forked from gammapy/gammapy
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models.py
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models.py
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# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""Spectral models for Gammapy."""
from __future__ import absolute_import, division, print_function, unicode_literals
import operator
import numpy as np
from scipy.optimize import brentq
import astropy.units as u
from astropy.table import Table
from ..utils.energy import EnergyBounds
from ..utils.nddata import NDDataArray, BinnedDataAxis
from ..utils.scripts import make_path
from ..utils.fitting import Parameter, Parameters, Model
from ..utils.interpolation import ScaledRegularGridInterpolator
from .utils import integrate_spectrum
__all__ = [
"SpectralModel",
"ConstantModel",
"CompoundSpectralModel",
"PowerLaw",
"PowerLaw2",
"ExponentialCutoffPowerLaw",
"ExponentialCutoffPowerLaw3FGL",
"PLSuperExpCutoff3FGL",
"LogParabola",
"TableModel",
"AbsorbedSpectralModel",
"Absorption",
]
class SpectralModel(Model):
"""Spectral model base class.
Derived classes should store their parameters as
`~gammapy.utils.modeling.Parameters`
See for example return pardict of
`~gammapy.spectrum.models.PowerLaw`.
"""
def __call__(self, energy):
"""Call evaluate method of derived classes"""
kwargs = dict()
for par in self.parameters.parameters:
quantity = par.quantity
if quantity.unit.physical_type == "energy":
quantity = quantity.to(energy.unit)
kwargs[par.name] = quantity
return self.evaluate(energy, **kwargs)
def __mul__(self, model):
if not isinstance(model, SpectralModel):
model = ConstantModel(const=model)
return CompoundSpectralModel(self, model, operator.mul)
def __rmul__(self, model):
# This is needed to support e.g. 5 * model
return self.__mul__(model)
def __add__(self, model):
if not isinstance(model, SpectralModel):
model = ConstantModel(const=model)
return CompoundSpectralModel(self, model, operator.add)
def __radd__(self, model):
return self.__add__(model)
def __sub__(self, model):
if not isinstance(model, SpectralModel):
model = ConstantModel(const=model)
return CompoundSpectralModel(self, model, operator.sub)
def __rsub__(self, model):
return self.__sub__(model)
def __truediv__(self, model):
if not isinstance(model, SpectralModel):
model = ConstantModel(const=model)
return CompoundSpectralModel(self, model, operator.truediv)
def __rtruediv__(self, model):
return self.__div__(model)
def _parse_uarray(self, uarray):
from uncertainties import unumpy
values = unumpy.nominal_values(uarray)
errors = unumpy.std_devs(uarray)
return values, errors
def _convert_energy(self, energy):
if "reference" in self.parameters.names:
return energy.to(self.parameters["reference"].unit)
elif "emin" in self.parameters.names:
return energy.to(self.parameters["emin"].unit)
else:
return energy
def evaluate_error(self, energy):
"""Evaluate spectral model with error propagation.
Parameters
----------
energy : `~astropy.units.Quantity`
Energy at which to evaluate
Returns
-------
flux, flux_error : tuple of `~astropy.units.Quantity`
Tuple of flux and flux error.
"""
energy = self._convert_energy(energy)
unit = self(energy).unit
upars = self.parameters._ufloats
uarray = self.evaluate(energy.value, **upars)
return self._parse_uarray(uarray) * unit
def integral(self, emin, emax, **kwargs):
r"""Integrate spectral model numerically.
.. math::
F(E_{min}, E_{max}) = \int_{E_{min}}^{E_{max}} \phi(E) dE
If array input for ``emin`` and ``emax`` is given you have to set
``intervals=True`` if you want the integral in each energy bin.
Parameters
----------
emin, emax : `~astropy.units.Quantity`
Lower and upper bound of integration range.
**kwargs : dict
Keyword arguments passed to :func:`~gammapy.spectrum.integrate_spectrum`
"""
return integrate_spectrum(self, emin, emax, **kwargs)
def integral_error(self, emin, emax, **kwargs):
"""Integrate spectral model numerically with error propagation.
Parameters
----------
emin, emax : `~astropy.units.Quantity`
Lower adn upper bound of integration range.
**kwargs : dict
Keyword arguments passed to func:`~gammapy.spectrum.integrate_spectrum`
Returns
-------
integral, integral_error : tuple of `~astropy.units.Quantity`
Tuple of integral flux and integral flux error.
