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complete_bichoher.py
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complete_bichoher.py
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# -*- coding: utf-8 -*-
"""COMPLETE Bichoher.ipynb
Automatically generated by Colaboratory.
Original file is located at
https://colab.research.google.com/drive/1C1avva0wjZm9yoN2JP9iaREvfp5T7u97
# **Libereires**
"""
import sklearn
from sklearn import preprocessing
import IPython.display as ipd
import scipy
from scipy.stats import norm, kurtosis
from scipy.linalg import hankel
from scipy.fft import fft,fftshift
from scipy.stats import skew
from scipy import signal
import librosa, librosa.display
import numpy as np
import statistics
import math
import matplotlib.pyplot as plt
from pathlib import Path
"""# **# Usefull Functions**"""
all_true_var_ang = [0,0,0,0]
all_true_var_bic = [0,0,0,0]
all_true_std_ang = [0,0,0,0]
all_true_std_bic = [0,0,0,0]
all_true_skew_ang = [0,0,0,0]
all_true_skew_bic = [0,0,0,0]
all_true_kurtosis_ang = [0,0,0,0]
all_true_kurtosis_bic = [0,0,0,0]
all_fake_var_ang = [0,0,0,0]
all_fake_var_bic = [0,0,0,0]
all_fake_std_ang = [0,0,0,0]
all_fake_std_bic = [0,0,0,0]
all_fake_skew_ang = [0,0,0,0]
all_fake_skew_bic = [0,0,0,0]
all_fake_kurtosis_ang = [0,0,0,0]
all_fake_kurtosis_bic = [0,0,0,0]
def next_power_of_2(x):
return 1 if x == 0 else 2**math.ceil(math.log2(x))
def normalizer(data):
oldmin = min(data)
oldmax = max(data)
oldrange = oldmax - oldmin
newmin = 0.
newmax = 1.
newrange = newmax - newmin
if oldrange == 0: # Deal with the case where rvalue is constant:
if oldmin < newmin: # If rvalue < newmin, set all rvalue values to newmin
newval = newmin
elif oldmin > newmax: # If rvalue > newmax, set all rvalue values to newmax
newval = newmax
else: # If newmin <= rvalue <= newmax, keep rvalue the same
newval = oldmin
normal = [newval for v in data]
else:
scale = newrange / oldrange
normal = [(v - oldmin) * scale + newmin for v in data]
return normal
"""# **Bicoherence**"""
# [bic,waxis] = bicoher (y, nfft, wind, segsamp, overlap)
# y - data vector or time-series
# nfft - fft length [default = power of two > segsamp]
# actual size used is power of two greater than 'nsamp'
# wind - specifies the time-domain window to be applied to each
# data segment; should be of length 'segsamp' (see below);
# otherwise, the default Hanning window is used.
# segsamp - samples per segment [default: such that we have 8 segments]
# - if x is a matrix, segsamp is set to the number of rows
# overlap - percentage overlap, allowed range [0,99]. [default = 50];
# - if x is a matrix, overlap is set to 0.
# bic - estimated bicoherence: an nfft x nfft array, with origin
# at the center, and axes pointing down and to the right.
# waxis - vector of frequencies associated with the rows and columns
# of bic; sampling frequency is assumed to be 1.
def bicoher(y, nfft, winds, nsamp, overlap,normalization):
#--------------------parameter checks---------------------
means = [0,0]
ly = len(y)
nrecs = 1
if (ly == 1):
y = (np.array(y)).reshape((-1, 1))
ly = nrecs;
nrecs = 1;
if nfft is None:
nfft = 128
if overlap is None:
overlap = 50
overlap = max(0,min(overlap,99))
if nrecs > 1:
overlap = 0
if nrecs > 1 :
nsamp = ly
if nrecs == 1 and nsamp <= 0:
