Replace sub matrices in the correspondant matrix (MATLAB)

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 =

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

     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 0 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
     

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

Answer 1

[Voss]

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

[high speed]

@_ Thank you so much! it works

[Voss]

You're welcome!