[819] | 1 | // |
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| 2 | // ******************************************************************** |
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| 3 | // * License and Disclaimer * |
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| 4 | // * * |
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| 5 | // * The Geant4 software is copyright of the Copyright Holders of * |
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| 6 | // * the Geant4 Collaboration. It is provided under the terms and * |
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| 7 | // * conditions of the Geant4 Software License, included in the file * |
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| 8 | // * LICENSE and available at http://cern.ch/geant4/license . These * |
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| 9 | // * include a list of copyright holders. * |
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| 10 | // * * |
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| 11 | // * Neither the authors of this software system, nor their employing * |
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| 12 | // * institutes,nor the agencies providing financial support for this * |
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| 13 | // * work make any representation or warranty, express or implied, * |
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| 14 | // * regarding this software system or assume any liability for its * |
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| 15 | // * use. Please see the license in the file LICENSE and URL above * |
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| 16 | // * for the full disclaimer and the limitation of liability. * |
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| 17 | // * * |
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| 18 | // * This code implementation is the result of the scientific and * |
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| 19 | // * technical work of the GEANT4 collaboration. * |
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| 20 | // * By using, copying, modifying or distributing the software (or * |
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| 21 | // * any work based on the software) you agree to acknowledge its * |
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| 22 | // * use in resulting scientific publications, and indicate your * |
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| 23 | // * acceptance of all terms of the Geant4 Software license. * |
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| 24 | // ******************************************************************** |
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| 25 | // |
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| 26 | template <class Function> |
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| 27 | G4bool G4Solver<Function>::Bisection(Function & theFunction) |
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| 28 | { |
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| 29 | // Check the interval before start |
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| 30 | if (a > b || std::abs(a-b) <= tolerance) |
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| 31 | { |
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| 32 | G4cerr << "G4Solver::Bisection: The interval must be properly set." << G4endl; |
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| 33 | return false; |
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| 34 | } |
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| 35 | G4double fa = theFunction(a); |
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| 36 | G4double fb = theFunction(b); |
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| 37 | if (fa*fb > 0.0) |
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| 38 | { |
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| 39 | G4cerr << "G4Solver::Bisection: The interval must include a root." << G4endl; |
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| 40 | return false; |
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| 41 | } |
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| 42 | |
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| 43 | G4double eps=tolerance*(b-a); |
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| 44 | |
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| 45 | |
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| 46 | // Finding the root |
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| 47 | for (G4int i = 0; i < MaxIter; i++) |
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| 48 | { |
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| 49 | G4double c = (a+b)/2.0; |
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| 50 | if ((b-a) < eps) |
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| 51 | { |
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| 52 | root = c; |
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| 53 | return true; |
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| 54 | } |
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| 55 | G4double fc = theFunction(c); |
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| 56 | if (fc == 0.0) |
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| 57 | { |
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| 58 | root = c; |
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| 59 | return true; |
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| 60 | } |
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| 61 | if (fa*fc < 0.0) |
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| 62 | { |
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| 63 | a=c; |
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| 64 | fa=fc; |
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| 65 | } |
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| 66 | else |
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| 67 | { |
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| 68 | b=c; |
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| 69 | fb=fc; |
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| 70 | } |
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| 71 | } |
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| 72 | G4cerr << "G4Solver::Bisection: Excedded maximum number of iterations whithout convegence." << G4endl; |
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| 73 | return false; |
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| 74 | } |
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| 75 | |
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| 76 | |
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| 77 | template <class Function> |
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| 78 | G4bool G4Solver<Function>::RegulaFalsi(Function & theFunction) |
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| 79 | { |
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| 80 | // Check the interval before start |
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| 81 | if (a > b || std::abs(a-b) <= tolerance) |
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| 82 | { |
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| 83 | G4cerr << "G4Solver::RegulaFalsi: The interval must be properly set." << G4endl; |
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| 84 | return false; |
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| 85 | } |
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| 86 | G4double fa = theFunction(a); |
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| 87 | G4double fb = theFunction(b); |
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| 88 | if (fa*fb > 0.0) |
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| 89 | { |
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| 90 | G4cerr << "G4Solver::RegulaFalsi: The interval must include a root." << G4endl; |
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| 91 | return false; |
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| 92 | } |
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| 93 | |
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| 94 | G4double eps=tolerance*(b-a); |
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| 95 | |
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| 96 | |
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| 97 | // Finding the root |
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| 98 | for (G4int i = 0; i < MaxIter; i++) |
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| 99 | { |
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| 100 | G4double c = (a*fb-b*fa)/(fb-fa); |
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| 101 | G4double delta = std::min(std::abs(c-a),std::abs(b-c)); |
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| 102 | if (delta < eps) |
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| 103 | { |
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| 104 | root = c; |
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| 105 | return true; |
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| 106 | } |
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| 107 | G4double fc = theFunction(c); |
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| 108 | if (fc == 0.0) |
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| 109 | { |
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| 110 | root = c; |
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| 111 | return true; |
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| 112 | } |
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| 113 | if (fa*fc < 0.0) |
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| 114 | { |
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| 115 | b=c; |
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| 116 | fb=fc; |
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| 117 | } |
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| 118 | else |
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| 119 | { |
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| 120 | a=c; |
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| 121 | fa=fc; |
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| 122 | } |
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| 123 | } |
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| 124 | G4cerr << "G4Solver::Bisection: Excedded maximum number of iterations whithout convegence." << G4endl; |
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| 125 | return false; |
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| 126 | |
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| 127 | } |
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| 128 | |
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| 129 | template <class Function> |
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| 130 | G4bool G4Solver<Function>::Brent(Function & theFunction) |
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| 131 | { |
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| 132 | |
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| 133 | const G4double precision = 3.0e-8; |
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| 134 | |
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| 135 | // Check the interval before start |
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| 136 | if (a > b || std::abs(a-b) <= tolerance) |
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| 137 | { |
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| 138 | G4cerr << "G4Solver::Brent: The interval must be properly set." << G4endl; |
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| 139 | return false; |
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| 140 | } |
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| 141 | G4double fa = theFunction(a); |
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| 142 | G4double fb = theFunction(b); |
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| 143 | if (fa*fb > 0.0) |
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| 144 | { |
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| 145 | G4cerr << "G4Solver::Brent: The interval must include a root." << G4endl; |
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| 146 | return false; |
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| 147 | } |
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| 148 | |
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| 149 | G4double c = b; |
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| 150 | G4double fc = fb; |
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| 151 | G4double d = 0.0; |
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| 152 | G4double e = 0.0; |
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| 153 | |
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| 154 | for (G4int i=0; i < MaxIter; i++) |
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| 155 | { |
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| 156 | // Rename a,b,c and adjust bounding interval d |
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| 157 | if (fb*fc > 0.0) |
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| 158 | { |
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| 159 | c = a; |
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| 160 | fc = fa; |
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| 161 | d = b - a; |
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| 162 | e = d; |
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| 163 | } |
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| 164 | if (std::abs(fc) < std::abs(fb)) |
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| 165 | { |
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| 166 | a = b; |
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| 167 | b = c; |
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| 168 | c = a; |
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| 169 | fa = fb; |
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| 170 | fb = fc; |
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| 171 | fc = fa; |
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| 172 | } |
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| 173 | G4double Tol1 = 2.0*precision*std::abs(b) + 0.5*tolerance; |
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| 174 | G4double xm = 0.5*(c-b); |
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| 175 | if (std::abs(xm) <= Tol1 || fb == 0.0) |
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| 176 | { |
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| 177 | root = b; |
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| 178 | return true; |
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| 179 | } |
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| 180 | // Inverse quadratic interpolation |
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| 181 | if (std::abs(e) >= Tol1 && std::abs(fa) > std::abs(fb)) |
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| 182 | { |
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| 183 | G4double s = fb/fa; |
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| 184 | G4double p = 0.0; |
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| 185 | G4double q = 0.0; |
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| 186 | if (a == c) |
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| 187 | { |
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| 188 | p = 2.0*xm*s; |
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| 189 | q = 1.0 - s; |
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| 190 | } |
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| 191 | else |
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| 192 | { |
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| 193 | q = fa/fc; |
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| 194 | G4double r = fb/fc; |
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| 195 | p = s*(2.0*xm*q*(q-r)-(b-a)*(r-1.0)); |
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| 196 | q = (q-1.0)*(r-1.0)*(s-1.0); |
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| 197 | } |
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| 198 | // Check bounds |
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| 199 | if (p > 0.0) q = -q; |
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| 200 | p = std::abs(p); |
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| 201 | G4double min1 = 3.0*xm*q-std::abs(Tol1*q); |
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| 202 | G4double min2 = std::abs(e*q); |
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| 203 | if (2.0*p < std::min(min1,min2)) |
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| 204 | { |
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| 205 | // Interpolation |
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| 206 | e = d; |
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| 207 | d = p/q; |
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| 208 | } |
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| 209 | else |
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| 210 | { |
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| 211 | // Bisection |
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| 212 | d = xm; |
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| 213 | e = d; |
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| 214 | } |
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| 215 | } |
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| 216 | else |
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| 217 | { |
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| 218 | // Bounds decreasing too slowly, use bisection |
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| 219 | d = xm; |
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| 220 | e = d; |
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| 221 | } |
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| 222 | // Move last guess to a |
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| 223 | a = b; |
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| 224 | fa = fb; |
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| 225 | if (std::abs(d) > Tol1) b += d; |
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| 226 | else |
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| 227 | { |
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| 228 | if (xm >= 0.0) b += std::abs(Tol1); |
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| 229 | else b -= std::abs(Tol1); |
