ExpCutoffPowerLaw3FGLSpectralModel¶

class gammapy.modeling.models.ExpCutoffPowerLaw3FGLSpectralModel(**kwargs)[source]¶

Bases: gammapy.modeling.models.SpectralModel

Spectral exponential cutoff power-law model used for 3FGL.

For more information see Exponential cutoff power law spectral model used for 3FGL.

Parameters

indexQuantity: \(\Gamma\)
amplitudeQuantity: \(\phi_0\)
referenceQuantity: \(E_0\)
ecutQuantity: \(E_{C}\)

Attributes Summary

`amplitude`	A model parameter.
`covariance`
`default_parameters`
`ecut`	A model parameter.
`frozen`	Frozen status of a model, True if all parameters are frozen
`index`	A model parameter.
`is_norm_spectral_model`	Whether model is a norm spectral model
`parameters`	Parameters (`Parameters`)
`reference`	A model parameter.
`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, index, amplitude, …)	Evaluate the model (static function).
`evaluate_error`(energy[, epsilon])	Evaluate spectral model with error propagation.
`freeze`()	Freeze all parameters
`from_dict`(data)
`from_parameters`(parameters, **kwargs)	Create model from parameter list
`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

amplitude¶

A model parameter.

Note that the parameter value has been split into a factor and scale like this:

value = factor x scale

Users should interact with the value, quantity or min and max properties and consider the fact that there is a factor` and scale an implementation detail.

That was introduced for numerical stability in parameter and error estimation methods, only in the Gammapy optimiser interface do we interact with the factor, factor_min and factor_max properties, i.e. the optimiser “sees” the well-scaled problem.

Parameters

namestr: Name
valuefloat or Quantity: Value
scalefloat, optional: Scale (sometimes used in fitting)
unitUnit or str, optional: Unit
minfloat, optional: Minimum (sometimes used in fitting)
maxfloat, optional: Maximum (sometimes used in fitting)
frozenbool, optional: Frozen? (used in fitting)
errorfloat: Parameter error
scan_minfloat: Minimum value for the parameter scan. Overwrites scan_n_sigma.
scan_maxfloat: Minimum value for the parameter scan. Overwrites scan_n_sigma.
scan_n_values: int: Number of values to be used for the parameter scan.
scan_n_sigmaint: Number of sigmas to scan.
scan_values: `numpy.array`: Scan values. Overwrites all of the scan keywords before.
scale_method{‘scale10’, ‘factor1’, None}: Method used to set factor and scale
interp{“lin”, “sqrt”, “log”}: Parameter scaling to use for the scan.

covariance¶

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

ecut¶

A model parameter.

Note that the parameter value has been split into a factor and scale like this:

value = factor x scale

Users should interact with the value, quantity or min and max properties and consider the fact that there is a factor` and scale an implementation detail.

That was introduced for numerical stability in parameter and error estimation methods, only in the Gammapy optimiser interface do we interact with the factor, factor_min and factor_max properties, i.e. the optimiser “sees” the well-scaled problem.

Parameters

namestr: Name
valuefloat or Quantity: Value
scalefloat, optional: Scale (sometimes used in fitting)
unitUnit or str, optional: Unit
minfloat, optional: Minimum (sometimes used in fitting)
maxfloat, optional: Maximum (sometimes used in fitting)
frozenbool, optional: Frozen? (used in fitting)
errorfloat: Parameter error
scan_minfloat: Minimum value for the parameter scan. Overwrites scan_n_sigma.
scan_maxfloat: Minimum value for the parameter scan. Overwrites scan_n_sigma.
scan_n_values: int: Number of values to be used for the parameter scan.
scan_n_sigmaint: Number of sigmas to scan.
scan_values: `numpy.array`: Scan values. Overwrites all of the scan keywords before.
scale_method{‘scale10’, ‘factor1’, None}: Method used to set factor and scale
interp{“lin”, “sqrt”, “log”}: Parameter scaling to use for the scan.

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

index¶

A model parameter.

Note that the parameter value has been split into a factor and scale like this:

value = factor x scale

Users should interact with the value, quantity or min and max properties and consider the fact that there is a factor` and scale an implementation detail.

That was introduced for numerical stability in parameter and error estimation methods, only in the Gammapy optimiser interface do we interact with the factor, factor_min and factor_max properties, i.e. the optimiser “sees” the well-scaled problem.

Parameters

namestr: Name
valuefloat or Quantity: Value
scalefloat, optional: Scale (sometimes used in fitting)
unitUnit or str, optional: Unit
minfloat, optional: Minimum (sometimes used in fitting)
maxfloat, optional: Maximum (sometimes used in fitting)
frozenbool, optional: Frozen? (used in fitting)
errorfloat: Parameter error
scan_minfloat: Minimum value for the parameter scan. Overwrites scan_n_sigma.
scan_maxfloat: Minimum value for the parameter scan. Overwrites scan_n_sigma.
scan_n_values: int: Number of values to be used for the parameter scan.
scan_n_sigmaint: Number of sigmas to scan.
scan_values: `numpy.array`: Scan values. Overwrites all of the scan keywords before.
scale_method{‘scale10’, ‘factor1’, None}: Method used to set factor and scale
interp{“lin”, “sqrt”, “log”}: Parameter scaling to use for the scan.

is_norm_spectral_model¶: Whether model is a norm spectral model

parameters¶: Parameters (Parameters)

reference¶

A model parameter.

Note that the parameter value has been split into a factor and scale like this:

value = factor x scale

Users should interact with the value, quantity or min and max properties and consider the fact that there is a factor` and scale an implementation detail.

That was introduced for numerical stability in parameter and error estimation methods, only in the Gammapy optimiser interface do we interact with the factor, factor_min and factor_max properties, i.e. the optimiser “sees” the well-scaled problem.

Parameters

namestr: Name
valuefloat or Quantity: Value
scalefloat, optional: Scale (sometimes used in fitting)
unitUnit or str, optional: Unit
minfloat, optional: Minimum (sometimes used in fitting)
maxfloat, optional: Maximum (sometimes used in fitting)
frozenbool, optional: Frozen? (used in fitting)
errorfloat: Parameter error
scan_minfloat: Minimum value for the parameter scan. Overwrites scan_n_sigma.
scan_maxfloat: Minimum value for the parameter scan. Overwrites scan_n_sigma.
scan_n_values: int: Number of values to be used for the parameter scan.
scan_n_sigmaint: Number of sigmas to scan.
scan_values: `numpy.array`: Scan values. Overwrites all of the scan keywords before.
scale_method{‘scale10’, ‘factor1’, None}: Method used to set factor and scale
interp{“lin”, “sqrt”, “log”}: Parameter scaling to use for the scan.

tag = ['ExpCutoffPowerLaw3FGLSpectralModel', 'ecpl-3fgl']¶

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.

static evaluate(energy, index, amplitude, reference, ecut)[source]¶: Evaluate the model (static function).

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)¶

classmethod from_parameters(parameters, **kwargs)¶

Create model from parameter list

Parameters

parametersParameters: Parameters for init

Returns

modelModel: Model instance

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