FeatureEstimation.py

# -*- coding: utf-8 -*-
"""
Updated Oct 18 2022

@author: Qianliang Li (glia@dtu.dk)

This script contains the code to estimate the following EEG features:
    1. Power Spectral Density
    2. Frontal Theta/Beta Ratio
    3. Asymmetry
    4. Peak Alpha Frequency
    5. 1/f Exponents
    6. Microstates
    7. Long-Range Temporal Correlation (DFA Exponent)
Source localization and functional connectivity
    8. Imaginary part of Coherence
    9. Weighted Phase Lag Index
    10. (Orthogonalized) Power Envelope Correlations
    11. Granger Causality

It should be run after Preprocessing.py

All features are saved in pandas DataFrame format for the machine learning
pipeline

Note that the code has not been changed to fit the demonstration dataset,
thus just running it might introduce some errors.
The code is provided to show how we performed the feature estimation
and if you are adapting the code, you should check if it fits your dataset
e.g. the questionnaire data, sensors and source parcellation etc

The script was written in Spyder. The outline panel can be used to navigate
the different parts easier (Default shortcut: Ctrl + Shift + O)
"""


# Set working directory
import os
wkdir = "/Users/benj3542/Desktop/Uni/Noter/Semester_6/Bachelor/resting-state-eeg-analysis/"
os.chdir(wkdir)

# Load all libraries from the Preamble
from Preamble import *

# %% Load preprocessed epochs and questionnaire data
load_path = "./PreprocessedData"

# Get filenames
files = []
for r, d, f in os.walk(load_path):
    for file in f:
        if ".fif" in file:
            files.append(os.path.join(r, file))
files.sort()

# Subject IDs
Subject_id = [0] * len(files)
for i in range(len(files)):
    temp = files[i].split("\\")
    temp = temp[-1].split("_")
    Subject_id[i] = int(temp[0][-1]) # Subject_id[i] = int(temp[0])

n_subjects = len(Subject_id)

# Load Final epochs
final_epochs = [0]*n_subjects
for n in range(n_subjects):
    final_epochs[n] = mne.read_epochs(fname = os.path.join(files[n]),
                    verbose=0)

# Load dropped epochs - used for gap idx in microstates
bad_subjects = [12345] # list with subjects that were excluded due to too many dropped epochs/chs
Drop_epochs_df = pd.read_pickle("./Preprocessing/dropped_epochs.pkl")

good_subject_df_idx = [not i in bad_subjects for i in Drop_epochs_df["Subject_ID"]]
Drop_epochs_df = Drop_epochs_df.loc[good_subject_df_idx,:]
Drop_epochs_df = Drop_epochs_df.sort_values(by=["Subject_ID"]).reset_index(drop=True)

### Load questionnaire data
# For the purposes of this demonstration I will make a dummy dataframe
# The original code imported csv files with questionnaire data and group status
final_qdf = pd.DataFrame({"Subject_ID":Subject_id,
                          "Age":[23,26],
                          "Gender":[0,0],
                          "Group_status":[0,1],
                          "PCL_total":[33,56],
                          "Q1":[1.2, 2.3],
                          "Q2":[1.7, 1.5],
                          "Qn":[2.1,1.0]})

# Define cases as >= 44 total PCL
# Type: numpy array with subject id
cases = np.array(final_qdf["Subject_ID"][final_qdf["PCL_total"]>=44])
n_groups = 2
Groups = ["CTRL", "PTSD"]

# Define folder for saving features
Feature_savepath = "./Features/"
Stat_savepath = "./Statistics/"
Model_savepath = "./Model/"

# %% Power spectrum features
Freq_Bands = {"delta": [1.25, 4.0],
              "theta": [4.0, 8.0],
              "alpha": [8.0, 13.0],
              "beta": [13.0, 30.0],
              "gamma": [30.0, 49.0]}
ch_names = final_epochs[0].info["ch_names"]
n_channels = final_epochs[0].info["nchan"]

# Pre-allocate memory
power_bands = [0]*len(final_epochs)

def power_band_estimation(n):
    # Get index for eyes open and eyes closed
    EC_index = final_epochs[n].events[:,2] == 1
    EO_index = final_epochs[n].events[:,2] == 2
    
    # Calculate the power spectral density
    psds, freqs = psd_multitaper(final_epochs[n], fmin = 1, fmax = 50) # output (epochs, channels, freqs)
    
    temp_power_band = []
    
    for fmin, fmax in Freq_Bands.values():
        # Calculate the power each frequency band
        psds_band = psds[:, :, (freqs >= fmin) & (freqs < fmax)].sum(axis=-1)
        # Calculate the mean for each eye status
        psds_band_eye = np.array([psds_band[EC_index,:].mean(axis=0),
                                      psds_band[EO_index,:].mean(axis=0)])
        # Append for each freq band
        temp_power_band.append(psds_band_eye)
        # Output: List with the 5 bands, and each element is a 2D array with eye status as 1st dimension and channels as 2nd dimension
    
    # The list is reshaped and absolute and relative power are calculated
    abs_power_band = np.reshape(temp_power_band, (5, 2, n_channels))
    abs_power_band = 10.*np.log10(abs_power_band) # Convert to decibel scale
    
    rel_power_band = np.reshape(temp_power_band, (5, 2, n_channels))
    rel_power_band = rel_power_band/np.sum(rel_power_band, axis=0, keepdims=True)
    # each eye condition and channel have been normalized to power in all 5 frequencies for that given eye condition and channel
    
    # Make one list in 1 dimension
    abs_power_values = np.concatenate(np.concatenate(abs_power_band, axis=0), axis=0)
    rel_power_values = np.concatenate(np.concatenate(rel_power_band, axis=0), axis=0)
    ## Output: First the channels, then the eye status and finally the frequency bands are concatenated
    ## E.g. element 26 is 3rd channel, eyes open, first frequency band
    #assert abs_power_values[26] == abs_power_band[0,1,2]
    #assert abs_power_values[47] == abs_power_band[0,1,23] # +21 channels to last
    #assert abs_power_values[50] == abs_power_band[1,0,2] # once all channels have been changed then the freq is changed and eye status
    
    # Get result
    res = np.concatenate([abs_power_values,rel_power_values],axis=0)
    return n, res

"""
with concurrent.futures.ProcessPoolExecutor() as executor:
    for n, result in executor.map(power_band_estimation, range(len(final_epochs))): # Function and arguments
        power_bands[n] = result
"""

for i in range(len(power_bands)):
    n, results = power_band_estimation(i)
    power_bands[i] = results

# Combine all data into one dataframe
# First the columns are prepared
n_subjects = len(Subject_id)

# The group status (PTSD/CTRL) is made using the information about the cases
Group_status = np.array(["CTRL"]*n_subjects)
Group_status[np.array([i in cases for i in Subject_id])] = "PTSD"

