wavelet.py

# -*- coding: utf-8 -*-
"""
Created on Sun Jan  8 10:46:22 2023

@author: asus
"""

import numpy as np
import pandas as pd
import matplotlib.pylab as plt
import matplotlib.ticker as plticker# has classes for tick-locating and -formatting
import seaborn as sns
from statsmodels.tsa import stattools
import scipy.interpolate as interp
from scipy.fft import fft, fftfreq, fftshift
import scipy
from scipy import fftpack
import scaleogram as scg 
import pywt

#%% Signal that changes frequency as the last time (matshow)

x = np.linspace(0,1/4,2500)
y1 = np.sin(2*np.pi*x*4)
#plt.plot(x,y1)
y2 = np.sin(2*np.pi*x*30)
#plt.plot(x,y2)
y3 = np.sin(2*np.pi*x*60)
#plt.plot(x,y3)
y4 = np.sin(2*np.pi*x*90)
#plt.plot(x,y4)

# Using only the first two waves 
signal = np.concatenate([y1,y2])
time = np.linspace(0,1,5000)
plt.plot(time,signal)

# Using only the first three waves 
signal = np.concatenate([y1,y2,y3])
time = np.linspace(0,1,7500)
plt.plot(time,signal)

# Using all waves
signal = np.concatenate([y1,y2,y3,y4])
N = 10000
time = np.linspace(0,1,N)

fig, ax = plt.subplots(figsize=(9, 5))
ax.plot(time,signal)
sns.despine(fig, bottom=False, left=False)
plt.show()



scales = np.arange(1,500)
waveletname = 'cgau1'
coef, freqs=pywt.cwt(signal, scales, waveletname)





len(abs(coef)) # 799 = length of scale
len(abs(coef[0])) #10000 = length of data








fig, ax = plt.subplots(figsize=(12, 5))
matshow_ = ax.matshow(np.abs(coef), aspect = 'auto', cmap='Reds',
                      vmax=abs(coef).max(), vmin=0) 
fig.colorbar(matshow_)
plt.gca().xaxis.tick_bottom() # it puts x axis from top to bottom of figure.



ax.set_xlim(xmin=0, xmax=N)

loc = plticker.MultipleLocator(base=2500)  # this locator puts ticks at regular intervals
ax.xaxis.set_major_locator(loc)

def numfmt(x, pos): # your custom formatter function: divide by 1000
    s = '{}'.format(x / N)
    return s
yfmt = plticker.FuncFormatter(numfmt) # create your custom formatter function
plt.gca().xaxis.set_major_formatter(yfmt) 

ax.set_title('Wavelet Transform of Signal (${}$)'.format(waveletname), fontsize=20)
ax.set_ylabel('Scales', fontsize=15)
ax.set_xlabel('Time', fontsize=15)

plt.show() 




#%% Sognal that changes frequency as the last time (imshow)
x = np.linspace(0,1/4,2500)
y1 = np.sin(2*np.pi*x*4)
#plt.plot(x,y1)
y2 = np.sin(2*np.pi*x*30)
#plt.plot(x,y2)
y3 = np.sin(2*np.pi*x*60)
#plt.plot(x,y3)
y4 = np.sin(2*np.pi*x*90)
#plt.plot(x,y4)

# Using only the first two waves 
signal = np.concatenate([y1,y2])
time = np.linspace(0,1,5000)
plt.plot(time,signal)

# Using only the first three waves 
signal = np.concatenate([y1,y2,y3])
time = np.linspace(0,1,7500)
plt.plot(time,signal)

# Using all waves
signal = np.concatenate([y1,y2,y3,y4])
N = 10000
time = np.linspace(0,1,N)
plt.plot(time,signal)

scales = np.arange(1,1500)
waveletname = 'cmorl1.5-1.0'#cmorl1.5-1.0
coef, freqs=pywt.cwt(signal,scales, waveletname)







fig, ax = plt.subplots(figsize=(12, 5))
imshow_ = plt.imshow(np.abs(coef), interpolation='bilinear', cmap='Reds', aspect='auto') #extent=[0, len(x), 1, len(scales)],
ax.set_title('Wavelet Transform of Signal (${}$)'.format(waveletname), fontsize=20)
ax.set_ylabel('Scales',fontsize=15)
ax.set_xlabel('Time', fontsize=15)
fig.colorbar(imshow_)

plt.gca().xaxis.tick_bottom() # it puts x axis from top to bottom of figure.

