如何沿着数组的特定维度执行操作? [英] How to perform operations along a certain dimension of an array?

问题描述

我有一个3D数组，其中包含五个3×4切片，定义如下:

I have a 3D array containing five 3-by-4 slices, defined as follows:

rng(3372061);
M = randi(100,3,4,5);

我想收集有关数组的一些统计信息:

I'd like to collect some statistics about the array:

• 每列中的最大值.
• 每一行的平均值.
• 每个切片中的标准差.

使用循环非常简单

sz = size(M);
colMax = zeros(1,4,5);
rowMean = zeros(3,1,5);
sliceSTD = zeros(1,1,5);

for indS = 1:sz(3)
  sl = M(:,:,indS);
  sliceSTD(indS) = std(sl(1:sz(1)*sz(2)));
  for indC = 1:sz(1)
    rowMean(indC,1,indS) = mean(sl(indC,:));
  end

  for indR = 1:sz(2)
    colMax(1,indR,indS) = max(sl(:,indR));
  end  
end

但是我不确定这是否是解决问题的最佳方法.

But I'm not sure that this is the best way to approach the problem.

我在 max 的文档中注意到的一种常见模式>， mean 和

A common pattern I noticed in the documentation of max, mean and std is that they allow to specify an additional dim input. For instance, in max:

M = max(A,[],dim)返回沿维度dim的最大元素.例如，如果A是矩阵，则max(A,[],2)是包含每一行最大值的列向量.

M = max(A,[],dim) returns the largest elements along dimension dim. For example, if A is a matrix, then max(A,[],2) is a column vector containing the maximum value of each row.

如何使用此语法简化代码?

How can I use this syntax to simplify my code?

推荐答案

当计算结果很重要时，MATLAB中的许多函数都允许规范维运算"(几个常见示例:min ，max，sum，prod，mean，std，size，median，prctile，bounds)-对于多维输入尤其重要.如未说明，未指定dim输入时，MATLAB可以自行选择尺寸.例如在max:

Many functions in MATLAB allow the specification of a "dimension to operate over" when it matters for the result of the computation (several common examples are: min, max, sum, prod, mean, std, size, median, prctile, bounds) - which is especially important for multidimensional inputs. When the dim input is not specified, MATLAB has a way of choosing the dimension on its own, as explained in the documentation; for example in max:

• 如果A是向量，则max(A)返回A的最大值.
• 如果A是矩阵，则max(A)是包含每一列最大值的行向量.
• 如果A是多维数组，则max(A)沿大小不等于1的第一个数组维操作，将元素视为向量.该尺寸的大小变为1，而所有其他尺寸的大小保持不变.如果A是一个空数组，其第一个维度的长度为零，则max(A)返回一个空数组，其大小与A相同.

• If A is a vector, then max(A) returns the maximum of A.
• If A is a matrix, then max(A) is a row vector containing the maximum value of each column.
• If A is a multidimensional array, then max(A) operates along the first array dimension whose size does not equal 1, treating the elements as vectors. The size of this dimension becomes 1 while the sizes of all other dimensions remain the same. If A is an empty array whose first dimension has zero length, then max(A) returns an empty array with the same size as A.

然后，使用...,dim)语法，我们可以按如下所示重写代码:

Then, using the ...,dim) syntax we can rewrite the code as follows:

rng(3372061);
M = randi(100,3,4,5);

colMax = max(M,[],1);
rowMean = mean(M,2);
sliceSTD = std(reshape(M,1,[],5),0,2); % we use `reshape` to turn each slice into a vector

这有几个优点:

• 代码更易于理解.
• 该代码可能更健壮，能够处理超出最初设计目的的输入.
• 代码可能更快.

总而言之:最好阅读正在使用的函数的文档，并尝试不同的语法，以免错过相似的机会来使您的代码更简洁.

In conclusion: it is always a good idea to read the documentation of functions you're using, and experiment with different syntaxes, so as not to miss similar opportunities to make your code more succinct.

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