"""
emin = self._convert_energy(emin)
emax = self._convert_energy(emax)
unit = self.integral(emin, emax, **kwargs).unit
upars = self.parameters._ufloats
def f(x):
return self.evaluate(x, **upars)
uarray = integrate_spectrum(f, emin.value, emax.value, **kwargs)
return self._parse_uarray(uarray) * unit
def energy_flux(self, emin, emax, **kwargs):
r"""Compute energy flux in given energy range.
.. math::
G(E_{min}, E_{max}) = \int_{E_{min}}^{E_{max}} E \phi(E) dE
Parameters
----------
emin, emax : `~astropy.units.Quantity`
Lower and upper bound of integration range.
**kwargs : dict
Keyword arguments passed to func:`~gammapy.spectrum.integrate_spectrum`
"""
def f(x):
return x * self(x)
return integrate_spectrum(f, emin, emax, **kwargs)
def energy_flux_error(self, emin, emax, **kwargs):
r"""Compute energy flux in given energy range with error propagation.
.. math::
G(E_{min}, E_{max}) = \int_{E_{min}}^{E_{max}} E \phi(E) dE
Parameters
----------
emin, emax : `~astropy.units.Quantity`
Lower bound of integration range.
**kwargs : dict
Keyword arguments passed to :func:`~gammapy.spectrum.integrate_spectrum`
Returns
-------
energy_flux, energy_flux_error : tuple of `~astropy.units.Quantity`
Tuple of energy flux and energy flux error.
"""
emin = self._convert_energy(emin)
emax = self._convert_energy(emax)
unit = self.energy_flux(emin, emax, **kwargs).unit
upars = self.parameters._ufloats
def f(x):
return x * self.evaluate(x, **upars)
uarray = integrate_spectrum(f, emin.value, emax.value, **kwargs)
return self._parse_uarray(uarray) * unit
def to_dict(self):
"""Convert to dict."""
retval = self.parameters.to_dict()
retval["name"] = self.__class__.__name__
return retval
@classmethod
def from_dict(cls, val):
"""Create from dict."""
classname = val.pop("name")
parameters = Parameters.from_dict(val)
model = globals()[classname]()
model.parameters = parameters
model.parameters.covariance = parameters.covariance
return model
def plot(
self,
energy_range,
ax=None,
energy_unit="TeV",
flux_unit="cm-2 s-1 TeV-1",
energy_power=0,
n_points=100,
**kwargs
):
"""Plot spectral model curve.
kwargs are forwarded to `matplotlib.pyplot.plot`
By default a log-log scaling of the axes is used, if you want to change
the y axis scaling to linear you can use::
from gammapy.spectrum.models import ExponentialCutoffPowerLaw
from astropy import units as u
pwl = ExponentialCutoffPowerLaw()
ax = pwl.plot(energy_range=(0.1, 100) * u.TeV)
ax.set_yscale('linear')
Parameters
----------
ax : `~matplotlib.axes.Axes`, optional
Axis
energy_range : `~astropy.units.Quantity`
Plot range
energy_unit : str, `~astropy.units.Unit`, optional
Unit of the energy axis
flux_unit : str, `~astropy.units.Unit`, optional
Unit of the flux axis
energy_power : int, optional
Power of energy to multiply flux axis with
n_points : int, optional
Number of evaluation nodes
Returns
-------
ax : `~matplotlib.axes.Axes`, optional
Axis
"""
import matplotlib.pyplot as plt
ax = plt.gca() if ax is None else ax
emin, emax = energy_range
energy = EnergyBounds.equal_log_spacing(emin, emax, n_points, energy_unit)
# evaluate model
flux = self(energy).to(flux_unit)
y = self._plot_scale_flux(energy, flux, energy_power)
ax.plot(energy.value, y.value, **kwargs)
self._plot_format_ax(ax, energy, y, energy_power)
return ax
def plot_error(
self,
energy_range,
ax=None,
energy_unit="TeV",
flux_unit="cm-2 s-1 TeV-1",
energy_power=0,
n_points=100,
**kwargs
):
"""Plot spectral model error band.
.. note::
This method calls ``ax.set_yscale("log", nonposy='clip')`` and
``ax.set_xscale("log", nonposx='clip')`` to create a log-log representation.
