LogParabolaSpectralModel¶

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

Bases: gammapy.modeling.models.SpectralModel

Spectral log parabola model.

For more information see Log Parabola Spectral Model.

Parameters

amplitudeQuantity: \(\phi_0\)
referenceQuantity: \(E_0\)
alphaQuantity: \(\alpha\)
betaQuantity: \(\beta\)

See also

LogParabolaNormSpectralModel

Attributes Summary

`alpha`	A model parameter.
`amplitude`	A model parameter.
`beta`	A model parameter.
`covariance`
`default_parameters`
`e_peak`	Spectral energy distribution peak energy (`Quantity`).
`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.
`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, amplitude, reference, …)	Evaluate the model (static function).
`evaluate_error`(energy[, epsilon])	Evaluate spectral model with error propagation.
`from_dict`(data)
`from_log10`(amplitude, reference, alpha, beta)	Construct from \(log_{10}\) parametrization.
`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)	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.
`spectral_index`(energy[, epsilon])	Compute spectral index at given energy.
`to_dict`([full_output])	Create dict for YAML serialisation

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)

beta¶

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:

\[E_{Peak} = E_{0} \exp{ (2 - \alpha) / (2 * \beta)}\]

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)

tag = ['LogParabolaSpectralModel', 'lp']¶

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(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.

Returns

energy_flux, energy_flux_errtuple of Quantity: Energy flux and energy flux error betwen energy_min and energy_max.

static evaluate(energy, amplitude, reference, alpha, beta)[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.

classmethod from_dict(data)¶

classmethod from_log10(amplitude, reference, alpha, beta)[source]¶: Construct from \(log_{10}\) parametrization.

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)¶

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.

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", 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