```# -*- coding: utf-8 -*-
import numpy as np
import pandas as pd
import scipy.signal

def signal_synchrony(signal1, signal2, method="hilbert", window_size=50):
"""Compute the synchrony (coupling) between two signals.

Compute a continuous index of coupling between two signals either using the 'Hilbert' method to get
the instantaneous phase synchrony, or using rolling window correlation.

The instantaneous phase synchrony measures the phase similarities between signals at each timepoint.
The phase refers to the angle of the signal, calculated through the hilbert transform, when it is
resonating between -pi to pi degrees. When two signals line up in phase their angular difference becomes zero.

For less clean signals, windowed correlations are widely used because of their simplicity, and can
be a good a robust approximation of synchrony between two signals. The limitation is the need to select a window.

Parameters
----------
signal1 : Union[list, np.array, pd.Series]
Time series in the form of a vector of values.
signal2 : Union[list, np.array, pd.Series]
Time series in the form of a vector of values.
method : str
The method to use. Can be one of 'hilbert' or 'correlation'.
window_size : int
Only used if `method='correlation'`. The number of samples to use for rolling correlation.

--------
signal_filter, signal_zerocrossings, signal_findpeaks

Returns
-------
array
A vector containing the phase of the signal, between 0 and 2*pi.

Examples
--------
>>> import neurokit2 as nk
>>>
>>> signal1 = nk.signal_simulate(duration=10, frequency=1)
>>> signal2 = nk.signal_simulate(duration=10, frequency=1.5)
>>>
>>> coupling_h = nk.signal_synchrony(signal1, signal2, method="hilbert")
>>> coupling_c = nk.signal_synchrony(signal1, signal2, method="correlation", window_size=1000/2)
>>>
>>> fig = nk.signal_plot([signal1, signal2, coupling_h, coupling_c])
>>> fig #doctest: +SKIP

References
----------
-  http://jinhyuncheong.com/jekyll/update/2017/12/10/Timeseries_synchrony_tutorial_and_simulations.html

"""
if method.lower() in ["hilbert", "phase"]:
coupling = _signal_synchrony_hilbert(signal1, signal2)
elif method.lower() in ["correlation"]:
coupling = _signal_synchrony_correlation(signal1, signal2, window_size=int(window_size))

else:
raise ValueError("NeuroKit error: signal_synchrony(): 'method' should be one of 'hilbert' or 'correlation'.")

return coupling

# =============================================================================
# Methods
# =============================================================================

def _signal_synchrony_hilbert(signal1, signal2):

hill1 = scipy.signal.hilbert(signal1)
hill2 = scipy.signal.hilbert(signal2)

phase1 = np.angle(hill1, deg=False)
phase2 = np.angle(hill2, deg=False)
synchrony = 1 - np.sin(np.abs(phase1 - phase2) / 2)

return synchrony

def _signal_synchrony_correlation(signal1, signal2, window_size, center=False):
"""Calculates pairwise rolling correlation at each time. Grabs the upper triangle, at each timepoints.

- window: window size of rolling corr in samples
- center: whether to center result (Default: False, so correlation values are listed on the right.)

"""
data = pd.DataFrame({"y1": signal1, "y2": signal2})

rolled = data.rolling(window=window_size, center=center).corr()
synchrony = rolled["y1"].loc[rolled.index.get_level_values(1) == "y2"].values

# Realign
synchrony = np.append(synchrony[int(window_size / 2) :], np.full(int(window_size / 2), np.nan))
synchrony[np.isnan(synchrony)] = np.nanmean(synchrony)

return synchrony
```