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25 // 25 //
26 // G4ChebyshevApproximation class implementati 26 // G4ChebyshevApproximation class implementation
27 // 27 //
28 // Author: V.Grichine, 24.04.97 28 // Author: V.Grichine, 24.04.97
29 // ------------------------------------------- 29 // --------------------------------------------------------------------
30 30
31 #include "G4ChebyshevApproximation.hh" 31 #include "G4ChebyshevApproximation.hh"
32 #include "G4PhysicalConstants.hh" 32 #include "G4PhysicalConstants.hh"
33 33
34 // Constructor for initialisation of the class 34 // Constructor for initialisation of the class data members.
35 // It creates the array fChebyshevCof[0,...,fN 35 // It creates the array fChebyshevCof[0,...,fNumber-1], fNumber = n ;
36 // which consists of Chebyshev coefficients de 36 // which consists of Chebyshev coefficients describing the function
37 // pointed by pFunction. The values a and b fi 37 // pointed by pFunction. The values a and b fix the interval of validity
38 // of the Chebyshev approximation. 38 // of the Chebyshev approximation.
39 39
40 G4ChebyshevApproximation::G4ChebyshevApproxima 40 G4ChebyshevApproximation::G4ChebyshevApproximation(function pFunction, G4int n,
41 41 G4double a, G4double b)
42 : fFunction(pFunction) 42 : fFunction(pFunction)
43 , fNumber(n) 43 , fNumber(n)
44 , fChebyshevCof(new G4double[fNumber]) 44 , fChebyshevCof(new G4double[fNumber])
45 , fMean(0.5 * (b + a)) 45 , fMean(0.5 * (b + a))
46 , fDiff(0.5 * (b - a)) 46 , fDiff(0.5 * (b - a))
47 { 47 {
48 G4int i = 0, j = 0; 48 G4int i = 0, j = 0;
49 G4double rootSum = 0.0, cofj = 0.0; 49 G4double rootSum = 0.0, cofj = 0.0;
50 auto tempFunction = new G4double[fNumber]; << 50 G4double* tempFunction = new G4double[fNumber];
51 G4double weight = 2.0 / fNumber; 51 G4double weight = 2.0 / fNumber;
52 G4double cof = 0.5 * weight * pi; 52 G4double cof = 0.5 * weight * pi; // pi/n
53 53
54 for(i = 0; i < fNumber; ++i) 54 for(i = 0; i < fNumber; ++i)
55 { 55 {
56 rootSum = std::cos(cof * (i + 0.5) 56 rootSum = std::cos(cof * (i + 0.5));
57 tempFunction[i] = fFunction(rootSum * fDif 57 tempFunction[i] = fFunction(rootSum * fDiff + fMean);
58 } 58 }
59 for(j = 0; j < fNumber; ++j) 59 for(j = 0; j < fNumber; ++j)
60 { 60 {
61 cofj = cof * j; 61 cofj = cof * j;
62 rootSum = 0.0; 62 rootSum = 0.0;
63 63
64 for(i = 0; i < fNumber; ++i) 64 for(i = 0; i < fNumber; ++i)
65 { 65 {
66 rootSum += tempFunction[i] * std::cos(co 66 rootSum += tempFunction[i] * std::cos(cofj * (i + 0.5));
67 } 67 }
68 fChebyshevCof[j] = weight * rootSum; 68 fChebyshevCof[j] = weight * rootSum;
69 } 69 }
70 delete[] tempFunction; 70 delete[] tempFunction;
71 } 71 }
72 72
73 // ------------------------------------------- 73 // --------------------------------------------------------------------
74 // 74 //
75 // Constructor for creation of Chebyshev coeff 75 // Constructor for creation of Chebyshev coefficients for mx-derivative
76 // from pFunction. The value of mx ! MUST BE ! 76 // from pFunction. The value of mx ! MUST BE ! < nx , because the result
77 // array of fChebyshevCof will be of (nx-mx) s 77 // array of fChebyshevCof will be of (nx-mx) size. The values a and b
78 // fix the interval of validity of the Chebysh 78 // fix the interval of validity of the Chebyshev approximation.
