Vectorized Distance

vectorize.m

%d=6378.1*acos(sin(2*pi*lat(i)/360)*sin(2*pi*lat(j)/360)+cos(2*pi*(lng(i)-lng(j))/360)*cos(2*pi*lat(i)/360)*cos(2*pi*lat(j)/360));
tic
N = 4000;

% test some distances
lat = rand(N,1)*180;
lng = rand(N,1)*180;

% the loopy way
d = zeros(N);
dnew = d;
toc
for i = 1:N
    for j = 1:N
        d(i,j)=6378.1*acos(sin(2*pi*lat(i)/360)*sin(2*pi*lat(j)/360)+cos(2*pi*(lng(i)-lng(j))/360)*cos(2*pi*lat(i)/360)*cos(2*pi*lat(j)/360));
    end
end
toc


% the vectorized way
tic
latrad = 2*pi*lat/360;
lngrep = repmat(lng,1,N);
d1 = sin(latrad)*sin(latrad)';
lngscale = cos(2*pi*(lngrep-lngrep')/360);
d2 = lngscale.*(cos(latrad)*cos(latrad)');
dnew = 6378.1*acos(d1+d2);
toc

The vectorized way performs between 10 and 100 times faster on my macbook pro.