285 lines
8.8 KiB
Plaintext
285 lines
8.8 KiB
Plaintext
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/* boost random/uniform_on_sphere.hpp header file
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*
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* Copyright Jens Maurer 2000-2001
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* Copyright Steven Watanabe 2011
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* Distributed under the Boost Software License, Version 1.0. (See
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* accompanying file LICENSE_1_0.txt or copy at
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* http://www.boost.org/LICENSE_1_0.txt)
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*
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* See http://www.boost.org for most recent version including documentation.
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*
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* $Id$
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*
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* Revision history
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* 2001-02-18 moved to individual header files
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*/
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#ifndef BOOST_RANDOM_UNIFORM_ON_SPHERE_HPP
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#define BOOST_RANDOM_UNIFORM_ON_SPHERE_HPP
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#include <vector>
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#include <algorithm> // std::transform
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#include <functional> // std::bind2nd, std::divides
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#include <boost/assert.hpp>
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#include <boost/random/detail/config.hpp>
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#include <boost/random/detail/operators.hpp>
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#include <boost/random/normal_distribution.hpp>
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namespace boost {
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namespace random {
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/**
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* Instantiations of class template uniform_on_sphere model a
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* \random_distribution. Such a distribution produces random
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* numbers uniformly distributed on the unit sphere of arbitrary
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* dimension @c dim. The @c Cont template parameter must be a STL-like
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* container type with begin and end operations returning non-const
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* ForwardIterators of type @c Cont::iterator.
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*/
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template<class RealType = double, class Cont = std::vector<RealType> >
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class uniform_on_sphere
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{
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public:
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typedef RealType input_type;
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typedef Cont result_type;
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class param_type
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{
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public:
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typedef uniform_on_sphere distribution_type;
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/**
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* Constructs the parameters of a uniform_on_sphere
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* distribution, given the dimension of the sphere.
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*/
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explicit param_type(int dim_arg = 2) : _dim(dim_arg)
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{
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BOOST_ASSERT(_dim >= 0);
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}
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/** Returns the dimension of the sphere. */
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int dim() const { return _dim; }
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/** Writes the parameters to a @c std::ostream. */
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BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, param_type, parm)
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{
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os << parm._dim;
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return os;
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}
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/** Reads the parameters from a @c std::istream. */
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BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, param_type, parm)
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{
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is >> parm._dim;
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return is;
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}
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/** Returns true if the two sets of parameters are equal. */
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BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(param_type, lhs, rhs)
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{ return lhs._dim == rhs._dim; }
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/** Returns true if the two sets of parameters are different. */
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BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(param_type)
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private:
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int _dim;
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};
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/**
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* Constructs a @c uniform_on_sphere distribution.
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* @c dim is the dimension of the sphere.
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*
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* Requires: dim >= 0
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*/
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explicit uniform_on_sphere(int dim_arg = 2)
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: _container(dim_arg), _dim(dim_arg) { }
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/**
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* Constructs a @c uniform_on_sphere distribution from its parameters.
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*/
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explicit uniform_on_sphere(const param_type& parm)
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: _container(parm.dim()), _dim(parm.dim()) { }
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// compiler-generated copy ctor and assignment operator are fine
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/** Returns the dimension of the sphere. */
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int dim() const { return _dim; }
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/** Returns the parameters of the distribution. */
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param_type param() const { return param_type(_dim); }
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/** Sets the parameters of the distribution. */
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void param(const param_type& parm)
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{
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_dim = parm.dim();
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_container.resize(_dim);
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}
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/**
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* Returns the smallest value that the distribution can produce.
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* Note that this is required to approximate the standard library's
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* requirements. The behavior is defined according to lexicographical
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* comparison so that for a container type of std::vector,
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* dist.min() <= x <= dist.max() where x is any value produced
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* by the distribution.
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*/
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result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () const
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{
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result_type result(_dim);
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if(_dim != 0) {
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result.front() = RealType(-1.0);
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}
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return result;
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}
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/**
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* Returns the largest value that the distribution can produce.
