COIN-OR::LEMON - Graph Library

source: lemon-1.0/lemon/random.h @ 102:81563e019fa4

Last change on this file since 102:81563e019fa4 was 102:81563e019fa4, checked in by Balazs Dezso <deba@…>, 12 years ago

Seeding random sequence

File size: 27.5 KB
Line 
1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2008
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
18
19/*
20 * This file contains the reimplemented version of the Mersenne Twister
21 * Generator of Matsumoto and Nishimura.
22 *
23 * See the appropriate copyright notice below.
24 *
25 * Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
26 * All rights reserved.                         
27 *
28 * Redistribution and use in source and binary forms, with or without
29 * modification, are permitted provided that the following conditions
30 * are met:
31 *
32 * 1. Redistributions of source code must retain the above copyright
33 *    notice, this list of conditions and the following disclaimer.
34 *
35 * 2. Redistributions in binary form must reproduce the above copyright
36 *    notice, this list of conditions and the following disclaimer in the
37 *    documentation and/or other materials provided with the distribution.
38 *
39 * 3. The names of its contributors may not be used to endorse or promote
40 *    products derived from this software without specific prior written
41 *    permission.
42 *
43 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
44 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
45 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
46 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE
47 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
48 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
49 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
50 * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
51 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
52 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
53 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
54 * OF THE POSSIBILITY OF SUCH DAMAGE.
55 *
56 *
57 * Any feedback is very welcome.
58 * http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
59 * email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
60 */
61
62#ifndef LEMON_RANDOM_H
63#define LEMON_RANDOM_H
64
65#include <algorithm>
66#include <iterator>
67#include <vector>
68
69#include <ctime>
70
71#include <lemon/math.h>
72#include <lemon/dim2.h>
73
74///\ingroup misc
75///\file
76///\brief Mersenne Twister random number generator
77
78namespace lemon {
79
80  namespace _random_bits {
81   
82    template <typename _Word, int _bits = std::numeric_limits<_Word>::digits>
83    struct RandomTraits {};
84
85    template <typename _Word>
86    struct RandomTraits<_Word, 32> {
87
88      typedef _Word Word;
89      static const int bits = 32;
90
91      static const int length = 624;
92      static const int shift = 397;
93     
94      static const Word mul = 0x6c078965u;
95      static const Word arrayInit = 0x012BD6AAu;
96      static const Word arrayMul1 = 0x0019660Du;
97      static const Word arrayMul2 = 0x5D588B65u;
98
99      static const Word mask = 0x9908B0DFu;
100      static const Word loMask = (1u << 31) - 1;
101      static const Word hiMask = ~loMask;
102
103
104      static Word tempering(Word rnd) {
105        rnd ^= (rnd >> 11);
106        rnd ^= (rnd << 7) & 0x9D2C5680u;
107        rnd ^= (rnd << 15) & 0xEFC60000u;
108        rnd ^= (rnd >> 18);
109        return rnd;
110      }
111
112    };
113
114    template <typename _Word>
115    struct RandomTraits<_Word, 64> {
116
117      typedef _Word Word;
118      static const int bits = 64;
119
120      static const int length = 312;
121      static const int shift = 156;
122
123      static const Word mul = Word(0x5851F42Du) << 32 | Word(0x4C957F2Du);
124      static const Word arrayInit = Word(0x00000000u) << 32 |Word(0x012BD6AAu);
125      static const Word arrayMul1 = Word(0x369DEA0Fu) << 32 |Word(0x31A53F85u);
126      static const Word arrayMul2 = Word(0x27BB2EE6u) << 32 |Word(0x87B0B0FDu);
127
128      static const Word mask = Word(0xB5026F5Au) << 32 | Word(0xA96619E9u);
129      static const Word loMask = (Word(1u) << 31) - 1;
130      static const Word hiMask = ~loMask;
131
132      static Word tempering(Word rnd) {
133        rnd ^= (rnd >> 29) & (Word(0x55555555u) << 32 | Word(0x55555555u));
