PiecewiseNormSpectralModel

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

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
frozen	Frozen status of a model, True if all parameters are frozen
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.
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.
freeze()	Freeze all parameters
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[, epsilon])	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.
inverse_all(values[, energy_min, energy_max])	Return energies for multiple function values of the spectral model.
plot(energy_bounds[, ax, sed_type, …])	Plot spectral model curve.
plot_error(energy_bounds[, ax, sed_type, …])	Plot spectral model error band.
reassign(datasets_names, new_datasets_names)	Reassign a model from one dataset to another
reference_fluxes(energy_axis)	Get reference fluxes for a given energy axis.
spectral_index(energy[, epsilon])	Compute spectral index at given energy.
to_dict([full_output])	Create dict for YAML serialisation
unfreeze()	Restore parameters frozen status to default

Attributes Documentation

covariance

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

energy

Energy nodes

frozen

Frozen status of a model, True if all parameters are frozen

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.

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.

epsilonfloat

Step size of the gradient evaluation. Given as a fraction of the parameter error.

Returns

energy_flux, energy_flux_errtuple of Quantity

Energy flux and energy flux error between energy_min and energy_max.

evaluate(energy, **norms)

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.

freeze()

Freeze all parameters

classmethod from_dict(data)

Create model from dict

classmethod from_parameters(parameters, **kwargs)

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, epsilon=0.0001, **kwargs)

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.

epsilonfloat

Step size of the gradient evaluation. Given as a fraction of the parameter error.

Returns

flux, flux_errtuple of Quantity

Integral flux and flux error between 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 energy bound of the roots finding

energy_maxQuantity

Upper energy bound of the roots finding

Returns

energyQuantity

Energies at which the model has the given value.

inverse_all(values, energy_min=<Quantity 0.1 TeV>, energy_max=<Quantity 100. TeV>)

Return energies for multiple function values of the spectral model.

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

Parameters

valuesQuantity

Function values of the spectral model.

energy_minQuantity

Lower energy bound of the roots finding

energy_maxQuantity

Upper energy bound of the roots finding

Returns

energylist of Quantity

each element contain the energies at which the model has corresponding value of values.

plot(energy_bounds, ax=None, sed_type='dnde', 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_bounds=(0.1, 100) * u.TeV)
ax.set_yscale('linear')

Parameters

axAxes, optional

Axis

energy_boundsQuantity

Plot energy bounds passed to MapAxis.from_energy_bounds

sed_type{“dnde”, “flux”, “eflux”, “e2dnde”}

Evaluation methods of the model

energy_powerint, optional

Power of energy to multiply flux axis with

n_pointsint, optional

Number of evaluation nodes

**kwargsdict

Keyword arguments forwarded to plot

Returns

axAxes, optional

Axis

plot_error(energy_bounds, ax=None, sed_type='dnde', energy_power=0, n_points=100, **kwargs)

Plot spectral model error band.

Note

This method calls ax.set_yscale("log", nonpositive='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() explicitly 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', nonpositive='clip') or plt.semilogy(nonpositive='clip').

Parameters

axAxes, optional

Axis

energy_boundsQuantity

Plot energy bounds passed to MapAxis.from_energy_bounds

sed_type{“dnde”, “flux”, “eflux”, “e2dnde”}

Evaluation methods of the model

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

reassign(datasets_names, new_datasets_names)

Reassign a model from one dataset to another

Parameters

datasets_namesstr or list

Name of the datasets where the model is currently defined

new_datasets_namesstr or list

Name of the datasets where the model should be defined instead. If multiple names are given the two list must have the save length, as the reassignment is element-wise.

Returns

modelModel

Reassigned model.

reference_fluxes(energy_axis)

Get reference fluxes for a given energy axis.

Parameters

energy_axisMapAxis

Energy axis

Returns

fluxesdict of Quantity

Reference fluxes

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)

Create dict for YAML serialisation

unfreeze()

Restore parameters frozen status to default