Distance between all points of two vectors

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Bineet_Mehra
Bineet_Mehra 2020-3-2
评论： Bineet_Mehra 2020-3-2
Hello,
'x' and 'y' are two vectors having respectively x and y coordinates of spatial locations.
x = [1;3;1;4;5]
y = [5;4;3;1;1]
I am trying to calculate distance between all the pairs (point 1 to 2, 2 to 3 etc, total 10). Here is what i did:
for i = 1:length(x)-1
for j = i+1:length(x)
D = (sqrt((x(i) - x(j)).^2 + (y(i) - y(j)).^2))
end
end
The distance D for all pairs are calculated correctly. How can i modify this code so that all the distances are saved in D as a vector.
Thanks
Bineet

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Guillaume
Guillaume 2020-3-2
编辑：Guillaume 2020-3-2
Loops are rarely needed in matlab. They just make the code more complicated. Case in point:
D = hypot(x-x.', y-y.');
All done!
If you just want the upper triangular matrix of the above as a vector:
Dvec = D(triu(true(size(D)), 1));
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Guillaume
Guillaume 2020-3-2
The easiest would have been to build a 2D matrix (as my first line of code does) and then extract the relevant part as a vector. For building the 2D matrix, you just need to add indexing into D:
D(i, j) = sqrt((x(i) - x(j)).^2 + (y(i) - y(j)).^2); %better written as hypot(x(i)-x(j), y(i)-y(j))
But it would be much better to preallocate the matrix before the loop:
D = zeros(numel(x)); %preallocation to avoid growing the matrix in the loop (which is slow)
for i = 1:numel(x)-1
for j = i+1:numel(x)
D(i, j) = hypot(x(i)-x(j), y(i)-y(j));
end
end
Dvec = D(triu(true(size(D)), 1));
If you want to build a vector from scratch:
Dvec = zeros(1, sum(1:numel(x)-1));
didx = 1;
for i = 1:numel(x)-1
for j = i+1:numel(x)
Dvec(idx) = hypot(x(i)-x(j), y(i)-y(j));
idx = idx + 1;
end
end
But overall:
D = hypot(x-x.', y-y.');
Dvec = D(triu(true(size(D)), 1));
is much simpler.

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