if(seriestype=="Endogenous"):

p=0.32 + 0.1*rnd.uniform()

slope= 0.4

else:

p=0.18 + 0.1*rnd.uniform()

slope=0.7

noValues=8192

noOrders = int(np.ceil(np.log2(noValues)))

y = np.array([1])

for n in range(noOrders):

y = next_step_1d(y, p)

if (slope):

fourierCoeff = fractal_spectrum_1d(noValues, slope/2)

meanVal = np.mean(y)

stdy = np.std(y)

x = np.fft.ifft(y - meanVal)

phase = np.angle(x)

x = fourierCoeff*np.exp(1j*phase)

x = np.fft.fft(x).real

x *= stdy/np.std(x)

x += meanVal

else:

x = y

y2 = np.zeros(y.size*2)

sign = np.random.rand(1, y.size) - 0.5

sign /= np.abs(sign)

y2[0:2*y.size:2] = y + sign*(1-2*p)*y

y2[1:2*y.size+1:2] = y - sign*(1-2*p)*y

ori_vector_size = noValues

ori_half_size = ori_vector_size//2

a = np.zeros(ori_vector_size)

for t2 in range(ori_half_size):

index = t2

t4 = 1 + ori_vector_size - t2

if (t4 >= ori_vector_size):

t4 = t2

coeff = (index + 1)**slope

a[t2] = coeff

a[t4] = coeff

a[1] = 0

"""Gaussian (1/f)**beta noise.

Based on the algorithm in:

Timmer, J. and Koenig, M.:

On generating power law noise.

Astron. Astrophys. 300, 707-710 (1995)

Normalised to unit variance

Parameters:

-----------

exponent : float

The power-spectrum of the generated noise is proportional to

S(f) = (1 / f)**beta

flicker / pink noise: exponent beta = 1

brown noise: exponent beta = 2

Furthermore, the autocorrelation decays proportional to lag**-gamma

with gamma = 1 - beta for 0 < beta < 1.

There may be finite-size issues for beta close to one.

shape : int or iterable

The output has the given shape, and the desired power spectrum in

the last coordinate. That is, the last dimension is taken as time,

and all other components are independent.

fmin : float, optional

Low-frequency cutoff.

Default: 0 corresponds to original paper. It is not actually

zero, but 1/samples.

Returns

-------

out : array

The samples.

Examples:

---------

# generate 1/f noise == pink noise == flicker noise

>>> import colorednoise as cn

>>> y = cn.powerlaw_psd_gaussian(1, 5)

"""

# Make sure size is a list so we can iterate it and assign to it.

try:

size = list(size)

except TypeError:

size = [size]

# The number of samples in each time series

samples = size[-1]

# Calculate Frequencies (we asume a sample rate of one)

# Use fft functions for real output (-> hermitian spectrum)

f = rfftfreq(samples)

# Build scaling factors for all frequencies

s_scale = f

fmin = max(fmin, 1./samples) # Low frequency cutoff

ix = np.sum(s_scale < fmin) # Index of the cutoff

if ix and ix < len(s_scale):

s_scale[:ix] = s_scale[ix]

s_scale = s_scale**(-exponent/2.)

# Calculate theoretical output standard deviation from scaling

w = s_scale[1:].copy()

w[-1] *= (1 + (samples % 2)) / 2. # correct f = +-0.5

sigma = 2 * np.sqrt(np.sum(w**2)) / samples

# Adjust size to generate one Fourier component per frequency

size[-1] = len(f)

# Add empty dimension(s) to broadcast s_scale along last

# dimension of generated random power + phase (below)

dims_to_add = len(size) - 1

s_scale = s_scale[(np.newaxis,) * dims_to_add + (Ellipsis,)]

# Generate scaled random power + phase

sr = rnd.normal(scale=s_scale, size=size)

si = rnd.normal(scale=s_scale, size=size)

# If the signal length is even, frequencies +/- 0.5 are equal

# so the coefficient must be real.

if not (samples % 2): si[...,-1] = 0

# Regardless of signal length, the DC component must be real

si[...,0] = 0

# Combine power + corrected phase to Fourier components

s = sr + 1J * si

# Transform to real time series & scale to unit variance

y = irfft(s, n=samples, axis=-1) / sigma

x=range(0,len(y))

'''

Gerador de Série Temporal Estocástica - V.1.2 por R.R.Rosa

Trata-se de um gerador randômico não-gaussiano sem classe de universalidade via PDF.

