#!/usr/bin/env python

'''Simple implementations of connectivity measures.'''

# Authors : [email protected]
#           [email protected]

import sys
import numpy as np
import matplotlib.pyplot as pl
import matplotlib.mlab as mlab


con_name = 'coh'
if con_name == '':
    print 'Please provided the connectivity method to use.'
    sys.exit()

amp = 1.
amp2 = 1.
sfreq = 1000.
#_________
nse_amp = 1
noise_mu = 0.1 # mean phase, "center" of noise distribution
nse_kappa = 2. # dispersion of noise dispritbution
phase_mu = np.abs(np.deg2rad(45)) # mean circular phase (ENTER IN DEGREE), "center" of phase distribution
phase_kappa = 10. # dispersion of phase dispritbution
#____
n_epochs = 120
epoch_length = 1 # make epoch of 1 second each
times = np.arange(0,epoch_length,1/(sfreq))
nfft = 512
#____
freq1_start = 150
freq1_end   = 220
freq_steps = 0.#___
freq2_start = freq1_start
freq2_end   = freq1_end
#___
freq_band1 = np.linspace(freq1_start, freq1_end, times.size)
freq_band2 = np.linspace(freq2_start, freq2_end, times.size)
"""#############################################################################
#_____________________________Signal generated in epochs_______________________#
#############################################################################"""

def simulate_x_y(times, n_epochs, amp, amp2, freq_band1, freq_band2, phase_mu, phase_kappa, nse_amp, noise_mu, nse_kappa):
    x  = np.zeros((n_epochs, times.size))
    y  = np.zeros((n_epochs, times.size))
    phase_shift_y = np.random.vonmises(phase_mu, phase_kappa, n_epochs)
    for i in range(0, n_epochs):
        print i
        for j in xrange(freq1_start,freq1_end):
            print j
            x[i] = (amp  * np.sin(2 * np.pi * freq_band1 * times                   )+ np.sin(2 * np.pi * j * times)) + nse_amp * np.random.normal(loc=noise_mu, scale= nse_kappa, size=times.size)
            y[i] = (amp2 * np.sin(2 * np.pi * freq_band2 * times + phase_shift_y[i])+ np.sin(2 * np.pi * j * times)) + nse_amp * np.random.normal(loc=noise_mu, scale= nse_kappa, size=times.size)

    return x, y, phase_shift_y

# return the values from the function is just for the coding process to check every variable
x, y, phase_shift_y = simulate_x_y(times, n_epochs, amp, amp2, freq_band1, freq_band2, phase_mu, phase_kappa, nse_amp, noise_mu, nse_kappa)

x0 = x.flatten()
y0 = y.flatten()

def compute_mean_psd_csd(x, y, n_epochs, nfft, sfreq):
    '''Computes mean of PSD and CSD for signals.'''
    n_freqs = nfft/2 + 1

    Rxy = np.zeros((n_epochs, n_freqs), dtype=complex)
    Rxx = np.zeros((n_epochs, n_freqs), dtype=complex)
    Ryy = np.zeros((n_epochs, n_freqs), dtype=complex)
    for i in range(n_epochs):
        Rxy[i], freqs = mlab.csd(x[i], y[i], NFFT=nfft, Fs=sfreq)
        Rxx[i], _____ = mlab.psd(x[i], NFFT=nfft, Fs=sfreq)
        Ryy[i], _____ = mlab.psd(y[i], NFFT=nfft, Fs=sfreq)

    Rxy_mean = np.mean(Rxy, axis=0)
    Rxx_mean = np.mean(Rxx, axis=0)
    Ryy_mean = np.mean(Ryy, axis=0)

    return freqs, Rxy, Rxy_mean, np.real(Rxx_mean), np.real(Ryy_mean)

def my_coherence(n_freqs, Rxy_mean, Rxx_mean, Ryy_mean):
    ''' Computes coherence. '''
    coh = np.zeros((n_freqs))
    for i in range(0, n_freqs):
        coh[i] = np.abs(Rxy_mean[i]) / np.sqrt(Rxx_mean[i] * Ryy_mean[i])

    return coh

def my_imcoh(n_freqs, Rxy_mean, Rxx_mean, Ryy_mean):
    ''' Computes imaginary coherence. '''
    imcoh = np.zeros((n_freqs))
    for i in range(0, n_freqs):
        imcoh[i] = np.imag(Rxy_mean[i]) / np.sqrt(Rxx_mean[i] * Ryy_mean[i])

    return imcoh

def my_cohy(n_freqs, Rxy_mean, Rxx_mean, Ryy_mean):
    ''' Computes coherency. '''
    cohy = np.zeros((n_freqs))
    for i in range(0, n_freqs):
        cohy[i] = np.real(Rxy_mean[i]) / np.sqrt(Rxx_mean[i] * Ryy_mean[i])

