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Asked by Ming on 22 Apr 2013

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 sum it up, I can't use loop, so I tried to use:

sum(reshape(A',N,N,K),3);

However, this command can't reshape sparse matrix into a 3-D array, is there any other way to do it? (without loop or converge to dense matrix)

Many Thanks

Answer by Teja Muppirala on 22 Apr 2013

Accepted answer

This seems to work well:

% Making some random data... N = 1000; K = 100; A = sprand(N*K,N,0.0001);

[r,c,val] = find(A); rnew = mod(r-1,N)+1; % Shift all the row values to [1-->N] Asum = accumarray([rnew c],val,[N N],[],[],true); % The answer

Teja Muppirala on 22 Apr 2013

I guess that last line would be simpler as this:

Asum = sparse(rnew,c,val,N,N);

Answer by Cedric Wannaz on 22 Apr 2013

Edited by Cedric Wannaz on 22 Apr 2013

Why can't you use a loop? Is `K` that large?

If you are looking for efficiency, I'd say that you could directly build `A` in a way that sums up these N*N blocks, by working on indices using a modulus for row indices. As SPARSE works like ACCUMARRAY when multiple indices are similar, you would have the summation. Example:

N = 4 ; I = randi(3*N, 5*N, 1) ; J = randi(N, 5*N, 1) ; V = 50 + randi(10, 5*N, 1) ;

% - First method: assumes that A already built. A = sparse(I, J, V, 3*N, N) ; full(A) [r,c,v] = find(A) ; r = 1 + mod(r-1, N) ; A_sum = sparse(r, c, v, N, N) ;

% - Second method: build directly the sum from indices. I = 1 + mod(I-1, N) ; B = sparse(I, J, V, N, N) ;

% - Check. full(A_sum) full(B) full(all(A_sum(:) == B(:)))

Running this, you get (RANDI will generate something else if you test it):

ans = 0 55 0 0 60 0 51 0 0 54 0 112 0 0 0 0 52 0 0 114 0 59 115 0 57 51 0 0 0 56 0 56 0 55 0 0 0 0 0 0 54 0 56 0 0 51 0 0

ans = 52 110 0 114 60 59 166 0 111 105 56 112 0 107 0 56

ans = 52 110 0 114 60 59 166 0 111 105 56 112 0 107 0 56

ans = 1

## 1 Comment

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/73110#comment_144787

What are the actual sizes you are working with?