Hi @LH
Instead of using the absolute difference for each dimension separately, compute the Euclidean distance between the rows of A and B. This is done using sqrt(sum((A - B_pair).^2, 2)). And then use min(distances) to find the index of the row in A that is closest to the current row in B.
This should ensure that each row in matrix B gets the identifier of the closest row in matrix A.
Refer to the snippet below:
close all
clear all
% Define the number of random numbers
n = 10;
% Define the min and max ranges of random values
stvar = [0 4]; % on the 1st dim
ndvar = [-1 1]; % on the 2nd dim
% Construct the first random matrix
A(:,1) = stvar(1) + (stvar(end) - stvar(1)) * rand(n,1); % first column
A(:,2) = ndvar(1) + (ndvar(end) - ndvar(1)) * rand(n,1); % second column
A = [A(:,1) A(:,2)]; % collect both columns into one matrix
% Propose the identifiers of matrix A
iden_A = randi([1, n/2], n, 1);
% Construct the second random matrix
B(:,1) = stvar(1) + (stvar(end) - stvar(1)) * rand(n,1); % first column
B(:,2) = ndvar(1) + (ndvar(end) - ndvar(1)) * rand(n,1); % second column
B = [B(:,1) B(:,2)]; % collect both columns into one matrix
% Finding the identifiers of matrix B
iden_B = [];
% Go through all receiving pairs of space and direction
for i = 1:size(B,1)
% Define the B pair
B_pair = B(i,:);
% Calculate the Euclidean distance between B_pair and all rows of A
distances = sqrt(sum((A - B_pair).^2, 2));
% Find the index of the minimum distance
[~, minloc] = min(distances);
% Assign the identifier of the closest row in A to the current row in B
iden_B = [iden_B; iden_A(minloc)];
end
% Display the results
disp('Matrix A:');
disp(A);
disp('Identifiers of Matrix A:');
disp(iden_A);
disp('Matrix B:');
disp(B);
disp('Identifiers of Matrix B:');
disp(iden_B);
Let's go through the first few rows of B and verify the calculations:
Row 1 of B: ( [0.9341, 0.0032] )
- Calculate Euclidean distances to each row in A:
distances = sqrt(sum((A - [0.9341, 0.0032]).^2, 2))
= [2.8259, 0.3990, 0.9344, 2.8985, 1.9816, 2.7432, 1.6181, 0.8511, 1.0655, 2.8735]
- The minimum distance is 0.3990, which corresponds to row 2 in A.
- Identifier for row 2 in A is 2.
- So, iden_B(1) = 2.
Row 2 of B: ( [0.7069, -0.3004] )
- Calculate Euclidean distances to each row in A:
distances = sqrt(sum((A - [0.7069, -0.3004]).^2, 2))
= [3.0764, 0.1033, 1.2538, 3.1488, 2.2337, 2.8363, 1.9807, 0.5451, 1.3885, 2.9975]
- The minimum distance is 0.1033, which corresponds to row 2 in A.
- Identifier for row 2 in A is 2.
- So, iden_B(2) = 2.
