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

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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.

Accepted Answer

Cedric
Cedric on 20 May 2013
Edited: Cedric on 20 May 2013
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.
  2 Comments
Matthew
Matthew on 21 May 2013
Thanks for your help Cedric it is much appreciated.
Cedric
Cedric on 21 May 2013
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.

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More Answers (1)

Iain
Iain on 20 May 2013
The simple answer:
for k = 1:numel(i)
a(i(k),j(k)) = -1;
end
1-D or logical indexing is probably better suited.
  4 Comments
James Tursa
James Tursa on 21 May 2013
Edited: James Tursa on 21 May 2013
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
Cedric on 21 May 2013
Edited: Cedric on 21 May 2013
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

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