Extracting sub matrix from sparse matrix

I have a large n by n sparse matrix A and a set of indices I \subset [1,..., n].

I want the sub matrix B = A(I,I), but doing so directly takes a long time, as A is sparse. By directly I literally mean typing B = A(I,I)

Any suggestions?

[Walter Roberson]

I have to wonder whether you want the diagonal A(I(1), I(1)), A(I(2), I(2)) and so on, or whether you want all the combinations A(I(1), I(1)), A(I(2), I(1)), A(I(3), I(1))... A(I(17), I(24))...

In the case of wanting the diagonal, then consider calling spdiags and indexing the result.

Answer 1

[Madheswaran]

Hello Daniel,

You can access elements of a sparse matrix using the syntax 'S(I, I)', where I is an array of indices and 'S' is sparse matrix. However, please note that the resulting matrix will also be a sparse matrix. If you require the result to be a dense matrix, you can convert it using the 'full' function. Below is a script that illustrates this process:

I = [1 3 5 8];
A = speye(100);

B = A(I, I); % B is a sparse matrix
disp(B);

   (1,1)        1
   (2,2)        1
   (3,3)        1
   (4,4)        1

B_dense = full(B); % B_dense is a dense matrix
disp(B_dense);

     1     0     0     0
     0     1     0     0
     0     0     1     0
     0     0     0     1

For additional details, please refer to the following documentations:

1. Accessing Sparse Matrices - https://mathworks.com/help/matlab/math/accessing-sparse-matrices.html
2. full function - https://mathworks.com/help/matlab/ref/full.html

Hope this helps!