134        rnd ^= (rnd << 17) & (Word(0x71D67FFFu) << 32 | Word(0xEDA60000u));
135        rnd ^= (rnd << 37) & (Word(0xFFF7EEE0u) << 32 | Word(0x00000000u));
136        rnd ^= (rnd >> 43);
137        return rnd;
138      }
139
140    };
141
142    template <typename _Word>
143    class RandomCore {
144    public:
145
146      typedef _Word Word;
147
148    private:
149
150      static const int bits = RandomTraits<Word>::bits;
151
152      static const int length = RandomTraits<Word>::length;
153      static const int shift = RandomTraits<Word>::shift;
154
155    public:
156
157      void initState() {
158        static const Word seedArray[4] = {
159          0x12345u, 0x23456u, 0x34567u, 0x45678u
160        };
161   
162        initState(seedArray, seedArray + 4);
163      }
164
165      void initState(Word seed) {
166
167        static const Word mul = RandomTraits<Word>::mul;
168
169        current = state;
170
171        Word *curr = state + length - 1;
172        curr[0] = seed; --curr;
173        for (int i = 1; i < length; ++i) {
174          curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i);
175          --curr;
176        }
177      }
178
179      template <typename Iterator>
180      void initState(Iterator begin, Iterator end) {
181
182        static const Word init = RandomTraits<Word>::arrayInit;
183        static const Word mul1 = RandomTraits<Word>::arrayMul1;
184        static const Word mul2 = RandomTraits<Word>::arrayMul2;
185
186
187        Word *curr = state + length - 1; --curr;
188        Iterator it = begin; int cnt = 0;
189        int num;
190
191        initState(init);
192
193        num = length > end - begin ? length : end - begin;
194        while (num--) {
195          curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1))
196            + *it + cnt;
197          ++it; ++cnt;
198          if (it == end) {
199            it = begin; cnt = 0;
200          }
201          if (curr == state) {
202            curr = state + length - 1; curr[0] = state[0];
203          }
204          --curr;
205        }
206
207        num = length - 1; cnt = length - (curr - state) - 1;
208        while (num--) {
209          curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2))
210            - cnt;
211          --curr; ++cnt;
212          if (curr == state) {
213            curr = state + length - 1; curr[0] = state[0]; --curr;
214            cnt = 1;
215          }
216        }
217       
218        state[length - 1] = Word(1) << (bits - 1);
219      }
220     
221      void copyState(const RandomCore& other) {
222        std::copy(other.state, other.state + length, state);
223        current = state + (other.current - other.state);
224      }
225
226      Word operator()() {
227        if (current == state) fillState();
228        --current;
229        Word rnd = *current;
230        return RandomTraits<Word>::tempering(rnd);
231      }
232
233    private:
234
235 
236      void fillState() {
237        static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask };
238        static const Word loMask = RandomTraits<Word>::loMask;
239        static const Word hiMask = RandomTraits<Word>::hiMask;
240
241        current = state + length;
242
243        register Word *curr = state + length - 1;
244        register long num;
245     
246        num = length - shift;
247        while (num--) {
248          curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
249            curr[- shift] ^ mask[curr[-1] & 1ul];
250          --curr;
251        }
252        num = shift - 1;
253        while (num--) {
254          curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
255            curr[length - shift] ^ mask[curr[-1] & 1ul];
256          --curr;
257        }
258        state[0] = (((state[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^
259          curr[length - shift] ^ mask[curr[length - 1] & 1ul];
260
261      }
262
263 
264      Word *current;
265      Word state[length];
266     
267    };
268
269
270    template <typename Result,
271              int shift = (std::numeric_limits<Result>::digits + 1) / 2>
272    struct Masker {
273      static Result mask(const Result& result) {
274        return Masker<Result, (shift + 1) / 2>::
275          mask(static_cast<Result>(result | (result >> shift)));
276      }
277    };
278   
279    template <typename Result>