ax.set_xlim(xmin=0, xmax=N)
loc = plticker.MultipleLocator(base=2500)  # this locator puts ticks at regular intervals
ax.xaxis.set_major_locator(loc)
def numfmt(x, pos): # your custom formatter function: divide by 1000
    s = '{}'.format(x / N)
    return s
yfmt = plticker.FuncFormatter(numfmt) # create your custom formatter function
plt.gca().xaxis.set_major_formatter(yfmt) 

ax.set_title('Wavelet Transform of Signal (${}$)'.format(waveletname), fontsize=20)
ax.set_ylabel('Scales', fontsize=15)
ax.set_xlabel('Time', fontsize=15)

plt.show() 




#%% Signal that changes frequency as the last time (contourf)
x = np.linspace(0,1/4,2500)
y1 = np.sin(2*np.pi*x*4)
#plt.plot(x,y1)
y2 = np.sin(2*np.pi*x*30)
#plt.plot(x,y2)
y3 = np.sin(2*np.pi*x*60)
#plt.plot(x,y3)
y4 = np.sin(2*np.pi*x*90)
#plt.plot(x,y4)

# Using only the first two waves 
signal = np.concatenate([y1,y2])
time = np.linspace(0,1,5000)
plt.plot(time,signal)

# Using only the first three waves 
signal = np.concatenate([y1,y2,y3])
time = np.linspace(0,1,7500)
plt.plot(time,signal)

# Using all waves
signal = np.concatenate([y1,y2,y3,y4])
N = 10000
time = np.linspace(0,1,N)
plt.plot(time,signal)

scales = np.arange(1,500)
waveletname = 'cgau1'
coef, freqs=pywt.cwt(signal, scales, waveletname)







fig, ax = plt.subplots(figsize=(12, 5))



contourf_ = ax.contourf(time, scales, np.abs(coef), cmap=plt.cm.Reds)#extend='both',


ax.set_title('Wavelet Transform of Signal (${}$)'.format(waveletname), fontsize=20)
ax.set_ylabel('Scales', fontsize=14)
ax.set_xlabel('Time (s)', fontsize=14)
fig.colorbar(contourf_)
plt.show()



fig, ax = plt.subplots(figsize=(12, 5))
contourf_ = ax.contourf(time, scales, np.abs(coef), cmap=plt.cm.Reds)#extend='both',
ax.set_title('Wavelet Transform of Signal (${}$)'.format(waveletname), fontsize=20)
ax.set_ylabel('Scales', fontsize=14)
ax.set_xlabel('Time (s)', fontsize=14)
ax.invert_yaxis()
fig.colorbar(contourf_)
plt.show()



#%% Example of signal that changes frequency in just one time interval

#Time domain signal
time = np.linspace(-1, 1, 200, endpoint=False)
signal  = np.cos(2 * np.pi * 7 * time) + np.real(np.exp(-7*(time-0.4)**2)*np.exp(1j*2*np.pi*2*(time-0.4)))

fig, ax = plt.subplots(figsize=(9, 5))
ax.plot(time,signal)
sns.despine(fig, bottom=False, left=False)
plt.show()

#Setting parameters for Continous Wavelet Transform
scales = np.arange(1,128)
waveletname='cmorl1.5-1.0'
coef, freqs=pywt.cwt(signal, scales, waveletname)



