def correlated_ts(c,delta_t = 0.1,N=1000):
# parameters for coupled oscillator
K,D = 1.0,1.0
data1 = langevin.time_series(A=1/K, D=D, delta_t=delta_t, N=N)
data2 = langevin.time_series(A=1/(K+np.abs(c)), D=D, delta_t=delta_t, N=N)
x1 = (data1 + data2)/2
if c>0:
x2 = (data1 - data2)/2
else:
x2 = (data2-data1)/2
return x1,x2
# initial prior
# both D and A have mean 1 and std 10
alpha_A = 2.1
beta_A = 1.1
alpha_D = 0.1
beta_D = 0.1
# compile model for reuse
sm = lcm.OU_DA()
sm.samples = 100000
result_array = None
for i in range(M):
print("***** Iteration ", i, " *****")
data = langevin.time_series(A=A, D=D, delta_t=delta_t, N=N)
# calculate autocorrelation function
f = np.fft.rfft(data)
acf = np.fft.irfft(f * np.conjugate(f))
acf = np.fft.fftshift(acf) / N
autocorr = acf[int(N / 2):]
y = autocorr[:min(int(N / 2), P)]
t = np.arange(min(int(N / 2), P))
mod = ExponentialModel()
pars = mod.guess(y, x=t)
try:
out = mod.fit(y, pars, x=t)
except:
fit_results = np.zeros(4)
# A have mean 1 and std 10
# B is uniform prior over [0,1] interval
alpha_A=2.1
beta_A=1.1
alpha_B=1
beta_B=1
# compile model for reuse
sm = lcm.OU_BA()
sm.samples=100000
result_array = None
for i in range(M):
print("***** Iteration ",i," *****")
data = langevin.time_series(A=A, D=D, delta_t=delta_t, N=N)
data_results = [data[0]**2, data[-1]**2, np.sum(data[1:-2]**2), np.sum(data[:-1]*data[1:])]
# calculate autocorrelation function
f = np.fft.rfft(data)
acf = np.fft.irfft(f * np.conjugate(f))
acf = np.fft.fftshift(acf) / N
autocorr = acf[int(N / 2):]
y = autocorr[:min(int(N / 2), P)]
t = np.arange(min(int(N / 2), P))
mod = ExponentialModel()
pars = mod.guess(y, x=t)
try:
def main():
parser = argparse.ArgumentParser()
parser.add_argument('-d',
'--output',
action='store',
default="./test",
help='output file name')
parser.add_argument('-a',
'--amplitude',
action='store',
type=float,
default=1.0,
help='amplitude of OU')
parser.add_argument('-r',
'--tau',
action='store',
type=float,
default=1.0,
help='relaxation time tau of OU')
parser.add_argument('-w',
'--noise',
action='store',
type=float,
default=1.0,
help='power of the noise')
parser.add_argument('-n',
'--length',
action='store',
type=int,
default=2000,
help='length of simulation in timesteps')
parser.add_argument('-s',
'--samples',
action='store',
type=int,
default=2000,
help='MCMC samples per run')
parser.add_argument('-b',
'--dtstart',
action='store',
type=float,
default=0.01,
help='delta t range start')
parser.add_argument('-e',
'--dtend',
action='store',
type=float,
default=2.0,
help='delta t range end')
parser.add_argument('-l',
'--dtlength',
action='store',
type=int,
default=50,
help='delta t range number of points')
parser.add_argument('-u',
'--duplicates',
action='store',
type=int,
default=1,
help='delta t range number of points')
# get arguments
arg = parser.parse_args()
filename = arg.output
a = arg.amplitude
tau = arg.tau
pn = arg.noise
n = arg.length
mc_samples = arg.samples
dtstart = arg.dtstart
dtend = arg.dtend
dtlength = arg.dtlength
dupl = arg.duplicates
delta_t_list = np.linspace(dtstart, dtend, dtlength)
result_array = None
for delta_t in delta_t_list:
print(delta_t)
for i in range(dupl):
data = langevin.time_series(A=a, D=a / tau, delta_t=delta_t, N=n)
dataN = data + np.random.normal(loc=0.0, scale=np.sqrt(pn), size=n)
with pm.Model() as model:
B = pm.Beta('B', alpha=5.0, beta=1.0)
A = pm.Uniform('A', lower=0, upper=5)
sigma = pm.Uniform('sigma', lower=0, upper=5)
path = Ornstein_Uhlenbeck('path', A=A, B=B, shape=len(dataN))
dataObs = pm.Normal('dataObs',
mu=path,
sigma=sigma,
observed=dataN)
trace = pm.sample(mc_samples, cores=4)
a_mean = trace['A'].mean()
b_mean = trace['B'].mean()
a_std = trace['A'].std()
b_std = trace['B'].std()
sigma_mean = trace['sigma'].mean()
sigma_std = trace['sigma'].std()
avgpath = np.mean(trace['path'], axis=0)
stddiff = np.std(data - avgpath)
stdpath = np.std(trace['path'], axis=0).mean()
results = [
delta_t, a_mean, a_std, b_mean, b_std, sigma_mean, sigma_std,
stddiff, stdpath
]
if result_array is None:
result_array = results
else:
result_array = np.vstack((result_array, results))
column_names = [
"delta_t", "a_mean", "a_std", "b_mean", "b_std", "sigma_mean",
"sigma_std", "stddiff", "stdpath"
]
df = pd.DataFrame(result_array, columns=column_names)
df.to_csv(filename + '.csv', index=False)
import numpy as np
import matplotlib.pyplot as plt, seaborn as sns
import lmfit as lm
from scipy import signal
from lmfit.models import ExponentialModel
import pandas as pd
from itertools import accumulate
import langevin
A1 = 1.0
A2 = 0.5
D = 1.0
delta_t=0.5
datadir='results/delta05/corr2/'
N=10000 # length of data set
P=1000 # range to fit acf
x1 = langevin.time_series(A1,D,delta_t,N)
x2 = langevin.time_series(A2,D,delta_t,N)
xx1 = (x1+x2)/2.0
xx2 = (x1-x2)/2.0
df = pd.DataFrame({'x1':xx1, 'x2':xx2})
df.to_csv(datadir+'data.csv',index=False)