Enum SobolRsgDirectionIntegers

Namespace

NanoQL.Numerics

Assembly

NanoQL.dll

The initialization numbers (free direction integers) of a SobolRsg (QuantLib's SobolRsg::DirectionIntegers). Their choice is crucial for the homogeneity properties of the sequence: Sobol defines two, Property A and Property A'.

public enum SobolRsgDirectionIntegers

Fields

Jaeckel = 1

Jäckel's, in his book (section 8.3), up to dimension 32. Coefficients for d ≤ 8 are the same as in Bratley and Fox, so Property A' holds for d ≤ 6 but Property A holds for d ≤ 32.

JoeKuoD5 = 4

A set of the Joe–Kuo numbers, 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/), tabulated up to dimension 2,000.

JoeKuoD6 = 5

A set of the Joe–Kuo numbers, tabulated up to dimension 21,200, every dimension the generator takes.

JoeKuoD7 = 6

A set of the Joe–Kuo numbers, tabulated up to dimension 1,900.

Kuo = 7

The Kuo numbers, due to Stephen Joe and Frances Kuo, tabulated up to dimension 4,926. They were generated to work with a different ordering of primitive polynomials for the first 40 or so dimensions, which is why they use the alternative primitive polynomials.

Kuo2 = 8

A second set of the Kuo numbers, tabulated up to dimension 3,947, with the alternative primitive polynomials.

Kuo3 = 9

A third set of the Kuo numbers, tabulated up to dimension 4,587, with the alternative primitive polynomials.

SobolLevitan = 2

Bratley and Fox's coefficients up to dimension 40, crediting unpublished work of Sobol' and Levitan (Bratley, P., Fox, B.L. (1988) "Algorithm 659: Implementing Sobol's quasirandom sequence generator," ACM Transactions on Mathematical Software 14:88-100). They satisfy Property A for d ≤ 20 and d = 23, 31, 33, 34, 37; Property A' holds for d ≤ 6.

SobolLevitanLemieux = 3

The coefficients of Lemieux, Cieslak, and Luttmer's implementation up to dimension 360: those for d ≤ 40 are the same as in Bratley and Fox, and for 40 < d ≤ 360 they have been calculated as optimal values based on the "resolution" criterion ("RandQMC user's guide - A package for randomized quasi-Monte Carlo methods in C," by C. Lemieux, M. Cieslak, and K. Luttmer, version January 13 2004).

Unit = 0

The unit initialization numbers suggested in "Numerical Recipes in C", 2nd edition, by Press, Teukolsky, Vetterling, and Flannery (section 7.7), which fail the test for Property A even for low dimensions.