Ranking vectors from highest to lowest including repeated ranks.

If I have a vector say [0.4 0.1 0.1 0.2 0.1 0.05 0.05], then I want to rank this vector with output [1 3 3 2 3 6 6] (i.e. ranking number in the usual way)

Currently I'm using

X =  [0.4 0.1 0.1 0.2 0.1 0.05 0.05]
Rnk = floor(tiedrank(-X));

This outputs:

Rnk = [1 4 4 2 4 6 6]

But this doesn't work because I want the third ranked element to output 3 in each case, but tiedrank function is computing the mean(3,4,5) = 4. This method does work when there are only 2 repeats because, for example, for the 0.05 elements, they should be rank 6, but tiedrank function computes mean(6,7)=6.5 and floor(6.5) = 6, and my vectors usually have several entries that are similar:

For example let

X =  [0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 ]
Rnk = floor(tiedrank(-X));

returns

Rnk = [5 5 5 5 5 5 5 5 5 5]

instead of [1 1 1 1 1 1 1 1 1 1 1] since the function computes mean(1,2,3,4,5,6,7,8,9,10) = 5.5 and floor(5.5) = 5. Is there a simple function that can yield me my desired output?

Answer 1

[Cameron]

I'm not sure how you want your ranking to occur. Why would your output be [1 3 3 2 3 6 6] instead of [1 3 3 2 3 4 4]? Either way, this is how I would do it.

X = [0.4 0.1 0.1 0.2 0.1 0.05 0.05];
[~,~,Rnk] = unique(-X)

Rnk = 7×1

1 3 3 2 3 4 4

[William]

Hi, Is there a way to make this work to show 6 instead of 4? It's because if you imagine a race in which there's and there's a tie for 2nd place, then the fourth person isn't 3rd, he's 4th? (Assume there's only 1 winner)

[Cameron]

I understand. In this case, I would do this

X = [0.4 0.1 0.1 0.2 0.1 0.05 0.05];
X_sorted = sort(-X);
[~,Rnk] = ismember(-X,X_sorted)

Rnk = 1×7

1 3 3 2 3 6 6

Answer 2

[Marco Riani]

Hi William, I did it using a loop. Please let me know if the code below is what you wanted

x=[0.4 0.1 0.1 0.2 0.1 0.05 0.05];
out=zeros(size(x));
for j=1:length(x)
    if max(x)>-Inf
        sel=x==max(x);
        out(sel)=sum(out>0)+1;
        x(sel)=-Inf;
    end
end
disp('Ranking')

Ranking

disp(out)

     1     3     3     2     3     6     6