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* Note that this is required to approximate the standard library's
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* requirements. The behavior is defined according to lexicographical
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* comparison so that for a container type of std::vector,
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* dist.min() <= x <= dist.max() where x is any value produced
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* by the distribution.
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*/
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result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const
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{
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result_type result(_dim);
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if(_dim != 0) {
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result.front() = RealType(1.0);
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}
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return result;
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}
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/**
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* Effects: Subsequent uses of the distribution do not depend
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* on values produced by any engine prior to invoking reset.
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*/
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void reset() {}
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/**
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* Returns a point uniformly distributed over the surface of
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* a sphere of dimension dim().
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*/
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template<class Engine>
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const result_type & operator()(Engine& eng)
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{
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using std::sqrt;
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switch(_dim)
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{
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case 0: break;
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case 1:
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{
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if(uniform_01<RealType>()(eng) < 0.5) {
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*_container.begin() = -1;
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} else {
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*_container.begin() = 1;
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}
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break;
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}
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case 2:
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{
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uniform_01<RealType> uniform;
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RealType sqsum;
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RealType x, y;
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do {
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x = uniform(eng) * 2 - 1;
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y = uniform(eng) * 2 - 1;
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sqsum = x*x + y*y;
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} while(sqsum == 0 || sqsum > 1);
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RealType mult = 1/sqrt(sqsum);
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typename Cont::iterator iter = _container.begin();
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*iter = x * mult;
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iter++;
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*iter = y * mult;
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break;
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}
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case 3:
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{
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uniform_01<RealType> uniform;
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RealType sqsum;
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RealType x, y;
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do {
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x = uniform(eng) * 2 - 1;
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y = uniform(eng) * 2 - 1;
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sqsum = x*x + y*y;
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} while(sqsum > 1);
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RealType mult = 2 * sqrt(1 - sqsum);
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typename Cont::iterator iter = _container.begin();
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*iter = x * mult;
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++iter;
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*iter = y * mult;
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++iter;
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*iter = 2 * sqsum - 1;
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break;
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}
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default:
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{
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detail::unit_normal_distribution<RealType> normal;
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RealType sqsum;
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do {
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sqsum = 0;
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for(typename Cont::iterator it = _container.begin();
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it != _container.end();
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++it) {
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RealType val = normal(eng);
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*it = val;
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sqsum += val * val;
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}
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} while(sqsum == 0);
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// for all i: result[i] /= sqrt(sqsum)
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std::transform(_container.begin(), _container.end(), _container.begin(),
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std::bind2nd(std::multiplies<RealType>(), 1/sqrt(sqsum)));
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}
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}
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return _container;
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}
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/**
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* Returns a point uniformly distributed over the surface of
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* a sphere of dimension param.dim().
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*/
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template<class Engine>
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result_type operator()(Engine& eng, const param_type& parm) const
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{
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return uniform_on_sphere(parm)(eng);
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}
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/** Writes the distribution to a @c std::ostream. */
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BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, uniform_on_sphere, sd)
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{
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os << sd._dim;
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return os;
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}
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/** Reads the distribution from a @c std::istream. */
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BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, uniform_on_sphere, sd)
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{
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is >> sd._dim;
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sd._container.resize(sd._dim);
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return is;
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}
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/**
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* Returns true if the two distributions will produce identical
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* sequences of values, given equal generators.
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*/
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BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(uniform_on_sphere, lhs, rhs)
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{ return lhs._dim == rhs._dim; }
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/**
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* Returns true if the two distributions may produce different
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* sequences of values, given equal generators.
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*/
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BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(uniform_on_sphere)
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private:
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result_type _container;
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int _dim;
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};
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} // namespace random
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using random::uniform_on_sphere;
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} // namespace boost
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#endif // BOOST_RANDOM_UNIFORM_ON_SPHERE_HPP
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