280    struct Masker<Result, 1> {
281      static Result mask(const Result& result) {
282        return static_cast<Result>(result | (result >> 1));
283      }
284    };
285
286    template <typename Result, typename Word,
287              int rest = std::numeric_limits<Result>::digits, int shift = 0,
288              bool last = rest <= std::numeric_limits<Word>::digits>
289    struct IntConversion {
290      static const int bits = std::numeric_limits<Word>::digits;
291   
292      static Result convert(RandomCore<Word>& rnd) {
293        return static_cast<Result>(rnd() >> (bits - rest)) << shift;
294      }
295     
296    };
297
298    template <typename Result, typename Word, int rest, int shift>
299    struct IntConversion<Result, Word, rest, shift, false> {
300      static const int bits = std::numeric_limits<Word>::digits;
301
302      static Result convert(RandomCore<Word>& rnd) {
303        return (static_cast<Result>(rnd()) << shift) |
304          IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd);
305      }
306    };
307
308
309    template <typename Result, typename Word,
310              bool one_word = (std::numeric_limits<Word>::digits <
311                               std::numeric_limits<Result>::digits) >
312    struct Mapping {
313      static Result map(RandomCore<Word>& rnd, const Result& bound) {
314        Word max = Word(bound - 1);
315        Result mask = Masker<Result>::mask(bound - 1);
316        Result num;
317        do {
318          num = IntConversion<Result, Word>::convert(rnd) & mask;
319        } while (num > max);
320        return num;
321      }
322    };
323
324    template <typename Result, typename Word>
325    struct Mapping<Result, Word, false> {
326      static Result map(RandomCore<Word>& rnd, const Result& bound) {
327        Word max = Word(bound - 1);
328        Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2>
329          ::mask(max);
330        Word num;
331        do {
332          num = rnd() & mask;
333        } while (num > max);
334        return num;
335      }
336    };
337
338    template <typename Result, int exp, bool pos = (exp >= 0)>
339    struct ShiftMultiplier {
340      static const Result multiplier() {
341        Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
342        res *= res;
343        if ((exp & 1) == 1) res *= static_cast<Result>(2.0);
344        return res;
345      }
346    };
347
348    template <typename Result, int exp>
349    struct ShiftMultiplier<Result, exp, false> {
350      static const Result multiplier() {
351        Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
352        res *= res;
353        if ((exp & 1) == 1) res *= static_cast<Result>(0.5);
354        return res;
355      }
356    };
357
358    template <typename Result>
359    struct ShiftMultiplier<Result, 0, true> {
360      static const Result multiplier() {
361        return static_cast<Result>(1.0);
362      }
363    };
364
365    template <typename Result>
366    struct ShiftMultiplier<Result, -20, true> {
367      static const Result multiplier() {
368        return static_cast<Result>(1.0/1048576.0);
369      }
370    };
371   
372    template <typename Result>
373    struct ShiftMultiplier<Result, -32, true> {
374      static const Result multiplier() {
375        return static_cast<Result>(1.0/424967296.0);
376      }
377    };
378
379    template <typename Result>
380    struct ShiftMultiplier<Result, -53, true> {
381      static const Result multiplier() {
382        return static_cast<Result>(1.0/9007199254740992.0);
383      }
384    };
385
386    template <typename Result>
387    struct ShiftMultiplier<Result, -64, true> {
388      static const Result multiplier() {
389        return static_cast<Result>(1.0/18446744073709551616.0);
390      }
391    };
392
393    template <typename Result, int exp>
394    struct Shifting {
395      static Result shift(const Result& result) {
396        return result * ShiftMultiplier<Result, exp>::multiplier();
397      }
398    };
399
400    template <typename Result, typename Word,
401              int rest = std::numeric_limits<Result>::digits, int shift = 0,
402              bool last = rest <= std::numeric_limits<Word>::digits>
403    struct RealConversion{
404      static const int bits = std::numeric_limits<Word>::digits;
405
406      static Result convert(RandomCore<Word>& rnd) {
