I am working with a sparse matrix of very large size:
U = sparse(a,b) % a and b are very large
On the hand, there exists the cell Ind which has 'a' rows. In each row, there exists a 'variate' number of elements, e.g. :
Ind{1} = [1 3 5 19 1000 1340]
Ind{2} = [9 100 1500 1600 8000 b]
...
Ind{a} = [3 5 6 90 1000 4300 5712 9480]
as could be seen the maximum index number in Ind{i} can be 'b'. For each of these index vector also exists a content matrix like 'c' :
c = [2 3 1 6 3 5 1 3 4 1 2 ... 5]
Here is the question, for each element in Ind{i}, I want to fill the 'row = i' and the 'col=Ind{i}' with c(Ind{i}), i.e.
for i = 1 : a
U(i,Ind{i}) = c(Ind{i}) ;
end
the problem is 'a' is very large and the loop takes long time to be computed. Any idea to avoid looping?
I'm not sure if there is a way to avoid the loop, but I do get a factor of 2-to-20 speed increase (I ranged a from 3 to 5,000 with b fixed at 10,000) by building three large vectors (two for row and column indices and one for values) and building the sparse matrix after the loop:
strides = cellfun(@numel,Ind);
n = sum(strides);
I(n,1) = 0;
J(n,1) = 0;
S(n,1) = 0;
bot = 1;
for k = 1:a
top = bot + strides(k) - 1 ;
mask = bot:top ;
%
I(mask) = k ;
J(mask) = Ind{k} ;
S(mask) = c(Ind{k}) ;
%
bot = top + 1;
end
U = sparse(I,J,S,a,b);
This is the recommend usage of sparse because assignments to a sparse matrix are more costly than regular arrays.