Question

Suppose now I have two vectors of same length:

A = [1 2 2 1];
B = [2 1 2 2];

I would like to create a matrix C whose dim=m*n, m=max(A), n=max(B).

C = zeros(m,n);
for i = 1:length(A)
   u = A(i);
   v = B(i);
   C(u,v)=C(u,v)+1;
end

and get

C =[0 2;
    1 1]

More precisely, we treat the according indices in A and B as rows and columns in C, and C(u,v) is the number of elements in {k | A(i)=u and B(i)=v, i = 1,2,…,length(A)}

Is there a faster way to do that?

Answer 1

Yes. Use sparse. It assembles (i.e., sums up) the matrix values for repeating row-column pairs for you. You need an additional vector with the values that will be assembled into the matrix entries. If you use ones(size(A)), you will have exactly what you need – counting of repeated row-column pairs

spA=sparse(A, B, ones(size(A)));
full(spA)

ans =

 0     2
 1     1

The same can be obtained by simply passing scalar 1 to sparse function instead of a vector of values.

For matrices that have a large number of zero entries this is absolutely crucial that you use sparse storage. Another function you could use is accumarray. It can essentially do the same thing, but also works on dense matrix structure:

AA=accumarray([A;B]', 1);

AA =

 0     2
 1     1

You can pass size argument to accumarray if you want to create a matrix of specific size

AA=accumarray([A;B]', 1, [2 3]);
AA =

 0     2     0
 1     1     0

Note that you can actually also make it produce sparse matrices, and use a different operator in assembly (i.e., not necessarily a sum)

AA=accumarray([A;B]', 1, [2 3], @sum, 0, true)

will produce a sparse matrix (last parameter set to true) using sum for assembly and 0 as a fill value, i.e. a value which is used in cases a given row-column pair does not exist in A/B.