For a data set X of size n, the Rank command ranks the elements of X according to their floating-point values.

By default, an array of ranks is returned, that is an array of distinct integers between 1 and n. By default the elements of X are ranks in the ascending order. Note that if i is different from j then ${\mathrm{data}}_i$ and ${\mathrm{data}}_j$ will receive distinct ranks even if data[i] = data[j].

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

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 ranked in the ascending or descending order. The default value is order=ascending.

output=table -- By default (output=rtable) different elements of X receive different ranks even if the two elements have the same numeric value. If this option is set to output=table then the elements of X will be ranked according to their position in the sorted sample with all multiple occurrences removed.

Each element of X can be any Maple expression, but this expression must be able to be evaluated to a floating-point number. Failure to evaluate to do so will generate an exception.

If the output option is set to output=table all elements in X must be of type numeric.

The Rank command leaves the original data set X unchanged.

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

$A≔\mathrm{Array}\left(\left[0.5\,0.7\,0.5\,0.1\,0.3\,0.1\,0.2\,0.1\right]\right)$

$A≔\left[\begin{array}{cccccccc}0.5& 0.7& 0.5& 0.1& 0.3& 0.1& 0.2& 0.1\end{array}\right]$

$R≔\mathrm{Rank}\left(A\right)$

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

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

$B≔\left[\begin{array}{cccccccc}0.1& 0.1& 0.1& 0.2& 0.3& 0.5& 0.5& 0.7\end{array}\right]$

$Q≔\mathrm{Rank}\left(A\,\mathrm{order}=\mathrm{descending}\right)$

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

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

$C≔\left[\begin{array}{cccccccc}0.7& 0.5& 0.5& 0.3& 0.2& 0.1& 0.1& 0.1\end{array}\right]$

$T≔\mathrm{Rank}\left(A\,\mathrm{output}=\mathrm{table}\right)$

$T≔table\left(\left[0.3=3\,0.7=5\,0.1=1\,0.5=4\,0.2=2\right]\right)$

$A\left[4\right],T\left[A\left[4\right]\right]$

$0.1,1$

$A\left[1\right],T\left[A\left[1\right]\right]$

$0.5,4$