QuantLib: a free/open-source library for quantitative finance
Fully annotated sources - version 1.32
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Sobol low-discrepancy sequence generator. More...
#include <ql/math/randomnumbers/sobolrsg.hpp>
Public Types | |
enum | DirectionIntegers { Unit , Jaeckel , SobolLevitan , SobolLevitanLemieux , JoeKuoD5 , JoeKuoD6 , JoeKuoD7 , Kuo , Kuo2 , Kuo3 } |
typedef Sample< std::vector< Real > > | sample_type |
Public Member Functions | |
SobolRsg (Size dimensionality, unsigned long seed=0, DirectionIntegers directionIntegers=Jaeckel) | |
void | skipTo (std::uint_least32_t n) |
const std::vector< std::uint_least32_t > & | nextInt32Sequence () const |
const SobolRsg::sample_type & | nextSequence () const |
const sample_type & | lastSequence () const |
Size | dimension () const |
Private Attributes | |
Size | dimensionality_ |
std::uint_least32_t | sequenceCounter_ = 0 |
bool | firstDraw_ = true |
sample_type | sequence_ |
std::vector< std::uint_least32_t > | integerSequence_ |
std::vector< std::vector< std::uint_least32_t > > | directionIntegers_ |
Static Private Attributes | |
static const int | bits_ = 8*sizeof(std::uint_least32_t) |
static const double | normalizationFactor_ |
Sobol low-discrepancy sequence generator.
A Gray code counter and bitwise operations are used for very fast sequence generation.
The implementation relies on primitive polynomials modulo two from the book "Monte Carlo Methods in Finance" by Peter Jäckel.
21 200 primitive polynomials modulo two are provided in QuantLib. Jäckel has calculated 8 129 334 polynomials: if you need that many dimensions you can replace the primitivepolynomials.cpp file included in QuantLib with the one provided in the CD of the "Monte Carlo Methods in Finance" book.
The choice of initialization numbers (also know as free direction integers) is crucial for the homogeneity properties of the sequence. Sobol defines two homogeneity properties: Property A and Property A'.
The unit initialization numbers suggested in "Numerical Recipes in C", 2nd edition, by Press, Teukolsky, Vetterling, and Flannery (section 7.7) fail the test for Property A even for low dimensions.
Bratley and Fox published coefficients of the free direction integers up to dimension 40, crediting unpublished work of Sobol' and Levitan. See Bratley, P., Fox, B.L. (1988) "Algorithm 659: Implementing Sobol's quasirandom sequence generator," ACM Transactions on Mathematical Software 14:88-100. These values satisfy Property A for d<=20 and d = 23, 31, 33, 34, 37; Property A' holds for d<=6.
Jäckel provides in his book (section 8.3) initialization numbers up to dimension 32. Coefficients for d<=8 are the same as in Bradley-Fox, so Property A' holds for d<=6 but Property A holds for d<=32.
The implementation of Lemieux, Cieslak, and Luttmer includes coefficients of the free direction integers up to dimension
For more info on Sobol' sequences see also "Monte Carlo Methods in Financial Engineering," by P. Glasserman, 2004, Springer, section 5.2.3
The Joe–Kuo numbers and the Kuo numbers are due to Stephen Joe and Frances Kuo.
S. Joe and F. Y. Kuo, Constructing Sobol sequences with better two-dimensional projections, preprint Nov 22 2007
See http://web.maths.unsw.edu.au/~fkuo/sobol/ for more information.
The Joe-Kuo numbers are available under a BSD-style license available at the above link.
Note that the Kuo numbers were generated to work with a different ordering of primitive polynomials for the first 40 or so dimensions which is why we have the Alternative Primitive Polynomials.
Definition at line 110 of file sobolrsg.hpp.
typedef Sample<std::vector<Real> > sample_type |
Definition at line 112 of file sobolrsg.hpp.
enum DirectionIntegers |
Enumerator | |
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Unit | |
Jaeckel | |
SobolLevitan | |
SobolLevitanLemieux | |
JoeKuoD5 | |
JoeKuoD6 | |
JoeKuoD7 | |
Kuo | |
Kuo2 | |
Kuo3 |
Definition at line 113 of file sobolrsg.hpp.
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explicit |
Definition at line 78482 of file sobolrsg.cpp.
void skipTo | ( | std::uint_least32_t | n | ) |
skip to the n-th sample in the low-discrepancy sequence
Definition at line 78774 of file sobolrsg.cpp.
const std::vector< std::uint_least32_t > & nextInt32Sequence | ( | ) | const |
const SobolRsg::sample_type & nextSequence | ( | ) | const |
Definition at line 125 of file sobolrsg.hpp.
const sample_type & lastSequence | ( | ) | const |
Definition at line 132 of file sobolrsg.hpp.
Size dimension | ( | ) | const |
Definition at line 133 of file sobolrsg.hpp.
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staticprivate |
Definition at line 135 of file sobolrsg.hpp.
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staticprivate |
Definition at line 136 of file sobolrsg.hpp.
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private |
Definition at line 137 of file sobolrsg.hpp.
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mutableprivate |
Definition at line 138 of file sobolrsg.hpp.
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mutableprivate |
Definition at line 139 of file sobolrsg.hpp.
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mutableprivate |
Definition at line 140 of file sobolrsg.hpp.
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mutableprivate |
Definition at line 141 of file sobolrsg.hpp.
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private |
Definition at line 142 of file sobolrsg.hpp.