VSB Power Line Blog - Permutation Entropy

permutation_entropy.py

def _embed(x, order=3, delay=1):
  N = len(x)
  # In our case, N-(order-1)*delay = 800000 - (3-1)*1 = 799998
  # Y.shape = 3x799998
  Y = np.zeros((order, N - (order - 1) * delay))
  for i in range(order):
    # Y[0] = x[0:799998], Y[1] = x[1:799999], Y[2] = x[3:800000]
    Y[i] = x[(i * delay) : (i * delay) + Y.shape[1]].T
  # Y.T[0] = [x[0],x[1],x[2]], Y.T[1] = [x[1],x[2],x[3]], ... , Y.T[799998] = [x[799998],x[799999],x[800000]]
  return Y.T

def factorial(val):
  if val == 1:
    return 1
  else:
    return val * factorial(val-1)

def perm_entropy(x, order=3, delay=1, normalize=False):
  x = np.array(x)
  ran_order = range(order)
  hashmult = np.power(order, ran_order)
  # Embed x and sort the order of permutations
  sorted_idx = _embed(x, order=order, delay=delay).argsort(kind='quicksort')
  # Associate unique integer to each permutations
  hashval = (np.multiply(sorted_idx, hashmult)).sum(1)
  # Return the counts
  _, c = np.unique(hashval, return_counts=True)
  # p is the probability of occurrence of each perumutation
  # np.true_divide() performs element wise division
  p = np.true_divide(c, c.sum())
  pe = -np.multiply(p, np.log2(p)).sum()
  if normalize:
    pe /= np.log2(factorial(order))
  return pe