Concatenate x amount of matrices

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Hampus Augustsson 2020-8-12

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编辑： hosein Javan 2020-8-13

I have a FEM problem that i want to solve with a matlab script so that it can be used for future questions. I´m trying to concatenate x number of known 4x4 matrices diagonaly to form a large 2(x+1),2(x+1) matrix. Examples would be one 4x4 matrice into a 4x4 matrice or three 4x4 matrice into a 8x8 matrix. in the end i want it to look like this but on a bigger scale:

A=[k1 -k1;-k1 k1], B=[k2,-k2; -k2 k2] => C=[k1 -k1 0 ; 0 -k1 + k2 k2; 0 -k2 k2]

I have tried to solve this with this code:

    K = sym(zeros( 2*(x+1) , 2*(x+1) ) );
    for k = 1:x
       K(k:2*((k+1)),k:(2*(k+1))) = K( k:(2*(k+1)) , k:(2*(k+1)) )+C{x};
    end

This is part of a script there the user defines the amount of matrices. I made similar loop so i belive its the indexing within the loop that is the problem but dont know how to solve it. Is it possible to solve this problem simply within this loop?

Thanks in advance

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hosein Javan 2020-8-12

if you could write a general form of your matrix in an image or latex equation, it would be more comprehensible. I can see no pattern of how A & B result in C. please explain more

Hampus Augustsson 2020-8-13

编辑：Matt J 2020-8-13

I see. I will attach an image that will hopefully make it more clear. This is what the smaller k1, k2 & k3 looks like and i think i have assembled the K matrix correctly. Sorry of it is unclear, got a bit cramped in the end

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Answer 1

David Hill 2020-8-13

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在 MATLAB Online 中打开

x=length(C);
K=zeros(2*(x+1));
for i=1:x
    K=K+blkdiag(repmat(zeros(2),i-1,i-1),C{i},repmat(zeros(2),x-i,x-i));
end

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Answer 2

Matt J 2020-8-13

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https://ww2.mathworks.cn/matlabcentral/answers/578766-concatenate-x-amount-of-matrices#answer_479340

See BLKDIAG

https://www.mathworks.com/help/matlab/ref/blkdiag.html

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Answer 3

hosein Javan 2020-8-13

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编辑：hosein Javan 2020-8-13

在 MATLAB Online 中打开

after a few (or maybe a lot!) thinking, I found the pattern. I used symbolic to specify each element by its name rather than value. actually it wasn't really concatenation since every 3 element the matrices overlap and we are taking their sums. it works for any number of "k" matrices which in here you called "x".

In the case of 3 matrices:

k{1} = sym('k1_',4); k{1}
k{2} = sym('k2_',4); k{2}
k{3} = sym('k3_',4); k{3}
x = length(k); % number of "k" matrices
n = 4 + (x-1)*2; % dimension of matrix "K" concatenated(not exactly!)
K = sym(zeros(n)); % initilize "K" by all zeros
for i = 1:x
    j = 2*i-1;
    K(j:j+3,j:j+3) = K(j:j+3,j:j+3) + k{i};
end
K

the result:

k{1} =
[ k1_1_1, k1_1_2, k1_1_3, k1_1_4]
[ k1_2_1, k1_2_2, k1_2_3, k1_2_4]
[ k1_3_1, k1_3_2, k1_3_3, k1_3_4]
[ k1_4_1, k1_4_2, k1_4_3, k1_4_4]
k{2} =
[ k2_1_1, k2_1_2, k2_1_3, k2_1_4]
[ k2_2_1, k2_2_2, k2_2_3, k2_2_4]
[ k2_3_1, k2_3_2, k2_3_3, k2_3_4]
[ k2_4_1, k2_4_2, k2_4_3, k2_4_4]
k{3} =
[ k3_1_1, k3_1_2, k3_1_3, k3_1_4]
[ k3_2_1, k3_2_2, k3_2_3, k3_2_4]
[ k3_3_1, k3_3_2, k3_3_3, k3_3_4]
[ k3_4_1, k3_4_2, k3_4_3, k3_4_4]
K =
[ k1_1_1, k1_1_2,          k1_1_3,          k1_1_4,               0,               0,      0,      0]
[ k1_2_1, k1_2_2,          k1_2_3,          k1_2_4,               0,               0,      0,      0]
[ k1_3_1, k1_3_2, k1_3_3 + k2_1_1, k1_3_4 + k2_1_2,          k2_1_3,          k2_1_4,      0,      0]
[ k1_4_1, k1_4_2, k1_4_3 + k2_2_1, k1_4_4 + k2_2_2,          k2_2_3,          k2_2_4,      0,      0]
[      0,      0,          k2_3_1,          k2_3_2, k2_3_3 + k3_1_1, k2_3_4 + k3_1_2, k3_1_3, k3_1_4]
[      0,      0,          k2_4_1,          k2_4_2, k2_4_3 + k3_2_1, k2_4_4 + k3_2_2, k3_2_3, k3_2_4]
[      0,      0,               0,               0,          k3_3_1,          k3_3_2, k3_3_3, k3_3_4]
[      0,      0,               0,               0,          k3_4_1,          k3_4_2, k3_4_3, k3_4_4]
 