PiecewiseNormSpectralModel¶

class gammapy.modeling.models.PiecewiseNormSpectralModel(energy, norms=None, interp='log')[source]¶

Bases: gammapy.modeling.models.SpectralModel

Piecewise spectral correction

with a free normalization at each fixed energy nodes.

For more information see Piecewise Norm Spectral Model.

Parameters

energyQuantity: Array of energies at which the model values are given (nodes).
normsndarray or list of Parameter: Array with the initial norms of the model at energies energy. A normalisation parameters is created for each value. Default is one at each node.
interpstr: Interpolation scaling in {“log”, “lin”}. Default is “log”

Attributes Summary

`covariance`
`default_parameters`
`energy`	Energy nodes
`is_norm_spectral_model`	Whether model is a norm spectral model
`norms`	Norm values
`parameters`	Parameters (`Parameters`)
`tag`
`type`

Methods Summary

`__call__`(energy)	Call self as a function.
`copy`()	A deep copy.
`create`(tag[, model_type])	Create a model instance.
`energy_flux`(energy_min, energy_max, **kwargs)	Compute energy flux in given energy range.
`energy_flux_error`(energy_min, energy_max[, …])	Evaluate the error of the energy flux of a given spectrum in
`evaluate`(energy, **norms)
`evaluate_error`(energy[, epsilon])	Evaluate spectral model with error propagation.
`from_dict`(data)	Create model from dict
`from_parameters`(parameters, **kwargs)	Create model from parameters
`integral`(energy_min, energy_max, **kwargs)	Integrate spectral model numerically if no analytical solution defined.
`integral_error`(energy_min, energy_max)	Evaluate the error of the integral flux of a given spectrum in a given energy range.
`inverse`(value[, energy_min, energy_max])	Return energy for a given function value of the spectral model.
`plot`(energy_range[, ax, energy_unit, …])	Plot spectral model curve.
`plot_error`(energy_range[, ax, energy_unit, …])	Plot spectral model error band.
`spectral_index`(energy[, epsilon])	Compute spectral index at given energy.
`to_dict`([full_output])	Create dict for YAML serialisation

Attributes Documentation

covariance¶

default_parameters = <gammapy.modeling.parameter.Parameters object>¶

energy¶: Energy nodes

is_norm_spectral_model¶: Whether model is a norm spectral model

norms¶: Norm values

parameters¶: Parameters (Parameters)

tag = ['PiecewiseNormSpectralModel', 'piecewise-norm']¶

type¶

Methods Documentation

__call__(energy)¶: Call self as a function.

copy()¶: A deep copy.

static create(tag, model_type=None, *args, **kwargs)¶

Create a model instance.

Examples

>>> from gammapy.modeling.models import Model
>>> spectral_model = Model.create("pl-2", model_type="spectral", amplitude="1e-10 cm-2 s-1", index=3)
>>> type(spectral_model)
gammapy.modeling.models.spectral.PowerLaw2SpectralModel

energy_flux(energy_min, energy_max, **kwargs)¶

Compute energy flux in given energy range.

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

Parameters

energy_min, energy_maxQuantity: Lower and upper bound of integration range.
**kwargsdict: Keyword arguments passed to func:integrate_spectrum

energy_flux_error(energy_min, energy_max, epsilon=0.0001, **kwargs)¶

Evaluate the error of the energy flux of a given spectrum in: a given energy range.

Parameters

energy_min, energy_maxQuantity: Lower and upper bound of integration range.

Returns

energy_flux, energy_flux_errtuple of Quantity: Energy flux and energy flux error betwen energy_min and energy_max.

evaluate(energy, **norms)[source]¶

evaluate_error(energy, epsilon=0.0001)¶

Evaluate spectral model with error propagation.

Parameters

energyQuantity: Energy at which to evaluate
epsilonfloat: Step size of the gradient evaluation. Given as a fraction of the parameter error.

Returns

dnde, dnde_errortuple of Quantity: Tuple of flux and flux error.

classmethod from_dict(data)[source]¶: Create model from dict

classmethod from_parameters(parameters, **kwargs)[source]¶: Create model from parameters

integral(energy_min, energy_max, **kwargs)¶

Integrate spectral model numerically if no analytical solution defined.

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

Parameters

energy_min, energy_maxQuantity: Lower and upper bound of integration range.
**kwargsdict: Keyword arguments passed to integrate_spectrum()

integral_error(energy_min, energy_max)¶

Evaluate the error of the integral flux of a given spectrum in a given energy range.

Parameters

energy_min, energy_maxQuantity: Lower and upper bound of integration range.

Returns

flux, flux_errtuple of Quantity: Integral flux and flux error betwen energy_min and energy_max.

inverse(value, energy_min=<Quantity 0.1 TeV>, energy_max=<Quantity 100. TeV>)¶

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

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

Parameters

valueQuantity: Function value of the spectral model.
energy_minQuantity: Lower bracket value in case solution is not unique.
energy_maxQuantity: Upper bracket value in case solution is not unique.

Returns

energyQuantity: Energies at which the model has the given value.

plot(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

axAxes, optional: Axis
energy_rangeQuantity: Plot range
energy_unitstr, Unit, optional: Unit of the energy axis
flux_unitstr, Unit, optional: Unit of the flux axis
energy_powerint, optional: Power of energy to multiply flux axis with
n_pointsint, optional: Number of evaluation nodes

Returns

axAxes, optional: Axis

plot_error(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

axAxes, optional: Axis
energy_rangeQuantity: Plot range
energy_unitstr, Unit, optional: Unit of the energy axis
flux_unitstr, Unit, optional: Unit of the flux axis
energy_powerint, optional: Power of energy to multiply flux axis with
n_pointsint, optional: Number of evaluation nodes
**kwargsdict: Keyword arguments forwarded to matplotlib.pyplot.fill_between

Returns

axAxes, optional: Axis

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

Compute spectral index at given energy.

Parameters

energyQuantity: Energy at which to estimate the index
epsilonfloat: Fractional energy increment to use for determining the spectral index.

Returns

indexfloat: Estimated spectral index.

to_dict(full_output=False)[source]¶: Create dict for YAML serialisation