Generating Block Matrix Dynamically

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Gözde Üstün 2020-6-27

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https://ww2.mathworks.cn/matlabcentral/answers/555739-generating-block-matrix-dynamically

评论： Gözde Üstün 2020-7-3

采纳的回答： Ameer Hamza

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Hello,

I am generating this matrix in 2d:

0.7071    0.7071
0.7071    0.7071

But for even number (and of course greater than 2) I need to generate that:

7071    0.7071  0        0
7071    0.7071  0        0
       0       0.7071   0.7071
       0       0.7071   0.7071   

But I can not handle with my size problem. Here is my code:

function [A,B] = CHSH2d(d)
    A=zeros(d,d,2,d);
    B=A;
    projectors_of_sigma_x = [1/sqrt(2)*[1;1],1/sqrt(2)*[1;-1]];
    for k = 1:d
        for l =1:d 
           A(:,:,1,k)=repmat(projectors_of_sigma_x(:,k),1,d);
           if d > 2 
              A(:,:,1,k) = blkdiag(A(:,:,1,k));
           end   
        end
    end
end

采纳的回答

Ameer Hamza 2020-6-27

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https://ww2.mathworks.cn/matlabcentral/answers/555739-generating-block-matrix-dynamically#answer_457948

编辑：Ameer Hamza 2020-6-27

在 MATLAB Online 中打开

This example show how to use blkdiag to create such a matrix

M = [0.7071    0.7071
     0.7071    0.7071];
 
n = 4;
M_cell = repmat({M}, 1, n/2);
M_out = blkdiag(M_cell{:})

Result

M_out =
    0.7071    0.7071         0         0
    0.7071    0.7071         0         0
         0         0    0.7071    0.7071
         0         0    0.7071    0.7071

You can avoid for-loop in your code.

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Ameer Hamza 2020-7-2

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See this

d = 4;
A=zeros(d,d,2,d);
B=A;
projectors_of_sigma_x = [1/sqrt(2)*[1;1],1/sqrt(2)*[1;-1]];
for k = 1:d/2 % what is pattern for k>d/2
    A(:,:,1,k)=repmat(projectors_of_sigma_x(:,k),d/2,d);
end

It saves the values of A(:,:1,1) and A(:,:1,2). But how to extent the patten beyond that for an arbitrary value of 'd' is not clear to me. The description you provided is clear for d=4, but what if d=8 or d=16.

Gözde Üstün 2020-7-3