2.))
rdiff = np.minimum(rdiff_c, rdiff_i)
angsep = angular_distance_fast(lon, lat, lon0, lat0)
pi = np.pi
rdiffs, angseps = np.meshgrid(rdiff, angsep)
return np.power(old_div(180.0, pi), 2) * 1.2154 / (pi * np.sqrt(pi) * rdiffs * (angseps + 0.06 * rdiffs)) * \
np.exp(old_div(-np.power(angseps, 2), rdiffs ** 2))
def get_boundaries(self):
# Truncate the function at the max of rdiff allowed
maximum_rdiff = self.rdiff0.max_value
min_latitude = max(-90., self.lat0.value - maximum_rdiff)
max_latitude = min(90., self.lat0.value + maximum_rdiff)
max_abs_lat = max(np.absolute(min_latitude), np.absolute(max_latitude))
if max_abs_lat > 89. or old_div(maximum_rdiff, np.cos(max_abs_lat * np.pi / 180.)) >= 180.:
min_longitude = 0.
max_longitude = 360.
else:
min_longitude = self.lon0.value - old_div(maximum_rdiff, np.cos(max_abs_lat * np.pi / 180.))
max_longitude = self.lon0.value + old_div(maximum_rdiff, np.cos(max_abs_lat * np.pi / 180.))
if min_longitude < 0.:
min_longitude += 360.
elif max_longitude > 360.:
max_longitude -= 360.
return (min_longitude, max_longitude), (min_latitude, max_latitude)
def get_total_spatial_integral(self, z=None):
"""
Returns the total integral (for 2D functions) or the integral over the spatial components (for 3D functions).
needs to be implemented in subclasses.
:return: an array of values of the integral (same dimension as z).
"""
if isinstance( z, u.Quantity):
z = z.value
return np.ones_like( z )
class Continuous_injection_diffusion_legacy(with_metaclass(FunctionMeta, Function3D)):
r"""
description :
Positron and electrons diffusing away from the accelerator
latex : $\left(\frac{180^\circ}{\pi}\right)^2 \frac{1.2154}{\sqrt{\pi^3} r_{\rm diff} ({\rm angsep} ({\rm x, y, lon_0, lat_0})+0.06 r_{\rm diff} )} \, {\rm exp}\left(-\frac{{\rm angsep}^2 ({\rm x, y, lon_0, lat_0})}{r_{\rm diff} ^2} \right)$
parameters :
lon0 :
desc : Longitude of the center of the source
initial value : 0.0
min : 0.0
max : 360.0
lat0 :
desc : Latitude of the center of the source
initial value : 0.0
min : -90.0
max : 90.0
rdiff0 :
desc : Projected diffusion radius. The maximum allowed value is used to define the truncation radius.
initial value : 1.0
min : 0
max : 20
delta :
desc : index for the diffusion coefficient
initial value : 0.5
min : 0.3
max : 0.6
fix : yes
uratio :
desc : ratio between u_cmb and u_B
initial value : 0.5
min : 0.01
max : 100.
fix : yes
piv :
desc : Pivot for the diffusion radius
initial value : 2e10
min : 0
fix : yes
piv2 :
desc : Pivot for converting gamma energy to electron energy (always be 1 TeV)
initial value : 1e9
min : 0
fix : yes
"""
def _set_units(self, x_unit, y_unit, z_unit, w_unit):
# lon0 and lat0 and rdiff have most probably all units of degrees. However,
# let's set them up here just to save for the possibility of using the
# formula with other units (although it is probably never going to happen)
self.lon0.unit = x_unit
self.lat0.unit = y_unit
self.rdiff0.unit = x_unit
# Delta is of course unitless
self.delta.unit = u.dimensionless_unscaled
self.uratio.unit = u.dimensionless_unscaled
# Piv has the same unit as energy (which is z)
self.piv.unit = z_unit
self.piv2.unit = z_unit
def evaluate(self, x, y, z, lon0, lat0, rdiff0, delta, uratio, piv, piv2):
lon, lat = x, y
energy = z
# energy in kev -> TeV.
# NOTE: the use of piv2 is necessary to preserve dimensional correctness: the logarithm can only be taken
# of a dimensionless quantity, so there must be a pivot there.
e_energy_piv2 = 17. * np.power(old_div(energy, piv2), 0.54 + 0.046 * np.log10(old_div(energy, piv2)))
e_piv_piv2 = 17. * np.power(old_div(piv, piv2), 0.54 + 0.046 * np.log10(old_div(piv, piv2)))
try:
rdiff = rdiff0 * np.power(old_div(e_energy_piv2, e_piv_piv2), old_div((delta - 1.), 2.)) * \
np.sqrt(1. + uratio * np.power(1. + 0.0107 * e_piv_piv2, -1.5)) / \
np.sqrt(1. + uratio * np.power(1. + 0.0107 * e_energy_piv2, -1.5))
except ValueError:
# This happens when using units, because astropy.units fails with the message:
# "ValueError: Quantities and Units may only be raised to a scalar power"
# Work around the problem with this loop, which is slow but using units is only for testing purposes or
# single calls, so it shouldn't matter too much
rdiff = np.array( [(rdiff0 * np.power(old_div(e_energy_piv2, e_piv_piv2), x)).value for x in (delta - 1.) / 2. * np.sqrt(1. + uratio * np.power(1. + 0.0107 * e_piv_piv2, -1.5)) /
np.sqrt(1. + uratio * np.power(1. + 0.0107 * e_energy_piv2, -1.5))]) * rdiff0.unit
angsep = angular_distance_fast(lon, lat, lon0, lat0)
pi = np.pi
rdiffs, angseps = np.meshgrid(rdiff, angsep)
return np.power(old_div(180.0, pi), 2) * 1.2154 / (pi * np.sqrt(pi) * rdiffs * (angseps + 0.06 * rdiffs)) * \
np.exp(old_div(-np.power(angseps, 2), rdiffs ** 2))
def get_boundaries(self):
# Truncate the function at the max of rdiff allowed
maximum_rdiff = self.rdiff0.max_value
min_latitude = max(-90., self.lat0.value - maximum_rdiff)
max_latitude = min(90., self.lat0.value + maximum_rdiff)
max_abs_lat = max(np.absolute(min_latitude), np.absolute(max_latitude))
if max_abs_lat > 89. or old_div(maximum_rdiff, np.cos(max_abs_lat * np.pi / 180.)) >= 180.:
min_longitude = 0.
max_longitude = 360.
else:
min_longitude = self.lon0.value - old_div(maximum_rdiff, np.cos(max_abs_lat * np.pi / 180.))
max_longitude = self.lon0.value + old_div(maximum_rdiff, np.cos(max_abs_lat * np.pi / 180.))
if min_longitude < 0.:
min_longitude += 360.
elif max_longitude > 360.:
max_longitude -= 360.
return (min_longitude, max_longitude), (min_latitude, max_latitude)
def get_total_spatial_integral(self, z=None):
"""
Returns the total integral (for 2D functions) or the integral over the spatial components (for 3D functions).
needs to be implemented in subclasses.
:return: an array of values of the integral (same dimension as z).
"""
if isinstance( z, u.Quantity):
z = z.value
return np.ones_like( z )
