def test_zn(self):
"""Test pulse phase calculation, frequency only."""
ph = np.array([0, 1])
np.testing.assert_array_almost_equal(z_n(ph), 8)
ph = np.array([])
np.testing.assert_array_almost_equal(z_n(ph), 0)
ph = np.array([0.2, 0.7])
ph2 = np.array([0, 0.5])
np.testing.assert_array_almost_equal(z_n(ph), z_n(ph2))
def test_zn(self):
"""Test pulse phase calculation, frequency only."""
ph = np.array([0, 1])
np.testing.assert_array_almost_equal(z_n(ph), 8)
ph = np.array([])
np.testing.assert_array_almost_equal(z_n(ph), 0)
ph = np.array([0.2, 0.7])
ph2 = np.array([0, 0.5])
np.testing.assert_array_almost_equal(z_n(ph), z_n(ph2))
def get_z2_label(phas, prof):
good = phas < 1
z2 = z_n(phas[good], n=2, norm=prof[good])
z2_detlev = z2_n_detection_level(n=2)
z2_label = r'$Z_2^2 = {:.1f} (90\% det. lev. {:.1f})$'.format(
z2, z2_detlev)
return z2_label
def pulsar_events_mp(length,
period,
ctrate,
pulsed_fraction,
mean_obs,
bkg_ctrate,
detlev,
nbin=128):
nustar_orb = 5808
dt = period / 20
# The total length of the time series should be the number of pointings times the time per orbit.
# Add one orbit for buffer.
N_orb = int(round(length / mean_obs, 0))
tot_len = (N_orb + 1) * nustar_orb
# The orbital period is 5808s. Every 5808s, a continuous observation with min_obs < length < max_obs begins
start_t = numpy.multiply(
numpy.arange(N_orb),
numpy.random.normal(loc=nustar_orb, scale=60, size=N_orb))
point_t = numpy.random.uniform(low=mean_obs - 500,
high=mean_obs + 500,
size=N_orb)
end_t = numpy.add(start_t, point_t)
times = numpy.arange(dt / 2, tot_len + dt / 2, dt)
cont_lc = numpy.random.poisson(
(ctrate *
(1 + pulsed_fraction * numpy.cos(2 * numpy.pi / period * times)) *
dt)) + numpy.random.poisson(bkg_ctrate * dt)
lc = Lightcurve(time=times,
counts=cont_lc,
gti=numpy.column_stack((start_t, end_t)),
dt=dt)
exposure = numpy.sum(point_t)
events = EventList()
events.gti = lc.gti
events.simulate_times(lc)
phase = numpy.arange(0, 1, 1 / nbin)
zsq = z_n(phase,
n=2,
norm=fold_events(events.time, 1 / period, nbin=nbin)[1])
detected = zsq > detlev
return (detected, exposure)
def test_zn_2(self):
np.testing.assert_almost_equal(z_n(np.arange(1), n=1, norm=1), 2)
np.testing.assert_almost_equal(z_n(np.arange(1), n=2, norm=1), 4)
np.testing.assert_almost_equal(z_n(np.arange(2), n=2, norm=1), 8)
np.testing.assert_almost_equal(z_n(np.arange(2) + 0.5, n=2, norm=1), 8)
def test_zn_2(self):
np.testing.assert_almost_equal(z_n(np.arange(1), n=1, norm=1), 2)
np.testing.assert_almost_equal(z_n(np.arange(1), n=2, norm=1), 4)
np.testing.assert_almost_equal(z_n(np.arange(2), n=2, norm=1), 8)
np.testing.assert_almost_equal(z_n(np.arange(2)+0.5, n=2, norm=1), 8)
def efold_search_AandB(events_A,
events_B,
f_min,
f_max,
f_steps,
fdots=None,
time_intervals=None,
nbin=32,
pi_min=35,
pi_max=260,
return_peak=False,
z_n=2):
