如何沿阵列的某个维度执行操作？

Question

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

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

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

• The maximum value in every column.
• The mean value in every row.
• The standard deviation within each slice.

This is quite straightforward using loops,

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

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

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) 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.

How can I use this syntax to simplify my code?

Answer 1

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 :

• 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 .

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

This has several advantages:

• The code is easier to understand.
• The code is potentially more robust, being able to handle inputs beyond those it was initially designed for.
• The code is likely faster.

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.