Input: n=número de pontos da série

res: resolução

'''

res = n/12

df = pd.DataFrame(np.random.randn(n) * np.sqrt(res) * np.sqrt(1 / 128.)).cumsum()

a=df[0].tolist()

a=statsfuncs.normalize(a)

x=range(0,n)

N=8192

rho=3.85 + 0.15*np.random.uniform()

tau = 1.1

x = [0.001]

y = [0.001]

for i in range(1,N):

y.append( tau*x[-1] )

x.append( rho*x[-1]*(1.0-x[-1]))

N=8192

a=1.350 + 0.05*np.random.uniform()

b=0.21 + 0.08*np.random.uniform()

x = [0.1]

y = [0.3]

for i in range(1,N):

y.append(b * x[-1])

x.append(y[-2] + 1.0 - a *x[-1]*x[-1])

values=[]

ilist=[]

rawdata=[]

for i in iterationlist:

for j in range(amount):

x,y=func(i)

alfa,xdfa,ydfa, reta = statsfuncs.dfa1d(y,1)

freqs, power, xdata, ydata, amp, index, powerlaw, INICIO, FIM = statsfuncs.psd(y)

psi,alphal,falpha=mfdfa.makemfdfa(y)

values.append([statsfuncs.variance(y), statsfuncs.skewness(y), statsfuncs.kurtosis(y)+3, alfa, index,psi])

ilist.append(i)

if graphs==True:

plt.plot(alphal, falpha, 'ko-', label=str(j))

if graphs==True:

plt.title("Espectro de Singularidade, para: {} {}".format(title,i))

plt.xlabel(r'$\alpha$')

plt.ylabel(r'$f(\alpha)$')

plt.grid('on', which = 'major')

plt.savefig("{}singularityspectrum{}".format(title,i))

plt.show()

rawdata.append([i,x,y, alfa, xdfa, ydfa, reta, freqs, power, xdata, ydata, amp, index, powerlaw, INICIO, FIM])

print(ilist)

d=np.array(d)

kk=pd.DataFrame({'Variance': d[:,0], 'Skewness': d[:,1], 'Kurtosis': d[:,2]})

K=20

model=KMeans()

visualizer = KElbowVisualizer(model, k=(1,K))

kIdx=visualizer.fit(kk) # Fit the data to the visualizer

visualizer.show() # Finalize and render the figure

kIdx=kIdx.elbow_value_

model=KMeans(n_clusters=kIdx).fit(kk)

# scatter plot

fig = plt.figure()

ax = Axes3D(fig) #.add_subplot(111))

cmap = plt.get_cmap('gnuplot')

clr = [cmap(i) for i in np.linspace(0, 1, kIdx)]

for i in range(0,kIdx):

ind = (model.labels_==i)

ax.scatter(d[ind,2],d[ind,1], d[ind,0], s=30, c=clr[i], label='Cluster %d'%i)

ax.set_xlabel("Kurtosis")

ax.set_ylabel("Skew")

ax.set_zlabel("Variance")

plt.title(title+': KMeans clustering with K=%d' % kIdx)

plt.legend()

plt.savefig(title+"clusters.png")

plt.show()

d=pd.DataFrame({'Variance': d[:,0], 'Skewness': d[:,1], 'Kurtosis': d[:,2], 'Alpha': d[:,3], 'Beta': d[:,4], "Psi": d[:,5], "Cluster": model.labels_}, index=ilist)

plt.figure(num=None, figsize=(8, 8), dpi=100, facecolor='w', edgecolor='k')

fig, ax = plt.subplots()

maior=max(xd)

polyX1=maior if maior > 4.4 else 4.4

polyY1=polyX1+1

polyY2=3/2.*polyX1+3

y_lim = polyY2 if polyY2 > 10 else 10

x = [0,polyX1,polyX1,0]

y = [1,polyY1,polyY2,3]

scale = 1

poly = Polygon( np.c_[x,y]*scale, facecolor='#1B9AAA', edgecolor='#1B9AAA', alpha=0.5)

ax.add_patch(poly)

ax.plot(xd,yd, marker="o", c="#e86a92", label=legend, linestyle='')