# A variable that codes the channels based on A/P localization is also made
Frontal_chs = ["Fp1", "Fpz", "Fp2", "AFz", "Fz", "F3", "F4", "F7", "F8"]
Central_chs = ["Cz", "C3", "C4", "T7", "T8", "FT7", "FC3", "FCz", "FC4", "FT8", "TP7", "CP3", "CPz", "CP4", "TP8"]
Posterior_chs = ["Pz", "P3", "P4", "P7", "P8", "POz", "O1", "O2", "Oz"]

Brain_region_labels = ["Frontal","Central","Posterior"]
Brain_region = np.array(ch_names, dtype = "<U9")
Brain_region[np.array([i in Frontal_chs for i in ch_names])] = Brain_region_labels[0]
Brain_region[np.array([i in Central_chs for i in ch_names])] = Brain_region_labels[1]
Brain_region[np.array([i in Posterior_chs for i in ch_names])] = Brain_region_labels[2]

# A variable that codes the channels based on M/L localization
Left_chs = ["Fp1", "F3", "F7", "FC3", "FT7", "C3", "T7", "CP3", "TP7", "P3", "P7", "O1"]
Right_chs = ["Fp2", "F4", "F8", "FC4", "FT8", "C4", "T8", "CP4", "TP8", "P4", "P8", "O2"]
Mid_chs = ["Fpz", "AFz", "Fz", "FCz", "Cz", "CPz", "Pz", "POz", "Oz"]

Brain_side = np.array(ch_names, dtype = "<U5")
Brain_side[np.array([i in Left_chs for i in ch_names])] = "Left"
Brain_side[np.array([i in Right_chs for i in ch_names])] = "Right"
Brain_side[np.array([i in Mid_chs for i in ch_names])] = "Mid"

# Eye status is added
eye_status = list(final_epochs[0].event_id.keys())
n_eye_status = len(eye_status)

# Frequency bands
freq_bands_name = list(Freq_Bands.keys())
n_freq_bands = len(freq_bands_name)

# Quantification (Abs/Rel)
quant_status = ["Absolute", "Relative"]
n_quant_status = len(quant_status)

# The dataframe is made by combining all the unlisted pds values
# Each row correspond to a different channel. It is reset after all channel names have been used
# Each eye status element is repeated n_channel times, before it is reset
# Each freq_band element is repeated n_channel * n_eye_status times, before it is reset
# Each quantification status element is repeated n_channel * n_eye_status * n_freq_bands times, before it is reset
power_df = pd.DataFrame(data = {"Subject_ID": [ele for ele in Subject_id for i in range(n_eye_status*n_quant_status*n_freq_bands*n_channels)],
                                "Group_status": [ele for ele in Group_status for i in range(n_eye_status*n_quant_status*n_freq_bands*n_channels)],
                                "Channel": ch_names*(n_eye_status*n_quant_status*n_freq_bands*n_subjects),
                                "Brain_region": list(Brain_region)*(n_eye_status*n_quant_status*n_freq_bands*n_subjects),
                                "Brain_side": list(Brain_side)*(n_eye_status*n_quant_status*n_freq_bands*n_subjects),
                                "Eye_status": [ele for ele in eye_status for i in range(n_channels)]*n_quant_status*n_freq_bands*n_subjects,
                                "Freq_band": [ele for ele in freq_bands_name for i in range(n_channels*n_eye_status)]*n_quant_status*n_subjects,
                                "Quant_status": [ele for ele in quant_status for i in range(n_channels*n_eye_status*n_freq_bands)]*n_subjects,
                                "PSD": list(np.concatenate(power_bands, axis=0))
                                })
# Absolute power is in decibels (10*log10(power))

# Fix Freq_band categorical order
power_df["Freq_band"] = power_df["Freq_band"].astype("category").\
            cat.reorder_categories(list(Freq_Bands.keys()), ordered=True)
"""
# Fix Brain_region categorical order
power_df["Brain_region"] = power_df["Brain_region"].astype("category").\
            cat.reorder_categories(Brain_region_labels, ordered=True)
"""
# Save the dataframe
power_df.to_pickle(os.path.join(Feature_savepath,"Power_df.pkl"))


# %% Theta-beta ratio
# Frontal theta/beta ratio has been implicated in cognitive control of attention
power_df = pd.read_pickle(os.path.join(Feature_savepath,"Power_df.pkl"))

eye_status = list(final_epochs[0].event_id)
n_eye_status = len(eye_status)

# Subset frontal absolute power
power_df_sub1 = power_df[(power_df["Quant_status"] == "Absolute")&
                         (power_df["Brain_region"] == "Frontal")]
# Subset frontal, midline absolute power
power_df_sub2 = power_df[(power_df["Quant_status"] == "Absolute")&
                            (power_df["Brain_region"] == "Frontal")&
                            (power_df["Brain_side"] == "Mid")]


# Calculate average frontal power theta
frontal_theta_mean_subject = power_df_sub1[power_df_sub1["Freq_band"] == "theta"].\
    groupby(["Subject_ID","Group_status","Eye_status"]).mean().reset_index()

# Calculate average frontal power beta
frontal_beta_mean_subject = power_df_sub1[power_df_sub1["Freq_band"] == "beta"].\
    groupby(["Subject_ID","Group_status","Eye_status"]).mean().reset_index()
# Extract all values
frontal_beta_subject_values = power_df_sub1[power_df_sub1["Freq_band"] == "beta"]

# Calculate average frontal, midline power theta
frontal_midline_theta_mean_subject = power_df_sub2[power_df_sub2["Freq_band"] == "theta"].\
    groupby(["Subject_ID","Group_status","Eye_status"]).mean().reset_index()
# Extract all values
frontal_midline_theta_subject_values = power_df_sub2[power_df_sub2["Freq_band"] == "theta"]


# Convert from dB to raw power
frontal_theta_mean_subject["PSD"] = 10**(frontal_theta_mean_subject["PSD"]/10)
frontal_beta_mean_subject["PSD"] = 10**(frontal_beta_mean_subject["PSD"]/10)
frontal_midline_theta_mean_subject["PSD"] = 10**(frontal_midline_theta_mean_subject["PSD"]/10)
frontal_beta_subject_values["PSD"] = 10**(frontal_beta_subject_values["PSD"]/10)
frontal_midline_theta_subject_values["PSD"] = 10**(frontal_midline_theta_subject_values["PSD"]/10)

frontal_beta_mean_subject.to_pickle(os.path.join(Feature_savepath,"fBMS_df.pkl"))
frontal_midline_theta_mean_subject.to_pickle(os.path.join(Feature_savepath,"fMTMS_df.pkl"))
frontal_beta_subject_values.to_pickle(os.path.join(Feature_savepath,"fBSV_df.pkl"))
frontal_midline_theta_subject_values.to_pickle(os.path.join(Feature_savepath,"fMTSV_df.pkl"))