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| 230 | } |
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| 231 | fb = theFunction(b); |
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| 232 | } |
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| 233 | G4cerr << "G4Solver::Brent: Number of iterations exceeded." << G4endl; |
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| 234 | return false; |
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| 235 | } |
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| 236 | |
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| 237 | |
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| 238 | |
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| 239 | template <class Function> |
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| 240 | G4bool G4Solver<Function>::Crenshaw(Function & theFunction) |
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| 241 | { |
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| 242 | // Check the interval before start |
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| 243 | if (a > b || std::abs(a-b) <= tolerance) |
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| 244 | { |
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| 245 | G4cerr << "G4Solver::Crenshaw: The interval must be properly set." << G4endl; |
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| 246 | return false; |
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| 247 | } |
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| 248 | |
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| 249 | G4double fa = theFunction(a); |
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| 250 | if (fa == 0.0) |
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| 251 | { |
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| 252 | root = a; |
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| 253 | return true; |
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| 254 | } |
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| 255 | |
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| 256 | G4double Mlast = a; |
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| 257 | |
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| 258 | G4double fb = theFunction(b); |
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| 259 | if (fb == 0.0) |
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| 260 | { |
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| 261 | root = b; |
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| 262 | return true; |
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| 263 | } |
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| 264 | |
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| 265 | if (fa*fb > 0.0) |
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| 266 | { |
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| 267 | G4cerr << "G4Solver::Crenshaw: The interval must include a root." << G4endl; |
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| 268 | return false; |
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| 269 | } |
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| 270 | |
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| 271 | |
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| 272 | for (G4int i=0; i < MaxIter; i++) |
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| 273 | { |
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| 274 | G4double c = 0.5 * (b + a); |
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| 275 | G4double fc = theFunction(c); |
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| 276 | if (fc == 0.0 || std::abs(c - a) < tolerance) |
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| 277 | { |
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| 278 | root = c; |
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| 279 | return true; |
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| 280 | } |
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| 281 | |
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| 282 | if (fc * fa > 0.0) |
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| 283 | { |
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| 284 | G4double tmp = a; |
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| 285 | a = b; |
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| 286 | b = tmp; |
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| 287 | tmp = fa; |
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| 288 | fa = fb; |
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| 289 | fb = tmp; |
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| 290 | } |
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| 291 | |
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| 292 | G4double fc0 = fc - fa; |
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| 293 | G4double fb1 = fb - fc; |
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| 294 | G4double fb0 = fb - fa; |
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| 295 | if (fb * fb0 < 2.0 * fc * fc0) |
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| 296 | { |
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| 297 | b = c; |
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| 298 | fb = fc; |
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| 299 | } |
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| 300 | else |
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| 301 | { |
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| 302 | G4double B = (c - a) / fc0; |
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| 303 | G4double C = (fc0 - fb1) / (fb1 * fb0); |
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| 304 | G4double M = a - B * fa * (1.0 - C * fc); |
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| 305 | G4double fM = theFunction(M); |
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| 306 | if (fM == 0.0 || std::abs(M - Mlast) < tolerance) |
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| 307 | { |
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| 308 | root = M; |
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| 309 | return true; |
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| 310 | } |
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| 311 | Mlast = M; |
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| 312 | if (fM * fa < 0.0) |
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| 313 | { |
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| 314 | b = M; |
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| 315 | fb = fM; |
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| 316 | } |
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| 317 | else |
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| 318 | { |
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| 319 | a = M; |
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| 320 | fa = fM; |
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| 321 | b = c; |
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| 322 | fb = fc; |
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| 323 | } |
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| 324 | } |
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| 325 | } |
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| 326 | return false; |
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| 327 | } |
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| 328 | |
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| 329 | |
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| 330 | |
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| 331 | |
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| 332 | template <class Function> |
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| 333 | void G4Solver<Function>::SetIntervalLimits(const G4double Limit1, const G4double Limit2) |
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| 334 | { |
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| 335 | if (std::abs(Limit1-Limit2) <= tolerance) |
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| 336 | { |
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| 337 | G4cerr << "G4Solver::SetIntervalLimits: Interval must be wider than tolerance." << G4endl; |
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| 338 | return; |
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| 339 | } |
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| 340 | if (Limit1 < Limit2) |
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| 341 | { |
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| 342 | a = Limit1; |
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| 343 | b = Limit2; |
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| 344 | } |
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| 345 | else |
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| 346 | { |
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| 347 | a = Limit2; |
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| 348 | b = Limit1; |
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| 349 | } |
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| 350 | return; |
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| 351 | } |
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| 352 | |
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