The additional argument ``nonposx='clip'`` avoids artefacts in the plot,
when the error band extends to negative values (see also
https://github.com/matplotlib/matplotlib/issues/8623).
When you call ``plt.loglog()`` or ``plt.semilogy()`` explicitely in your
plotting code and the error band extends to negative values, it is not
shown correctly. To circumvent this issue also use
``plt.loglog(nonposx='clip', nonposy='clip')``
or ``plt.semilogy(nonposy='clip')``.
Parameters
----------
ax : `~matplotlib.axes.Axes`, optional
Axis
energy_range : `~astropy.units.Quantity`
Plot range
energy_unit : str, `~astropy.units.Unit`, optional
Unit of the energy axis
flux_unit : str, `~astropy.units.Unit`, optional
Unit of the flux axis
energy_power : int, optional
Power of energy to multiply flux axis with
n_points : int, optional
Number of evaluation nodes
**kwargs : dict
Keyword arguments forwarded to `matplotlib.pyplot.fill_between`
Returns
-------
ax : `~matplotlib.axes.Axes`, optional
Axis
"""
import matplotlib.pyplot as plt
ax = plt.gca() if ax is None else ax
kwargs.setdefault("facecolor", "black")
kwargs.setdefault("alpha", 0.2)
kwargs.setdefault("linewidth", 0)
emin, emax = energy_range
energy = EnergyBounds.equal_log_spacing(emin, emax, n_points, energy_unit)
flux, flux_err = self.evaluate_error(energy).to(flux_unit)
y_lo = self._plot_scale_flux(energy, flux - flux_err, energy_power)
y_hi = self._plot_scale_flux(energy, flux + flux_err, energy_power)
where = (energy >= energy_range[0]) & (energy <= energy_range[1])
ax.fill_between(energy.value, y_lo.value, y_hi.value, where=where, **kwargs)
self._plot_format_ax(ax, energy, y_lo, energy_power)
return ax
def _plot_format_ax(self, ax, energy, y, energy_power):
ax.set_xlabel("Energy [{}]".format(energy.unit))
if energy_power > 0:
ax.set_ylabel("E{} * Flux [{}]".format(energy_power, y.unit))
else:
ax.set_ylabel("Flux [{}]".format(y.unit))
ax.set_xscale("log", nonposx="clip")
ax.set_yscale("log", nonposy="clip")
def _plot_scale_flux(self, energy, flux, energy_power):
try:
eunit = [_ for _ in flux.unit.bases if _.physical_type == "energy"][0]
except IndexError:
eunit = energy.unit
y = flux * np.power(energy, energy_power)
return y.to(flux.unit * eunit ** energy_power)
def spectral_index(self, energy, epsilon=1e-5):
"""Compute spectral index at given energy.
Parameters
----------
energy : `~astropy.units.Quantity`
Energy at which to estimate the index
epsilon : float
Fractional energy increment to use for determining the spectral index.
Returns
-------
index : float
Estimated spectral index.
"""
f1 = self(energy)
f2 = self(energy * (1 + epsilon))
return np.log(f1 / f2) / np.log(1 + epsilon)
def inverse(self, value, emin=0.1 * u.TeV, emax=100 * u.TeV):
"""Return energy for a given function value of the spectral model.
Calls the `scipy.optimize.brentq` numerical root finding method.
Parameters
----------
value : `~astropy.units.Quantity`
Function value of the spectral model.
emin : `~astropy.units.Quantity`
Lower bracket value in case solution is not unique.
emax : `~astropy.units.Quantity`
Upper bracket value in case solution is not unique.
Returns
-------
energy : `~astropy.units.Quantity`
Energies at which the model has the given ``value``.
