1 | // Basics.h is a part of the PYTHIA event generator. |
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2 | // Copyright (C) 2012 Torbjorn Sjostrand. |
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3 | // PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. |
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4 | // Please respect the MCnet Guidelines, see GUIDELINES for details. |
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5 | |
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6 | // Header file for basic, often-used helper classes. |
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7 | // RndmEngine: base class for external random number generators. |
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8 | // Rndm: random number generator. |
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9 | // Vec4: simple four-vectors. |
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10 | // RotBstMatrix: matrices encoding rotations and boosts of Vec4 objects. |
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11 | // Hist: simple one-dimensional histograms. |
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12 | |
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13 | #ifndef Pythia8_Basics_H |
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14 | #define Pythia8_Basics_H |
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15 | |
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16 | #include "PythiaStdlib.h" |
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17 | |
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18 | namespace Pythia8 { |
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19 | |
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20 | //========================================================================== |
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21 | |
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22 | // RndmEngine is the base class for external random number generators. |
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23 | // There is only one pure virtual method, that should do the generation. |
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24 | |
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25 | class RndmEngine { |
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26 | |
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27 | public: |
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28 | |
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29 | // A pure virtual method, wherein the derived class method |
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30 | // generates a random number uniformly distributed between 1 and 1. |
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31 | virtual double flat() = 0; |
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32 | |
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33 | protected: |
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34 | |
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35 | // Destructor. |
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36 | virtual ~RndmEngine() {} |
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37 | |
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38 | }; |
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39 | |
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40 | //========================================================================== |
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41 | |
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42 | // Rndm class. |
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43 | // This class handles random number generation according to the |
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44 | // Marsaglia-Zaman-Tsang algorithm. |
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45 | |
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46 | class Rndm { |
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47 | |
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48 | public: |
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49 | |
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50 | // Constructors. |
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51 | Rndm() : initRndm(false), seedSave(0), sequence(0), |
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52 | useExternalRndm(false), rndmEngPtr(0) { } |
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53 | Rndm(int seedIn) : initRndm(false), seedSave(0), sequence(0), |
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54 | useExternalRndm(false), rndmEngPtr(0) { init(seedIn);} |
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55 | |
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56 | // Possibility to pass in pointer for external random number generation. |
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57 | bool rndmEnginePtr( RndmEngine* rndmEngPtrIn); |
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58 | |
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59 | // Initialize, normally at construction or in first call. |
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60 | void init(int seedIn = 0) ; |
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61 | |
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62 | // Generate next random number uniformly between 0 and 1. |
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63 | double flat() ; |
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64 | |
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65 | // Generate random numbers according to exp(-x). |
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66 | double exp() { return -log(flat()) ;} |
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67 | |
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68 | // Generate random numbers according to x * exp(-x). |
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69 | double xexp() { return -log(flat() * flat()) ;} |
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70 | |
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71 | // Generate random numbers according to exp(-x^2/2). |
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72 | double gauss() {return sqrt(-2. * log(flat())) * cos(M_PI * flat());} |
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73 | |
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74 | // Generate two random numbers according to exp(-x^2/2-y^2/2). |
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75 | pair<double, double> gauss2() {double r = sqrt(-2. * log(flat())); |
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76 | double phi = 2. * M_PI * flat(); |
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77 | return pair<double, double>(r * sin(phi), r * cos(phi));} |
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78 | |
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79 | // Pick one option among vector of (positive) probabilities. |
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80 | int pick(const vector<double>& prob) ; |
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81 | |
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82 | // Save or read current state to or from a binary file. |
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83 | bool dumpState(string fileName); |
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84 | bool readState(string fileName); |
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85 | |
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86 | private: |
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87 | |
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88 | // Default random number sequence. |
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89 | static const int DEFAULTSEED; |
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90 | |
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91 | // State of the random number generator. |
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92 | bool initRndm; |
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93 | int i97, j97, defaultSeed, seedSave; |
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94 | long sequence; |
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95 | double u[97], c, cd, cm; |
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96 | |
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97 | // Pointer for external random number generation. |
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98 | bool useExternalRndm; |
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99 | RndmEngine* rndmEngPtr; |
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100 | |
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101 | }; |
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102 | |
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103 | //========================================================================== |
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104 | |
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105 | // Forward reference to RotBstMatrix class; needed in Vec4 class. |
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106 | class RotBstMatrix; |
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107 | |
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108 | //-------------------------------------------------------------------------- |
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109 | |
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110 | // Vec4 class. |
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111 | // This class implements four-vectors, in energy-momentum space. |
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112 | // (But can equally well be used to hold space-time four-vectors.) |
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113 | |
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114 | class Vec4 { |
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115 | |
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116 | public: |
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117 | |
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118 | // Constructors. |
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119 | Vec4(double xIn = 0., double yIn = 0., double zIn = 0., double tIn = 0.) |
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120 | : xx(xIn), yy(yIn), zz(zIn), tt(tIn) { } |
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121 | Vec4(const Vec4& v) : xx(v.xx), yy(v.yy), zz(v.zz), tt(v.tt) { } |
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122 | Vec4& operator=(const Vec4& v) { if (this != &v) { xx = v.xx; yy = v.yy; |
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123 | zz = v.zz; tt = v.tt; } return *this; } |
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124 | Vec4& operator=(double value) { xx = value; yy = value; zz = value; |
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125 | tt = value; return *this; } |
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126 | |
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127 | // Member functions for input. |
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128 | void reset() {xx = 0.; yy = 0.; zz = 0.; tt = 0.;} |
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129 | void p(double xIn, double yIn, double zIn, double tIn) |
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130 | {xx = xIn; yy = yIn; zz = zIn; tt = tIn;} |
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131 | void p(Vec4 pIn) {xx = pIn.xx; yy = pIn.yy; zz = pIn.zz; tt = pIn.tt;} |
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132 | void px(double xIn) {xx = xIn;} |
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133 | void py(double yIn) {yy = yIn;} |
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134 | void pz(double zIn) {zz = zIn;} |
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135 | void e(double tIn) {tt = tIn;} |
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136 | |
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137 | // Member functions for output. |
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138 | double px() const {return xx;} |
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139 | double py() const {return yy;} |
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140 | double pz() const {return zz;} |
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141 | double e() const {return tt;} |
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142 | double mCalc() const {double temp = tt*tt - xx*xx - yy*yy - zz*zz; |
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143 | return (temp >= 0.) ? sqrt(temp) : -sqrt(-temp);} |
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144 | double m2Calc() const {return tt*tt - xx*xx - yy*yy - zz*zz;} |
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145 | double pT() const {return sqrt(xx*xx + yy*yy);} |
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146 | double pT2() const {return xx*xx + yy*yy;} |
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147 | double pAbs() const {return sqrt(xx*xx + yy*yy + zz*zz);} |
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148 | double pAbs2() const {return xx*xx + yy*yy + zz*zz;} |
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149 | double eT() const {double temp = xx*xx + yy*yy; |
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150 | return tt * sqrt( temp / (temp + zz*zz) );} |
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151 | double eT2() const {double temp = xx*xx + yy*yy; |
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152 | return tt*tt * temp / (temp + zz*zz);} |
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153 | double theta() const {return atan2(sqrt(xx*xx + yy*yy), zz);} |
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154 | double phi() const {return atan2(yy,xx);} |
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155 | double thetaXZ() const {return atan2(xx,zz);} |
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156 | double pPos() const {return tt + zz;} |
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157 | double pNeg() const {return tt - zz;} |
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158 | |
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159 | // Member functions that perform operations. |
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160 | void rescale3(double fac) {xx *= fac; yy *= fac; zz *= fac;} |
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161 | void rescale4(double fac) {xx *= fac; yy *= fac; zz *= fac; tt *= fac;} |
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162 | void flip3() {xx = -xx; yy = -yy; zz = -zz;} |
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163 | void flip4() {xx = -xx; yy = -yy; zz = -zz; tt = -tt;} |
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164 | void rot(double thetaIn, double phiIn); |
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165 | void rotaxis(double phiIn, double nx, double ny, double nz); |
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166 | void rotaxis(double phiIn, const Vec4& n); |
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167 | void bst(double betaX, double betaY, double betaZ); |
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168 | void bst(double betaX, double betaY, double betaZ, double gamma); |
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169 | void bst(const Vec4& pIn); |
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170 | void bst(const Vec4& pIn, double mIn); |
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171 | void bstback(const Vec4& pIn); |
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172 | void bstback(const Vec4& pIn, double mIn); |
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173 | void rotbst(const RotBstMatrix& M); |
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174 | |
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175 | // Operator overloading with member functions |
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176 | Vec4 operator-() {Vec4 tmp; tmp.xx = -xx; tmp.yy = -yy; tmp.zz = -zz; |
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177 | tmp.tt = -tt; return tmp;} |
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178 | Vec4& operator+=(const Vec4& v) {xx += v.xx; yy += v.yy; zz += v.zz; |
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179 | tt += v.tt; return *this;} |
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180 | Vec4& operator-=(const Vec4& v) {xx -= v.xx; yy -= v.yy; zz -= v.zz; |
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181 | tt -= v.tt; return *this;} |
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182 | Vec4& operator*=(double f) {xx *= f; yy *= f; zz *= f; |
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183 | tt *= f; return *this;} |
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184 | Vec4& operator/=(double f) {xx /= f; yy /= f; zz /= f; |
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185 | tt /= f; return *this;} |
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186 | |
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187 | // Operator overloading with friends |
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188 | friend Vec4 operator+(const Vec4& v1, const Vec4& v2); |
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189 | friend Vec4 operator-(const Vec4& v1, const Vec4& v2); |
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190 | friend Vec4 operator*(double f, const Vec4& v1); |
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191 | friend Vec4 operator*(const Vec4& v1, double f); |
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192 | friend Vec4 operator/(const Vec4& v1, double f); |
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193 | friend double operator*(const Vec4& v1, const Vec4& v2); |
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194 | |
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195 | // Invariant mass of a pair and its square. |
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196 | friend double m(const Vec4& v1, const Vec4& v2); |
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197 | friend double m2(const Vec4& v1, const Vec4& v2); |
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198 | |
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199 | // Scalar and cross product of 3-vector parts. |
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200 | friend double dot3(const Vec4& v1, const Vec4& v2); |
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201 | friend Vec4 cross3(const Vec4& v1, const Vec4& v2); |
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202 | |
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203 | // theta is polar angle between v1 and v2. |
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204 | friend double theta(const Vec4& v1, const Vec4& v2); |
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205 | friend double costheta(const Vec4& v1, const Vec4& v2); |
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206 | |
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207 | // phi is azimuthal angle between v1 and v2 around z axis. |
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208 | friend double phi(const Vec4& v1, const Vec4& v2); |
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209 | friend double cosphi(const Vec4& v1, const Vec4& v2); |
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210 | |
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211 | // phi is azimuthal angle between v1 and v2 around n axis. |
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212 | friend double phi(const Vec4& v1, const Vec4& v2, const Vec4& n); |
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213 | friend double cosphi(const Vec4& v1, const Vec4& v2, const Vec4& n); |
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214 | |
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215 | // Print a four-vector |
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216 | friend ostream& operator<<(ostream&, const Vec4& v) ; |
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217 | |
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218 | private: |
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219 | |
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220 | // Constants: could only be changed in the code itself. |
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221 | static const double TINY; |
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222 | |
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223 | // The four-vector data members. |
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224 | double xx, yy, zz, tt; |
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225 | |
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226 | }; |
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227 | |
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228 | //-------------------------------------------------------------------------- |
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229 | |
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230 | // Namespace function declarations; friends of Vec4 class. |
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231 | |
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232 | // Implementation of operator overloading with friends. |
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233 | |
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234 | inline Vec4 operator+(const Vec4& v1, const Vec4& v2) |
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235 | {Vec4 v = v1 ; return v += v2;} |
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236 | |
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237 | inline Vec4 operator-(const Vec4& v1, const Vec4& v2) |
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238 | {Vec4 v = v1 ; return v -= v2;} |
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239 | |
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240 | inline Vec4 operator*(double f, const Vec4& v1) |
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241 | {Vec4 v = v1; return v *= f;} |
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242 | |
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243 | inline Vec4 operator*(const Vec4& v1, double f) |
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244 | {Vec4 v = v1; return v *= f;} |
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245 | |
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246 | inline Vec4 operator/(const Vec4& v1, double f) |
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247 | {Vec4 v = v1; return v /= f;} |
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248 | |
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249 | inline double operator*(const Vec4& v1, const Vec4& v2) |
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250 | {return v1.tt*v2.tt - v1.xx*v2.xx - v1.yy*v2.yy - v1.zz*v2.zz;} |
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251 | |
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252 | // Invariant mass of a pair and its square. |
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253 | double m(const Vec4& v1, const Vec4& v2); |
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254 | double m2(const Vec4& v1, const Vec4& v2); |
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255 | |
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256 | // Scalar and cross product of 3-vector parts. |
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257 | double dot3(const Vec4& v1, const Vec4& v2); |
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258 | Vec4 cross3(const Vec4& v1, const Vec4& v2); |
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259 | |
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260 | // theta is polar angle between v1 and v2. |
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261 | double theta(const Vec4& v1, const Vec4& v2); |
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262 | double costheta(const Vec4& v1, const Vec4& v2); |
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263 | |
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264 | // phi is azimuthal angle between v1 and v2 around z axis. |
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265 | double phi(const Vec4& v1, const Vec4& v2); |
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266 | double cosphi(const Vec4& v1, const Vec4& v2); |
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267 | |
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268 | // phi is azimuthal angle between v1 and v2 around n axis. |
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269 | double phi(const Vec4& v1, const Vec4& v2, const Vec4& n); |
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270 | double cosphi(const Vec4& v1, const Vec4& v2, const Vec4& n); |
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271 | |
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272 | // Print a four-vector. |
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273 | ostream& operator<<(ostream&, const Vec4& v) ; |
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274 | |
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275 | //========================================================================== |
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276 | |
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277 | // RotBstMatrix class. |
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278 | // This class implements 4 * 4 matrices that encode an arbitrary combination |
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279 | // of rotations and boosts, that can be applied to Vec4 four-vectors. |
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280 | |
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281 | class RotBstMatrix { |
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282 | |
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283 | public: |
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284 | |
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285 | // Constructors. |
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286 | RotBstMatrix() {for (int i = 0; i < 4; ++i) { for (int j = 0; j < 4; ++j) |
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287 | { M[i][j] = (i==j) ? 1. : 0.; } } } |
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288 | RotBstMatrix(const RotBstMatrix& Min) { |
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289 | for (int i = 0; i < 4; ++i) { for (int j = 0; j < 4; ++j) { |
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290 | M[i][j] = Min.M[i][j]; } } } |
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291 | RotBstMatrix& operator=(const RotBstMatrix& Min) {if (this != &Min) { |
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292 | for (int i = 0; i < 4; ++i) { for (int j = 0; j < 4; ++j) { |
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293 | M[i][j] = Min.M[i][j]; } } } return *this; } |
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294 | |
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295 | // Member functions. |
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296 | void rot(double = 0., double = 0.); |
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297 | void rot(const Vec4& p); |
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298 | void bst(double = 0., double = 0., double = 0.); |
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299 | void bst(const Vec4&); |
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300 | void bstback(const Vec4&); |
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301 | void bst(const Vec4&, const Vec4&); |
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302 | void toCMframe(const Vec4&, const Vec4&); |
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303 | void fromCMframe(const Vec4&, const Vec4&); |
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304 | void rotbst(const RotBstMatrix&); |
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305 | void invert(); |
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306 | void reset(); |
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307 | |
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308 | // Crude estimate deviation from unit matrix. |
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309 | double deviation() const; |
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310 | |
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311 | // Print a transformation matrix. |
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312 | friend ostream& operator<<(ostream&, const RotBstMatrix&) ; |
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313 | |
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314 | // Private members to be accessible from Vec4. |
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315 | friend class Vec4; |
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316 | |
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317 | private: |
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318 | |
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319 | // Constants: could only be changed in the code itself. |
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320 | static const double TINY; |
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321 | |
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322 | // The rotation-and-boost matrix data members. |
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323 | double M[4][4]; |
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324 | |
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325 | }; |
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326 | |
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327 | //-------------------------------------------------------------------------- |
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328 | |
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329 | // Namespace function declaration; friend of RotBstMatrix class. |
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330 | |
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331 | // Print a transformation matrix. |
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332 | ostream& operator<<(ostream&, const RotBstMatrix&) ; |
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333 | |
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334 | //========================================================================== |
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335 | |
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336 | // Hist class. |
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337 | // This class handles a single histogram at a time. |
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338 | |
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339 | class Hist{ |
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340 | |
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341 | public: |
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342 | |
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343 | // Constructors, including copy constructors. |
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344 | Hist() {;} |
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345 | Hist(string titleIn, int nBinIn = 100, double xMinIn = 0., |
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346 | double xMaxIn = 1.) { |
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347 | book(titleIn, nBinIn, xMinIn, xMaxIn);} |
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348 | Hist(const Hist& h) |
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349 | : title(h.title), nBin(h.nBin), nFill(h.nFill), xMin(h.xMin), |
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350 | xMax(h.xMax), dx(h.dx), under(h.under), inside(h.inside), |
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351 | over(h.over), res(h.res) { } |
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352 | Hist(string titleIn, const Hist& h) |
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353 | : title(titleIn), nBin(h.nBin), nFill(h.nFill), xMin(h.xMin), |
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354 | xMax(h.xMax), dx(h.dx), under(h.under), inside(h.inside), |
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355 | over(h.over), res(h.res) { } |
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356 | Hist& operator=(const Hist& h) { if(this != &h) { |
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357 | nBin = h.nBin; nFill = h.nFill; xMin = h.xMin; xMax = h.xMax; |
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358 | dx = h.dx; under = h.under; inside = h.inside; over = h.over; |
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359 | res = h.res; } return *this; } |
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360 | |
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361 | // Book a histogram. |
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362 | void book(string titleIn = " ", int nBinIn = 100, double xMinIn = 0., |
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363 | double xMaxIn = 1.) ; |
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364 | |
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365 | // Set title of a histogram. |
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366 | void name(string titleIn = " ") {title = titleIn; } |
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367 | |
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368 | // Reset bin contents. |
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369 | void null() ; |
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370 | |
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371 | // Fill bin with weight. |
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372 | void fill(double x, double w = 1.) ; |
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373 | |
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374 | // Print a histogram with overloaded << operator. |
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375 | friend ostream& operator<<(ostream& os, const Hist& h) ; |
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376 | |
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377 | // Print histogram contents as a table (e.g. for Gnuplot). |
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378 | void table(ostream& os = cout) const ; |
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379 | void table(string fileName) const { |
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380 | ofstream streamName(fileName.c_str()); table(streamName); } |
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381 | |
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382 | // Print a table out of two histograms with same x axis. |
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383 | friend void table(const Hist& h1, const Hist& h2, ostream& os) ; |
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384 | friend void table(const Hist& h1, const Hist& h2, string fileName) ; |
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385 | |
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386 | // Return content of specific bin: -1 gives underflow and nBin overflow. |
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387 | double getBinContent(int iBin) ; |
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388 | |
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389 | // Return number of entries |
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390 | int getEntries() {return nFill; } |
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391 | |
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392 | // Check whether another histogram has same size and limits. |
