I need to calculate the distance matrix between these locations in ev charging stations placement

I'm working on an EV charging station project and have coordinates of potential station locations. I need to calculate the distance matrix between these locations using MATLAB. How can I efficiently compute this matrix based on the coordinates provided

Answer 1

[recent works]

% Assuming chargingStationCoordinates contains the coordinates of potential charging stations

% Calculate distance matrix between charging stations

numStations = size(chargingStationCoordinates, 1);

distanceMatrix = zeros(numStations);

for i = 1:numStations

for j = 1:numStations

distanceMatrix(i, j) = norm(chargingStationCoordinates(i, :) - chargingStationCoordinates(j, :));

end

end

disp('Distance Matrix:');

disp(distanceMatrix);

Answer 2

[Konrad]

Hi,

let's say you have 10 2d coordinates of charging stations

pos = rand(10,2);

Then one efficient way of computing the distance matrix would be:

m = pos * pos';
dist = sqrt(bsxfun(@plus, diag(m), diag(m)') - 2*m);

[Konrad]

Note that since 2016 or so, Matlab does implicit singleton expansion, i.e. you don't need the bsxfun() but you can write:

%sqrt(diag(m) + diag(m)' - 2*m)

which seems to be considerably faster.

EDIT: After some more testing it's not much of a difference:

tic;
for k = 1:1000
    pos = rand(200,2);
    m = pos * pos';
    dist = sqrt(diag(m)+diag(m)' - 2*m);
end
toc

Elapsed time is 0.130854 seconds.

tic;
for k = 1:1000
    pos = rand(200,2);
    m = pos * pos';
    dist = sqrt(bsxfun(@plus, diag(m), diag(m)') - 2*m);
end
toc

Elapsed time is 0.148703 seconds.

A different approach using the Pythagorean theorem:

tic;
for k = 1:1000
    pos = rand(200,2);
    dist = sqrt(sum(  (permute(pos,[1 3 2])-permute(pos,[3 1 2])).^2  ,3));
end
toc

Elapsed time is 0.166725 seconds.