# Calculate mean for each group and take ratio for whole group
# To confirm trend observed in PSD plots
mean_group_f_theta = frontal_theta_mean_subject.iloc[:,1:].groupby(["Group_status","Eye_status"]).mean()
mean_group_f_beta = frontal_beta_mean_subject.iloc[:,1:].groupby(["Group_status","Eye_status"]).mean()
mean_group_f_theta_beta_ratio = mean_group_f_theta/mean_group_f_beta

# Calculate ratio for each subject
frontal_theta_beta_ratio = frontal_theta_mean_subject.copy()
frontal_theta_beta_ratio["PSD"] = frontal_theta_mean_subject["PSD"]/frontal_beta_mean_subject["PSD"]

# Take the natural log of ratio 
frontal_theta_beta_ratio["PSD"] = np.log(frontal_theta_beta_ratio["PSD"])

# Rename and save feature
frontal_theta_beta_ratio.rename(columns={"PSD":"TBR"},inplace=True)
# Add dummy variable for re-using plot code
dummy_variable = ["Frontal Theta Beta Ratio"]*frontal_theta_beta_ratio.shape[0]
frontal_theta_beta_ratio.insert(3, "Measurement", dummy_variable )

# frontal_theta_beta_ratio.to_pickle(os.path.join(Feature_savepath,"fTBR_df.pkl"))

"""
# %% Frequency bands asymmetry
# Defined as ln(right) - ln(left)
# Thus we should only work with the absolute values and undo the dB transformation
# Here I avg over all areas. I.e. mean((ln(F4)-ln(F3),(ln(F8)-ln(F7),(ln(Fp2)-ln(Fp1))) for frontal
ROI = ["Frontal", "Central", "Posterior"]
qq = "Absolute" # only calculate asymmetry for absolute
# Pre-allocate memory
asymmetry = np.zeros(shape=(len(np.unique(power_df["Subject_ID"])),
                             len(np.unique(power_df["Eye_status"])),
                             len(list(Freq_Bands.keys())),
                             len(ROI)))

def calculate_asymmetry(i):
    ii = np.unique(power_df["Subject_ID"])[i]
    temp_asymmetry = np.zeros(shape=(len(np.unique(power_df["Eye_status"])),
                             len(list(Freq_Bands.keys())),
                             len(ROI)))
    for e in range(len(np.unique(power_df["Eye_status"]))):
        ee = np.unique(power_df["Eye_status"])[e]
        for f in range(len(list(Freq_Bands.keys()))):
            ff = list(Freq_Bands.keys())[f]
            
            # Get the specific part of the df
            temp_power_df = power_df[(power_df["Quant_status"] == qq) &
                                     (power_df["Eye_status"] == ee) &
                                     (power_df["Subject_ID"] == ii) &
                                     (power_df["Freq_band"] == ff)].copy()
            
            # Convert from dB to raw power
            temp_power_df.loc[:,"PSD"] = np.array(10**(temp_power_df["PSD"]/10))
            
            # Calculate the power asymmetry
            for r in range(len(ROI)):
                rr = ROI[r]
                temp_power_roi_df = temp_power_df[(temp_power_df["Brain_region"] == rr)&
                                                  ~(temp_power_df["Brain_side"] == "Mid")]
                # Sort using channel names to make sure F8-F7 and not F4-F7 etc.
                temp_power_roi_df = temp_power_roi_df.sort_values("Channel").reset_index(drop=True)
                # Get the log power
                R_power = temp_power_roi_df[(temp_power_roi_df["Brain_side"] == "Right")]["PSD"]
                ln_R_power = np.log(R_power) # get log power
                L_power = temp_power_roi_df[(temp_power_roi_df["Brain_side"] == "Left")]["PSD"]
                ln_L_power = np.log(L_power) # get log power
                # Pairwise subtraction followed by averaging
                asymmetry_value = np.mean(np.array(ln_R_power) - np.array(ln_L_power))
                # Save it to the array
                temp_asymmetry[e,f,r] = asymmetry_value
    # Print progress
    print("{} out of {} finished testing".format(i+1,n_subjects))
    return i, temp_asymmetry

with concurrent.futures.ProcessPoolExecutor() as executor:
    for i, res in executor.map(calculate_asymmetry, range(len(np.unique(power_df["Subject_ID"])))): # Function and arguments
        asymmetry[i,:,:,:] = res

# Prepare conversion of array to df using flatten
n_subjects = len(Subject_id)

# The group status (PTSD/CTRL) is made using the information about the cases
Group_status = np.array(["CTRL"]*n_subjects)
Group_status[np.array([i in cases for i in Subject_id])] = "PTSD"

# Eye status is added
eye_status = list(final_epochs[0].event_id.keys())
n_eye_status = len(eye_status)

# Frequency bands
freq_bands_name = list(Freq_Bands.keys())
n_freq_bands = len(freq_bands_name)

# ROIs
n_ROI = len(ROI)

# Make the dataframe                
asymmetry_df = pd.DataFrame(data = {"Subject_ID": [ele for ele in Subject_id for i in range(n_eye_status*n_freq_bands*n_ROI)],
                                     "Group_status": [ele for ele in Group_status for i in range(n_eye_status*n_freq_bands*n_ROI)],
                                     "Eye_status": [ele for ele in eye_status for i in range(n_freq_bands*n_ROI)]*(n_subjects),
                                     "Freq_band": [ele for ele in freq_bands_name for i in range(n_ROI)]*(n_subjects*n_eye_status),
                                     "ROI": list(ROI)*(n_subjects*n_eye_status*n_freq_bands),
                                     "Asymmetry_score": asymmetry.flatten(order="C")
                                     })
# Flatten with order=C means that it first goes through last axis,
# then repeat along 2nd last axis, and then repeat along 3rd last etc

# Asymmetry numpy to pandas conversion check
random_point=321
asymmetry_df.iloc[random_point]

i = np.where(np.unique(power_df["Subject_ID"]) == asymmetry_df.iloc[random_point]["Subject_ID"])[0]
e = np.where(np.unique(power_df["Eye_status"]) == asymmetry_df.iloc[random_point]["Eye_status"])[0]
f = np.where(np.array(list(Freq_Bands.keys())) == asymmetry_df.iloc[random_point]["Freq_band"])[0]
r = np.where(np.array(ROI) == asymmetry_df.iloc[random_point]["ROI"])[0]

assert asymmetry[i,e,f,r] == asymmetry_df.iloc[random_point]["Asymmetry_score"]