nsamp = np.fix(ly/ (8 - 7 * overlap/100))
if nfft < nsamp:
nfft = 2^next_power_of_2(nsamp)
overlap = int(np.fix( nsamp * overlap/100))
nadvance = nsamp - overlap
nrecs = int(np.fix ( (ly*nrecs - overlap) / nadvance))
if winds is None:
wind = np.hanning(nsamp)
if winds == 'hann':
wind = scipy.signal.hann(nsamp)
elif winds == 'hamm':
wind = scipy.signal.hamming(nsamp)
rw = len(wind)
cw = 1
if min(rw,cw) != 1 or max(rw,cw) != nsamp:
print(['Segment size is ',str(nsamp)])
print(['"wind" array is ',str(rw),' by ',str(cw)])
print(['Using default Hanning window'])
wind = np.hanning(nsamp);
#---------------- accumulate triple products ----------------------
bic = np.zeros((nfft,nfft))
Pyy = np.zeros((1,nfft))
Yf12 = np.zeros((nfft,nfft))
ind = np.array(np.arange(0,nsamp))
for i in range(0, nrecs):
ys = y[ind[0]:ind[-1]+1]
ys = (ys- np.mean(ys))*wind
Yf = np.array(fft(ys,nfft))/ nsamp
CYf = np.conjugate(Yf)
Pyy = Pyy + Yf * CYf
CYf_shi = np.roll(CYf,1)
Yf12 = hankel(CYf,CYf_shi)
bic = bic + (Yf * Yf.reshape((-1, 1))) * Yf12
ind = ind + nadvance
bicc = bic / nrecs
angles=(sum(np.angle(bicc)))
means[0] = np.mean(angles)
X_mag,X_phase=librosa.magphase(fftshift(bicc))
Pyy = Pyy / nrecs
Pyy_shi = np.roll(Pyy,1)
mask = hankel(Pyy,Pyy_shi)
if normalization==1 : # -------- Defualt
den = (Pyy * Pyy.reshape((-1, 1))*mask)
bic = abs(bicc)**2 /abs(den)
elif normalization == 2: #---------- papre
den = (abs(Pyy * Pyy.reshape((-1, 1)))**2 * abs(mask)**2)
bic = (bicc) / np.sqrt(den)
elif normalization == 3: # -------- 1 wiki
den = pow(abs(Pyy),2) * pow(abs(Pyy.reshape((-1, 1))),2) * abs(mask)**2
denn = pow(den,-2)
bic = abs(bicc) / denn
elif normalization == 4: # --------- 2 wiki
den = (abs(Pyy * Pyy.reshape((-1, 1)))**2 * abs(mask)**2)
bic = abs(bicc)**2 / (den)
elif normalization == 5: # --------- 3 wiki
den = abs(Pyy * Pyy.reshape((-1, 1)) * mask)
bic = abs(bicc) / (den)
biccc = fftshift(bic)
means[1] = np.mean(biccc)
var_ang = np.var (angles)/means[1]
var_bic = np.var (biccc)/means[1]
std_ang = np.std (angles)
std_bic = np.std (biccc)
skew_ang = skew(angles)
skew_bic = skew(np.sum(biccc))
kurtosis_ang = kurtosis(angles)
kurtosis_bic = kurtosis(np.sum(biccc))
statistic = [var_ang,var_bic,std_ang,std_bic,skew_ang,skew_bic,kurtosis_ang,kurtosis_bic]
den = (Pyy * Pyy.reshape((-1, 1))*mask)
bic = abs(bicc)**2 /abs(den)
means[1] = np.mean(bic)
biccc = fftshift(bic)
return angles,bic,means,statistic
"""# X^2 **Nonlinearity**
# **Signal generation**
"""
fs = 44100
N = 1e4
time = np.arange(N) / float(fs)
x = -np.sin(2*np.pi*40*time )
noise_volts = np.random.normal(0, .05, len(x))
x=x+noise_volts
X = x**2+x
"""# **Testing parameters**"""
# ---------------- Params
# [bic,waxis] = bicoher (y, nfft, wind, segsamp, overlap)
#nfft = [64, 128, 512, 1024,2048]
#wind = ['hann', 'hamm']
#segsamp = [64,128,256,512]
#overlap = [30,50,70]
nfft = [1024]
wind = ['hann']
segsamp = [32]
overlap = [50]
alpha = np.array([.1,.4,.8,1])
subn = len(alpha)+1
## ---------- Plots -----------------
subp = -1
plt.figure(figsize=(20,20))
for i in range(0, len(nfft)):
for j in range(0, len(wind)):
for k in range(0, len(segsamp)):
for o in range(0, len(overlap)):
plt.subplot(subn,3,1)
plt.plot(x)
plt.title('signal x')
subp = 1 + subp
anglez_x,bic_x,meansx,statistic_x= bicoher(x,nfft[i],wind[j],segsamp[k],overlap[o],21)
