PiecewiseNormSpectralModel

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

Bases: 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. Normalisation parameters are 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 as a Parameters object.
parameters_unique_names
pivot_energy	Pivot or decorrelation energy, for a given spectral model calculated numerically.
tag
type

Methods Summary

__call__(energy)	Call self as a function.
copy(**kwargs)	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 a given energy range.
evaluate(energy, **norms)
evaluate_error(energy[, epsilon])	Evaluate spectral model with error propagation.
freeze()	Freeze all parameters.
from_dict(data, **kwargs)	Create model from dictionary.
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.
spectral_index_error(energy[, epsilon])	Evaluate the error on spectral index at the given energy.
to_dict([full_output])	Create dictionary 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 as a Parameters object.

parameters_unique_names

pivot_energy

Pivot or decorrelation energy, for a given spectral model calculated numerically.

It is defined as the energy at which the correlation between the spectral parameters is minimized.

Returns:

pivot energyQuantity

The energy at which the statistical error in the computed flux is smallest. If no minimum is found, NaN will be returned.

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

type

Methods Documentation

__call__(energy)

Call self as a function.

copy(**kwargs)

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 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, optional

Step size of the gradient evaluation. Given as a fraction of the parameter error. Default is 1e-4.

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, optional

Step size of the gradient evaluation. Given as a fraction of the parameter error. Default is 1e-4.

Returns:

dnde, dnde_errortuple of Quantity

Tuple of flux and flux error.

freeze()

Freeze all parameters.

classmethod from_dict(data, **kwargs)

Create model from dictionary.

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, optional

Step size of the gradient evaluation. Given as a fraction of the parameter error. Default is 1e-4.

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, optional

Lower energy bound of the roots finding. Default is 0.1 TeV.

energy_maxQuantity, optional

Upper energy bound of the roots finding. Default is 100 TeV.

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, optional

Lower energy bound of the roots finding. Default is 0.1 TeV.

energy_maxQuantity, optional

Upper energy bound of the roots finding. Default is 100 TeV.

Returns:

energylist of Quantity

Each element contains 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.

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:

energy_boundsQuantity, list of Quantity or MapAxis

Energy bounds between which the model is to be plotted. Or an axis defining the energy bounds between which the model is to be plotted.

axAxes, optional

Matplotlib axes. Default is None.

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

Evaluation methods of the model. Default is “dnde”.

energy_powerint, optional

Power of energy to multiply flux axis with. Default is 0.

n_pointsint, optional

Number of evaluation nodes. Default is 100.

**kwargsdict

Keyword arguments forwarded to plot.

Returns:

axAxes, optional

Matplotlib axes.

Notes

If energy_bounds is supplied as a list, tuple, or Quantity, an energy_axis is created internally with n_points bins between the given bounds.

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 matplotlib/matplotlib#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:

energy_boundsQuantity, list of Quantity or MapAxis

Energy bounds between which the model is to be plotted. Or an axis defining the energy bounds between which the model is to be plotted.

axAxes, optional

Matplotlib axes. Default is None.

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

Evaluation methods of the model. Default is “dnde”.

energy_powerint, optional

Power of energy to multiply flux axis with. Default is 0.

n_pointsint, optional

Number of evaluation nodes. Default is 100.

**kwargsdict

Keyword arguments forwarded to matplotlib.pyplot.fill_between.

Returns:

axAxes, optional

Matplotlib axes.

Notes

If energy_bounds is supplied as a list, tuple, or Quantity, an energy_axis is created internally with n_points bins between the given bounds.

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, optional

Fractional energy increment to use for determining the spectral index. Default is 1e-5.

Returns:

indexfloat

Estimated spectral index.

spectral_index_error(energy, epsilon=1e-05)

Evaluate the error on spectral index at the given energy.

Parameters:

energyQuantity

Energy at which to estimate the index.

epsilonfloat, optional

Fractional energy increment to use for determining the spectral index. Default is 1e-5.

Returns:

index, index_errortuple of float

Estimated spectral index and its error.

to_dict(full_output=False)

Create dictionary for YAML serialisation.

unfreeze()

Restore parameters frozen status to default.