| 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 // G4GaussLegendreQ class implementation <<
27 // 26 //
28 // Author: V.Grichine, 13.05.1997 << 27 // $Id: G4GaussLegendreQ.cc 69546 2013-05-08 09:50:34Z gcosmo $
29 // ------------------------------------------- << 28 //
30 29
31 #include "G4GaussLegendreQ.hh" 30 #include "G4GaussLegendreQ.hh"
32 #include "G4PhysicalConstants.hh" 31 #include "G4PhysicalConstants.hh"
33 32
34 G4GaussLegendreQ::G4GaussLegendreQ(function pF << 33 G4GaussLegendreQ::G4GaussLegendreQ( function pFunction )
35 : G4VGaussianQuadrature(pFunction) << 34 : G4VGaussianQuadrature(pFunction)
36 {} << 35 {
>> 36 }
37 37
38 // ------------------------------------------- 38 // --------------------------------------------------------------------------
39 // 39 //
40 // Constructor for GaussLegendre quadrature me 40 // Constructor for GaussLegendre quadrature method. The value nLegendre sets
41 // the accuracy required, i.e the number of po 41 // the accuracy required, i.e the number of points where the function pFunction
42 // will be evaluated during integration. The c 42 // will be evaluated during integration. The constructor creates the arrays for
43 // abscissas and weights that are used in Gaus << 43 // abscissas and weights that are used in Gauss-Legendre quadrature method.
44 // The values a and b are the limits of integr 44 // The values a and b are the limits of integration of the pFunction.
45 // nLegendre MUST BE EVEN !!! 45 // nLegendre MUST BE EVEN !!!
46 46
47 G4GaussLegendreQ::G4GaussLegendreQ(function pF << 47 G4GaussLegendreQ::G4GaussLegendreQ( function pFunction,
48 : G4VGaussianQuadrature(pFunction) << 48 G4int nLegendre )
>> 49 : G4VGaussianQuadrature(pFunction)
49 { 50 {
50 const G4double tolerance = 1.6e-10; << 51 const G4double tolerance = 1.6e-10 ;
51 G4int k = nLegendre; << 52 G4int k = nLegendre ;
52 fNumber = (nLegendre + 1) / << 53 fNumber = (nLegendre + 1)/2 ;
53 if(2 * fNumber != k) << 54 if(2*fNumber != k)
54 { << 55 {
55 G4Exception("G4GaussLegendreQ::G4GaussLege << 56 G4Exception("G4GaussLegendreQ::G4GaussLegendreQ()", "InvalidCall",
56 FatalException, "Invalid nLege << 57 FatalException, "Invalid nLegendre argument !") ;
57 } << 58 }
58 G4double newton0 = 0.0, newton1 = 0.0, temp1 << 59 G4double newton0=0.0, newton1=0.0,
59 temp = 0.0; << 60 temp1=0.0, temp2=0.0, temp3=0.0, temp=0.0 ;
60 << 61
61 fAbscissa = new G4double[fNumber]; << 62 fAbscissa = new G4double[fNumber] ;
62 fWeight = new G4double[fNumber]; << 63 fWeight = new G4double[fNumber] ;
63 << 64
64 for(G4int i = 1; i <= fNumber; ++i) // Loop << 65 for(G4int i=1;i<=fNumber;i++) // Loop over the desired roots
65 { << 66 {
66 newton0 = std::cos(pi * (i - 0.25) / (k + << 67 newton0 = std::cos(pi*(i - 0.25)/(k + 0.5)) ; // Initial root
67 do << 68 do // approximation
68 { << 69 { // loop of Newton's method
69 temp1 = 1.0; << 70 temp1 = 1.0 ;
70 temp2 = 0.0; << 71 temp2 = 0.0 ;
71 for(G4int j = 1; j <= k; ++j) << 72 for(G4int j=1;j<=k;j++)
72 { << 73 {
73 temp3 = temp2; << 74 temp3 = temp2 ;
74 temp2 = temp1; << 75 temp2 = temp1 ;
