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EcoMug.h
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EcoMug.h
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/////////////////////////////////////////////////////////////////////////////////////
// EcoMug: Efficient COsmic MUon Generator //
// Copyright (C) 2023 Davide Pagano <[email protected]> //
// //
// EcoMug is based on the following work: //
// D. Pagano, G. Bonomi, A. Donzella, A. Zenoni, G. Zumerle, N. Zurlo, //
// "EcoMug: an Efficient COsmic MUon Generator for cosmic-ray muons applications", //
// doi:10.1016/j.nima.2021.165732 //
// //
// This program is free software: you can redistribute it and/or modify //
// it under the terms of the GNU General Public License as published by //
// the Free Software Foundation, either version 3 of the License, or //
// (at your option) any later version. //
// //
// This program is distributed in the hope that it will be useful, //
// but WITHOUT ANY WARRANTY; without even the implied warranty of //
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the //
// GNU General Public License for more details. //
// //
// You should have received a copy of the GNU General Public License //
// along with this program. If not, see <https://www.gnu.org/licenses/>. //
/////////////////////////////////////////////////////////////////////////////////////
#ifndef EcoMug_H
#define EcoMug_H
#include <cmath>
#include <array>
#include <random>
#include <functional>
#include <iostream>
#include <initializer_list>
#include <sstream>
#define ECOMUG_VERSION "2.1"
#ifndef M_PI
# define M_PI_NOT_DEFINED
# define M_PI 3.14159265358979323846
#endif
namespace EMUnits {
// Default units:
// meter (m)
// second (s)
// Giga electron Volt (GeV)
// radian (rad)
// Lengths and areas
static const double m = 1.;
static const double cm = 1.e-2*m;
static const double mm = 1.e-3*m;
static const double km = 1000.*m;
static const double mm2 = mm*mm;
static const double cm2 = cm*cm;
static const double m2 = m*m;
static const double km2 = km*km;
// Angles
static const double rad = 1.;
static const double mrad = 1.e-3*rad;
static const double deg = (M_PI/180.0)*rad;
// Time
static const double s = 1.;
static const double ms = 1.e-3*s;
static const double us = 1.e-6*s;
static const double ns = 1.e-9*s;
static const double min = 60.*s;
static const double hour = 60.*min;
static const double day = 24.*hour;
static const double hertz = 1./s;
// Energy/momentum
static const double GeV = 1.;
static const double MeV = 1.e-3*GeV;
static const double keV = 1.e-3*MeV;
static const double TeV = 1.e+6*MeV;
static const double eV = 1.e-6*MeV;
};
///////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////
//! Class for the logging system
class EMLog {
public:
enum TLogLevel {ERROR, WARNING, INFO, DEBUG};
enum TMsgType {EcoMug, EMRandom, EMMultiGen, EMMaximization, UNKNOWN};
EMLog() {};
virtual ~EMLog() {
os << std::endl;
fprintf(stderr, "%s", os.str().c_str());
fflush(stderr);
};
std::ostringstream& Get(TLogLevel level = INFO);
void Get(TLogLevel level, const std::string& msg, TMsgType type = EcoMug) {
std::cout << "[EcoMug v" << ECOMUG_VERSION << "] [";
std::cout << ToString(level);
if (type != UNKNOWN) std::cout << " in " << ToString(type);
std::cout << "]: ";
std::cout << std::string(level > DEBUG ? level - DEBUG : 0, '\t');
std::cout << msg << "\n";
};
public:
static std::string ToString(TLogLevel level) {
static const char* const buffer[] = {"ERROR", "WARNING", "INFO", "DEBUG"};
return buffer[level];
};
static std::string ToString(TMsgType type) {
static const char* const buffer[] = {"EcoMug", "EMRandom", "EMMultiGen", "EMMaximization", "UNKNOWN"};
return buffer[type];
};
static TLogLevel FromString(const std::string& level) {
if (level == "DEBUG")
return DEBUG;
if (level == "INFO")
return INFO;
if (level == "WARNING")
return WARNING;
if (level == "ERROR")
return ERROR;
EMLog().Get(WARNING) << "Unknown logging level '" << level << "'. Using INFO level as default.";
return INFO;
};
static EMLog::TLogLevel ReportingLevel;
private:
EMLog(const EMLog&);
EMLog& operator =(const EMLog&);
std::ostringstream os;
};
#define EMLogger(level, msg, type) \
if (level > EMLog::ReportingLevel) ; \
else EMLog().Get(level, msg, type)
//EMLog::TLogLevel EMLog::ReportingLevel = WARNING;
///////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////
//! Fast generation of random numbers
//! This class is based on the xoroshiro128+ generator.
