ExpCutoffPowerLawNormSpectralModel#

class gammapy.modeling.models.ExpCutoffPowerLawNormSpectralModel(index=None, norm=None, reference=None, lambda_=None, alpha=None, **kwargs)[source]#

Bases: gammapy.modeling.models.spectral.SpectralModel

Norm spectral exponential cutoff power-law model.

Parameters

indexQuantity: \(\Gamma\). Default is 1.5.
normQuantity: \(\phi_0\). Default is 1.
referenceQuantity: \(E_0\). Default is 1 TeV.
lambda_Quantity: \(\lambda\). Default is 0.1 TeV-1.
alphaQuantity: \(\alpha\). Default is 1.

See also

ExpCutoffPowerLawSpectralModel

Attributes Summary

`alpha`	A model parameter.
`covariance`
`default_parameters`
`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.
`lambda_`	A model parameter.
`norm`	A model parameter.
`parameters`	Parameters as a `Parameters` object.
`pivot_energy`	Pivot or decorrelation energy, for a given spectral model calculated numerically.
`reference`	A model parameter.
`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, index, norm, reference, ...)	Evaluate the model (static function).
`evaluate_error`(energy[, epsilon])	Evaluate spectral model with error propagation.
`freeze`()	Freeze all parameters.
`from_dict`(data, **kwargs)
`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.
`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

alpha#

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 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_normbool: Whether the parameter represents the flux norm of the model.
priorPrior: Prior set on the parameter.

covariance#

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

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.

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 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_normbool: Whether the parameter represents the flux norm of the model.
priorPrior: Prior set on the parameter.

is_norm_spectral_model#: Whether model is a norm spectral model.

lambda_#

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.

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 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_normbool: Whether the parameter represents the flux norm of the model.
priorPrior: Prior set on the parameter.

norm#

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.

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 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_normbool: Whether the parameter represents the flux norm of the model.
priorPrior: Prior set on the parameter.

parameters#: Parameters as a Parameters object.

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.

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.

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 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_normbool: Whether the parameter represents the flux norm of the model.
priorPrior: Prior set on the parameter.

tag = ['ExpCutoffPowerLawNormSpectralModel', 'ecpl-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.

static evaluate(energy, index, norm, reference, lambda_, alpha)[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, 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)#

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, 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: Plot energy bounds passed to MapAxis.from_energy_bounds.
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.

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

energy_boundsQuantity: Plot energy bounds passed to from_energy_bounds.
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.

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.