Monte Carlo Simulation with Parfor

I am conducting a Monte Carlo simulation of a stochastic differential equation, and trying to parallelize each random walk. Take a simplified example:

parfor j=1:N
    for i=2:M
        W(j,i) = W(j,i-1) + N(j,i);
    end
end

Matlab complains because it can't slice W(j,i-1) because of the 'i-1' indexing. To me, this seems silly because I am still not doing anything that couples each iteration of the parfor (each iteration of parfor works on a separate row).

Is there a way around this that is hopefully elegant and simple?

Answer 1

[Walter Roberson]

parfor j=1:N
    W(j,:) = W(j,:) + cumsum([0, N(j,:)]));
end

I am presuming here that the N of the "parfor" is some variable different than the "N" that is indexed.

If you are working with a subset of the row then:

W(j,:) = W(j,:) + [cumsum([0, N(j,1:M)], zeros(1,size(N,2)-M)]

If this code is all there is to it, do the whole incrementing by array operations:

[rows, cols] = size(W);
W = W + [cumsum(zeros(rows,1), N(:,1:M)],2), zeros(rows, cols-M-1)];

The more general solution to the problem in the way expressed is

parfor j=1:N
    thisrow = W(j,:);
    thisN = N(j,:);
    for i=2:M
        thisrow(i) = thisrow(i-1) + thisN(i);
    end
    W(j,:) = thisrow;
end

[Walter Roberson]

Thinking again:

 parfor j=1:N
    W(j,:) = cumsum([W(j,1), N(j,:)]);
  end

and appropriate corrections to the other versions. For example,

W = cumsum([W(:,1), N],2);