Given a couple of vectors with priorities, is there a fast built-in function to find the index of the largest value?

Consider that there exist three 10-dimensional vectors p1, p2, and p3, and the priority is given in order p1>p2>p3.

I want to find an index that is the largest in p1, the largest in p2 in case of a tie in p1, the largest in p3 in case of a tie in both p1 and p2, and randomly selected in case of a tie in all p1, p2, and p3.

That is, the code can be constructed as follows for given p1, p2, p3.

p1 = [1,  9, 3, 8,  4,  9, 1,  9,  5,  9];  % given
p2 = [5, 15, 6, 7, 10, 10, 5, 15,  1, 15];  % given
p3 = [1, 25, 3, 4, 11,  4, 1, 25, 99, 15];  % given
ind_p1 = (p1 == max(p1));   % Output: ind_p1 = [0, 1, 0, 0, 0, 1, 0, 1, 0, 1]
p2_prime = p2.*ind_p1;  % Output: p2_prime = [0, 15, 0, 0, 0, 10, 0, 15, 0, 15]
ind_p2 = (p2_prime == max(p2_prime));   % ind_p2 = [0, 1, 0, 0, 0, 0, 0, 1, 0, 1]
p3_prime = p3.*ind_p2;  % p3_prime = [0, 25, 0, 0, 0, 0, 0, 25, 0, 15]
ind_p3 = find(p3_prime == max(p3_prime));   % ind_p3 = [2, 8]
ind = ind_p3(randi(length(ind_p3)));   % ind = 2 or 8
result = [ind, p1(ind), p2(ind), p3(ind)];  % result = [2, 9, 15, 25] or [8, 9, 15, 25]

I think the code for the above purpose will be used a lot in a wide variety of places.

Are there any quick (or code-readable) built-in MATLAB functions to produce the above results?

Answer 1

[Bruno Luong]

p1 = [1,  9, 3, 8,  4,  9, 1,  9,  5,  9];  % given
p2 = [5, 15, 6, 7, 10, 10, 5, 15,  1, 15];  % given
p3 = [1, 25, 3, 4, 11,  4, 1, 25, 99, 15];  % given

[pmax,loc] = sortrows([p1;p2;p3]');
result = [loc(end),pmax(end,:)]