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diff --git a/extern/quadriflow/3rd/lemon-1.3.1/lemon/random.h b/extern/quadriflow/3rd/lemon-1.3.1/lemon/random.h new file mode 100644 index 00000000000..8de74ede8a9 --- /dev/null +++ b/extern/quadriflow/3rd/lemon-1.3.1/lemon/random.h @@ -0,0 +1,1005 @@ +/* -*- mode: C++; indent-tabs-mode: nil; -*- + * + * This file is a part of LEMON, a generic C++ optimization library. + * + * Copyright (C) 2003-2009 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport + * (Egervary Research Group on Combinatorial Optimization, EGRES). + * + * Permission to use, modify and distribute this software is granted + * provided that this copyright notice appears in all copies. For + * precise terms see the accompanying LICENSE file. + * + * This software is provided "AS IS" with no warranty of any kind, + * express or implied, and with no claim as to its suitability for any + * purpose. + * + */ + +/* + * This file contains the reimplemented version of the Mersenne Twister + * Generator of Matsumoto and Nishimura. + * + * See the appropriate copyright notice below. + * + * Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura, + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * 3. The names of its contributors may not be used to endorse or promote + * products derived from this software without specific prior written + * permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS + * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE + * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES + * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR + * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, + * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED + * OF THE POSSIBILITY OF SUCH DAMAGE. + * + * + * Any feedback is very welcome. + * http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html + * email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space) + */ + +#ifndef LEMON_RANDOM_H +#define LEMON_RANDOM_H + +#include <algorithm> +#include <iterator> +#include <vector> +#include <limits> +#include <fstream> + +#include <lemon/math.h> +#include <lemon/dim2.h> + +#ifndef WIN32 +#include <sys/time.h> +#include <ctime> +#include <sys/types.h> +#include <unistd.h> +#else +#include <lemon/bits/windows.h> +#endif + +///\ingroup misc +///\file +///\brief Mersenne Twister random number generator + +namespace lemon { + + namespace _random_bits { + + template <typename _Word, int _bits = std::numeric_limits<_Word>::digits> + struct RandomTraits {}; + + template <typename _Word> + struct RandomTraits<_Word, 32> { + + typedef _Word Word; + static const int bits = 32; + + static const int length = 624; + static const int shift = 397; + + static const Word mul = 0x6c078965u; + static const Word arrayInit = 0x012BD6AAu; + static const Word arrayMul1 = 0x0019660Du; + static const Word arrayMul2 = 0x5D588B65u; + + static const Word mask = 0x9908B0DFu; + static const Word loMask = (1u << 31) - 1; + static const Word hiMask = ~loMask; + + + static Word tempering(Word rnd) { + rnd ^= (rnd >> 11); + rnd ^= (rnd << 7) & 0x9D2C5680u; + rnd ^= (rnd << 15) & 0xEFC60000u; + rnd ^= (rnd >> 18); + return rnd; + } + + }; + + template <typename _Word> + struct RandomTraits<_Word, 64> { + + typedef _Word Word; + static const int bits = 64; + + static const int length = 312; + static const int shift = 156; + + static const Word mul = Word(0x5851F42Du) << 32 | Word(0x4C957F2Du); + static const Word arrayInit = Word(0x00000000u) << 32 |Word(0x012BD6AAu); + static const Word arrayMul1 = Word(0x369DEA0Fu) << 32 |Word(0x31A53F85u); + static const Word arrayMul2 = Word(0x27BB2EE6u) << 32 |Word(0x87B0B0FDu); + + static const Word mask = Word(0xB5026F5Au) << 32 | Word(0xA96619E9u); + static const Word loMask = (Word(1u) << 31) - 1; + static const Word hiMask = ~loMask; + + static Word tempering(Word rnd) { + rnd ^= (rnd >> 29) & (Word(0x55555555u) << 32 | Word(0x55555555u)); + rnd ^= (rnd << 17) & (Word(0x71D67FFFu) << 32 | Word(0xEDA60000u)); + rnd ^= (rnd << 37) & (Word(0xFFF7EEE0u) << 32 | Word(0x00000000u)); + rnd ^= (rnd >> 43); + return rnd; + } + + }; + + template <typename _Word> + class RandomCore { + public: + + typedef _Word Word; + + private: + + static const int bits = RandomTraits<Word>::bits; + + static const int length = RandomTraits<Word>::length; + static const int shift = RandomTraits<Word>::shift; + + public: + + void initState() { + static const Word seedArray[4] = { + 0x12345u, 0x23456u, 0x34567u, 0x45678u + }; + + initState(seedArray, seedArray + 4); + } + + void initState(Word seed) { + + static const Word mul = RandomTraits<Word>::mul; + + current = state; + + Word *curr = state + length - 1; + curr[0] = seed; --curr; + for (int i = 1; i < length; ++i) { + curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i); + --curr; + } + } + + template <typename Iterator> + void initState(Iterator begin, Iterator end) { + + static const Word init = RandomTraits<Word>::arrayInit; + static const Word mul1 = RandomTraits<Word>::arrayMul1; + static const Word mul2 = RandomTraits<Word>::arrayMul2; + + + Word *curr = state + length - 1; --curr; + Iterator it = begin; int cnt = 0; + int num; + + initState(init); + + num = length > end - begin ? length : end - begin; + while (num--) { + curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1)) + + *it + cnt; + ++it; ++cnt; + if (it == end) { + it = begin; cnt = 0; + } + if (curr == state) { + curr = state + length - 1; curr[0] = state[0]; + } + --curr; + } + + num = length - 1; cnt = length - (curr - state) - 1; + while (num--) { + curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2)) + - cnt; + --curr; ++cnt; + if (curr == state) { + curr = state + length - 1; curr[0] = state[0]; --curr; + cnt = 1; + } + } + + state[length - 1] = Word(1) << (bits - 1); + } + + void copyState(const RandomCore& other) { + std::copy(other.state, other.state + length, state); + current = state + (other.current - other.state); + } + + Word operator()() { + if (current == state) fillState(); + --current; + Word rnd = *current; + return RandomTraits<Word>::tempering(rnd); + } + + private: + + + void fillState() { + static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask }; + static const Word loMask = RandomTraits<Word>::loMask; + static const Word hiMask = RandomTraits<Word>::hiMask; + + current = state + length; + + register Word *curr = state + length - 1; + register long num; + + num = length - shift; + while (num--) { + curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^ + curr[- shift] ^ mask[curr[-1] & 1ul]; + --curr; + } + num = shift - 1; + while (num--) { + curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^ + curr[length - shift] ^ mask[curr[-1] & 1ul]; + --curr; + } + state[0] = (((state[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^ + curr[length - shift] ^ mask[curr[length - 1] & 1ul]; + + } + + + Word *current; + Word state[length]; + + }; + + + template <typename Result, + int shift = (std::numeric_limits<Result>::digits + 1) / 2> + struct Masker { + static Result mask(const Result& result) { + return Masker<Result, (shift + 1) / 2>:: + mask(static_cast<Result>(result | (result >> shift))); + } + }; + + template <typename Result> + struct Masker<Result, 1> { + static Result mask(const Result& result) { + return static_cast<Result>(result | (result >> 1)); + } + }; + + template <typename Result, typename Word, + int rest = std::numeric_limits<Result>::digits, int shift = 0, + bool last = rest <= std::numeric_limits<Word>::digits> + struct IntConversion { + static const int bits = std::numeric_limits<Word>::digits; + + static Result convert(RandomCore<Word>& rnd) { + return static_cast<Result>(rnd() >> (bits - rest)) << shift; + } + + }; + + template <typename Result, typename Word, int rest, int shift> + struct IntConversion<Result, Word, rest, shift, false> { + static