407        return Shifting<Result, - shift - rest>::
408          shift(static_cast<Result>(rnd() >> (bits - rest)));
409      }
410    };
411
412    template <typename Result, typename Word, int rest, int shift>
413    struct RealConversion<Result, Word, rest, shift, false> {
414      static const int bits = std::numeric_limits<Word>::digits;
415
416      static Result convert(RandomCore<Word>& rnd) {
417        return Shifting<Result, - shift - bits>::
418          shift(static_cast<Result>(rnd())) +
419          RealConversion<Result, Word, rest-bits, shift + bits>::
420          convert(rnd);
421      }
422    };
423
424    template <typename Result, typename Word>
425    struct Initializer {
426
427      template <typename Iterator>
428      static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) {
429        std::vector<Word> ws;
430        for (Iterator it = begin; it != end; ++it) {
431          ws.push_back(Word(*it));
432        }
433        rnd.initState(ws.begin(), ws.end());
434      }
435
436      static void init(RandomCore<Word>& rnd, Result seed) {
437        rnd.initState(seed);
438      }
439    };
440
441    template <typename Word>
442    struct BoolConversion {
443      static bool convert(RandomCore<Word>& rnd) {
444        return (rnd() & 1) == 1;
445      }
446    };
447
448    template <typename Word>
449    struct BoolProducer {
450      Word buffer;
451      int num;
452     
453      BoolProducer() : num(0) {}
454
455      bool convert(RandomCore<Word>& rnd) {
456        if (num == 0) {
457          buffer = rnd();
458          num = RandomTraits<Word>::bits;
459        }
460        bool r = (buffer & 1);
461        buffer >>= 1;
462        --num;
463        return r;
464      }
465    };
466
467  }
468
469  /// \ingroup misc
470  ///
471  /// \brief Mersenne Twister random number generator
472  ///
473  /// The Mersenne Twister is a twisted generalized feedback
474  /// shift-register generator of Matsumoto and Nishimura. The period
475  /// of this generator is \f$ 2^{19937} - 1 \f$ and it is
476  /// equi-distributed in 623 dimensions for 32-bit numbers. The time
477  /// performance of this generator is comparable to the commonly used
478  /// generators.
479  ///
480  /// This implementation is specialized for both 32-bit and 64-bit
481  /// architectures. The generators differ sligthly in the
482  /// initialization and generation phase so they produce two
483  /// completly different sequences.
484  ///
485  /// The generator gives back random numbers of serveral types. To
486  /// get a random number from a range of a floating point type you
487  /// can use one form of the \c operator() or the \c real() member
488  /// function. If you want to get random number from the {0, 1, ...,
489  /// n-1} integer range use the \c operator[] or the \c integer()
490  /// method. And to get random number from the whole range of an
491  /// integer type you can use the argumentless \c integer() or \c
492  /// uinteger() functions. After all you can get random bool with
493  /// equal chance of true and false or given probability of true
494  /// result with the \c boolean() member functions.
495  ///
496  ///\code
497  /// // The commented code is identical to the other
498  /// double a = rnd();                     // [0.0, 1.0)
499  /// // double a = rnd.real();             // [0.0, 1.0)
500  /// double b = rnd(100.0);                // [0.0, 100.0)
501  /// // double b = rnd.real(100.0);        // [0.0, 100.0)
502  /// double c = rnd(1.0, 2.0);             // [1.0, 2.0)
503  /// // double c = rnd.real(1.0, 2.0);     // [1.0, 2.0)
504  /// int d = rnd[100000];                  // 0..99999
505  /// // int d = rnd.integer(100000);       // 0..99999
506  /// int e = rnd[6] + 1;                   // 1..6
507  /// // int e = rnd.integer(1, 1 + 6);     // 1..6
508  /// int b = rnd.uinteger<int>();          // 0 .. 2^31 - 1
509  /// int c = rnd.integer<int>();           // - 2^31 .. 2^31 - 1
510  /// bool g = rnd.boolean();               // P(g = true) = 0.5
511  /// bool h = rnd.boolean(0.8);            // P(h = true) = 0.8
512  ///\endcode
513  ///
514  /// LEMON provides a global instance of the random number
515  /// generator which name is \ref lemon::rnd "rnd". Usually it is a
516  /// good programming convenience to use this global generator to get
517  /// random numbers.