//! https://prng.di.unimi.it/
class EMRandom {
public:
EMRandom() {
std::random_device rd;
std::mt19937 gen(rd());
std::uniform_int_distribution<std::uint64_t> dis(0, std::numeric_limits<std::uint64_t>::max());
s[0] = dis(gen);
s[1] = dis(gen);
};
void SetSeed(std::uint64_t seed) {
s[0] = seed;
s[1] = seed;
};
double GenerateRandomDouble() {
std::uint64_t x = next();
return to_double(x);
};
double GenerateRandomDouble(double x1, double x2) {
return (x2-x1)*GenerateRandomDouble()+x1;
};
int64_t rotl(const std::uint64_t x, int k) {
return (x << k) | (x >> (64 - k));
};
std::uint64_t next() {
const std::uint64_t s0 = s[0];
std::uint64_t s1 = s[1];
const std::uint64_t result = s0 + s1;
s1 ^= s0;
s[0] = rotl(s0, 55) ^ s1 ^ (s1 << 14);
s[1] = rotl(s1, 36);
return result;
};
double to_double(std::uint64_t x) {
union U {
std::uint64_t i;
double d;
};
U u = { UINT64_C(0x3FF) << 52 | x >> 12 };
return u.d - 1.0;
};
std::uint64_t s[2];
};
///////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////
//! Class for maximization based on "Whale Optimization Algorithm"
//! doi:10.1016/j.advengsoft.2016.01.008
class EMMaximization {
private:
EMRandom mRandom;
std::size_t mPopSize;
std::size_t mNIter;
int mGenMethod; // 0 = sky, 1 = cylinder, 2 = hspere
double m_a;
double m_a2;
std::vector<std::vector<double> > mRanges;
std::vector<std::vector<double> > mPopulation;
double mBestCost;
std::vector<double> mBestSolution;
std::function<double(double, double)> mFunc;
public:
EMMaximization(const EMRandom& random, int genMethod) : mRandom(random), mPopSize(200),
mNIter(500), mGenMethod(genMethod), m_a(0.), m_a2(0.), mBestCost(-1.) {
mFunc = &DefaultJ;
};
///////////////////////////////////////////////////////////////
static double DefaultJ(double p, double theta) {
double n = std::max(0.1, 2.856-0.655*log(p));
return 1600*pow(p, 0.279)*pow(cos(theta), n);
}
///////////////////////////////////////////////////////////////
void SetParameters(double minP, double maxP, double minTheta, double maxTheta) {
mRanges.push_back({minP, maxP});
mRanges.push_back({minTheta, maxTheta});
}
///////////////////////////////////////////////////////////////
void SetParameters(double minP, double maxP, double minTheta, double maxTheta, double minPhi, double maxPhi) {
mRanges.push_back({minP, maxP});
mRanges.push_back({minTheta, maxTheta});
mRanges.push_back({minPhi, maxPhi});
mRanges.push_back({0, M_PI/2.});
}
///////////////////////////////////////////////////////////////
void SetFunction(std::function<double(double, double)> func) {
mFunc = func;
}
///////////////////////////////////////////////////////////////
double SkyFunc(double p, double theta) {
return mFunc(p, theta)*cos(theta)*sin(theta);
}
///////////////////////////////////////////////////////////////
double CylFunc(double p, double theta) {
return mFunc(p, theta)*pow(sin(theta), 2);
}
///////////////////////////////////////////////////////////////
double HSFunc(double p, double theta, double phi, double theta0) {
return mFunc(p, theta)*(sin(theta0)*sin(theta)*cos(phi) + cos(theta0)*cos(theta))*sin(theta);
}
///////////////////////////////////////////////////////////////
double Evaluate(std::vector<double> &v) {
if (mGenMethod == 0) {
return SkyFunc(v[0], v[1]);
} else if (mGenMethod == 1) {
return CylFunc(v[0], v[1]);
} else {
return HSFunc(v[0], v[1], v[2], v[3]);
}
return -1;
}
///////////////////////////////////////////////////////////////
void Evaluate() {
double value;
for (std::size_t i = 0; i < mPopSize; ++i) {
value = Evaluate(mPopulation[i]);
if (value > mBestCost) {
mBestCost = value;
mBestSolution = mPopulation[i];
}
}
}
///////////////////////////////////////////////////////////////
void Init() {
std::size_t dim = mRanges.size();
mPopulation.resize(mPopSize);
for (std::size_t i = 0; i < mPopSize; ++i) {
mPopulation[i].resize(dim);
for (std::size_t j = 0; j < dim; ++j) {
mPopulation[i][j] = mRandom.GenerateRandomDouble(mRanges[j][0], mRanges[j][1]);
}
}
}
///////////////////////////////////////////////////////////////
void UpdateParameters(std::size_t t) {
m_a = 2. - t*(2./mNIter);
m_a2 = -1. + t*((-1.)/mNIter);
}
