Correlation Integral

Calculates the correlation integral. Does not take self-distance into account. Memory complexity is len(data)*len(Rs). Calculations are done with single precision floating point data, and the theoretical maximum data length is 3.037.000.499 points divided by the number of Rs that you want to calculate

Usage

To import the library run:

import correlation_integral as ci

Three methods can be used

ci.euclidean
ci.manhattan
ci.chebyshev

All three methods take the following arguments:

• data: one-dimensional float32 numpy array with the data
• dims: integer specifying the dimension for which to calculate the correlation integral
• r : one-dimensional float32 numpy array with the distances to calculate the correlation integral for

And they return the following output:

• cd: one-dimensional float32 numpy array which contains the correlation-integral for each r given in the input

The signature looks like this:

cd = ci.euclidean(data,dims,r)

Installation

pip install correlation-integral

Example

import correlation_integral as ci
import numpy as np
import matplotlib.pyplot as plt

# example Henon map - create & plot data
a=1.4;
b=0.3;

x=np.zeros(shape=(10000+5000),dtype=np.float32)
y=np.zeros(shape=(10000+5000),dtype=np.float32)
x[0]=1
y[0]=0
for i in range(1,len(x)-1):
    x[i+1]=1-a*x[i]**2+y[i]
    y[i+1]=b*x[i]

x=x[5000:]
y=y[5000:]


# correlation integral analysis done only with x-variable
nrsteps=10;
dims=np.arange(1,16) # calculate for d=1 uptil d=16
nrdims=dims.size;
rs=np.logspace(-2.5,0.5,nrsteps)
Cds=np.zeros((nrsteps,nrdims));

print("Start")
for j in range(nrdims):
  Cds[:,j] = ci.chebyshev(x,dims[j],rs)
  print("x",end="")
print("\nDONE!")

# Plot the results
for i in range(len(dims)):
  plt.plot(rs,Cds[:,i])
plt.xscale("log")
plt.yscale("log")
plt.show()