Simple way to create a block-diagonal matrix from a single vector.

Question

Jon B. 2021-11-28

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1597509-simple-way-to-create-a-block-diagonal-matrix-from-a-single-vector

评论： Star Strider 2021-11-28

采纳的回答： Star Strider

在 MATLAB Online 中打开

I am working with a vector of the following form

and I would like to transform this vector into a block-diagonal matrix

without resorting to any sort of looping.

If I call the above vector x the following does, in principle, work

Z = reshape(x',3,4)';
[eye(2),zeros(2),zeros(2,4);zeros(2,4),zeros(2),eye(2)]*blkdiag(Z,Z)

It's just that my actual vector is fairly high dimensional and I feel that there must be a more organic way to obtain the same result, i.e., a way that does not rely on the manual construction of a selection matrix and that does not require typing

blkdiag(Z,Z,Z,Z,Z,Z,Z,Z,Z,Z,Z,Z,Z,..)

everytime the dimensionality changes. So essentialy, I would like to take a vector populate the first n coordinates of the first row of a matrix with the first n coodinates of this vector, fill in the rest of this row with zeros, move to the second row, populate the first first n coordinates with the second (!) n coordinates coordinates of my vector and continue until I reached the

-st coordinate of my vectore, then I start populating the first n cooridnates of the

-st row of my matrix with zeros and the second n cooridnates with the next elements of my vector, and so on...

I'd very much appreciate any pointers.

Thanks!

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Answer 1

Star Strider 2021-11-28

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1597509-simple-way-to-create-a-block-diagonal-matrix-from-a-single-vector#answer_842129

在 MATLAB Online 中打开

I don’t understand exactly what ‘z’ is or what the desired result is.

One possibility is to replicate the original matrix using repmat, then create it as a cell array using mat2cell, and then providing that result as the argument to blkdiag.

If I understand the problem correctly, this approach appears to provide the automation desired —

d = 3;                                      % Matrix Dimension (For This Simulation)
n = 5;                                      % Desired Number Of Repititions
z = randi([10 99],d)                        % Matrix To Be Replicated
z = 3×3
    28    52    96
    17    59    94
    57    97    85
zm = repmat(z,1,n)
zm = 3×15
    28    52    96    28    52    96    28    52    96    28    52    96    28    52    96
    17    59    94    17    59    94    17    59    94    17    59    94    17    59    94
    57    97    85    57    97    85    57    97    85    57    97    85    57    97    85
zmc = mat2cell(repmat(z,1,n), d, ones(1,n)*d)
zmc = 1×5 cell array
    {3×3 double}    {3×3 double}    {3×3 double}    {3×3 double}    {3×3 double}
zmc{1}                                      % Demonstrate That The Result Is As Desired
ans = 3×3
    28    52    96
    17    59    94
    57    97    85
zmc{end}                                    % Demonstrate That The Result Is As Desired
ans = 3×3
    28    52    96
    17    59    94
    57    97    85
BD = blkdiag(zmc{:})                        % Show Final Result
BD = 15×15
    28    52    96     0     0     0     0     0     0     0     0     0     0     0     0
    17    59    94     0     0     0     0     0     0     0     0     0     0     0     0
    57    97    85     0     0     0     0     0     0     0     0     0     0     0     0
     0     0     0    28    52    96     0     0     0     0     0     0     0     0     0
     0     0     0    17    59    94     0     0     0     0     0     0     0     0     0
     0     0     0    57    97    85     0     0     0     0     0     0     0     0     0
     0     0     0     0     0     0    28    52    96     0     0     0     0     0     0
     0     0     0     0     0     0    17    59    94     0     0     0     0     0     0
     0     0     0     0     0     0    57    97    85     0     0     0     0     0     0
     0     0     0     0     0     0     0     0     0    28    52    96     0     0     0

This replicates the original matrix, segments the replicated matrix into a cell array (a comma-separated list, exactly what blkdiag wants for an argument), then creates the bolck diagonal matrix.

.