#contourf

fig, ax = plt.subplots(figsize=(12, 2))
contourf_ = ax.contourf(time, scales, np.abs(coef), cmap=plt.cm.Reds)#extend='both',
ax.set_title('Wavelet Transform of Signal (${}$)'.format(waveletname), fontsize=20)
ax.set_ylabel('Scales', fontsize=14)
ax.set_xlabel('Time (s)', fontsize=14)
ax.set_xlim(-1,1)
ax.invert_yaxis()
fig.colorbar(contourf_)
plt.show()

fig, ax = plt.subplots(figsize=(12, 2))
contourf_ = ax.contourf(time, freqs, np.abs(coef), cmap=plt.cm.Reds)#extend='both',
ax.set_title('Wavelet Transform of Signal (${}$)'.format(waveletname), fontsize=20)
ax.set_ylabel('Scales', fontsize=14)
ax.set_xlabel('Time (s)', fontsize=14)
ax.set_xlim(-1,1)
ax.invert_yaxis()
fig.colorbar(contourf_)
plt.show()




#matshow
fig, ax = plt.subplots(figsize=(12, 5))
matshow_ = ax.matshow(np.abs(coef), extent=[-1, 1, 31, 1], aspect = 'auto', cmap='Reds',
                      vmax=abs(coef).max(), vmin=0) # removing extent=[-1, 1, 1, 31] it turns right.
fig.colorbar(matshow_)

plt.gca().xaxis.tick_bottom() # it puts x axis from top to bottom of figure.
loc = plticker.MultipleLocator(base=0.25)  # this locator puts ticks at regular intervals
ax.xaxis.set_major_locator(loc)

ax.set_title('Wavelet Transform of Signal (${}$)'.format(waveletname), fontsize=20)
ax.set_ylabel('Scales', fontsize=15)
ax.set_xlabel('Time', fontsize=15)
plt.show() 





#imshow
fig, ax = plt.subplots(figsize=(12, 5))
imshow_ = plt.imshow(np.abs(coef), cmap='Reds', aspect='auto', extent=[-1, 1, 31, 1],
           vmax=abs(coef).max(), vmin=0)  # extent=[-1, 1, 1, 31],
fig.colorbar(imshow_)

loc = plticker.MultipleLocator(base=0.25)  # this locator puts ticks at regular intervals
ax.xaxis.set_major_locator(loc)

ax.set_title('Wavelet Transform of Signal (${}$)'.format(waveletname), fontsize=20)
ax.set_ylabel('Scales', fontsize=15)
ax.set_xlabel('Time', fontsize=15)
plt.show() 




#%%Sinusoidal wave with constant frequency.

x = np.linspace(0,1,1000)
y = np.sin(2*np.pi*x*4)

fig, ax = plt.subplots(figsize=(9, 5))
ax.plot(x,y)
sns.despine(fig, bottom=False, left=False)
plt.show()



#Setting parameters for Continous Wavelet Transform
scales = np.arange(1,256)
waveletname='cgau1'
coef, freqs=pywt.cwt(y, scales, waveletname)



#contourf in log viene più quello che ci aspettiamo
fig, ax = plt.subplots(figsize=(12, 2))
contourf_ = ax.contourf(x, scales, np.log(np.abs(coef)), cmap=plt.cm.Reds)#extend='both',
ax.set_title('Wavelet Transform of Signal (${}$)'.format(waveletname), fontsize=20)
ax.set_ylabel('Scales', fontsize=14)
ax.set_xlabel('Time (s)', fontsize=14)
fig.colorbar(contourf_)
plt.show()



#matshow
fig, ax = plt.subplots(figsize=(12, 5))
matshow_ = ax.matshow(np.abs(coef),  aspect = 'auto', cmap='Reds',
                      vmax=abs(coef).max(), vmin=0) 
fig.colorbar(matshow_)
plt.gca().xaxis.tick_bottom() # it puts x axis from top to bottom of figure.

