A Fast Algorithm For The Construction of Sobol Sequences
A more efficient Gray code implementation was proposed by Antonov and Saleev.
As for the generation of Sobol numbers, they are clearly aided by the use of Gray code instead of n for constructing the n-th point draw.
Suppose we have already generated all the Sobol sequence draws up to n − 1, and kept in memory the values xn−1,j for all the required dimensions. Since the Gray code G(n) differs from that of the preceding one G(n − 1) by just a single, say the k-th, bit (which is a rightmost bit of n − 1), all that needs to be done is a single XOR operation for each dimension in order to propagate all of the xn−1 to xn, i.e.
Read more about this topic: Sobol Sequence
Famous quotes containing the words fast and/or construction:
“There is an animal inside me,
clutching fast to my heart,
a huge crab.”
—Anne Sexton (1928–1974)
“Striving toward a goal puts a more pleasing construction on our advance toward death.”
—Mason Cooley (b. 1927)