What is an efficient way to create a sparse matrix from a set of data?

Hey,

Consider following matrix:

x1 y1
x1 y2
x1 y3
x2 y1
x2 y4
x3 y5

I need to convert this matrix to a sparse matrix, i.e. all elements are zero except the element denoted at row xi and column yj. For this example the spars matrix will be as below:

     y1  y2  y3  y4  y5
------------------------
x1|   1  1   1   0   0
x2|   1  0   0   1   0
x3|   0  0   0   0   1

The number of rows and columns are in order of several hundred thousands, hence the matrix is huge. The matrix only contains values 0 or 1.

What is an efficient algorithm to create this matrix?

Thanks

Answer 1

[Matt J]

A=sparse(I,J,1);

Although, if the non-zero entries I,J are 0 and 1, you can save significant memory if you make the matrix type logical instead of type double,

A=sparse(I,J,true);

[John D'Errico]

I would want to add that if your matrix is roughly 50% 0 and 1 as is shown, then it is not really sparse. In fact, it may take as much (or more) memory to create as sparse in that case.

So use sparse storage when you can. But remember that a sparse matrix needs to be truly sparse to be a gain. For example...

A = rand(1000) > 0.5;
B = sparse(A);

whos
  Name         Size                Bytes  Class      Attributes

    A         1000x1000            1000000  logical              
    B         1000x1000            4511329  logical    sparse

So, A is a full logical matrix, with 50% zeros. B is the sparse form of that matrix. In fact, the sparse logical form in B requires 4.5 times as much memory to store!