Program Listing for File RNGController.h¶
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//This file is part of necsim project which is released under MIT license.
//See file **LICENSE.txt** or visit https://opensource.org/licenses/MIT) for full license details.
#ifndef FATTAIL_H
#define FATTAIL_H
#include <cstdio>
#include <string>
#include <iomanip>
#define _USE_MATH_DEFINES
#include <cmath>
#include <algorithm>
#include <vector>
#include <iostream>
#include <fstream>
#include <climits>
#include "Logging.h"
#include "Xoroshiro256plus.h"
#define PARAM_R 3.44428647676
using namespace std;
namespace random_numbers
{
/* tabulated values for the heigt of the Ziggurat levels */
constexpr static double ytab[128] = {1, 0.963598623011, 0.936280813353, 0.913041104253, 0.892278506696,
0.873239356919, 0.855496407634, 0.838778928349, 0.822902083699, 0.807732738234,
0.793171045519, 0.779139726505, 0.765577436082, 0.752434456248, 0.739669787677,
0.727249120285, 0.715143377413, 0.703327646455, 0.691780377035, 0.68048276891,
0.669418297233, 0.65857233912, 0.647931876189, 0.637485254896, 0.62722199145,
0.617132611532, 0.607208517467, 0.597441877296, 0.587825531465, 0.578352913803,
0.569017984198, 0.559815170911, 0.550739320877, 0.541785656682, 0.532949739145,
0.524227434628, 0.515614886373, 0.507108489253, 0.498704867478, 0.490400854812,
0.482193476986, 0.47407993601, 0.466057596125, 0.458123971214, 0.450276713467,
0.442513603171, 0.434832539473, 0.427231532022, 0.419708693379, 0.41226223212,
0.404890446548, 0.397591718955, 0.390364510382, 0.383207355816, 0.376118859788,
0.369097692334, 0.362142585282, 0.355252328834, 0.348425768415, 0.341661801776,
0.334959376311, 0.328317486588, 0.321735172063, 0.31521151497, 0.308745638367,
0.302336704338, 0.29598391232, 0.289686497571, 0.283443729739, 0.27725491156,
0.271119377649, 0.265036493387, 0.259005653912, 0.253026283183, 0.247097833139,
0.241219782932, 0.235391638239, 0.229612930649, 0.223883217122, 0.218202079518,
0.212569124201, 0.206983981709, 0.201446306496, 0.195955776745, 0.190512094256,
0.185114984406, 0.179764196185, 0.174459502324, 0.169200699492, 0.1639876086,
0.158820075195, 0.153697969964, 0.148621189348, 0.143589656295, 0.138603321143,
0.133662162669, 0.128766189309, 0.123915440582, 0.119109988745, 0.114349940703,
0.10963544023, 0.104966670533, 0.100343857232, 0.0957672718266,
0.0912372357329, 0.0867541250127, 0.082318375932, 0.0779304915295,
0.0735910494266, 0.0693007111742, 0.065060233529, 0.0608704821745,
0.056732448584, 0.05264727098, 0.0486162607163, 0.0446409359769,
0.0407230655415, 0.0368647267386, 0.0330683839378, 0.0293369977411,
0.0256741818288, 0.0220844372634, 0.0185735200577, 0.0151490552854,
0.0118216532614, 0.00860719483079, 0.00553245272614, 0.00265435214565};
/* tabulated values for 2^24 times x[i]/x[i+1],
* used to accept for U*x[i+1]<=x[i] without any floating point operations */
constexpr static unsigned long ktab[128] = {0, 12590644, 14272653, 14988939, 15384584, 15635009, 15807561, 15933577,
16029594, 16105155, 16166147, 16216399, 16258508, 16294295, 16325078,
16351831, 16375291, 16396026, 16414479, 16431002, 16445880, 16459343,
16471578, 16482744, 16492970, 16502368, 16511031, 16519039, 16526459,
16533352, 16539769, 16545755, 16551348, 16556584, 16561493, 16566101,
16570433, 16574511, 16578353, 16581977, 16585398, 16588629, 16591685,
16594575, 16597311, 16599901, 16602354, 16604679, 16606881, 16608968,
16610945, 16612818, 16614592, 16616272, 16617861, 16619363, 16620782,
16622121, 16623383, 16624570, 16625685, 16626730, 16627708, 16628619,
16629465, 16630248, 16630969, 16631628, 16632228, 16632768, 16633248,
