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/* -*- 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> &params)
{
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