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 | // * * |
---|
21 | // * Parts of this code which have been developed by QinetiQ Ltd * |
---|
22 | // * under contract to the European Space Agency (ESA) are the * |
---|
23 | // * intellectual property of ESA. Rights to use, copy, modify and * |
---|
24 | // * redistribute this software for general public use are granted * |
---|
25 | // * in compliance with any licensing, distribution and development * |
---|
26 | // * policy adopted by the Geant4 Collaboration. This code has been * |
---|
27 | // * written by QinetiQ Ltd for the European Space Agency, under ESA * |
---|
28 | // * contract 17191/03/NL/LvH (Aurora Programme). * |
---|
29 | // * * |
---|
30 | // * By using, copying, modifying or distributing the software (or * |
---|
31 | // * any work based on the software) you agree to acknowledge its * |
---|
32 | // * use in resulting scientific publications, and indicate your * |
---|
33 | // * acceptance of all terms of the Geant4 Software license. * |
---|
34 | // ******************************************************************** |
---|
35 | // |
---|
36 | // %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
37 | // |
---|
38 | // MODULE: G4Bessel.cc |
---|
39 | // |
---|
40 | // Version: B.1 |
---|
41 | // Date: 15/04/04 |
---|
42 | // Author: P R Truscott |
---|
43 | // Organisation: QinetiQ Ltd, UK |
---|
44 | // Customer: ESA/ESTEC, NOORDWIJK |
---|
45 | // Contract: 17191/03/NL/LvH |
---|
46 | // |
---|
47 | // %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
48 | // |
---|
49 | // CHANGE HISTORY |
---|
50 | // -------------- |
---|
51 | // |
---|
52 | // 18 Noevmber 2003, P R Truscott, QinetiQ Ltd, UK |
---|
53 | // Created. |
---|
54 | // |
---|
55 | // 15 March 2004, P R Truscott, QinetiQ Ltd, UK |
---|
56 | // Beta release |
---|
57 | // |
---|
58 | // %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
59 | //////////////////////////////////////////////////////////////////////////////// |
---|
60 | // |
---|
61 | #include "G4Bessel.hh" |
---|
62 | //////////////////////////////////////////////////////////////////////////////// |
---|
63 | // |
---|
64 | G4Bessel::G4Bessel () |
---|
65 | {;} |
---|
66 | //////////////////////////////////////////////////////////////////////////////// |
---|
67 | // |
---|
68 | G4Bessel::~G4Bessel () |
---|
69 | {;} |
---|
70 | //////////////////////////////////////////////////////////////////////////////// |
---|
71 | // |
---|
72 | G4double G4Bessel::I0 (G4double x) |
---|
73 | { |
---|
74 | const G4double P1 = 1.0, |
---|
75 | P2 = 3.5156229, |
---|
76 | P3 = 3.0899424, |
---|
77 | P4 = 1.2067492, |
---|
78 | P5 = 0.2659732, |
---|
79 | P6 = 0.0360768, |
---|
80 | P7 = 0.0045813; |
---|
81 | const G4double Q1 = 0.39894228, |
---|
82 | Q2 = 0.01328592, |
---|
83 | Q3 = 0.00225319, |
---|
84 | Q4 =-0.00157565, |
---|