"""
eunit = "TeV"
energies = []
for val in np.atleast_1d(value):
def f(x):
# scale by 1e12 to achieve better precision
energy = u.Quantity(x, eunit, copy=False)
y = self(energy).to_value(value.unit)
return 1e12 * (y - val.value)
energy = brentq(f, emin.to_value(eunit), emax.to_value(eunit))
energies.append(energy)
return u.Quantity(energies, eunit, copy=False)
class ConstantModel(SpectralModel):
r"""Constant model
.. math::
\phi(E) = k
Parameters
----------
const : `~astropy.units.Quantity`
:math:`k`
"""
def __init__(self, const):
self.parameters = Parameters([Parameter("const", const)])
@staticmethod
def evaluate(energy, const):
"""Evaluate the model (static function)."""
return np.ones(np.atleast_1d(energy).shape) * const
class CompoundSpectralModel(SpectralModel):
"""Represents the algebraic combination of two
`~gammapy.spectrum.models.SpectralModel`
"""
def __init__(self, model1, model2, operator):
self.model1 = model1
self.model2 = model2
self.operator = operator
# TODO: Think about how to deal with covariance matrix
@property
def parameters(self):
val = self.model1.parameters.parameters + self.model2.parameters.parameters
return Parameters(val)
@parameters.setter
def parameters(self, parameters):
idx = len(self.model1.parameters.parameters)
self.model1.parameters.parameters = parameters.parameters[:idx]
self.model2.parameters.parameters = parameters.parameters[idx:]
def __str__(self):
ss = self.__class__.__name__
ss += "\n Component 1 : {}".format(self.model1)
ss += "\n Component 2 : {}".format(self.model2)
ss += "\n Operator : {}".format(self.operator)
return ss
def __call__(self, energy):
val1 = self.model1(energy)
val2 = self.model2(energy)
return self.operator(val1, val2)
def to_dict(self):
retval = dict()
retval["model1"] = self.model1.to_dict()
retval["model2"] = self.model2.to_dict()
retval["operator"] = self.operator
class PowerLaw(SpectralModel):
r"""Spectral power-law model.
.. math::
\phi(E) = \phi_0 \cdot \left( \frac{E}{E_0} \right)^{-\Gamma}
Parameters
----------
index : `~astropy.units.Quantity`
:math:`\Gamma`
amplitude : `~astropy.units.Quantity`
:math:`\phi_0`
reference : `~astropy.units.Quantity`
:math:`E_0`
Examples
--------
This is how to plot the default `PowerLaw` model::
from astropy import units as u
from gammapy.spectrum.models import PowerLaw
pwl = PowerLaw()
pwl.plot(energy_range=[0.1, 100] * u.TeV)
plt.show()
"""
def __init__(self, index=2.0, amplitude="1e-12 cm-2 s-1 TeV-1", reference="1 TeV"):
self.parameters = Parameters(
[
Parameter("index", index),
Parameter("amplitude", amplitude),
Parameter("reference", reference, frozen=True),
]
)
@staticmethod
def evaluate(energy, index, amplitude, reference):
"""Evaluate the model (static function)."""
return amplitude * np.power((energy / reference), -index)
def integral(self, emin, emax, **kwargs):
r"""Integrate power law analytically.
.. math::
F(E_{min}, E_{max}) = \int_{E_{min}}^{E_{max}}\phi(E)dE = \left.
\phi_0 \frac{E_0}{-\Gamma + 1} \left( \frac{E}{E_0} \right)^{-\Gamma + 1}
\right \vert _{E_{min}}^{E_{max}}
Parameters
----------
emin, emax : `~astropy.units.Quantity`
Lower and upper bound of integration range
"""
# kwargs are passed to this function but not used
# this is to get a consistent API with SpectralModel.integral()
pars = self.parameters
if np.isclose(pars["index"].value, 1):
e_unit = emin.unit
prefactor = pars["amplitude"].quantity * pars["reference"].quantity.to(
e_unit
)
upper = np.log(emax.to_value(e_unit))
lower = np.log(emin.to_value(e_unit))
else:
val = -1 * pars["index"].value + 1
prefactor = pars["amplitude"].quantity * pars["reference"].quantity / val
upper = np.power((emax / pars["reference"].quantity), val)
lower = np.power((emin / pars["reference"].quantity), val)
return prefactor * (upper - lower)
def integral_error(self, emin, emax, **kwargs):
r"""Integrate power law analytically with error propagation.
Parameters
----------
emin, emax : `~astropy.units.Quantity`
Lower and upper bound of integration range.
Returns
-------
integral, integral_error : tuple of `~astropy.units.Quantity`
Tuple of integral flux and integral flux error.