///////////////////////////////////////////////////////////////
void Move() {
double r1, r2, A, C, b, l, rw, p, D_tmp, D_best, distance;
std::vector<double> tmp;
for (std::size_t i = 0; i < mPopulation.size(); ++i) {
r1 = mRandom.GenerateRandomDouble();
r2 = mRandom.GenerateRandomDouble();
A = 2*m_a*r1-m_a;
C = 2*r2;
b = 1.;
l = (m_a2-1)*mRandom.GenerateRandomDouble()+1;
p = mRandom.GenerateRandomDouble();
for (std::size_t j = 0; j < mPopulation[0].size(); ++j) {
if (p < 0.5) {
if (fabs(A) >= 1) {
rw = floor(mRandom.GenerateRandomDouble()*mPopulation.size());
tmp = mPopulation[rw];
D_tmp = fabs(C*tmp[j] - mPopulation[i][j]);
mPopulation[i][j] = tmp[j] - A*D_tmp;
} else {
D_best = fabs(C*mBestSolution[j] - mPopulation[i][j]);
mPopulation[i][j] = mBestSolution[j]-A*D_best;
}
} else {
distance = fabs(mBestSolution[j] - mPopulation[i][j]);
mPopulation[i][j] = distance*exp(b*l)*cos(l*2*M_PI) + mBestSolution[j];
}
if (mPopulation[i][j] < mRanges[j][0]) mPopulation[i][j] = mRanges[j][0];
if (mPopulation[i][j] > mRanges[j][1]) mPopulation[i][j] = mRanges[j][1];
}
}
}
///////////////////////////////////////////////////////////////
double Maximize() {
Init();
Evaluate();
for (std::size_t iter = 1; iter < mNIter; ++iter) {
UpdateParameters(iter);
Move();
Evaluate();
}
return mBestCost;
}
};
///////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////
//! Class for the generation of cosmic muons
class EcoMug {
friend class EMRandom;
public:
/// Possible generation methods
enum EMGeometry {
Sky, ///< generation from a plane (flat sky)
Cylinder, ///< generation from a cylinder
HSphere ///< generation from a half-sphere
};
private:
EMGeometry mGenMethod;
std::array<double, 3> mGenerationPosition;
double mGenerationTheta;
double mGenerationPhi;
double mGenerationMomentum;
double mMinimumMomentum;
double mMaximumMomentum;
double mMinimumTheta;
double mMaximumTheta;
double mMinimumPhi;
double mMaximumPhi;
int mCharge;
double mHorizontalRate;
double mCylinderMinPositionPhi;
double mCylinderMaxPositionPhi;
double mHSphereMinPositionPhi;
double mHSphereMaxPositionPhi;
double mHSphereMinPositionTheta;
double mHSphereMaxPositionTheta;
double mHSphereCosMinPositionTheta;
double mHSphereCosMaxPositionTheta;
double mJPrime;
double mN;
double mRandAccRej;
double mPhi0;
double mTheta0;
bool mAccepted;
std::array<double, 2> mSkySize;
std::array<double, 3> mSkyCenterPosition;
double mCylinderHeight;
double mCylinderRadius;
std::array<double, 3> mCylinderCenterPosition;
double mHSphereRadius;
double mMaxFuncSkyCylinder;
std::array<double, 3> mHSphereCenterPosition;
bool mCustomJ;
EMRandom mRandom;
std::default_random_engine mEngineC;
std::discrete_distribution<int> mDiscDistC;
std::array<double, 3> mMaxJ;
std::array<double, 3> mMaxCustomJ;
std::function<double(double, double)> mJ;
public:
// Default constructor
EcoMug() : mGenMethod(Sky),
mGenerationPosition({{0., 0., 0.}}), mGenerationTheta(0.), mGenerationPhi(0.),
mGenerationMomentum(0.), mMinimumMomentum(0.01), mMaximumMomentum(1000.),
mMinimumTheta(0.), mMaximumTheta(M_PI/2.), mMinimumPhi(0.), mMaximumPhi(2.*M_PI),
mCharge(1), mHorizontalRate(129*EMUnits::hertz/EMUnits::m2), mCylinderMinPositionPhi(0.), mCylinderMaxPositionPhi(2.*M_PI),
mHSphereMinPositionPhi(0.), mHSphereMaxPositionPhi(2.*M_PI), mHSphereMinPositionTheta(0.),
mHSphereMaxPositionTheta(M_PI/2.), mHSphereCosMinPositionTheta(1.), mHSphereCosMaxPositionTheta(0.),
mJPrime(0.), mN(0.), mRandAccRej(0.), mPhi0(0.), mTheta0(0.), mAccepted(false),
mSkySize({{0., 0.}}), mSkyCenterPosition({{0., 0., 0.}}), mCylinderHeight(0.),
mCylinderRadius(0.), mCylinderCenterPosition({{0., 0., 0.}}), mHSphereRadius(0.),
mMaxFuncSkyCylinder(5.3176), mHSphereCenterPosition({{0., 0., 0.}}), mCustomJ(false),
mEngineC(std::random_device{}()) {
mDiscDistC = std::discrete_distribution<int>({128, 100});
mMaxJ = {-1., -1., -1.};
mMaxCustomJ = {-1., -1., -1.};
};
// Copy constructor
EcoMug(const EcoMug& t) {
mGenMethod = t.mGenMethod;
mGenerationPosition = t.mGenerationPosition;
mGenerationTheta = t.mGenerationTheta;
mGenerationPhi = t.mGenerationPhi;
mGenerationMomentum = t.mGenerationMomentum;