518  class Random {
519  private:
520
521    // Architecture word
522    typedef unsigned long Word;
523   
524    _random_bits::RandomCore<Word> core;
525    _random_bits::BoolProducer<Word> bool_producer;
526   
527
528  public:
529
530    /// \brief Default constructor
531    ///
532    /// Constructor with constant seeding.
533    Random() { core.initState(); }
534
535    /// \brief Constructor with seed
536    ///
537    /// Constructor with seed. The current number type will be converted
538    /// to the architecture word type.
539    template <typename Number>
540    Random(Number seed) {
541      _random_bits::Initializer<Number, Word>::init(core, seed);
542    }
543
544    /// \brief Constructor with array seeding
545    ///
546    /// Constructor with array seeding. The given range should contain
547    /// any number type and the numbers will be converted to the
548    /// architecture word type.
549    template <typename Iterator>
550    Random(Iterator begin, Iterator end) {
551      typedef typename std::iterator_traits<Iterator>::value_type Number;
552      _random_bits::Initializer<Number, Word>::init(core, begin, end);
553    }
554
555    /// \brief Copy constructor
556    ///
557    /// Copy constructor. The generated sequence will be identical to
558    /// the other sequence. It can be used to save the current state
559    /// of the generator and later use it to generate the same
560    /// sequence.
561    Random(const Random& other) {
562      core.copyState(other.core);
563    }
564
565    /// \brief Assign operator
566    ///
567    /// Assign operator. The generated sequence will be identical to
568    /// the other sequence. It can be used to save the current state
569    /// of the generator and later use it to generate the same
570    /// sequence.
571    Random& operator=(const Random& other) {
572      if (&other != this) {
573        core.copyState(other.core);
574      }
575      return *this;
576    }
577
578    /// \brief Seeding random sequence
579    ///
580    /// Seeding the random sequence. The current number type will be
581    /// converted to the architecture word type.
582    template <typename Number>
583    void seed(Number seed) {
584      _random_bits::Initializer<Number, Word>::init(core, seed);
585    }
586
587    /// \brief Seeding random sequence
588    ///
589    /// Seeding the random sequence. The given range should contain
590    /// any number type and the numbers will be converted to the
591    /// architecture word type.
592    template <typename Iterator>
593    void seed(Iterator begin, Iterator end) {
594      typedef typename std::iterator_traits<Iterator>::value_type Number;
595      _random_bits::Initializer<Number, Word>::init(core, begin, end);
596    }
597
598    /// \brief Returns a random real number from the range [0, 1)
599    ///
600    /// It returns a random real number from the range [0, 1). The
601    /// default Number type is \c double.
602    template <typename Number>
603    Number real() {
604      return _random_bits::RealConversion<Number, Word>::convert(core);
605    }
606
607    double real() {
608      return real<double>();
609    }
610
611    /// \brief Returns a random real number the range [0, b)
612    ///
613    /// It returns a random real number from the range [0, b).
614    template <typename Number>
615    Number real(Number b) {
616      return real<Number>() * b;
617    }
618
619    /// \brief Returns a random real number from the range [a, b)
620    ///
621    /// It returns a random real number from the range [a, b).
622    template <typename Number>
623    Number real(Number a, Number b) {
624      return real<Number>() * (b - a) + a;
625    }
626
627    /// \brief Returns a random real number from the range [0, 1)
628    ///
629    /// It returns a random double from the range [0, 1).
630    double operator()() {
631      return real<double>();
632    }
633
634    /// \brief Returns a random real number from the range [0, b)
635    ///
636    /// It returns a random real number from the range [0, b).
637    template <typename Number>
638    Number operator()(Number b) {
639      return real<Number>() * b;
640    }
641
642    /// \brief Returns a random real number from the range [a, b)
643    ///
644    /// It returns a random real number from the range [a, b).
645    template <typename Number>
646    Number operator()(Number a, Number b) {
647      return real<Number>() * (b - a) + a;
648    }
649
650    /// \brief Returns a random integer from a range
651    ///
652    /// It returns a random integer from the range {0, 1, ..., b - 1}.