ax.plot(0, 4.187999875999753, label="logistic", marker='+', c='black')

ax.plot(0, 1.7962675925351856, label ="uniform", marker='^',c='black')

ax.plot(4, 9, label="exponential", marker='s', c='black')

ax.plot(0, 3, label="normal", marker='*',c='black')

ax.plot(np.arange(0,polyX1,0.1), 3/2.*np.arange(0,polyX1,0.1)+3, label="gamma", linestyle='-',c='black')

ax.plot(np.arange(0,polyX1,0.1), 2*np.arange(0,polyX1,0.1)+3, label="lognormal", linestyle='-.',c='black')

ax.legend()

ax.set_ylim(y_lim,0)

ax.set_xlim(-0.2,polyX1)

plt.xlabel("Skewness²")

plt.title(title+": Cullen and Frey map")

plt.ylabel("Kurtosis")

plt.savefig(title+legend+"cullenfrey.png")

kk=pd.DataFrame({'Skew²': s2, 'Kurtosis': k, 'Alpha': alpha, 'Beta': beta})

K=8

model=KMeans()

visualizer = KElbowVisualizer(model, k=(1,K))

kIdx=visualizer.fit(kk.drop(columns="Beta")) # Fit the data to the visualizer

visualizer.show() # Finalize and render the figure

kIdx=kIdx.elbow_value_

model=KMeans(n_clusters=kIdx).fit(kk.drop(columns="Beta"))

fig = plt.figure()

ax = Axes3D(fig)

cmap = plt.get_cmap('gnuplot')

clr = [cmap(i) for i in np.linspace(0, 1, kIdx)]

for i in range(0,kIdx):

ind = (model.labels_==i)

ax.scatter(kk["Skew²"][ind],kk["Kurtosis"][ind], kk["Alpha"][ind], s=30, c=clr[i], label='Cluster %d'%i)

ax.set_xlabel("Skew²")

ax.set_ylabel("Kurtosis")

ax.set_zlabel(r"$\alpha$")

ax.legend()

plt.title(title+": EDF-K-means")

plt.savefig(title+"EDF.png")

plt.show()

model=KMeans()

visualizer = KElbowVisualizer(model, k=(1,K))

kIdx=visualizer.fit(kk.drop(columns="Alpha")) # Fit the data to the visualizer

visualizer.show() # Finalize and render the figure

kIdx=kIdx.elbow_value_

model=KMeans(n_clusters=kIdx).fit(kk.drop(columns="Alpha"))

fig = plt.figure()

ax = Axes3D(fig)

cmap = plt.get_cmap('gnuplot')

clr = [cmap(i) for i in np.linspace(0, 1, kIdx)]

for i in range(0,kIdx):

ind = (model.labels_==i)

ax.scatter(kk["Skew²"][ind],kk["Kurtosis"][ind], kk["Beta"][ind], s=30, c=clr[i], label='Cluster %d'%i)

ax.set_xlabel("Skew²")

ax.set_ylabel("Kurtosis")

ax.set_zlabel(r"$\beta$")

ax.legend()

plt.title(title+": EPSB-K-means")

plt.savefig(title+"EPSB.png")

SMALL_SIZE = 10

MEDIUM_SIZE = 15

BIGGER_SIZE = 20

plt.rc('font', size=SMALL_SIZE) # controls default text sizes

plt.rc('axes', titlesize=MEDIUM_SIZE) # fontsize of the axes title

plt.rc('axes', labelsize=MEDIUM_SIZE) # fontsize of the x and y labels

plt.rc('xtick', labelsize=SMALL_SIZE) # fontsize of the tick labels

plt.rc('ytick', labelsize=SMALL_SIZE) # fontsize of the tick labels

plt.rc('legend', fontsize=MEDIUM_SIZE) # legend fontsize

plt.rc('figure', titlesize=BIGGER_SIZE) # fontsize of the figure title

kk=pd.DataFrame({'Skew²': s2, 'Kurtosis': k, 'Alpha': alpha, 'Beta': beta, "Entity": ilist})

