Memory usage with parallel evaluation

[markdewing]

For large integrals and using parallel evaluation, the memory usage for the array of regions to evaluate becomes a limiting factor, before the size of the heap becomes an issue.
Would imposing a maximum batch size maintain correctness of the parallel algorithm?
That is, break out of the inner 'do' loop in the parallel branch of rulecubature if nR exceeds a fixed size.

It seems to work empirically in a few cases, but I'm unsure of the theory.

[stevengj]

Yes, it will still be correct with a maximum batch size. (The serial case is basically just a maximum batch size of 1.)

[loliverhennigh]

Is this mini batching implemented? This would be extremely helpful for me. Great library by the way!

[stevengj]

No, it's not currently implemented, but it would be trivial to do. Just set a maximum number of iterations for this loop:

cubature/hcubature.c

Lines 983 to 996 in 6bda3b2

	do {
	if (nR + 2 > nR_alloc) {
	nR_alloc = (nR + 2) * 2;
	R = (region *) realloc(R, nR_alloc * sizeof(region));
	if (!R) goto bad;
	}
	R[nR] = heap_pop(&regions);
	for (j = 0; j < fdim; ++j) ee[j].err -= R[nR].ee[j].err;
	if (cut_region(R+nR, R+nR+1)) goto bad;
	numEval += r->num_points * 2;
	nR += 2;
	if (converged(fdim, ee, reqAbsError, reqRelError, norm))
	break; /* other regions have small errs */
	} while (regions.n > 0 && (numEval < maxEval || !maxEval));

For example, change the final line to:

} while (regions.n > 0 && (numEval < maxEval || !maxEval) && nR < 100)

to set an upper bound of 100 sub-regions per iteration.

[loliverhennigh]

Neat, I will look at this. Right now my solution is to break up the batch in my given integration function. I am trying to integrate the output of a neural network and the evaluations are costly memory wise.

[markdewing]

I've implemented the maximum batch size in a branch here

https://github.com/markdewing/cubature-1/tree/max_batch_size