Algorithm 2. Calculate the approximate and sample entropy.

Input: Timeseries

Output: ApEn, SampEn

$x(l),l=1,2,..,M\leftarrow$ Given a time series

$p\leftarrow$ Embedding dimension

$z\leftarrow$ Tolerance

Stage 1: Extend x(l) to the pth vector $U_p(l)$

$U_p(l)=[x(l),u(l+1),...,u(l+p-1)]\leftarrow l=1,2,...,M-p+1$

Stage 2: Calculate the distance between $U_p(l)$ and $U_p(j)$

$D[U_p(l),U_p(j)]=ma{x}_{t=0,1,...,p-1}\{|x(l+t)-x(j+t)|\}\leftarrow j=1,2,...,M-p+1$ and $j\ne l$

Stage 3: Compute approximate entropy

Measure the regularity and frequency of patterns within tolerance r :

$$C_l^p(z)=\frac{\mathrm{N}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{j}\mathrm{s}\mathrm{u}\mathrm{c}\mathrm{h}\mathrm{t}\mathrm{h}\mathrm{a}\mathrm{t}\mathrm{D}[{\mathrm{U}}_{\mathrm{p}}(\mathrm{l}),{\mathrm{U}}_{\mathrm{p}}(\mathrm{j})]\le \mathrm{z}}{M-p+1}$$

Compute the mean value of the logarithm of $C_l^p(z)$:

$${\psi }^p(z)=\frac{{\sum }_{l=1}^{M-p+1}ln[C_l^p(z)]}{M-p+1}$$

The ApEn can be defined:

$$ApEn(p,z)={\psi }^p(z)-{\psi }^{p+1}(z)$$

Stage 4: Compute sample entropy

Compute the two coefficients:

$$A_l^p(z)=\frac{{\sum }_{\mathrm{j}=1,\mathrm{j}\ne \mathrm{l}}^{\mathrm{M}-\mathrm{p}}numberoftimesthatD[U_{p+1}(l),U_{p+1}(j)]<z}{M-p-1}$$

$$B_l^p(z)=\frac{{\sum }_{\mathrm{j}=1,\mathrm{j}\ne \mathrm{l}}^{\mathrm{M}-\mathrm{p}}numberoftimesthatD[U_p(l),U_p(j)]<z}{M-p-1}$$

Add them as fallow:

$$A^p(z)=\frac{{\sum }_{l=1}^{M-p}{A}_l^p(z)}{M-p}$$

$$B^p(z)=\frac{{\sum }_{l=1}^{M-p}{B}_l^p(z)}{M-p}$$

The SampEn can be defined:

$$SampEn(p,z)=-ln[\frac{A^p(z)}{B^p(z)}]$$