Construct a large sparse matrix

Hi, everyone

I am currently constructing a very large sparse square matrix which is made by several smaller sparse matrices, for example:

A is a n-by-n sparse matrix, B is a m-by-m sparse matrix.

if I want to produce another matrix J=blkdiag(A,B), do I have to put sparse command outside blkdiag? i.e. J=sparse(blkdiag(A,B))

Similar for H=kron(A,B), is there any improvement at all if write H=sparse(kron(A,B))?

Answer 1

[Cedric]

Nowadays most functions are able to work on sparse matrices and output sparse matrices. If you want to be sure that it is working, use ISSPARSE to check on a small case study, e.g.

 >> A = sparse([2 0 3; 4 5 0; 0 0 6]) ;
 >> B = sparse([0 1 0; 2 0 2; 3 3 0]) ;

 >> C = kron(A, B) ;
 >> issparse(C)
 ans =
     1

 >> C = blkdiag(A, B) ;
 >> issparse(C)
 ans =
     1

There is no advantage in using SPARSE on a matrix that is already sparse.

Note that the situation where you convert a dense version of a large matrix to sparse can/should rarely happen. You generally have to build the matrix directly as a sparse matrix, using a call like

 S = sparse(I, J, V, m, n) ;

where I and J are vectors of respectively row and column indices, V is a vector of values, and m and n define the size.

One of the rare cases where you transform a dense matrix to sparse is when you build a small matrix that must be used as a basis for building a larger one, which seems to be your case.