Ranking and Sorting

The Rank() function returns the positions of the numbers in a vector or list, as if the numbers were sorted from lowest to highest.

E = [1 -2 3 -4 0 5 1 8 -7];

R = Rank( E );

[9, 4, 2, 5, 7, 1, 3, 6, 8]

If E were sorted from lowest to highest, the first number would be -7. The position of -7 in E is 9.

The original matrix E can then be sorted using the matrix R as subscripts to E.

sortedE = E[R];

[-7,- 4, -2, 0, 1, 1, 3, 5, 8]

The Ranking Tie() function returns ranks for the values in a vector or list, with ranks for ties averaged. Similarly, Ranking() returns ranks for the values in a vector or list, but the ties are ranked arbitrarily.

E = [1 -2 3 -4 0 5 1 8 -7];

Ranking Tie( E );

[5.5, 3, 7, 2, 4, 8, 5.5, 9, 1]

E = [1 -2 3 -4 0 5 1 8 -7];

Ranking( E );

[5, 3, 7, 2, 4, 8, 6, 9, 1]

The Sort Ascending() and Sort Descending() functions sort vectors.

E = [1 -2 3 -4 0 5 1 8 -7];

Sort Ascending( E );

[-7 -4 -2 0 1 1 3 5 8]

E = [1 -2 3 -4 0 5 1 8 -7];

Sort Descending( E );

[8 5 3 1 1 0 -2 -4 -7]

If the argument is not a vector or list, an error message is generated.