plt.subplot(subn,3,2)
plt.imshow(20*np.log10(abs(fftshift(bic_x))))
plt.title('signal x with NFFT= {}'.format(nfft[i]) + ', Window= {}'.format(wind[j]) + ', segsamp= {}'.format(segsamp[k]) + ', overlap= {}'.format(overlap[o]))
plt.subplot(subn,3,3)
plt.hist(anglez_x,7)
plt.subplots_adjust(hspace=0.5)
plt.subplots_adjust(wspace=0.5)
plt.figure(figsize=(20,20))
for hhh in range(0, len(alpha)):
for i in range(0, len(nfft)):
for j in range(0, len(wind)):
for k in range(0, len(segsamp)):
for o in range(0, len(overlap)):
X = alpha[hhh]*x**2+x
subp=subp+3
plt.subplot(subn,3,subp+1)
plt.plot(X)
plt.title('signal X with Alpha = {}'.format(alpha[hhh]))
anglez_X,bic_x,meansX,statistic_X= bicoher(X,nfft[i],wind[j],segsamp[k],overlap[o],2)
plt.subplot(subn,3,subp+2)
plt.imshow(20*np.log10(abs(fftshift(bic_x))))
plt.title('signal X with NFFT= {}'.format(nfft[i]) + ', Window= {}'.format(wind[j]) + ', segsamp= {}'.format(segsamp[k]) + ', overlap= {}'.format(overlap[o]))
plt.subplot(subn,3,subp+3)
plt.subplots_adjust(hspace=0.5)
plt.subplots_adjust(wspace=0.5)
plt.hist(anglez_X,7)
all_true_var_ang[0] = statistic_x[0]
all_true_var_bic[0] = statistic_x[1]
all_true_std_ang[0] = statistic_x[2]
all_true_std_bic[0] = statistic_x[3]
all_true_skew_ang[0] = statistic_x[4]
all_true_skew_bic[0] = statistic_x[5]
all_true_kurtosis_ang[0] = statistic_x[6]
all_true_kurtosis_bic[0] = statistic_x[7]
all_fake_var_ang[0] = statistic_X[0]
all_fake_var_bic[0] = statistic_X[1]
all_fake_std_ang[0] = statistic_X[2]
all_fake_std_bic[0] = statistic_X[3]
all_fake_skew_ang[0] = statistic_X[4]
all_fake_skew_bic[0] = statistic_X[5]
all_fake_kurtosis_ang[0] = statistic_X[6]
all_fake_kurtosis_bic[0] = statistic_X[7]
print('var_ang')
print('x = ',statistic_x[0], 'X = ',statistic_X[0])
print('var_bic')
print('x = ',statistic_x[1], 'X = ',statistic_X[1])
print('std_ang' )
print('x = ',statistic_x[2], 'X = ',statistic_X[2])
print('std_bic')
print('x = ',statistic_x[3], 'X = ',statistic_X[3])
print('skew_ang')
print('x = ',statistic_x[4], 'X = ',statistic_X[4])
print('skew_bic')
print('x = ',statistic_x[5], 'X = ',statistic_X[5])
print('kurtosis_ang')
print('x = ',statistic_x[6], 'X = ',statistic_X[6])
print('kurtosis_bic')
print('x = ',statistic_x[7], 'X = ',statistic_X[7])
""""""
X = x / np.sqrt(1+x**2)
#nfft = [64, 128, 512, 1024,2048]
#wind = ['hann', 'hamm']
#segsamp = [64,128,256,512]
#overlap = [30,50,70]
nfft = [2048]
wind = ['hann']
segsamp = [32]
overlap = [50]
subn=2
subp=3
## ---------- Plots -----------------
plt.figure(figsize=(20,20))
for i in range(0, len(nfft)):
for j in range(0, len(wind)):
for k in range(0, len(segsamp)):
for o in range(0, len(overlap)):
plt.subplot(subn,3,1)
plt.plot(x)
plt.title('True Signal')
subp = 1 + subp
anglez_x,bic_x,meansx,statistic_x= bicoher(x,nfft[i],wind[j],segsamp[k],overlap[o],3)
plt.subplot(subn,3,2)
plt.imshow(20*np.log10(abs(fftshift(bic_x))))
plt.title('signal x with NFFT= {}'.format(nfft[i]) + ', Window= {}'.format(wind[j]) + ', segsamp= {}'.format(segsamp[k]) + ', overlap= {}'.format(overlap[o]))
plt.subplot(subn,3,3)
plt.hist(anglez_x,20)
plt.subplots_adjust(hspace=0.5)
plt.subplots_adjust(wspace=0.5)
plt.figure(figsize=(20,20))
for i in range(0, len(nfft)):
for j in range(0, len(wind)):