653    template <typename Number>
654    Number integer(Number b) {
655      return _random_bits::Mapping<Number, Word>::map(core, b);
656    }
657
658    /// \brief Returns a random integer from a range
659    ///
660    /// It returns a random integer from the range {a, a + 1, ..., b - 1}.
661    template <typename Number>
662    Number integer(Number a, Number b) {
663      return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
664    }
665
666    /// \brief Returns a random integer from a range
667    ///
668    /// It returns a random integer from the range {0, 1, ..., b - 1}.
669    template <typename Number>
670    Number operator[](Number b) {
671      return _random_bits::Mapping<Number, Word>::map(core, b);
672    }
673
674    /// \brief Returns a random non-negative integer
675    ///
676    /// It returns a random non-negative integer uniformly from the
677    /// whole range of the current \c Number type. The default result
678    /// type of this function is <tt>unsigned int</tt>.
679    template <typename Number>
680    Number uinteger() {
681      return _random_bits::IntConversion<Number, Word>::convert(core);
682    }
683
684    unsigned int uinteger() {
685      return uinteger<unsigned int>();
686    }
687
688    /// \brief Returns a random integer
689    ///
690    /// It returns a random integer uniformly from the whole range of
691    /// the current \c Number type. The default result type of this
692    /// function is \c int.
693    template <typename Number>
694    Number integer() {
695      static const int nb = std::numeric_limits<Number>::digits +
696        (std::numeric_limits<Number>::is_signed ? 1 : 0);
697      return _random_bits::IntConversion<Number, Word, nb>::convert(core);
698    }
699
700    int integer() {
701      return integer<int>();
702    }
703   
704    /// \brief Returns a random bool
705    ///
706    /// It returns a random bool. The generator holds a buffer for
707    /// random bits. Every time when it become empty the generator makes
708    /// a new random word and fill the buffer up.
709    bool boolean() {
710      return bool_producer.convert(core);
711    }
712
713    ///\name Non-uniform distributions
714    ///
715   
716    ///@{
717   
718    /// \brief Returns a random bool
719    ///
720    /// It returns a random bool with given probability of true result.
721    bool boolean(double p) {
722      return operator()() < p;
723    }
724
725    /// Standard Gauss distribution
726
727    /// Standard Gauss distribution.
728    /// \note The Cartesian form of the Box-Muller
729    /// transformation is used to generate a random normal distribution.
730    /// \todo Consider using the "ziggurat" method instead.
731    double gauss()
732    {
733      double V1,V2,S;
734      do {
735        V1=2*real<double>()-1;
736        V2=2*real<double>()-1;
737        S=V1*V1+V2*V2;
738      } while(S>=1);
739      return std::sqrt(-2*std::log(S)/S)*V1;
740    }
741    /// Gauss distribution with given mean and standard deviation
742
743    /// Gauss distribution with given mean and standard deviation.
744    /// \sa gauss()
745    double gauss(double mean,double std_dev)
746    {
747      return gauss()*std_dev+mean;
748    }
749
750    /// Exponential distribution with given mean
751
752    /// This function generates an exponential distribution random number
753    /// with mean <tt>1/lambda</tt>.
754    ///
755    double exponential(double lambda=1.0)
756    {
757      return -std::log(1.0-real<double>())/lambda;
758    }
759
760    /// Gamma distribution with given integer shape
761
762    /// This function generates a gamma distribution random number.
763    ///
764    ///\param k shape parameter (<tt>k>0</tt> integer)
765    double gamma(int k)
766    {
767      double s = 0;
768      for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
769      return s;
770    }
771   
772    /// Gamma distribution with given shape and scale parameter
773
774    /// This function generates a gamma distribution random number.
