Matlab Indexing Sparse Matrix

Question

Let's say we have the following sparse matrix defined by this 3 vectors:

[lines, columns, values] = find(A)

lines =

     1
     2
     3
     5
     1
     3
     3
     5
     4
     5


columns =

     1
     2
     2
     2
     3
     3
     4
     4
     5
     5


values =

     3
     4
     7
     3
     1
     5
     9
     6
     2
     5

What I am trying to achieve is to access the element at the position (2, 2)

I know you can do values(lines == 2) (values(columns == 2)) which will return all the values from second row (column).

My question is how can you do something like values(lines == 2 && columns == 2) to get the value at A(2,2)?

Answer 1

If you want to access elements in a sparse matrix, or any other matrix for that matter. This has no overhead whatsoever. If anyone can prove me wrong on this one, I would very much like to see a benchmark of it, because then I have missed something very important!

a = Q(2,2);

If you want to add elements to a sparse matrix, this is also very simple. I don't think there are any faster ways to do this either. Again, if anyone can prove me wrong, please share your benchmark results!

If you have:

lines = [ 1
     2
     3
     5
     1];


columns = [1
     2
     2
     2
     3];


values = [3
     4
     7
     3
     1];
 
 Q = sparse(lines, columns, values)
  (1, 1) ->  3
  (2, 2) ->  4
  (3, 2) ->  7
  (5, 2) ->  3
  (1, 3) ->  1

 [linesF, columnsF, valuesF] = find(Q)
 
 %% Now add the value 12 to position (3,1)
 linesF = [linesF; 3];
 columnsF = [columnsF; 1];
 valuesF = [valuesF; 12];
 
 Q = sparse(linesF, columnsF, valuesF)
 
  (1, 1) ->  3
  (3, 1) ->  12
  (2, 2) ->  4
  (3, 2) ->  7
  (5, 2) ->  3
  (1, 3) ->  1

This works because there is nothing saying the row and column vectors must be sorted in any way.

Benchmark

S = sprand(10000,10000,0.0005);
tic
for ii = 1:1000
    var = S(r,c);
end
toc
Elapsed time is 0.010705 seconds.

[i,j,s] = find(S);
tic
for ii = 1:1000
    var = s((i == r & j == c);  % (r,c) is a random non-zero element in s
end
toc
Elapsed time is 0.296547 seconds.

Answer 2

In support of Robert's answer , here's a snapshot that proves that no conversion to full happens in accessing elements of a sparse matrix

I create a sparse matrix that would occupy 1e5^2 * 8bytes ~ 74.5 GB in RAM if it were full. Then I retrieve the subscripts to nonzero elements of S and access the first element (without loss of generality).

On the right side of the pic, nowhere the memory jumps to > 16 GB. The only (hardly) noticeable bump happens when I create S.