1 | /* boost random/uniform_on_sphere.hpp header file |
2 | * |
3 | * Copyright Jens Maurer 2000-2001 |
4 | * Copyright Steven Watanabe 2011 |
5 | * Distributed under the Boost Software License, Version 1.0. (See |
6 | * accompanying file LICENSE_1_0.txt or copy at |
7 | * http://www.boost.org/LICENSE_1_0.txt) |
8 | * |
9 | * See http://www.boost.org for most recent version including documentation. |
10 | * |
11 | * $Id$ |
12 | * |
13 | * Revision history |
14 | * 2001-02-18 moved to individual header files |
15 | */ |
16 | |
17 | #ifndef BOOST_RANDOM_UNIFORM_ON_SPHERE_HPP |
18 | #define BOOST_RANDOM_UNIFORM_ON_SPHERE_HPP |
19 | |
20 | #include <vector> |
21 | #include <algorithm> // std::transform |
22 | #include <functional> // std::bind2nd, std::divides |
23 | #include <boost/assert.hpp> |
24 | #include <boost/random/detail/config.hpp> |
25 | #include <boost/random/detail/operators.hpp> |
26 | #include <boost/random/normal_distribution.hpp> |
27 | |
28 | namespace boost { |
29 | namespace random { |
30 | |
31 | /** |
32 | * Instantiations of class template uniform_on_sphere model a |
33 | * \random_distribution. Such a distribution produces random |
34 | * numbers uniformly distributed on the unit sphere of arbitrary |
35 | * dimension @c dim. The @c Cont template parameter must be a STL-like |
36 | * container type with begin and end operations returning non-const |
37 | * ForwardIterators of type @c Cont::iterator. |
38 | */ |
39 | template<class RealType = double, class Cont = std::vector<RealType> > |
40 | class uniform_on_sphere |
41 | { |
42 | public: |
43 | typedef RealType input_type; |
44 | typedef Cont result_type; |
45 | |
46 | class param_type |
47 | { |
48 | public: |
49 | |
50 | typedef uniform_on_sphere distribution_type; |
51 | |
52 | /** |
53 | * Constructs the parameters of a uniform_on_sphere |
54 | * distribution, given the dimension of the sphere. |
55 | */ |
56 | explicit param_type(int dim_arg = 2) : _dim(dim_arg) |
57 | { |
58 | BOOST_ASSERT(_dim >= 0); |
59 | } |
60 | |
61 | /** Returns the dimension of the sphere. */ |
62 | int dim() const { return _dim; } |
63 | |
64 | /** Writes the parameters to a @c std::ostream. */ |
65 | BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, param_type, parm) |
66 | { |
67 | os << parm._dim; |
68 | return os; |
69 | } |
70 | |
71 | /** Reads the parameters from a @c std::istream. */ |
72 | BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, param_type, parm) |
73 | { |
74 | is >> parm._dim; |
75 | return is; |
76 | } |
77 | |
78 | /** Returns true if the two sets of parameters are equal. */ |
79 | BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(param_type, lhs, rhs) |
80 | { return lhs._dim == rhs._dim; } |
81 | |
82 | /** Returns true if the two sets of parameters are different. */ |
83 | BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(param_type) |
84 | |
85 | private: |
86 | int _dim; |
87 | }; |
88 | |
89 | /** |
90 | * Constructs a @c uniform_on_sphere distribution. |
91 | * @c dim is the dimension of the sphere. |
92 | * |
93 | * Requires: dim >= 0 |
94 | */ |
95 | explicit uniform_on_sphere(int dim_arg = 2) |
96 | : _container(dim_arg), _dim(dim_arg) { } |
97 | |
98 | /** |
99 | * Constructs a @c uniform_on_sphere distribution from its parameters. |
100 | */ |
101 | explicit uniform_on_sphere(const param_type& parm) |
102 | : _container(parm.dim()), _dim(parm.dim()) { } |
103 | |
104 | // compiler-generated copy ctor and assignment operator are fine |
105 | |
106 | /** Returns the dimension of the sphere. */ |
107 | int dim() const { return _dim; } |
108 | |
109 | /** Returns the parameters of the distribution. */ |
110 | param_type param() const { return param_type(_dim); } |
111 | /** Sets the parameters of the distribution. */ |
112 | void param(const param_type& parm) |
113 | { |
114 | _dim = parm.dim(); |
115 | _container.resize(_dim); |
116 | } |
117 | |
118 | /** |
119 | * Returns the smallest value that the distribution can produce. |
120 | * Note that this is required to approximate the standard library's |
121 | * requirements. The behavior is defined according to lexicographical |
122 | * comparison so that for a container type of std::vector, |
123 | * dist.min() <= x <= dist.max() where x is any value produced |
124 | * by the distribution. |
125 | */ |
126 | result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () const |
127 | { |
128 | result_type result(_dim); |
129 | if(_dim != 0) { |
130 | result.front() = RealType(-1.0); |
131 | } |