const int bits = std::numeric_limits<Word>::digits; + + static Result convert(RandomCore<Word>& rnd) { + return (static_cast<Result>(rnd()) << shift) | + IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd); + } + }; + + + template <typename Result, typename Word, + bool one_word = (std::numeric_limits<Word>::digits < + std::numeric_limits<Result>::digits) > + struct Mapping { + static Result map(RandomCore<Word>& rnd, const Result& bound) { + Word max = Word(bound - 1); + Result mask = Masker<Result>::mask(bound - 1); + Result num; + do { + num = IntConversion<Result, Word>::convert(rnd) & mask; + } while (num > max); + return num; + } + }; + + template <typename Result, typename Word> + struct Mapping<Result, Word, false> { + static Result map(RandomCore<Word>& rnd, const Result& bound) { + Word max = Word(bound - 1); + Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2> + ::mask(max); + Word num; + do { + num = rnd() & mask; + } while (num > max); + return num; + } + }; + + template <typename Result, int exp> + struct ShiftMultiplier { + static const Result multiplier() { + Result res = ShiftMultiplier<Result, exp / 2>::multiplier(); + res *= res; + if ((exp & 1) == 1) res *= static_cast<Result>(0.5); + return res; + } + }; + + template <typename Result> + struct ShiftMultiplier<Result, 0> { + static const Result multiplier() { + return static_cast<Result>(1.0); + } + }; + + template <typename Result> + struct ShiftMultiplier<Result, 20> { + static const Result multiplier() { + return static_cast<Result>(1.0/1048576.0); + } + }; + + template <typename Result> + struct ShiftMultiplier<Result, 32> { + static const Result multiplier() { + return static_cast<Result>(1.0/4294967296.0); + } + }; + + template <typename Result> + struct ShiftMultiplier<Result, 53> { + static const Result multiplier() { + return static_cast<Result>(1.0/9007199254740992.0); + } + }; + + template <typename Result> + struct ShiftMultiplier<Result, 64> { + static const Result multiplier() { + return static_cast<Result>(1.0/18446744073709551616.0); + } + }; + + template <typename Result, int exp> + struct Shifting { + static Result shift(const Result& result) { + return result * ShiftMultiplier<Result, exp>::multiplier(); + } + }; + + template <typename Result, typename Word, + int rest = std::numeric_limits<Result>::digits, int shift = 0, + bool last = rest <= std::numeric_limits<Word>::digits> + struct RealConversion{ + static const int bits = std::numeric_limits<Word>::digits; + + static Result convert(RandomCore<Word>& rnd) { + return Shifting<Result, shift + rest>:: + shift(static_cast<Result>(rnd() >> (bits - rest))); + } + }; + + template <typename Result, typename Word, int rest, int shift> + struct RealConversion<Result, Word, rest, shift, false> { + static const int bits = std::numeric_limits<Word>::digits; + + static Result convert(RandomCore<Word>& rnd) { + return Shifting<Result, shift + bits>:: + shift(static_cast<Result>(rnd())) + + RealConversion<Result, Word, rest-bits, shift + bits>:: + convert(rnd); + } + }; + + template <typename Result, typename Word> + struct Initializer { + + template <typename Iterator> + static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) { + std::vector<Word> ws; + for (Iterator it = begin; it != end; ++it) { + ws.push_back(Word(*it)); + } + rnd.initState(ws.begin(), ws.end()); + } + + static void init(RandomCore<Word>& rnd, Result seed) { + rnd.initState(seed); + } + }; + + template <typename Word> + struct BoolConversion { + static bool convert(RandomCore<Word>& rnd) { + return (rnd() & 1) == 1; + } + }; + + template <typename Word> + struct BoolProducer { + Word buffer; + int num; + + BoolProducer() : num(0) {} + + bool convert(RandomCore<Word>& rnd) { + if (num == 0) { + buffer = rnd(); + num = RandomTraits<Word>::bits; + } + bool r = (buffer & 1); + buffer >>= 1; + --num; + return r; + } + }; + + } + + /// \ingroup misc + /// + /// \brief Mersenne Twister