COIN-OR::LEMON - Graph Library

source: lemon-1.0/lemon/random.h @ 92:5d4decd1b870

Last change on this file since 92:5d4decd1b870 was 92:5d4decd1b870, checked in by Alpar Juttner <alpar@…>, 12 years ago

Poisson distribution added

File size: 26.8 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 Returns a random real number from the range [0, 1)
579    ///
580    /// It returns a random real number from the range [0, 1). The
581    /// default Number type is \c double.
582    template <typename Number>
583    Number real() {
584      return _random_bits::RealConversion<Number, Word>::convert(core);
585    }
586
587    double real() {
588      return real<double>();
589    }
590
591    /// \brief Returns a random real number the range [0, b)
592    ///
593    /// It returns a random real number from the range [0, b).
594    template <typename Number>
595    Number real(Number b) {
596      return real<Number>() * b;
597    }
598
599    /// \brief Returns a random real number from the range [a, b)
600    ///
601    /// It returns a random real number from the range [a, b).
602    template <typename Number>
603    Number real(Number a, Number b) {
604      return real<Number>() * (b - a) + a;
605    }
606
607    /// \brief Returns a random real number from the range [0, 1)
608    ///
609    /// It returns a random double from the range [0, 1).
610    double operator()() {
611      return real<double>();
612    }
613
614    /// \brief Returns a random real number from the range [0, b)
615    ///
616    /// It returns a random real number from the range [0, b).
617    template <typename Number>
618    Number operator()(Number b) {
619      return real<Number>() * b;
620    }
621
622    /// \brief Returns a random real number from the range [a, b)
623    ///
624    /// It returns a random real number from the range [a, b).
625    template <typename Number>
626    Number operator()(Number a, Number b) {
627      return real<Number>() * (b - a) + a;
628    }
629
630    /// \brief Returns a random integer from a range
631    ///
632    /// It returns a random integer from the range {0, 1, ..., b - 1}.
633    template <typename Number>
634    Number integer(Number b) {
635      return _random_bits::Mapping<Number, Word>::map(core, b);
636    }
637
638    /// \brief Returns a random integer from a range
639    ///
640    /// It returns a random integer from the range {a, a + 1, ..., b - 1}.
641    template <typename Number>
642    Number integer(Number a, Number b) {
643      return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
644    }
645
646    /// \brief Returns a random integer from a range
647    ///
648    /// It returns a random integer from the range {0, 1, ..., b - 1}.
649    template <typename Number>
650    Number operator[](Number b) {
651      return _random_bits::Mapping<Number, Word>::map(core, b);
652    }
653
654    /// \brief Returns a random non-negative integer
655    ///
656    /// It returns a random non-negative integer uniformly from the
657    /// whole range of the current \c Number type. The default result
658    /// type of this function is <tt>unsigned int</tt>.
659    template <typename Number>
660    Number uinteger() {
661      return _random_bits::IntConversion<Number, Word>::convert(core);
662    }
663
664    unsigned int uinteger() {
665      return uinteger<unsigned int>();
666    }
667
668    /// \brief Returns a random integer
669    ///
670    /// It returns a random integer uniformly from the whole range of
671    /// the current \c Number type. The default result type of this
672    /// function is \c int.
673    template <typename Number>
674    Number integer() {
675      static const int nb = std::numeric_limits<Number>::digits +
676        (std::numeric_limits<Number>::is_signed ? 1 : 0);
677      return _random_bits::IntConversion<Number, Word, nb>::convert(core);
678    }
679
680    int integer() {
681      return integer<int>();
682    }
683   
684    /// \brief Returns a random bool
685    ///
686    /// It returns a random bool. The generator holds a buffer for
687    /// random bits. Every time when it become empty the generator makes
688    /// a new random word and fill the buffer up.
689    bool boolean() {
690      return bool_producer.convert(core);
691    }
692
693    ///\name Non-uniform distributions
694    ///
695   
696    ///@{
697   
698    /// \brief Returns a random bool
699    ///
700    /// It returns a random bool with given probability of true result.
701    bool boolean(double p) {
702      return operator()() < p;
703    }
704
705    /// Standard Gauss distribution
706
707    /// Standard Gauss distribution.
708    /// \note The Cartesian form of the Box-Muller
709    /// transformation is used to generate a random normal distribution.
710    /// \todo Consider using the "ziggurat" method instead.
711    double gauss()
712    {
713      double V1,V2,S;
714      do {
715        V1=2*real<double>()-1;
716        V2=2*real<double>()-1;
717        S=V1*V1+V2*V2;
718      } while(S>=1);
719      return std::sqrt(-2*std::log(S)/S)*V1;
720    }
721    /// Gauss distribution with given mean and standard deviation
722
723    /// Gauss distribution with given mean and standard deviation.
