def _compute_thresholds(t,
y,
dy,
omegas,
confidence=None,
nbootstraps=1000):
"""
Determine periodicity significance thresholds. Thresholds are obtained by repeatedly subsampling data, then compiling a distribution of maximum power levels detected in each sample.
Args:
t (np.ndarray) - timepoints
y (np.ndarray) - values
dy (np.ndarray) - estimated measurement error
omega (np.ndarray) - spectral frequencies tests
confidence (array like) - confidence levels to assess, length C
nbootstraps (int) - number of boostrap samples
Returns:
thresholds (np.ndarray) - spectral power thresholds, length C
"""
if confidence is None:
confidence = [95, 99, 99.9]
# get seed for random state
seed = np.random.randint(0, 1000)
# assemble spectral powers for null models (random subsamples)
null_ps = lomb_scargle_bootstrap(t,
y,
dy,
omegas,
generalized=True,
N_bootstraps=nbootstraps,
random_state=seed)
# compute significance thresholds
thresholds = {c: np.percentile(null_ps, c) for c in confidence}
return thresholds
def get_period_sigf(jd, mag, mag_e): #parameters: time, mag, mag error
omega = frequency_grid(0.1, 1850) # grid of frequencies
p = lomb_scargle(
jd, mag, mag_e, omega,
generalized=True) # Lomb-Scargle power associated to omega
peak = max(p) #power associated with best_period
best_period = LS_peak_to_period(omega,
p) #estimates a period from periodogram
# Get significance via bootstrap
D = lomb_scargle_bootstrap(jd,
mag,
mag_e,
omega,
generalized=True,
N_bootstraps=1000,
random_state=0)
sig1, sig5 = np.percentile(
D, [99, 95]) # 95% and 99% confidence, to compare with peak
return best_period, peak, sig5, sig1
omega = np.linspace(17, 22, 1000)
# Notice the typo: we used y rather than y_obs
if typo is True:
P_S = lomb_scargle(t, y, dy, omega, generalized=False)
P_G = lomb_scargle(t, y, dy, omega, generalized=True)
else:
P_S = lomb_scargle(t, y_obs, dy, omega, generalized=False)
P_G = lomb_scargle(t, y_obs, dy, omega, generalized=True)
#------------------------------------------------------------
# Get significance via bootstrap
D = lomb_scargle_bootstrap(t,
y_obs,
dy,
omega,
generalized=True,
N_bootstraps=1000,
random_state=0)
sig1, sig5 = np.percentile(D, [99, 95])
#------------------------------------------------------------
# Plot the results
fig = plt.figure(figsize=(5, 3.75))
# First panel: input data
ax = fig.add_subplot(211)
ax.errorbar(t, y_obs, dy, fmt='.k', lw=1, ecolor='gray')
ax.plot([-2, 32], [10, 10], ':k', lw=1)
ax.set_xlim(-2, 32)
P = 0.3
t = np.random.randint(100, size=N) + 0.3 + 0.4 * np.random.random(N)
y = 10 + np.sin(2 * np.pi * t / P)
dy = 0.5 + 0.5 * np.random.random(N)
y_obs = np.random.normal(y, dy)
#------------------------------------------------------------
# Compute periodogram
period = 10 ** np.linspace(-1, 0, 10000)
omega = 2 * np.pi / period
PS = lomb_scargle(t, y_obs, dy, omega, generalized=True)
#------------------------------------------------------------
# Get significance via bootstrap
D = lomb_scargle_bootstrap(t, y_obs, dy, omega, generalized=True,
N_bootstraps=1000, random_state=0)
sig1, sig5 = np.percentile(D, [99, 95])
#------------------------------------------------------------
# Plot the results
fig = plt.figure()
fig.subplots_adjust(left=0.1, right=0.9, hspace=0.25)
# First panel: the data
ax = fig.add_subplot(211)
ax.errorbar(t, y_obs, dy, fmt='.k', lw=1, ecolor='gray')
ax.set_xlabel('time (days)')
ax.set_ylabel('flux')
ax.set_xlim(-5, 105)
# Second panel: the periodogram & significance levels
# compute upper flux limit and plot as arrow or triangle
upperlim2 = np.append(upperlim2,
zp2[i] - 2.5 * np.log10(snu * sigflux2[i]))
upperlim2date = np.append(upperlim2date, mjd1[i])
#------------------------------------------------------------
# Compute periodogram
period = np.linspace(1, 50, 100000)
omega = 2 * np.pi / period
#PS = lomb_scargle(t, y_obs, dy, omega, generalized=True)
PS = lomb_scargle(mag1date, mag1, mag1sig, omega, generalized = True)
#------------------------------------------------------------
# Get significance via bootstrap
D = lomb_scargle_bootstrap(mag1date, mag1, mag1sig, omega, generalized = True,
N_bootstraps=500, random_state=0)
sig1, sig5 = np.percentile(D, [99, 95])
#------------------------------------------------------------
# Plot the results
fig = plt.figure(figsize=(5, 3.75))
fig.subplots_adjust(left=0.1, right=0.9, hspace=0.25)
# First panel: the data
ax = fig.add_subplot(211)
ax.errorbar(mag1date, mag1, mag1sig, fmt='.k', lw=1, ecolor='gray')
ax.set_xlabel('time (days)')
ax.set_ylabel('flux')
ax.set_xlim(mag1date[0] - 50, mag1date[-1] + 50)
ax.set_ylim(16, max(mag1) + 0.5)