Creating a block matrix of matrices?

I have a problem where I'm trying to create a matrix of the form

 [A B 0 0; 0 A B 0; 0 0 A B; 0 0 0 A];

However, this is in block matrix notation. That means all of the elements are matrices of appropriate size so that this concatenation works. I saw the blkdiag function, but it doesn't look like it's going to work for this, because the elements overlap in certain columns.

For example, if A = [1 1] and B = [2 2] this matrix would look like:

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

Does anyone have any suggestions how to do this in a parsimonious way?

[Image Analyst]

Your second row is [0 A B 0] yet your example does not show that. Your example shows [0 0 A B 0 0], so which is it? Does it shift over by one zero, or the number of elements in A, or by the number of elements in B?

We can't give the answer you want until we know for sure which it is.

[jgg]

The zeroes in the block representation are blocks of zeros, as in block matrix notation; that was unclear. Basically, the blocks shift and the zeros just backfill as necessary based on the sizes of the blocks. See blkdiag for roughly the idea.

Answer 1

[Hang Qian]

Hello,

If the FOR loop is not your choice, you may consider the following:

>> A = [1 1];

>> B = [2 2];

>> C = blkdiag(A,A,A,A);

>> C(1:end-1,3:end) = C(1:end-1,3:end) + blkdiag(B,B,B)

If you’d like something slightly more general,

>> nrow=2;ncol=3;

>> A=rand(nrow,ncol);B=rand(nrow,ncol);

>> C = blkdiag(A,A,A,A);

>> C(1:end-nrow,ncol+1:end) = C(1:end-nrow,ncol+1:end) + blkdiag(B,B,B)

Regards,

- Hang Qian

[jgg]

This is good, but I was hoping for a more general solution that didn't reply on the blocks being the same across rows. I guess I was hoping there was some kind of block matrix notation in Matlab.

Answer 2

[Mark Britten-Jones]

This is by far the easiest way to do this. Create the blocks. Create a 2-D cell array and place the blocks into the appropriate cells. And then convert to a matrix by cell2mat. I have used this where I have used loops over the cell blocks to create quite complicated matrices and you do not have to worry about the indexes at the matrix level. Bonus! See the cell2mat documenation for rules regarding permissable block sizes. (They do not all have to be of the same size.)

A = [1 1];

B = [2 2];

Z = [ 0 0]

Ccell = {A, B, Z, Z; Z, A, B, Z; Z, Z, A, B; Z, Z, Z, A};

C = cell2mat(Ccell);

[Jon]

Actually in the example you give it is not necessary to use the cell arrays at all. You can directly assign:

C =[A B Z Z;Z A B Z;Z Z A B;Z Z Z A]