"""
# kwargs are passed to this function but not used
# this is to get a consistent API with SpectralModel.integral()
emin = self._convert_energy(emin)
emax = self._convert_energy(emax)
unit = self.integral(emin, emax, **kwargs).unit
upars = self.parameters._ufloats
if np.isclose(upars["index"].nominal_value, 1):
prefactor = upars["amplitude"] * upars["reference"]
upper = np.log(emax.value)
lower = np.log(emin.value)
else:
val = -1 * upars["index"] + 1
prefactor = upars["amplitude"] * upars["reference"] / val
upper = np.power((emax.value / upars["reference"]), val)
lower = np.power((emin.value / upars["reference"]), val)
uarray = prefactor * (upper - lower)
return self._parse_uarray(uarray) * unit
def energy_flux(self, emin, emax):
r"""Compute energy flux in given energy range analytically.
.. math::
G(E_{min}, E_{max}) = \int_{E_{min}}^{E_{max}}E \phi(E)dE = \left.
\phi_0 \frac{E_0^2}{-\Gamma + 2} \left( \frac{E}{E_0} \right)^{-\Gamma + 2}
\right \vert _{E_{min}}^{E_{max}}
Parameters
----------
emin, emax : `~astropy.units.Quantity`
Lower and upper bound of integration range.
"""
pars = self.parameters
val = -1 * pars["index"].value + 2
if np.isclose(val, 0):
# see https://www.wolframalpha.com/input/?i=a+*+x+*+(x%2Fb)+%5E+(-2)
# for reference
temp = pars["amplitude"].quantity * pars["reference"].quantity ** 2
return temp * np.log(emax / emin)
else:
prefactor = (
pars["amplitude"].quantity * pars["reference"].quantity ** 2 / val
)
upper = (emax / pars["reference"].quantity) ** val
lower = (emin / pars["reference"].quantity) ** val
return prefactor * (upper - lower)
def energy_flux_error(self, emin, emax, **kwargs):
r"""Compute energy flux in given energy range analytically with error propagation.
Parameters
----------
emin, emax : `~astropy.units.Quantity`
Lower and upper bound of integration range.
Returns
-------
energy_flux, energy_flux_error : tuple of `~astropy.units.Quantity`
Tuple of energy flux and energy flux error.
"""
emin = self._convert_energy(emin)
emax = self._convert_energy(emax)
unit = self.energy_flux(emin, emax, **kwargs).unit
upars = self.parameters._ufloats
val = -1 * upars["index"] + 2
if np.isclose(val.nominal_value, 0):
# see https://www.wolframalpha.com/input/?i=a+*+x+*+(x%2Fb)+%5E+(-2)
# for reference
temp = upars["amplitude"] * upars["reference"] ** 2
uarray = temp * np.log(emax.value / emin.value)
else:
prefactor = upars["amplitude"] * upars["reference"] ** 2 / val
upper = (emax.value / upars["reference"]) ** val
lower = (emin.value / upars["reference"]) ** val
uarray = prefactor * (upper - lower)
return self._parse_uarray(uarray) * unit
def inverse(self, value):
"""Return energy for a given function value of the spectral model.
Parameters
----------
value : `~astropy.units.Quantity`
Function value of the spectral model.
"""
p = self.parameters
base = value / p["amplitude"].quantity
return p["reference"].quantity * np.power(base, -1.0 / p["index"].value)
class PowerLaw2(SpectralModel):
r"""Spectral power-law model with integral as amplitude parameter.
See also: https://fermi.gsfc.nasa.gov/ssc/data/analysis/scitools/source_models.html
.. math::
\phi(E) = F_0 \cdot \frac{\Gamma + 1}{E_{0, max}^{-\Gamma + 1}
- E_{0, min}^{-\Gamma + 1}} \cdot E^{-\Gamma}
Parameters
----------
index : `~astropy.units.Quantity`
Spectral index :math:`\Gamma`
amplitude : `~astropy.units.Quantity`
Integral flux :math:`F_0`.
emin : `~astropy.units.Quantity`
Lower energy limit :math:`E_{0, min}`.
emax : `~astropy.units.Quantity`
Upper energy limit :math:`E_{0, max}`.
