Htykuut

given a number of Actors A (1..n)
and a number of Subjects S (1..m)
and a number of Positions P (1..o)

and each actor can have one position on one subject P (a,s)
and each position can be expressed as an integer,

so that with 5 Actors and 3 Subjects the 15 Positions may look like this:

$$X=left[begin{array}{ccccc}1&1&-1&0&0\2&-3&0&0&1\2&-3&0&0&-1end{array}right]$$

Now if the distance between 2 positions is defined as D (p1,p2)=abs (p1-p2)

I'm trying to rank the subjects (here: horizontal) based on the average distance between all actors' positions on that subject.

On software, I could simply loop all subjects, foreach subject, loop all actors, foreach actor, calc the distance to all other actors. Sum it up and average that.

But it doesnt feel efficient. for example, if actor X has a distance D to actor Y, then Y has a distance D to X too; and if actor Z has a distance 0 to actor Y, then X must have a distance D to Z, too. Just looping the whole set will make these redundant calculations.

Is there a more efficient way to rank the subjects based on the average distances between the actors ? I'm hoping for some matrix operators to do this.