MATLAB矢量化的成对距离
我正在努力化一个函数，该函数在两个矢量x = 2xn和v = 2xm之间执行一些成对的差异，对于某个任意n，M。我在n = 1时可以工作功能适用于具有n个任意的输入。
实际上，我希望此功能要做的是x的每一列找到x（：，列）（A 2x1）和V（A 2xm）之间的范围差异。
类似的帖子是 this ，尽管我无法推广它。
当前实施
function mat = vecDiff(x,v)
diffVec = bsxfun(@minus, x, v);
mat = diffVec ./ vecnorm(diffVec);
示例
x =
1
1
v =
1 3 5
2 4 6
----
vecDiff(x,v) =
0 -0.5547 -0.6247
-1.0000 -0.8321 -0.7809
I'm struggling to vectorise a function which performs a somewhat pairwise difference between two vectors x = 2xN and v = 2xM, for some arbitrary N, M. I have this to work when N = 1, although, I would like to vectorise this function to apply to inputs with N arbitrary.
Indeed, what I want this function to do is for each column of x find the normed difference between x(:,column) (a 2x1) and v (a 2xM).
A similar post is this, although I haven't been able to generalise it.
Current implementation
function mat = vecDiff(x,v)
diffVec = bsxfun(@minus, x, v);
mat = diffVec ./ vecnorm(diffVec);
Example
x =
1
1
v =
1 3 5
2 4 6
----
vecDiff(x,v) =
0 -0.5547 -0.6247
-1.0000 -0.8321 -0.7809
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评论（2）
您的方法可以如下适合您的需求：
x或v的尺寸，以便其列数变为 third>第三 dimension。我在下面的代码中选择v。bsxfun）to计算A是2×M×n差异数组，其中m和nnx和v的列数。如果您希望按其他顺序输出尺寸，则可能需要以不同的方式应用
PERTER。Your approach can be adapted as follows to suit your needs:
xorvso that its number of columns becomes the third dimension. I'm choosingvin the code below.bsxfun) to compute a2×M×Narray of differences, whereMandNare the numbers of columns ofxandv.You may need to apply
permutedifferently if you want the dimensions of the output in another order.假设您的两个输入矩阵是A（A 2 X N矩阵）和B（A 2 X M矩阵），其中每列代表不同的观察值（请注意，这不是表示数据的传统方式）。
请注意，输出的大小为n x m x 2。
out = zeros（n，m，2）;我们可以使用内置函数
pdist2找到它们之间的距离。dists = pdist2（a。'，b。'）;（矩阵的方向所需的换位）才能获得单个x和y距离，我想到的最简单的方法就是使用repmat：
然后，我们可以通过前面找到的距离进行归一化：
这返回矩阵
out，其中位置的元素（i，j，：）是a（：，i）和b（：j）之间的规范距离。Suppose your two input matrices are A (a 2 x N matrix) and B (a 2 x M matrix), where each column represents a different observation (note that this is not the traditional way to represent data).
Note that the output will be of the size N x M x 2.
out = zeros(N, M, 2);We can find the distance between them using the builtin function
pdist2.dists = pdist2(A.', B.');(with the transpositions required for the orientation of the matrices)To get the individual x and y distances, the easiest way I can think of is using repmat:
And we can then normalise this by the distances found earlier:
This returns a matrix
outwhere the elements at position(i, j, :)are the components of the normed distance betweenA(:,i)andB(:,j).