#loc = plticker.MultipleLocator(base=0.25)  # this locator puts ticks at regular intervals
#ax.xaxis.set_major_locator(loc)
ax.set_xlim(0,1000)
def numfmt(x, pos): # your custom formatter function: divide by 1000
    s = '{}'.format(x / 1000)
    return s
yfmt = plticker.FuncFormatter(numfmt) # create your custom formatter function
plt.gca().xaxis.set_major_formatter(yfmt) 

ax.set_title('Wavelet Transform of Signal (${}$)'.format(waveletname), fontsize=20)
ax.set_ylabel('Scales', fontsize=15)
ax.set_xlabel('Time', fontsize=15)
ax.invert_yaxis()
plt.show() 


#imshow
fig, ax = plt.subplots(figsize=(12, 5))
imshow_ = plt.imshow(np.abs(coef), extent=[min(x), max(x), min(scales), max(scales)], cmap='Reds', aspect='auto',
           vmax=abs(coef).max(), vmin=0)  
fig.colorbar(imshow_)
ax.set_title('Wavelet Transform of Signal (${}$)'.format(waveletname), fontsize=20)
ax.set_ylabel('Scales', fontsize=15)
ax.set_xlabel('Time', fontsize=15)
ax.invert_yaxis()
plt.show() 




#%% Just to know.

import numpy as np
import ssqueezepy
from ssqueezepy import cwt, Wavelet
from ssqueezepy.experimental import scale_to_freq
from ssqueezepy.visuals import imshow

t = np.linspace(-1, 1, 200, endpoint=False)
sig = (np.cos(2 * np.pi * 7 * t) +
       np.real(np.exp(-7*(t-0.4)**2)*np.exp(1j*2*np.pi*2*(t-0.4))))

plt.plot(t,sig)

wavelet = Wavelet(('gmw', {'beta': 4}))
Wx, scales = cwt(sig, wavelet, padtype='zero')

freqs = scale_to_freq(scales, wavelet, N=len(sig), fs=1/(t[1] - t[0]))
imshow(Wx, cmap='Reds', abs=1, yticks=freqs,  xticks=t, xlabel="time [sec]", ylabel="frequency [Hz]")

ssqueezepy.wavs()
ssqueezepy.Wavelet('cmhat').info()



#%%Squeezepy in our case

autorepressor_results = pd.read_csv('autorepressor_gillespiesimulation_results.csv',sep= " ")
autorepressor_results
RNAs = autorepressor_results['Number of RNA molecules']

time = autorepressor_results['Time']

xvals = np.arange(autorepressor_results['Time'].iloc[0], autorepressor_results['Time'].iloc[-1], 0.01)
f_RNAs = interp.interp1d(time, RNAs, kind='previous')
yinterp_RNAs = f_RNAs(xvals)



wavelet = Wavelet(('gmw', {'beta': 4}))
Wx, scales = cwt(yinterp_RNAs, wavelet, padtype='zero')

freqs = scale_to_freq(scales, wavelet, N=len(yinterp_RNAs), fs=1/0.01)
imshow(Wx, abs=1, yticks=freqs,  xticks=xvals, xlabel="time [sec]", ylabel="frequency [Hz]")

ssqueezepy.wavs()
ssqueezepy.Wavelet('cmhat').info()




proteins = autorepressor_results['Number of proteins']

time = autorepressor_results['Time']

xvals = np.arange(autorepressor_results['Time'].iloc[0], autorepressor_results['Time'].iloc[-1], 0.01)
f_proteins = interp.interp1d(time, proteins, kind='previous')
yinterp_proteins = f_proteins(xvals)



wavelet = Wavelet(('gmw', {'beta': 4}))
Wx, scales = cwt(yinterp_proteins, wavelet, padtype='zero')

freqs = scale_to_freq(scales, wavelet, N=len(yinterp_proteins), fs=1/0.01)
imshow(Wx, abs=1, yticks=freqs,  xticks=xvals, xlabel="time [sec]", ylabel="frequency [Hz]")

ssqueezepy.wavs()
ssqueezepy.Wavelet('cmhat').info()


#%%
x = np.linspace(0,1/4,2500)
y1 = np.sin(2*np.pi*x*4)
#plt.plot(x,y1)
y2 = np.sin(2*np.pi*x*30)
#plt.plot(x,y2)
y3 = np.sin(2*np.pi*x*60)
#plt.plot(x,y3)
y4 = np.sin(2*np.pi*x*90)
#plt.plot(x,y4)