85 | Q5 = 0.00916281, |
---|
86 | Q6 =-0.02057706, |
---|
87 | Q7 = 0.02635537, |
---|
88 | Q8 =-0.01647633, |
---|
89 | Q9 = 0.00392377; |
---|
90 | |
---|
91 | G4double I = 0.0; |
---|
92 | if (std::fabs(x) < 3.75) |
---|
93 | { |
---|
94 | G4double y = std::pow(x/3.75, 2.0); |
---|
95 | I = P1+y*(P2+y*(P3+y*(P4+y*(P5+y*(P6+y*P7))))); |
---|
96 | } |
---|
97 | else |
---|
98 | { |
---|
99 | G4double ax = std::fabs(x); |
---|
100 | G4double y = 3.75/ax; |
---|
101 | I = std::exp(ax) / std::sqrt(ax) * |
---|
102 | (Q1+y*(Q2+y*(Q3+y*(Q4+y*(Q5+y*(Q6+y*(Q7+y*(Q8+y*Q9)))))))); |
---|
103 | } |
---|
104 | return I; |
---|
105 | } |
---|
106 | //////////////////////////////////////////////////////////////////////////////// |
---|
107 | // |
---|
108 | G4double G4Bessel::K0 (G4double x) |
---|
109 | { |
---|
110 | const G4double P1 =-0.57721566, |
---|
111 | P2 = 0.42278420, |
---|
112 | P3 = 0.23069756, |
---|
113 | P4 = 0.03488590, |
---|
114 | P5 = 0.00262698, |
---|
115 | P6 = 0.00010750, |
---|
116 | P7 = 0.00000740; |
---|
117 | const G4double Q1 = 1.25331414, |
---|
118 | Q2 =-0.07832358, |
---|
119 | Q3 = 0.02189568, |
---|
120 | Q4 =-0.01062446, |
---|
121 | Q5 = 0.00587872, |
---|
122 | Q6 =-0.00251540, |
---|
123 | Q7 = 0.00053208; |
---|
124 | |
---|
125 | G4double K = 0.0; |
---|
126 | if (x <= 2.0) |
---|
127 | { |
---|
128 | G4double y = x * x / 4.0; |
---|
129 | K = (-std::log(x/2.0)) * I0(x) + |
---|
130 | P1+y*(P2+y*(P3+y*(P4+y*(P5+y*(P6+y*P7))))); |
---|
131 | } |
---|
132 | else |
---|
133 | { |
---|
134 | G4double y = 2.0 / x; |
---|
135 | K = std::exp(-x) / std::sqrt(x) * |
---|
136 | (Q1+y*(Q2+y*(Q3+y*(Q4+y*(Q5+y*(Q6+y*Q7)))))); |
---|
137 | } |
---|
138 | return K; |
---|
139 | } |
---|
140 | //////////////////////////////////////////////////////////////////////////////// |
---|
141 | // |
---|
142 | G4double G4Bessel::I1 (G4double x) |
---|
143 | { |
---|
144 | const G4double P1 = 0.5, |
---|
145 | P2 = 0.87890594, |
---|
146 | P3 = 0.51498869, |
---|
147 | P4 = 0.15084934, |
---|
148 | P5 = 0.02658733, |
---|
149 | P6 = 0.00301532, |
---|
150 | P7 = 0.00032411; |
---|
151 | const G4double Q1 = 0.39894228, |
---|
152 | Q2 =-0.03988024, |
---|
153 | Q3 =-0.00362018, |
---|
154 | Q4 = 0.00163801, |
---|
155 | Q5 =-0.01031555, |
---|
156 | Q6 = 0.02282967, |
---|
157 | Q7 =-0.02895312, |
---|
158 | Q8 = 0.01787654, |
---|
159 | Q9 =-0.00420059; |
---|
160 | |
---|
161 | G4double I = 0.0; |
---|
162 | if (std::fabs(x) < 3.75) |
---|
163 | { |
---|
164 | G4double ax = std::fabs(x); |
---|
165 | G4double y = std::pow(x/3.75, 2.0); |
---|
166 | I = ax*(P1+y*(P2+y*(P3+y*(P4+y*(P5+y*(P6+y*P7)))))); |
---|
167 | } |
---|
168 | else |
---|
169 | { |
---|
170 | G4double ax = std::fabs(x); |
---|
171 | G4double y = 3.75/ax; |
---|
172 | I = std::exp(ax) / std::sqrt(ax) * |
---|
173 | (Q1+y*(Q2+y*(Q3+y*(Q4+y*(Q5+y*(Q6+y*(Q7+y*(Q8+y*Q9)))))))); |
---|
