MATLAB: Large Sparse Matrix Summation

large sparse matrix summationMATLAB

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

Best 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

Related Solutions

MATLAB: Hi, guys. How would one extract the lower triangle of a matrix without using the tril function and witout a for loop

You could use bsxfun and rot90 to generate a matrix of indices:

>> N = 5;
>> K = 0; % select the diagonal
>> A = 1:N;
>> B = rot90(bsxfun(@plus,A,A(:)))-1;

Now lets try it on matrix of random values and extract only the lower diagonal elements:

>> X = rand(N);
>> X(B<=N+K)
ans =
    0.81472
    0.90579
    0.12699
    0.91338
    0.63236
     0.2785
    0.54688
    0.95751
    0.96489
    0.95717
    0.48538
    0.80028
    0.79221
    0.95949
    0.67874

And you can see that it extracts all of the lower-triangle values, matching those given by tril:

>> tril(X)
ans =
    0.81472            0            0            0            0
    0.90579       0.2785            0            0            0
    0.12699      0.54688      0.95717            0            0
    0.91338      0.95751      0.48538      0.79221            0
    0.63236      0.96489      0.80028      0.95949      0.67874

Note that this method also gives direct control over which diagonal you start with using the value K, just like the second argument of tril.

MATLAB: Construct a large sparse matrix

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.

Best Answer

Related Solutions

MATLAB: Hi, guys. How would one extract the lower triangle of a matrix without using the tril function and witout a for loop

MATLAB: Construct a large sparse matrix

Related Question