Replace sub matrices in the correspondant matrix (MATLAB)

Question

high speed 2022-3-10

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1668644-replace-sub-matrices-in-the-correspondant-matrix-matlab

评论： Voss 2022-3-10

采纳的回答： Voss

在 MATLAB Online 中打开

Dear

I have this program for m=4 for example:

m=4;
P=hankel(1:m,m:-1:1);
a=zeros(m-1,m-1,m-2);
a(:,:,1)=eye(m-1);
for k=2:m-1 
    a(:,:,k)=circshift(a(:,:,k-1),1,2 );
    Pm=zeros(m-1);
end

the correspondant matrix P is:

P =
   2     3     4
   3     4     3
   4     3     2
   3     2     1

where the sub matrix a which is an identity matrix is considered as '1' in the matrix P.

The other two sub-matrices which are shifts of a are considered as '2' and '3' respectively in P.

And Pm is considered as '4' in P.

I want to replace '1', '2', '3' and '4' in P with their correspondant sub matrices. And the result must be:

P =
0 0 0 1 0 0 0 1 0 0 0
1 0 0 0 1 1 0 0 0 0 0
0 1 1 0 0 0 1 0 0 0 0
1 0 0 0 1 0 0 0 0 0 1
0 1 1 0 0 0 0 0 1 0 0
0 0 0 1 0 0 0 0 0 1 0
0 1 0 0 0 0 0 0 0 1 0
0 0 0 0 0 1 0 0 0 0 1
1 0 0 0 0 0 1 0 1 0 0
0 0 0 0 1 0 1 0 1 0 0
0 0 1 0 0 0 0 1 0 1 0
0 0 0 1 0 1 0 0 0 0 1
     

How can I program this in general way for any m value please!

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Answer 1

Voss 2022-3-10

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1668644-replace-sub-matrices-in-the-correspondant-matrix-matlab#answer_914684

编辑：Voss 2022-3-10

在 MATLAB Online 中打开

m=4;
P=hankel(1:m,m:-1:1);
a = zeros(m-1,m-1,m);
a(:,:,1) = eye(m-1);
for k = 2:m-1 
    a(:,:,k) = circshift(a(:,:,k-1),1,2);
end
a(:,:,m) = zeros(m-1);
P_new = zeros(m*(m-1));
for ii = 1:m
    for jj = 1:m
        P_new((m-1)*(ii-1)+(1:m-1),(m-1)*(jj-1)+(1:m-1)) = a(:,:,P(ii,jj));
    end
end
disp(P_new);
     1     0     0     0     1     0     0     0     1     0     0     0
     0     1     0     0     0     1     1     0     0     0     0     0
     0     0     1     1     0     0     0     1     0     0     0     0
     0     1     0     0     0     1     0     0     0     0     0     1
     0     0     1     1     0     0     0     0     0     1     0     0
     1     0     0     0     1     0     0     0     0     0     1     0
     0     0     1     0     0     0     0     0     1     0     1     0
     1     0     0     0     0     0     1     0     0     0     0     1
     0     1     0     0     0     0     0     1     0     1     0     0
     0     0     0     0     0     1     0     1     0     1     0     0
     0     0     0     1     0     0     0     0     1     0     1     0
     0     0     0     0     1     0     1     0     0     0     0     1