# Save the dataframe
asymmetry_df.to_pickle(os.path.join(Feature_savepath,"asymmetry_df.pkl"))

# %% Using FOOOF
# Peak alpha frequency (PAF) and 1/f exponent (OOF)
# Using the FOOOF algorithm (Fitting oscillations and one over f)
# Published by Donoghue et al, 2020 in Nature Neuroscience
# To start, FOOOF takes the freqs and power spectra as input
n_channels = final_epochs[0].info["nchan"]
ch_names = final_epochs[0].info["ch_names"]
sfreq = final_epochs[0].info["sfreq"]
Freq_Bands = {"delta": [1.25, 4.0],
              "theta": [4.0, 8.0],
              "alpha": [8.0, 13.0],
              "beta": [13.0, 30.0],
              "gamma": [30.0, 49.0]}
n_freq_bands = len(Freq_Bands)

# From visual inspection there seems to be problem if PSD is too steep at the start
# To overcome this problem, we try multiple start freq
OOF_r2_thres = 0.95 # a high threshold as we allow for overfitting
PAF_r2_thres = 0.90 # a more lenient threshold for PAF, as it is usually still captured even if fit for 1/f is not perfect
freq_start_it_range = [2,3,4,5,6]
freq_end = 40 # Stop freq at 40Hz to not be influenced by the Notch Filter

eye_status = list(final_epochs[0].event_id.keys())
n_eye_status = len(eye_status)

PAF_data = np.zeros((n_subjects,n_eye_status,n_channels,3)) # CF, power, band_width
OOF_data = np.zeros((n_subjects,n_eye_status,n_channels,2)) # offset and exponent

def FOOOF_estimation(i):
    PAF_data0 = np.zeros((n_eye_status,n_channels,3)) # CF, power, band_width
    OOF_data0 = np.zeros((n_eye_status,n_channels,2)) # offset and exponent
    # Get Eye status
    eye_idx = [final_epochs[i].events[:,2] == 1, final_epochs[i].events[:,2] == 2] # EC and EO
    # Calculate the power spectral density
    psd, freqs = psd_multitaper(final_epochs[i], fmin = 1, fmax = 50) # output (epochs, channels, freqs)
    # Retrieve psds for the 2 conditions and calculate mean across epochs
    psds = []
    for e in range(n_eye_status):
        # Get the epochs for specific eye condition
        temp_psd = psd[eye_idx[e],:,:]
        # Calculate the mean across epochs
        temp_psd = np.mean(temp_psd, axis=0)
        # Save
        psds.append(temp_psd)
    # Try multiple start freq
    PAF_data00 = np.zeros((n_eye_status,n_channels,len(freq_start_it_range),3)) # CF, power, band_width
    OOF_data00 = np.zeros((n_eye_status,n_channels,len(freq_start_it_range),2)) # offset and exponent
    r2s00 = np.zeros((n_eye_status,n_channels,len(freq_start_it_range)))
    for e in range(n_eye_status):
        psds_avg = psds[e]
        for f in range(len(freq_start_it_range)):
            # Initiate FOOOF group for analysis of multiple PSD
            fg = fooof.FOOOFGroup()
            # Set the frequency range to fit the model
            freq_range = [freq_start_it_range[f], freq_end] # variable freq start to 49Hz
            # Fit to each source PSD separately, but in parallel
            fg.fit(freqs,psds_avg,freq_range,n_jobs=1)
            # Extract aperiodic parameters
            aps = fg.get_params('aperiodic_params')
            # Extract peak parameters
            peaks = fg.get_params('peak_params')
            # Extract goodness-of-fit metrics
            r2s = fg.get_params('r_squared')
            # Save OOF and r2s
            OOF_data00[e,:,f] = aps
            r2s00[e,:,f] = r2s
            # Find the alpha peak with greatest power
            for c in range(n_channels):
                peaks0 = peaks[peaks[:,3] == c]
                # Subset the peaks within the alpha band
                in_alpha_band = (peaks0[:,0] >= Freq_Bands["alpha"][0]) & (peaks0[:,0] <= Freq_Bands["alpha"][1])
                if sum(in_alpha_band) > 0: # Any alpha peaks?
                    # Choose the peak with the highest power
                    max_alpha_idx = np.argmax(peaks0[in_alpha_band,1])
                    # Save results
                    PAF_data00[e,c,f] = peaks0[in_alpha_band][max_alpha_idx,:-1]
                else:
                    # No alpha peaks
                    PAF_data00[e,c,f] = [np.nan]*3
    # Check criterias
    good_fits_OOF = (r2s00 > OOF_r2_thres) & (OOF_data00[:,:,:,1] > 0) # r^2 > 0.95 and exponent > 0
    good_fits_PAF = (r2s00 > PAF_r2_thres) & (np.isfinite(PAF_data00[:,:,:,0])) # r^2 > 0.90 and detected peak in alpha band
    # Save the data or NaN if criterias were not fulfilled
    for e in range(n_eye_status):
        for c in range(n_channels):
            if sum(good_fits_OOF[e,c]) == 0: # no good OOF estimation
                OOF_data0[e,c] = [np.nan]*2
            else: # Save OOF associated with greatest r^2 that fulfilled criterias
                OOF_data0[e,c] = OOF_data00[e,c,np.argmax(r2s00[e,c,good_fits_OOF[e,c]])]
            if sum(good_fits_PAF[e,c]) == 0: # no good PAF estimation
                PAF_data0[e,c] = [np.nan]*3
            else: # Save PAF associated with greatest r^2 that fulfilled criterias
                PAF_data0[e,c] = PAF_data00[e,c,np.argmax(r2s00[e,c,good_fits_PAF[e,c]])]
    print("Finished {} out of {} subjects".format(i+1,n_subjects))
    return i, PAF_data0, OOF_data0

# Get current time
c_time1 = time.localtime()
c_time1 = time.strftime("%a %d %b %Y %H:%M:%S", c_time1)
print(c_time1)

with concurrent.futures.ProcessPoolExecutor() as executor:
    for i, PAF_result, OOF_result in executor.map(FOOOF_estimation, range(n_subjects)): # Function and arguments
        PAF_data[i] = PAF_result
        OOF_data[i] = OOF_result

# Save data
with open(Feature_savepath+"PAF_data_arr.pkl", "wb") as file:
    pickle.dump(PAF_data, file)
with open(Feature_savepath+"OOF_data_arr.pkl", "wb") as file:
    pickle.dump(OOF_data, file)

# Get current time
c_time2 = time.localtime()
c_time2 = time.strftime("%a %d %b %Y %H:%M:%S", c_time2)
print("Started", c_time1, "\nFinished",c_time2)