K=8

model=KMeans()

visualizer = KElbowVisualizer(model, k=(1,K))

kIdx=visualizer.fit(kk.drop(columns=["Beta", "Entity"])) # Fit the data to the visualizer

visualizer.show() # Finalize and render the figure

kIdx=kIdx.elbow_value_

model=KMeans(n_clusters=kIdx).fit(kk.drop(columns=["Beta", "Entity"]))

print(len(model.labels_))

fig = plt.figure(figsize=(20,15))

ax = Axes3D(fig)

cmap = plt.get_cmap('gnuplot')

ilist2=list(set(ilist))

clr = [cmap(i) for i in np.linspace(0, 1, len(ilist2))]

for i in range(0,len(ilist2)):

ind = (kk["Entity"]==ilist2[i])

ax.scatter(kk["Skew²"][ind],kk["Kurtosis"][ind], kk["Alpha"][ind], s=120, c=clr[i], label=ilist2[i])

ax.set_xlabel("Skew²")

ax.set_ylabel("Kurtosis")

ax.set_zlabel(r"$\alpha$")

ax.legend()

plt.title(title+": EDF-K-means")

plt.savefig("datasetandcovidEDF.png")

plt.show()

kk=pd.DataFrame({'Skew²': s2, 'Kurtosis': k, 'Alpha': alpha, 'Beta': beta, "Entity": ilist}, index=model.labels_)

kk.sort_index(inplace=True)

kk.to_csv("clusteringalpha.csv")

model=KMeans()

visualizer = KElbowVisualizer(model, k=(1,K))

kIdx=visualizer.fit(kk.drop(columns=["Alpha", "Entity"])) # Fit the data to the visualizer

visualizer.show() # Finalize and render the figure

kIdx=kIdx.elbow_value_

model=KMeans(n_clusters=kIdx).fit(kk.drop(columns=["Alpha", "Entity"]))

fig = plt.figure(figsize=(20,15))

ax = Axes3D(fig)

cmap = plt.get_cmap('gnuplot')

clr = [cmap(i) for i in np.linspace(0, 1, len(ilist2))]

for i in range(0,len(ilist2)):

ind = (kk["Entity"]==ilist2[i])

ax.scatter(kk["Skew²"][ind],kk["Kurtosis"][ind], kk["Beta"][ind], s=120, c=clr[i], label=ilist2[i])

ax.set_xlabel("Skew²")

ax.set_ylabel("Kurtosis")

ax.set_zlabel(r"$\beta$")

ax.legend()

plt.title(title+": EPSB-K-means")

plt.savefig("datasetandcovidEPSB.png")

plt.show()

kk=pd.DataFrame({'Skew²': s2, 'Kurtosis': k, 'Alpha': alpha, 'Beta': beta, "Entity": ilist}, index=model.labels_)

kk.sort_index(inplace=True)

for i in range(len(rawdata)):

#Plot e ajuste do histograma da série temporal

(mu, sigma) = norm.fit(rawdata[0][2])

# rv_nrm = norm(loc=mu, scale=sigma)

# Estimate GEV:

n=8192

ypoints=[min(rawdata[0][2]) + (i/n) * (max(rawdata[0][2])-min(rawdata[0][2])) for i in range(0, n+1)]

gev_fit = genextreme.fit(rawdata[0][2])

# GEV parameters from fit:

c, loc, scale = gev_fit

mean, var, skew, kurt = genextreme.stats(c, moments='mvsk')

rv_gev = genextreme(c, loc=loc, scale=scale)

# Create data from estimated GEV to plot:

gev_pdf = rv_gev.pdf(ypoints)

plt.title((title+"\nMu= {1:.3}, Sigma={2:.3}.").format(rawdata[i][0], mu, sigma))

n, bins, patches = plt.hist(rawdata[0][2], 60, density=1, facecolor='powderblue', alpha=0.75, label="Normalized data")

plt.plot(np.arange(min(bins), max(bins), (max(bins) - min(bins))/len(rawdata[0][2])), gev_pdf[:len(rawdata[0][2])],'r-', lw=5, alpha=0.6, label='genextreme pdf')

plt.ylabel("Probability Density")

plt.xlabel("Value")

plt.legend()

plt.savefig("PDF"+filename.format(i))

plt.show()

plt.figure(figsize=(20, 12))

