Creation of a block-diagonal sparse matrix

I would like to create a block-diagonal matrix with the following properties:

• The matrix must consist of submatrices A1, A2, ... on the diagonal and zeroes elsewhere.
• Each submatrix will be square, but dimensions vary.
• Each n-by-n submatrix takes the following shape:

   eye(n) - ones(1/n)

• Since there are many such submatrices, the overall matrix must be sparse.

What I have is a vector which holds the dimensions of each submatrix. So, if the vector is, say, b=[1,5,3,...], then the first submatrix A1 would have to be 1-by-1, A2 is 5-by-5, A3 is 3-by-3, and so on. How do I go from there to the creation of my matrix?

Two answers were given on a related quation. The first, based upon blkdiag, won't work, because it would involve temporarily creating the full matrix, and I run out of memory. The second seems preferable, but I can't wrap my head around how to adopt it to my setting.

[Matt J]

What is ones(1/n)? Taken literally, it should give an error for any integer n>1,

    >> ones(1/2)
    Error using ones
    Size inputs must be integers.

[Jasper]

Good catch, that was a typo. It should have read:

 eye(n) - ones(n).*(1/n)

Answer 1

[Matt J]

The first, based upon blkdiag, won't work, because it would involve temporarily creating the full matrix, and I run out of memory.

BLKDIAG will give you a sparse result if you first convert its inputs to sparse type, like below,

    >> A=sparse(ones(3)); B=sparse(ones(2)); C=blkdiag(A,B)

    C =

       (1,1)        1
       (2,1)        1
       (3,1)        1
       (1,2)        1
       (2,2)        1
       (3,2)        1
       (1,3)        1
       (2,3)        1
       (3,3)        1
       (4,4)        1
       (5,4)        1
       (4,5)        1
       (5,5)        1

    >> full(C)

    ans =

         1     1     1     0     0
         1     1     1     0     0
         1     1     1     0     0
         0     0     0     1     1
         0     0     0     1     1

[Matt J]

So, you could do,

        n=length(b);
        B=cell(1,n);

        for i=1:n

           B{i}=sparse(MakeNextBlock(  b(i) );

        end

        finalresult = blkdiag(B{:});