Examples
--------
This is how to plot the default `PowerLaw2` model::
from astropy import units as u
from gammapy.spectrum.models import PowerLaw2
pwl2 = PowerLaw2()
pwl2.plot(energy_range=[0.1, 100] * u.TeV)
plt.show()
"""
def __init__(
self, amplitude="1e-12 cm-2 s-1", index=2, emin="0.1 TeV", emax="100 TeV"
):
self.parameters = Parameters(
[
Parameter("amplitude", amplitude),
Parameter("index", index),
Parameter("emin", emin, frozen=True),
Parameter("emax", emax, frozen=True),
]
)
@staticmethod
def evaluate(energy, amplitude, index, emin, emax):
"""Evaluate the model (static function)."""
top = -index + 1
# to get the energies dimensionless we use a modified formula
bottom = emax - emin * (emin / emax) ** (-index)
return amplitude * (top / bottom) * np.power(energy / emax, -index)
def integral(self, emin, emax, **kwargs):
r"""Integrate power law analytically.
.. math::
F(E_{min}, E_{max}) = F_0 \cdot \frac{E_{max}^{\Gamma + 1} \
- E_{min}^{\Gamma + 1}}{E_{0, max}^{\Gamma + 1} \
- E_{0, min}^{\Gamma + 1}}
Parameters
----------
emin, emax : `~astropy.units.Quantity`
Lower and upper bound of integration range.
"""
pars = self.parameters
temp1 = np.power(emax, -pars["index"].value + 1)
temp2 = np.power(emin, -pars["index"].value + 1)
top = temp1 - temp2
temp1 = np.power(pars["emax"].quantity, -pars["index"].value + 1)
temp2 = np.power(pars["emin"].quantity, -pars["index"].value + 1)
bottom = temp1 - temp2
return pars["amplitude"].quantity * top / bottom
def integral_error(self, emin, emax, **kwargs):
r"""Integrate power law analytically with error propagation.
Parameters
----------
emin, emax : `~astropy.units.Quantity`
Lower and upper bound of integration range.
Returns
-------
integral, integral_error : tuple of `~astropy.units.Quantity`
Tuple of integral flux and integral flux error.
"""
emin = self._convert_energy(emin)
emax = self._convert_energy(emax)
unit = self.integral(emin, emax, **kwargs).unit
upars = self.parameters._ufloats
temp1 = np.power(emax.value, -upars["index"] + 1)
temp2 = np.power(emin.value, -upars["index"] + 1)
top = temp1 - temp2
temp1 = np.power(upars["emax"], -upars["index"] + 1)
temp2 = np.power(upars["emin"], -upars["index"] + 1)
bottom = temp1 - temp2
uarray = upars["amplitude"] * top / bottom
return self._parse_uarray(uarray) * unit
def inverse(self, value):
"""Return energy for a given function value of the spectral model.
Parameters
----------
value : `~astropy.units.Quantity`
Function value of the spectral model.
"""
p = self.parameters
amplitude, index, emin, emax = (
p["amplitude"].quantity,
p["index"].value,
p["emin"].quantity,
p["emax"].quantity,
)
# to get the energies dimensionless we use a modified formula
top = -index + 1
bottom = emax - emin * (emin / emax) ** (-index)
term = (bottom / top) * (value / amplitude)
return np.power(term.to_value(""), -1.0 / index) * emax
class ExponentialCutoffPowerLaw(SpectralModel):
r"""Spectral exponential cutoff power-law model.
.. math::
\phi(E) = \phi_0 \cdot \left(\frac{E}{E_0}\right)^{-\Gamma} \exp(-\lambda E)
Parameters
----------
index : `~astropy.units.Quantity`
:math:`\Gamma`
amplitude : `~astropy.units.Quantity`
:math:`\phi_0`
reference : `~astropy.units.Quantity`
:math:`E_0`
lambda_ : `~astropy.units.Quantity`
:math:`\lambda`
Examples
--------
This is how to plot the default `ExponentialCutoffPowerLaw` model::
from astropy import units as u
from gammapy.spectrum.models import ExponentialCutoffPowerLaw
ecpl = ExponentialCutoffPowerLaw()
ecpl.plot(energy_range=[0.1, 100] * u.TeV)
plt.show()
"""
def __init__(
self,
index=1.5,
amplitude="1e-12 cm-2 s-1 TeV-1",
reference="1 TeV",
lambda_="0.1 TeV-1",
):
self.parameters = Parameters(
[
Parameter("index", index),
Parameter("amplitude", amplitude),
Parameter("reference", reference, frozen=True),
Parameter("lambda_", lambda_),
]
)
@staticmethod
def evaluate(energy, index, amplitude, reference, lambda_):
"""Evaluate the model (static function)."""
pwl = amplitude * (energy / reference) ** (-index)
try:
cutoff = np.exp(-energy * lambda_)
except AttributeError:
from uncertainties.unumpy import exp
cutoff = exp(-energy * lambda_)
return pwl * cutoff
@property
def e_peak(self):
r"""Spectral energy distribution peak energy (`~astropy.utils.Quantity`).