#Plot da série temporal

ax1 = plt.subplot(211)

ax1.set_title(title.format(rawdata[i][0]), fontsize=18)

if pmodel==True:

ax1.plot(rawdata[i][2], color="firebrick", linestyle='-', label="Data")

elif chaosnoise==True:

ax1.plot(rawdata[i][1],rawdata[i][2], color="firebrick", marker= 'o', linestyle='', label="Data")

else:

ax1.plot(rawdata[i][1],rawdata[i][2], color="firebrick", linestyle='-', label="Data")

#Plot e cálculo do DFA

ax2 = plt.subplot(223)

ax2.set_title(r"Detrended Fluctuation Analysis $\alpha$={0:.3}".format(rawdata[i][3]), fontsize=15)

ax2.plot(rawdata[i][4],rawdata[i][5], marker='o', linestyle='', color="#12355B", label="{0:.3}".format(rawdata[i][3]))

ax2.plot(rawdata[i][4], rawdata[i][6], color="#9DACB2")

#Plot e cáculo do PSD

ax3 = plt.subplot(224)

ax3.set_title(r"Power Spectrum Density $\beta$={0:.3}".format(rawdata[i][12]), fontsize=15)

ax3.set_yscale('log')

ax3.set_xscale('log')

ax3.plot(rawdata[i][7], rawdata[i][8], '-', color = 'deepskyblue', alpha = 0.7)

ax3.plot(rawdata[i][9], rawdata[i][10], color = "darkblue", alpha = 0.8)

ax3.axvline(rawdata[i][7][rawdata[i][14]], color = "darkblue", linestyle = '--')

ax3.axvline(rawdata[i][7][rawdata[i][15]], color = "darkblue", linestyle = '--')

ax3.plot(rawdata[i][9], rawdata[i][13](rawdata[i][9], rawdata[i][11], rawdata[i][12]),color="#D65108", linestyle='-', linewidth = 3, label = '{0:.3}$'.format(rawdata[i][12]))

ax2.set_xlabel("log(s)")

ax2.set_ylabel("log F(s)")

ax3.set_xlabel("Frequência (Hz)")

ax3.set_ylabel("Potência")

ax3.legend()

plt.savefig(filename.format(i))

choice=input("Qual distribuição escolher:\n1 - GRNG\n2 - Colored Noise\n3 - pmodel\n4 - Chaos Noise \n5 - Ler de um arquivo\n6 - Sair\n\n")

if(choice=="1"):

'''

Começando pela série GRNG, serão gerados 8 famílias de sinais com elementos 2^n

sendo que n varia de 6 até 13, ou, 64 a 8192 e para cada família serão gerados

10 sinais diferentes e guardados todos eles numa lista rawdata, seus momentos

estatísticos serão guardados em d, e ilist é uma lista de iteração para cada N

usada para identificar corretamente os valores no DataFrame que será gerado.

Feito esse conjunto de dados, serão feitas as análises, começando pelo Detrended

Fluctuation Analysis e o Power Spectrum Density, que serão mostrados em um gráfico.

Essas duas análises serão feitas só para um de cada família gerada.

Depois disso será feito o agrupamento dos momentos estatísticos pelo método

K-Means, que fará um gráfico mostrando o agrupamento, e finalizando fazendo

o mapeamento de Cullen e Frey, um para cada família das séries.

'''

title="Série: GRNG. Quantidade de Dados N={0}"

i=[2**i for i in range(6,14)]

d,ilist,rawdata=makeseries(randomseries, i,10, "GRNG", True)

filename="GRNGserietemporalpsddfa{}.png"

makeGraphs(rawdata,title,filename)

title="GRNG"

d=makeK(d,ilist, title)

elif(choice=="2"):

'''

De maneira semelhante ao GRNG, serão feitas as mesmas coisas para as famílias

de ruído colorido White Noise, Pink Noise e Red Noise. Gerando 20 sinais para

cada uma dessas famílias.

Aqui será feito em adição um histograma que será ajustado numa gaussiana com

parâmetros mu e sigma.

'''

title="Série: Colored Noise. Expoente = {0}"

d,ilist,rawdata=makeseries(powerlaw_psd_gaussian, range(0,3), 20, "colorednoise", True)

while(0 in ilist or 1 in ilist or 2 in ilist):

ilist[ilist.index(0)] = 'white noise'

ilist[ilist.index(1)] = 'pink noise'

ilist[ilist.index(2)] = 'red noise'

filename="CNserietemporalpsddfa{}.png"

makeGraphs(rawdata, title, filename)

title="colorednoise"

d=makeK(d,ilist, title)

elif(choice=="3"):

'''

Para o pmodel serão feitas as mesmas análises que o GRNG, com as famílias

Endógeno e Exógeno, que geram valores aleatórios para cada família.