75 temp1 = ((2.0 * j - 1.0) * newton0 * t << 76 temp1 = ((2.0*j - 1.0)*newton0*temp2 - (j - 1.0)*temp3)/j ;
>> 77 }
>> 78 temp = k*(newton0*temp1 - temp2)/(newton0*newton0 - 1.0) ;
>> 79 newton1 = newton0 ;
>> 80 newton0 = newton1 - temp1/temp ; // Newton's method
76 } 81 }
77 temp = k * (newton0 * temp1 - temp2) << 82 while(std::fabs(newton0 - newton1) > tolerance) ;
78 newton1 = newton0; << 83
79 newton0 = newton1 - temp1 / temp; // Ne << 84 fAbscissa[fNumber-i] = newton0 ;
80 } while(std::fabs(newton0 - newton1) > tol << 85 fWeight[fNumber-i] = 2.0/((1.0 - newton0*newton0)*temp*temp) ;
81 << 86 }
82 fAbscissa[fNumber - i] = newton0; <<
83 fWeight[fNumber - i] = 2.0 / ((1.0 - new <<
84 } <<
85 } 87 }
86 88
87 // ------------------------------------------- 89 // --------------------------------------------------------------------------
88 // 90 //
89 // Returns the integral of the function to be 91 // Returns the integral of the function to be pointed by fFunction between a
90 // and b, by 2*fNumber point Gauss-Legendre in 92 // and b, by 2*fNumber point Gauss-Legendre integration: the function is
91 // evaluated exactly 2*fNumber times at interi 93 // evaluated exactly 2*fNumber times at interior points in the range of
92 // integration. Since the weights and abscissa 94 // integration. Since the weights and abscissas are, in this case, symmetric
93 // around the midpoint of the range of integra 95 // around the midpoint of the range of integration, there are actually only
94 // fNumber distinct values of each. 96 // fNumber distinct values of each.
95 97
96 G4double G4GaussLegendreQ::Integral(G4double a << 98 G4double
>> 99 G4GaussLegendreQ::Integral(G4double a, G4double b) const
97 { 100 {
98 G4double xMean = 0.5 * (a + b), xDiff = 0.5 << 101 G4double xMean = 0.5*(a + b),
99 dx = 0.0; << 102 xDiff = 0.5*(b - a),
100 for(G4int i = 0; i < fNumber; ++i) << 103 integral = 0.0, dx = 0.0 ;
101 { << 104 for(G4int i=0;i<fNumber;i++)
102 dx = xDiff * fAbscissa[i]; << 105 {
103 integral += fWeight[i] * (fFunction(xMean << 106 dx = xDiff*fAbscissa[i] ;
104 } << 107 integral += fWeight[i]*(fFunction(xMean + dx) + fFunction(xMean - dx)) ;
105 return integral *= xDiff; << 108 }
>> 109 return integral *= xDiff ;
106 } 110 }
107 111
108 // ------------------------------------------- 112 // --------------------------------------------------------------------------
109 // 113 //
110 // Returns the integral of the function to be 114 // Returns the integral of the function to be pointed by fFunction between a
111 // and b, by ten point Gauss-Legendre integrat 115 // and b, by ten point Gauss-Legendre integration: the function is evaluated
112 // exactly ten times at interior points in the 116 // exactly ten times at interior points in the range of integration. Since the
113 // weights and abscissas are, in this case, sy 117 // weights and abscissas are, in this case, symmetric around the midpoint of
114 // the range of integration, there are actuall 118 // the range of integration, there are actually only five distinct values of
115 // each. 119 // each.
