def periodogram(x, rv, f, max_period):
'''
Computes a Lomb-Scargle Periodogram of the input RV data.
This was adapted from Jake Vanderplas' article "Fast Lomb-Scargle Periodograms in Python."
Parameters
----------
x : list
The times at which the data points were gathered.
rv : list
The values of the measurand at the corresponding time, x.
f : float
The number of samples to take over the interval.
max_period : float
The maximum of the interval of periods to check.
Returns
-------
periods : array_like[len(f)]
Equally spaced array of possible period values.
powers : array_like[len(f)]
The calculated Power values over the range of periods,
these form the normalized Lomb-Scargle Periodogram.
delta_x : float
The smallest separation between two values in x.
'''
from scipy.signal import lombscargle
# Sort the time data chronologically.
x = np.sort(np.array(x))
rv = np.array(rv)
# Start delta_x very large
delta_x = np.inf
# Iteratively lower delta_x
for i in range(0, len(x)-2):
if x[i+1]-x[i] < delta_x and x[i+1]-x[i] != 0:
delta_x = x[i+1]-x[i]
# Compute the periodogram
periods = np.linspace(delta_x, max_period, num = f)
ang_freqs = 2 * pi / periods
powers = lombscargle(x, rv - rv.mean(), ang_freqs)
powers *= 2 / (len(x) * rv.std() ** 2)
return periods, powers, delta_x
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