random number generator + /// + /// The Mersenne Twister is a twisted generalized feedback + /// shift-register generator of Matsumoto and Nishimura. The period + /// of this generator is \f$ 2^{19937} - 1 \f$ and it is + /// equi-distributed in 623 dimensions for 32-bit numbers. The time + /// performance of this generator is comparable to the commonly used + /// generators. + /// + /// This implementation is specialized for both 32-bit and 64-bit + /// architectures. The generators differ sligthly in the + /// initialization and generation phase so they produce two + /// completly different sequences. + /// + /// The generator gives back random numbers of serveral types. To + /// get a random number from a range of a floating point type you + /// can use one form of the \c operator() or the \c real() member + /// function. If you want to get random number from the {0, 1, ..., + /// n-1} integer range use the \c operator[] or the \c integer() + /// method. And to get random number from the whole range of an + /// integer type you can use the argumentless \c integer() or \c + /// uinteger() functions. After all you can get random bool with + /// equal chance of true and false or given probability of true + /// result with the \c boolean() member functions. + /// + ///\code + /// // The commented code is identical to the other + /// double a = rnd(); // [0.0, 1.0) + /// // double a = rnd.real(); // [0.0, 1.0) + /// double b = rnd(100.0); // [0.0, 100.0) + /// // double b = rnd.real(100.0); // [0.0, 100.0) + /// double c = rnd(1.0, 2.0); // [1.0, 2.0) + /// // double c = rnd.real(1.0, 2.0); // [1.0, 2.0) + /// int d = rnd[100000]; // 0..99999 + /// // int d = rnd.integer(100000); // 0..99999 + /// int e = rnd[6] + 1; // 1..6 + /// // int e = rnd.integer(1, 1 + 6); // 1..6 + /// int b = rnd.uinteger<int>(); // 0 .. 2^31 - 1 + /// int c = rnd.integer<int>(); // - 2^31 .. 2^31 - 1 + /// bool g = rnd.boolean(); // P(g = true) = 0.5 + /// bool h = rnd.boolean(0.8); // P(h = true) = 0.8 + ///\endcode + /// + /// LEMON provides a global instance of the random number + /// generator which name is \ref lemon::rnd "rnd". Usually it is a + /// good programming convenience to use this global generator to get + /// random numbers. + class Random { + private: + + // Architecture word + typedef unsigned long Word; + + _random_bits::RandomCore<Word> core; + _random_bits::BoolProducer<Word> bool_producer; + + + public: + + ///\name Initialization + /// + /// @{ + + /// \brief Default constructor + /// + /// Constructor with constant seeding. + Random() { core.initState(); } + + /// \brief Constructor with seed + /// + /// Constructor with seed. The current number type will be converted + /// to the architecture word type. + template <typename Number> + Random(Number seed) { + _random_bits::Initializer<Number, Word>::init(core, seed); + } + + /// \brief Constructor with array seeding + /// + /// Constructor with array seeding. The given range should contain + /// any number type and the numbers will be converted to the + /// architecture word type. + template <typename Iterator> + Random(Iterator begin, Iterator end) { + typedef typename std::iterator_traits<Iterator>::value_type Number; + _random_bits::Initializer<Number, Word>::init(core, begin, end); + } + + /// \brief Copy constructor + /// + /// Copy constructor. The generated sequence will be identical to + /// the other sequence. It can be used to save the current state + /// of the generator and later use it to generate the same + /// sequence. + Random(const Random& other) { + core.copyState(other.core); + } + + /// \brief Assign operator + /// + /// Assign operator. The generated sequence will be identical to + /// the other sequence. It can be used to save the current state + /// of the generator and later use it to generate the same + /// sequence. + Random& operator=(const Random& other) { + if (&other != this) { + core.copyState(other.core); + } + return *this; + } + + /// \brief Seeding random sequence + /// + /// Seeding the random sequence. The current number type will be + /// converted to the architecture word type. + template <typename Number> + void seed(Number seed) { + _random_bits::Initializer<Number, Word>::init(core, seed); + } + + /// \brief Seeding random sequence + /// + /// Seeding the random sequence. The given range should contain + /// any number type and the numbers will be converted to the + /// architecture word type. + template <typename Iterator> + void seed(Iterator begin, Iterator end) { + typedef typename std::iterator_traits<Iterator>::value_type Number; + _random_bits::Initializer<Number, Word>::init(core, begin, end); + } + + /// \brief Seeding from file or from process id and time + /// + /// By default, this function calls the \c seedFromFile() member + /// function with the <tt>/dev/urandom</tt> file. If it does not success, + /// it uses the \c seedFromTime(). + /// \return Currently always \c true. + bool seed() { +#ifndef WIN32 + if (seedFromFile("/dev/urandom", 0)) return true; +#endif + if (seedFromTime()) return true; + return false; + } + + /// \brief Seeding from file + /// + /// Seeding the random sequence from file. The linux kernel has two + /// devices, <tt>/dev/random</tt> and <tt>/dev/urandom</tt> which + /// could give good seed values for pseudo random generators (The + /// difference between two devices is that the <tt>random</tt> may + /// block the reading operation while the kernel can give good + /// source of randomness, while the <tt>urandom</tt> does not + /// block the input, but it could give back bytes with worse + /// entropy). + /// \param file The source file + /// \param offset The offset, from the file read. + /// \return \c true when the seeding successes. +#ifndef WIN32 + bool seedFromFile(const std::string& file = "/dev/urandom", int offset = 0) +#else + bool seedFromFile(const std::string& file = "", int offset = 0) +#endif + { + std::ifstream rs(file.c_str()); + const int size = 4; + Word buf[size]; + if (offset != 0 && !rs.seekg(offset)) return false; + if (!rs.read(reinterpret_cast<char*>(buf), sizeof(buf))) return false; + seed(buf, buf + size); + return true; + } + + /// \brief Seding from process id and time + /// + /// Seding from process id and time. This function uses the + /// current process id and the current time for initialize the + /// random sequence. + /// \return Currently always \c true. + bool seedFromTime() { +#ifndef WIN32 + timeval tv; + gettimeofday(&tv, 0); + seed(getpid() + tv.tv_sec + tv.tv_usec); +#else + seed(bits::getWinRndSeed()); +#endif + return true; + } + + /// @} + + ///\name Uniform Distributions + /// + /// @{ + + /// \brief Returns a random real number from the range [0, 1) + /// + /// It returns a random real number from the range [0, 1). The + /// default Number type is \c double. + template <typename Number> + Number real() { + return _random_bits::RealConversion<Number, Word>::convert(core); + } + + double real() { + return real<double>(); + } + + /// \brief Returns a random real number from the range [0, 1) + /// + /// It returns a random double from the range [0, 1). + double operator()() { + return real<double>(); + } + + /// \brief Returns a random real number from the range [0, b) + /// + /// It returns a random real number from the range [0, b). + double operator()(double b) { + return real<double>() * b; + } + + /// \brief Returns a random real number from the range [a, b) + /// + /// It returns a random real number from the range [a, b). + double operator()(double a, double b) { + return real<double>() * (b - a) + a; + } + + /// \brief Returns a random integer from a range + /// + /// It returns a random integer from the range {0, 1, ..., b - 1}. + template <typename Number> + Number integer(Number b) { + return _random_bits::Mapping<Number, Word>::map(core, b); + } + + /// \brief Returns a random integer from a