775    ///
776    ///\param k shape parameter (<tt>k>0</tt>)
777    ///\param theta scale parameter
778    ///
779    double gamma(double k,double theta=1.0)
780    {
781      double xi,nu;
782      const double delta = k-std::floor(k);
783      const double v0=E/(E-delta);
784      do {
785        double V0=1.0-real<double>();
786        double V1=1.0-real<double>();
787        double V2=1.0-real<double>();
788        if(V2<=v0)
789          {
790            xi=std::pow(V1,1.0/delta);
791            nu=V0*std::pow(xi,delta-1.0);
792          }
793        else
794          {
795            xi=1.0-std::log(V1);
796            nu=V0*std::exp(-xi);
797          }
798      } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
799      return theta*(xi-gamma(int(std::floor(k))));
800    }
801   
802    /// Weibull distribution
803
804    /// This function generates a Weibull distribution random number.
805    ///
806    ///\param k shape parameter (<tt>k>0</tt>)
807    ///\param lambda scale parameter (<tt>lambda>0</tt>)
808    ///
809    double weibull(double k,double lambda)
810    {
811      return lambda*pow(-std::log(1.0-real<double>()),1.0/k);
812    } 
813     
814    /// Pareto distribution
815
816    /// This function generates a Pareto distribution random number.
817    ///
818    ///\param k shape parameter (<tt>k>0</tt>)
819    ///\param x_min location parameter (<tt>x_min>0</tt>)
820    ///
821    double pareto(double k,double x_min)
822    {
823      return exponential(gamma(k,1.0/x_min));
824    } 
825     
826    /// Poisson distribution
827
828    /// This function generates a Poisson distribution random number with
829    /// parameter \c lambda.
830    ///
831    /// The probability mass function of this distribusion is
832    /// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f]
833    /// \note The algorithm is taken from the book of Donald E. Knuth titled
834    /// ''Seminumerical Algorithms'' (1969). Its running time is linear in the
835    /// return value.
836   
837    int poisson(double lambda)
838    {
839      const double l = std::exp(-lambda);
840      int k=0;
841      double p = 1.0;
842      do {
843        k++;
844        p*=real<double>();
845      } while (p>=l);
846      return k-1;
847    } 
848     
849    ///@}
850   
851    ///\name Two dimensional distributions
852    ///
853
854    ///@{
855   
856    /// Uniform distribution on the full unit circle
857
858    /// Uniform distribution on the full unit circle.
859    ///
860    dim2::Point<double> disc()
861    {
862      double V1,V2;
863      do {
864        V1=2*real<double>()-1;
865        V2=2*real<double>()-1;
866       
867      } while(V1*V1+V2*V2>=1);
868      return dim2::Point<double>(V1,V2);
869    }
870    /// A kind of two dimensional Gauss distribution
871
872    /// This function provides a turning symmetric two-dimensional distribution.
873    /// Both coordinates are of standard normal distribution, but they are not
874    /// independent.
875    ///
876    /// \note The coordinates are the two random variables provided by
877    /// the Box-Muller method.
878    dim2::Point<double> gauss2()
879    {
880      double V1,V2,S;
881      do {
882        V1=2*real<double>()-1;
883        V2=2*real<double>()-1;
884        S=V1*V1+V2*V2;
885      } while(S>=1);
886      double W=std::sqrt(-2*std::log(S)/S);
887      return dim2::Point<double>(W*V1,W*V2);
888    }
889    /// A kind of two dimensional exponential distribution
890
891    /// This function provides a turning symmetric two-dimensional distribution.
892    /// The x-coordinate is of conditionally exponential distribution
893    /// with the condition that x is positive and y=0. If x is negative and
894    /// y=0 then, -x is of exponential distribution. The same is true for the
895    /// y-coordinate.
896    dim2::Point<double> exponential2()
897    {
898      double V1,V2,S;
899      do {
900        V1=2*real<double>()-1;
901        V2=2*real<double>()-1;
902        S=V1*V1+V2*V2;
903      } while(S>=1);
904      double W=-std::log(S)/S;
905      return dim2::Point<double>(W*V1,W*V2);
906    }
907
908    ///@}   
909  };
910
911
912  extern Random rnd;
913
914}
915
916#endif
Note: See TracBrowser for help on using the repository browser.