replace part of matrix to another matrix

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

[Stephen23]

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

[mohammed hussein]

thank you very much for your answer , this is exactly what i want

Answer 2

[Walter Roberson]

A=[1 2 ;3 4];
B=[5 6;7 8];
C=[9 10;11 12];
D=[13 14;15 16];
newvals = {A, B, C, D};
a = zeros(5,5);
for K = 1 : length(newvals)
  a(K:K+1, K:K+1) = newvals{K};
end

[mohammed hussein]

Thank you very much for your answer

Answer 3

[Andrei Bobrov]

In your case (without loop)

k = cat(3,A,B,D,C);
[m,n,q] = size(k);
a = full(gallery('tridiag',q*m/2+1,1,1,1));
ii = ((1:m*n-1) + (0:q-1)'*m*n)';
a(a>0) = k([ii(:);prod([m,n,q])]);

in general case (with for..end loop)

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

[m,n] = cellfun(@(x)size(x),C(:));
s = sum(m-1) + 1;
a = zeros(s,sum(n-1)+1);
jj = 1;
for ii = 1:numel(m)
    id = jj + (0:m(ii)-1)' + s*(0:n(ii)-1);
    a(id) = C{ii};
    jj = id(end);
end

All for MATLAB >= R2016b

[mohammed hussein]

Thank you very much for your answer