Semi-transpose a matrix

Dear Matlab Experts,

I want to block-transpose a matrix i.e. a set of elements are forming a block of elements. My goal is to transpose the blocks such that within each block, the order of elements remains unchanged. I guess the below example helps to clarify my question:

a = [1 2 3 4 5 6
     0 3 2 1 2 3 
     0 0 0 1 1 1    
     8 9 9 1 2 3]

Now,Assume that each row plays a role of a block thus the matrix a has 4 blocks with the size of 4*1 that is,

a = [block1; block2; block3; block4]

I need to transpose in the block-based order so the desired outcome has the following form:

   [1 2 3 4 5 6 0 3 2 1 2 3 0 0 0 1 1 1 8 9 9 1 2 3]

Your helps will be appreciated. Thank you so much

Answer 1

[Andrei Bobrov]

" blocks are the matrix of 2*3"

[m,n] = size(a);
p = 2;
q = 3;

out = cell2mat(mat2cell(a,p*ones(m/p,1),q*ones(n/q,1))');

or

a = [1 2 3 4 5 6
     0 3 2 1 2 3 
     0 0 0 1 1 1    
     8 9 9 1 2 3];

[m,n] = size(a);
p = 2;
q = 3;
t = reshape(a,p,m/p,q,n/q);
z = permute(t,[1 4 3 2]);
out = reshape(z,n/q*p,[])

Answer 2

[Azzi Abdelmalek]

a = [1 2 3 4 5 6
   0 3 2 1 2 3 
   0 0 0 1 1 1    
   8 9 9 1 2 3]
b=a'
b=b(:)'

Or

b=reshape(a',1,[])

[Homayoon]

Thanks Azzi, first a minor modification is needed in your answer which changes it to

b=reshape(a',1,[])

however, the question is general and your answer is limited to the cases when each row is treated as a block. How can you extend the answer to the cases such as

 [ block1, block2
   block3, block4] %which for the example provided in the question blocks are the matrix of 2*3 i.e.
block1 = [1 2 3;0 3 2] similar for other blocks.

the desired outcome in this case will be:

[block1, block3
 block2, block4]

[Azzi Abdelmalek]

You can use cell arrays

b1=randi(10,4)
b2=randi(10,4)
b3=randi(10,4)
b4=randi(10,4)
A={b1,b2;b3,b4}
idx=reshape(1:numel(A),size(A))'
out=cell2mat(A(idx))