shannoning

A (lightning) fast permutation entropy calculator using Eigen.

Permutation entropy

The permutation entropy of order $n \geq 2$ is defined as

$$ H(n) = - \sum p(\pi) \log p(\pi) $$

where the sum runs over all $n!$ permutations $\pi$ of order $n$ . It is clear that $0 \leq H(n) \leq \log n!$ where the lower bound is attained for an increasing or decreasing sequence of (deterministic) values, and the upper bound for a completely random system (i.i.d. sequence).

Dependencies

• Eigen (3.4-rc1)

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References

[1] Bandt, C., & Pompe, B. (2002). Permutation entropy: a natural complexity measure for time series. Physical review letters, 88(17), 174102.