feat():initial version

install/boost_1_75_0/include/boost/random/sobol.hpp

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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