724    /// \sa gauss()
725    double gauss(double mean,double std_dev)
726    {
727      return gauss()*std_dev+mean;
728    }
729
730    /// Exponential distribution with given mean
731
732    /// This function generates an exponential distribution random number
733    /// with mean <tt>1/lambda</tt>.
734    ///
735    double exponential(double lambda=1.0)
736    {
737      return -std::log(1.0-real<double>())/lambda;
738    }
739
740    /// Gamma distribution with given integer shape
741
742    /// This function generates a gamma distribution random number.
743    ///
744    ///\param k shape parameter (<tt>k>0</tt> integer)
745    double gamma(int k)
746    {
747      double s = 0;
748      for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
749      return s;
750    }
751   
752    /// Gamma distribution with given shape and scale parameter
753
754    /// This function generates a gamma distribution random number.
755    ///
756    ///\param k shape parameter (<tt>k>0</tt>)
757    ///\param theta scale parameter
758    ///
759    double gamma(double k,double theta=1.0)
760    {
761      double xi,nu;
762      const double delta = k-std::floor(k);
763      const double v0=E/(E-delta);
764      do {
765        double V0=1.0-real<double>();
766        double V1=1.0-real<double>();
767        double V2=1.0-real<double>();
768        if(V2<=v0)
769          {
770            xi=std::pow(V1,1.0/delta);
771            nu=V0*std::pow(xi,delta-1.0);
772          }
773        else
774          {
775            xi=1.0-std::log(V1);
776            nu=V0*std::exp(-xi);
777          }
778      } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
779      return theta*(xi-gamma(int(std::floor(k))));
780    }
781   
782    /// Weibull distribution
783
784    /// This function generates a Weibull distribution random number.
785    ///
786    ///\param k shape parameter (<tt>k>0</tt>)
787    ///\param lambda scale parameter (<tt>lambda>0</tt>)
788    ///
789    double weibull(double k,double lambda)
790    {
791      return lambda*pow(-std::log(1.0-real<double>()),1.0/k);
792    } 
793     
794    /// Pareto distribution
795
796    /// This function generates a Pareto distribution random number.
797    ///
798    ///\param k shape parameter (<tt>k>0</tt>)
799    ///\param x_min location parameter (<tt>x_min>0</tt>)
800    ///
801    double pareto(double k,double x_min)
802    {
803      return exponential(gamma(k,1.0/x_min));
804    } 
805     
806    /// Poisson distribution
807
808    /// This function generates a Poisson distribution random number with
809    /// parameter \c lambda.
810    ///
811    /// The probability mass function of this distribusion is
812    /// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f]
813    /// \note The algorithm is taken from the book of Donald E. Knuth titled
814    /// ''Seminumerical Algorithms'' (1969). Its running time is linear in the
815    /// return value.
816   
817    int poisson(double lambda)
818    {
819      const double l = std::exp(-lambda);
820      int k=0;
821      double p = 1.0;
822      do {
823        k++;
824        p*=real<double>();
825      } while (p>=l);
826      return k-1;
827    } 
828     
829    ///@}
830   
831    ///\name Two dimensional distributions
832    ///
833
834    ///@{
835   
836    /// Uniform distribution on the full unit circle
837
838    /// Uniform distribution on the full unit circle.
839    ///
840    dim2::Point<double> disc()
841    {
842      double V1,V2;
843      do {
844        V1=2*real<double>()-1;
845        V2=2*real<double>()-1;
846       
847      } while(V1*V1+V2*V2>=1);
848      return dim2::Point<double>(V1,V2);
849    }
850    /// A kind of two dimensional Gauss distribution
851
852    /// This function provides a turning symmetric two-dimensional distribution.
853    /// Both coordinates are of standard normal distribution, but they are not
854    /// independent.
855    ///
856    /// \note The coordinates are the two random variables provided by
857    /// the Box-Muller method.
858    dim2::Point<double> gauss2()
859    {
860      double V1,V2,S;
861      do {
862        V1=2*real<double>()-1;
863        V2=2*real<double>()-1;
864        S=V1*V1+V2*V2;
865      } while(S>=1);
866      double W=std::sqrt(-2*std::log(S)/S);
867      return dim2::Point<double>(W*V1,W*V2);
868    }
869    /// A kind of two dimensional exponential distribution
870
871    /// This function provides a turning symmetric two-dimensional distribution.
872    /// The x-coordinate is of conditionally exponential distribution
873    /// with the condition that x is positive and y=0. If x is negative and
874    /// y=0 then, -x is of exponential distribution. The same is true for the
875    /// y-coordinate.
876    dim2::Point<double> exponential2()
877    {
878      double V1,V2,S;
879      do {
880        V1=2*real<double>()-1;
881        V2=2*real<double>()-1;
882        S=V1*V1+V2*V2;
883      } while(S>=1);
884      double W=-std::log(S)/S;
885      return dim2::Point<double>(W*V1,W*V2);
886    }
887
888    ///@}   
889  };
890
891
892  extern Random rnd;
893
894}
895
896#endif
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