79 79
80 G4ChebyshevApproximation::G4ChebyshevApproxima 80 G4ChebyshevApproximation::G4ChebyshevApproximation(function pFunction, G4int nx,
81 81 G4int mx, G4double a,
82 82 G4double b)
83 : fFunction(pFunction) 83 : fFunction(pFunction)
84 , fNumber(nx) 84 , fNumber(nx)
85 , fChebyshevCof(new G4double[fNumber]) 85 , fChebyshevCof(new G4double[fNumber])
86 , fMean(0.5 * (b + a)) 86 , fMean(0.5 * (b + a))
87 , fDiff(0.5 * (b - a)) 87 , fDiff(0.5 * (b - a))
88 { 88 {
89 if(nx <= mx) 89 if(nx <= mx)
90 { 90 {
91 G4Exception("G4ChebyshevApproximation::G4C 91 G4Exception("G4ChebyshevApproximation::G4ChebyshevApproximation()",
92 "InvalidCall", FatalException, 92 "InvalidCall", FatalException, "Invalid arguments !");
93 } 93 }
94 G4int i = 0, j = 0; 94 G4int i = 0, j = 0;
95 G4double rootSum = 0.0, cofj = 0.0; 95 G4double rootSum = 0.0, cofj = 0.0;
96 auto tempFunction = new G4double[fNumber]; << 96 G4double* tempFunction = new G4double[fNumber];
97 G4double weight = 2.0 / fNumber; 97 G4double weight = 2.0 / fNumber;
98 G4double cof = 0.5 * weight * pi; 98 G4double cof = 0.5 * weight * pi; // pi/nx
99 99
100 for(i = 0; i < fNumber; ++i) 100 for(i = 0; i < fNumber; ++i)
101 { 101 {
102 rootSum = std::cos(cof * (i + 0.5) 102 rootSum = std::cos(cof * (i + 0.5));
103 tempFunction[i] = fFunction(rootSum * fDif 103 tempFunction[i] = fFunction(rootSum * fDiff + fMean);
104 } 104 }
105 for(j = 0; j < fNumber; ++j) 105 for(j = 0; j < fNumber; ++j)
106 { 106 {
107 cofj = cof * j; 107 cofj = cof * j;
108 rootSum = 0.0; 108 rootSum = 0.0;
109 109
110 for(i = 0; i < fNumber; ++i) 110 for(i = 0; i < fNumber; ++i)
111 { 111 {
112 rootSum += tempFunction[i] * std::cos(co 112 rootSum += tempFunction[i] * std::cos(cofj * (i + 0.5));
113 } 113 }
114 fChebyshevCof[j] = weight * rootSum; // c 114 fChebyshevCof[j] = weight * rootSum; // corresponds to pFunction
115 } 115 }
116 // Chebyshev coefficients for (mx)-derivativ 116 // Chebyshev coefficients for (mx)-derivative of pFunction
117 117
118 for(i = 1; i <= mx; ++i) 118 for(i = 1; i <= mx; ++i)
119 { 119 {
120 DerivativeChebyshevCof(tempFunction); 120 DerivativeChebyshevCof(tempFunction);
121 fNumber--; 121 fNumber--;
122 for(j = 0; j < fNumber; ++j) 122 for(j = 0; j < fNumber; ++j)
123 { 123 {
124 fChebyshevCof[j] = tempFunction[j]; // 124 fChebyshevCof[j] = tempFunction[j]; // corresponds to (i)-derivative
125 } 125 }
126 } 126 }
127 delete[] tempFunction; // delete of dynamic 127 delete[] tempFunction; // delete of dynamically allocated tempFunction
128 } 128 }
129 129
130 // ------------------------------------------- 130 // ------------------------------------------------------
131 // 131 //
132 // Constructor for creation of Chebyshev coeff 132 // Constructor for creation of Chebyshev coefficients for integral
133 // from pFunction. 133 // from pFunction.
