search multiple results for multiple conditions

THE CONTEXT:

I have a set of points in a virtual 2D space. Every point has its own x and y coordinate in space.

P = [1,2 ; 2 5; 4 6; 7 8; ...] % first column are x coordinates and second column are y coordinates

If I want to find the point that is closest to the first one [1,2] I can find the distance between the first point an the other points:

dis = sqrt((P(:,1)-1).^2 + (P(:,2)-2).^2)
dis = [0 ; 3.1623 ; 5 ; 8.4853 ; ...]

if I then search for the second smallest value in 'dis' I know which point is closest to the first point

THE QUESTION:

To generate the closest point for every point I can use a for loop

for i=1:length(P)
    dis = sqrt((P(:,1)-P(i,1).^2 + (P(:,2)-P(i,2).^2);
    index = secondsmallest(dis)   % find index of second smallest value somehow
    P_indices(i) = index;         % store index in an array'
end

Is there a way to find these indices without using a for loop?

.

Kind regards

Kjartan

Answer 1

[Star Strider]

I would use the pdist (link) function. You can use ordinary matrix indexing to find the indices of the various values. Also see the sort (link) function, as well as the functions linked in and at the end of the documentation pages.

Answer 2

[dpb]

doc pdist

Answer 3

[Jan]

for i=1:length(P)
  dis2 = (P(:,1) - P(i,1).^2 + (P(:,2) - P(i,2).^2;  % Omit SQRT() to save time
  index = secondsmallest(dis2);   % find index of second smallest value somehow
  P_indices(i) = index;           % store index in an array'
end

function k = secondsmallest(x)
[~, k] = min(x);
x(k)   = Inf;
[~, k] = min(x);
end

This is faster than sorting the complete vector.

Be sure that P_indices is pre-allocated before the loop.