16633671, 16634034, 16634340, 16634586, 16634774, 16634903, 16634972,
16634980, 16634926, 16634810, 16634628, 16634381, 16634066, 16633680,
16633222, 16632688, 16632075, 16631380, 16630598, 16629726, 16628757,
16627686, 16626507, 16625212, 16623794, 16622243, 16620548, 16618698,
16616679, 16614476, 16612071, 16609444, 16606571, 16603425, 16599973,
16596178, 16591995, 16587369, 16582237, 16576520, 16570120, 16562917,
16554758, 16545450, 16534739, 16522287, 16507638, 16490152, 16468907,
16442518, 16408804, 16364095, 16301683, 16207738, 16047994, 15704248,
15472926};
/* tabulated values of 2^{-24}*x[i] */
constexpr static double wtab[128] = {1.62318314817e-08, 2.16291505214e-08, 2.54246305087e-08, 2.84579525938e-08,
3.10340022482e-08, 3.33011726243e-08, 3.53439060345e-08, 3.72152672658e-08,
3.8950989572e-08, 4.05763964764e-08, 4.21101548915e-08, 4.35664624904e-08,
4.49563968336e-08, 4.62887864029e-08, 4.75707945735e-08, 4.88083237257e-08,
5.00063025384e-08, 5.11688950428e-08, 5.22996558616e-08, 5.34016475624e-08,
5.44775307871e-08, 5.55296344581e-08, 5.65600111659e-08, 5.75704813695e-08,
5.85626690412e-08, 5.95380306862e-08, 6.04978791776e-08, 6.14434034901e-08,
6.23756851626e-08, 6.32957121259e-08, 6.42043903937e-08, 6.51025540077e-08,
6.59909735447e-08, 6.68703634341e-08, 6.77413882848e-08, 6.8604668381e-08,
6.94607844804e-08, 7.03102820203e-08, 7.11536748229e-08, 7.1991448372e-08,
7.2824062723e-08, 7.36519550992e-08, 7.44755422158e-08, 7.52952223703e-08,
7.61113773308e-08, 7.69243740467e-08, 7.77345662086e-08, 7.85422956743e-08,
7.93478937793e-08, 8.01516825471e-08, 8.09539758128e-08, 8.17550802699e-08,
8.25552964535e-08, 8.33549196661e-08, 8.41542408569e-08, 8.49535474601e-08,
8.57531242006e-08, 8.65532538723e-08, 8.73542180955e-08, 8.8156298059e-08,
8.89597752521e-08, 8.97649321908e-08, 9.05720531451e-08, 9.138142487e-08,
9.21933373471e-08, 9.30080845407e-08, 9.38259651738e-08, 9.46472835298e-08,
9.54723502847e-08, 9.63014833769e-08, 9.71350089201e-08, 9.79732621669e-08,
9.88165885297e-08, 9.96653446693e-08, 1.00519899658e-07, 1.0138063623e-07,
1.02247952126e-07, 1.03122261554e-07, 1.04003996769e-07, 1.04893609795e-07,
1.05791574313e-07, 1.06698387725e-07, 1.07614573423e-07, 1.08540683296e-07,
1.09477300508e-07, 1.1042504257e-07, 1.11384564771e-07, 1.12356564007e-07,
1.13341783071e-07, 1.14341015475e-07, 1.15355110887e-07, 1.16384981291e-07,
1.17431607977e-07, 1.18496049514e-07, 1.19579450872e-07, 1.20683053909e-07,
1.21808209468e-07, 1.2295639141e-07, 1.24129212952e-07, 1.25328445797e-07,
1.26556042658e-07, 1.27814163916e-07, 1.29105209375e-07, 1.30431856341e-07,
1.31797105598e-07, 1.3320433736e-07, 1.34657379914e-07, 1.36160594606e-07,
1.37718982103e-07, 1.39338316679e-07, 1.41025317971e-07, 1.42787873535e-07,
1.44635331499e-07, 1.4657889173e-07, 1.48632138436e-07, 1.50811780719e-07,
1.53138707402e-07, 1.55639532047e-07, 1.58348931426e-07, 1.61313325908e-07,
1.64596952856e-07, 1.68292495203e-07, 1.72541128694e-07, 1.77574279496e-07,
1.83813550477e-07, 1.92166040885e-07, 2.05295471952e-07, 2.22600839893e-07};
class RNGController : public virtual Xoroshiro256plus
{
private:
bool seeded;
uint64_t seed;
// for the L value of the dispersal kernel (the width - does not affect the shape).
double tau;
// for the sigma value of the dispersal kernel (the variance of a normal distribution).
double sigma;
typedef double (RNGController::*fptr)(); // once setup will contain the dispersal function to use for this simulation.
fptr dispersalFunction;
// once setup will contain the dispersal function for the minimum dispersal distance.