# Scan over frequency and do epoch folding.
A_mask = np.sqrt(
np.square(events_A.x - events_A.centroid[0]) +
np.square(events_A.y - events_A.centroid[1])) <= events_A.radius
B_mask = np.sqrt(
np.square(events_B.x - events_B.centroid[0]) +
np.square(events_B.y - events_B.centroid[1])) <= events_B.radius
temp_time = np.concatenate([events_A.time[A_mask], events_B.time[B_mask]])
sorted_arg = np.argsort(temp_time)
temp_time = temp_time[sorted_arg]
temp_pi = np.concatenate([events_A.pi[A_mask],
events_B.pi[B_mask]])[sorted_arg]
joined_ev = EventList_ext(time=temp_time,
gti=sting_gti.cross_two_gtis(
events_A.gti, events_B.gti),
pi=temp_pi)
ref_time = joined_ev.time[0]
f_arr = np.linspace(f_min, f_max, num=f_steps)
# if fdots:
# fgrid, fdgrid, z_stats = z_n_search(joined_ev.time, f_arr, nharm=z_n, nbin=nbin, gti=joined_ev.gti, fdots=fdots, segment_size=1e6)
# else:
# fgrid, z_stats = z_n_search(joined_ev.time, f_arr, nharm=z_n, nbin=nbin, gti=joined_ev.gti, fdots=fdots, segment_size=1e6)
pi_mask = ((joined_ev.pi > pi_min) * (joined_ev.pi < pi_max)).astype(bool)
# The times to actually fold into a profile
fold_times = joined_ev.time[pi_mask] - ref_time
z_stats = []
if fdots is not None:
f_grid, fd_grid = np.meshgrid(f_arr, fdots)
z_stats = np.zeros(f_grid.shape)
for x in tqdm(range(f_steps)):
for y in range(len(fdots)):
# The phase of each folded event
fold_phases = plsr.pulse_phase(fold_times,
*[f_grid[y, x], fd_grid[y, x]])
z_stats[y, x] = plsr.z_n(fold_phases, n=z_n)
z_prob = stats.z2_n_logprobability(z_stats,
ntrial=(f_steps * len(fdots)),
n=z_n)
if return_peak:
max_yx = np.unravel_index(np.argmax(z_stats, axis=None),
z_stats.shape)
phase_bins, profile, profile_err, _ = \
joined_ev.fold_events(*[f_grid[max_yx], fd_grid[max_yx]], time_intervals = time_intervals, \
nbin = nbin, ref_time = ref_time, region_filter=False, pi_min=pi_min, pi_max=pi_max, weight_pos=False, z_n=z_n)
return f_grid, fd_grid, z_prob, z_stats, phase_bins, profile, profile_err
else:
return f_grid, fd_grid, z_prob, z_stats
else:
for f in tqdm(f_arr):
# The phase of each folded event
fold_phases = plsr.pulse_phase(fold_times, f)
z_stat = plsr.z_n(fold_phases, n=z_n)
# _, _, _, z_stat = \
# joined_ev.fold_events(f, time_intervals = time_intervals, \
# nbin = nbin, ref_time = joined_ev.time[0], region_filter=False, pi_min=pi_min, pi_max=pi_max, weight_pos=False, z_n=z_n)
z_stats.append(z_stat)
z_stats = np.array(z_stats)
z_prob = stats.z2_n_logprobability(z_stats, ntrial=len(f_arr), n=z_n)
if return_peak:
phase_bins, profile, profile_err, _ = \
joined_ev.fold_events(f_arr[np.argmax(z_stats)], time_intervals = time_intervals, \
nbin = nbin, ref_time = ref_time, region_filter=False, pi_min=pi_min, pi_max=pi_max, weight_pos=False, z_n=z_n)
return f_arr, z_prob, z_stats, phase_bins, profile, profile_err
else:
return f_arr, z_prob, z_stats
def fold_events(self,
*frequency_derivatives,
time_intervals=None,
pi_min=35,
pi_max=1909,
region_filter=False,
centroid=None,
radius=None,
ref_time=None,
nbin=64,
weights=1,
gtis=None,
expocorr=False,
weight_pos=False,
z_n=2):
# Epoch folding without livetime correction.
# Includes region and energy filtering, position weighting, and custom weighting.
if region_filter or weight_pos:
if centroid == None:
centroid = self.centroid
if radius == None:
radius = self.radius
if time_intervals == None:
time_intervals = [[self.time[0], self.time[-1]]]
if ref_time == None:
ref_time = self.time[0]
if gtis == None:
gtis = self.gti
time_mask = np.zeros(np.shape(self.time))
if np.shape(time_intervals)[-1] != 2:
print('The array of time intervals has the wrong shape')
return None
for interval in time_intervals:
start_time, end_time = interval
if (start_time < np.min(self.time)):
print('Invalid start time')
return None
elif (end_time > np.max(self.time)):
print('Invalid end time')
return None
time_mask = time_mask + ((self.time >= start_time) *
(self.time <= end_time))
time_mask = time_mask.astype(bool)
pi_mask = ((self.pi > pi_min) * (self.pi < pi_max)).astype(bool)
reg_mask = np.ones(np.shape(self.time)).astype(bool)
p_weights = 1.0
if region_filter:
# if weight_pos:
# print('Region filtering overrides position weighting.')
reg_mask = (np.sqrt(
np.square(self.x - centroid[0]) +
np.square(self.y - centroid[1])) < radius).astype(bool)
elif weight_pos:
# print('Make sure you have called set_xy_weights')
p_weights = self.xy_weights[time_mask * pi_mask * reg_mask]
# print([g.x_mean, g.y_mean, g.amplitude, g.x_stddev, g.y_stddev])
# The times to actually fold into a profile
fold_times = self.time[time_mask * pi_mask * reg_mask]
# The phase of each folded event
fold_phases = plsr.pulse_phase(fold_times, *frequency_derivatives)
phase_bins, profile, profile_err = plsr.fold_events(fold_times, *frequency_derivatives, ref_time=ref_time, \
nbin=nbin, weights=weights * p_weights, gtis=gtis, expocorr=expocorr)
z_stat = plsr.z_n(fold_phases, n=z_n, norm=weights * p_weights)
return phase_bins, profile, profile_err, z_stat
def fold_events_ltcorr(self, *frequency_derivatives, time_intervals= None, pi_min=35, pi_max=1909, \
region_filter=False, centroid = None, radius=None, ref_time=None, nbin = 64, weights = 1, gtis = None, expocorr=False, weight_pos=False):
# Do Epoch folding to look for pulsations while also correction for livetime variations. This is important for high count rates and high pulse fractions.
# Includes region and energy filtering, position weighting, and custom weighting.
if centroid == None:
centroid = self.centroid
if radius == None:
radius = self.radius
if time_intervals == None:
time_intervals = [[self.time[0], self.time[-1]]]
if ref_time == None:
ref_time = self.time[0]
if gtis == None:
gtis = self.gti
time_mask = np.zeros(np.shape(self.time))
if np.shape(time_intervals)[-1] != 2:
print('The array of time intervals has the wrong shape')
return None
for interval in time_intervals:
start_time, end_time = interval
if (start_time < np.min(self.time)):
print('Invalid start time')
return None
elif (end_time > np.max(self.time)):
print('Invalid end time')
return None
time_mask = time_mask + ((self.time >= start_time) *
(self.time <= end_time))
time_mask = time_mask.astype(bool)
pi_mask = ((self.pi > pi_min) * (self.pi < pi_max)).astype(bool)
reg_mask = np.ones(np.shape(self.time)).astype(bool)
p_weights = 1.0
if region_filter:
if weight_pos:
print('Region filtering overrides position weighting.')
reg_mask = (np.sqrt(
np.square(self.x - centroid[0]) +
np.square(self.y - centroid[1])) < radius).astype(bool)
elif weight_pos:
# print('Make sure you have called set_xy_weights')
p_weights = self.xy_weights[time_mask * pi_mask * reg_mask]
# print([g.x_mean, g.y_mean, g.amplitude, g.x_stddev, g.y_stddev])
# The times to actually fold into a profile
fold_times = self.time[time_mask * pi_mask * reg_mask]
# The phase of each folded event
fold_phases = plsr.pulse_phase(fold_times, *frequency_derivatives)
# We should use PRIOR from every event though
temp_times = self.time[time_mask]
temp_prior = self.prior[time_mask]
temp_phases = plsr.pulse_phase(temp_times, *frequency_derivatives)
# print(frequency_derivatives)
p_derivs = plsr.p_to_f(*frequency_derivatives)
p_t = np.zeros(np.shape(temp_times))
# Taylor expand P(t)
for i in range(len(p_derivs)):
p_t = p_t + (p_derivs[i] * np.power(temp_times - ref_time, i) /
scipy.special.factorial(i, exact=True))
phase_bins, profile, profile_err = plsr.fold_events(fold_times, *frequency_derivatives, ref_time=ref_time, \
nbin=nbin, weights=weights * p_weights, gtis=gtis, expocorr=expocorr)
livetime_profile = np.zeros(np.shape(profile))
# During which phase bin did PRIOR start counting before each event?
start_bins = np.floor(nbin * (temp_phases - (temp_prior / p_t)))
# What phase bin is each event at?
end_bins = np.floor(nbin * temp_phases)
# Add 1 to every phase bin for which PRIOR was active.
for i in range(len(start_bins)):
start = start_bins[i]
end = end_bins[i]
# print(start)
# If PRIOR started counting in a previous cycle, add 1 to each full cycle and to the partial cycles
if start < 0:
for j in range(int(np.floor(np.abs(start) / nbin))):
livetime_profile = livetime_profile + 1
livetime_profile[int(start %
nbin):] = livetime_profile[int(start %
nbin):] + 1
livetime_profile[:int(end)] = livetime_profile[:int(end)] + 1
# Else, just add 1 to the portion of this cycle during which PRIOR was counting
else:
livetime_profile[int(start):int(
end)] = livetime_profile[int(start):int(end)] + 1
# livetime corresponding to the phase bin for each photon
fold_lts = np.array(
[livetime_profile[int(b)] for b in np.floor(nbin * fold_phases)])
z_stat = plsr.z_n(fold_phases,
n=2,
norm=weights * p_weights * np.max(livetime_profile) /
fold_lts)
# livetime_profile = livetime_profile/np.max(livetime_profile)
return phase_bins, profile, profile_err, livetime_profile, z_stat