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