MATLAB: Closest Points between two datasets without using pdist2

MATLABminimum distancevectorization

Hi, i have two matrices A, of size mx2, and B, of size nx2.
Each row of both matrices identifies a point in 2D space. What i want to do is to write a code, that does not involve loops and pdist2, as fast as possible, that tells me the indices of the row of both A and B such that the distance squared of the two points is the minimum one.
Example:
A=[5 6;
1 2;
3 4
1 8];
B=[3 0;
2 1;
4 1;
3 5;
1 2];
My function must be like [indA,indB]=function(A_matrix,B_matrix)
I want as output [2,5]=function(A,B)
I found a solution using for-loops but i really would like to find a solution using repmat that involves vectorization.
Thanks

Best Answer

A=[5 6;
     1 2;
     3 4
     1 8];
B=[3 0;
     2 1;
     4 1;
     3 5;
     1 2];
P = permute(sum((A-permute(B,[3 2 1])).^2,2),[1 3 2])   %will be size(A,1) by size(B,1)
P = 4×5
    40    34    26     5    32
     8     2    10    13     0
    16    10    10     1     8
    68    50    58    13    36

●
A_idx_in_B = sum(cumprod(P ~= min(P,[],1),1),1)+1
A_idx_in_B = 1×5
     2     2     2     3     2

●
B_idx_in_A = sum(cumprod(P ~= min(P,[],2),2),2)+1
B_idx_in_A = 4×1
     4
     5
     4
     4

●
This code resolves ties in favor of the first match.
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