mMinimumMomentum = t.mMinimumMomentum;
mMaximumMomentum = t.mMaximumMomentum;
mMinimumTheta = t.mMinimumTheta;
mMaximumTheta = t.mMaximumTheta;
mMinimumPhi = t.mMinimumPhi;
mMaximumPhi = t.mMaximumPhi;
mCharge = t.mCharge;
mHorizontalRate = t.mHorizontalRate;
mCylinderMinPositionPhi = t.mCylinderMinPositionPhi;
mCylinderMaxPositionPhi = t.mCylinderMaxPositionPhi;
mHSphereMinPositionPhi = t.mHSphereMinPositionPhi;
mHSphereMaxPositionPhi = t.mHSphereMaxPositionPhi;
mHSphereMinPositionTheta = t.mHSphereMinPositionTheta;
mHSphereMaxPositionTheta = t.mHSphereMaxPositionTheta;
mHSphereCosMinPositionTheta = t.mHSphereCosMinPositionTheta;
mHSphereCosMaxPositionTheta = t.mHSphereCosMaxPositionTheta;
mJPrime = t.mJPrime;
mN = t.mN;
mRandAccRej = t.mRandAccRej;
mPhi0 = t.mPhi0;
mTheta0 = t.mTheta0;
mAccepted = t.mAccepted;
mSkySize = t.mSkySize;
mSkyCenterPosition = t.mSkyCenterPosition;
mCylinderHeight = t.mCylinderHeight;
mCylinderRadius = t.mCylinderRadius;
mCylinderCenterPosition = t.mCylinderCenterPosition;
mHSphereRadius = t.mHSphereRadius;
mMaxFuncSkyCylinder = t.mMaxFuncSkyCylinder;
mHSphereCenterPosition = t.mHSphereCenterPosition;
mCustomJ = t.mCustomJ;
mRandom = t.mRandom;
mEngineC = t.mEngineC;
mDiscDistC = t.mDiscDistC;
mMaxJ = t.mMaxJ;
mMaxCustomJ = t.mMaxCustomJ;
mJ = t.mJ;
};
///////////////////////////////////////////////////////////////
// Methods to access the parameters of the generated muon
///////////////////////////////////////////////////////////////
/// Get the generation position
const std::array<double, 3>& GetGenerationPosition() const {
return mGenerationPosition;
};
/// Get the generation momentum
double GetGenerationMomentum() const {
return mGenerationMomentum;
};
/// Get the generation momentum
void GetGenerationMomentum(std::array<double, 3>& momentum) const {
momentum = {
mGenerationMomentum*sin(mGenerationTheta)*cos(mGenerationPhi),
mGenerationMomentum*sin(mGenerationTheta)*sin(mGenerationPhi),
mGenerationMomentum*cos(mGenerationTheta)
};
};
/// Get the generation theta
double GetGenerationTheta() const {
return mGenerationTheta;
};
/// Get the generation phi
double GetGenerationPhi() const {
return mGenerationPhi;
};
/// Get charge
int GetCharge() const {
return mCharge;
};
///////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////
// Methods for the geometry of the generation
///////////////////////////////////////////////////////////////
/// Set generation from sky
void SetUseSky() {
mGenMethod = Sky;
};
/// Set cylindrical generation
void SetUseCylinder() {
mGenMethod = Cylinder;
};
/// Set half-sphere generation
void SetUseHSphere() {
mGenMethod = HSphere;
};
/// Set the generation method (Sky, Cylinder or HSphere)
void SetGenerationMethod(EMGeometry genM) {
mGenMethod = genM;
};
/// Get the generation method (Sky, Cylinder or HSphere)
EMGeometry GetGenerationMethod() const {
return mGenMethod;
};
///////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////
// Common methods to all geometries
///////////////////////////////////////////////////////////////
/// Set the differential flux J. Accepted functions are like
/// double J(double momentum, double theta)
/// momentum has to be in GeV/c and theta in radians
void SetDifferentialFlux(std::function<double(double, double)> J) {
mJ = J;
mCustomJ = true;
};
/// Set the seed for the internal PRNG (if 0 a random seed is used)
void SetSeed(std::uint64_t seed) {
if (seed > 0) mRandom.SetSeed(seed);
};
/// Set minimum generation Momentum
void SetMinimumMomentum(double momentum) {
mMinimumMomentum = momentum;
};
/// Set maximum generation Momentum
void SetMaximumMomentum(double momentum) {
mMaximumMomentum = momentum;
};
/// Set minimum generation Theta
void SetMinimumTheta(double theta) {
mMinimumTheta = theta;
};
/// Set maximum generation Theta
void SetMaximumTheta(double theta) {
mMaximumTheta = theta;
};
/// Set minimum generation Phi
void SetMinimumPhi(double phi) {
mMinimumPhi = phi;
};
/// Set maximum generation Phi
void SetMaximumPhi(double phi) {
mMaximumPhi = phi;
};
/// Set the rate of cosmic ray muons per square unit are through
/// a horizontal surface. Default value is 129 Hz/m^2.
