def draw_time_grid(color='blue'):
"""
"""
times = [3600., 3600.*24., 3600.*24.*7.]
labels = ['1 hour', '1 day', '1 week']
for t, l in zip(times, labels):
plt.axvline(t, linestyle='dashed', color=color)
ymin, ymax = plt.gca().get_ylim()
y = ymin + 1.05*(ymax - ymin)
plt.text(t, y, l, ha='center', color=color)
def draw_time_grid(color='blue'):
"""
"""
times = [3600., 3600. * 24., 3600. * 24. * 7.]
labels = ['1 hour', '1 day', '1 week']
for t, l in zip(times, labels):
plt.axvline(t, linestyle='dashed', color=color)
ymin, ymax = plt.gca().get_ylim()
y = ymin + 1.05 * (ymax - ymin)
plt.text(t, y, l, ha='center', color=color)
def _plot_vslice(energy, position):
"""Convenience function to plot a generic vertical slice of the
energy dispersion.
"""
ax = plt.subplot(2, 2, position)
vslice = self.matrix.vslice(energy)
vslice.plot(overlay=False, show=False)
plt.text(0.1, 0.9, '$E = %.2f\\ \\rm{keV}$' % energy,
transform=ax.transAxes)
ppf = vslice.build_ppf()
eres = 0.5*(ppf(0.8413) - ppf(0.1586))/ppf(0.5)
plt.text(0.1, 0.85, '$\sigma_E/E = %.3f$' % eres,
transform=ax.transAxes)
def _plot_vslice(energy, position):
"""Convenience function to plot a generic vertical slice of the
energy dispersion.
"""
ax = plt.subplot(2, 2, position)
vslice = self.matrix.vslice(energy)
vslice.plot(overlay=False, show=False)
plt.text(0.1,
0.9,
'$E = %.2f\\ \\rm{keV}$' % energy,
transform=ax.transAxes)
ppf = vslice.build_ppf()
eres = 0.5 * (ppf(0.8413) - ppf(0.1586)) / ppf(0.5)
plt.text(0.1,
0.85,
'$\sigma_E/E = %.3f$' % eres,
transform=ax.transAxes)
def plot(self, show=False, stat=True, text_size=15, **options):
"""Plot the fit results.
"""
from ximpol.utils.matplotlib_ import pyplot as plt
_x = numpy.linspace(0., 2*numpy.pi, 100)
_y = xAzimuthalResponseGenerator.fit_function(_x, *self.popt)
plt.plot(_x, _y, **options)
if stat:
posh = 0.02
posv = 0.25
delv = 0.07
for text in self.latex().split(','):
text = text.strip()
plt.text(posh, posv, text, transform=plt.gca().transAxes,
fontsize=text_size)
posv -= delv
if show:
plt.show()
def plot(self, show=False, stat=True, text_size=15, **options):
"""Plot the fit results.
"""
from ximpol.utils.matplotlib_ import pyplot as plt
_x = numpy.linspace(0., 2*numpy.pi, 100)
_y = xAzimuthalResponseGenerator.fit_function(_x, *self.popt)
plt.plot(_x, _y, **options)
if stat:
posh = 0.02
posv = 0.25
delv = 0.07
for text in self.latex().split(','):
text = text.strip()
plt.text(posh, posv, text, transform=plt.gca().transAxes,
fontsize=text_size)
posv -= delv
if show:
plt.show()
def plot_bin(self, i, show=True, fit=True):
"""Plot the azimuthal distribution for the i-th energy slice.
"""
_emin = self.emin[i]
_emax = self.emax[i]
_emean = self.emean[i]
label = '%.2f-%.2f $<$%.2f$>$ keV' % (_emin, _emax, _emean)
plt.errorbar(self.phi_x, self.phi_y[i], yerr=numpy.sqrt(self.phi_y[i]),
fmt='o')
if fit:
fit_results = self.fit_bin(i)
fit_results.plot(label=label)
plt.axis([0., 2*numpy.pi, 0.0, 1.2*self.phi_y[i].max()])
plt.xlabel('Azimuthal angle [rad]')
plt.ylabel('Counts/bin')
plt.text(0.02, 0.92, label, transform=plt.gca().transAxes,
fontsize=15)
if show:
plt.show()
def view(self, show=True):
"""Plot the energy dispersion.
