Creating an augmented matrix a set of matrices

Hi all,

I'm writing some code and feel like there should be a way to do this better but I am not sure how.

I want to produce a finite termination of this:

from an matrix A where are matrices.

For example, I might want to make

with .

So far I've succefully done this with a loop. Is there a way to do it via vectorisation?

Thank you for your advice :-)

Here's my draft attempts. s tells me how many rows I want, I also do not know what k is before I start. The augmented matrix in the literature tends to be written as 𝒜hence me calling it "curlyA".

A(:,:, 1) = [1, 3; 0 1]; A(:,:, 2) = [1, 1; 1 1]; %A(:,:, 3) = [0, 0; 0 0]; 

[n, ~, k] = size(A);
s = 2;

curlyA = zeros(n*(s+1)); % construct augmented curly A

max_col = reshape(permute(A(:,:, 1:k),[2 1 3]),size(A,2),[])'; % make first column of curly A for this order pole
if k < size(curlyA, 1)
    max_col(size(curlyA, 1), n) = 0; % if we don't have enough rows, add zeros
end

for ii = 1:s+1
    curlyA((ii-1)*n+1:end, (ii-1)*n+1:ii*n) = max_col(1:((s+1)-ii+1)*n, :); % construct curly A from max_col
end

Answer 1

[Stephen23]

A = cat(3,[1,3;0,1],[1,1;1,1],[0,0;0,0]);
C = num2cell(A,1:2);
X = 1+tril(toeplitz(1:numel(C)));
C = [{zeros(2)};C(:)];
M = cell2mat(C(X))

M = 6×6

1 3 0 0 0 0 0 1 0 0 0 0 1 1 1 3 0 0 1 1 0 1 0 0 0 0 1 1 1 3 0 0 1 1 0 1