how to solve Ring topology?

hi

i have two matrix, y contains the variable and d contains their solutions. Now first, i want to pair them in ring format (circle shape). as 5 elements are in y matrix which means 5 different pairs will be build containing total three variable, one is itself and other two are their adjacent.

y=[x1 x2 x3 x4 x5] matrix results following values 
d=[z1 z2 z3 z4 z5]

for pair x5 x1 x2    measure       z5 z1 z2 (selects minimum value and give output value correspond in y matrix)
         x1 x2 x3                  z1 z2 z3
         x2 x3 x4                  z2 z3 z4
         x3 x4 x5                  z3 z4 z5
         x4 x5 x1                  z4 z5 z1

for e.g y= [2 3 1 5 6]
        d= [2 1 5 4 3]

in pair 6 2 3  (Y matrix), 3 gives less output 1 compared to 2(2) and 6(3). the output must 3.

Kindly help me. i will be highly thankful to you

with best regards.
mudasir ahmed

Answer 1

[Guillaume]

Here is a simple way to generate your triplets (they're not pairs!):

triplets = @(v) [circshift(v, [0 1]); v; circshift(v, [0 -1])]';

And here is how to get your output:

y = [2 3 1 5 6];
d = [2 1 5 4 3];

triplets = @(v) [circshift(v, [0 1]); v; circshift(v, [0 -1])]';
ytriplets = triplets(y)
dtriplets = triplets(d)
[~, col] = min(dtriplets, [], 2);
out = ytriplets(sub2ind(size(ytriplets), [1:size(ytriplets, 1)]', col))