sobolrsg.hpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2003, 2004 Ferdinando Ametrano
 Copyright (C) 2006 Richard Gould
 Copyright (C) 2007 Mark Joshi
 
 This file is part of QuantLib, a free-software/open-source library
 for financial quantitative analysts and developers - http://quantlib.org/
 
 QuantLib is free software: you can redistribute it and/or modify it
 under the terms of the QuantLib license.  You should have received a
 copy of the license along with this program; if not, please email
 <quantlib-dev@lists.sf.net>. The license is also available online at
 <http://quantlib.org/license.shtml>.
 
 This program is distributed in the hope that it will be useful, but WITHOUT
 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
 FOR A PARTICULAR PURPOSE.  See the license for more details.
*/
 
/*! \file sobolrsg.hpp
    \brief Sobol low-discrepancy sequence generator
*/
 
#ifndef quantlib_sobol_ld_rsg_hpp
#define quantlib_sobol_ld_rsg_hpp
 
#include <ql/methods/montecarlo/sample.hpp>
#include <cstdint>
#include <vector>
 
namespace QuantLib {
 
    //! 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        integers up to dimension 40, crediting unpublished work of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
        360.  Coefficients for d<=40 are the same as in Bradley-Fox.
        For dimension 40<d<=360 the coefficients have
        been calculated as optimal values based on the "resolution"
        criterion. See "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, and
        references cited there
        (http://www.math.ucalgary.ca/~lemieux/randqmc.html).
        The values up to d<=360 has been provided to the QuantLib team by
        Christiane Lemieux, private communication, September 2004.
 
        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.
 
        \test
        - the correctness of the returned values is tested by
          reproducing known good values.
        - the correctness of the returned values is tested by checking
          their discrepancy against known good values.
    */
    class SobolRsg {
      public:
        typedef Sample<std::vector<Real> > sample_type;
        enum DirectionIntegers {
            Unit, Jaeckel, SobolLevitan, SobolLevitanLemieux,
            JoeKuoD5, JoeKuoD6, JoeKuoD7,
            Kuo, Kuo2, Kuo3 };
        /*! The so called generating integer is chosen to be \f$\gamma(n) = n\f$ if useGrayCode is set to false and
            \f$\gamma(n) = G(n)\f$ where \f$G(n)\f$ is the Gray code of \f$n\f$ otherwise. The Sobol integers are then
            constructed using formula 8.20 resp. 8.23, see "Monte Carlo Methods in Finance" by Peter Jäckel. The default
            is to use the Gray code since this allows a faster sequence generation. The Burley2020SobolRsg relies on an
            underlying SobolRsg not using the Gray code on the other hand due to its specific way of constructing the
            integer sequence.
 
            \pre dimensionality must be <= PPMT_MAX_DIM
         */
        explicit SobolRsg(Size dimensionality,
                          unsigned long seed = 0,
                          DirectionIntegers directionIntegers = Jaeckel,
                          bool useGrayCode = true);
        /*! skip to the n-th sample in the low-discrepancy sequence */
        const std::vector<std::uint32_t>& skipTo(std::uint32_t n) const;
        const std::vector<std::uint32_t>& nextInt32Sequence() const;
 
        const SobolRsg::sample_type& nextSequence() const {
            const std::vector<std::uint32_t>& v = nextInt32Sequence();
            // normalize to get a double in (0,1)
            for (Size k = 0; k < dimensionality_; ++k)
                sequence_.value[k] = v[k] * (0.5 / (1UL << 31));
            return sequence_;
        }
        const sample_type& lastSequence() const { return sequence_; }
        Size dimension() const { return dimensionality_; }
      private:
        Size dimensionality_;
        mutable std::uint32_t sequenceCounter_ = 0;
        mutable bool firstDraw_ = true;
        mutable sample_type sequence_;
        mutable std::vector<std::uint32_t> integerSequence_;
        std::vector<std::vector<std::uint32_t>> directionIntegers_;
        bool useGrayCode_;
    };
 
}
 
#endif