Overlapping non-square block-diagonal matirce

I would like to build a block matrice with overlapping non-square blocks.

Example 1:

[1,2,1,0,0,0,0;
 0,0,1,2,1,0,0;
 0,0,0,0,1,2,1]    

Example 2:

X = [1,1,zeros(1,5),1,2,1,zeros(1,5),1,1];
[X, zeros(1,4);
 zeros(1,2), X, zeros(1,2);
 zeros(1,4), X

Because of sparsity I would prefer to use a sparse matrix.

Answer 1

[J. Alex Lee]

As long as there are well defined rules for the blocks and their positions in the matrix, direct use of the sparse() function should work well...try this

% the block
blk = [1 2 1]

% size of the block
w = size(blk,2)
h = size(blk,1)

% number of blocks
N = 5

% how much to shift blocks
vshft = 1; % vertical
hshft = 2; % horizontal

% i think this is right...
nRows = vshft*(N-1) + h
nCols = hshft*(N-1) + w

% pre-allocate
B = sparse(nRows,nCols);

% the subscripts of the original block
% these are to be shifted for indexing into the final matrix
% maybe there's a better way to do this
[jdx0,idx0] = meshgrid(1:w,1:h)

for k = 1:N
    idx = idx0 + (k-1)*vshft;
    jdx = jdx0 + (k-1)*hshft;
    % in case you want really overlapping to add overlapping blocks
    B = B + sparse(idx(:),jdx(:),blk(:),nRows,nCols);
end

full(B)