def sanity_expCorrRN_Example1(self):
"""
Sanity of example 1 for expCorrRN
"""
import matplotlib.pylab as plt
from PyAstronomy import pyasl
# Generate 200 exponentially correlated Gaussian
# random numbers with a decay time of 5
c1 = pyasl.expCorrRN(200, 5)
# Generate 200 exponentially correlated Gaussian
# random numbers with decay time 10, mean 4, and
# standard deviation of 2.3.
#
# The results are: The correlated random numbers,
# the uncorrelated numbers used as input, and the
# correlated coefficient (exp(-1/tau)).
c2, g, f = pyasl.expCorrRN(200, 10, mean=4.0, std=2.3, fullOut=True)
plt.subplot(2, 1, 1)
plt.plot(range(200), c1, 'bp-')
plt.subplot(2, 1, 2)
plt.plot(range(200), c2, 'bp-')
plt.plot(range(200), g, 'g.')
def sanity_expCorrRN_Example1(self):
"""
Sanity of example 1 for expCorrRN
"""
import matplotlib.pylab as plt
from PyAstronomy import pyasl
# Generate 200 exponentially correlated Gaussian
# random numbers with a decay time of 5
c1 = pyasl.expCorrRN(200, 5)
# Generate 200 exponentially correlated Gaussian
# random numbers with decay time 10, mean 4, and
# standard deviation of 2.3.
#
# The results are: The correlated random numbers,
# the uncorrelated numbers used as input, and the
# correlated coefficient (exp(-1/tau)).
c2, g, f = pyasl.expCorrRN(200, 10, mean=4.0, std=2.3, fullOut=True)
plt.subplot(2,1,1)
plt.plot(range(200), c1, 'bp-')
plt.subplot(2,1,2)
plt.plot(range(200), c2, 'bp-')
plt.plot(range(200), g, 'g.')
def sanity_expCorrRN_Example2(self):
"""
Sanity of example 2 for expCorrRN
"""
import numpy as np
import matplotlib.pylab as plt
from PyAstronomy import pyasl
# Generate n exponentially correlated Gaussian
# random numbers with a decay time, tau
n = 500
tau = 5.
c1 = pyasl.expCorrRN(n, tau)
# Obtain autocorrelation function
ac = np.correlate(c1, c1, mode="full")[n - 1:]
# Plot correlated random numbers and autocorrelation
# function along with exponential model.
x = np.arange(float(n))
plt.subplot(2, 1, 1)
plt.plot(x, c1, 'bp-')
plt.subplot(2, 1, 2)
plt.plot(x, ac, 'b.')
plt.plot(x, np.exp(-x / tau) * ac.max(), 'r--')
def sanity_expCorrRN_Example2(self):
"""
Sanity of example 2 for expCorrRN
"""
import numpy as np
import matplotlib.pylab as plt
from PyAstronomy import pyasl
# Generate n exponentially correlated Gaussian
# random numbers with a decay time, tau
n = 500
tau = 5.
c1 = pyasl.expCorrRN(n, tau)
# Obtain autocorrelation function
ac = np.correlate(c1, c1, mode="full")[n-1:]
# Plot correlated random numbers and autocorrelation
# function along with exponential model.
x = np.arange(float(n))
plt.subplot(2,1,1)
plt.plot(x, c1, 'bp-')
plt.subplot(2,1,2)
plt.plot(x, ac, 'b.')
plt.plot(x, np.exp(-x/tau)*ac.max(), 'r--')
def Simulate_ARIMA_Like_Timeseries(arparams, maparams, num_samples, A1=6, A2=0.5):
TS = Generate_ARMA_Timeseries_Data(arparams, maparams, num_samples, frac = 0)
TS_LRD = Generate_ARMA_Timeseries_Data(arparams, maparams, num_samples, frac = 1)
TS_non_stationary = np.cumsum(TS)
TS_LRD_non_stationary = np.cumsum(TS_LRD)
W_Noise = np.random.normal(0,1, len(TS))
TS_Periodic_F1 = Generate_Periodic_Signal(288, len(TS))
TS_Periodic_F2 = Generate_Periodic_Signal(356/12.0*288, len(TS))
corr, uncorr, f = pyasl.expCorrRN(len(TS), 25, mean=4.0, std=2.3, fullOut=True)
brownian_ser = np.empty((1,len(TS)+1))
brownian_ser[:, 0] = 50
brownian(brownian_ser[:,0], len(TS), dt=2e-5, delta=10, out=brownian_ser[:,1:])
brownian_ser = brownian_ser[0][:-1]
df = pd.DataFrame()
df.loc[:,'TS_ARIMA'] = TS
df.loc[:,'TS_ARIMA_LRD'] = TS_LRD
df.loc[:,'TS_Non_Stationary'] = TS_non_stationary
df.loc[:,'TS_LRD_Non_Stationary'] = TS_LRD_non_stationary
df.loc[:,'Periodic'] = A1*TS_Periodic_F1 + W_Noise
df.loc[:,'Periodic_Multiple_Seasonality'] = (A1*TS_Periodic_F1)*(A2*TS_Periodic_F2) + W_Noise
df.loc[:,'SARIMA'] = (A2*TS_Periodic_F1)*(A1*TS)
df.loc[:,'SARFIMA'] = (A1*TS_Periodic_F1)*(TS_LRD)
df.loc[:,'Periodic_Non_Stationary'] = ((A1*TS_Periodic_F1)*TS_non_stationary
+ W_Noise)
df.loc[:,'Periodic_Non_Stationary_LRD'] = ((A1*TS_Periodic_F1)*TS_LRD_non_stationary
+ W_Noise)
df.loc[:,'Exp_Corr_RN'] = corr
df.loc[:,'Brownian'] = brownian_ser
color = ['red','blue','green','orange',
'black', 'magenta','indigo','violet',
'brown','gold','olive','gray']
columns = df.columns.tolist()
fig_TS, ax_TS = plt.subplots(6,2,figsize = (16,12))
fig_ACF, ax_ACF = plt.subplots(6,2,figsize = (16,12))
fig_FFT, ax_FFT = plt.subplots(6,2,figsize = (16,12))
counter = 0
for i in range(0, 6):
for j in range(0, 2):
print columns[counter]
df[[columns[counter]]].plot(ax = ax_TS[i][j], color = color[counter], legend = False)
ax_TS[i][j].grid()
#ax_TS[i][j].legend(loc = 1)
ax_TS[i][j].set_title(columns[counter])
if 'Periodic' in columns[counter]:
lags = 5000
lim = [0, 0.00005]
v_lines = False
else:
lags = 100
lim = [0,0.00175]
v_lines = True
tsaplots.plot_acf(df[columns[counter]], ax = ax_ACF[i][j], lags = lags,
title = 'ACF of '+columns[counter], color = color[counter],
marker = 'x', use_vlines = v_lines)
ax_ACF[i][j].axhline(0)
ax_ACF[i][j].grid()
f, Pxx_den = signal.periodogram(df[columns[counter]], 1/(5*60.0))
ax_FFT[i][j].plot(f, np.sqrt(Pxx_den), color = color[counter])
ax_FFT[i][j].set_title('FFt of '+columns[counter])
ax_FFT[i][j].grid()
ax_FFT[i][j].set_xlim(lim)
counter += 1
fig_TS.tight_layout()
fig_ACF.tight_layout()
fig_FFT.tight_layout()
fig_TS.savefig('TS.pdf')
fig_ACF.savefig('ACF.pdf')
fig_FFT.savefig('FFT.pdf')
return df