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99adacae | 1 | /************************************************************************** |
2 | * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. * | |
3 | * * | |
4 | * Author: The ALICE Off-line Project. * | |
5 | * Contributors are mentioned in the code where appropriate. * | |
6 | * * | |
7 | * Permission to use, copy, modify and distribute this software and its * | |
8 | * documentation strictly for non-commercial purposes is hereby granted * | |
9 | * without fee, provided that the above copyright notice appears in all * | |
10 | * copies and that both the copyright notice and this permission notice * | |
11 | * appear in the supporting documentation. The authors make no claims * | |
12 | * about the suitability of this software for any purpose. It is * | |
13 | * provided "as is" without express or implied warranty. * | |
14 | **************************************************************************/ | |
15 | ||
b09247a2 | 16 | #include <cstdlib> |
99adacae | 17 | #include "AliCheb3DCalc.h" |
5406439e | 18 | #include <TSystem.h> |
99adacae | 19 | |
20 | ClassImp(AliCheb3DCalc) | |
21 | ||
40389866 | 22 | //__________________________________________________________________________________________ |
23 | AliCheb3DCalc::AliCheb3DCalc() : | |
24 | fNCoefs(0), | |
25 | fNRows(0), | |
26 | fNCols(0), | |
27 | fNElemBound2D(0), | |
28 | fNColsAtRow(0), | |
29 | fColAtRowBg(0), | |
30 | fCoefBound2D0(0), | |
31 | fCoefBound2D1(0), | |
32 | fCoefs(0), | |
33 | fTmpCf1(0), | |
34 | fTmpCf0(0) | |
5406439e | 35 | { |
36 | // default constructor | |
37 | } | |
99adacae | 38 | |
40389866 | 39 | //__________________________________________________________________________________________ |
40 | AliCheb3DCalc::AliCheb3DCalc(const AliCheb3DCalc& src) : | |
41 | TNamed(src), | |
42 | fNCoefs(src.fNCoefs), | |
43 | fNRows(src.fNRows), | |
44 | fNCols(src.fNCols), | |
45 | fNElemBound2D(src.fNElemBound2D), | |
46 | fNColsAtRow(0), | |
47 | fColAtRowBg(0), | |
48 | fCoefBound2D0(0), | |
49 | fCoefBound2D1(0), | |
50 | fCoefs(0), | |
51 | fTmpCf1(0), | |
52 | fTmpCf0(0) | |
99adacae | 53 | { |
5406439e | 54 | // copy constructor |
55 | // | |
40389866 | 56 | if (src.fNColsAtRow) { |
57 | fNColsAtRow = new Int_t[fNRows]; | |
58 | for (int i=fNRows;i--;) fNColsAtRow[i] = src.fNColsAtRow[i]; | |
59 | } | |
60 | if (src.fColAtRowBg) { | |
61 | fColAtRowBg = new Int_t[fNRows]; | |
62 | for (int i=fNRows;i--;) fColAtRowBg[i] = src.fColAtRowBg[i]; | |
63 | } | |
64 | if (src.fCoefBound2D0) { | |
65 | fCoefBound2D0 = new Int_t[fNElemBound2D]; | |
66 | for (int i=fNElemBound2D;i--;) fCoefBound2D0[i] = src.fCoefBound2D0[i]; | |
67 | } | |
68 | if (src.fCoefBound2D1) { | |
69 | fCoefBound2D1 = new Int_t[fNElemBound2D]; | |
70 | for (int i=fNElemBound2D;i--;) fCoefBound2D1[i] = src.fCoefBound2D1[i]; | |
71 | } | |
72 | if (src.fCoefs) { | |
73 | fCoefs = new Float_t[fNCoefs]; | |
74 | for (int i=fNCoefs;i--;) fCoefs[i] = src.fCoefs[i]; | |
75 | } | |
76 | if (src.fTmpCf1) fTmpCf1 = new Float_t[fNCols]; | |
77 | if (src.fTmpCf0) fTmpCf0 = new Float_t[fNRows]; | |
99adacae | 78 | } |
79 | ||
40389866 | 80 | //__________________________________________________________________________________________ |
81 | AliCheb3DCalc::AliCheb3DCalc(FILE* stream) : | |
82 | fNCoefs(0), | |
83 | fNRows(0), | |
84 | fNCols(0), | |