174 | } |
---|
175 | if (x < 0.0) I = -I; |
---|
176 | return I; |
---|
177 | } |
---|
178 | //////////////////////////////////////////////////////////////////////////////// |
---|
179 | // |
---|
180 | G4double G4Bessel::K1 (G4double x) |
---|
181 | { |
---|
182 | const G4double P1 = 1.0, |
---|
183 | P2 = 0.15443144, |
---|
184 | P3 =-0.67278579, |
---|
185 | P4 =-0.18156897, |
---|
186 | P5 =-0.01919402, |
---|
187 | P6 =-0.00110404, |
---|
188 | P7 =-0.00004686; |
---|
189 | const G4double Q1 = 1.25331414, |
---|
190 | Q2 = 0.23498619, |
---|
191 | Q3 =-0.03655620, |
---|
192 | Q4 = 0.01504268, |
---|
193 | Q5 =-0.00780353, |
---|
194 | Q6 = 0.00325614, |
---|
195 | Q7 =-0.00068245; |
---|
196 | |
---|
197 | G4double K = 0.0; |
---|
198 | if (x <= 2.0) |
---|
199 | { |
---|
200 | G4double y = x * x / 4.0; |
---|
201 | K = std::log(x/2.0)*I1(x) + 1.0/x * |
---|
202 | (P1+y*(P2+y*(P3+y*(P4+y*(P5+y*(P6+y*P7)))))); |
---|
203 | } |
---|
204 | else |
---|
205 | { |
---|
206 | G4double y = 2.0 / x; |
---|
207 | K = std::exp(-x) / std::sqrt(x) * |
---|
208 | (Q1+y*(Q2+y*(Q3+y*(Q4+y*(Q5+y*(Q6+y*Q7)))))); |
---|
209 | } |
---|
210 | return K; |
---|
211 | } |
---|
212 | //////////////////////////////////////////////////////////////////////////////// |
---|
213 | // |
---|
214 | G4double G4Bessel::pI0 (G4double x) |
---|
215 | { |
---|
216 | const G4double A0 = 0.1250000000000E+00, |
---|
217 | A1 = 7.0312500000000E-02, |
---|
218 | A2 = 7.3242187500000E-02, |
---|
219 | A3 = 1.1215209960938E-01, |
---|
220 | A4 = 2.2710800170898E-01, |
---|
221 | A5 = 5.7250142097473E-01, |
---|
222 | A6 = 1.7277275025845E+00, |
---|
223 | A7 = 6.0740420012735E+00, |
---|
224 | A8 = 2.4380529699556E+01, |
---|
225 | A9 = 1.1001714026925E+02, |
---|
226 | A10 = 5.5133589612202E+02, |
---|
227 | A11 = 3.0380905109224E+03; |
---|
228 | |
---|
229 | G4double I = 0.0; |
---|
230 | if (x == 0.0) |
---|
231 | { |
---|
232 | I = 1.0; |
---|
233 | } |
---|
234 | else if (x < 18.0) |
---|
235 | { |
---|
236 | I = 1.0; |
---|
237 | G4double y = x * x; |
---|
238 | G4double s = 1.0; |
---|
239 | for (G4int i=1; i<101; i++) |
---|
240 | { |
---|
241 | s *= 0.25 * y / i / i; |
---|
242 | I += s; |
---|
243 | if (std::abs(s/I) < 1.0E-15) break; |
---|
244 | } |
---|
245 | } |
---|
246 | else |
---|
247 | { |
---|
248 | G4double y = 1.0 / x; |
---|
249 | I = std::exp(x) / std::sqrt(twopi*x) * |
---|
250 | (1.0 + y*(A0+y*(A1+y*(A2+y*(A3+y*(A4+y*(A5+y*(A6+y*(A7+y*(A8+y*(A9+y*(A10+y*A11)))))))))))); |
---|
251 | } |
---|
252 | |
---|
253 | return I; |
---|
254 | } |
---|
255 | //////////////////////////////////////////////////////////////////////////////// |
---|
256 | // |
---|
257 | G4double G4Bessel::pI1 (G4double x) |
---|
258 | { |
---|
259 | const G4double A0 = -0.3750000000000E+00, |
---|
260 | A1 = -1.1718750000000E-01, |
---|
261 | A2 = -1.0253906250000E-01, |
---|
