如何将矩阵划分为大小不相等的子矩阵? [英] How can I divide a matrix into unequally-sized submatrices?

问题描述

我想知道是否可以使用mat2cell函数将MxN矩阵划分为具有相同列大小N和大约相同行大小~M/10的10个子矩阵?如果mod(M, 10) == 0，则所有子矩阵都将具有相同的大小，否则，一些矩阵将具有+/- 1行.通过mat2cell函数可以做到这一点吗?

I am wondering if it is possible to use the mat2cell function to divide an MxN matrix into 10 submatrices with the same column size, N, and approximately the same row size ~M/10? If mod(M, 10) == 0 then all submatrices will have the same size, otherwise a few matrices will have +/-1 row. Is this possible via the mat2cell function?

作为参考，如果行大小都相同，则相当简单，如下所示:
如何将矩阵划分为相等的部分?

For reference, if the row sizes are all the same it's fairly straightforward, as explained here:
How to divide a matrix into equals parts?

推荐答案

这是使用 linspace ， round 和 diff :

Here's a simple solution using the functions linspace, round, and diff:

[M, N] = size(mat);  % Matrix size
nSub = 10;           % Number of submatrices
cMat = mat2cell(mat, diff(round(linspace(0, M, nSub+1))), N);

此方法将以更统一的方式在单元阵列的结果单元之间分配额外的行.请注意使用mat = magic(5);(左)和mat = magic(13);(右)应用上述方法时将获得的这些输出:

This approach will distribute extra rows in a more uniform fashion across the resulting cells of the cell array. Note these outputs that you will get when applying the above using mat = magic(5); (left) and mat = magic(13); (right):

cMat =              cMat = 

    [1x5 double]        [1x13 double]
    [0x5 double]        [2x13 double]
    [1x5 double]        [1x13 double]
    [0x5 double]        [1x13 double]
    [1x5 double]        [2x13 double]
    [0x5 double]        [1x13 double]
    [1x5 double]        [1x13 double]
    [0x5 double]        [1x13 double]
    [1x5 double]        [2x13 double]
    [0x5 double]        [1x13 double]

如果您希望随机分配多余的行，可以使用 randperm 像这样:

If you'd prefer a random distribution of extra rows, you can use randperm like so:

subSizes = diff(round(linspace(0, M, nSub+1)));
cMat = mat2cell(mat, subSizes(randperm(nSub)), N);

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