    return cohy

def my_plv(n_freqs, Rxy, Rxy_mean):
    ''' Computes PLV. '''
    Rxy_plv = np.zeros((n_epochs, n_freqs), dtype=np.complex)
    for i in range(0, n_epochs):
        Rxy_plv[i] = Rxy[i] / np.abs(Rxy[i])

    plv = np.abs(np.mean(Rxy_plv, axis=0))
    return plv

def my_pli(n_freqs, Rxy, Rxy_mean):
    ''' Computes PLI. '''
    Rxy_pli = np.zeros((n_epochs, n_freqs), dtype=np.complex)
    for i in range(0, n_epochs):
        Rxy_pli[i] = np.sign(np.imag(Rxy[i]))

    pli = np.abs(np.mean(Rxy_pli, axis=0))
    return pli

def my_wpli(n_freqs, Rxy, Rxy_mean):
    ''' Computes WPLI. '''
    Rxy_wpli_1 = np.zeros((n_epochs, n_freqs), dtype=complex)
    Rxy_wpli_2 = np.zeros((n_epochs, n_freqs), dtype=complex)
    for i in range(0, n_epochs):
        Rxy_wpli_1[i] = np.imag(Rxy[i])
        Rxy_wpli_2[i] = np.abs(np.imag(Rxy[i]))

    # handle divide by zero
    denom = np.mean(Rxy_wpli_2, axis=0)
    idx_denom = np.where(denom == 0.)
    denom[idx_denom] = 1.
    wpli = np.abs(np.mean(Rxy_wpli_1, axis=0)) / denom
    wpli[idx_denom] = 0.
    return wpli


def my_con(x, y, n_epochs, nfft, sfreq, con_name='coh'):
    '''Computes connectivity measure mentioned on provided signal pair and its surrogates.'''
    n_freqs = nfft/2 + 1
    freqs, Rxy, Rxy_mean, Rxx_mean, Ryy_mean = compute_mean_psd_csd(x, y, n_epochs, nfft, sfreq)

    # compute surrogates
    x_surr = x.copy()
    y_surr = y.copy()
    np.random.shuffle(x_surr)
    np.random.shuffle(y_surr)
    freqs_surro, Rxy_s, Rxy_s_mean, Rxx_s_mean, Ryy_s_mean = compute_mean_psd_csd(x_surr, y_surr, n_epochs, nfft, sfreq)

    m = {
        'coh':   lambda: (my_coherence(n_freqs, Rxy_mean, Rxx_mean, Ryy_mean), my_coherence(n_freqs, Rxy_s_mean, Rxx_s_mean, Ryy_s_mean)),
        'imcoh': lambda: (my_imcoh(n_freqs, Rxy_mean, Rxx_mean, Ryy_mean), my_imcoh(n_freqs, Rxy_s_mean, Rxx_s_mean, Ryy_s_mean)),
        'cohy':  lambda: (my_cohy(n_freqs, Rxy_mean, Rxx_mean, Ryy_mean), my_cohy(n_freqs, Rxy_s_mean, Rxx_s_mean, Ryy_s_mean)),
        'plv':   lambda: (my_plv(n_freqs, Rxy, Rxy_mean), my_plv(n_freqs, Rxy_s, Rxy_s_mean)),
        'pli':   lambda: (my_pli(n_freqs, Rxy, Rxy_mean), my_pli(n_freqs, Rxy_s, Rxy_s_mean)),
        'wpli':  lambda: (my_wpli(n_freqs, Rxy, Rxy_mean), my_wpli(n_freqs, Rxy_s, Rxy_s_mean)),
        }
    return m[con_name]() + (freqs, freqs_surro)

con, con_surro, freqs, freqs_surro = my_con(x, y, n_epochs, nfft, sfreq, con_name)

#----------------
# plot results
fig = pl.figure('Connectivity')
ax = fig.add_subplot(2, 1, 1)
pl.plot(freqs, con)
#pl.plot(freqs_surro, con_surro)
pl.title("Connectivity Method is %s" %(con_name), color="black", fontsize=20)
pl.xlabel("Frequency [ Hz ]", color="black", fontsize=14)
pl.ylabel("Connectivity Value [   ]", color="black", fontsize=14)
pl.ylim(0,1.1)
pl.grid()
pl.legend(['%s'%con_name,'ImCoh','PLV','PLI','WPLI'])
#-----------------
ax = fig.add_subplot(2, 1, 2)
ax = pl.subplot(2, 1, 2, polar=True)
pl.title("Phase Shift for mu=%srad and kappa= %s" %(phase_mu, phase_kappa), color="black", fontsize=16)
radii = np.ones((n_epochs))
pl.grid()
bars = ax.bar(phase_shift_y, radii, bottom=0., width=0.001)
ax.set_yticklabels([])
pl.grid()
#----------------

pl.ion()
pl.show()
pl.tight_layout()