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:
“The wand is will; thou, fancy, saddle art,
Girt fast by memory; and while I spur
My horse, he spurs with sharp desire my heart;”
—Sir Philip Sidney (1554–1586)
“When the leaders choose to make themselves bidders at an auction of popularity, their talents, in the construction of the state, will be of no service. They will become flatterers instead of legislators; the instruments, not the guides, of the people.”
—Edmund Burke (1729–1797)