MATLAB: Creation of a block-diagonal sparse matrix

block diagonalsparse

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.

Best Answer

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
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