The OrderByRank command orders the elements/rows of X according to their ranks.

The first parameter X is the data set - given as e.g. a Vector.

The second parameter R is the ranks data (also specified as a data set).

The options argument can contain one or more of the options shown below.

order = ascending or descending -- Indicate whether the elements of X should be sorted in the ascending or descending order. The default value is order=ascending.

unique=truefalse -- If this option is set to true, all multiple occurrences of elements from X will be removed. The default value is unique=false.

The OrderByRank command creates a copy of the original Array.

$\mathrm{with}\left(\mathrm{Statistics}\right)\:$

$A≔\mathrm{Array}\left(\left[a\,b\,c\,d\,e\,f\,g\,h\right]\right)$

$A≔\left[\begin{array}{cccccccc}a& b& c& d& e& f& g& h\end{array}\right]$

$B≔\mathrm{Array}\left(\left[5\,4\,3\,7\,6\,2\,8\,1\right]\right)$

$B≔\left[\begin{array}{cccccccc}5& 4& 3& 7& 6& 2& 8& 1\end{array}\right]$

$\mathrm{OrderByRank}\left(A\,B\right)$

$\left[\begin{array}{cccccccc}h& f& c& b& a& e& d& g\end{array}\right]$

$A≔\mathrm{Array}\left(\left[5.\,4.\,3.\,7.\,6.\,2.\,8.\,1.\right]\right)$

$A≔\left[\begin{array}{cccccccc}5.& 4.& 3.& 7.& 6.& 2.& 8.& 1.\end{array}\right]$

$B≔\mathrm{Array}\left(\left[a\,b\,c\,d\,e\,f\,g\,h\right]\right)$

$B≔\left[\begin{array}{cccccccc}a& b& c& d& e& f& g& h\end{array}\right]$

$C≔\mathrm{Rank}\left(A\right)$

$C≔\left[\begin{array}{cccccccc}5& 4& 3& 7& 6& 2& 8& 1\end{array}\right]$

$\mathrm{OrderByRank}\left(A\,C\right)$

$\left[\begin{array}{cccccccc}1.& 2.& 3.& 4.& 5.& 6.& 7.& 8.\end{array}\right]$

$\mathrm{OrderByRank}\left(B\,C\right)$

$\left[\begin{array}{cccccccc}h& f& c& b& a& e& d& g\end{array}\right]$

$X≔\mathrm{Array}\left(\left[a\,b\,c\,d\right]\right)$

$X≔\left[\begin{array}{cccc}a& b& c& d\end{array}\right]$

$Y≔\mathrm{Array}\left(\left[2\,3\,4\,1\right]\right)$

$Y≔\left[\begin{array}{cccc}2& 3& 4& 1\end{array}\right]$

$\mathrm{OrderByRank}\left(X\,Y\right)$

$\left[\begin{array}{cccc}d& a& b& c\end{array}\right]$

$Z≔\mathrm{Array}\left(\left[2\,3\,4\,3\right]\right)$

$Z≔\left[\begin{array}{cccc}2& 3& 4& 3\end{array}\right]$

$\mathrm{OrderByRank}\left(X\,Z\right)$

Error, (in Statistics:-OrderByRank) duplicate rank: 3

$\mathrm{OrderByRank}\left(X\,Z\,\mathrm{unique}=\mathrm{true}\right)$

$\left[\begin{array}{ccc}a& d& c\end{array}\right]$

$A≔\mathrm{Array}\left(1..6\,1..2\,\left[\left[10\,a\right]\,\left[5\,b\right]\,\left[-2\,c\right]\,\left[3\,d\right]\,\left[7\,e\right]\,\left[20\,f\right]\right]\right)$

$A≔\left[\begin{array}{cc}10& a\\ 5& b\\ \mathrm{-2}& c\\ 3& d\\ 7& e\\ 20& f\end{array}\right]$

$R≔\mathrm{Rank}\left(A\left[1..-1,1\right]\right)$

$R≔\left[\begin{array}{cccccc}5& 3& 1& 2& 4& 6\end{array}\right]$

$\mathrm{OrderByRank}\left(A\,R\right)$

$\left[\begin{array}{cc}\mathrm{-2}& c\\ 3& d\\ 5& b\\ 7& e\\ 10& a\\ 20& f\end{array}\right]$