85 | fNElemBound2D(0), | |
86 | fNColsAtRow(0), | |
87 | fColAtRowBg(0), | |
88 | fCoefBound2D0(0), | |
89 | fCoefBound2D1(0), | |
90 | fCoefs(0), | |
91 | fTmpCf1(0), | |
92 | fTmpCf0(0) | |
99adacae | 93 | { |
5406439e | 94 | // constructor from coeffs. streem |
40389866 | 95 | LoadData(stream); |
99adacae | 96 | } |
97 | ||
40389866 | 98 | //__________________________________________________________________________________________ |
99 | AliCheb3DCalc& AliCheb3DCalc::operator=(const AliCheb3DCalc& rhs) | |
99adacae | 100 | { |
5406439e | 101 | // assignment operator |
40389866 | 102 | if (this != &rhs) { |
103 | Clear(); | |
104 | SetName(rhs.GetName()); | |
105 | SetTitle(rhs.GetTitle()); | |
106 | fNCoefs = rhs.fNCoefs; | |
107 | fNRows = rhs.fNRows; | |
108 | fNCols = rhs.fNCols; | |
109 | if (rhs.fNColsAtRow) { | |
110 | fNColsAtRow = new Int_t[fNRows]; | |
111 | for (int i=fNRows;i--;) fNColsAtRow[i] = rhs.fNColsAtRow[i]; | |
99adacae | 112 | } |
40389866 | 113 | if (rhs.fColAtRowBg) { |
114 | fColAtRowBg = new Int_t[fNRows]; | |
115 | for (int i=fNRows;i--;) fColAtRowBg[i] = rhs.fColAtRowBg[i]; | |
99adacae | 116 | } |
40389866 | 117 | if (rhs.fCoefBound2D0) { |
118 | fCoefBound2D0 = new Int_t[fNElemBound2D]; | |
119 | for (int i=fNElemBound2D;i--;) fCoefBound2D0[i] = rhs.fCoefBound2D0[i]; | |
99adacae | 120 | } |
40389866 | 121 | if (rhs.fCoefBound2D1) { |
122 | fCoefBound2D1 = new Int_t[fNElemBound2D]; | |
123 | for (int i=fNElemBound2D;i--;) fCoefBound2D1[i] = rhs.fCoefBound2D1[i]; | |
99adacae | 124 | } |
40389866 | 125 | if (rhs.fCoefs) { |
126 | fCoefs = new Float_t[fNCoefs]; | |
127 | for (int i=fNCoefs;i--;) fCoefs[i] = rhs.fCoefs[i]; | |
99adacae | 128 | } |
40389866 | 129 | if (rhs.fTmpCf1) fTmpCf1 = new Float_t[fNCols]; |
130 | if (rhs.fTmpCf0) fTmpCf0 = new Float_t[fNRows]; | |
131 | } | |
132 | return *this; | |
99adacae | 133 | } |
134 | ||
135 | //__________________________________________________________________________________________ | |
5406439e | 136 | void AliCheb3DCalc::Clear(const Option_t*) |
99adacae | 137 | { |
138 | // delete all dynamycally allocated structures | |
139 | if (fTmpCf1) { delete[] fTmpCf1; fTmpCf1 = 0;} | |
140 | if (fTmpCf0) { delete[] fTmpCf0; fTmpCf0 = 0;} | |
141 | if (fCoefs) { delete[] fCoefs; fCoefs = 0;} | |
142 | if (fCoefBound2D0) { delete[] fCoefBound2D0; fCoefBound2D0 = 0; } | |
143 | if (fCoefBound2D1) { delete[] fCoefBound2D1; fCoefBound2D1 = 0; } | |
144 | if (fNColsAtRow) { delete[] fNColsAtRow; fNColsAtRow = 0; } | |
145 | if (fColAtRowBg) { delete[] fColAtRowBg; fColAtRowBg = 0; } | |
146 | // | |
147 | } | |
148 | ||
99adacae | 149 | //__________________________________________________________________________________________ |
5406439e | 150 | void AliCheb3DCalc::Print(const Option_t* ) const |
99adacae | 151 | { |
5406439e | 152 | // print info |
99adacae | 153 | printf("Chebyshev parameterization data %s for 3D->1 function.\n",GetName()); |
154 | int nmax3d = 0; | |
155 | for (int i=fNElemBound2D;i--;) if (fCoefBound2D0[i]>nmax3d) nmax3d = fCoefBound2D0[i]; | |
156 | printf("%d coefficients in %dx%dx%d matrix\n",fNCoefs,fNRows,fNCols,nmax3d); | |
157 | // | |
158 | } | |
159 | ||
160 | //__________________________________________________________________________________________ | |
5406439e | 161 | Float_t AliCheb3DCalc::Eval(const Float_t *par) const |
