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S - NxN sparse matrix.
A - Mx1 vector.

The non zero values of S are the indexes of A.
I want to calculate a vector x such that in the i'th entry of x:
for each non zero value j in the i'th row of S , take A[j] and calculate the sum of all this j's and put it in the i'th entry of x.

in pseudo it should look like this:

  for i = 1:N
     for j = 1:N
        if( s[i][j] != 0)
           x[i] += s[ A[i,j] ]

how can i do it in matlab in the most efficient way?

Shai
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IceCube
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3 Answers3

1

Let's try using find and accumarray:

[ii jj sij] = find( S );
x = accumarray( ii, A(sij), [1 size(S,1)] );
Shai
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0

This is just matrix multiplication:

x = (S~=0)*A(1:size(S,2));

Matlab does matrix multiplication efficiently with sparse matrices, so this should be pretty fast.

Luis Mendo
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This is actually like Shai's answer, but uses nonzeros(S) instead sij: 

[ii jj] = find( S );
x = accumarray( ii, A(nonzeros(S)), [size(S,1), 1] ).'
IceCube
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    This is essentially [Shai's answer](http://stackoverflow.com/a/29671739/2586922). You should accept that answer (specially if Shai makes the correction) instead of posting your own – Luis Mendo Apr 16 '15 at 15:22