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/* boost random/sobol.hpp header file
*
* Copyright Justinas Vygintas Daugmaudis 2010-2018
* Distributed under the Boost Software License, Version 1.0. (See
* accompanying file LICENSE_1_0.txt or copy at
* http://www.boost.org/LICENSE_1_0.txt)
*/
#ifndef BOOST_RANDOM_SOBOL_HPP
#define BOOST_RANDOM_SOBOL_HPP
#include <boost/random/detail/sobol_table.hpp>
#include <boost/random/detail/gray_coded_qrng.hpp>
namespace boost {
namespace random {
/** @cond */
namespace qrng_detail {
// sobol_lattice sets up the random-number generator to produce a Sobol
// sequence of at most max dims-dimensional quasi-random vectors.
// Adapted from ACM TOMS algorithm 659, see
// http://doi.acm.org/10.1145/42288.214372
template<typename UIntType, unsigned w, typename SobolTables>
struct sobol_lattice
{
typedef UIntType value_type;
BOOST_STATIC_ASSERT(w > 0u);
BOOST_STATIC_CONSTANT(unsigned, bit_count = w);
private:
typedef std::vector<value_type> container_type;
public:
explicit sobol_lattice(std::size_t dimension)
{
resize(dimension);
}
// default copy c-tor is fine
void resize(std::size_t dimension)
{
dimension_assert("Sobol", dimension, SobolTables::max_dimension);
// Initialize the bit array
container_type cj(bit_count * dimension);
// Initialize direction table in dimension 0
for (unsigned k = 0; k != bit_count; ++k)
cj[dimension*k] = static_cast<value_type>(1);
// Initialize in remaining dimensions.
for (std::size_t dim = 1; dim < dimension; ++dim)
{
const typename SobolTables::value_type poly = SobolTables::polynomial(dim-1);
if (poly > std::numeric_limits<value_type>::max()) {
boost::throw_exception( std::range_error("sobol: polynomial value outside the given value type range") );
}
const unsigned degree = multiprecision::msb(poly); // integer log2(poly)
// set initial values of m from table
for (unsigned k = 0; k != degree; ++k)
cj[dimension*k + dim] = SobolTables::minit(dim-1, k);
// Calculate remaining elements for this dimension,
// as explained in Bratley+Fox, section 2.
for (unsigned j = degree; j < bit_count; ++j)
{
typename SobolTables::value_type p_i = poly;
const std::size_t bit_offset = dimension*j + dim;
cj[bit_offset] = cj[dimension*(j-degree) + dim];
for (unsigned k = 0; k != degree; ++k, p_i >>= 1)
{
int rem = degree - k;
cj[bit_offset] ^= ((p_i & 1) * cj[dimension*(j-rem) + dim]) << rem;
}
}
}
// Shift columns by appropriate power of 2.
unsigned p = 1u;
for (int j = bit_count-1-1; j >= 0; --j, ++p)
{
const std::size_t bit_offset = dimension * j;
for (std::size_t dim = 0; dim != dimension; ++dim)
cj[bit_offset + dim] <<= p;
}
bits.swap(cj);
}
typename container_type::const_iterator iter_at(std::size_t n) const
{
BOOST_ASSERT(!(n > bits.size()));
return bits.begin() + n;
}
private:
container_type bits;
};
} // namespace qrng_detail
typedef detail::qrng_tables::sobol default_sobol_table;
/** @endcond */
//!Instantiations of class template sobol_engine model a \quasi_random_number_generator.
//!The sobol_engine uses the algorithm described in
//! \blockquote
//![Bratley+Fox, TOMS 14, 88 (1988)]
//!and [Antonov+Saleev, USSR Comput. Maths. Math. Phys. 19, 252 (1980)]
//! \endblockquote
//!
//!\attention sobol_engine skips trivial zeroes at the start of the sequence. For example, the beginning
//!of the 2-dimensional Sobol sequence in @c uniform_01 distribution will look like this:
//!\code{.cpp}
//!0.5, 0.5,
//!0.75, 0.25,
//!0.25, 0.75,
//!0.375, 0.375,
//!0.875, 0.875,
//!...