for k in range(0, len(segsamp)):
for o in range(0, len(overlap)):
plt.subplot(subn,3,4)
plt.plot(X)
plt.title('Fake Signal')
anglez_X,bic_X,meansX,statistic_X= bicoher(X,nfft[i],wind[j],segsamp[k],overlap[o],3)
plt.subplot(subn,3,5)
plt.imshow(20*np.log10(abs(fftshift(bic_X))))
plt.title('signal X with NFFT= {}'.format(nfft[i]) + ', Window= {}'.format(wind[j]) + ', segsamp= {}'.format(segsamp[k]) + ', overlap= {}'.format(overlap[o]))
plt.subplot(subn,3,6)
plt.subplots_adjust(hspace=0.5)
plt.subplots_adjust(wspace=0.5)
plt.hist(anglez_X,20)
all_true_var_ang[1] = statistic_x[0]
all_true_var_bic[1] = statistic_x[1]
all_true_std_ang[1] = statistic_x[2]
all_true_std_bic[1] = statistic_x[3]
all_true_skew_ang[1] = statistic_x[4]
all_true_skew_bic[1] = statistic_x[5]
all_true_kurtosis_ang[1] = statistic_x[6]
all_true_kurtosis_bic[1] = statistic_x[7]
all_fake_var_ang[1] = statistic_X[0]
all_fake_var_bic[1] = statistic_X[1]
all_fake_std_ang[1] = statistic_X[2]
all_fake_std_bic[1] = statistic_X[3]
all_fake_skew_ang[1] = statistic_X[4]
all_fake_skew_bic[1] = statistic_X[5]
all_fake_kurtosis_ang[1] = statistic_X[6]
all_fake_kurtosis_bic[1] = statistic_X[7]
print('var_ang')
print(' x = ',statistic_x[0], 'X = ',statistic_X[0])
print('var_bic')
print(' x = ',statistic_x[1], 'X = ',statistic_X[1])
print('std_ang' )
print(' x = ',statistic_x[2], 'X = ',statistic_X[2])
print('std_bic')
print(' x = ',statistic_x[3], 'X = ',statistic_X[3])
print('skew_ang')
print(' x = ',statistic_x[4], 'X = ',statistic_X[4])
print('skew_bic')
print(' x = ',statistic_x[5], 'X = ',statistic_X[5])
print('kurtosis_ang')
print(' x = ',statistic_x[6], 'X = ',statistic_X[6])
print('kurtosis_bic')
print(' x = ',statistic_x[7], 'X = ',statistic_X[7])
"""# **tanh**"""
X = np.tanh(x)
#nfft = [64, 128, 512, 1024,2048]
#wind = ['hann', 'hamm']
#segsamp = [64,128,256,512]
#overlap = [30,50,70]
nfft = [2048]
wind = ['hann']
segsamp = [32]
overlap = [50]
subn=2
subp=3
## ---------- Plots -----------------
plt.figure(figsize=(20,20))
for i in range(0, len(nfft)):
for j in range(0, len(wind)):
for k in range(0, len(segsamp)):
for o in range(0, len(overlap)):
plt.subplot(subn,3,1)
plt.plot(x)
plt.title('True Signal')
subp = 1 + subp
anglez_x,bic_x,meansx,statistic_x= bicoher(x,nfft[i],wind[j],segsamp[k],overlap[o],3)
plt.subplot(subn,3,2)
plt.imshow(20*np.log10(abs(fftshift(bic_x))))
plt.title('signal x with NFFT= {}'.format(nfft[i]) + ', Window= {}'.format(wind[j]) + ', segsamp= {}'.format(segsamp[k]) + ', overlap= {}'.format(overlap[o]))
plt.subplot(subn,3,3)
plt.hist(anglez_x,20)
plt.subplots_adjust(hspace=0.5)
plt.subplots_adjust(wspace=0.5)
plt.figure(figsize=(20,20))
for i in range(0, len(nfft)):
for j in range(0, len(wind)):
for k in range(0, len(segsamp)):
for o in range(0, len(overlap)):
plt.subplot(subn,3,4)
plt.plot(X)
plt.title('Fake Signal')
anglez_X,bic_x,meansX,statistic_X= bicoher(X,nfft[i],wind[j],segsamp[k],overlap[o],3)
plt.subplot(subn,3,5)
plt.imshow(20*np.log10(abs(fftshift(bic_x))))
plt.title('signal X with NFFT= {}'.format(nfft[i]) + ', Window= {}'.format(wind[j]) + ', segsamp= {}'.format(segsamp[k]) + ', overlap= {}'.format(overlap[o]))
plt.subplot(subn,3,6)
plt.subplots_adjust(hspace=0.5)
plt.subplots_adjust(wspace=0.5)
plt.hist(anglez_X,20)
all_true_var_ang[2] = statistic_x[0]