"""
from ximpol.utils.matplotlib_ import pyplot as plt
plt.figure('Energy redistribution')
self.matrix.plot(show=False)
plt.figure('Energy bounds')
self.ebounds.plot(overlay=False, show=False)
energy = 0.5*(self.matrix.xmin() + self.matrix.xmax())
plt.figure('Energy dispersion @ %.2f keV' % energy)
vslice = self.matrix.vslice(energy)
vslice.plot(overlay=False, show=False)
plt.text(0.1, 0.9, '$E = %.2f\\ \\rm{keV}$' % energy,
transform=plt.gca().transAxes)
ppf = vslice.build_ppf()
eres = 0.5*(ppf(0.8413) - ppf(0.1586))/ppf(0.5)
plt.text(0.1, 0.85, '$\sigma_E/E = %.3f$' % eres,
transform=plt.gca().transAxes)
if show:
plt.show()
def plot_pol_map_from_ascii():
output_file = get_output_file()
logger.info('Opening file %s for plotting...' % output_file)
emin,emax, degree, degree_error, angle, angle_error, counts = numpy.loadtxt(output_file, delimiter=',', unpack=True)
_ra = numpy.linspace(ra_min, ra_max, num_points)
_dec = numpy.linspace(dec_min, dec_max, num_points)
_ra, _dec = numpy.meshgrid(_ra, _dec)
fig = plt.figure()
for i in range(len(E_BINNING) - 1):
sigma_array = degree[emin==E_BINNING[i]]/degree_error[emin==E_BINNING[i]]
pol_array = degree[emin==E_BINNING[i]].reshape((num_points,num_points))
sigma_array = sigma_array.reshape((num_points,num_points))
ax1 = fig.add_subplot()
label = 'XIPE %.1d ks'%(DURATION/1000.)
plt.contourf(_ra,_dec,pol_array)
cbar = plt.colorbar()
cbar.ax.set_ylabel('Polarization degree')
plt.text(0.02, 0.92, label, transform=plt.gca().transAxes,
fontsize=20,color='w')
plt.xlabel('RA')
plt.ylabel('DEC')
# fig.gca().add_artist(psf)
plt.show()
ax2 = fig.add_subplot()
plt.contourf(_ra,_dec,sigma_array)
cbar2 = plt.colorbar()
cbar2.ax.set_ylabel('Sigma')
plt.text(0.02, 0.92, label, transform=plt.gca().transAxes,
fontsize=20,color='w')
plt.xlabel('RA')
plt.ylabel('DEC')
plt.show()
def plot_bin(self, i, show=True, fit=True):
"""Plot the azimuthal distribution for the i-th energy slice.
"""
_emin = self.emin[i]
_emax = self.emax[i]
_emean = self.emean[i]
label = '%.2f-%.2f $<$%.2f$>$ keV' % (_emin, _emax, _emean)
plt.errorbar(self.phi_x,
self.phi_y[i],
yerr=numpy.sqrt(self.phi_y[i]),
fmt='o')
if fit:
fit_results = self.fit_bin(i)
fit_results.plot(label=label)
view_range = 1.5 * (self.phi_y[i].max() - self.phi_y[i].min())
view_ymin = self.phi_y[i].min() - view_range
view_ymax = self.phi_y[i].max() + view_range
plt.axis([0., 2 * numpy.pi, view_ymin, view_ymax])
plt.xlabel('Azimuthal angle [rad]')
plt.ylabel('Counts/bin')
plt.text(0.02, 0.92, label, transform=plt.gca().transAxes, fontsize=15)
if show:
plt.show()
numpy.random.seed(10)
_color = numpy.random.random((3, len(blazar_list)))
# numpy.random.seed(1)
# _disp = numpy.random.uniform(0.7, 2., len(blazar_list))
plt.figure("Average polarization degree", (11, 8))
_x = numpy.logspace(-13, -7, 100)
for obs_time in [1.0e3, 10.0e3, 100.0e3, 1.0e6]:
_y = 100.0 * mdp_ref * numpy.sqrt(OBS_TIME_REF / obs_time * FLUX_REF / _x)
plt.plot(_x, _y, color=GRID_COLOR, ls="dashed", lw=0.6)
_i = 51
if obs_time is 1.0e3:
_x_text = _x[_i]
_y_text = _y[_i]
plt.text(_x_text, _y_text, "$T_{obs} =$ %d ks" % (obs_time / 1000.0), color=GRID_COLOR, rotation=-43.0, size=14)
_x_text /= 10
plt.xscale("log")
plt.yscale("log")
plt.xlabel("Integral energy flux %.0f-%.0f keV [erg cm$^{-2}$ s$^{-1}$]" % (E_MIN, E_MAX))
plt.ylabel("MDP 99% CL [%]")
for j, blazar in enumerate(blazar_list):
_x_max = blazar["flux_max"]
_x_min = blazar["flux_min"]
_y_max = blazar["p_opt_max"]
_y_min = blazar["p_opt_min"]
plt.plot([_x_min, _x_max, _x_max], [_y_max, _y_max, _y_min], color=_color[:, j], lw=1.5)
_x_text = numpy.sqrt((_x_max) * (_x_min))
if j in mirror_list:
_y_text = 0.88 * _y_max
def test_power_law_stationary(self):
"""Test a time-independent power law.