116 120
117 G4double G4GaussLegendreQ::QuickIntegral(G4dou << 121 G4double
>> 122 G4GaussLegendreQ::QuickIntegral(G4double a, G4double b) const
118 { 123 {
119 // From Abramowitz M., Stegan I.A. 1964 , Ha << 124 // From Abramowitz M., Stegan I.A. 1964 , Handbook of Math... , p. 916
120 125
121 static const G4double abscissa[] = { 0.14887 << 126 static const G4double abscissa[] = { 0.148874338981631, 0.433395394129247,
122 0.67940 << 127 0.679409568299024, 0.865063366688985,
123 0.97390 << 128 0.973906528517172 } ;
124 << 129
125 static const G4double weight[] = { 0.2955242 << 130 static const G4double weight[] = { 0.295524224714753, 0.269266719309996,
126 0.2190863 << 131 0.219086362515982, 0.149451349150581,
127 0.0666713 << 132 0.066671344308688 } ;
128 G4double xMean = 0.5 * (a + b), xDiff = 0.5 << 133 G4double xMean = 0.5*(a + b),
129 dx = 0.0; << 134 xDiff = 0.5*(b - a),
130 for(G4int i = 0; i < 5; ++i) << 135 integral = 0.0, dx = 0.0 ;
131 { << 136 for(G4int i=0;i<5;i++)
132 dx = xDiff * abscissa[i]; << 137 {
133 integral += weight[i] * (fFunction(xMean + << 138 dx = xDiff*abscissa[i] ;
134 } << 139 integral += weight[i]*(fFunction(xMean + dx) + fFunction(xMean - dx)) ;
135 return integral *= xDiff; << 140 }
>> 141 return integral *= xDiff ;
136 } 142 }
137 143
138 // ------------------------------------------- 144 // -------------------------------------------------------------------------
139 // 145 //
140 // Returns the integral of the function to be 146 // Returns the integral of the function to be pointed by fFunction between a
141 // and b, by 96 point Gauss-Legendre integrati 147 // and b, by 96 point Gauss-Legendre integration: the function is evaluated
142 // exactly ten times at interior points in the 148 // exactly ten times at interior points in the range of integration. Since the
143 // weights and abscissas are, in this case, sy 149 // weights and abscissas are, in this case, symmetric around the midpoint of
144 // the range of integration, there are actuall 150 // the range of integration, there are actually only five distinct values of
145 // each. 151 // each.
146 152
147 G4double G4GaussLegendreQ::AccurateIntegral(G4 << 153 G4double
148 { << 154 G4GaussLegendreQ::AccurateIntegral(G4double a, G4double b) const
149 // From Abramowitz M., Stegan I.A. 1964 , Ha << 155 {
150 << 156 // From Abramowitz M., Stegan I.A. 1964 , Handbook of Math... , p. 919
151 static const G4double abscissa[] = { << 157
152 0.016276744849602969579, 0.048812985136049 << 158 static const
153 0.081297495464425558994, 0.113695850110665 << 159 G4double abscissa[] = {
154 0.145973714654896941989, 0.178096882367618 << 160 0.016276744849602969579, 0.048812985136049731112,
155 << 161 0.081297495464425558994, 0.113695850110665920911,
156 0.210031310460567203603, 0.241743156163840 << 162 0.145973714654896941989, 0.178096882367618602759, // 6
157 0.273198812591049141487, 0.304364944354496 << 163
158 0.335208522892625422616, 0.365696861472313 << 164 0.210031310460567203603, 0.241743156163840012328,
159 << 165 0.273198812591049141487, 0.304364944354496353024,
160 0.395797649828908603285, 0.425478988407300 << 166 0.335208522892625422616, 0.365696861472313635031, // 12
161 0.454709422167743008636, 0.483457973920596 << 167
162 0.511694177154667673586, 0.539388108324357 << 168 0.395797649828908603285, 0.425478988407300545365,
163 << 169 0.454709422167743008636, 0.483457973920596359768,
164 0.566510418561397168404, 0.593032364777572 << 170 0.511694177154667673586, 0.539388108324357436227, // 18
165 0.618925840125468570386, 0.644163403784967 << 171
166 0.668718310043916153953, 0.692564536642171 << 172 0.566510418561397168404, 0.593032364777572080684,
167 << 173 0.618925840125468570386, 0.644163403784967106798,
168 0.715676812348967626225, 0.738030643744400 << 174 0.668718310043916153953, 0.692564536642171561344, // 24
169 0.759602341176647498703, 0.780369043867433 << 175
170 0.800308744139140817229, 0.819400310737931 << 176 0.715676812348967626225, 0.738030643744400132851,
171 << 177 0.759602341176647498703, 0.780369043867433217604,
172 0.837623511228187121494, 0.854959033434601 << 178 0.800308744139140817229, 0.819400310737931675539, // 30
