Sorting and functional arithmetic of two vectors

I have a set of data say

x = [10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9]

y = rand(20,1)

In x there are 9 couplets such that sum of their modulus is 10

x(1)+ x(11) = x(2)+ x(10)= x(3)+ x(9)=. . . = x(5)+ x(7) = 10

and

x(12)+ x(20) = x(13)+ x(20) = . . . = x(15)+ x(17) = -10

based on this property i want to make subsets of y

ie [y(1),y(11)], [y(2),y(10],... [y(12),y(20)]...[y(15),y(17)]

Someway I want the output to be

z = [f(y(1),y(11)) f(y(2),y(10)) . . . f(y(12),y(20)) . . . f(y(15),y(17))]

where f is a mathematical function say f(a,b) = sqrt(a^2+b^2)

Any suggestions ?

note: x(6)+x(6) = 10 and x(16)x(16) = -10 In that context f(y(6),y(6)) and f(y(16),y(26)) are not essential but its fine if algorithm includes the two

Answer 1

[Andrei Bobrov]

lin = 1:length(x);
idx=sortrows([repmat(lin',1,2);nchoosek(lin,2)],1);
ouridx = idx(abs(sum(x(idx),2))==10,:);
y = rand(20,1);
z = ...
   arrayfun(@(i1)sqrt(y(ouridx(i1,1))^2+y(ouridx(i1,2))^2),(1:size(ouridx,1))');

[Andrei Bobrov]

CORRECTED (07/01/2011 18:25 MSK)