typedef double (RNGController::*fptr2)(const double &min_distance);
fptr2 dispersalFunctionMinDistance;
// the probability that dispersal comes from the uniform distribution. This is only relevant for uniform dispersals.
double m_prob;
// the cutoff for the uniform dispersal function i.e. the maximum value to be drawn from the uniform distribution.
double cutoff;
public:
RNGController() : Xoroshiro256plus(), seeded(false), seed(0), tau(0.0), sigma(0.0), dispersalFunction(nullptr),
dispersalFunctionMinDistance(nullptr), m_prob(0.0), cutoff(0.0)
{
}
void setSeed(uint64_t seed) override
{
if(!seeded)
{
Xoroshiro256plus::setSeed(seed);
this->seed = seed;
seeded = true;
}
else
{
throw runtime_error("Trying to set the seed again: this can only be set once.");
}
}
void wipeSeed()
{
seeded = false;
}
unsigned long i0(unsigned long max)
{
return (unsigned long) (d01() * (max + 1));
}
double norm()
{
unsigned long U, sign, i, j;
double x, y;
while(true)
{
U = i0(UINT32_MAX);
i = U & 0x0000007F; /* 7 bit to choose the step */
sign = U & 0x00000080; /* 1 bit for the sign */
j = U >> 8; /* 24 bit for the x-value */
x = j * wtab[i];
if(j < ktab[i])
{
break;
}
if(i < 127)
{
double y0, y1;
y0 = ytab[i];
y1 = ytab[i + 1];
y = y1 + (y0 - y1) * d01();
}
else
{
x = PARAM_R - log(1.0 - d01()) / PARAM_R;
y = exp(-PARAM_R * (x - 0.5 * PARAM_R)) * d01();
}
if(y < exp(-0.5 * x * x))
{
break;
}
}
return sign ? sigma * x : -sigma * x;
}
double rayleigh()
{
return sigma * pow(-2 * log(d01()), 0.5);
}
double rayleighMinDist(const double &dist)
{
double min_prob = rayleighCDF(dist);
double rand_prob = min_prob + (1 - min_prob) * d01();
double out = sigma * pow(-2 * log(rand_prob), 0.5);
if(out < dist)
{
// This probably means that the rayleigh distribution has a less-than-machine-precision probability of
// producing this distance.
// Therefore, we just return the distance
return dist;
}
return out;
}
double rayleighCDF(const double &dist)
{
return 1 - exp(-pow(dist, 2.0) / (2.0 * pow(sigma, 2.0)));
}
void setDispersalParams(const double sigmain, const double tauin)
{
sigma = sigmain;
tau = tauin; // used to invert the sign here, doesn't any more.
}
double fattail(double z)
{
double result;
result = pow((pow(d01(), (1.0 / (1.0 - z))) - 1.0), 0.5);
return result;
}
double fattailCDF(const double &distance)
{
return (1 - pow((1 + ((distance * distance) / (tau * sigma * sigma))), (-tau / 2)));
}
double fattailMinDistance(const double &min_distance)
{
double prob = fattailCDF(min_distance);
double random_number = 1 - (prob + d01() * (1 - prob));
double result = sigma * pow((tau * (pow(random_number, -2.0 / tau)) - 1.0), 0.5);
// This is an approximation for scenarios when the probability of dispersing very long distances
// is less than machine precision
if(result < min_distance)
{
result = fattail() + min_distance;
}
return result;
}
// this new version corrects the 1.0 to 2.0 and doesn't require the values to be passed every time.