This creates a count spectrum with no time dependence, i.e., with
only two (identical) interpolating time points on the auxiliary
(time) axis. The power-law parameters (C and gamma) are constant
>>> tmin = 0.
>>> tmax = 100.
>>> C = 1.
>>> Gamma = 2.
>>>
>>> def powerlaw(E, t):
>>> return C*numpy.power(E, -Gamma)
>>>
>>> _t = numpy.linspace(tmin, tmax, 2)
>>> count_spectrum = xCountSpectrum(powerlaw, self.aeff, _t)
and the underlying xUnivariateAuxGenerator looks like.
.. image:: ../figures/test_power_law_stationary_2d.png
Then a vertical slice (i.e., an interpolated linear spline) is taken
in the middle of the auxiliary axis
>>> tref = 0.5*(tmin + tmax)
>>> ref_slice = count_spectrum.slice(tref)
and the y-values of the spline are compared with the direct product of
the effective area and the input spectrum:
>>> _x = self.aeff.x
>>> _y = C*numpy.power(_x, -Gamma)*self.aeff.y
(Note that in general the two are technically not the same thing, as
going from the count spectrum to the slice we do interpolate in time,
although in this particular case the interpolation is trivial).
If everything goes well, they should be on top of each other.
The figure below is also showing the original power-law spectrum
multiplied by the peak effective area.
.. image:: ../figures/test_power_law_stationary_slice.png
"""
tmin = 0.
tmax = 100.
tref = 0.5*(tmin + tmax)
C = 1.
Gamma = 2.
def powerlaw(E, t):
"""Function defining a time-dependent energy spectrum.
"""
return C*numpy.power(E, -Gamma)
_t = numpy.linspace(tmin, tmax, 2)
count_spectrum = xCountSpectrum(powerlaw, self.aeff, _t)
count_spectrum.plot(show=False)
overlay_tag(color='white')
save_current_figure('test_power_law_stationary_2d.png',
show=self.interactive)
ref_slice = count_spectrum.slice(tref)
_x = self.aeff.x
_y = C*numpy.power(_x, -Gamma)*self.aeff.y.max()
plt.plot(_x, _y, '-', label='Original power-law spectrum')
_y = C*numpy.power(_x, -Gamma)*self.aeff.y
_mask = _y > 0.
_x = _x[_mask]
_y = _y[_mask]
delta = abs((_y - ref_slice(_x))/_y).max()
self.assertTrue(delta < 1e-3, 'max deviation %.9f' % delta)
plt.plot(_x, _y, 'o', label='Direct convolution with aeff')
ref_slice.plot(logx=True, logy=True, show=False,
label='xCountSpectrum output')
overlay_tag()
plt.text(0.1, 0.1, 'Max. difference = %.3e' % delta,
transform=plt.gca().transAxes)
plt.legend(bbox_to_anchor=(0.75, 0.5))
plt.axis([0.6, 10, None, None])
save_current_figure('test_power_law_stationary_slice.png',
show=self.interactive)
def test_power_law_rvs(self, num_events=1000000):
"""Test the generation of event energies from a count power-law
spectrum convoluted with the effective area.
This turned out to be more tricky than we anticipated. Since the
convolution of the source spectrum with the effective area falls
pretty quickly at high energy, there's typically very few events above
a few keV and, as a consequence, the slope of the corresponding ppf is
fairly steep close to one.
