Distance between all points of two vectors

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

Answer 1

[Guillaume]

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));

[Bineet_Mehra]

Thanks Guillaume,

there is an error while computing Dvec

Array indices must be positive integers or logical values.

thanks

[Guillaume]

Do'h! Fixed (replace ones by true)

[Bineet_Mehra]

thanks works well !!

[Bineet_Mehra]

Though the problem is solved, i wonder what changes we can make to the for loop above to get the same result. Just out of curosity !!!

[Guillaume]

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.

[Bineet_Mehra]

thanks Guillaume !!!