all_true_var_bic[2] = statistic_x[1]
all_true_std_ang[2] = statistic_x[2]
all_true_std_bic[2] = statistic_x[3]
all_true_skew_ang[2] = statistic_x[4]
all_true_skew_bic[2] = statistic_x[5]
all_true_kurtosis_ang[2] = statistic_x[6]
all_true_kurtosis_bic[2] = statistic_x[7]
all_fake_var_ang[2] = statistic_X[0]
all_fake_var_bic[2] = statistic_X[1]
all_fake_std_ang[2] = statistic_X[2]
all_fake_std_bic[2] = statistic_X[3]
all_fake_skew_ang[2] = statistic_X[4]
all_fake_skew_bic[2] = statistic_X[5]
all_fake_kurtosis_ang[2] = statistic_X[6]
all_fake_kurtosis_bic[2] = statistic_X[7]
print('var_ang')
print(' x = ',statistic_x[0], 'X = ',statistic_X[0])
print('var_bic')
print(' x = ',statistic_x[1], 'X = ',statistic_X[1])
print('std_ang' )
print(' x = ',statistic_x[2], 'X = ',statistic_X[2])
print('std_bic')
print(' x = ',statistic_x[3], 'X = ',statistic_X[3])
print('skew_ang')
print(' x = ',statistic_x[4], 'X = ',statistic_X[4])
print('skew_bic')
print(' x = ',statistic_x[5], 'X = ',statistic_X[5])
print('kurtosis_ang')
print(' x = ',statistic_x[6], 'X = ',statistic_X[6])
print('kurtosis_bic')
print(' x = ',statistic_x[7], 'X = ',statistic_X[7])
"""# **Fearture Extractor**"""
!apt-get install subversion #this is to be able to import an audio folder form a github depository
"""# TRUE"""
!svn checkout https://github.com/enzojam/true.git # import the audio folder
truelist = [str(file) for file in Path('/content/true.git/trunk/').glob('*.wav')] # are taking all the files in the path directory that start with kick_ and have and mp3 extension and for each one we get the string to the path
truelist # they are basically lists of paths
true_signals = list (librosa.load(p)[0] for p in truelist) #we create a list in which each component is the correspong wav file anche we sotre it in the list
"""# FAKE"""
!svn checkout https://github.com/enzojam/fake.git
fakelist = [str(file) for file in Path('/content/fake.git/trunk/').glob('*.wav')]
fakelist
# we store alle the features in 1 matrix
# feature_table = np.vstack((kick_features,snare_features))
#print(feature_table.shape) # we have concatenated the 2 features
files_table= truelist+ fakelist
fake_signals = list (librosa.load(p)[0] for p in fakelist)
"""# ***Features***"""
x = true_signals[7]
X = fake_signals[13]
# ---------------- Params
# [bic,waxis] = bicoher (y, nfft, wind, segsamp, overlap)
#nfft = [64, 128, 512, 1024,2048]
#wind = ['hann', 'hamm']
#segsamp = [64,128,256,512]
#overlap = [30,50,70]
nfft = [2048]
wind = ['hann']
segsamp = [32]
overlap = [50]
subn=2
subp=3
## ---------- Plots -----------------
plt.figure(figsize=(20,20))
for i in range(0, len(nfft)):
for j in range(0, len(wind)):
for k in range(0, len(segsamp)):
for o in range(0, len(overlap)):
plt.subplot(subn,3,1)
plt.plot(x)
plt.title('True Signal')
subp = 1 + subp
anglez_x,bic_x,meansx,statistic_x= bicoher(x,nfft[i],wind[j],segsamp[k],overlap[o],3)
plt.subplot(subn,3,2)
plt.imshow(20*np.log10(abs(fftshift(bic_x))))
plt.title('signal x with NFFT= {}'.format(nfft[i]) + ', Window= {}'.format(wind[j]) + ', segsamp= {}'.format(segsamp[k]) + ', overlap= {}'.format(overlap[o]))
plt.subplot(subn,3,3)
plt.hist(anglez_x,20)
plt.subplots_adjust(hspace=0.5)
plt.subplots_adjust(wspace=0.5)
plt.figure(figsize=(20,20))