This is the peak in E^2 x dN/dE and is given by:
.. math::
E_{Peak} = (2 - \Gamma) / \lambda
"""
p = self.parameters
reference = p["reference"].quantity
index = p["index"].quantity
lambda_ = p["lambda_"].quantity
if index >= 2:
return np.nan * reference.unit
else:
return (2 - index) / lambda_
class ExponentialCutoffPowerLaw3FGL(SpectralModel):
r"""Spectral exponential cutoff power-law model used for 3FGL.
Note that the parametrization is different from `ExponentialCutoffPowerLaw`:
.. math::
\phi(E) = \phi_0 \cdot \left(\frac{E}{E_0}\right)^{-\Gamma}
\exp \left( \frac{E_0 - E}{E_{C}} \right)
Parameters
----------
index : `~astropy.units.Quantity`
:math:`\Gamma`
amplitude : `~astropy.units.Quantity`
:math:`\phi_0`
reference : `~astropy.units.Quantity`
:math:`E_0`
ecut : `~astropy.units.Quantity`
:math:`E_{C}`
Examples
--------
This is how to plot the default `ExponentialCutoffPowerLaw3FGL` model::
from astropy import units as u
from gammapy.spectrum.models import ExponentialCutoffPowerLaw3FGL
ecpl_3fgl = ExponentialCutoffPowerLaw3FGL()
ecpl_3fgl.plot(energy_range=[0.1, 100] * u.TeV)
plt.show()
"""
def __init__(
self,
index=1.5,
amplitude="1e-12 cm-2 s-1 TeV-1",
reference="1 TeV",
ecut="10 TeV",
):
self.parameters = Parameters(
[
Parameter("index", index),
Parameter("amplitude", amplitude),
Parameter("reference", reference, frozen=True),
Parameter("ecut", ecut),
]
)
@staticmethod
def evaluate(energy, index, amplitude, reference, ecut):
"""Evaluate the model (static function)."""
pwl = amplitude * (energy / reference) ** (-index)
try:
cutoff = np.exp((reference - energy) / ecut)
except AttributeError:
from uncertainties.unumpy import exp
cutoff = exp((reference - energy) / ecut)
return pwl * cutoff
class PLSuperExpCutoff3FGL(SpectralModel):
r"""Spectral super exponential cutoff power-law model used for 3FGL.
.. math::
\phi(E) = \phi_0 \cdot \left(\frac{E}{E_0}\right)^{-\Gamma_1}
\exp \left( \left(\frac{E_0}{E_{C}} \right)^{\Gamma_2} -
\left(\frac{E}{E_{C}} \right)^{\Gamma_2}
\right)
Parameters
----------
index_1 : `~astropy.units.Quantity`
:math:`\Gamma_1`
index_2 : `~astropy.units.Quantity`
:math:`\Gamma_2`
amplitude : `~astropy.units.Quantity`
:math:`\phi_0`
reference : `~astropy.units.Quantity`
:math:`E_0`
ecut : `~astropy.units.Quantity`
:math:`E_{C}`
Examples
--------
This is how to plot the default `PLSuperExpCutoff3FGL` model::
from astropy import units as u
from gammapy.spectrum.models import PLSuperExpCutoff3FGL
secpl_3fgl = PLSuperExpCutoff3FGL()
secpl_3fgl.plot(energy_range=[0.1, 100] * u.TeV)
plt.show()
"""
def __init__(
self,
index_1=1.5,
index_2=2,
amplitude="1e-12 cm-2 s-1 TeV-1",
reference="1 TeV",
ecut="10 TeV",
):
self.parameters = Parameters(
[
Parameter("index_1", index_1),
Parameter("index_2", index_2),
Parameter("amplitude", amplitude),
Parameter("reference", reference, frozen=True),
Parameter("ecut", ecut),
]
)