# Using only the first two waves 
signal = np.concatenate([y1,y2])
time = np.linspace(0,1,5000)
plt.plot(time,signal)

# Using only the first three waves 
signal = np.concatenate([y1,y2,y3])
time = np.linspace(0,1,7500)
plt.plot(time,signal)

# Using all waves
signal = np.concatenate([y1,y2,y3,y4])
N = 10000
time = np.linspace(0,1,N)
plt.plot(time,signal)



wavelet = Wavelet(('gmw', {'beta': 4}))
Wx, scales = cwt(signal, wavelet, padtype='zero')

freqs = scale_to_freq(scales, wavelet, N=len(signal), fs=1/(time[1] - time[0]))
imshow(Wx, cmap='Reds', abs=1, yticks=freqs,  xticks=time, xlabel="time (a.u.)", ylabel="frequency (a.u.)")

ssqueezepy.wavs()
ssqueezepy.Wavelet('cmhat').info()

#%%
results = pd.read_csv('removed_warmup_ka1ki0.5gillespieresults_seed1.csv', sep= " ")
results = pd.read_csv('ka0.1ki1gillespieresults_seed1.csv', sep= " ")
results = pd.read_csv('autorepressor_gillespiesimulation_results.csv', sep= " ")
results = pd.read_csv('removed_warmup_nfkb_gillespieresults.csv', sep= " ")



results.iloc[2490]
results
results = results.iloc[:4291]
results = results.iloc[:14000]
results = results.iloc[:2490]

RNAs = results['Number of RNA molecules']

time = results['Time']

xvals = np.arange(results['Time'].iloc[0], results['Time'].iloc[-1], 0.01)
f_RNAs = interp.interp1d(time, RNAs, kind='previous')
yinterp_RNAs = f_RNAs(xvals)



wavelet = Wavelet(('gmw', {'beta': 4}))
Wx, scales = cwt(yinterp_RNAs, wavelet, padtype='zero')

freqs = scale_to_freq(scales, wavelet, N=len(yinterp_RNAs), fs=1/0.01)# è la frequenza del segnale così come lo era per l'onda sinusoidale.
imshow(Wx, title="NF-kB products (RNAs)",cmap='Reds', abs=1, yticks=freqs,  xticks=xvals, xlabel="time (a.u.)", ylabel="frequency (a.u.)")

ssqueezepy.wavs()
ssqueezepy.Wavelet('cmhat').info()




proteins = results['Number of proteins']

time = results['Time']

xvals = np.arange(results['Time'].iloc[0], results['Time'].iloc[-1], 0.01)
f_proteins = interp.interp1d(time, proteins, kind='previous')
yinterp_proteins = f_proteins(xvals)



wavelet = Wavelet(('gmw', {'beta': 4}))
Wx, scales = cwt(yinterp_proteins, wavelet, padtype='zero')

freqs = scale_to_freq(scales, wavelet, N=len(yinterp_proteins), fs=1/0.01)
imshow(Wx, title="CWT First model ka=0.1,ki=1 (Proteins)",cmap='Reds', abs=1, yticks=freqs,  xticks=xvals, xlabel="time (a.u.)", ylabel="frequency (a.u.)")

ssqueezepy.wavs()
ssqueezepy.Wavelet('cmhat').info()




#%% Our molecules data

#PROVA A METTERE IN ATTO IL CONSIGLIO DEL PROFESSORE OSSIA DI CONSIDERARE LA DISTRIBUZIONE DI OGNI RIGA.