for i in range(0, len(nfft)):
for j in range(0, len(wind)):
for k in range(0, len(segsamp)):
for o in range(0, len(overlap)):
plt.subplot(subn,3,4)
plt.plot(X)
plt.title('Fake Signal')
anglez_X,bic_x,meansX,statistic_X= bicoher(X,nfft[i],wind[j],segsamp[k],overlap[o],3)
plt.subplot(subn,3,5)
plt.imshow(20*np.log10(abs(fftshift(bic_x))))
plt.title('signal X with NFFT= {}'.format(nfft[i]) + ', Window= {}'.format(wind[j]) + ', segsamp= {}'.format(segsamp[k]) + ', overlap= {}'.format(overlap[o]))
plt.subplot(subn,3,6)
plt.subplots_adjust(hspace=0.5)
plt.subplots_adjust(wspace=0.5)
plt.hist(anglez_X,20)
all_true_var_ang[3] = statistic_x[0]
all_true_var_bic[3] = statistic_x[1]
all_true_std_ang[3] = statistic_x[2]
all_true_std_bic[3] = statistic_x[3]
all_true_skew_ang[3] = statistic_x[4]
all_true_skew_bic[3] = statistic_x[5]
all_true_kurtosis_ang[3] = statistic_x[6]
all_true_kurtosis_bic[3] = statistic_x[7]
all_fake_var_ang[3] = statistic_X[0]
all_fake_var_bic[3] = statistic_X[1]
all_fake_std_ang[3] = statistic_X[2]
all_fake_std_bic[3] = statistic_X[3]
all_fake_skew_ang[3] = statistic_X[4]
all_fake_skew_bic[3] = statistic_X[5]
all_fake_kurtosis_ang[3] = statistic_X[6]
all_fake_kurtosis_bic[3] = statistic_X[7]
X = fake_signals[13]
ipd.display(ipd.Audio(X, rate=22050)) # we use idp.Audio to listen to each note
x = true_signals[7]
ipd.display(ipd.Audio(x, rate=22050)) # we use idp.Audio to listen to each note
plt.figure(figsize=(20,6))
plt.subplot(1,3,3)
plt.scatter(-10*np.log10(all_fake_var_bic[3]),-10*np.log10(all_fake_std_bic[3]),c='r',marker = '*')
plt.scatter(-10*np.log10(all_true_var_bic[3]),-10*np.log10(all_true_std_bic[3]),c='m',marker = 'd')
plt.title('Mixed data')
plt.xlabel('var Bic')
plt.ylabel('STD Bic')
plt.legend((' fake','True'))
print('var_ang')
print('x = ',statistic_x[0], 'X = ',statistic_X[0])
print('var_bic')
print('x = ',statistic_x[1], 'X = ',statistic_X[1])
print('std_ang' )
print('x = ',statistic_x[2], 'X = ',statistic_X[2])
print('std_bic')
print('x = ',statistic_x[3], 'X = ',statistic_X[3])
print('skew_ang')
print('x = ',statistic_x[4], 'X = ',statistic_X[4])
print('skew_bic')
print('x = ',statistic_x[5], 'X = ',statistic_X[5])
print('kurtosis_ang')
print('x = ',statistic_x[6], 'X = ',statistic_X[6])
print('kurtosis_bic')
print('x = ',statistic_x[7], 'X = ',statistic_X[7])
"""# **PLOT**"""
plt.figure(figsize=(6,20))
plt.subplot(3,1,1)
plt.scatter(10*np.log10(all_true_var_ang[0]),10*np.log10(all_true_var_bic[0]),c='r',marker='*')
plt.scatter(10*np.log10(all_true_var_ang[1]),10*np.log10(all_true_var_bic[1]),c='b',marker='1')
plt.scatter(10*np.log10(all_true_var_ang[2]),10*np.log10(all_true_var_bic[2]),c='g',marker='x')
plt.scatter(10*np.log10(all_true_var_ang[3]),10*np.log10(all_true_var_bic[3]),c='y',marker='d')
plt.title('Truth data')
plt.xlabel('Var Ang')
plt.ylabel('Var Bic')
plt.legend(('x^2','x/sqrt(1+x2)','tanh','wavnet'))
plt.figure(figsize=(6,20))
plt.subplot(3,1,2)
plt.scatter(10*np.log10(all_fake_var_ang[0]),10*np.log10(all_fake_var_bic[0]),c='r',marker='*')
plt.scatter(10*np.log10(all_fake_var_ang[1]),10*np.log10(all_fake_var_bic[1]),c='b',marker='1')
plt.scatter(10*np.log10(all_fake_var_ang[2]),10*np.log10(all_fake_var_bic[2]),c='g',marker='x')
plt.scatter(10*np.log10(all_fake_var_ang[3]),10*np.log10(all_fake_var_bic[3]),c='y',marker='d')