132 | return result; |
133 | } |
134 | /** |
135 | * Returns the largest value that the distribution can produce. |
136 | * Note that this is required to approximate the standard library's |
137 | * requirements. The behavior is defined according to lexicographical |
138 | * comparison so that for a container type of std::vector, |
139 | * dist.min() <= x <= dist.max() where x is any value produced |
140 | * by the distribution. |
141 | */ |
142 | result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const |
143 | { |
144 | result_type result(_dim); |
145 | if(_dim != 0) { |
146 | result.front() = RealType(1.0); |
147 | } |
148 | return result; |
149 | } |
150 | |
151 | /** |
152 | * Effects: Subsequent uses of the distribution do not depend |
153 | * on values produced by any engine prior to invoking reset. |
154 | */ |
155 | void reset() {} |
156 | |
157 | /** |
158 | * Returns a point uniformly distributed over the surface of |
159 | * a sphere of dimension dim(). |
160 | */ |
161 | template<class Engine> |
162 | const result_type & operator()(Engine& eng) |
163 | { |
164 | using std::sqrt; |
165 | switch(_dim) |
166 | { |
167 | case 0: break; |
168 | case 1: |
169 | { |
170 | if(uniform_01<RealType>()(eng) < 0.5) { |
171 | *_container.begin() = -1; |
172 | } else { |
173 | *_container.begin() = 1; |
174 | } |
175 | break; |
176 | } |
177 | case 2: |
178 | { |
179 | uniform_01<RealType> uniform; |
180 | RealType sqsum; |
181 | RealType x, y; |
182 | do { |
183 | x = uniform(eng) * 2 - 1; |
184 | y = uniform(eng) * 2 - 1; |
185 | sqsum = x*x + y*y; |
186 | } while(sqsum == 0 || sqsum > 1); |
187 | RealType mult = 1/sqrt(sqsum); |
188 | typename Cont::iterator iter = _container.begin(); |
189 | *iter = x * mult; |
190 | iter++; |
191 | *iter = y * mult; |
192 | break; |
193 | } |
194 | case 3: |
195 | { |
196 | uniform_01<RealType> uniform; |
197 | RealType sqsum; |
198 | RealType x, y; |
199 | do { |
200 | x = uniform(eng) * 2 - 1; |
201 | y = uniform(eng) * 2 - 1; |
202 | sqsum = x*x + y*y; |
203 | } while(sqsum > 1); |
204 | RealType mult = 2 * sqrt(1 - sqsum); |
205 | typename Cont::iterator iter = _container.begin(); |
206 | *iter = x * mult; |
207 | ++iter; |
208 | *iter = y * mult; |
209 | ++iter; |
210 | *iter = 2 * sqsum - 1; |
211 | break; |
212 | } |
213 | default: |
214 | { |
215 | detail::unit_normal_distribution<RealType> normal; |
216 | RealType sqsum; |
217 | do { |
218 | sqsum = 0; |
219 | for(typename Cont::iterator it = _container.begin(); |
220 | it != _container.end(); |
221 | ++it) { |
222 | RealType val = normal(eng); |
223 | *it = val; |
224 | sqsum += val * val; |
225 | } |
226 | } while(sqsum == 0); |
227 | // for all i: result[i] /= sqrt(sqsum) |
228 | std::transform(_container.begin(), _container.end(), _container.begin(), |
229 | std::bind2nd(std::multiplies<RealType>(), 1/sqrt(sqsum))); |
230 | } |
231 | } |
232 | return _container; |
233 | } |
234 | |
235 | /** |
236 | * Returns a point uniformly distributed over the surface of |
237 | * a sphere of dimension param.dim(). |
238 | */ |
239 | template<class Engine> |
240 | result_type operator()(Engine& eng, const param_type& parm) const |
241 | { |
242 | return uniform_on_sphere(parm)(eng); |
243 | } |
244 | |
245 | /** Writes the distribution to a @c std::ostream. */ |
246 | BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, uniform_on_sphere, sd) |
247 | { |
248 | os << sd._dim; |
249 | return os; |
250 | } |
251 | |
252 | /** Reads the distribution from a @c std::istream. */ |
253 | BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, uniform_on_sphere, sd) |
254 | { |
255 | is >> sd._dim; |
256 | sd._container.resize(sd._dim); |
257 | return is; |
258 | } |
259 | |
260 | /** |
261 | * Returns true if the two distributions will produce identical |
262 | * sequences of values, given equal generators. |
263 | */ |
264 | BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(uniform_on_sphere, lhs, rhs) |
265 | { return lhs._dim == rhs._dim; } |
266 | |
267 | /** |
268 | * Returns true if the two distributions may produce different |
269 | * sequences of values, given equal generators. |
270 | */ |
271 | BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(uniform_on_sphere) |
272 | |
273 | private: |
274 | result_type _container; |
275 | int _dim; |
276 | }; |
277 | |
278 | } // namespace random |
279 | |
280 | using random::uniform_on_sphere; |
281 | |
282 | } // namespace boost |
283 | |
284 | #endif // BOOST_RANDOM_UNIFORM_ON_SPHERE_HPP |
285 | |