How to create a matrix with special block diagonal structure

Question

Romio 2022-5-25

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https://ww2.mathworks.cn/matlabcentral/answers/1726825-how-to-create-a-matrix-with-special-block-diagonal-structure

回答： Stephen23 2022-5-25

I would like to create a matrix that has the following structure ( The blue dots are ones and the rest is zeros)

the number of the dots is determined by the triangular sequence. For example, the above matrix was obtained with n = 8. So is there any way to program this for any arbitrary n?

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Answer 1

DGM 2022-5-25

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在 MATLAB Online 中打开

Here's one way. I'm sure there are plenty of others.

n = 8;

sz = sum(1:n);

A = zeros(sz);

idx0 = 1;

for k = 1:n

A(idx0:idx0+k-1,idx0:idx0+k-1) = 1;

idx0 = idx0+k;

end

A = tril(A);

imshow(A)

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Answer 2

Steven Lord 2022-5-25

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https://ww2.mathworks.cn/matlabcentral/answers/1726825-how-to-create-a-matrix-with-special-block-diagonal-structure#answer_971485

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n = 8;

c = cell(1, n);

for k = 1:n

c{k} = tril(ones(k));

end

B = blkdiag(c{:});

spy(B)

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Answer 3

Torsten 2022-5-25

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https://ww2.mathworks.cn/matlabcentral/answers/1726825-how-to-create-a-matrix-with-special-block-diagonal-structure#answer_971435

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ntriangles = 4;
n = ntriangles*(ntriangles+1)/2;
A = zeros(n);
rowstart = 1;
rowend = 1;
for i = 1:ntriangles
    for jrow = rowstart:rowend
        A(jrow:rowend,jrow) = 1.0;
    end
    rowstart = rowend + 1;
    rowend = rowstart + i;
end