void SetHorizontalRate(double rate) {
mHorizontalRate = rate;
};
/// Get minimum generation Momentum
double GetMinimumMomentum() const {
return mMinimumMomentum;
};
/// Get maximum generation Momentum
double GetMaximumMomentum() const {
return mMaximumMomentum;
};
/// Get minimum generation Theta
double GetMinimumTheta() const {
return mMinimumTheta;
};
/// Get maximum generation Theta
double GetMaximumTheta() const {
return mMaximumTheta;
};
/// Get minimum generation Phi
double GetMinimumPhi() const {
return mMinimumPhi;
};
/// Get maximum generation Phi
double GetMaximumPhi() const {
return mMaximumPhi;
};
/// Get horizontal rate of cosmic muons
double GetHorizontalRate() const {
return mHorizontalRate;
};
/// Get the generation surface area
double GetGenSurfaceArea() const {
double area = 0.;
if (mGenMethod == Sky) {
area = mSkySize[0]*mSkySize[1];
} else if (mGenMethod == Cylinder) {
// A = \Delta\phi r h
area = (mCylinderMaxPositionPhi-mCylinderMinPositionPhi)*mCylinderRadius*mCylinderHeight;
} else {
// A = \Delta\phi r^2\left(\cos\theta_{min} - \cos\theta_{max}\right)
area = (mHSphereMaxPositionPhi-mHSphereMinPositionPhi)*pow(mHSphereRadius, 2)*(cos(mHSphereMinPositionTheta) - cos(mHSphereMaxPositionTheta));
}
return area;
};
/// Get the average rate of cosmic muons as well the error on it
/// The optional parameter npoints defines the number
/// of points to be used in the MC integration of the J'
void GetAverageGenRateAndError(double &rate, double &error, int npoints = 1e7) {
// 129.0827 is the integral of the J'prime for the sky in
// the full range of theta, phi and up to 3 TeV in energy.
// For custom J it is the user who should account for the correction.
double k = mHorizontalRate/129.0827;
if (mGenMethod == Sky) {
if (mCustomJ) {
MCJprimeCustomSkyIntegration(rate, error, npoints);
return;
} else MCJprimeSkyIntegration(rate, error, npoints);
} else if (mGenMethod == Cylinder) {
if (mCustomJ) {
MCJprimeCustomCylinderIntegration(rate, error, npoints);
return;
} else MCJprimeCylinderIntegration(rate, error, npoints);
} else {
if (mCustomJ) {
MCJprimeCustomHSphereIntegration(rate, error, npoints);
return;
} else MCJprimeHSphereIntegration(rate, error, npoints);
}
rate *= k;
error *= k;
};
/// Get the average rate of cosmic muons
/// The optional parameter npoints defines the number
/// of points to be used in the MC integration of the J'
double GetAverageGenRate(int npoints = 1e7) {
double rate, error;
GetAverageGenRateAndError(rate, error, npoints);
return rate;
};
/// Get the estimated corresponding to the provided statistics
double GetEstimatedTime(int nmuons) {
if (mCustomJ) return 0.;
return (nmuons/(GetGenSurfaceArea()/EMUnits::m2))/(GetAverageGenRate()/EMUnits::hertz*EMUnits::m2);
};
///////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////
// Methods for the plane-based generation
///////////////////////////////////////////////////////////////
/// Set sky size
void SetSkySize(const std::array<double, 2>& size) {
mSkySize = size;
};
/// Set sky center position
void SetSkyCenterPosition(const std::array<double, 3>& position) {
mSkyCenterPosition = position;
};
double GetSkySize(unsigned int index) {
return mSkySize[index];
};
///////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////
// Methods for the cylinder-based generation
///////////////////////////////////////////////////////////////
/// Set cylinder radius
void SetCylinderRadius(double radius) {
mCylinderRadius = radius;
};
/// Set cylinder height
void SetCylinderHeight(double height) {
mCylinderHeight = height;
};
/// Set cylinder center position
void SetCylinderCenterPosition(const std::array<double, 3>& position) {
mCylinderCenterPosition = position;
};
void SetCylinderMinPositionPhi(double phi) {
mCylinderMinPositionPhi = phi;
};
void SetCylinderMaxPositionPhi(double phi) {
mCylinderMaxPositionPhi = phi;
};
/// Get cylinder radius
double GetCylinderRadius() const {
return mCylinderRadius;
};