134 134
135 G4ChebyshevApproximation::G4ChebyshevApproxima 135 G4ChebyshevApproximation::G4ChebyshevApproximation(function pFunction,
136 136 G4double a, G4double b,
137 137 G4int n)
138 : fFunction(pFunction) 138 : fFunction(pFunction)
139 , fNumber(n) 139 , fNumber(n)
140 , fChebyshevCof(new G4double[fNumber]) 140 , fChebyshevCof(new G4double[fNumber])
141 , fMean(0.5 * (b + a)) 141 , fMean(0.5 * (b + a))
142 , fDiff(0.5 * (b - a)) 142 , fDiff(0.5 * (b - a))
143 { 143 {
144 G4int i = 0, j = 0; 144 G4int i = 0, j = 0;
145 G4double rootSum = 0.0, cofj = 0.0; 145 G4double rootSum = 0.0, cofj = 0.0;
146 auto tempFunction = new G4double[fNumber]; << 146 G4double* tempFunction = new G4double[fNumber];
147 G4double weight = 2.0 / fNumber; 147 G4double weight = 2.0 / fNumber;
148 G4double cof = 0.5 * weight * pi; 148 G4double cof = 0.5 * weight * pi; // pi/n
149 149
150 for(i = 0; i < fNumber; ++i) 150 for(i = 0; i < fNumber; ++i)
151 { 151 {
152 rootSum = std::cos(cof * (i + 0.5) 152 rootSum = std::cos(cof * (i + 0.5));
153 tempFunction[i] = fFunction(rootSum * fDif 153 tempFunction[i] = fFunction(rootSum * fDiff + fMean);
154 } 154 }
155 for(j = 0; j < fNumber; ++j) 155 for(j = 0; j < fNumber; ++j)
156 { 156 {
157 cofj = cof * j; 157 cofj = cof * j;
158 rootSum = 0.0; 158 rootSum = 0.0;
159 159
160 for(i = 0; i < fNumber; ++i) 160 for(i = 0; i < fNumber; ++i)
161 { 161 {
162 rootSum += tempFunction[i] * std::cos(co 162 rootSum += tempFunction[i] * std::cos(cofj * (i + 0.5));
163 } 163 }
164 fChebyshevCof[j] = weight * rootSum; // c 164 fChebyshevCof[j] = weight * rootSum; // corresponds to pFunction
165 } 165 }
166 // Chebyshev coefficients for integral of pF 166 // Chebyshev coefficients for integral of pFunction
167 167
168 IntegralChebyshevCof(tempFunction); 168 IntegralChebyshevCof(tempFunction);
169 for(j = 0; j < fNumber; ++j) 169 for(j = 0; j < fNumber; ++j)
170 { 170 {
171 fChebyshevCof[j] = tempFunction[j]; // co 171 fChebyshevCof[j] = tempFunction[j]; // corresponds to integral
172 } 172 }
173 delete[] tempFunction; // delete of dynamic 173 delete[] tempFunction; // delete of dynamically allocated tempFunction
174 } 174 }
175 175
176 // ------------------------------------------- 176 // ---------------------------------------------------------------
177 // 177 //
178 // Destructor deletes the array of Chebyshev c 178 // Destructor deletes the array of Chebyshev coefficients
179 179
180 G4ChebyshevApproximation::~G4ChebyshevApproxim 180 G4ChebyshevApproximation::~G4ChebyshevApproximation()
181 { 181 {
182 delete[] fChebyshevCof; 182 delete[] fChebyshevCof;
183 } 183 }
184 184
185 // ------------------------------------------- 185 // ---------------------------------------------------------------
186 // 186 //
187 // Access function for Chebyshev coefficients 187 // Access function for Chebyshev coefficients
188 // 188 //
189 189
190 G4double G4ChebyshevApproximation::GetChebyshe 190 G4double G4ChebyshevApproximation::GetChebyshevCof(G4int number) const
191 { 191 {
192 if(number < 0 && number >= fNumber) 192 if(number < 0 && number >= fNumber)
193 { 193 {
194 G4Exception("G4ChebyshevApproximation::Get 194 G4Exception("G4ChebyshevApproximation::GetChebyshevCof()", "InvalidCall",
195 FatalException, "Argument out 195 FatalException, "Argument out of range !");
196 } 196 }
197 return fChebyshevCof[number]; 197 return fChebyshevCof[number];
198 } 198 }
199 199
200 // ------------------------------------------- 200 // --------------------------------------------------------------
201 // 201 //
202 // Evaluate the value of fFunction at the poin 202 // Evaluate the value of fFunction at the point x via the Chebyshev coefficients
203 // fChebyshevCof[0,...,fNumber-1] 203 // fChebyshevCof[0,...,fNumber-1]
204 204
205 G4double G4ChebyshevApproximation::ChebyshevEv 205 G4double G4ChebyshevApproximation::ChebyshevEvaluation(G4double x) const
206 { 206 {
207 G4double evaluate = 0.0, evaluate2 = 0.0, te 207 G4double evaluate = 0.0, evaluate2 = 0.0, temp = 0.0, xReduced = 0.0,
