Question

I have a matrix A with size (nr,nc), a vector of column indices B (so B has size (nr,1) and every element in B is an integer between 1 and nc), and I want to do something to every element in A that is of the form A(i,B(i)) for i between 1 and nr, efficiency being the key concern.
For concreteness, say C is a vector of size (nr,1), the goal is to do

for i=1:nr 
A(i,B(i))=A(i,B(i))+C(i)
end

more efficiently. The context is usually that nr>>nc (because when nr is large vectorization is efficient for many operations). I have gotten a factor 3 speedup by using an indicator function approach:

for k=1:nc
A(:,k)=A(:,k)+(k==B).*C
end

Are there other ways (more efficient hopefully) to do this?
I guess this is similar to many questions on double-indexing, but it’s concretely one I run into all the time.

Answer 1

Use linear indexing:

idx = sub2ind(size(A), 1:nr, B');
A(idx) = A(idx) + C';

or (edited version with one less transpose)

idx = sub2ind(size(A), (1:nr)', B);
A(idx) = A(idx) + C;