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