| 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 <<
27 // 26 //
28 // Author: E.Medernach, 19.12.2000 - First imp << 27 // $Id: G4PolynomialSolver.icc 67970 2013-03-13 10:10:06Z gcosmo $
29 // ------------------------------------------- << 28 //
>> 29 // class G4PolynomialSolver
>> 30 //
>> 31 // 19.12.00 E.Medernach, First implementation
>> 32 //
30 33
31 #define POLEPSILON 1e-12 << 34 #define POLEPSILON 1e-12
32 #define POLINFINITY 9.0E99 << 35 #define POLINFINITY 9.0E99
33 #define ITERATION 12 // 20 But 8 is really en << 36 #define ITERATION 12 // 20 But 8 is really enough for Newton with a good guess
34 37
35 template <class T, class F> 38 template <class T, class F>
36 G4PolynomialSolver<T, F>::G4PolynomialSolver(T << 39 G4PolynomialSolver<T,F>::G4PolynomialSolver (T* typeF, F func, F deriv,
37 G 40 G4double precision)
38 { 41 {
39 Precision = precision; << 42 Precision = precision ;
40 FunctionClass = typeF; << 43 FunctionClass = typeF ;
41 Function = func; << 44 Function = func ;
42 Derivative = deriv; << 45 Derivative = deriv ;
43 } 46 }
44 47
45 template <class T, class F> 48 template <class T, class F>
46 G4PolynomialSolver<T, F>::~G4PolynomialSolver( << 49 G4PolynomialSolver<T,F>::~G4PolynomialSolver ()
47 {} << 50 {
>> 51 }
48 52
49 template <class T, class F> 53 template <class T, class F>
50 G4double G4PolynomialSolver<T, F>::solve(G4dou << 54 G4double G4PolynomialSolver<T,F>::solve(G4double IntervalMin,
51 G4dou << 55 G4double IntervalMax)
52 { 56 {
53 return Newton(IntervalMin, IntervalMax); << 57 return Newton(IntervalMin,IntervalMax);
54 } 58 }
55 59
>> 60
56 /* If we want to be general this could work fo 61 /* If we want to be general this could work for any
57 polynomial of order more that 4 if we find 62 polynomial of order more that 4 if we find the (ORDER + 1)
58 control points 63 control points
59 */ 64 */
60 #define NBBEZIER 5 65 #define NBBEZIER 5
61 66
62 template <class T, class F> 67 template <class T, class F>
63 G4int G4PolynomialSolver<T, F>::BezierClipping << 68 G4int
64 << 69 G4PolynomialSolver<T,F>::BezierClipping(/*T* typeF,F func,F deriv,*/
65 << 70 G4double *IntervalMin,
>> 71 G4double *IntervalMax)
66 { 72 {
67 /** BezierClipping is a clipping interval Ne 73 /** BezierClipping is a clipping interval Newton method **/
68 /** It works by clipping the area where the 74 /** It works by clipping the area where the polynomial is **/
69 75
70 G4double P[NBBEZIER][2], D[2]; << 76 G4double P[NBBEZIER][2],D[2];
71 G4double NewMin, NewMax; << 77 G4double NewMin,NewMax;
72 78
73 G4int IntervalIsVoid = 1; 79 G4int IntervalIsVoid = 1;
74 << 80
75 /*** Calculating Control Points ***/ 81 /*** Calculating Control Points ***/
76 /* We see the polynomial as a Bezier curve f 82 /* We see the polynomial as a Bezier curve for some control points to find */
77 83
78 /* 84 /*
79 For 5 control points (polynomial of degree 85 For 5 control points (polynomial of degree 4) this is:
80 << 86
81 0 p0 = F((*IntervalMin)) 87 0 p0 = F((*IntervalMin))
82 1/4 p1 = F((*IntervalMin)) + ((*Interval 88 1/4 p1 = F((*IntervalMin)) + ((*IntervalMax) - (*IntervalMin))/4
83 * F'((*IntervalMin)) 89 * F'((*IntervalMin))
84 2/4 p2 = 1/6 * (16*F(((*IntervalMax) + ( 90 2/4 p2 = 1/6 * (16*F(((*IntervalMax) + (*IntervalMin))/2)
85 - (p0 + 4*p1 + 4*p3 + p4 << 91 - (p0 + 4*p1 + 4*p3 + p4))
86 3/4 p3 = F((*IntervalMax)) - ((*Interval 92 3/4 p3 = F((*IntervalMax)) - ((*IntervalMax) - (*IntervalMin))/4
87 * F'((*IntervalMax)) 93 * F'((*IntervalMax))
88 1 p4 = F((*IntervalMax)) 94 1 p4 = F((*IntervalMax))
89 */ << 95 */
90 96
91 /* x,y,z,dx,dy,dz are constant during search 97 /* x,y,z,dx,dy,dz are constant during searching */
92 98
93 D[0] = (FunctionClass->*Derivative)(*Interva 99 D[0] = (FunctionClass->*Derivative)(*IntervalMin);
94 << 100
95 P[0][0] = (*IntervalMin); 101 P[0][0] = (*IntervalMin);
96 P[0][1] = (FunctionClass->*Function)(*Interv 102 P[0][1] = (FunctionClass->*Function)(*IntervalMin);
>> 103
97 104
98 if(std::fabs(P[0][1]) < Precision) << 105 if (std::fabs(P[0][1]) < Precision) {
99 { <<
100 return 1; 106 return 1;
101 } 107 }
102 << 108
103 if(((*IntervalMax) - (*IntervalMin)) < POLEP << 109 if (((*IntervalMax) - (*IntervalMin)) < POLEPSILON) {
104 { <<
105 return 1; 110 return 1;
106 } 111 }
107 112
108 P[1][0] = (*IntervalMin) + ((*IntervalMax) - << 113 P[1][0] = (*IntervalMin) + ((*IntervalMax) - (*IntervalMin))/4;
109 P[1][1] = P[0][1] + (((*IntervalMax) - (*Int << 114 P[1][1] = P[0][1] + (((*IntervalMax) - (*IntervalMin))/4.0) * D[0];
110 115
111 D[1] = (FunctionClass->*Derivative)(*Interva 116 D[1] = (FunctionClass->*Derivative)(*IntervalMax);
112 117
113 P[4][0] = (*IntervalMax); 118 P[4][0] = (*IntervalMax);
114 P[4][1] = (FunctionClass->*Function)(*Interv 119 P[4][1] = (FunctionClass->*Function)(*IntervalMax);
>> 120
>> 121 P[3][0] = (*IntervalMax) - ((*IntervalMax) - (*IntervalMin))/4;
>> 122 P[3][1] = P[4][1] - ((*IntervalMax) - (*IntervalMin))/4 * D[1];
>> 123
>> 124 P[2][0] = ((*IntervalMax) + (*IntervalMin))/2;
>> 125 P[2][1] = (16*(FunctionClass->*Function)(((*IntervalMax)+(*IntervalMin))/2)
>> 126 - (P[0][1] + 4*P[1][1] + 4*P[3][1] + P[4][1]))/6 ;
>> 127
>> 128 {
>> 129 G4double Intersection ;
>> 130 G4int i,j;
>> 131
>> 132 NewMin = (*IntervalMax) ;
>> 133 NewMax = (*IntervalMin) ;
>> 134
>> 135 for (i=0;i<5;i++)
>> 136 for (j=i+1;j<5;j++)
>> 137 {
>> 138 /* there is an intersection only if each have different signs */
>> 139 if (((P[j][1] > -Precision) && (P[i][1] < Precision)) ||
>> 140 ((P[j][1] < Precision) && (P[i][1] > -Precision))) {
>> 141 IntervalIsVoid = 0;
>> 142 Intersection = P[j][0] - P[j][1]*((P[i][0] - P[j][0])/
>> 143 (P[i][1] - P[j][1]));
>> 144 if (Intersection < NewMin) {
>> 145 NewMin = Intersection;
>> 146 }
>> 147 if (Intersection > NewMax) {
>> 148 NewMax = Intersection;
>> 149 }
>> 150 }
>> 151 }
115 152
116 P[3][0] = (*IntervalMax) - ((*IntervalMax) - << 153
117 P[3][1] = P[4][1] - ((*IntervalMax) - (*Inte << 154 if (IntervalIsVoid != 1) {
118 <<
119 P[2][0] = ((*IntervalMax) + (*IntervalMin)) <<
120 P[2][1] = <<
121 (16 * (FunctionClass->*Function)(((*Interv <<
122 (P[0][1] + 4 * P[1][1] + 4 * P[3][1] + P[ <<
123 6; <<
124 <<
125 { <<
126 G4double Intersection; <<
127 G4int i, j; <<
128 <<
129 NewMin = (*IntervalMax); <<
130 NewMax = (*IntervalMin); <<
131 <<
132 for(i = 0; i < 5; ++i) <<
133 for(j = i + 1; j < 5; ++j) <<
134 { <<
135 /* there is an intersection only if ea <<
136 if(((P[j][1] > -Precision) && (P[i][1] <<
137 ((P[j][1] < Precision) && (P[i][1] <<
138 { <<
139 IntervalIsVoid = 0; <<
140 Intersection = <<
141 P[j][0] - P[j][1] * ((P[i][0] - P[ <<
142 if(Intersection < NewMin) <<
143 { <<
144 NewMin = Intersection; <<
145 } <<
146 if(Intersection > NewMax) <<
147 { <<
148 NewMax = Intersection; <<
149 } <<
150 } <<
151 } <<
152 <<
153 if(IntervalIsVoid != 1) <<
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 { <<
162 return -1; 161 return -1;
163 } 162 }
164 << 163
165 return 0; 164 return 0;
166 } 165 }
167 166
168 template <class T, class F> 167 template <class T, class F>
169 G4double G4PolynomialSolver<T, F>::Newton(G4do << 168 G4double G4PolynomialSolver<T,F>::Newton (G4double IntervalMin,
170 G4do 169 G4double IntervalMax)
171 { 170 {
172 /* So now we have a good guess and an interv 171 /* So now we have a good guess and an interval where
173 if there are an intersection the root mus 172 if there are an intersection the root must be */
174 173
175 G4double Value = 0; << 174 G4double Value = 0;
176 G4double Gradient = 0; 175 G4double Gradient = 0;
177 G4double Lambda; << 176 G4double Lambda ;
178 <<
179 G4int i = 0; <<
180 G4int j = 0; <<
181 177
>> 178 G4int i=0;
>> 179 G4int j=0;
>> 180
>> 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 ; <<
188 187
189 if(NewtonIsSafe == -1) << 188 if (NewtonIsSafe == -1) {
190 { <<
191 return POLINFINITY; 189 return POLINFINITY;
192 } 190 }
193 } 191 }
194 192
195 Lambda = IntervalMin; 193 Lambda = IntervalMin;
196 Value = (FunctionClass->*Function)(Lambda); << 194 Value = (FunctionClass->*Function)(Lambda);
>> 195
197 196
198 // while ((std::fabs(Value) > Precision)) { 197 // while ((std::fabs(Value) > Precision)) {
199 while(j != -1) << 198 while (j != -1) {
200 { << 199
201 Value = (FunctionClass->*Function)(Lambda) 200 Value = (FunctionClass->*Function)(Lambda);
202 201
203 Gradient = (FunctionClass->*Derivative)(La 202 Gradient = (FunctionClass->*Derivative)(Lambda);
204 203
205 Lambda = Lambda - Value / Gradient; << 204 Lambda = Lambda - Value/Gradient ;
206 205
207 if(std::fabs(Value) <= Precision) << 206 if (std::fabs(Value) <= Precision) {
208 { << 207 j ++;
209 ++j; << 208 if (j == 2) {
210 if(j == 2) << 209 j = -1;
211 { << 210 }
212 j = -1; << 211 } else {
213 } << 212 i ++;
214 } << 213
215 else << 214 if (i > ITERATION)
216 { << 215 return POLINFINITY;
217 ++i; << 216 }
218 <<
219 if(i > ITERATION) <<
220 return POLINFINITY; <<
221 } <<
222 } 217 }
223 return Lambda; << 218 return Lambda ;
224 } 219 }
225 220