plt.title('Fake data')
plt.xlabel('Var Ang')
plt.ylabel('Var Bic')
plt.legend(('x^2','x/sqrt(1+x2)','tanh','wavnet'))
plt.figure(figsize=(6,20))
plt.subplot(3,1,3)
plt.scatter(10*np.log10(all_fake_var_ang[0]),10*np.log10(all_fake_var_bic[0]),c='r',marker='*')
plt.scatter(10*np.log10(all_fake_var_ang[1]),10*np.log10(all_fake_var_bic[1]),c='b',marker='1')
plt.scatter(10*np.log10(all_fake_var_ang[2]),10*np.log10(all_fake_var_bic[2]),c='g',marker='x')
plt.scatter(10*np.log10(all_fake_var_ang[3]),10*np.log10(all_fake_var_bic[3]),c='y',marker='d')
plt.scatter(10*np.log10(all_true_var_ang[0]),10*np.log10(all_true_var_bic[0]),c='m',marker='*')
plt.scatter(10*np.log10(all_true_var_ang[1]),10*np.log10(all_true_var_bic[1]),c='m',marker='1')
plt.scatter(10*np.log10(all_true_var_ang[2]),10*np.log10(all_true_var_bic[2]),c='m',marker='x')
plt.scatter(10*np.log10(all_true_var_ang[3]),10*np.log10(all_true_var_bic[3]),c='m',marker='d')
plt.title('Mixed data')
plt.xlabel('Var Ang')
plt.ylabel('Var Bic')
plt.legend((' fake x^2','fake x/sqrt(1+x2)','fake tanh','fake wavnet','x^2','x/sqrt(1+x2)','tanh','wavnet'))
plt.figure(figsize=(20,6))
plt.subplot(1,3,1)
plt.scatter(all_true_std_ang[0],10*np.log10(all_true_std_bic[0]),c='r',marker = '*')
plt.scatter(all_true_std_ang[1],10*np.log10(all_true_std_bic[1]),c='b',marker = '1')
plt.scatter(all_true_std_ang[2],10*np.log10(all_true_std_bic[2]),c='g',marker = 'x')
plt.scatter(all_true_std_ang[3],10*np.log10(all_true_std_bic[3]),c='y',marker = 'd')
plt.title('Truth data')
plt.xlabel('STD Ang')
plt.ylabel('STD Bic')
plt.legend(('x^2','x/sqrt(1+x2)','tanh','wavnet'))
plt.figure(figsize=(20,6))
plt.subplot(1,3,2)
plt.scatter(all_fake_std_ang[0],10*np.log10(all_fake_std_bic[0]),c='r',marker = '*')
plt.scatter(all_fake_std_ang[1],10*np.log10(all_fake_std_bic[1]),c='b',marker = '1')
plt.scatter(all_fake_std_ang[2],10*np.log10(all_fake_std_bic[2]),c='g',marker = 'x')
plt.scatter(all_fake_std_ang[3],10*np.log10(all_fake_std_bic[3]),c='y',marker = 'd')
plt.title('Fake data')
plt.xlabel('STD Ang')
plt.ylabel('STD Bic')
plt.legend(('x^2','x/sqrt(1+x2)','tanh','wavnet'))
plt.figure(figsize=(20,6))
plt.subplot(1,3,3)
plt.scatter(all_fake_std_ang[0],10*np.log10(all_fake_std_bic[0]),c='r',marker = '*')
plt.scatter(all_fake_std_ang[1],10*np.log10(all_fake_std_bic[1]),c='b',marker = '1')
plt.scatter(all_fake_std_ang[2],10*np.log10(all_fake_std_bic[2]),c='g',marker = 'x')
plt.scatter(all_fake_std_ang[3],10*np.log10(all_fake_std_bic[3]),c='y',marker = 'd')
plt.scatter(all_true_std_ang[0],10*np.log10(all_true_std_bic[0]),c='m',marker = '*')
plt.scatter(all_true_std_ang[1],10*np.log10(all_true_std_bic[1]),c='m',marker = '1')
plt.scatter(all_true_std_ang[2],10*np.log10(all_true_std_bic[2]),c='m',marker = 'x')
plt.scatter(all_true_std_ang[3],10*np.log10(all_true_std_bic[3]),c='m',marker = 'd')
plt.title('Mixed data')
plt.xlabel('STD Ang')
plt.ylabel('STD Bic')
plt.legend((' fake x^2','fake x/sqrt(1+x2)','fake tanh','fake wavnet','x^2','x/sqrt(1+x2)','tanh','wavnet'))
plt.figure(figsize=(20,6))
plt.subplot(1,3,1)
plt.scatter(all_true_skew_ang[0],all_true_skew_bic[0],c='r')
plt.scatter(all_true_skew_ang[1],all_true_skew_bic[1],c='b')
plt.scatter(all_true_skew_ang[2],all_true_skew_bic[2],c='g')
