Algorithm 4: PE [34]

Input: The time series $x$, the embedding dimension $m$.

Output: PE ($x$, $m$).

Define:  ${\left({\mathit{\pi }}^m\right)}_k$ is the k-th permutation of ${\mathit{\pi }}^m$, time delay $\tau$ = 1.

1: function PE ($x$, $m$)

2:  PE$\leftarrow$0

3:  N$\leftarrow$length ($x$)

4:   $c\leftarrow {\left\{0\right\}}_{m!}$

5:   $p\leftarrow {\left\{0\right\}}_{m!}$

6:   ${\mathit{\pi }}^m\leftarrow \left\{0,1,\dots ,m-1\right\}$

7:   ${\Pi }^m\leftarrow \left\{{\mathit{\pi }}^m,{\left({\mathit{\pi }}^m\right)}_1,\dots ,{\left({\mathit{\pi }}^m\right)}_{m!-1}\right\}$

8:  for j = 0$\to j$= N$-m$ do

9:    ${\mathit{x}}_j^m\leftarrow \left\{x_j,x_{j+1},\dots ,x_{j+m-1}\right\}$

10:    $sort\left({\mathit{x}}_j^m,{\mathit{\pi }}^m\right)\to \left({\mathit{y}}_j^m,{\mathit{\pi }}_j^m\right)$

11:   for i = 0$\to i$ = $m!-1$ do

12:   if ${\mathit{\pi }}_j^m=={\Pi }_i^m$ then

13:     $c_i=c_i+1$

14:   break

15:   end for

16:  end for

17: for k = 0$\to k$ = $m!-1$ do

18:     $p_k\leftarrow \frac{c_k}{\left(N-m-1\right)}$

19:   if $p_k>0$ then

20:     $PE=PE+\left(-p_{k}lo{g}_2{p}_k\right)$

21:   end if

22:  end for

23:  return PE

24: end function