ExpCutoffPowerLawSpectralModel

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

Bases: gammapy.modeling.models.SpectralModel

Spectral exponential cutoff power-law model.

For more information see Exponential cutoff power law spectral model.

Parameters
indexQuantity

\(\Gamma\)

amplitudeQuantity

\(\phi_0\)

referenceQuantity

\(E_0\)

lambda_Quantity

\(\lambda\)

alphaQuantity

\(\alpha\)

Attributes Summary

alpha

A model parameter.

amplitude

A model parameter.

covariance

default_parameters

e_peak

Spectral energy distribution peak energy (Quantity).

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.

parameters

Parameters (Parameters)

reference

A model parameter.

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, 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.

plot(energy_range[, ax, energy_unit, …])

Plot spectral model curve.

plot_error(energy_range[, ax, energy_unit, …])

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

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)

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)

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

Spectral energy distribution peak energy (Quantity).

This is the peak in E^2 x dN/dE and is given by:

\[E_{Peak} = \left(\frac{2 - \Gamma}{\alpha}\right)^{1/\alpha} / \lambda\]
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)

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.

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)

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)

tag = ['ExpCutoffPowerLawSpectralModel', 'ecpl']
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)
<class '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.

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 betwen energy_min and energy_max.

static evaluate(energy, index, amplitude, 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

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 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", 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() 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', nonpositive='clip') or plt.semilogy(nonpositive='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

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 lenght, 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