plt.scatter(all_true_skew_ang[3],all_true_skew_bic[3],c='y')
plt.title('Truth data')
plt.xlabel('Skew Ang')
plt.ylabel('Skew Bic')
plt.legend(('x^2','x/sqrt(1+x2)','tanh','wavnet'))
plt.figure(figsize=(20,6))
plt.subplot(1,3,2)
plt.scatter(all_fake_skew_ang[0],all_fake_skew_bic[0],c='r')
plt.scatter(all_fake_skew_ang[1],all_fake_skew_bic[1],c='b')
plt.scatter(all_fake_skew_ang[2],all_fake_skew_bic[2],c='g')
plt.scatter(all_fake_skew_ang[3],all_fake_skew_bic[3],c='y')
plt.title('Fake data')
plt.xlabel('Skew Ang')
plt.ylabel('Skew Bic')
plt.legend(('x^2','x/sqrt(1+x2)','tanh','wavnet'))
plt.figure(figsize=(20,6))
plt.subplot(1,3,3)
plt.scatter(all_true_skew_ang[0],all_true_skew_bic[0],c='m',marker ='*')
plt.scatter(all_true_skew_ang[1],all_true_skew_bic[1],c='m',marker ='1')
plt.scatter(all_true_skew_ang[2],all_true_skew_bic[2],c='m',marker ='x')
plt.scatter(all_true_skew_ang[3],all_true_skew_bic[3],c='m',marker ='d')
plt.scatter(all_fake_skew_ang[0],all_fake_skew_bic[0],c='r',marker ='*')
plt.scatter(all_fake_skew_ang[1],all_fake_skew_bic[1],c='b',marker ='1')
plt.scatter(all_fake_skew_ang[2],all_fake_skew_bic[2],c='g',marker ='x')
plt.scatter(all_fake_skew_ang[3],all_fake_skew_bic[3],c='y',marker ='d')
plt.title('Mixed data')
plt.xlabel('Skew Ang')
plt.ylabel('Skew Bic')
plt.legend(('x^2','x/sqrt(1+x2)','tanh','wavnet',' fake x^2','fake x/sqrt(1+x2)','fake tanh','fake wavnet'))
plt.figure(figsize=(20,6))
plt.subplot(1,3,1)
plt.scatter(all_true_kurtosis_ang[0],all_true_kurtosis_bic[0],c='r',marker = '*')
plt.scatter(all_true_kurtosis_ang[1],all_true_kurtosis_bic[1],c='b',marker = '1')
plt.scatter(all_true_kurtosis_ang[2],all_true_kurtosis_bic[2],c='g',marker = 'x')
plt.scatter(all_true_kurtosis_ang[3],all_true_kurtosis_bic[3],c='y',marker = 'd')
plt.title('Truth data')
plt.xlabel('Kurtosis Ang')
plt.ylabel('Kurtosis Bic')
plt.legend(('x^2','x/sqrt(1+x2)','tanh','wavnet'))
plt.figure(figsize=(20,6))
plt.subplot(1,3,2)
plt.scatter(all_fake_kurtosis_ang[0],all_fake_kurtosis_bic[0],c='r',marker = '*')
plt.scatter(all_fake_kurtosis_ang[1],all_fake_kurtosis_bic[1],c='b',marker = '1')
plt.scatter(all_fake_kurtosis_ang[2],all_fake_kurtosis_bic[2],c='g',marker = 'x')
plt.scatter(all_fake_kurtosis_ang[3],all_fake_kurtosis_bic[3],c='y', marker = 'd')
plt.title('Fake data')
plt.xlabel('Kurtosis Ang')
plt.ylabel('Kurtosis Bic')
plt.legend(('x^2','x/sqrt(1+x2)','tanh','wavnet'))
plt.figure(figsize=(20,6))
plt.subplot(1,3,3)
plt.scatter(all_true_kurtosis_ang[0],all_true_kurtosis_bic[0],c='m',marker = '*')
plt.scatter(all_true_kurtosis_ang[1],all_true_kurtosis_bic[1],c='m',marker = '1')
plt.scatter(all_true_kurtosis_ang[2],all_true_kurtosis_bic[2],c='m',marker = 'x')
plt.scatter(all_true_kurtosis_ang[3],all_true_kurtosis_bic[3],c='m',marker = 'd')
plt.scatter(all_fake_kurtosis_ang[0],all_fake_kurtosis_bic[0],c='r',marker = '*')
plt.scatter(all_fake_kurtosis_ang[1],all_fake_kurtosis_bic[1],c='b',marker = '1')
plt.scatter(all_fake_kurtosis_ang[2],all_fake_kurtosis_bic[2],c='g',marker = 'x')
plt.scatter(all_fake_kurtosis_ang[3],all_fake_kurtosis_bic[3],c='y',marker = 'd')
plt.title('mixed data')
plt.xlabel('Kurtosis Ang')
plt.ylabel('Kurtosis Bic')
plt.legend(('x^2','x/sqrt(1+x2)','tanh','wavnet',' fake x^2','fake x/sqrt(1+x2)','fake tanh','fake wavnet'))