# Convert to Pandas dataframe (only keep mean parameter for PAF)
# The dimensions will each be a column with numbers and the last column will be the actual values
ori = PAF_data[:,:,:,0]
arr = np.column_stack(list(map(np.ravel, np.meshgrid(*map(np.arange, ori.shape), indexing="ij"))) + [ori.ravel()])
PAF_data_df = pd.DataFrame(arr, columns = ["Subject_ID", "Eye_status", "Channel", "Value"])
# Change from numerical coding to actual values

index_values = [Subject_id,eye_status,ch_names]
temp_df = PAF_data_df.copy() # make temp df to not sequential overwrite what is changed
for col in range(len(index_values)):
    col_name = PAF_data_df.columns[col]
    for shape in range(ori.shape[col]):
        temp_df.loc[PAF_data_df.iloc[:,col] == shape,col_name]\
        = index_values[col][shape]
PAF_data_df = temp_df # replace original df 

# Add group status
Group_status = np.array(["CTRL"]*len(PAF_data_df["Subject_ID"]))
Group_status[np.array([i in cases for i in PAF_data_df["Subject_ID"]])] = "PTSD"
# Add to dataframe
PAF_data_df.insert(3, "Group_status", Group_status)

# Global peak alpha
PAF_data_df_global = PAF_data_df.groupby(["Subject_ID", "Group_status", "Eye_status"]).mean().reset_index() # by default pandas mean skip nan
# Add dummy variable for re-using plot code
dummy_variable = ["Global Peak Alpha Frequency"]*PAF_data_df_global.shape[0]
PAF_data_df_global.insert(3, "Measurement", dummy_variable )

# Regional peak alpha
# A variable that codes the channels based on A/P localization is also made
Frontal_chs = ["Fp1", "Fpz", "Fp2", "AFz", "Fz", "F3", "F4", "F7", "F8"]
Central_chs = ["Cz", "C3", "C4", "T7", "T8", "FT7", "FC3", "FCz", "FC4", "FT8", "TP7", "CP3", "CPz", "CP4", "TP8"]
Posterior_chs = ["Pz", "P3", "P4", "P7", "P8", "POz", "O1", "O2", "Oz"]

Brain_region = np.array(ch_names, dtype = "<U9")
Brain_region[np.array([i in Frontal_chs for i in ch_names])] = "Frontal"
Brain_region[np.array([i in Central_chs for i in ch_names])] = "Central"
Brain_region[np.array([i in Posterior_chs for i in ch_names])] = "Posterior"

PAF_data_df.insert(4, "Brain_region", list(Brain_region)*int(PAF_data_df.shape[0]/len(Brain_region)))

# Save the dataframes
PAF_data_df.to_pickle(os.path.join(Feature_savepath,"PAF_data_FOOOF_df.pkl"))
PAF_data_df_global.to_pickle(os.path.join(Feature_savepath,"PAF_data_FOOOF_global_df.pkl"))

# Convert to Pandas dataframe (only keep exponent parameter for OOF)
# The dimensions will each be a column with numbers and the last column will be the actual values
ori = OOF_data[:,:,:,1]
arr = np.column_stack(list(map(np.ravel, np.meshgrid(*map(np.arange, ori.shape), indexing="ij"))) + [ori.ravel()])
PAF_data_df = pd.DataFrame(arr, columns = ["Subject_ID", "Eye_status", "Channel", "Value"])
# Change from numerical coding to actual values

index_values = [Subject_id,eye_status,ch_names]
temp_df = PAF_data_df.copy() # make temp df to not sequential overwrite what is changed
for col in range(len(index_values)):
    col_name = PAF_data_df.columns[col]
    for shape in range(ori.shape[col]):
        temp_df.loc[PAF_data_df.iloc[:,col] == shape,col_name]\
        = index_values[col][shape]
OOF_data_df = temp_df # replace original df 

# Add group status
Group_status = np.array(["CTRL"]*len(OOF_data_df["Subject_ID"]))
Group_status[np.array([i in cases for i in OOF_data_df["Subject_ID"]])] = "PTSD"
# Add to dataframe
OOF_data_df.insert(3, "Group_status", Group_status)

# Regional OOF
OOF_data_df.insert(4, "Brain_region", list(Brain_region)*int(PAF_data_df.shape[0]/len(Brain_region)))

# Save the dataframes
OOF_data_df.to_pickle(os.path.join(Feature_savepath,"OOF_data_FOOOF_df.pkl"))
"""
# %% Microstate analysis
# The function takes the data as a numpy array (n_t, n_ch)
# The data is already re-referenced to common average
# Variables for the clustering function are extracted
sfreq = final_epochs[0].info["sfreq"]
eye_status = list(final_epochs[0].event_id.keys())
n_eye_status = len(eye_status)
ch_names = final_epochs[0].info["ch_names"]
n_channels = len(ch_names)
locs = np.zeros((n_channels,2)) # xy coordinates of the electrodes
for c in range(n_channels):
    locs[c] = final_epochs[0].info["chs"][c]["loc"][0:2]

# The epochs are transformed to numpy arrays
micro_data = []
EC_micro_data = []
EO_micro_data = []
for i in range(n_subjects):
    # Transform data to correct shape
    micro_data.append(final_epochs[i].get_data()) # get data
    arr_shape = micro_data[i].shape # get shape
    micro_data[i] = micro_data[i].swapaxes(1,2) # swap ch and time axis
    micro_data[i] = micro_data[i].reshape(arr_shape[0]*arr_shape[2],arr_shape[1]) # reshape by combining epochs and times
    # Get indices for eyes open and closed
    EC_index = final_epochs[i].events[:,2] == 1
    EO_index = final_epochs[i].events[:,2] == 2
    # Repeat with 4s * sample frequency to correct for concatenation of times and epochs
    EC_index = np.repeat(EC_index,4*sfreq)
    EO_index = np.repeat(EO_index,4*sfreq)
    # Save data where it is divided into eye status
    EC_micro_data.append(micro_data[i][EC_index])
    EO_micro_data.append(micro_data[i][EO_index])

# Global explained variance and Cross-validation criterion is used to determine number of microstates
# First all data is concatenated to find the optimal number of maps for all data
micro_data_all = np.vstack(micro_data)

# Determine the number of clusters
# I use a slightly modified kmeans function which returns the cv_min
global_gev = []
cv_criterion = []
for n_maps in range(2,7):
    maps, L, gfp_peaks, gev, cv_min = kmeans_return_all(micro_data_all, n_maps)
    global_gev.append(np.sum(gev))
    cv_criterion.append(cv_min)
# Save run results
cluster_results = np.array([global_gev,cv_criterion])
np.save("Microstate_n_cluster_test_results.npy", cluster_results) # (gev/cv_crit, n_maps from 2 to 6)

#cluster_results = np.load("Microstate_n_cluster_test_results.npy")
#global_gev = cluster_results[0,:]
#cv_criterion = cluster_results[1,:]