173 0.871388505909296502874, 0.886894517402420 << 179
174 0.901460635315852341319, 0.915071423120898 << 180 0.837623511228187121494, 0.854959033434601455463,
175 << 181 0.871388505909296502874, 0.886894517402420416057,
176 0.927712456722308690965, 0.939370339752755 << 182 0.901460635315852341319, 0.915071423120898074206, // 36
177 0.950032717784437635756, 0.959688291448742 << 183
178 0.968326828463264212174, 0.975939174585136 << 184 0.927712456722308690965, 0.939370339752755216932,
179 << 185 0.950032717784437635756, 0.959688291448742539300,
180 0.982517263563014677447, 0.988054126329623 << 186 0.968326828463264212174, 0.975939174585136466453, // 42
181 0.992543900323762624572, 0.995981842987209 << 187
182 0.998364375863181677724, 0.999689503883230 << 188 0.982517263563014677447, 0.988054126329623799481,
183 }; << 189 0.992543900323762624572, 0.995981842987209290650,
184 << 190 0.998364375863181677724, 0.999689503883230766828 // 48
185 static const G4double weight[] = { << 191 } ;
186 0.032550614492363166242, 0.032516118713868 << 192
187 0.032447163714064269364, 0.032343822568575 << 193 static const
188 0.032206204794030250669, 0.032034456231992 << 194 G4double weight[] = {
189 << 195 0.032550614492363166242, 0.032516118713868835987,
190 0.031828758894411006535, 0.031589330770727 << 196 0.032447163714064269364, 0.032343822568575928429,
191 0.031316425596862355813, 0.031010332586313 << 197 0.032206204794030250669, 0.032034456231992663218, // 6
192 0.030671376123669149014, 0.030299915420827 << 198
193 << 199 0.031828758894411006535, 0.031589330770727168558,
194 0.029896344136328385984, 0.029461089958167 << 200 0.031316425596862355813, 0.031010332586313837423,
195 0.028994614150555236543, 0.028497411065085 << 201 0.030671376123669149014, 0.030299915420827593794, // 12
196 0.027970007616848334440, 0.027412962726029 << 202
197 << 203 0.029896344136328385984, 0.029461089958167905970,
198 0.026826866725591762198, 0.026212340735672 << 204 0.028994614150555236543, 0.028497411065085385646,
199 0.025570036005349361499, 0.024900633222483 << 205 0.027970007616848334440, 0.027412962726029242823, // 18
200 0.024204841792364691282, 0.023483399085926 << 206
201 << 207 0.026826866725591762198, 0.026212340735672413913,
202 0.022737069658329374001, 0.021966644438744 << 208 0.025570036005349361499, 0.024900633222483610288,
203 0.021172939892191298988, 0.020356797154333 << 209 0.024204841792364691282, 0.023483399085926219842, // 24
204 0.019519081140145022410, 0.018660679627411 << 210
205 << 211 0.022737069658329374001, 0.021966644438744349195,
206 0.017782502316045260838, 0.016885479864245 << 212 0.021172939892191298988, 0.020356797154333324595,
207 0.015970562902562291381, 0.015038721026994 << 213 0.019519081140145022410, 0.018660679627411467385, // 30
208 0.014090941772314860916, 0.013128229566961 << 214
209 << 215 0.017782502316045260838, 0.016885479864245172450,
210 0.012151604671088319635, 0.011162102099838 << 216 0.015970562902562291381, 0.015038721026994938006,
211 0.010160770535008415758, 0.009148671230783 << 217 0.014090941772314860916, 0.013128229566961572637, // 36
212 0.008126876925698759217, 0.007096470791153 << 218
213 << 219 0.012151604671088319635, 0.011162102099838498591,
214 0.006058545504235961683, 0.005014202742927 << 220 0.010160770535008415758, 0.009148671230783386633,
215 0.003964554338444686674, 0.002910731817934 << 221 0.008126876925698759217, 0.007096470791153865269, // 42
216 0.001853960788946921732, 0.000796792065552 << 222
217 }; << 223 0.006058545504235961683, 0.005014202742927517693,
218 G4double xMean = 0.5 * (a + b), xDiff = 0.5 << 224 0.003964554338444686674, 0.002910731817934946408,
219 dx = 0.0; << 225 0.001853960788946921732, 0.000796792065552012429 // 48
220 for(G4int i = 0; i < 48; ++i) << 226 } ;
221 { << 227 G4double xMean = 0.5*(a + b),
222 dx = xDiff * abscissa[i]; << 228 xDiff = 0.5*(b - a),
223 integral += weight[i] * (fFunction(xMean + << 229 integral = 0.0, dx = 0.0 ;
224 } << 230 for(G4int i=0;i<48;i++)
225 return integral *= xDiff; << 231 {
>> 232 dx = xDiff*abscissa[i] ;
>> 233 integral += weight[i]*(fFunction(xMean + dx) + fFunction(xMean - dx)) ;
>> 234 }
>> 235 return integral *= xDiff ;
226 } 236 }
227 237