range + /// + /// It returns a random integer from the range {a, a + 1, ..., b - 1}. + template <typename Number> + Number integer(Number a, Number b) { + return _random_bits::Mapping<Number, Word>::map(core, b - a) + a; + } + + /// \brief Returns a random integer from a range + /// + /// It returns a random integer from the range {0, 1, ..., b - 1}. + template <typename Number> + Number operator[](Number b) { + return _random_bits::Mapping<Number, Word>::map(core, b); + } + + /// \brief Returns a random non-negative integer + /// + /// It returns a random non-negative integer uniformly from the + /// whole range of the current \c Number type. The default result + /// type of this function is <tt>unsigned int</tt>. + template <typename Number> + Number uinteger() { + return _random_bits::IntConversion<Number, Word>::convert(core); + } + + unsigned int uinteger() { + return uinteger<unsigned int>(); + } + + /// \brief Returns a random integer + /// + /// It returns a random integer uniformly from the whole range of + /// the current \c Number type. The default result type of this + /// function is \c int. + template <typename Number> + Number integer() { + static const int nb = std::numeric_limits<Number>::digits + + (std::numeric_limits<Number>::is_signed ? 1 : 0); + return _random_bits::IntConversion<Number, Word, nb>::convert(core); + } + + int integer() { + return integer<int>(); + } + + /// \brief Returns a random bool + /// + /// It returns a random bool. The generator holds a buffer for + /// random bits. Every time when it become empty the generator makes + /// a new random word and fill the buffer up. + bool boolean() { + return bool_producer.convert(core); + } + + /// @} + + ///\name Non-uniform Distributions + /// + ///@{ + + /// \brief Returns a random bool with given probability of true result. + /// + /// It returns a random bool with given probability of true result. + bool boolean(double p) { + return operator()() < p; + } + + /// Standard normal (Gauss) distribution + + /// Standard normal (Gauss) distribution. + /// \note The Cartesian form of the Box-Muller + /// transformation is used to generate a random normal distribution. + double gauss() + { + double V1,V2,S; + do { + V1=2*real<double>()-1; + V2=2*real<double>()-1; + S=V1*V1+V2*V2; + } while(S>=1); + return std::sqrt(-2*std::log(S)/S)*V1; + } + /// Normal (Gauss) distribution with given mean and standard deviation + + /// Normal (Gauss) distribution with given mean and standard deviation. + /// \sa gauss() + double gauss(double mean,double std_dev) + { + return gauss()*std_dev+mean; + } + + /// Lognormal distribution + + /// Lognormal distribution. The parameters are the mean and the standard + /// deviation of <tt>exp(X)</tt>. + /// + double lognormal(double n_mean,double n_std_dev) + { + return std::exp(gauss(n_mean,n_std_dev)); + } + /// Lognormal distribution + + /// Lognormal distribution. The parameter is an <tt>std::pair</tt> of + /// the mean and the standard deviation of <tt>exp(X)</tt>. + /// + double lognormal(const std::pair<double,double> ¶ms) + { + return std::exp(gauss(params.first,params.second)); + } + /// Compute the lognormal parameters from mean and standard deviation + + /// This function computes the lognormal parameters from mean and + /// standard deviation. The return value can direcly be passed to + /// lognormal(). + std::pair<double,double> lognormalParamsFromMD(double mean, + double std_dev) + { + double fr=std_dev/mean; + fr*=fr; + double lg=std::log(1+fr); + return std::pair<double,double>(std::log(mean)-lg/2.0,std::sqrt(lg)); + } + /// Lognormal distribution with given mean and standard deviation + + /// Lognormal distribution with given mean and standard deviation. + /// + double lognormalMD(double mean,double std_dev) + { + return lognormal(lognormalParamsFromMD(mean,std_dev)); + } + + /// Exponential distribution with given mean + + /// This function generates an exponential distribution