GaussianSpectralModel

class gammapy.modeling.models.GaussianSpectralModel(norm=<Quantity 1.e-12 1 / (cm2 s)>, mean=<Quantity 1. TeV>, sigma=<Quantity 2. TeV>)[source]

Bases: gammapy.modeling.models.SpectralModel

Gaussian spectral model.

\[\phi(E) = \frac{N_0}{\sigma \sqrt{2\pi}} \exp{ \frac{- \left( E-\bar{E} \right)^2 }{2 \sigma^2} }\]
Parameters:
norm : Quantity

\(N_0\)

mean : Quantity

\(\bar{E}\)

sigma : Quantity

\(\sigma\)

Examples

This is how to plot the default Gaussian spectral model:

from astropy import units as u
from gammapy.modeling.models import GaussianSpectralModel

gaussian = GaussianSpectralModel()
gaussian.plot(energy_range=[0.1, 100] * u.TeV)
plt.show()

Attributes Summary

parameters Parameters (Parameters)
tag

Methods Summary

__call__(self, energy) Call self as a function.
copy(self) A deep copy.
create(tag, \*args, \*\*kwargs) Create a model instance.
energy_flux(self, emin, emax) Compute energy flux in given energy range analytically.
energy_flux_error(self, emin, emax, \*\*kwargs) Compute energy flux in given energy range with error propagation.
evaluate(energy, norm, mean, sigma)
evaluate_error(self, energy) Evaluate spectral model with error propagation.
from_dict(data)
integral(self, emin, emax, \*\*kwargs) Integrate Gaussian analytically.
integral_error(self, emin, emax, \*\*kwargs) Integrate spectral model numerically with error propagation.
inverse(self, value[, emin, emax]) Return energy for a given function value of the spectral model.
plot(self, energy_range[, ax, energy_unit, …]) Plot spectral model curve.
plot_error(self, energy_range[, ax, …]) Plot spectral model error band.
spectral_index(self, energy[, epsilon]) Compute spectral index at given energy.
to_dict(self)

Attributes Documentation

parameters

Parameters (Parameters)

tag = 'GaussianSpectralModel'

Methods Documentation

__call__(self, energy)

Call self as a function.

copy(self)

A deep copy.

static create(tag, *args, **kwargs)

Create a model instance.

Examples

>>> from gammapy.modeling import Model
>>> spectral_model = Model.create("PowerLaw2SpectralModel", amplitude="1e-10 cm-2 s-1", index=3)
>>> type(spectral_model)
gammapy.modeling.models.spectral.PowerLaw2SpectralModel
energy_flux(self, emin, emax)[source]

Compute energy flux in given energy range analytically.

\[G(E_{min}, E_{max}) = \frac{N_0 \sigma}{\sqrt{2*\pi}}* \left[ - \exp(\frac{E_{min}-\bar{E}}{\sqrt{2} \sigma}) \right]_{E_{min}}^{E_{max}} + \frac{N_0 * \bar{E}}{2} \left[ erf(\frac{E - \bar{E}}{\sqrt{2} \sigma}) \right]_{E_{min}}^{E_{max}}\]
Parameters:
emin, emax : Quantity

Lower and upper bound of integration range.

energy_flux_error(self, emin, emax, **kwargs)

Compute energy flux in given energy range with error propagation.

\[G(E_{min}, E_{max}) = \int_{E_{min}}^{E_{max}} E \phi(E) dE\]
Parameters:
emin, emax : Quantity

Lower bound of integration range.

**kwargs : dict

Keyword arguments passed to integrate_spectrum()

Returns:
energy_flux, energy_flux_error : tuple of Quantity

Tuple of energy flux and energy flux error.

static evaluate(energy, norm, mean, sigma)[source]
evaluate_error(self, energy)

Evaluate spectral model with error propagation.

Parameters:
energy : Quantity

Energy at which to evaluate

Returns:
flux, flux_error : tuple of Quantity

Tuple of flux and flux error.

classmethod from_dict(data)
integral(self, emin, emax, **kwargs)[source]

Integrate Gaussian analytically.

\[F(E_{min}, E_{max}) = \frac{N_0}{2} \left[ erf(\frac{E - \bar{E}}{\sqrt{2} \sigma})\right]_{E_{min}}^{E_{max}}\]
Parameters:
emin, emax : Quantity

Lower and upper bound of integration range

integral_error(self, emin, emax, **kwargs)

Integrate spectral model numerically with error propagation.

Parameters:
emin, emax : Quantity

Lower adn upper bound of integration range.

**kwargs : dict

Keyword arguments passed to func:integrate_spectrum

Returns:
integral, integral_error : tuple of Quantity

Tuple of integral flux and integral flux error.

inverse(self, value, emin=<Quantity 0.1 TeV>, emax=<Quantity 100. TeV>)

Return energy for a given function value of the spectral model.

Calls the scipy.optimize.brentq numerical root finding method.

Parameters:
value : Quantity

Function value of the spectral model.

emin : Quantity

Lower bracket value in case solution is not unique.

emax : Quantity

Upper bracket value in case solution is not unique.

Returns:
energy : Quantity

Energies at which the model has the given value.

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.modeling.models import ExpCutoffPowerLawSpectralModel
from astropy import units as u

pwl = ExpCutoffPowerLawSpectralModel()
ax = pwl.plot(energy_range=(0.1, 100) * u.TeV)
ax.set_yscale('linear')
Parameters:
ax : Axes, optional

Axis

energy_range : Quantity

Plot range

energy_unit : str, Unit, optional

Unit of the energy axis

flux_unit : str, 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 : Axes, optional

Axis

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 : Axes, optional

Axis

energy_range : Quantity

Plot range

energy_unit : str, Unit, optional

Unit of the energy axis

flux_unit : str, 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 : Axes, optional

Axis

spectral_index(self, energy, epsilon=1e-05)

Compute spectral index at given energy.

Parameters:
energy : 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.

to_dict(self)