MATLAB: Replace part of matrix to another matrix

Question

Hi i have many matrices in same size , i want to add all of them together in one matrix with replace the last quarter of each one to binning of next one until complete the matrix and the rest will be zeros . for example

a =zeros(5,5)
A=[1 2 ;3 4];
B=[5 6;7 8];
C=[9 10;11 12];
D=[13 14;15 16];

the answer

a=
     1     2     0     0     0
     3     5     6     0     0
     0     7     9    10     0
     0     0    11    13    14
     0     0     0    15    16

thank you very much for helping

Answer 1

For any size matrices, even combinations of different sizes:

C = {[1,2;3,4],[5,6;7,8],[9,10;11,12],[13,14;15,16]};
num = numel(C);
szr = cellfun('size',C,1);
szc = cellfun('size',C,2);
csr = cumsum([0,szr-1]);
csc = cumsum([0,szc-1]);
M = zeros(1+csr(end),1+csc(end));
for k = 1:num
  idr = csr(k)+(1:szr(k));
  idc = csc(k)+(1:szc(k));
  M(idr,idc) = C{k};
end

Giving:

>> M
M =
         1           2           0           0           0
         3           5           6           0           0
         0           7           9          10           0
         0           0          11          13          14
         0           0           0          15          16

It works perfectly with any size matrices, e.g.:

C = {[1,2;3,4],[5,6;7,8],[1,2,3;4,5,6;7,8,9],[9,10;11,12],[13,14;15,16]};

gives

M =
         1           2           0           0           0           0           0
         3           5           6           0           0           0           0
         0           7           1           2           3           0           0
         0           0           4           5           6           0           0
         0           0           7           8           9          10           0
         0           0           0           0          11          13          14
         0           0           0           0           0          15          16