Rank of array element @ model

Index number $\begin{array}{l}rg(x_i)\end{array}$ of a given array element $\begin{array}{l}x_i\end{array}$ in a low-to-high sorted array:

(1)	$\begin{array}{l}\displaystyle \{ x \} = \{ x_1, x_2, x_3 ... x_n \} \rightarrow \{ rg(x) \} = \{ x_{i_1}, x_{i_2}, x_{i_3} ... x_{i_n} \}, \, {\rm where} \, x_{i_1} \leq x_{i_2} \leq x_{i_3} ... \leq x_{i_n}\end{array}$

so that $\begin{array}{l}rg(x_k) = k\end{array}$

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