How can I output specific point of data to a sparse matrix.

Hi all,

I have a sparse matrix:

a = sparse(9,9)

I also have two sets of information:

i =

     7
     8
     9

j =

     1
     2
     6

So, I want to take i as a row reference and j as a column reference and output it to the sparse matrix. So, if I do:

a(i,j) = -1

Output Window:

a =

   (7,1)       -1
   (8,1)       -1
   (9,1)       -1
   (7,2)       -1
   (8,2)       -1
   (9,2)       -1
   (7,6)       -1
   (8,6)       -1
   (9,6)       -1

When I only want:

a =

   (7,1)       -1
   (8,2)       -1
   (9,6)       -1

or, I only to output to a when position of i is equal to position of j. I have tried certain things with "for" and "if" loops but haven't been able to come up with the right answer.

Can anyone please help me with this, thank you in advance.

Answer 1

[Cedric]

It is much more efficient to build the matrix directly with "i", "j" as indices of non zeros elements and a vector of values (or a scalar), rather than building an empty matrix and indexing it later to set values. Example:

 >> I = [4,2,8] ;
 >> J = [1,7,3] ;
 >> V = -1 ;
 >> n = 9 ;
 >> S = sparse(I, J, V, n, n)
 S =
   (4,1)       -1
   (8,3)       -1
   (2,7)       -1

 >> full(S)
 ans =
     0     0     0     0     0     0     0     0     0
     0     0     0     0     0     0    -1     0     0
     0     0     0     0     0     0     0     0     0
    -1     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     0     0     0     0     0     0     0
     0     0    -1     0     0     0     0     0     0
     0     0     0     0     0     0     0     0     0

Now what you did wrong in your attempt is not related to sparse matrices, but to indexing. You could use e.g. SUB2IND to get a linear index based on "i" and "j", which would solve your problem.

[Matthew]

Thanks for your help Cedric it is much appreciated.

[Cedric]

You're welcome! Let me know if you have any additional question related to this matter, and please [ Accept ] the answer if it fully solved your problem.

Answer 2

[Iain]

The simple answer:

for k = 1:numel(i)

a(i(k),j(k)) = -1;

end

1-D or logical indexing is probably better suited.

[James Tursa]

The for loop shown above has a potential data copy bottleneck that can severly decrease performance. Unless "a" is preallocated to have enough memory to contain all the values, the loop will repeatedly reallocate & copy data to make room for more values.

[Iain]

Agreed, but he has preallocated ;)

[James Tursa]

No, he hasn't. That's the point. The command a = sparse(9,9) only creates an empty skeleton of a sparse matrix with no memory pre-allocated for any data. To get the data memory preallocated one would have to do something like a = sparse([],[],[],9,9,numel(J)). For a small matrix this data memory preallocation doesn't make much difference, but for a large matrix it can make a significant difference.

Another problem with the loop is sorting the data. Every time you add an element to the matrix in a loop MATLAB has to resort the internal data to make room for the new value. The loop forces MATLAB to do this one element at a time, which can cause repeated data copying of large chunks of memory again. Cedric's method above let's MATLAB do the necessary sorting in one fell swoop internally.

[Cedric]

To illustrate:

 >> n = 1000 ;                              % Square mat. size.
 >> n_nz = 3*n ;                            % # non-zero elements.

 >> A_full = zeros(n, n) ;                  % Full, for comparison.
 >> A_spalloc = spalloc(n, n, n_nz) ;
 >> A_sparse_prealloc = sparse([], [], [], n, n, n_nz) ;
 >> A_sparse = sparse(n, n) ;

 >> whos
  Name               Size           Bytes     Class     Attributes
  A_full             1000x1000      8000000   double              
  A_spalloc          1000x1000      56008     double    sparse    
  A_sparse           1000x1000      8024      double    sparse    
  A_sparse_prealloc  1000x1000      56008     double    sparse    
  n                  1x1            8         double              
  n_nz               1x1            8         double

The reference document if you want to understand how sparse matrices are stored, Iain, is the following: Gilbert et al., 1992