[819] | 1 | // |
---|
| 2 | // ******************************************************************** |
---|
| 3 | // * License and Disclaimer * |
---|
| 4 | // * * |
---|
| 5 | // * The Geant4 software is copyright of the Copyright Holders of * |
---|
| 6 | // * the Geant4 Collaboration. It is provided under the terms and * |
---|
| 7 | // * conditions of the Geant4 Software License, included in the file * |
---|
| 8 | // * LICENSE and available at http://cern.ch/geant4/license . These * |
---|
| 9 | // * include a list of copyright holders. * |
---|
| 10 | // * * |
---|
| 11 | // * Neither the authors of this software system, nor their employing * |
---|
| 12 | // * institutes,nor the agencies providing financial support for this * |
---|
| 13 | // * work make any representation or warranty, express or implied, * |
---|
| 14 | // * regarding this software system or assume any liability for its * |
---|
| 15 | // * use. Please see the license in the file LICENSE and URL above * |
---|
| 16 | // * for the full disclaimer and the limitation of liability. * |
---|
| 17 | // * * |
---|
| 18 | // * This code implementation is the result of the scientific and * |
---|
| 19 | // * technical work of the GEANT4 collaboration. * |
---|
| 20 | // * By using, copying, modifying or distributing the software (or * |
---|
| 21 | // * any work based on the software) you agree to acknowledge its * |
---|
| 22 | // * use in resulting scientific publications, and indicate your * |
---|
| 23 | // * acceptance of all terms of the Geant4 Software license. * |
---|
| 24 | // ******************************************************************** |
---|
| 25 | // |
---|
| 26 | // |
---|
| 27 | // G4 Tools program: NuMu DIS(Q2) fixed step integration |
---|
| 28 | // ..................................................... |
---|
| 29 | // Created: M.V. Kossov, CERN/ITEP(Moscow), 20-Dec-2005 |
---|
| 30 | // |
---|
| 31 | //===================================================================== |
---|
| 32 | #include "globals.hh" |
---|
| 33 | #include <iostream> |
---|
| 34 | #include <fstream> |
---|
| 35 | #include <vector> |
---|
| 36 | #include "G4ios.hh" |
---|
| 37 | //#include <CLHEP/GenericFunctions/LogGamma.hh> |
---|
| 38 | |
---|
| 39 | // Solution for randomization of the high order polinoms is tabulated |
---|
| 40 | |
---|
| 41 | double poli(double x, int n) // f=n*x^(n-1)-(n-1)*x^n=R(0-1), n>2, as n=2 has analSolution |
---|
| 42 | { |
---|
| 43 | double p=x; |
---|
| 44 | int n1=n-1; |
---|
| 45 | for(int i=1; i<n1; i++) p*=x; |
---|
| 46 | return p*(n-n1*x); |
---|
| 47 | } |
---|
| 48 | |
---|
| 49 | double dpoli(double x, int n) // df=n*(n-1)*x^(n-2)-(n-1)*n*x^(n-1), n>2 (n=2 has analSol) |
---|
| 50 | { |
---|
| 51 | double p=x; |
---|
| 52 | int n1=n-1; |
---|
| 53 | if(n>3) for(int i=2; i<n1; i++) p*=x; |
---|
| 54 | return p*n*n1*(1.-x); |
---|
| 55 | } |
---|
| 56 | // One can define for tabulation more similar functions |
---|
| 57 | |
---|
| 58 | int main() |
---|
| 59 | { |
---|
| 60 | const double eps=.0000001; // relative accuracy of the integral calculation |
---|
| 61 | // ============= |
---|
| 62 | int nSub=10; |
---|
| 63 | double dSub=1./nSub; |
---|
| 64 | for(int n=3; n<12; n++) |
---|
| 65 | { |
---|
| 66 | G4cout<<"n="<<n<<G4endl; |
---|
| 67 | G4double s=0.; |
---|
| 68 | for(int i=1; i<nSub; i++) |
---|
| 69 | { |
---|
| 70 | s+=dSub; |
---|
| 71 | G4double r=std::pow(s,(n-1.5)/1.5); |
---|
| 72 | G4double x=0.5; |
---|
| 73 | if(n==3) |
---|
| 74 | { |
---|
| 75 | if (r==0.5) x=0.5; |
---|
| 76 | else if(r<0.5) x=std::sqrt(r+r)*(.5+.1579*(r-.5)); |
---|
| 77 | else x=1.-std::sqrt(2.-r-r)*(.5+.1579*(.5-r)); |
---|
| 78 | } |
---|
| 79 | else |
---|
| 80 | { |
---|
| 81 | G4int n1=n-1; |
---|
| 82 | G4double r1=n1; |
---|
| 83 | G4double r2=r1-1.; |
---|
| 84 | G4double rr=r2/r1; |
---|
| 85 | G4double rp=std::pow(rr,n1); |
---|
| 86 | G4double p2=rp+rp; |
---|
| 87 | if (r==rr) x=p2; |
---|
| 88 | else |
---|
| 89 | { |
---|
| 90 | if(r<rr) |
---|
| 91 | { |
---|
| 92 | G4double pr=0.; |
---|
| 93 | G4double pra=0.; |
---|
| 94 | if(n>7) |
---|
| 95 | { |
---|
| 96 | if(n>9) |
---|
| 97 | { |
---|
| 98 | if(n>10) // >10(11) |
---|
| 99 | { |
---|
| 100 | pr=.614/std::pow((n+1+1.25),.75); |
---|
| 101 | pra=.915/std::pow((n+1+6.7),1.75); |
---|
| 102 | } |
---|
| 103 | else // 10 |
---|
| 104 | { |
---|
| 105 | pr=.09945; |
---|
| 106 | pra=.00667; |
---|
| 107 | } |
---|
| 108 | } |
---|
| 109 | else |
---|
| 110 | { |
---|
| 111 | if(n>8) // 9 |
---|
| 112 | { |
---|
| 113 | pr=.1064; |
---|
| 114 | pra=.00741; |
---|
| 115 | } |
---|
| 116 | else // 8 |
---|
| 117 | { |
---|
| 118 | pr=.11425; |
---|
| 119 | pra=.00828; |
---|
| 120 | } |
---|
| 121 | } |
---|
| 122 | } |
---|
| 123 | else |
---|
| 124 | { |
---|
| 125 | if(n>5) |
---|
| 126 | { |
---|
| 127 | if(n>6) // 7 |
---|
| 128 | { |
---|
| 129 | pr=.12347; |
---|
| 130 | pra=.00926; |
---|
| 131 | } |
---|
| 132 | else // 6 |
---|
| 133 | { |
---|
| 134 | pr=.13405; |
---|
| 135 | pra=.01027; |
---|
| 136 | } |
---|
| 137 | } |
---|
| 138 | else |
---|
| 139 | { |
---|
| 140 | if(n>4) // 5 |
---|
| 141 | { |
---|
| 142 | pr=.1454; |
---|
| 143 | pra=.01112; |
---|
| 144 | } |
---|
| 145 | else // 4 |
---|
| 146 | { |
---|
| 147 | pr=.15765; |
---|
| 148 | pra=.00965; |
---|
| 149 | } |
---|
| 150 | } |
---|
| 151 | } |
---|
| 152 | x=std::pow((r/p2),(1.-rr+pra))*(rr+pr*(r-p2)); |
---|
| 153 | } |
---|
| 154 | else |
---|
| 155 | { |
---|
| 156 | G4double sr=0.; |
---|
| 157 | if(n>7) |
---|
| 158 | { |
---|
| 159 | if(n>9) |
---|
| 160 | { |
---|
| 161 | if(n>10) sr=.86/(n+1+1.05); // >10(11) |
---|
| 162 | else sr=.0774; // 10 |
---|
| 163 | } |
---|
| 164 | else |
---|
| 165 | { |
---|
| 166 | if(n>8) sr=.0849; // 9 |
---|
| 167 | else sr=.0938; // 8 |
---|
| 168 | } |
---|
| 169 | } |
---|
| 170 | else |
---|
| 171 | { |
---|
| 172 | if(n>5) |
---|
| 173 | { |
---|
| 174 | if(n>6) sr=.1047; // 7 |
---|
| 175 | else sr=.1179; // 6 |
---|
| 176 | } |
---|
| 177 | else |
---|
| 178 | { |
---|
| 179 | if(n>7) sr=.1339; // 5 |
---|
| 180 | else sr=.15135; // 4 |
---|
| 181 | } |
---|
| 182 | } |
---|
| 183 | x=1.-std::sqrt((1.-r)/(1.-p2))*(1.-rr+sr*(p2-r)); |
---|
| 184 | } |
---|
| 185 | } |
---|
| 186 | } |
---|
| 187 | G4double dx=x; |
---|
| 188 | G4double f=poli(x,n)-r; |
---|
| 189 | G4int it=0; |
---|
| 190 | while(std::fabs(f/r)>eps) |
---|
| 191 | { |
---|
| 192 | it++; |
---|
| 193 | G4double df=dpoli(x,n); |
---|
| 194 | //G4cout<<"n="<<n<<", r="<<r<<", f="<<f<<", d="<<df<<", x="<<x<<", i="<<it<<G4endl; |
---|
| 195 | x-=f/df; |
---|
| 196 | f=poli(x,n)-r; |
---|
| 197 | } |
---|
| 198 | dx=std::fabs(dx-x); |
---|
| 199 | G4double d=std::fabs(f/r); |
---|
| 200 | G4cout<<"n="<<n<<",r="<<r<<", Final: f="<<d<<",x="<<x<<",d="<<dx<<",it="<<it<<G4endl; |
---|
| 201 | } // End of loop over r |
---|
| 202 | } // End of loop over n |
---|
| 203 | return 0; |
---|
| 204 | } |
---|