autorepressor_results = pd.read_csv('autorepressor_gillespiesimulation_results.csv',sep= " ")
autorepressor_results
RNAs = autorepressor_results['Number of RNA molecules']
proteins = autorepressor_results['Number of proteins']
time = autorepressor_results['Time']

xvals = np.arange(autorepressor_results['Time'].iloc[0], autorepressor_results['Time'].iloc[-1], 0.01)




firstmodel_results = pd.read_csv('removed_warmup_ka1ki0.5gillespieresults_seed1.csv', sep= " ")
RNAs = firstmodel_results['Number of RNA molecules']
proteins = firstmodel_results['Number of proteins']
time = firstmodel_results['Time']

xvals = np.arange(firstmodel_results['Time'].iloc[0], firstmodel_results['Time'].iloc[-1], 0.01)



results = pd.read_csv('removed_warmup_nfkb_gillespieresults.csv', sep= " ")
RNAs = results['Number of RNA molecules']
time = results['Time']

xvals = np.arange(results['Time'].iloc[0], results['Time'].iloc[-1], 0.01)



f_RNAs = interp.interp1d(time, RNAs, kind='previous')
yinterp_RNAs = f_RNAs(xvals)

f_proteins = interp.interp1d(time, proteins, kind='previous')
yinterp_proteins = f_proteins(xvals)

df_RNAs = pd.DataFrame(zip(yinterp_RNAs,xvals), columns = ['RNAs','Time'])
df_proteins = pd.DataFrame(zip(yinterp_proteins,xvals), columns = ['proteins','Time'])


signal_RNAs = df_RNAs['RNAs']
signal_proteins = df_proteins['proteins']

#####################Time Domain Signal
fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(10, 5))
ax.plot(df_RNAs['Time'], df_RNAs['RNAs'])
ax.set_ylabel('# of RNAs')
ax.set_xlabel('Time')
ax.set_title('Interpolated data (dt=0.01)')
sns.despine(fig, bottom=False, left=False)
plt.show()

fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(10, 5))
ax.plot(df_proteins['Time'], df_proteins['proteins'])
ax.set_ylabel('# of proteins')
ax.set_xlabel('Time')
ax.set_title('Interpolated data (dt=0.01)')
sns.despine(fig, bottom=False, left=False)
plt.show()
###################################################

signal_RNAs = np.ascontiguousarray(signal_RNAs)

signal_proteins = np.ascontiguousarray(signal_proteins)

scales = np.arange(1,400)
waveletname = 'cmorl1.5-1.0'#cgau1'
coef_RNAs, freqs_RNAs = pywt.cwt(signal_RNAs, scales, waveletname)
coef_proteins, freqs_proteins = pywt.cwt(signal_proteins, scales, waveletname)


#======================================================================

len(coef_RNAs)
len(coef_RNAs[250])
len(xvals)

trend_150 = [np.abs(i) for i in coef_RNAs[100]]

trend_250 = [np.abs(i) for i in coef_RNAs[250]]

trend_350 = [np.abs(i) for i in coef_RNAs[350]]
trend_250
type(xvals)


plt.hist(trend_150)
trend_150 = np.ascontiguousarray(trend_150)
plt.plot(xvals,trend_150)

plt.hist(trend_250)
trend_250 = np.ascontiguousarray(trend_250)
plt.plot(xvals,trend_250)

plt.hist(trend_350)
trend_350 = np.ascontiguousarray(trend_350)
plt.plot(xvals,trend_350)



#========================================================================
#contourf(di cui ci fidiamo di meno perché potrebbe avere artifatti)

#freq =  1/scales

fig, ax = plt.subplots(figsize=(12, 5))

contourf_ = ax.contourf(xvals, scales, np.abs(coef_RNAs), cmap=plt.cm.Reds)#extend='both',

ax.set_title('Wavelet Transform of Signal (${}$) RNAs'.format(waveletname), fontsize=20)
ax.set_ylabel('Scales', fontsize=14)
ax.set_xlabel('Time (s)', fontsize=14)
ax.set_ylim(top=0.2)
fig.colorbar(contourf_)
ax.invert_yaxis()
plt.show()



fig, ax = plt.subplots(figsize=(12, 5))

contourf_ = ax.contourf(xvals, scales, np.abs(coef_proteins), cmap=plt.cm.Reds)#extend='both',

ax.set_title('Wavelet Transform of Signal (${}$) Proteins'.format(waveletname), fontsize=20)
ax.set_ylabel('Scales', fontsize=14)
ax.set_xlabel('Time (s)', fontsize=14)
fig.colorbar(contourf_)
ax.invert_yaxis()
plt.show()