/// Get cylinder height
double GetCylinderHeight() const {
return mCylinderHeight;
};
/// Get cylinder center position
const std::array<double, 3>& GetCylinderCenterPosition() const {
return mCylinderCenterPosition;
};
///////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////
// Methods for the half sphere-based generation
///////////////////////////////////////////////////////////////
/// Set half-sphere radius
void SetHSphereRadius(double radius) {
mHSphereRadius = radius;
};
/// Set half-sphere center position
void SetHSphereCenterPosition(const std::array<double, 3>& position) {
mHSphereCenterPosition = position;
};
void SetHSphereMinPositionPhi(double phi) {
mHSphereMinPositionPhi = phi;
};
void SetHSphereMaxPositionPhi(double phi) {
mHSphereMaxPositionPhi = phi;
};
void SetHSphereMinPositionTheta(double theta) {
mHSphereMinPositionTheta = theta;
mHSphereCosMinPositionTheta = cos(mHSphereMinPositionTheta);
};
void SetHSphereMaxPositionTheta(double theta) {
mHSphereMaxPositionTheta = theta;
mHSphereCosMaxPositionTheta = cos(mHSphereMaxPositionTheta);
};
/// Get half-sphere radius
double GetHSphereRadius() const {
return mHSphereRadius;
};
/// Get half-sphere center position
const std::array<double, 3>& GetHSphereCenterPosition() const {
return mHSphereCenterPosition;
};
///////////////////////////////////////////////////////////////
private:
double F1Cumulative(double x) {
return 1. - 8.534790171171021/pow(x + 2.68, 87./40.);
};
double F1Inverse(double x) {
return (2.68 - 2.68*pow(1. - x, 40./87.))/pow(1. - x, 40./87.);
};
double maxSkyJFunc() {
return 1600*pow(mMaximumMomentum, 0.279)*pow(cos(0.76158), 1.1)*sin(0.76158);
};
double maxCylJFunc() {
return 1600*pow(mMaximumMomentum, 0.279)*pow(cos(1.35081), 0.1)*pow(sin(1.35081), 2);
};
double maxHSJFunc() {
return 1600*pow(mMaximumMomentum, 0.279)*pow(cos(1.26452), 0.1)*(sin(1.26452)*sin(1.26452)+cos(1.26452)*cos(1.26452))*sin(1.26452);
};
double GenerateMomentumF1() {
double z = mRandom.GenerateRandomDouble(F1Cumulative(mMinimumMomentum), F1Cumulative(mMaximumMomentum));
return F1Inverse(z);
};
void GeneratePositionSky() {
mGenerationPosition[0] = mRandom.GenerateRandomDouble(mSkyCenterPosition[0]-mSkySize[0]/2., mSkyCenterPosition[0]+mSkySize[0]/2.);
mGenerationPosition[1] = mRandom.GenerateRandomDouble(mSkyCenterPosition[1]-mSkySize[1]/2., mSkyCenterPosition[1]+mSkySize[1]/2.);
mGenerationPosition[2] = mSkyCenterPosition[2];
};
void GeneratePositionCylinder() {
mPhi0 = mRandom.GenerateRandomDouble(mCylinderMinPositionPhi, mCylinderMaxPositionPhi);
mGenerationPosition[0] = mCylinderCenterPosition[0] + mCylinderRadius*cos(mPhi0);
mGenerationPosition[1] = mCylinderCenterPosition[1] + mCylinderRadius*sin(mPhi0);
mGenerationPosition[2] = mRandom.GenerateRandomDouble(mCylinderCenterPosition[2]-mCylinderHeight/2., mCylinderCenterPosition[2]+mCylinderHeight/2.);
};
void ComputeMaximumCustomJ() {
EMMaximization maximizer(mRandom, mGenMethod);
maximizer.SetFunction(mJ);
if (mGenMethod == 0 || mGenMethod == 1) {
maximizer.SetParameters(mMinimumMomentum, mMaximumMomentum, mMinimumTheta, mMaximumTheta);
} else {
maximizer.SetParameters(mMinimumMomentum, mMaximumMomentum, mMinimumTheta, mMaximumTheta, mMinimumPhi, mMaximumPhi);
}
mMaxCustomJ[mGenMethod] = maximizer.Maximize();
};
void ComputeMaximum() {
EMMaximization maximizer(mRandom, mGenMethod);
if (mGenMethod == 0 || mGenMethod == 1) {
maximizer.SetParameters(mMinimumMomentum, mMaximumMomentum, mMinimumTheta, mMaximumTheta);
} else {
maximizer.SetParameters(mMinimumMomentum, mMaximumMomentum, mMinimumTheta, mMaximumTheta, mMinimumPhi, mMaximumPhi);
}
mMaxJ[mGenMethod] = maximizer.Maximize();
};
void MCJprimeCustomSkyIntegration(double &rate, double &error, int npoints) {
double I = 0., I2 = 0., value = 0.;
for (auto i = 0; i < npoints; ++i) {
mGenerationTheta = mRandom.GenerateRandomDouble(mMinimumTheta, mMaximumTheta);
mGenerationMomentum = mRandom.GenerateRandomDouble(mMinimumMomentum, mMaximumMomentum);
