Question

我正在尝试优化这段代码并摆脱实现的嵌套循环。我发现将矩阵应用于pdist函数存在困难

例如，1 + j // -1 + j // -1 + j // -1-j是初始点，我试图通过最小距离逼近点检测0.5 + 0.7j 。
任何帮助表示赞赏

function result = minDisDetector( newPoints, InitialPoints)
result = [];
for i=1:length(newPoints)
    minDistance = Inf;
    for j=1:length(InitialPoints)

        X = [real(newPoints(i)) imag(newPoints(i));real(InitialPoints(j)) imag(InitialPoints(j))];
        d = pdist(X,'euclidean');

        if d < minDistance
            minDistance = d;
            index = j;
        end
    end
    result = [result; InitialPoints(index)]; 
end     
end

Answer 1

您可以使用Speed-efficient classification in Matlab中列出的有效欧几里德距离计算 vectorized solution -

%// Setup the input vectors of real and imaginary into Mx2 & Nx2 arrays
A = [real(InitialPoints) imag(InitialPoints)];
Bt = [real(newPoints).' ; imag(newPoints).'];

%// Calculate squared euclidean distances. This is one of the vectorized
%// variations of performing efficient euclidean distance calculation using 
%// matrix multiplication linked earlier in this post.
dists = [A.^2 ones(size(A)) -2*A ]*[ones(size(Bt)) ; Bt.^2 ; Bt];

%// Find min index for each Bt & extract corresponding elements from InitialPoints
[~,min_idx] = min(dists,[],1);
result_vectorized = InitialPoints(min_idx);

快速运行时测试，newPoints为400 x 1＆amp; InitialPoints为1000 x 1：

-------------------- With Original Approach
Elapsed time is 1.299187 seconds.
-------------------- With Proposed Approach
Elapsed time is 0.000263 seconds.

Answer 2

解决方案非常简单。但是，您确实需要我的cartprod.m function来生成笛卡尔积。

首先为每个变量生成随机复杂数据。

newPoints = exp(i * pi * rand(4,1));
InitialPoints = exp(i * pi * rand(100,1));

使用newPoints生成InitialPoints和cartprod的笛卡尔积。

C = cartprod(newPoints,InitialPoints);

第1列和第2列的差异是复数的距离。然后abs将找到距离的大小。

A = abs( C(:,1) - C(:,2) );

由于生成了笛卡尔积，因此它首先排列newPoints个变量：

我们需要reshape它并使用min获得最小距离以找到最小距离。我们需要转置来找到每个newPoints的最小值。否则，如果没有转置，我们将获得每个InitialPoints的最小值。

[m,i] = min( reshape( D, length(newPoints) , [] )' );

m为您提供分数，而i则为您提供分数。如果您需要获得最低initialPoints，请使用：

result = initialPoints( mod(b-1,length(initialPoints) + 1 );

Answer 3

通过使用欧几里德范数引入逐元素运算来计算距离，可以消除嵌套循环。如下所示。

    result = zeros(1,length(newPoints)); % initialize result vector
    for i=1:length(newPoints)
        dist = abs(newPoints(i)-InitialPoints); %calculate distances
        [value, index] =  min(dist);
        result(i) = InitialPoints(index);
    end

MATLAB中复杂向量的速度有效分类

3 个答案: