| Geant4 Cross Reference |
1 // 1 //
2 // ******************************************* 2 // ********************************************************************
3 // * License and Disclaimer 3 // * License and Disclaimer *
4 // * 4 // * *
5 // * The Geant4 software is copyright of th 5 // * The Geant4 software is copyright of the Copyright Holders of *
6 // * the Geant4 Collaboration. It is provided 6 // * the Geant4 Collaboration. It is provided under the terms and *
7 // * conditions of the Geant4 Software License 7 // * conditions of the Geant4 Software License, included in the file *
8 // * LICENSE and available at http://cern.ch/ 8 // * LICENSE and available at http://cern.ch/geant4/license . These *
9 // * include a list of copyright holders. 9 // * include a list of copyright holders. *
10 // * 10 // * *
11 // * Neither the authors of this software syst 11 // * Neither the authors of this software system, nor their employing *
12 // * institutes,nor the agencies providing fin 12 // * institutes,nor the agencies providing financial support for this *
13 // * work make any representation or warran 13 // * work make any representation or warranty, express or implied, *
14 // * regarding this software system or assum 14 // * regarding this software system or assume any liability for its *
15 // * use. Please see the license in the file 15 // * use. Please see the license in the file LICENSE and URL above *
16 // * for the full disclaimer and the limitatio 16 // * for the full disclaimer and the limitation of liability. *
17 // * 17 // * *
18 // * This code implementation is the result 18 // * This code implementation is the result of the scientific and *
19 // * technical work of the GEANT4 collaboratio 19 // * technical work of the GEANT4 collaboration. *
20 // * By using, copying, modifying or distri 20 // * By using, copying, modifying or distributing the software (or *
21 // * any work based on the software) you ag 21 // * any work based on the software) you agree to acknowledge its *
22 // * use in resulting scientific publicati 22 // * use in resulting scientific publications, and indicate your *
23 // * acceptance of all terms of the Geant4 Sof 23 // * acceptance of all terms of the Geant4 Software license. *
24 // ******************************************* 24 // ********************************************************************
25 // 25 //
26 // G4PolynomialSolver inline methods implement 26 // G4PolynomialSolver inline methods implementation
27 // 27 //
28 // Author: E.Medernach, 19.12.2000 - First imp 28 // Author: E.Medernach, 19.12.2000 - First implementation
29 // ------------------------------------------- 29 // --------------------------------------------------------------------
30 30
31 #define POLEPSILON 1e-12 31 #define POLEPSILON 1e-12
32 #define POLINFINITY 9.0E99 32 #define POLINFINITY 9.0E99
33 #define ITERATION 12 // 20 But 8 is really en 33 #define ITERATION 12 // 20 But 8 is really enough for Newton with a good guess
34 34
35 template <class T, class F> 35 template <class T, class F>
36 G4PolynomialSolver<T, F>::G4PolynomialSolver(T 36 G4PolynomialSolver<T, F>::G4PolynomialSolver(T* typeF, F func, F deriv,
37 G 37 G4double precision)
38 { 38 {
39 Precision = precision; 39 Precision = precision;
40 FunctionClass = typeF; 40 FunctionClass = typeF;
41 Function = func; 41 Function = func;
42 Derivative = deriv; 42 Derivative = deriv;
43 } 43 }
44 44
45 template <class T, class F> 45 template <class T, class F>
46 G4PolynomialSolver<T, F>::~G4PolynomialSolver( 46 G4PolynomialSolver<T, F>::~G4PolynomialSolver()
47 {} 47 {}
48 48
49 template <class T, class F> 49 template <class T, class F>
50 G4double G4PolynomialSolver<T, F>::solve(G4dou 50 G4double G4PolynomialSolver<T, F>::solve(G4double IntervalMin,
51 G4dou 51 G4double IntervalMax)
52 { 52 {
53 return Newton(IntervalMin, IntervalMax); 53 return Newton(IntervalMin, IntervalMax);
54 } 54 }
55 55
56 /* If we want to be general this could work fo 56 /* If we want to be general this could work for any
57 polynomial of order more that 4 if we find 57 polynomial of order more that 4 if we find the (ORDER + 1)
58 control points 58 control points
59 */ 59 */
60 #define NBBEZIER 5 60 #define NBBEZIER 5
61 61
62 template <class T, class F> 62 template <class T, class F>
63 G4int G4PolynomialSolver<T, F>::BezierClipping 63 G4int G4PolynomialSolver<T, F>::BezierClipping(/*T* typeF,F func,F deriv,*/
64 64 G4double* IntervalMin,
65 65 G4double* IntervalMax)
66 { 66 {
67 /** BezierClipping is a clipping interval Ne 67 /** BezierClipping is a clipping interval Newton method **/
68 /** It works by clipping the area where the 68 /** It works by clipping the area where the polynomial is **/
69 69
70 G4double P[NBBEZIER][2], D[2]; 70 G4double P[NBBEZIER][2], D[2];
71 G4double NewMin, NewMax; 71 G4double NewMin, NewMax;
72 72
73 G4int IntervalIsVoid = 1; 73 G4int IntervalIsVoid = 1;
74 74
75 /*** Calculating Control Points ***/ 75 /*** Calculating Control Points ***/
76 /* We see the polynomial as a Bezier curve f 76 /* We see the polynomial as a Bezier curve for some control points to find */
77 77
78 /* 78 /*
79 For 5 control points (polynomial of degree 79 For 5 control points (polynomial of degree 4) this is:
80 80
81 0 p0 = F((*IntervalMin)) 81 0 p0 = F((*IntervalMin))
82 1/4 p1 = F((*IntervalMin)) + ((*Interval 82 1/4 p1 = F((*IntervalMin)) + ((*IntervalMax) - (*IntervalMin))/4
83 * F'((*IntervalMin)) 83 * F'((*IntervalMin))
84 2/4 p2 = 1/6 * (16*F(((*IntervalMax) + ( 84 2/4 p2 = 1/6 * (16*F(((*IntervalMax) + (*IntervalMin))/2)
85 - (p0 + 4*p1 + 4*p3 + p4 85 - (p0 + 4*p1 + 4*p3 + p4))
86 3/4 p3 = F((*IntervalMax)) - ((*Interval 86 3/4 p3 = F((*IntervalMax)) - ((*IntervalMax) - (*IntervalMin))/4
87 * F'((*IntervalMax)) 87 * F'((*IntervalMax))
88 1 p4 = F((*IntervalMax)) 88 1 p4 = F((*IntervalMax))
89 */ 89 */
90 90
91 /* x,y,z,dx,dy,dz are constant during search 91 /* x,y,z,dx,dy,dz are constant during searching */
92 92
93 D[0] = (FunctionClass->*Derivative)(*Interva 93 D[0] = (FunctionClass->*Derivative)(*IntervalMin);
94 94
95 P[0][0] = (*IntervalMin); 95 P[0][0] = (*IntervalMin);
96 P[0][1] = (FunctionClass->*Function)(*Interv 96 P[0][1] = (FunctionClass->*Function)(*IntervalMin);
97 97
98 if(std::fabs(P[0][1]) < Precision) 98 if(std::fabs(P[0][1]) < Precision)
99 { 99 {
100 return 1; 100 return 1;
101 } 101 }
102 102
103 if(((*IntervalMax) - (*IntervalMin)) < POLEP 103 if(((*IntervalMax) - (*IntervalMin)) < POLEPSILON)
104 { 104 {
105 return 1; 105 return 1;
106 } 106 }
107 107
108 P[1][0] = (*IntervalMin) + ((*IntervalMax) - 108 P[1][0] = (*IntervalMin) + ((*IntervalMax) - (*IntervalMin)) / 4;
109 P[1][1] = P[0][1] + (((*IntervalMax) - (*Int 109 P[1][1] = P[0][1] + (((*IntervalMax) - (*IntervalMin)) / 4.0) * D[0];
110 110
111 D[1] = (FunctionClass->*Derivative)(*Interva 111 D[1] = (FunctionClass->*Derivative)(*IntervalMax);
112 112
113 P[4][0] = (*IntervalMax); 113 P[4][0] = (*IntervalMax);
114 P[4][1] = (FunctionClass->*Function)(*Interv 114 P[4][1] = (FunctionClass->*Function)(*IntervalMax);
115 115
116 P[3][0] = (*IntervalMax) - ((*IntervalMax) - 116 P[3][0] = (*IntervalMax) - ((*IntervalMax) - (*IntervalMin)) / 4;
117 P[3][1] = P[4][1] - ((*IntervalMax) - (*Inte 117 P[3][1] = P[4][1] - ((*IntervalMax) - (*IntervalMin)) / 4 * D[1];
118 118
119 P[2][0] = ((*IntervalMax) + (*IntervalMin)) 119 P[2][0] = ((*IntervalMax) + (*IntervalMin)) / 2;
120 P[2][1] = 120 P[2][1] =
121 (16 * (FunctionClass->*Function)(((*Interv 121 (16 * (FunctionClass->*Function)(((*IntervalMax) + (*IntervalMin)) / 2) -
122 (P[0][1] + 4 * P[1][1] + 4 * P[3][1] + P[ 122 (P[0][1] + 4 * P[1][1] + 4 * P[3][1] + P[4][1])) /
123 6; 123 6;
124 124
125 { 125 {
126 G4double Intersection; 126 G4double Intersection;
127 G4int i, j; 127 G4int i, j;
128 128
129 NewMin = (*IntervalMax); 129 NewMin = (*IntervalMax);
130 NewMax = (*IntervalMin); 130 NewMax = (*IntervalMin);
131 131
132 for(i = 0; i < 5; ++i) 132 for(i = 0; i < 5; ++i)
133 for(j = i + 1; j < 5; ++j) 133 for(j = i + 1; j < 5; ++j)
134 { 134 {
135 /* there is an intersection only if ea 135 /* there is an intersection only if each have different signs */
136 if(((P[j][1] > -Precision) && (P[i][1] 136 if(((P[j][1] > -Precision) && (P[i][1] < Precision)) ||
137 ((P[j][1] < Precision) && (P[i][1] 137 ((P[j][1] < Precision) && (P[i][1] > -Precision)))
138 { 138 {
139 IntervalIsVoid = 0; 139 IntervalIsVoid = 0;
140 Intersection = 140 Intersection =
141 P[j][0] - P[j][1] * ((P[i][0] - P[ 141 P[j][0] - P[j][1] * ((P[i][0] - P[j][0]) / (P[i][1] - P[j][1]));
142 if(Intersection < NewMin) 142 if(Intersection < NewMin)
143 { 143 {
144 NewMin = Intersection; 144 NewMin = Intersection;
145 } 145 }
146 if(Intersection > NewMax) 146 if(Intersection > NewMax)
147 { 147 {
148 NewMax = Intersection; 148 NewMax = Intersection;
149 } 149 }
150 } 150 }
151 } 151 }
152 152
153 if(IntervalIsVoid != 1) 153 if(IntervalIsVoid != 1)
154 { 154 {
155 (*IntervalMax) = NewMax; 155 (*IntervalMax) = NewMax;
156 (*IntervalMin) = NewMin; 156 (*IntervalMin) = NewMin;
157 } 157 }
158 } 158 }
159 159
160 if(IntervalIsVoid == 1) 160 if(IntervalIsVoid == 1)
161 { 161 {
162 return -1; 162 return -1;
163 } 163 }
164 164
165 return 0; 165 return 0;
166 } 166 }
167 167
168 template <class T, class F> 168 template <class T, class F>
169 G4double G4PolynomialSolver<T, F>::Newton(G4do 169 G4double G4PolynomialSolver<T, F>::Newton(G4double IntervalMin,
170 G4do 170 G4double IntervalMax)
171 { 171 {
172 /* So now we have a good guess and an interv 172 /* So now we have a good guess and an interval where
173 if there are an intersection the root mus 173 if there are an intersection the root must be */
174 174
175 G4double Value = 0; 175 G4double Value = 0;
176 G4double Gradient = 0; 176 G4double Gradient = 0;
177 G4double Lambda; 177 G4double Lambda;
178 178
179 G4int i = 0; 179 G4int i = 0;
180 G4int j = 0; 180 G4int j = 0;
181 181
182 /* Reduce interval before applying Newton Me 182 /* Reduce interval before applying Newton Method */
183 { 183 {
184 G4int NewtonIsSafe; 184 G4int NewtonIsSafe;
185 185
186 while((NewtonIsSafe = BezierClipping(&Inte 186 while((NewtonIsSafe = BezierClipping(&IntervalMin, &IntervalMax)) == 0)
187 ; 187 ;
188 188
189 if(NewtonIsSafe == -1) 189 if(NewtonIsSafe == -1)
190 { 190 {
191 return POLINFINITY; 191 return POLINFINITY;
192 } 192 }
193 } 193 }
194 194
195 Lambda = IntervalMin; 195 Lambda = IntervalMin;
196 Value = (FunctionClass->*Function)(Lambda); 196 Value = (FunctionClass->*Function)(Lambda);
197 197
198 // while ((std::fabs(Value) > Precision)) { 198 // while ((std::fabs(Value) > Precision)) {
199 while(j != -1) 199 while(j != -1)
200 { 200 {
201 Value = (FunctionClass->*Function)(Lambda) 201 Value = (FunctionClass->*Function)(Lambda);
202 202
203 Gradient = (FunctionClass->*Derivative)(La 203 Gradient = (FunctionClass->*Derivative)(Lambda);
204 204
205 Lambda = Lambda - Value / Gradient; 205 Lambda = Lambda - Value / Gradient;
206 206
207 if(std::fabs(Value) <= Precision) 207 if(std::fabs(Value) <= Precision)
208 { 208 {
209 ++j; 209 ++j;
210 if(j == 2) 210 if(j == 2)
211 { 211 {
212 j = -1; 212 j = -1;
213 } 213 }
214 } 214 }
215 else 215 else
216 { 216 {
217 ++i; 217 ++i;
218 218
219 if(i > ITERATION) 219 if(i > ITERATION)
220 return POLINFINITY; 220 return POLINFINITY;
221 } 221 }
222 } 222 }
223 return Lambda; 223 return Lambda;
224 } 224 }
225 225