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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