.. image:: ../figures/test_power_law_rvs_vppf.png
This implies that the ppf in each slice must be properly sampled
close to 1 (initial tests showed, e.g., that a uniform grid with
100 points between 0 and 1 was not enough to throw meaningful random
numbers for a typical power-law source spectrum). This is particularly
true for soft spectral indices---which is why we picked `Gamma = 3.`
for this test.
.. image:: ../figures/test_power_law_rvs_counts.png
"""
tmin = 0.
tmax = 100.
tref = 0.5*(tmin + tmax)
C = 1.
Gamma = 3.
def powerlaw(E, t):
"""Function defining a time-dependent energy spectrum.
"""
return C*numpy.power(E, -Gamma)
_t = numpy.linspace(tmin, tmax, 2)
count_spectrum = xCountSpectrum(powerlaw, self.aeff, _t)
count_spectrum.vppf.vslice(tref).plot(show=False, overlay=True)
overlay_tag()
save_current_figure('test_power_law_rvs_vppf.png',
show=self.interactive)
ref_slice = count_spectrum.slice(tref)
_time = numpy.full(num_events, tref)
_energy = count_spectrum.rvs(_time)
_binning = numpy.linspace(self.aeff.xmin(), self.aeff.xmax(), 100)
obs, bins, patches = plt.hist(_energy, bins=_binning,
histtype='step', label='Random energies')
plt.yscale('log')
# We want to overlay the reference count-spectrum slice, normalized
# to the total number of events simulated.
bin_width = (bins[1] - bins[0])
scale = num_events*bin_width/ref_slice.norm()
_x = 0.5*(bins[:-1] + bins[1:])
_y = scale*ref_slice(_x)
plt.plot(_x, _y, label='Underlying pdf')
# And, for the chisquare, we do correctly integrate the slice in each
# energy bin, rather than evaluating it at the bin center.
exp = []
scale = num_events/ref_slice.norm()
for _emin, _emax in zip(bins[:-1], bins[1:]):
exp.append(scale*ref_slice.integral(_emin, _emax))
exp = numpy.array(exp)
_mask = exp > 0.
exp = exp[_mask]
obs = obs[_mask]
chi2 = ((exp - obs)**2/exp).sum()
ndof = len(obs)
chi2_min = ndof - 3*numpy.sqrt(2*ndof)
chi2_max = ndof + 3*numpy.sqrt(2*ndof)
self.assertTrue(chi2 > chi2_min, 'chisquare too low (%.2f/%d)' %\
(chi2, ndof))
self.assertTrue(chi2 < chi2_max, 'chisquare too high (%.2f/%d)' %\
(chi2, ndof))
plt.text(0.5, 0.1, '$\chi^2$/ndof = %.2f/%d' % (chi2, ndof),
transform=plt.gca().transAxes)
plt.legend(bbox_to_anchor=(0.85, 0.75))
overlay_tag()
save_current_figure('test_power_law_rvs_counts.png',
show=self.interactive)
def test_power_law_variable(self):
"""Test a time-dependent power law.
This creates a time-dependent count spectrum, where the two parameters
of the underlying power law (C and Gamma) vary linearly with time, in
opposite direction, between 1 and 2.
>>> def C(t):
>>> return 1. + (t - tmin)/(tmax - tmin)
>>>
>>> def Gamma(t):
>>> return 2. - (t - tmin)/(tmax - tmin)
>>>
>>> def powerlaw(E, t):
>>> return C(t)*numpy.power(E, -Gamma(t))
(Beware: this does not mean that you can interpolate linearly between
the two time extremes, as both parameters vary at the same time and
the spectral shape does not evolve linearly with time---we're sampling
the time axis with 100 points).
The underlying xUnivariateAuxGenerator looks like.
.. image:: ../figures/test_power_law_variable_2d.png
Then a vertical slice (i.e., an interpolated linear spline) is taken
in the middle of the auxiliary axis and the y-values of the spline
are compared with the direct product of the effective area and the
count spectrum (evaluated at the same time). If everything goes well,
they should be on top of each other. The figure below is also showing
the orignal power-law spectrum multiplied by the peak effective area.
.. image:: ../figures/test_power_law_variable_slice.png
Finally, we do test the light-curve building by comparing it with the
values from a direct intergration of the vertical slices on a
fixed-spacing grid. Note that, since the normalization increases with
time and the spectral index becomes harder, the light-curve increases
more than linearly.
