矢量化向量之间的距离计算 [英] Vectorizing distance calculation between vectors

问题描述

我给出了一个3×1000（及后来的3×10 000）矩阵 cord ，其中包含我的像素的三维坐标。
$ b

我的意图是计算所有像素之间的距离，我用一个for循环（见下面）来做，但是我将不得不很快计算这个庞大的矩阵，并且想知道是否我可以矢量化代码，使其更快...？
$ b $ $ p $ dist = zeros（size（cord，2），size（线，2））;
for i = 1：size（cord，2）
for j = 1：size（cord，2）
dist（i，j）= norm（cord（：，i） - 帘线（：，J））;
dist（j，i）= dist（i，j）;
end
end


解决方案

< a href =http://www.mathworks.es/es/help/stats/pdist.html =nofollow> pdist 确实如此那。 squareform 是需要以正方形对称矩阵的形式得到结果：

$ $ $ $ $ $ c $ dist dist = squareform（pdist（cord。'）） ;

I have a 3 X 1000 (and later 3 X 10 000) matrix cord given, which contains the three dimensional coordinates for my pixels.

My intention is to calculate the distance between all the pixels, and I do it with a for loop (see below), but I will have to calculate this for huge matrices soon, and am wondering if I could vectorize the code for making it faster...?

dist = zeros(size(cord,2),size(cord,2)); 
for i = 1:size(cord,2)
    for j = 1:size(cord,2)
        dist(i,j) = norm(cord(:,i)-cord(:,j));
        dist(j,i) = dist(i,j);
    end 
end

解决方案

pdist does exactly that. squareform is needed to get the result in the form of a square, symmetric matrix:

dist = squareform(pdist(cord.'));

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