matlab - 对矩阵的每 n 行求和

Question

有什么方法可以对矩阵中每组三行的列值求和吗？
我可以手动总结三行。

例如

% matrix is the one I wanna store the new data.
% data is the original dataset.
matrix(1,1:end) = sum(data(1:3, 1:end))
matrix(2,1:end) = sum(data(4:6, 1:end))
...

但是如果数据集很大，这就不行了。
有什么方法可以自动执行此操作而无需循环？

Answer 1

还有其他四种方式:

1. 必需的 for 循环:

   % for-loop over each three rows
   matrix = zeros(size(data,1)/3, size(data,2));
   counter = 1;
   for i=1:3:size(data,1)
       matrix(counter,:) = sum(data(i:i+3-1,:));
       counter = counter + 1;
   end
   

2. 使用 mat2cell 进行平铺:

   % divide each three rows into a cell
   matrix = mat2cell(data, ones(1,size(data,1)/3)*3);
   
   % compute the sum of rows in each cell
   matrix = cell2mat(cellfun(@sum, matrix, 'UniformOutput',false));
   

3. 使用三维(基于 this ):

   % put each three row into a separate 3rd dimension slice
   matrix = permute(reshape(data', [], 3, size(data,1)/3), [2 1 3]);
   
   % sum rows, and put back together
   matrix = permute(sum(matrix), [3 2 1]);
   

4. 使用accumarray:

   % build array of group indices [1,1,1,2,2,2,3,3,3,...]
   idx = floor(((1:size(data,1))' - 1)/3) + 1;
   
   % use it to accumulate rows (appliead to each column separately)
   matrix = cell2mat(arrayfun(@(i)accumarray(idx,data(:,i)), 1:size(data,2), ...
       'UniformOutput',false));
   

当然，目前所有的解决方案都假设行数可以被 3 整除。