matlab - 基于每行的列索引折叠矩阵每一行的有效方法

Question

我想通过根据为每行指定的列索引执行操作来按行减少矩阵中的列数。给出以下示例数据:

M = magic(4);
col_ind = [1; 3; 2; 4];

我想制作一个三列矩阵，第一列包含每行到指定列索引的行总和，第二列包含该行中 M 的值，由列索引指定，最后一列包含该行中其余条目的行总和，即生成矩阵 M_out:

M_out = nan(4,3);
for i = 1:4
    M_out(i, :) = [sum(M(i, 1:col_ind(i)-1), 2), ...
        M(i, col_ind(i)), sum(M(i, col_ind(i)+1:end), 2)];

end

这样:

>> M_out

M_out =

     0    16    18
    16    10     8
     9     7    18
    33     1     0

Answer 1

根据Stewie's comment ，我将在这里使用 tril 来完成此操作。第二列很简单，使用 sub2ind 。那么第三列就变得微不足道了:

T = tril(ones(size(M, 2)), -1);
M_out = zeros(size(M, 1), 3);
M_out(:, 1) = sum(T(col_ind,:) .* M, 2);
M_out(:, 2) = M(sub2ind(size(M), (1:size(M, 1)).', col_ind));
M_out(:, 3) = sum(M, 2) - sum(M_out, 2);

---

或者，使用 cumsum 会更高效一些:

cs = cumsum(M, 2);
M_out = zeros(size(M, 1), 3);
M_out(:, 2) = M(sub2ind(size(M), (1:size(M, 1)).', col_ind));
M_out(:, 1) = cs(sub2ind(size(cs), (1:size(cs, 1)).', col_ind)) - M_out(:, 2);
M_out(:, 3) = cs(:, end) - sum(M_out, 2);