MATLAB: How to write a code in matlab for this loop to rank? For all p ∈ D Do For all q ∈ Nk(p) Do R ← Rank p by q End End

MATLAB

Ranking a point

If by "Rank p by q" you mean sort, take a look at the SORT and SORTROWS functions.

p = 5;
q = 19;
data = rand(p, q);
R = rank(data);

As long as you use the single-output version of 'dmperm'

 p = dmperm(A);

and only permute the rows of matrix A, getting A(p,:), then the elements of x are not permuted.

A permutation of both the rows and columns of A, A(p,q), will permute the elements of x by q. To get x back to the original order is accomplished by

 x(q) = x;

which amounts to the inverse permutation of q.