How to Rank Same Values with Sam

Reference: http://www.ilovematlab.cn/thread-448152-1-1.html
Language: Matlab

We enter into array A some students' grades

A = [85 90 92 91 85 83 75 90 92 98 85 87]

A =
85 90 92 91 85 83 75 90 92 98 85 87

and sort A by descend.

[B,I] = sort(A,'descend');
I(I) = (1:numel(A))'; % very cool code
ranking1 = sortrows([A;I]',2)

ranking1 =
98 1
92 2
92 3
91 4
90 5
90 6
87 7
85 8
85 9
85 10
83 11
75 12

Here the ranking I ranks all same grade with various ranking (e.g. 85 marks has No.8 and No.9), thus we need take the first rankings to the same grades.
Now we firstly get unique elements from array A.

[C,ia,ic] = unique(A);
% here C = A(ia) and A = C(ic).
% by default, C is sorted by ascend
C

C =
75 83 85 87 90 91 92 98

C is the unique grades among original grades, each unique grade need share same ranking.

ia

ia =
7 6 1 12 2 4 3 10

ia is the index of elements of C in A, which corresponds to the most left of the elements if any element in C is repeated in A.

ic

ic =
3 5 7 6 3 2 1 5 7 8 3 4

ic stores indices of each element of A in C.
And ia(ic) (right column below) is taking the first ranking if repeated.

[A',I',ia(ic)]

ans =
85 8 1
90 5 2
92 2 3
91 4 4
85 9 1
83 11 6
75 12 7
90 6 2
92 3 3
98 1 10
85 10 1
87 7 12

So, ranking same value same rank is shown below

ranking2 = sortrows([A;I(ia(ic))]',2)

ranking2 =
98 1
92 2
92 2
91 4
90 5
90 5
87 7
85 8
85 8
85 8
83 11
75 12

That's it.