Exponentially correlated Gaussian random numbers¶
- PyAstronomy.pyasl.expCorrRN(n, tau, mean=0.0, std=1.0, rnos=None, fullOut=False)¶
Generate exponentially correlated random numbers.
This procedure implements the prescription given by Deserno 2002 (“How to generate exponentially correlated Gaussian random numbers”). The autocorrelation function of the resulting numbers decays with the predefined “decay time”, tau. The correlation coefficient of the resulting numbers is given by exp(-1/tau).
- Parameters
- nint
Number of numbers to be generated.
- taufloat
Decay time
- meanfloat, optional
Mean of the numbers to be generated. Default is 0.0.
- stdfloat, optional
Standard deviation of the generated numbers. Default is 1.0.
- rnosarray, optional
Uncorrelated Gaussian random numbers with mean 0.0 and standard deviation 1.0 to be used to generate correlated random numbers. If not given, Gaussian random numbers will be obtained using numpy.random.normal.
- fullOutboolean, optional
If False (default), only the correlated random numbers will be returned.
- Returns
- Correlated RNsarray
Correlated Gaussian random numbers.
- Uncorrelated RNsarray, optional
The uncorrelated random numbers used to generate the correlated numbers (only of fullOut is True).
- Correlation coefficientfloat
The correlation coefficient (exp(-1/tau), only of fullOut is True).
Example: Generating correlated numbers¶
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.')
plt.show()
Example: Exploring the autocorrelation function¶
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--')
plt.show()
