How to transfer a sparse matrix into a block diagnal matrix efficiently?

Hi, Everyone:

Suppose I have a very large M*N sparse matrix A, where M=K*N, I need to equally split it into K N*N matrices and put all of them on the diagnal of a large matrix,i.e.:

 [N*N(1) 0 0 0...0 0 0 ;
 0 0 N*N(2) 0 0 ... 0 ;
 0 0    .   0 0 ... 0 ;
 0 0 0 0  . 0 0 ... 0 ;
 0 0 0 0 0  . 0 ... 0 ;
 0 0 ... 0 0 0 0 N*N(K)]'

I can't use loop because K is very big, so I tried to use:

 B=mat2cell(A,N*ones(K,1),N);       
 C=[blkdiag(B{1:end,1})];

But I found mat2cell is still quite slow when K is very big, is there any other more efficient way to do this?

Many Thanks

Answer 1

[Cedric]

I would go for something like:

 % - Build example case.
 K = 3 ;
 N = 4 ; 
 A = sparse(randi(10, K*N, N)-1) ;

 % - Extract rows,cols,vals, and reindex columns.
 [r,c,v] = find(A) ;
 c = c + floor((r-1)/N) * N ;

 % - Build block diagonal version.
 B = sparse(r, c, v, K*N, K*N)

With this, you have:

 >> full(A)
 ans =
     8     9     6     6
     9     4     7     3
     1     8     7     9
     9     1     3     0
     6     4     6     4
     0     9     1     3
     2     7     7     7
     5     9     0     7
     9     6     2     1
     9     0     0     4
     1     8     0     4
     9     9     8     6

 >> full(B)
 ans =
     8     9     6     6     0     0     0     0     0     0     0     0
     9     4     7     3     0     0     0     0     0     0     0     0
     1     8     7     9     0     0     0     0     0     0     0     0
     9     1     3     0     0     0     0     0     0     0     0     0
     0     0     0     0     6     4     6     4     0     0     0     0
     0     0     0     0     0     9     1     3     0     0     0     0
     0     0     0     0     2     7     7     7     0     0     0     0
     0     0     0     0     5     9     0     7     0     0     0     0
     0     0     0     0     0     0     0     0     9     6     2     1
     0     0     0     0     0     0     0     0     9     0     0     4
     0     0     0     0     0     0     0     0     1     8     0     4
     0     0     0     0     0     0     0     0     9     9     8     6

Answer 2

[Ming]

Thank you very much Cedric, you are a genius and super kind!

[Cedric]

Thank you Ming, I'm glad it helped!

The trick with sparse matrices construction/transformation is often to work on indices rather than on matrices themselves.