Bugs item #3511954, was opened at 2012-03-27 08:18
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Category: None
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By:
https://me.yahoo.com/a/Df.Slpks ()
Assigned to: Nobody/Anonymous (nobody)
Summary: Inconsistent Gray Code usage in Sobol Sequence
Initial Comment:
I am referring to the C++ implementation of Sobol low discrepancy sequences in sobolrsg.cpp. The problem I see is also present in the Java port.
SobolRsg::skipTo converts the skip index to a Gray Code, to which it applies the directionIntegers. This looks correct.
SobolRsg::nextInt32Sequence has this comment:
// instead of using the counter n as new unique generating integer
// for the n-th draw use the Gray code G(n) as proposed
// by Antonov and Saleev
However, I do not see the sequenceCounter_ being converted into a Gray Code.
I propose the following change to nextInt32Sequence:
const std::vector<unsigned long>& SobolRsg::nextInt32Sequence() const
{
if (firstDraw_) {
// it was precomputed in the constructor
firstDraw_ = false;
return integerSequence_;
}
// increment the counter
sequenceCounter_++;
// did we overflow?
QL_REQUIRE(sequenceCounter_ != 0, "period exceeded");
// instead of using the counter n as new unique generating integer
// for the n-th draw use the Gray code G(n) as proposed
// by Antonov and Saleev
unsigned long n = sequenceCounter_ ^ (sequenceCounter_ >> 1); // *** LINE CHANGED ***
// Find rightmost zero bit of n
int j = 0;
while (n & 1) { n >>= 1; j++; }
for (Size k=0; k<dimensionality_; k++) {
// XOR the appropriate direction number into each component of
// the integer sequence to obtain a new Sobol integer for that
// component
integerSequence_[k] ^= directionIntegers_[k][j];
}
return integerSequence_;
}
Alternately, you could make the use of Gray Codes an option on the algorithm. Of course, I could be mistaken, and only skip needs the Gray Code.
Thank you for providing this library!
Paul Anton Chernoch
Karen Clark and Co.
Boston, MA
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