value = mJ(mGenerationMomentum, mGenerationTheta)*cos(mGenerationTheta)*sin(mGenerationTheta);
I += value;
I2 += pow(value, 2);
}
double V = (mMaximumMomentum-mMinimumMomentum)*(mMaximumTheta-mMinimumTheta)*(mMaximumPhi-mMinimumPhi);
double expected = I/npoints;
double expectedSquare = I2/npoints;
rate = V*I/npoints;
error = V*pow((expectedSquare-pow(expected,2))/(npoints-1), 0.5);
};
void MCJprimeCustomCylinderIntegration(double &rate, double &error, int npoints) {
double I = 0., I2 = 0., value = 0.;
for (auto i = 0; i < npoints; ++i) {
mGenerationTheta = mRandom.GenerateRandomDouble(mMinimumTheta, mMaximumTheta);
mGenerationPhi = mRandom.GenerateRandomDouble(mMinimumPhi, mMaximumPhi);
mGenerationMomentum = mRandom.GenerateRandomDouble(mMinimumMomentum, mMaximumMomentum);
value = mJ(mGenerationMomentum, mGenerationTheta)*pow(sin(mGenerationTheta), 2)*cos(mGenerationPhi);
if (value < 0) value = 0;
I += value;
I2 += pow(value, 2);
}
double V = (mMaximumMomentum-mMinimumMomentum)*(mMaximumTheta-mMinimumTheta)*(mMaximumPhi-mMinimumPhi);
double expected = I/npoints;
double expectedSquare = I2/npoints;
rate = V*I/npoints;
error = V*pow((expectedSquare-pow(expected,2))/(npoints-1), 0.5);
};
void MCJprimeCustomHSphereIntegration(double &rate, double &error, int npoints) {
double I = 0., I2 = 0., value = 0.;
for (auto i = 0; i < npoints; ++i) {
mTheta0 = mRandom.GenerateRandomDouble(mHSphereMinPositionTheta, mHSphereMaxPositionTheta);
mGenerationTheta = mRandom.GenerateRandomDouble(mMinimumTheta, mMaximumTheta);
mGenerationPhi = mRandom.GenerateRandomDouble(mMinimumPhi, mMaximumPhi);
mGenerationMomentum = mRandom.GenerateRandomDouble(mMinimumMomentum, mMaximumMomentum);
value = mJ(mGenerationMomentum, mGenerationTheta)*(sin(mTheta0)*sin(mGenerationTheta)*sin(mGenerationTheta)*cos(mGenerationPhi)+cos(mTheta0)*cos(mGenerationTheta)*sin(mGenerationTheta))*sin(mTheta0);
if (value < 0) value = 0;
I += value;
I2 += pow(value, 2);
}
double V = (mMaximumMomentum-mMinimumMomentum)*(mMaximumTheta-mMinimumTheta)*(mMaximumPhi-mMinimumPhi)*(mHSphereMaxPositionTheta-mHSphereMinPositionTheta);
double expected = I/npoints;
double expectedSquare = I2/npoints;
rate = V*I/npoints;
error = V*pow((expectedSquare-pow(expected,2))/(npoints-1), 0.5);
};
void MCJprimeSkyIntegration(double &rate, double &error, int npoints) {
double I = 0., I2 = 0., value = 0.;
for (auto i = 0; i < npoints; ++i) {
mGenerationTheta = mRandom.GenerateRandomDouble(mMinimumTheta, mMaximumTheta);
mGenerationMomentum = mRandom.GenerateRandomDouble(mMinimumMomentum, mMaximumMomentum);
mN = 2.856-0.655*log(mGenerationMomentum);
if (mN < 0.1) mN = 0.1;
value = 1600*pow(mGenerationMomentum+2.68, -3.175)*pow(mGenerationMomentum, 0.279)*pow(cos(mGenerationTheta), mN+1)*sin(mGenerationTheta);
I += value;
I2 += pow(value, 2);
}
double V = (mMaximumMomentum-mMinimumMomentum)*(mMaximumTheta-mMinimumTheta)*(mMaximumPhi-mMinimumPhi);
double expected = I/npoints;
double expectedSquare = I2/npoints;
rate = V*I/npoints;
error = V*pow((expectedSquare-pow(expected,2))/(npoints-1), 0.5);
};
void MCJprimeCylinderIntegration(double &rate, double &error, int npoints) {
double I = 0., I2 = 0., value = 0.;
for (auto i = 0; i < npoints; ++i) {
mGenerationTheta = mRandom.GenerateRandomDouble(mMinimumTheta, mMaximumTheta);
mGenerationPhi = mRandom.GenerateRandomDouble(mMinimumPhi, mMaximumPhi);
mGenerationMomentum = mRandom.GenerateRandomDouble(mMinimumMomentum, mMaximumMomentum);
mN = 2.856-0.655*log(mGenerationMomentum);
if (mN < 0.1) mN = 0.1;
value = 1600*pow(mGenerationMomentum+2.68, -3.175)*pow(mGenerationMomentum, 0.279)*pow(cos(mGenerationTheta), mN)*pow(sin(mGenerationTheta), 2)*cos(mGenerationPhi);
if (value < 0) value = 0;
I += value;
I2 += pow(value, 2);
}
double V = (mMaximumMomentum-mMinimumMomentum)*(mMaximumTheta-mMinimumTheta)*(mMaximumPhi-mMinimumPhi);
double expected = I/npoints;
double expectedSquare = I2/npoints;
rate = V*I/npoints;