#imshow
fig, ax = plt.subplots(figsize=(12, 5))
imshow_ = ax.imshow(np.abs(coef_RNAs), cmap='Reds', aspect='auto')  #extent=[min(xvals), max(xvals), min(scales), max(scales)], , vmax=abs(coef).max(), vmin=0
ax.set_title('Wavelet Transform of Signal (${}$) RNAs'.format(waveletname), fontsize=20)
ax.set_ylabel('Scales', fontsize=14)
ax.set_xlabel('Time (s)', fontsize=14)

ax.set_xlim(0,100000)#100000
def numfmt(x, pos): # your custom formatter function: divide by 1000
    s = '{}'.format(int(x / 100))
    return s
yfmt = plticker.FuncFormatter(numfmt) # create your custom formatter function
plt.gca().xaxis.set_major_formatter(yfmt) 

fig.colorbar(imshow_)
plt.show() 

# Perchè sull'asse x plotta 100000 punti ? Forse è la lunghezza di xvals.

len(xvals)#99990

#AUMENTA IL TEMPO LIMITE.

fig, ax = plt.subplots(figsize=(12, 5))
imshow_ = ax.imshow(np.abs(coef_proteins),cmap='Reds', aspect='auto')  #extent=[min(xvals), max(xvals), min(scales), max(scales)], vmax=np.abs(coef_proteins).max(), vmin=0
ax.set_title('Wavelet Transform of Signal (${}$) Proteins'.format(waveletname), fontsize=20)
ax.set_ylabel('Scales', fontsize=14)
ax.set_xlabel('Time (s)', fontsize=14)

ax.set_xlim(0,100000)
def numfmt(x, pos): # your custom formatter function: divide by 1000
    s = '{}'.format(int(x / 100))
    return s
yfmt = plticker.FuncFormatter(numfmt) # create your custom formatter function
plt.gca().xaxis.set_major_formatter(yfmt) 

fig.colorbar(imshow_)
plt.show() 

#Trova un modo per quantificare la periodicità delle strisce rosse




#matshow
fig, ax = plt.subplots(figsize=(12, 5))
matshow_ = ax.matshow(np.abs(coef_RNAs),  aspect = 'auto', cmap='Reds',
                      vmax=abs(coef).max(), vmin=0) 
fig.colorbar(matshow_)
plt.gca().xaxis.tick_bottom() # it puts x axis from top to bottom of figure.

#loc = plticker.MultipleLocator(base=0.25)  # this locator puts ticks at regular intervals
#ax.xaxis.set_major_locator(loc)
ax.set_xlim(0,100000)
def numfmt(x, pos): # your custom formatter function: divide by 1000
    s = '{}'.format(int(x / 100))
    return s
yfmt = plticker.FuncFormatter(numfmt) # create your custom formatter function
plt.gca().xaxis.set_major_formatter(yfmt) 

ax.set_title('Wavelet Transform of Signal (${}$) RNAs'.format(waveletname), fontsize=20)
ax.set_ylabel('Scales', fontsize=15)
ax.set_xlabel('Time', fontsize=15)
#ax.invert_yaxis()
plt.show() 



fig, ax = plt.subplots(figsize=(12, 5))
matshow_ = ax.matshow(np.abs(coef_proteins),  aspect = 'auto', cmap='Reds',
                      vmax=abs(coef).max(), vmin=0) 
fig.colorbar(matshow_)
plt.gca().xaxis.tick_bottom() # it puts x axis from top to bottom of figure.

ax.set_xlim(0,100000)
def numfmt(x, pos): # your custom formatter function: divide by 1000
    s = '{}'.format(int(x / 100))
    return s
yfmt = plticker.FuncFormatter(numfmt) # create your custom formatter function
plt.gca().xaxis.set_major_formatter(yfmt) 

ax.set_title('Wavelet Transform of Signal (${}$) Proteins'.format(waveletname), fontsize=20)
ax.set_ylabel('Scales', fontsize=15)
ax.set_xlabel('Time', fontsize=15)
#ax.invert_yaxis()
plt.show()