TemplateSpectralModel¶

class gammapy.modeling.models.TemplateSpectralModel(energy, values, norm=1, tilt=0, reference='1 TeV', interp_kwargs=None, meta=None)[source]¶

Bases: gammapy.modeling.models.SpectralModel

A model generated from a table of energy and value arrays.

the units returned will be the units of the values array provided at initialization. The model will return values interpolated in log-space, returning 0 for energies outside of the limits of the provided energy array.

Class implementation follows closely what has been done in naima.models.TemplateSpectralModel

Parameters:

energy : Quantity array: Array of energies at which the model values are given
values : array: Array with the values of the model at energies energy.
norm : float: Model scale that is multiplied to the supplied arrays. Defaults to 1.
interp_kwargs : dict: Interpolation keyword arguments pass to scipy.interpolate.interp1d. By default all values outside the interpolation range are set to zero. If you want to apply linear extrapolation you can pass interp_kwargs={'fill_value': 'extrapolate', 'kind': 'linear'}. If you want to choose the interpolation scaling applied to values, you can use interp_kwargs={"values_scale": "log"}.
meta : dict, optional: Meta information, meta[‘filename’] will be used for serialization

Attributes Summary

`energy`
`meta`
`norm`
`parameters`	Parameters (`Parameters`)
`tag`
`values`

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, \\kwargs)	Compute energy flux in given energy range.
`energy_flux_error`(self, emin, emax, \\kwargs)	Compute energy flux in given energy range with error propagation.
`evaluate`(self, energy, norm, tilt, reference)	Evaluate the model (static function).
`evaluate_error`(self, energy)	Evaluate spectral model with error propagation.
`from_dict`(data)
`integral`(self, emin, emax, \\kwargs)	Integrate spectral model numerically.
`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.
`read_fermi_isotropic_model`(filename, \\kwargs)	Read Fermi isotropic diffuse model.
`read_xspec_model`(filename, param, \\kwargs)	Read XSPEC table model.
`spectral_index`(self, energy[, epsilon])	Compute spectral index at given energy.
`to_dict`(self)

Attributes Documentation

energy¶

meta¶

norm¶

parameters¶: Parameters (Parameters)

tag = 'TemplateSpectralModel'¶

values¶

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, **kwargs)¶

Compute energy flux in given energy range.

\[G(E_{min}, E_{max}) = \int_{E_{min}}^{E_{max}} E \phi(E) dE\]

Parameters:	emin, emax : `Quantity` Lower and upper bound of integration range. **kwargs : dict Keyword arguments passed to func:`integrate_spectrum`

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.

evaluate(self, energy, norm, tilt, reference)[source]¶: Evaluate the model (static function).

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)[source]¶

integral(self, emin, emax, **kwargs)¶

Integrate spectral model numerically.

\[F(E_{min}, E_{max}) = \int_{E_{min}}^{E_{max}} \phi(E) dE\]

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 : `Quantity` Lower and upper bound of integration range. **kwargs : dict Keyword arguments passed to `integrate_spectrum()`

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

classmethod read_fermi_isotropic_model(filename, **kwargs)[source]¶

Read Fermi isotropic diffuse model.

See LAT Background models

Parameters:	filename : str filename

classmethod read_xspec_model(filename, param, **kwargs)[source]¶

Read XSPEC table model.

The input is a table containing absorbed values from a XSPEC model as a function of energy.

TODO: Format of the file should be described and discussed in https://gamma-astro-data-formats.readthedocs.io/en/latest/index.html

Parameters:	filename : str File containing the XSPEC model param : float Model parameter value

Examples

Fill table from an EBL model (Franceschini, 2008)

>>> from gammapy.modeling.models import TemplateSpectralModel
>>> filename = '$GAMMAPY_DATA/ebl/ebl_franceschini.fits.gz'
>>> table_model = TemplateSpectralModel.read_xspec_model(filename=filename, param=0.3)

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)[source]¶