error = V*pow((expectedSquare-pow(expected,2))/(npoints-1), 0.5);
};
void MCJprimeHSphereIntegration(double &rate, double &error, int npoints) {
double I = 0., I2 = 0., value = 0.;
for (auto i = 0; i < npoints; ++i) {
mTheta0 = mRandom.GenerateRandomDouble(mHSphereMinPositionTheta, mHSphereMaxPositionTheta);
mGenerationTheta = mRandom.GenerateRandomDouble(mMinimumTheta, mMaximumTheta);
mGenerationPhi = mRandom.GenerateRandomDouble(mMinimumPhi, mMaximumPhi);
mGenerationMomentum = mRandom.GenerateRandomDouble(mMinimumMomentum, mMaximumMomentum);
mN = 2.856-0.655*log(mGenerationMomentum);
if (mN < 0.1) mN = 0.1;
value = 1600*pow(mGenerationMomentum+2.68, -3.175)*pow(mGenerationMomentum, 0.279)*pow(cos(mGenerationTheta), mN)*(sin(mTheta0)*sin(mGenerationTheta)*sin(mGenerationTheta)*cos(mGenerationPhi)+cos(mTheta0)*cos(mGenerationTheta)*sin(mGenerationTheta))*sin(mTheta0);
if (value < 0) value = 0;
I += value;
I2 += pow(value, 2);
}
double V = (mMaximumMomentum-mMinimumMomentum)*(mMaximumTheta-mMinimumTheta)*(mMaximumPhi-mMinimumPhi)*(mHSphereMaxPositionTheta-mHSphereMinPositionTheta);
double expected = I/npoints;
double expectedSquare = I2/npoints;
rate = V*I/npoints;
error = V*pow((expectedSquare-pow(expected,2))/(npoints-1), 0.5);
};
public:
///////////////////////////////////////////////////////////////
/// Generate a cosmic muon from the pre-defined J
///////////////////////////////////////////////////////////////
void Generate() {
mAccepted = false;
if (mMaxJ[mGenMethod] < 0) ComputeMaximum();
// Sky or cylinder generation
if (mGenMethod == Sky || mGenMethod == Cylinder) {
// Generation of the momentum and theta angle
while (!mAccepted) {
mRandAccRej = mRandom.GenerateRandomDouble();
mGenerationTheta = mRandom.GenerateRandomDouble(mMinimumTheta, mMaximumTheta);
mGenerationMomentum = GenerateMomentumF1();
mN = 2.856-0.655*log(mGenerationMomentum);
if (mN < 0.1) mN = 0.1;
if (mGenMethod == Sky) {
mJPrime = 1600*pow(mGenerationMomentum, 0.279)*pow(cos(mGenerationTheta), mN+1)*sin(mGenerationTheta);
if (mMaxJ[mGenMethod]*mRandAccRej < mJPrime) mAccepted = true;
}
if(mGenMethod == Cylinder) {
mJPrime = 1600*pow(mGenerationMomentum, 0.279)*pow(cos(mGenerationTheta), mN)*pow(sin(mGenerationTheta), 2);
if (mMaxJ[mGenMethod]*mRandAccRej < mJPrime) mAccepted = true;
}
}
mGenerationTheta = M_PI - mGenerationTheta;
// Generation of the position and phi angle
if (mGenMethod == Sky) {
GeneratePositionSky();
mGenerationPhi = mRandom.GenerateRandomDouble(mMinimumPhi, mMaximumPhi);
}
if (mGenMethod == Cylinder) {
mAccepted = false;
GeneratePositionCylinder();
while (!mAccepted) {
mRandAccRej = mRandom.GenerateRandomDouble();
mGenerationPhi = mRandom.GenerateRandomDouble(mMinimumPhi, mMaximumPhi);
if (mRandAccRej < fabs(cos(mGenerationPhi))) mAccepted = true;
}
mGenerationPhi = mGenerationPhi + mPhi0;
if (mGenerationPhi >= 2.*M_PI) mGenerationPhi -= 2.*M_PI;
// Check if the muon is inward
if (sin(mGenerationTheta)*cos(mGenerationPhi)*mGenerationPosition[0] + sin(mGenerationTheta)*sin(mGenerationPhi)*mGenerationPosition[1] > 0) Generate();
}
}
// Half-sphere generation
if (mGenMethod == HSphere) {
// Generation point on the half-sphere
mPhi0 = mRandom.GenerateRandomDouble(mHSphereMinPositionPhi, mHSphereMaxPositionPhi);
while (!mAccepted) {
mRandAccRej = mRandom.GenerateRandomDouble();
mTheta0 = acos(mRandom.GenerateRandomDouble(mHSphereCosMaxPositionTheta, mHSphereCosMinPositionTheta));
mGenerationTheta = mRandom.GenerateRandomDouble(mMinimumTheta, mMaximumTheta);
mGenerationPhi = mRandom.GenerateRandomDouble(mMinimumPhi, mMaximumPhi);
mGenerationMomentum = GenerateMomentumF1();
mN = 2.856-0.655*log(mGenerationMomentum);
if (mN < 0.1) mN = 0.1;
mJPrime = 1600*pow(mGenerationMomentum, 0.279)*pow(cos(mGenerationTheta), mN)*(sin(mGenerationTheta)*sin(mTheta0)*cos(mGenerationPhi)+cos(mGenerationTheta)*cos(mTheta0))*sin(mGenerationTheta);
if (mJPrime > 0 && mMaxJ[mGenMethod]*mRandAccRej < mJPrime) mAccepted = true;
}