# Evaluate best n_maps
plt.figure()
plt.plot(np.linspace(2,6,len(cv_criterion)),(cv_criterion/np.sum(cv_criterion)), label="CV Criterion")
plt.plot(np.linspace(2,6,len(cv_criterion)),(global_gev/np.sum(global_gev)), label="GEV")
plt.legend()
plt.ylabel("Normalized to total")
# The lower CV the better.
# But the higher GEV the better.
# Based on the plots and the recommendation by vong Wegner & Laufs 2018
# we used 5 microstates

# In order to compare between groups, I fix the microstates by clustering on data from both groups
# Due to instability of maps when running multiple times, I increased n_maps from 4 to 6
n_maps = 5
mode = ["aahc", "kmeans", "kmedoids", "pca", "ica"][1]

# K-means is stochastic, thus I run it multiple times in order to find the maps with highest GEV
# Each K-means is run 5 times and best map is chosen. But I do this 10 times more, so in total 50 times!
n_run = 10
# Pre-allocate memory
microstate_cluster_results = []

# Parallel processing can only be implemented by ensuring different seeds
# Otherwise the iteration would be the same.
# However the k-means already use parallel processing so making outer loop with
# concurrent processes make it use too many processors
# Get current time
c_time1 = time.localtime()
c_time1 = time.strftime("%a %d %b %Y %H:%M:%S", c_time1)
print(c_time1)

for r in range(n_run):
    maps = [0]*2
    m_labels = [0]*2
    gfp_peaks = [0]*2
    gev = [0]*2
    # Eyes closed
    counter = 0
    maps_, x_, gfp_peaks_, gev_ = clustering(
        np.vstack(np.array(EC_micro_data)), sfreq, ch_names, locs, mode, n_maps, doplot=False) # doplot=True is bugged
    maps[counter] = maps_
    m_labels[counter] = x_
    gfp_peaks[counter] = gfp_peaks_
    gev[counter] = gev_
    counter += 1
    # Eyes open
    maps_, x_, gfp_peaks_, gev_ = clustering(
        np.vstack(np.array(EO_micro_data)), sfreq, ch_names, locs, mode, n_maps, doplot=False) # doplot=True is bugged
    maps[counter] = maps_
    m_labels[counter] = x_
    gfp_peaks[counter] = gfp_peaks_
    gev[counter] = gev_
    counter += 1
    
    microstate_cluster_results.append([maps, m_labels, gfp_peaks, gev])
    print("Finished {} out of {}".format(r+1, n_run))

# Get current time
c_time2 = time.localtime()
c_time2 = time.strftime("%a %d %b %Y %H:%M:%S", c_time2)
print("Started", c_time1, "\nFinished",c_time2)

# Save the results
with open(Feature_savepath+"Microstate_5_maps_10x5_k_means_results.pkl", "wb") as file:
    pickle.dump(microstate_cluster_results, file)

# # Load
# with open(Feature_savepath+"Microstate_4_maps_10x5_k_means_results.pkl", "rb") as file:
#     microstate_cluster_results = pickle.load(file)

# Find the best maps (Highest GEV across all the K-means clusters)
EC_total_gevs = np.sum(np.vstack(np.array(microstate_cluster_results)[:,3,0]), axis=1) # (runs, maps/labels/gfp/gev, ec/eo)
EO_total_gevs = np.sum(np.vstack(np.array(microstate_cluster_results)[:,3,1]), axis=1)
Best_EC_idx = np.argmax(EC_total_gevs)
Best_EO_idx = np.argmax(EO_total_gevs)
# Update the variables for the best maps
maps = [microstate_cluster_results[Best_EC_idx][0][0],microstate_cluster_results[Best_EO_idx][0][1]]
m_labels = [microstate_cluster_results[Best_EC_idx][1][0],microstate_cluster_results[Best_EO_idx][1][1]]
gfp_peaks = [microstate_cluster_results[Best_EC_idx][2][0],microstate_cluster_results[Best_EO_idx][2][1]]
gev = [microstate_cluster_results[Best_EC_idx][3][0],microstate_cluster_results[Best_EO_idx][3][1]]

# Plot the maps
plt.style.use('default')
labels = ["EC", "EO"] #Eyes-closed, Eyes-open
for i in range(len(labels)):    
    fig, axarr = plt.subplots(1, n_maps, figsize=(20,5))
    fig.patch.set_facecolor('white')
    for imap in range(n_maps):
        mne.viz.plot_topomap(maps[i][imap,:], pos = final_epochs[0].info, axes = axarr[imap]) # plot
        axarr[imap].set_title("GEV: {:.2f}".format(gev[i][imap]), fontsize=16, fontweight="bold") # title
    fig.suptitle("Microstates: {}".format(labels[i]), fontsize=20, fontweight="bold")

# Manual re-order the maps
# Due the random initiation of K-means this have to be modified every time clusters are made!
# Assign map labels (e.g. 0, 2, 1, 3)
order = [0]*2
order[0] = [3,0,1,2,4] # EC
order[1] = [3,1,0,2,4] # EO
for i in range(len(order)):
    maps[i] = maps[i][order[i],:] # re-order maps
    gev[i] = gev[i][order[i]] # re-order GEV
    # Make directory to find and replace map labels
    dic0 = {value:key for key, value in enumerate(order[i])}
    m_labels[i][:] = [dic0.get(n, n) for n in m_labels[i]] # re-order labels

# The maps seems to be correlated both negatively and positively (see spatial correlation plots)
# Thus the sign of the map does not really reflect which areas are positive or negative (absolute)
# But more which areas are different during each state (relatively)
# I can therefore change the sign of the map for the visualizaiton
sign_swap = [[1,-1,1,1,1],[1,1,1,-1,1]]
for i in range(len(order)):
    for m in range(n_maps):
        maps[i][m] *= sign_swap[i][m]

# Plot the maps and save
save_path = "/Users/benj3542/Desktop/Uni/Noter/Semester_6/Bachelor/resting-state-eeg-analysis/Figures/Microstates"
labels = ["EC", "EO"]
for i in range(len(labels)):    
    fig, axarr = plt.subplots(1, n_maps, figsize=(20,5))
    fig.patch.set_facecolor('white')
    for imap in range(n_maps):
        mne.viz.plot_topomap(maps[i][imap,:], pos = final_epochs[0].info, axes = axarr[imap]) # plot
        axarr[imap].set_title("GEV: {:.2f}".format(gev[i][imap]), fontsize=16, fontweight="bold") # title
    fig.suptitle("Microstates: {} - Total GEV: {:.2f}".format(labels[i],sum(gev[i])), fontsize=20, fontweight="bold")
    # Save the figure
    fig.savefig(os.path.join(save_path,str("Microstates_{}".format(labels[i]) + ".png")))

# Calculate spatial correlation between maps and actual data points (topography)
# The sign of the map is changed so the correlation is positive
# By default the code looks for highest spatial correlation (regardless of sign)
# Thus depending on random initiation point the map might be opposite
plt.style.use('ggplot')
def spatial_correlation(data, maps):
    n_t = data.shape[0]
    n_ch = data.shape[1]
    data = data - data.mean(axis=1, keepdims=True)