double fattail()
{
double result;
// old function version (kept for reference)
// result = (tau * pow((pow(d01(),(2.0/(2.0-sigma)))-1.0),0.5));
result = (sigma * pow((tau * (pow(d01(), -2.0 / tau)) - 1.0), 0.5));
return result;
}
double fattail_old()
{
double result;
result = (sigma * pow((pow(d01(), (2.0 / (2.0 + tau))) - 1.0), 0.5));
return result;
}
double direction()
{
return (d01() * 2 * M_PI);
}
bool event(double event_probability)
{
if(event_probability < 0.000001)
{
if(d01() <= 0.000001)
{
return (event(event_probability * 1000000.0));
}
return false;
}
if(event_probability > 0.999999)
{
return (!(event(1.0 - event_probability)));
}
return (d01() <= event_probability);
}
double normUniform()
{
// Check if the dispersal event comes from the uniform distribution
if(d01() < m_prob)
{
// Then it does come from the uniform distribution
return uniform();
}
return rayleigh();
}
double normUniformMinDistance(const double &min_distance)
{
if(d01() < m_prob)
{
// Then it does come from the uniform distribution
return uniformMinDistance(min_distance);
}
return rayleighMinDist(min_distance);
}
double uniform()
{
return d01() * cutoff;
}
double uniformMinDistance(const double &min_distance)
{
if(min_distance > cutoff)
{
// Note this may introduce problems for studies of extremely isolated islands
// I've left this in to make it much easier to deal with scenarios where the
// disappearing habitat pixel is further from the nearest habitat pixel than
// the maximum dispersal distance
return min_distance;
}
return min_distance + d01() * (cutoff - min_distance);
}
double uniformUniform()
{
if(d01() < 0.5)
{
// Then value comes from the first uniform distribution
return (uniform() * 0.1);
}
// Then the value comes from the second uniform distribution
return 0.9 * cutoff + (uniform() * 0.1);
}
double uniformUniformMinDistance(const double &min_distance)
{
if(d01() < 0.5)
{
// Then value comes from the first uniform distribution
if(min_distance > cutoff * 0.1)
{
return uniformMinDistance(min_distance * 10) * 0.1;
}
}
// Then the value comes from the second uniform distribution
return uniformMinDistance(max(min_distance, 0.9 * cutoff));
}
void setDispersalMethod(const string &dispersal_method, const double &m_probin, const double &cutoffin)
{
if(dispersal_method == "normal")
{
dispersalFunction = &RNGController::rayleigh;
dispersalFunctionMinDistance = &RNGController::rayleighMinDist;
if(sigma < 0)
{
throw invalid_argument("Cannot have negative sigma with normal dispersal");
}
}
else if(dispersal_method == "fat-tail" || dispersal_method == "fat-tailed")
{
dispersalFunction = &RNGController::fattail;
dispersalFunctionMinDistance = &RNGController::fattailMinDistance;
if(tau < 0 || sigma < 0)
{
throw invalid_argument("Cannot have negative sigma or tau with fat-tailed dispersal");
}
}
else if(dispersal_method == "norm-uniform")
{
dispersalFunction = &RNGController::normUniform;
dispersalFunctionMinDistance = &RNGController::normUniformMinDistance;
if(sigma < 0)
{
throw invalid_argument("Cannot have negative sigma with normal dispersal");
}
}
else if(dispersal_method == "uniform-uniform")
{
// This is just here for testing purposes
dispersalFunction = &RNGController::uniformUniform;
dispersalFunctionMinDistance = &RNGController::uniformUniformMinDistance;
}
// Also provided the old version of the fat-tailed dispersal kernel
else if(dispersal_method == "fat-tail-old")
{
dispersalFunction = &RNGController::fattail_old;
dispersalFunctionMinDistance = &RNGController::fattailMinDistance;
if(tau > -2 || sigma < 0)
{
throw invalid_argument(
"Cannot have sigma < 0 or tau > -2 with fat-tailed dispersal (old implementation).");
}
}
else
{
throw runtime_error("Dispersal method not detected. Check implementation exists");
}
m_prob = m_probin;
cutoff = cutoffin;
}
double dispersal()
{
return min(double(LONG_MAX), (this->*dispersalFunction)());
}
double dispersalMinDistance(const double &min_distance)
{
return min(double(LONG_MAX), (this->*dispersalFunctionMinDistance)(min_distance));
}
unsigned long randomLogarithmic(long double alpha)
{
double u_2 = d01();
if(u_2 > alpha)
{
return 1;
}
long double h = log(1 - alpha);
long double q = 1 - exp(d01() * h);
if(u_2 < (q * q))
{
return static_cast<unsigned long>(floor(1 + log(u_2) / log(q)));
}
else if(u_2 > q)
{
return 1;
}
else
{
return 2;
}
}
double randomExponential(double lambda)
{
return exponentialDistribution(lambda, d01());
}
template<typename T>
const static T exponentialDistribution(const T lambda, const T r)
{
return -log(r) / lambda;
}
friend ostream &operator<<(ostream &os, const RNGController &r)
{
os << setprecision(64);
os << r.seed << "," << r.seeded << ",";
os << r.tau << "," << r.sigma << "," << r.m_prob << "," << r.cutoff << ",";
os << static_cast<const Xoroshiro256plus &>(r);
return os;
}
friend istream &operator>>(istream &is, RNGController &r)
{
char delim;
is >> r.seed >> delim >> r.seeded >> delim >> r.tau >> delim >> r.sigma >> delim >> r.m_prob >> delim;
is >> r.cutoff >> delim >> static_cast<Xoroshiro256plus &>(r);
return is;
}
};
}
#endif