//!\endcode
//!
//!In the following documentation @c X denotes the concrete class of the template
//!sobol_engine returning objects of type @c UIntType, u and v are the values of @c X.
//!
//!Some member functions may throw exceptions of type @c std::range_error. This
//!happens when the quasi-random domain is exhausted and the generator cannot produce
//!any more values. The length of the low discrepancy sequence is given by \f$L=Dimension \times (2^{w} - 1)\f$.
template<typename UIntType, unsigned w, typename SobolTables = default_sobol_table>
class sobol_engine
: public qrng_detail::gray_coded_qrng<
qrng_detail::sobol_lattice<UIntType, w, SobolTables>
>
{
typedef qrng_detail::sobol_lattice<UIntType, w, SobolTables> lattice_t;
typedef qrng_detail::gray_coded_qrng<lattice_t> base_t;
public:
//!Effects: Constructs the default `s`-dimensional Sobol quasi-random number generator.
//!
//!Throws: bad_alloc, invalid_argument, range_error.
explicit sobol_engine(std::size_t s)
: base_t(s)
{}
// default copy c-tor is fine
#ifdef BOOST_RANDOM_DOXYGEN
//=========================Doxygen needs this!==============================
typedef UIntType result_type;
/** @copydoc boost::random::niederreiter_base2_engine::min() */
static BOOST_CONSTEXPR result_type min BOOST_PREVENT_MACRO_SUBSTITUTION ()
{ return (base_t::min)(); }
/** @copydoc boost::random::niederreiter_base2_engine::max() */
static BOOST_CONSTEXPR result_type max BOOST_PREVENT_MACRO_SUBSTITUTION ()
{ return (base_t::max)(); }
/** @copydoc boost::random::niederreiter_base2_engine::dimension() */
std::size_t dimension() const { return base_t::dimension(); }
/** @copydoc boost::random::niederreiter_base2_engine::seed() */
void seed()
{
base_t::seed();
}
/** @copydoc boost::random::niederreiter_base2_engine::seed(UIntType) */
void seed(UIntType init)
{
base_t::seed(init);
}
/** @copydoc boost::random::niederreiter_base2_engine::operator()() */
result_type operator()()
{
return base_t::operator()();
}
/** @copydoc boost::random::niederreiter_base2_engine::discard(boost::uintmax_t) */
void discard(boost::uintmax_t z)
{
base_t::discard(z);
}
/** Returns true if the two generators will produce identical sequences of outputs. */
BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(sobol_engine, x, y)
{ return static_cast<const base_t&>(x) == y; }
/** Returns true if the two generators will produce different sequences of outputs. */
BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(sobol_engine)
/** Writes the textual representation of the generator to a @c std::ostream. */
BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, sobol_engine, s)
{ return os << static_cast<const base_t&>(s); }
/** Reads the textual representation of the generator from a @c std::istream. */
BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, sobol_engine, s)
{ return is >> static_cast<base_t&>(s); }
#endif // BOOST_RANDOM_DOXYGEN
};
/**
* @attention This specialization of \sobol_engine supports up to 3667 dimensions.
*
* Data on the primitive binary polynomials `a` and the corresponding starting values `m`
* for Sobol sequences in up to 21201 dimensions was taken from
*
* @blockquote
* S. Joe and F. Y. Kuo, Constructing Sobol sequences with better two-dimensional projections,
* SIAM J. Sci. Comput. 30, 2635-2654 (2008).
* @endblockquote
*
* See the original tables up to dimension 21201: https://web.archive.org/web/20170802022909/http://web.maths.unsw.edu.au/~fkuo/sobol/new-joe-kuo-6.21201
*
* For practical reasons the default table uses only the subset of binary polynomials `a` < 2<sup>16</sup>.
*
* However, it is possible to provide your own table to \sobol_engine should the default one be insufficient.
*/
typedef sobol_engine<boost::uint_least64_t, 64u, default_sobol_table> sobol;
} // namespace random
} // namespace boost
#endif // BOOST_RANDOM_SOBOL_HPP