PowerLawSpectralModel

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

Bases: gammapy.modeling.models.SpectralModel

Spectral power-law model.

For more information see Power Law Spectral Model.

Parameters
indexQuantity

\(\Gamma\)

amplitudeQuantity

\(\phi_0\)

referenceQuantity

\(E_0\)

Attributes Summary

amplitude

A model parameter.

covariance

default_parameters

index

A model parameter.

is_norm_spectral_model

Whether model is a norm spectral model

parameters

Parameters (Parameters)

pivot_energy

The decorrelation energy is defined as:

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(emin, emax, **kwargs)

Compute energy flux in given energy range.

energy_flux_error(emin, emax[, epsilon])

Evaluate the error of the energy flux of a given spectrum in

evaluate(energy, index, amplitude, reference)

Evaluate the model (static function).

evaluate_energy_flux(emin, emax, index, …)

Compute energy flux in given energy range analytically (static function).

evaluate_error(energy[, epsilon])

Evaluate spectral model with error propagation.

evaluate_integral(emin, emax, index, …)

Integrate power law analytically (static function).

from_dict(data)

from_parameters(parameters, **kwargs)

Create model from parameter list

integral(emin, emax, **kwargs)

Integrate spectral model numerically if no analytical solution defined.

integral_error(emin, emax)

Evaluate the error of the integral flux of a given spectrum in a given energy range.

inverse(value)

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.

spectral_index(energy[, epsilon])

Compute spectral index at given energy.

to_dict([full_output])

Create dict for YAML serialisation

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)

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

parameters

Parameters (Parameters)

pivot_energy

The decorrelation energy is defined as:

\[E_D = E_0 * \exp{cov(\phi_0, \Gamma) / (\phi_0 \Delta \Gamma^2)}\]

Formula (1) in https://arxiv.org/pdf/0910.4881.pdf

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 = ['PowerLawSpectralModel', 'pl']
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)
gammapy.modeling.models.spectral.PowerLaw2SpectralModel
energy_flux(emin, emax, **kwargs)

Compute energy flux in given energy range.

\[G(E_{min}, E_{max}) = \int_{E_{min}}^{E_{max}} E \phi(E) dE\]
Parameters
emin, emaxQuantity

Lower and upper bound of integration range.

**kwargsdict

Keyword arguments passed to func:integrate_spectrum

energy_flux_error(emin, emax, epsilon=0.0001, **kwargs)
Evaluate the error of the energy flux of a given spectrum in

a given energy range.

Parameters
emin, emaxQuantity

Lower and upper bound of integration range.

Returns
energy_flux, energy_flux_errtuple of Quantity

Energy flux and energy flux error betwen emin and emax.

static evaluate(energy, index, amplitude, reference)[source]

Evaluate the model (static function).

static evaluate_energy_flux(emin, emax, index, amplitude, reference)[source]

Compute energy flux in given energy range analytically (static function).

\[G(E_{min}, E_{max}) = \int_{E_{min}}^{E_{max}}E \phi(E)dE = \left. \phi_0 \frac{E_0^2}{-\Gamma + 2} \left( \frac{E}{E_0} \right)^{-\Gamma + 2} \right \vert _{E_{min}}^{E_{max}}\]
Parameters
emin, emaxQuantity

Lower and upper bound of integration range.

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.

static evaluate_integral(emin, emax, index, amplitude, reference)[source]

Integrate power law analytically (static function).

\[F(E_{min}, E_{max}) = \int_{E_{min}}^{E_{max}}\phi(E)dE = \left. \phi_0 \frac{E_0}{-\Gamma + 1} \left( \frac{E}{E_0} \right)^{-\Gamma + 1} \right \vert _{E_{min}}^{E_{max}}\]
Parameters
emin, emaxQuantity

Lower and upper bound of integration range

classmethod from_dict(data)
classmethod from_parameters(parameters, **kwargs)

Create model from parameter list

Parameters
parametersParameters

Parameters for init

Returns
modelModel

Model instance

integral(emin, emax, **kwargs)

Integrate spectral model numerically if no analytical solution defined.

\[F(E_{min}, E_{max}) = \int_{E_{min}}^{E_{max}} \phi(E) dE\]
Parameters
emin, emaxQuantity

Lower and upper bound of integration range.

**kwargsdict

Keyword arguments passed to integrate_spectrum()

integral_error(emin, emax)

Evaluate the error of the integral flux of a given spectrum in a given energy range.

Parameters
emin, emaxQuantity

Lower and upper bound of integration range.

Returns
flux, flux_errtuple of Quantity

Integral flux and flux error betwen emin and emax.

inverse(value)[source]

Return energy for a given function value of the spectral model.

Parameters
valueQuantity

Function value of the spectral model.

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

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