    # GFP peaks
    gfp = np.std(data, axis=1)
    gfp_peaks = locmax(gfp)
    gfp_values = gfp[gfp_peaks]
    gfp2 = np.sum(gfp_values**2) # normalizing constant in GEV
    n_gfp = gfp_peaks.shape[0]

    # Spatial correlation
    C = np.dot(data, maps.T)
    C /= (n_ch*np.outer(gfp, np.std(maps, axis=1)))
    L = np.argmax(C**2, axis=1) # C is squared here which means the maps do no retain information about the sign of the correlation
    
    return C

C_EC = spatial_correlation(np.vstack(np.array(EC_micro_data)), maps[0])
C_EO = spatial_correlation(np.vstack(np.array(EO_micro_data)), maps[1])
C = [C_EC, C_EO]

# Plot the distribution of spatial correlation for each label and each map
labels = ["EC", "EO"]
for i in range(len(labels)):
    fig, axarr = plt.subplots(n_maps, n_maps, figsize=(16,16))
    for Lmap in range(n_maps):
        for Mmap in range(n_maps):
            sns.distplot(C[i][m_labels[i] == Lmap,Mmap], ax = axarr[Lmap,Mmap])
            axarr[Lmap,Mmap].set_xlabel("Spatial correlation")
    plt.suptitle("Distribution of spatial correlation_{}".format(labels[i]), fontsize=20, fontweight="bold")
    # Add common x and y axis labels by making one big axis
    fig.add_subplot(111, frameon=False)
    plt.tick_params(labelcolor="none", top="off", bottom="off", left="off", right="off") # hide tick labels and ticks
    plt.grid(False) # remove global grid
    plt.xlabel("Microstate number", labelpad=20)
    plt.ylabel("Label number", labelpad=10)
    fig.savefig(os.path.join(save_path,str("Microstates_Spatial_Correlation_Label_State_{}".format(labels[i]) + ".png")))

# Plot the distribution of spatial correlation for all data and each map
labels = ["EC", "EO"]
for i in range(len(labels)):
    fig, axarr = plt.subplots(1,n_maps, figsize=(20,5))
    for imap in range(n_maps):
        sns.distplot(C[i][:,imap], ax = axarr[imap])
        plt.xlabel("Spatial correlation")
    plt.suptitle("Distribution of spatial correlation", fontsize=20, fontweight="bold")
    # Add common x and y axis labels by making one big axis
    fig.add_subplot(111, frameon=False)
    plt.tick_params(labelcolor="none", top="off", bottom="off", left="off", right="off") # hide tick labels and ticks
    plt.grid(False) # remove global grid
    plt.xlabel("Microstate number", labelpad=20)
    plt.ylabel("Label number")

# Prepare for calculation of transition matrix
# I modified the function, so it takes the list argument gap_index
# gap_index should have the indices right before gaps in data

# Gaps: Between dropped epochs, trials (eo/ec) and subjects
# The between subjects gaps is removed by dividing the data into subjects
n_trials = 5
n_epoch_length = final_epochs[0].get_data().shape[2]

micro_labels = []
micro_subject_EC_idx = [0]
micro_subject_EO_idx = [0]
gaps_idx = []
gaps_trials_idx = []
for i in range(n_subjects):
    # Get indices for subject
    micro_subject_EC_idx.append(micro_subject_EC_idx[i]+EC_micro_data[i].shape[0])
    temp_EC = m_labels[0][micro_subject_EC_idx[i]:micro_subject_EC_idx[i+1]]
    # Get labels for subject i EO
    micro_subject_EO_idx.append(micro_subject_EO_idx[i]+EO_micro_data[i].shape[0])
    temp_EO = m_labels[1][micro_subject_EO_idx[i]:micro_subject_EO_idx[i+1]]
    # Save
    micro_labels.append([temp_EC,temp_EO]) # (subject, eye)
    
    # Get indices with gaps
    # Dropped epochs are first considered
    # Each epoch last 4s, which correspond to 2000 samples and a trial is 15 epochs - dropped epochs
    # Get epochs for each condition
    EC_drop_epochs = Drop_epochs_df.iloc[i,1:][Drop_epochs_df.iloc[i,1:] <= 75].to_numpy()
    EO_drop_epochs = Drop_epochs_df.iloc[i,1:][(Drop_epochs_df.iloc[i,1:] >= 75)&
                                            (Drop_epochs_df.iloc[i,1:] <= 150)].to_numpy()
    # Get indices for the epochs for EC that were dropped and correct for changing index due to drop
    EC_drop_epochs_gaps_idx = []
    counter = 0
    for d in range(len(EC_drop_epochs)):
        drop_epoch_number = EC_drop_epochs[d]
        Drop_epoch_idx = (drop_epoch_number-counter)*n_epoch_length # counter subtracted as the drop index is before dropped
        EC_drop_epochs_gaps_idx.append(Drop_epoch_idx-1) # -1 for point just before gap
        counter += 1
    # Negative index might occur if the first epochs were removed. This index is not needed for transition matrix
    if len(EC_drop_epochs_gaps_idx) > 0:
        for d in range(len(EC_drop_epochs_gaps_idx)): # check all, e.g. if epoch 0,1,2,3 are dropped then all should be caught
            if EC_drop_epochs_gaps_idx[0] == -1:
                EC_drop_epochs_gaps_idx = EC_drop_epochs_gaps_idx[1:len(EC_drop_epochs)]
    
    # Get indices for the epochs for EO that were dropped and correct for changing index due to drop
    EO_drop_epochs_gaps_idx = []
    counter = 0
    for d in range(len(EO_drop_epochs)):
        drop_epoch_number = EO_drop_epochs[d]-75
        Drop_epoch_idx = (drop_epoch_number-counter)*n_epoch_length # counter subtracted as the drop index is before dropped
        EO_drop_epochs_gaps_idx.append(Drop_epoch_idx-1) # -1 for point just before gap
        counter += 1
    # Negative index might occur if the first epoch was removed. This index is not needed for transition matrix
    if len(EO_drop_epochs_gaps_idx) > 0:
        for d in range(len(EO_drop_epochs_gaps_idx)): # check all, e.g. if epoch 0,1,2,3 are dropped then all should be caught
            if EO_drop_epochs_gaps_idx[0] == -1:
                EO_drop_epochs_gaps_idx = EO_drop_epochs_gaps_idx[1:len(EO_drop_epochs)]
    
