“分类"向量(撤消排序) [英] "Desort" a vector (undo a sorting)

问题描述

在Matlab中，sort返回排序后的向量和索引向量，该向量显示哪个向量元素已移动到哪里:

In Matlab, sort returns both the sorted vector and an index vector showing which vector element has been moved where:

[v, ix] = sort(u);

在这里，v是包含u的所有元素但已排序的向量. ix是显示u中v的每个元素的原始位置的向量.使用Matlab的语法u(ix) == v.

Here, v is a vector containing all the elements of u, but sorted. ix is a vector showing the original position of each element of v in u. Using Matlab's syntax, u(ix) == v.

我的问题:如何从v和ix获取u?

当然，我可以简单地使用:

Of course, I could simply use:

w = zero(size(v));

for i = 1:length(v)
    w(ix(i)) = v(i)
end

if nnz(w == u) == length(u)
    print('Success!');
else
    print('Failed!');
end

但是我有一种舌尖的感觉，那就是有一种更加优雅，单一陈述，矢量化的方式来实现这一目标.

But I am having this tip-of-the-tongue feeling that there is a more elegant, single-statement, vectorized way of doing this.

如果您想知道为什么需要这样做而不是仅使用u :我正在尝试实现Benjamini-Hochberg过程，该过程根据向量的位置来调整向量的每个元素排序后，但是调整后恢复原始顺序对我来说很重要.

If you are wondering why one would need to do this instead of just using u: I was trying to implement the Benjamini-Hochberg procedure which adjusts each element of the vector based on its position after sorting, but recovering the original order after adjusting was important for me.

推荐答案

解决方案是:

w(ix) = v;

这是有效的Matlab操作，条件是w至少与v一样大，或者尚未声明.

This is a valid Matlab operation provided that w is either at least as big as v, or not yet declared.

示例:

>> u = [4 8 10 6 2];
>> [v, ix] = sort(u)

    v = 2 4 6 8 10        
    ix = 5 1 4 2 3

>> u(ix)

    ans = 2 4 6 8 10

>> w(ix) = v

    w = 4 8 10 6 2

(为平凡的问题回答道歉，但是我在输入问题时意识到了解决方案，并认为这可能对某人有用.)

(Apologies for the trivial question-answer, but I realized the solution as I was typing the question, and thought it might be useful to someone.)

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