208 xReduced2 = 0.0; 208 xReduced2 = 0.0;
209 209
210 if((x - fMean + fDiff) * (x - fMean - fDiff) 210 if((x - fMean + fDiff) * (x - fMean - fDiff) > 0.0)
211 { 211 {
212 G4Exception("G4ChebyshevApproximation::Che 212 G4Exception("G4ChebyshevApproximation::ChebyshevEvaluation()",
213 "InvalidCall", FatalException, 213 "InvalidCall", FatalException, "Invalid argument !");
214 } 214 }
215 xReduced = (x - fMean) / fDiff; 215 xReduced = (x - fMean) / fDiff;
216 xReduced2 = 2.0 * xReduced; 216 xReduced2 = 2.0 * xReduced;
217 for(G4int i = fNumber - 1; i >= 1; --i) 217 for(G4int i = fNumber - 1; i >= 1; --i)
218 { 218 {
219 temp = evaluate; 219 temp = evaluate;
220 evaluate = xReduced2 * evaluate - evaluat 220 evaluate = xReduced2 * evaluate - evaluate2 + fChebyshevCof[i];
221 evaluate2 = temp; 221 evaluate2 = temp;
222 } 222 }
223 return xReduced * evaluate - evaluate2 + 0.5 223 return xReduced * evaluate - evaluate2 + 0.5 * fChebyshevCof[0];
224 } 224 }
225 225
226 // ------------------------------------------- 226 // ------------------------------------------------------------------
227 // 227 //
228 // Returns the array derCof[0,...,fNumber-2], 228 // Returns the array derCof[0,...,fNumber-2], the Chebyshev coefficients of the
229 // derivative of the function whose coefficien 229 // derivative of the function whose coefficients are fChebyshevCof
230 230
231 void G4ChebyshevApproximation::DerivativeCheby 231 void G4ChebyshevApproximation::DerivativeChebyshevCof(G4double derCof[]) const
232 { 232 {
233 G4double cof = 1.0 / fDiff; 233 G4double cof = 1.0 / fDiff;
234 derCof[fNumber - 1] = 0.0; 234 derCof[fNumber - 1] = 0.0;
235 derCof[fNumber - 2] = 2 * (fNumber - 1) * fC 235 derCof[fNumber - 2] = 2 * (fNumber - 1) * fChebyshevCof[fNumber - 1];
236 for(G4int i = fNumber - 3; i >= 0; --i) 236 for(G4int i = fNumber - 3; i >= 0; --i)
237 { 237 {
238 derCof[i] = derCof[i + 2] + 2 * (i + 1) * 238 derCof[i] = derCof[i + 2] + 2 * (i + 1) * fChebyshevCof[i + 1];
239 } 239 }
240 for(G4int j = 0; j < fNumber; ++j) 240 for(G4int j = 0; j < fNumber; ++j)
241 { 241 {
242 derCof[j] *= cof; 242 derCof[j] *= cof;
243 } 243 }
244 } 244 }
245 245
246 // ------------------------------------------- 246 // ------------------------------------------------------------------------
247 // 247 //
248 // This function produces the array integralCo 248 // This function produces the array integralCof[0,...,fNumber-1] , the Chebyshev
249 // coefficients of the integral of the functio 249 // coefficients of the integral of the function whose coefficients are
250 // fChebyshevCof[]. The constant of integratio 250 // fChebyshevCof[]. The constant of integration is set so that the integral
251 // vanishes at the point (fMean - fDiff), i.e. 251 // vanishes at the point (fMean - fDiff), i.e. at the begining of the interval
252 // of validity (we start the integration from 252 // of validity (we start the integration from this point).
253 // 253 //
254 254
255 void G4ChebyshevApproximation::IntegralChebysh 255 void G4ChebyshevApproximation::IntegralChebyshevCof(
256 G4double integralCof[]) const 256 G4double integralCof[]) const
257 { 257 {
258 G4double cof = 0.5 * fDiff, sum = 0.0, facto 258 G4double cof = 0.5 * fDiff, sum = 0.0, factor = 1.0;
259 for(G4int i = 1; i < fNumber - 1; ++i) 259 for(G4int i = 1; i < fNumber - 1; ++i)
260 { 260 {
261 integralCof[i] = cof * (fChebyshevCof[i - 261 integralCof[i] = cof * (fChebyshevCof[i - 1] - fChebyshevCof[i + 1]) / i;
262 sum += factor * integralCof[i]; 262 sum += factor * integralCof[i];
263 factor = -factor; 263 factor = -factor;
264 } 264 }
265 integralCof[fNumber - 1] = cof * fChebyshevC 265 integralCof[fNumber - 1] = cof * fChebyshevCof[fNumber - 2] / (fNumber - 1);
266 sum += factor * integralCof[fNumber - 1]; 266 sum += factor * integralCof[fNumber - 1];
267 integralCof[0] = 2.0 * sum; // set the cons 267 integralCof[0] = 2.0 * sum; // set the constant of integration
268 } 268 }
269 269