    # Gaps between trials
    Trial_indices = [0, 15, 30, 45, 60, 75] # all the indices for start and end of the 5 trials
    EC_trial_gaps_idx = []
    EO_trial_gaps_idx = []
    counter_EC = 0
    counter_EO = 0
    for t in range(len(Trial_indices)-2): # -2 as start and end is not used in transition matrix
        temp_drop = EC_drop_epochs[(EC_drop_epochs >= Trial_indices[t])&
                            (EC_drop_epochs < Trial_indices[t+1])]
        # Correct the trial id for any potential drops within that trial
        counter_EC += len(temp_drop)
        trial_idx_corrected_for_drops = 15*(t+1)-counter_EC
        EC_trial_gaps_idx.append((trial_idx_corrected_for_drops*n_epoch_length)-1) # multiply id with length of epoch and subtract 1
        
        temp_drop = EO_drop_epochs[(EO_drop_epochs >= Trial_indices[t]+75)&
                            (EO_drop_epochs < Trial_indices[t+1]+75)]
        # Correct the trial id for any potential drops within that trial
        counter_EO += len(temp_drop)
        trial_idx_corrected_for_drops = 15*(t+1)-counter_EO
        EO_trial_gaps_idx.append((trial_idx_corrected_for_drops*n_epoch_length)-1) # multiply id with length of epoch and subtract 1
    
    # Concatenate all drop indices
    gaps_idx.append([np.unique(np.sort(EC_drop_epochs_gaps_idx+EC_trial_gaps_idx)),
                    np.unique(np.sort(EO_drop_epochs_gaps_idx+EO_trial_gaps_idx))])
    # Make on with trial gaps only for use in LRTC analysis
    gaps_trials_idx.append([EC_trial_gaps_idx,EO_trial_gaps_idx])

# Save the gap idx files
np.save("Gaps_idx.npy",np.array(gaps_idx))
np.save("Gaps_trials_idx.npy",np.array(gaps_trials_idx))

# %% Calculate microstate features
# Symbol distribution (also called ratio of time covered RTT)
# Transition matrix
# Shannon entropy
EC_p_hat = p_empirical(m_labels[0], n_maps)
EO_p_hat = p_empirical(m_labels[1], n_maps)
# Sanity check: Overall between EC and EO

microstate_time_data = np.zeros((n_subjects,n_eye_status,n_maps))
microstate_transition_data = np.zeros((n_subjects,n_eye_status,n_maps,n_maps))
microstate_entropy_data = np.zeros((n_subjects,n_eye_status))
for i in range(n_subjects):
    # Calculate ratio of time covered
    temp_EC_p_hat = p_empirical(micro_labels[i][0], n_maps)
    temp_EO_p_hat = p_empirical(micro_labels[i][1], n_maps)
    # Calculate transition matrix
    """
    temp_EC_T_hat = T_empirical(micro_labels[i][0], n_maps, gaps_idx[i][0])
    temp_EO_T_hat = T_empirical(micro_labels[i][1], n_maps, gaps_idx[i][1])
    """
    temp_EC_T_hat = T_empirical(micro_labels[i][0], n_maps)
    temp_EO_T_hat = T_empirical(micro_labels[i][1], n_maps)
    # Calculate Shannon entropy
    temp_EC_h_hat = H_1(micro_labels[i][0], n_maps)
    temp_EO_h_hat = H_1(micro_labels[i][1], n_maps)
    
    # Save the data
    microstate_time_data[i,0,:] = temp_EC_p_hat
    microstate_time_data[i,1,:] = temp_EO_p_hat
    microstate_transition_data[i,0,:,:] = temp_EC_T_hat
    microstate_transition_data[i,1,:,:] = temp_EO_T_hat
    microstate_entropy_data[i,0] = temp_EC_h_hat/max_entropy(n_maps) # ratio of max entropy
    microstate_entropy_data[i,1] = temp_EO_h_hat/max_entropy(n_maps) # ratio of max entropy

# Save transition data
np.save(Feature_savepath+"microstate_transition_data.npy", microstate_transition_data)
# Convert transition data to dataframe for further processing with other features
# Transition matrix should be read as probability of row to column
microstate_transition_data_arr =\
     microstate_transition_data.reshape((n_subjects,n_eye_status,n_maps*n_maps)) # flatten 4 x 4 matrix to 1D
transition_info = ["M1->M1", "M1->M2", "M1->M3", "M1->M4", "M1->M5",
                   "M2->M1", "M2->M2", "M2->M3", "M2->M4", "M2-M5",
                   "M3->M1", "M3->M2", "M3->M3", "M3->M4", "M3->M5",
                   "M4->M1", "M4->M2", "M4->M3", "M4->M4", "M4->M5",
                   "M5->M1", "M5->M2", "M5->M3", "M5->M4", "M5->M5"]

arr = np.column_stack(list(map(np.ravel, np.meshgrid(*map(np.arange, microstate_transition_data_arr.shape), indexing="ij"))) + [microstate_transition_data_arr.ravel()])
microstate_transition_data_df = pd.DataFrame(arr, columns = ["Subject_ID", "Eye_status", "Transition", "Value"])
# Change from numerical coding to actual values
eye_status = list(final_epochs[0].event_id.keys())

index_values = [Subject_id,eye_status,transition_info]
for col in range(len(index_values)):
    col_name = microstate_transition_data_df.columns[col]
    for shape in reversed(range(microstate_transition_data_arr.shape[col])): # notice this is the shape of original numpy array. Not shape of DF
        microstate_transition_data_df.loc[microstate_transition_data_df.iloc[:,col] == shape,col_name]\
        = index_values[col][shape]

# Add group status
Group_status = np.array(["CTRL"]*len(microstate_transition_data_df["Subject_ID"]))
Group_status[np.array([i in cases for i in microstate_transition_data_df["Subject_ID"]])] = "PTSD"
# Add to dataframe
microstate_transition_data_df.insert(2, "Group_status", Group_status)

# Save df
microstate_transition_data_df.to_pickle(os.path.join(Feature_savepath,"microstate_transition_data_df.pkl"))

# Convert time covered data to Pandas dataframe
# The dimensions will each be a column with numbers and the last column will be the actual values
arr = np.column_stack(list(map(np.ravel, np.meshgrid(*map(np.arange, microstate_time_data.shape), indexing="ij"))) + [microstate_time_data.ravel()])
microstate_time_df = pd.DataFrame(arr, columns = ["Subject_ID", "Eye_status", "Microstate", "Value"])
# Change from numerical coding to actual values
eye_status = list(final_epochs[0].event_id.keys())
microstates = [1,2,3,4,5]

index_values = [Subject_id,eye_status,microstates]
for col in range(len(index_values)):
    col_name = microstate_time_df.columns[col]
    for shape in reversed(range(microstate_time_data.shape[col])): # notice this is the shape of original numpy array. Not shape of DF
        microstate_time_df.loc[microstate_time_df.iloc[:,col] == shape,col_name]\
        = index_values[col][shape]