262 | A3 = -1.4419555664063E-01, |
---|
263 | A4 = -2.775764465332E-01, |
---|
264 | A5 = -6.7659258842468E-01, |
---|
265 | A6 = -1.9935317337513E+00, |
---|
266 | A7 = -6.8839142681099E+00, |
---|
267 | A8 = -2.7248827311269E+01, |
---|
268 | A9 = -1.2159789187654E+02, |
---|
269 | A10 = -6.0384407670507E+02, |
---|
270 | A11 = -3.3022722944809E+03; |
---|
271 | |
---|
272 | G4double I = 0.0; |
---|
273 | if (x == 0.0) |
---|
274 | { |
---|
275 | I = 0.0; |
---|
276 | } |
---|
277 | else if (x < 18.0) |
---|
278 | { |
---|
279 | I = 1.0; |
---|
280 | G4double y = x * x; |
---|
281 | G4double s = 1.0; |
---|
282 | for (G4int i=1; i<101; i++) |
---|
283 | { |
---|
284 | s *= 0.25 * y / i / (i+1.0); |
---|
285 | I += s; |
---|
286 | if (std::abs(s/I) < 1.0E-15) break; |
---|
287 | } |
---|
288 | I *= 0.5 * x; |
---|
289 | |
---|
290 | } |
---|
291 | else |
---|
292 | { |
---|
293 | G4double y = 1.0 / x; |
---|
294 | I = std::exp(x) / std::sqrt(twopi*x) * |
---|
295 | (1.0 + y*(A0+y*(A1+y*(A2+y*(A3+y*(A4+y*(A5+y*(A6+y*(A7+y*(A8+y*(A9+y*(A10+y*A11)))))))))))); |
---|
296 | } |
---|
297 | |
---|
298 | return I; |
---|
299 | } |
---|
300 | //////////////////////////////////////////////////////////////////////////////// |
---|
301 | // |
---|
302 | G4double G4Bessel::pK0 (G4double x) |
---|
303 | { |
---|
304 | const G4double A0 = 0.1250000000000E+00, |
---|
305 | A1 = 0.2109375000000E+00, |
---|
306 | A2 = 1.0986328125000E+00, |
---|
307 | A3 = 1.1775970458984E+01, |
---|
308 | A4 = 2.1461706161499E+02, |
---|
309 | A5 = 5.9511522710323E+03, |
---|
310 | A6 = 2.3347645606175E+05, |
---|
311 | A7 = 1.2312234987631E+07; |
---|
312 | |
---|
313 | G4double K = 0.0; |
---|
314 | if (x == 0.0) |
---|
315 | { |
---|
316 | K = 1.0E+307; |
---|
317 | } |
---|
318 | else if (x < 9.0) |
---|
319 | { |
---|
320 | G4double y = x * x; |
---|
321 | G4double C = -std::log(x/2.0) - 0.5772156649015329; |
---|
322 | G4double s = 1.0; |
---|
323 | G4double t = 0.0; |
---|
324 | for (G4int i=1; i<51; i++) |
---|
325 | { |
---|
326 | s *= 0.25 * y / i / i; |
---|
327 | t += 1.0 / i ; |
---|
328 | K += s * (t+C); |
---|
329 | } |
---|
330 | K += C; |
---|
331 | } |
---|
332 | else |
---|
333 | { |
---|
334 | G4double y = 1.0 / x / x; |
---|
335 | K = 0.5 / x / pI0(x) * |
---|
336 | (1.0 + y*(A0+y*(A1+y*(A2+y*(A3+y*(A4+y*(A5+y*(A6+y*A7)))))))); |
---|
337 | } |
---|
338 | |
---|
339 | return K; |
---|
340 | } |
---|
341 | //////////////////////////////////////////////////////////////////////////////// |
---|
342 | // |
---|
343 | G4double G4Bessel::pK1 (G4double x) |
---|
344 | { |
---|
345 | G4double K = 0.0; |
---|
346 | if (x == 0.0) |
---|
347 | K = 1.0E+307; |
---|
348 | else |
---|
349 | K = (1.0/x - pI1(x)*pK0(x)) / pI0(x); |
---|
350 | return K; |
---|
351 | } |
---|
352 | //////////////////////////////////////////////////////////////////////////////// |
---|
353 | // |
---|