Overlaying several matrices diagonally to create a larger matrix

Question

Edvardas 2014-11-10

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/162082-overlaying-several-matrices-diagonally-to-create-a-larger-matrix

编辑： Chris Dan 2019-11-10

Hello,

I am currently struggling to figure a way out to connect around 10-12 8x8 matrices diagonally in a way as shown in this image

Where essentially the corner 4x4 from the 8x8 matrix would be overlayed diagonally. Everything else in the final matrix is to be zero.

Hence was wondering if anyone has any experience of forming matrices like this and perhaps would be able to help.

So far the only solution I have figured out is basically this:

% 8x8 matrix
m = (miu*l/420).*[156 0 0 22*l 54 0 0 -13*l;...
    0 156 -22*l 0 0 54 13*l 0;...
    0 -22*l 4*l^2 0 0 -13*l -3*l^2 0;...
    22*l 0 0 4*l^2 13*l 0 0 -3*l^2;...
    54 0 0 13*l 156 0 0 -22*l;...
    0 54 -13*l 0 0 156 22*l 0;...
    0 13*l -3*l^2 0 0 22*l 4*l^2 0;...
    -13*l 0 0 -3*l^2 -22*l 0 0 4*l^2];
%miu and l varies, so m = m1; m2 m3... etc.
%create large matrix of zeros
M=zeros(52);
M(1:8,1:8)=m1;
M(5:12, 5:12) = m2;
M(9:16, 9:16) = m3;
M(13:20, 13:20) = m4;
M(17:24, 17:24) = m5;
M(21:28, 21:28) = m6;
M(25:32, 25:32) = m7;
M(29:36, 29:36) = m8;
M(33:40, 33:40) = m9;
M(37:44, 37:44) = m10;
M(41:48, 41:48) = m11;
M(45:52, 45:52) = m12;

Which I think is a very crude solution and for large matrices is not feasible, was thinking of somehow introducing a loop to do it automatically (in which case would also need to figure how to calculate the necessary size for the zeros matrix). So yeah, perhaps someone will know a trick or two.

Kind regards, Edvardas

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Dishant Arora 2014-11-10

Add a for loop.

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Answer 1

Orion 2014-11-10

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https://ww2.mathworks.cn/matlabcentral/answers/162082-overlaying-several-matrices-diagonally-to-create-a-larger-matrix#answer_158383

编辑：Orion 2014-11-10

在 MATLAB Online 中打开

% Assuming all your m1,m2,...,m12 variables exist and are size 8x8
NumberOfSubMat = 12;
% Initialize M
M=zeros(4+4*NumberOfSubMat);
for i = 1:NumberOfSubMat
    index = (1:8)+4*(i-1);
    M(index,index) = eval(['m' num2str(i)]);
end

Note : the use of eval is not optimized.

Instead of createing a lot of data m1,...,m100, you should create a cell array, which component being your varying 8x8 array.

m{1} = (miu*l/420).*[156 0 0 22*l 54 0 0 -13*l;...
    0 156 -22*l 0 0 54 13*l 0;...
    0 -22*l 4*l^2 0 0 -13*l -3*l^2 0;...
    22*l 0 0 4*l^2 13*l 0 0 -3*l^2;...
    54 0 0 13*l 156 0 0 -22*l;...
    0 54 -13*l 0 0 156 22*l 0;...
    0 13*l -3*l^2 0 0 22*l 4*l^2 0;...
    -13*l 0 0 -3*l^2 -22*l 0 0 4*l^2];
m{2} = ...
m{12} = ...
and so, you can do a cleaner loop
for i = 1:NumberOfSubMat
    index = (1:8)+4*(i-1);
    M(index,index) = m{i};
end