.. image:: ../figures/test_power_law_variable_lc.png
"""
tmin = 0.
tmax = 100.
tref = 0.5*(tmin + tmax)
def C(t):
"""Time-dependent C---equals to 1 @ tmin and 2 @ tmax.
"""
return 1. + (t - tmin)/(tmax - tmin)
def Gamma(t):
"""Time-dependent C---equals to 2 @ tmin and 1 @ tmax.
"""
return 2. - (t - tmin)/(tmax - tmin)
def powerlaw(E, t):
"""Function defining a time-dependent energy spectrum.
"""
return C(t)*numpy.power(E, -Gamma(t))
_t = numpy.linspace(tmin, tmax, 100)
count_spectrum = xCountSpectrum(powerlaw, self.aeff, _t)
count_spectrum.plot(show=False)
overlay_tag(color='white')
save_current_figure('test_power_law_variable_2d.png',
show=self.interactive)
ref_slice = count_spectrum.slice(tref)
_x = self.aeff.x
_y = self.aeff.y.max()*C(tref)*numpy.power(_x, -Gamma(tref))
plt.plot(_x, _y, '-', label='Original power-law spectrum')
_y = C(tref)*numpy.power(_x, -Gamma(tref))*self.aeff.y
_mask = _y > 0.
_x = _x[_mask]
_y = _y[_mask]
delta = abs((_y - ref_slice(_x))/_y).max()
self.assertTrue(delta < 1e-3, 'max deviation %.9f' % delta)
plt.plot(_x, _y, 'o', label='Direct convolution with aeff')
ref_slice.plot(logx=True, logy=True, show=False,
label='xCountSpectrum output')
overlay_tag()
plt.text(0.1, 0.1, 'Max. difference = %.3e' % delta,
transform=plt.gca().transAxes)
plt.legend(bbox_to_anchor=(0.75, 0.5))
plt.axis([0.6, 10, None, None])
save_current_figure('test_power_law_variable_slice.png',
show=self.interactive)
_x = numpy.linspace(tmin, tmax, 33)
_y = []
for _xp in _x:
_y.append(count_spectrum.slice(_xp).norm())
_y = numpy.array(_y)
plt.plot(_x, _y, 'o', label='Direct integral flux values')
delta = abs((_y - count_spectrum.light_curve(_x))/_y).max()
self.assertTrue(delta < 1e-3, 'max deviation %.9f' % delta)
count_spectrum.light_curve.plot(show=False,
label='xCountSpectrum light-curve')
overlay_tag()
plt.legend(bbox_to_anchor=(0.65, 0.75))
plt.text(0.5, 0.1, 'Max. difference = %.3e' % delta,
transform=plt.gca().transAxes)
save_current_figure('test_power_law_variable_lc.png',
show=self.interactive)
obs_plan_list = parse_obs_plan_list(PRIORITY_ONLY)
mirror_list = [5, 6, 7, 8]
numpy.random.seed(1)
_color = numpy.random.random((3, len(obs_plan_list)))
numpy.random.seed(17)
_disp = numpy.random.uniform(0.9, 1.4, len(obs_plan_list))
plt.figure('Average polarization degree', (14, 10))
_x = numpy.logspace(-13, -7, 100)
for obs_time in [1.e3, 10.e3, 100.e3, 1.e6]:
_y = 100.* mdp_ref * numpy.sqrt(OBS_TIME_REF/obs_time * FLUX_REF/_x)
plt.plot(_x, _y, color=GRID_COLOR, ls='dashed', lw=0.5)
_i = 53
plt.text(_x[_i], _y[_i], '$T_{obs} =$ %d ks' % (obs_time/1000.),
color=GRID_COLOR, rotation=-45.)
plt.xscale('log')
plt.yscale('log')
plt.xlabel('Integral energy flux %.0f-%.0f keV [erg cm$^{-2}$ s$^{-1}$]' %\
(E_MIN, E_MAX))
plt.ylabel('MDP 99% CL [%]')
for j, source in enumerate(obs_plan_list):
_x = source['flux']
_y = source['mdp']*_disp[j]
plt.plot(_x, _y, 'o', color=_color[:,j])
_text = source['name']
if source['notes'] is not '':
_text += '\n' + source['notes']
if j in mirror_list:
_y *= 0.8
