def analytical_butterfly(self):
"""Calculate butterfly analytically
Disclaimer: Only available for PowerLaw assuming no correlation
Returns
-------
x : float
Energy array [TeV]
butterfly : float
Butterfly
"""
from gammapy.spectrum import df_over_f
if self.spectral_model is not 'PowerLaw':
raise NotImplementedError('Analytical butterfly calculation'
'not implemented for model {}'.format(
self.spectral_model))
x_min = np.log10(self.fit_range[0].value)
x_max = np.log10(self.fit_range[1].value)
x = np.logspace(x_min, x_max, 1000) * self.energy_range.unit
x = x.to('TeV').value
e0 = self.parameters.reference.to('TeV').value
f0 = self.parameters.norm.to('cm-2 s-1 TeV-1').value
df0 = self.parameter_errors.norm.to('cm-2 s-1 TeV-1').value
dg = self.parameter_errors.index.value
cov = 0
butterfly = df_over_f(x, e0, f0, df0, dg, cov) * y
return x, butterfly
def plot_fit_function(self, ax=None, butterfly=True, energy_unit='TeV',
flux_unit='cm-2 s-1 TeV-1', e_power=0, **kwargs):
"""Plot fit function
kwargs are forwarded to :func:`~matplotlib.pyplot.errorbar`
Parameters
----------
ax : `~matplolib.axes`, optional
Axis
energy_unit : str, `~astropy.units.Unit`, optional
Unit of the energy axis
flux_unit : str, `~astropy.units.Unit`, optional
Unit of the flux axis
e_power : int
Power of energy to multiply flux axis with
Returns
-------
ax : `~matplolib.axes`, optional
Axis
"""
import matplotlib.pyplot as plt
from gammapy.spectrum import df_over_f
ax = plt.gca() if ax is None else ax
func = self.to_sherpa_model()
x_min = np.log10(self.energy_range[0].value)
x_max = np.log10(self.energy_range[1].value)
x = np.logspace(x_min, x_max, 10000) * self.energy_range.unit
y = func(x.to('keV').value) * Unit('cm-2 s-1 keV-1')
# Todo: Find better solution
if butterfly:
e = x.to('TeV').value
e0 = self.parameters.reference.to('TeV').value
f0 = self.parameters.norm.to('cm-2 s-1 TeV-1').value
df0 = self.parameter_errors.norm.to('cm-2 s-1 TeV-1').value
dg = self.parameter_errors.index.value
cov = 0
e = df_over_f(e, e0, f0, df0, dg, cov) * y
else:
e = np.zeros(shape=x.shape()) * Unit(flux_unit)
x = x.to(energy_unit).value
y = y.to(flux_unit).value
e = e.to(flux_unit).value
y, e = np.asarray([y, e]) * np.power(x, e_power)
flux_unit = Unit(flux_unit) * np.power(Unit(energy_unit), e_power)
ax.errorbar(x, y, yerr=e, **kwargs)
ax.set_xlabel('Energy [{}]'.format(energy_unit))
ax.set_ylabel('Flux [{}]'.format(flux_unit))
return ax
def _eval_butterfly_analytical(self, x):
"""Evaluate butterfly using hard-coded formulas"""
if self.spectral_model == 'PowerLaw':
from gammapy.spectrum import df_over_f
f = self.evaluate(x)
x = x.to('TeV').value
e0 = self.parameters.reference.to('TeV').value
f0 = self.parameters.norm.to('cm-2 s-1 TeV-1').value
df0 = self.parameter_errors.norm.to('cm-2 s-1 TeV-1').value
dg = self.parameter_errors.index.value
# TODO: Fix this!
cov = 0
df_over_f = df_over_f(x, e0, f0, df0, dg, cov)
val = df_over_f * f
# Errors are symmetric
return (val, val)
else:
raise NotImplementedError('Analytical butterfly calculation'
' not implemented for model {}'.format(
self.spectral_model))
def _eval_butterfly_analytical(self, x):
"""Evaluate butterfly using hard-coded formulas"""
if self.spectral_model == 'PowerLaw':
from gammapy.spectrum import df_over_f
f = self.evaluate(x)
x = x.to('TeV').value
e0 = self.parameters.reference.to('TeV').value
f0 = self.parameters.norm.to('cm-2 s-1 TeV-1').value
df0 = self.parameter_errors.norm.to('cm-2 s-1 TeV-1').value
dg = self.parameter_errors.index.value
# TODO: Fix this!
cov = 0
df_over_f = df_over_f(x, e0, f0, df0, dg, cov)
val = df_over_f * f
# Errors are symmetric
return (val, val)
else:
raise NotImplementedError('Analytical butterfly calculation'
' not implemented for model {}'.format(
self.spectral_model))