Valores entre 0.32~0.42 e 0.18~0.28, respectivamente, gerando 30 valores

aleatórios onde cada um gera seu sinal totalizando em 60 sinais.

'''

qtd=1

p=[]

for i in range(qtd):

p.append("Endogenous")

for i in range(qtd):

p.append("Exogenous")

title="Série: pmodel. {0}"

d,ilist,rawdata=makeseries(pmodel, p,30, "pmodel", True)

filename="Pmodelserietemporalpsddfa{}.png"

makeGraphs(rawdata, title, filename, pmodel=True)

title="pmodel"

d=makeK(d,ilist, title)

elif(choice=="4"):

'''

Na série Chaos Noise seguirão as mesmas análises, usando as séries Logística

e Henon, ambas vão gerar parâmetros aleatórios dentro de um intervalo de

rho=3.85~4 para a série logística, e a=1.35~1.4, b=0.21~0.29 para a série de

Henon.

Totalizando em 60 sinais no total.

'''

title="Série: Chaos Noise. {0}"

d,ilist,rawdata=makeseries(Logistic, ["Logistic"], 30, "Chaos Noise", True)

aux1,aux2,aux3=makeseries(HenonMap, ["Henon"], 30, "Chaos Noise", True)

rawdata+=aux3

d+=aux1

ilist+=aux2

filename="Chaosserietemporalpsddfa{}.png"

makeGraphs(rawdata, title, filename, chaosnoise=True)

title="chaosnoise"

d=makeK(d,ilist, title)

elif(choice=="5"):

namefile=["sol3ghz.dat","surftemp504.txt", "covidbrasil.dat"]

ilist=namefile

d=[]

for file in namefile:

fileread=open(file)

y=[]

for line in fileread:

y.append(float(line))

alfa,xdfa,ydfa, reta = statsfuncs.dfa1d(y,1)

freqs, power, xdata, ydata, amp, index, powerlaw, INICIO, FIM = statsfuncs.psd(y)

d.append([statsfuncs.variance(y), statsfuncs.skewness(y), statsfuncs.kurtosis(y)+3, alfa, index, 0])

QTD=10

d2,ilist2,rawdata=makeseries(randomseries, [8192],QTD)

for i in d2:

d.append(i)

for j in ilist2:

ilist.append(j)

d2,ilist2,rawdata=makeseries(powerlaw_psd_gaussian, range(0,3), QTD//3)

for i in d2:

d.append(i)

for j in ilist2:

ilist.append(j)

d2,ilist2,rawdata=makeseries(pmodel, ["Exogenous", "Endogenous"] , QTD//2)

for i in d2:

d.append(i)

for j in ilist2:

ilist.append(j)

d2,ilist2,rawdata=makeseries(Logistic, ["Logistic"], QTD//2)

for i in d2:

d.append(i)

for j in ilist2:

ilist.append(j)

d2,ilist2,rawdata=makeseries(HenonMap, ["Henon"], QTD//2)

for i in d2:

d.append(i)

for j in ilist2:

ilist.append(j)

s2=[]

k=[]

alpha=[]

beta=[]

for i in range(len(d)):

s2.append(d[i][1]**2)

k.append(d[i][2])

alpha.append(d[i][3])

beta.append(d[i][4])

makespaces62(s2,k,alpha,beta,"All signals and Brazil Covid data", "Brazil", ilist)

return d

else:

return

#Fazendo o clustering, via kmeans, dos momentos estatísticos obtidos.

ilist=set(ilist) #tirando valores duplicados

for j in ilist:

#Fazendo listas pra plotar em outras funções

s2=[i**2 for i in d.filter(like=str(j), axis=0)['Skewness']] #skew²

k=d.filter(like=str(j),axis=0)["Kurtosis"]

alpha=d.filter(like=str(j),axis=0)["Alpha"]

beta=d.filter(like=str(j),axis=0)["Beta"]

legend=str(j)

cullenfrey(s2,k, legend, title) #Mapa de cullen e frey

makespaces(s2,k, alpha, beta, legend, title)