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393 | bool sameSize(const Hist& h) const ; |
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394 | |
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395 | // Take logarithm (base 10 or e) of bin contents. |
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396 | void takeLog(bool tenLog = true) ; |
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397 | |
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398 | // Take square root of bin contents. |
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399 | void takeSqrt() ; |
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400 | |
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401 | // Operator overloading with member functions |
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402 | Hist& operator+=(const Hist& h) ; |
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403 | Hist& operator-=(const Hist& h) ; |
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404 | Hist& operator*=(const Hist& h) ; |
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405 | Hist& operator/=(const Hist& h) ; |
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406 | Hist& operator+=(double f) ; |
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407 | Hist& operator-=(double f) ; |
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408 | Hist& operator*=(double f) ; |
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409 | Hist& operator/=(double f) ; |
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410 | |
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411 | // Operator overloading with friends |
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412 | friend Hist operator+(double f, const Hist& h1); |
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413 | friend Hist operator+(const Hist& h1, double f); |
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414 | friend Hist operator+(const Hist& h1, const Hist& h2); |
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415 | friend Hist operator-(double f, const Hist& h1); |
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416 | friend Hist operator-(const Hist& h1, double f); |
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417 | friend Hist operator-(const Hist& h1, const Hist& h2); |
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418 | friend Hist operator*(double f, const Hist& h1); |
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419 | friend Hist operator*(const Hist& h1, double f); |
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420 | friend Hist operator*(const Hist& h1, const Hist& h2); |
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421 | friend Hist operator/(double f, const Hist& h1); |
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422 | friend Hist operator/(const Hist& h1, double f); |
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423 | friend Hist operator/(const Hist& h1, const Hist& h2); |
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424 | |
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425 | private: |
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426 | |
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427 | // Constants: could only be changed in the code itself. |
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428 | static const int NBINMAX, NCOLMAX, NLINES; |
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429 | static const double TOLERANCE, TINY, SMALLFRAC, DYAC[]; |
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430 | static const char NUMBER[]; |
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431 | |
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432 | // Properties and contents of a histogram. |
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433 | string title; |
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434 | int nBin, nFill; |
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435 | double xMin, xMax, dx, under, inside, over; |
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436 | vector<double> res; |
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437 | |
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438 | }; |
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439 | |
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440 | //-------------------------------------------------------------------------- |
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441 | |
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442 | // Namespace function declarations; friends of Hist class. |
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443 | |
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444 | // Print a histogram with overloaded << operator. |
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445 | ostream& operator<<(ostream& os, const Hist& h) ; |
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446 | |
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447 | // Print a table out of two histograms with same x axis. |
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448 | void table(const Hist& h1, const Hist& h2, ostream& os = cout) ; |
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449 | void table(const Hist& h1, const Hist& h2, string fileName) ; |
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450 | |
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451 | // Operator overloading with friends |
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452 | Hist operator+(double f, const Hist& h1); |
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453 | Hist operator+(const Hist& h1, double f); |
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454 | Hist operator+(const Hist& h1, const Hist& h2); |
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455 | Hist operator-(double f, const Hist& h1); |
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456 | Hist operator-(const Hist& h1, double f); |
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457 | Hist operator-(const Hist& h1, const Hist& h2); |
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458 | Hist operator*(double f, const Hist& h1); |
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459 | Hist operator*(const Hist& h1, double f); |
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460 | Hist operator*(const Hist& h1, const Hist& h2); |
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461 | Hist operator/(double f, const Hist& h1); |
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462 | Hist operator/(const Hist& h1, double f); |
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463 | Hist operator/(const Hist& h1, const Hist& h2); |
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464 | |
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465 | //========================================================================== |
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466 | |
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467 | } // end namespace Pythia8 |
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468 | |
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469 | #endif // end Pythia8_Basics_H |
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