random number + /// with mean <tt>1/lambda</tt>. + /// + double exponential(double lambda=1.0) + { + return -std::log(1.0-real<double>())/lambda; + } + + /// Gamma distribution with given integer shape + + /// This function generates a gamma distribution random number. + /// + ///\param k shape parameter (<tt>k>0</tt> integer) + double gamma(int k) + { + double s = 0; + for(int i=0;i<k;i++) s-=std::log(1.0-real<double>()); + return s; + } + + /// Gamma distribution with given shape and scale parameter + + /// This function generates a gamma distribution random number. + /// + ///\param k shape parameter (<tt>k>0</tt>) + ///\param theta scale parameter + /// + double gamma(double k,double theta=1.0) + { + double xi,nu; + const double delta = k-std::floor(k); + const double v0=E/(E-delta); + do { + double V0=1.0-real<double>(); + double V1=1.0-real<double>(); + double V2=1.0-real<double>(); + if(V2<=v0) + { + xi=std::pow(V1,1.0/delta); + nu=V0*std::pow(xi,delta-1.0); + } + else + { + xi=1.0-std::log(V1); + nu=V0*std::exp(-xi); + } + } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi)); + return theta*(xi+gamma(int(std::floor(k)))); + } + + /// Weibull distribution + + /// This function generates a Weibull distribution random number. + /// + ///\param k shape parameter (<tt>k>0</tt>) + ///\param lambda scale parameter (<tt>lambda>0</tt>) + /// + double weibull(double k,double lambda) + { + return lambda*pow(-std::log(1.0-real<double>()),1.0/k); + } + + /// Pareto distribution + + /// This function generates a Pareto distribution random number. + /// + ///\param k shape parameter (<tt>k>0</tt>) + ///\param x_min location parameter (<tt>x_min>0</tt>) + /// + double pareto(double k,double x_min) + { + return exponential(gamma(k,1.0/x_min))+x_min; + } + + /// Poisson distribution + + /// This function generates a Poisson distribution random number with + /// parameter \c lambda. + /// + /// The probability mass function of this distribusion is + /// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f] + /// \note The algorithm is taken from the book of Donald E. Knuth titled + /// ''Seminumerical Algorithms'' (1969). Its running time is linear in the + /// return value. + + int poisson(double lambda) + { + const double l = std::exp(-lambda); + int k=0; + double p = 1.0; + do { + k++; + p*=real<double>(); + } while (p>=l); + return k-1; + } + + ///@} + + ///\name Two Dimensional Distributions + /// + ///@{ + + /// Uniform distribution on the full unit circle + + /// Uniform distribution on the full unit circle. + /// + dim2::Point<double> disc() + { + double V1,V2; + do { + V1=2*real<double>()-1; + V2=2*real<double>()-1; + + } while(V1*V1+V2*V2>=1); + return dim2::Point<double>(V1,V2); + } + /// A kind of two dimensional normal (Gauss) distribution + + /// This function provides a turning symmetric two-dimensional distribution. + /// Both coordinates are of standard normal distribution, but they are not + /// independent. + /// + /// \note The coordinates are the two random variables provided by + /// the Box-Muller method. + dim2::Point<double> gauss2() + { + double V1,V2,S; + do { + V1=2*real<double>()-1; + V2=2*real<double>()-1; + S=V1*V1+V2*V2; + } while(S>=1); + double W=std::sqrt(-2*std::log(S)/S); + return dim2::Point<double>(W*V1,W*V2); + } + /// A kind of two dimensional exponential distribution + + /// This function provides a turning symmetric two-dimensional distribution. + /// The x-coordinate is of conditionally exponential distribution + /// with the condition that x is positive and y=0. If x is negative and + /// y=0 then, -x is of exponential distribution. The same is true for the + /// y-coordinate. + dim2::Point<double> exponential2() + { + double V1,V2,S; + do { + V1=2*real<double>()-1; + V2=2*real<double>()-1; + S=V1*V1+V2*V2; + } while(S>=1); + double W=-std::log(S)/S; + return dim2::Point<double>(W*V1,W*V2); + } + + ///@} + }; + + + extern Random rnd; + +} + +#endif |