Matlab：两个向量之间的欧几里得范数（或差）
我想计算向量G与数组C的每一行之间的欧式距离，同时将每一行除以向量GSD中的值。我所做的似乎效率很低。我最大的开销是多少？ 我可以加快速度吗？
m=1E7;
G=1E5*rand(1,8);
C=1E5*[zeros(m,1),rand(m,8)];
GSD=10*rand(1,8);
%I've taken the log10 of the values because G and C are very large in magnitude.
%Don't know if it's worth it.
for i=1:m
dG(i,1)=norm((log10(G)-log10(C(i,2:end)))/log10(GSD));
end
使用下面的示例，它们给出的答案并不完全相同。实际上，它们都没有给出相同的答案（请参见下图，使用：
dG = pdist2(log10(G),log10(C(:,2:end)),'mahalanobis',diag(log10(GSD))); %(1)
dG = sqrt(sum((log10(G)-log10(C(:,2:end))./log10(GSD)).^2,2));
tmp=bsxfun(@rdivide,bsxfun(@minus,log10(G),log10(C(:,2:end))),log10(GSD)); %(4)
dG = sqrt(sum(tmp.^2,2));
2 个答案:
答案 0 :(得分：1)
您可以使用pdist2(x,y)计算/* Copyright (c) myEd (made by students, for students.) 2018. */
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</html>中所有元素之间的成对距离，因此您的示例将类似于
x其中名称对y将dG = pdist2(log10(G),log10(C(:,2:end)),'mahalanobis',diag(log10(GSD)).^2);
作为权重放在Eucledean上，这被称为马氏距离。
请注意，Mahalanobis距离最初用于规范化数据，因此必须将“协方差”作为第四个输入，然后MATLAB会在对角线处找到（元素对角的平方根的Cholesky分解，如下所示） ）。
隐式扩展
在较新的MATLAB版本中，也可以只是隐式扩展，因为第一个条目只有一个向量。
'mahalanobis',diag(log10(GSD)).^2这可能会快一点，但是我更喜欢log10(GSD)解决方案，因为我发现它更清晰。
答案 1 :(得分：1)
浮点应该处理大范围的输入数据，直到float数据到某个点为止，而double数据到任何合理值为止
realmax('single')
ans =
3.4028e+38
realmax('double')
ans =
1.7977e+308
如果1e7值在+/- 1e5范围内，则您可以预期欧几里得距离的平方在+/- 1e17范围内（5 + 5 + 7），这两种格式都可以轻松处理。 >
在任何情况下，您都应该对代码进行矢量化处理以消除循环（Matlab的处理历史非常低效，尤其是在旧版本中）
对于新版本（2016b和更高版本），只需使用：
tmp=(log10(G)-log10(C(:,2:end)))./log10(GSD);
dG = sqrt(sum(tmp.^2,2)); %row-by-row norm
请注意，您必须使用./（按元素划分），而不是/（按矩阵右划分）。
以下代码将随处可见
tmp=bsxfun(@rdivide,bsxfun(@minus,log10(G),log10(C(:,2:end))),log10(GSD));
dG = sqrt(sum(tmp.^2,2)); %row-by-row norm
但是，我认为使用log10是一个数学错误。结果dG将不是欧几里得范数。您应该坚持加权差异的均方根：
dG = sqrt(sum(bsxfun(@rdivide,bsxfun(@minus,G,C(:,2:end)),GSD).^2,2)); % all versions
dG = sqrt(sum((G-C(:,2:end)./GSD).^2,2)); %R2016b and later
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