PowerLawSpectralModel#
- class gammapy.modeling.models.PowerLawSpectralModel(**kwargs)[source]#
Bases:
SpectralModel
Spectral power-law model.
For more information see Power law spectral model.
- Parameters:
Attributes Summary
A model parameter.
Frozen status of a model, True if all parameters are frozen.
A model parameter.
Whether model is a norm spectral model.
Parameters as a
Parameters
object.The pivot or decorrelation energy is defined as:
A model parameter.
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, amplitude, reference)Evaluate the model (static function).
evaluate_energy_flux
(energy_min, energy_max, ...)Compute energy flux in given energy range analytically (static function).
evaluate_error
(energy[, epsilon])Evaluate spectral model with error propagation.
evaluate_integral
(energy_min, energy_max, ...)Integrate power law analytically (static function).
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, *args)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
- 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
ormin
andmax
properties and consider the fact that there is afactor`
andscale
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
andfactor_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).
- unit
Unit
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
andscale
.- interp{“lin”, “sqrt”, “log”}
Parameter scaling to use for the scan.
- is_normbool
Whether the parameter represents the flux norm of the model.
- prior
Prior
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
ormin
andmax
properties and consider the fact that there is afactor`
andscale
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
andfactor_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).
- unit
Unit
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
andscale
.- interp{“lin”, “sqrt”, “log”}
Parameter scaling to use for the scan.
- is_normbool
Whether the parameter represents the flux norm of the model.
- prior
Prior
Prior set on the parameter.
- is_norm_spectral_model#
Whether model is a norm spectral model.
- parameters#
Parameters as a
Parameters
object.
- parameters_unique_names#
- pivot_energy#
The pivot or 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
- Returns:
- pivot energy
Quantity
If no minimum is found, NaN will be returned.
- pivot energy
- 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
ormin
andmax
properties and consider the fact that there is afactor`
andscale
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
andfactor_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).
- unit
Unit
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
andscale
.- interp{“lin”, “sqrt”, “log”}
Parameter scaling to use for the scan.
- is_normbool
Whether the parameter represents the flux norm of the model.
- prior
Prior
Prior set on the parameter.
- tag = ['PowerLawSpectralModel', 'pl']#
- 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_max
Quantity
Lower and upper bound of integration range.
- **kwargsdict
Keyword arguments passed to
integrate_spectrum()
.
- energy_min, energy_max
- 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_max
Quantity
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.
- energy_min, energy_max
- Returns:
- energy_flux, energy_flux_errtuple of
Quantity
Energy flux and energy flux error between energy_min and energy_max.
- energy_flux, energy_flux_errtuple of
- static evaluate_energy_flux(energy_min, energy_max, 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:
- energy_min, energy_max
Quantity
Lower and upper bound of integration range.
- energy_min, energy_max
- evaluate_error(energy, epsilon=0.0001)#
Evaluate spectral model with error propagation.
- static evaluate_integral(energy_min, energy_max, 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:
- energy_min, energy_max
Quantity
Lower and upper bound of integration range.
- energy_min, energy_max
- freeze()#
Freeze all parameters.
- classmethod from_dict(data, **kwargs)#
- classmethod from_parameters(parameters, **kwargs)#
Create model from parameter list.
- Parameters:
- parameters
Parameters
Parameters for init.
- parameters
- Returns:
- model
Model
Model instance.
- model
- 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_max
Quantity
Lower and upper bound of integration range.
- **kwargsdict
Keyword arguments passed to
integrate_spectrum()
.
- energy_min, energy_max
- 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_max
Quantity
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.
- energy_min, energy_max
- Returns:
- flux, flux_errtuple of
Quantity
Integral flux and flux error between energy_min and energy_max.
- flux, flux_errtuple of
- inverse(value, *args)[source]#
Return energy for a given function value of the spectral model.
- Parameters:
- value
Quantity
Function value of the spectral model.
- 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:
- Returns:
- energylist of
Quantity
Each element contains the energies at which the model has corresponding value of
values
.
- energylist of
- 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_bounds
Quantity
, list ofQuantity
orMapAxis
Energy bounds between which the model is to be plotted. Or an axis defining the energy bounds between which the model is to be plotted.
- ax
Axes
, 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
.
- energy_bounds
- Returns:
- ax
Axes
, optional Matplotlib axes.
- ax
Notes
If
energy_bounds
is supplied as a list, tuple, or Quantity, anenergy_axis
is created internally withn_points
bins between the given bounds.
- 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')
andax.set_xscale("log", nonposx='clip')
to create a log-log representation. The additional argumentnonposx='clip'
avoids artefacts in the plot, when the error band extends to negative values (see also matplotlib/matplotlib#8623).When you call
plt.loglog()
orplt.semilogy()
explicitly in your plotting code and the error band extends to negative values, it is not shown correctly. To circumvent this issue also useplt.loglog(nonposx='clip', nonpositive='clip')
orplt.semilogy(nonpositive='clip')
.- Parameters:
- energy_bounds
Quantity
, list ofQuantity
orMapAxis
Energy bounds between which the model is to be plotted. Or an axis defining the energy bounds between which the model is to be plotted.
- ax
Axes
, 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
.
- energy_bounds
- Returns:
- ax
Axes
, optional Matplotlib axes.
- ax
Notes
If
energy_bounds
is supplied as a list, tuple, or Quantity, anenergy_axis
is created internally withn_points
bins between the given bounds.
- 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:
- model
Model
Reassigned model.
- model
- reference_fluxes(energy_axis)#
Get reference fluxes for a given energy axis.
- Parameters:
- energy_axis
MapAxis
Energy axis.
- energy_axis
- Returns:
- fluxesdict of
Quantity
Reference fluxes.
- fluxesdict of
- spectral_index(energy, epsilon=1e-05)#
Compute spectral index at given energy.
- Parameters:
- energy
Quantity
Energy at which to estimate the index.
- epsilonfloat, optional
Fractional energy increment to use for determining the spectral index. Default is 1e-5.
- energy
- Returns:
- indexfloat
Estimated spectral index.
- spectral_index_error(energy, epsilon=1e-05)#
Evaluate the error on spectral index at the given energy.
- Parameters:
- energy
Quantity
Energy at which to estimate the index.
- epsilonfloat, optional
Fractional energy increment to use for determining the spectral index. Default is 1e-5.
- energy
- 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.