99adacae | 162 | { |
163 | // evaluate Chebyshev parameterization for 3D function. | |
164 | // VERY IMPORTANT: par must contain the function arguments ALREADY MAPPED to [-1:1] interval | |
5406439e | 165 | const Float_t &z = par[2]; |
166 | const Float_t &y = par[1]; | |
167 | const Float_t &x = par[0]; | |
99adacae | 168 | // |
169 | int ncfRC; | |
170 | for (int id0=fNRows;id0--;) { | |
171 | int nCLoc = fNColsAtRow[id0]; // number of significant coefs on this row | |
5406439e | 172 | int col0 = fColAtRowBg[id0]; // beginning of local column in the 2D boundary matrix |
99adacae | 173 | for (int id1=nCLoc;id1--;) { |
5406439e | 174 | int id = id1+col0; |
99adacae | 175 | fTmpCf1[id1] = (ncfRC=fCoefBound2D0[id]) ? ChebEval1D(z,fCoefs + fCoefBound2D1[id], ncfRC) : 0.0; |
176 | } | |
177 | fTmpCf0[id0] = nCLoc>0 ? ChebEval1D(y,fTmpCf1,nCLoc):0.0; | |
178 | } | |
179 | return ChebEval1D(x,fTmpCf0,fNRows); | |
180 | // | |
181 | } | |
182 | ||
40389866 | 183 | //__________________________________________________________________________________________ |
5406439e | 184 | Float_t AliCheb3DCalc::EvalDeriv(int dim, const Float_t *par) const |
40389866 | 185 | { |
186 | // evaluate Chebyshev parameterization derivative in given dimension for 3D function. | |
187 | // VERY IMPORTANT: par must contain the function arguments ALREADY MAPPED to [-1:1] interval | |
5406439e | 188 | const Float_t &z = par[2]; |
189 | const Float_t &y = par[1]; | |
190 | const Float_t &x = par[0]; | |
40389866 | 191 | // |
192 | int ncfRC; | |
193 | for (int id0=fNRows;id0--;) { | |
194 | int nCLoc = fNColsAtRow[id0]; // number of significant coefs on this row | |
1cf34ee8 | 195 | if (!nCLoc) {fTmpCf0[id0]=0; continue;} |
196 | // | |
5406439e | 197 | int col0 = fColAtRowBg[id0]; // beginning of local column in the 2D boundary matrix |
40389866 | 198 | for (int id1=nCLoc;id1--;) { |
5406439e | 199 | int id = id1+col0; |
1cf34ee8 | 200 | if (!(ncfRC=fCoefBound2D0[id])) { fTmpCf1[id1]=0; continue;} |
201 | if (dim==2) fTmpCf1[id1] = ChebEval1Deriv(z,fCoefs + fCoefBound2D1[id], ncfRC); | |
202 | else fTmpCf1[id1] = ChebEval1D(z,fCoefs + fCoefBound2D1[id], ncfRC); | |
40389866 | 203 | } |
1cf34ee8 | 204 | if (dim==1) fTmpCf0[id0] = ChebEval1Deriv(y,fTmpCf1,nCLoc); |
205 | else fTmpCf0[id0] = ChebEval1D(y,fTmpCf1,nCLoc); | |
40389866 | 206 | } |
207 | return (dim==0) ? ChebEval1Deriv(x,fTmpCf0,fNRows) : ChebEval1D(x,fTmpCf0,fNRows); | |
208 | // | |
209 | } | |
210 | ||
1cf34ee8 | 211 | //__________________________________________________________________________________________ |
5406439e | 212 | Float_t AliCheb3DCalc::EvalDeriv2(int dim1,int dim2, const Float_t *par) const |
1cf34ee8 | 213 | { |
214 | // evaluate Chebyshev parameterization 2n derivative in given dimensions for 3D function. | |
215 | // VERY IMPORTANT: par must contain the function arguments ALREADY MAPPED to [-1:1] interval | |
5406439e | 216 | const Float_t &z = par[2]; |
217 | const Float_t &y = par[1]; | |
218 | const Float_t &x = par[0]; | |
1cf34ee8 | 219 | // |
220 | Bool_t same = dim1==dim2; | |
221 | int ncfRC; | |
222 | for (int id0=fNRows;id0--;) { | |
223 | int nCLoc = fNColsAtRow[id0]; // number of significant coefs on this row | |
224 | if (!nCLoc) {fTmpCf0[id0]=0; continue;} | |
225 | // | |
5406439e | 226 | int col0 = fColAtRowBg[id0]; // beginning of local column in the 2D boundary matrix |
1cf34ee8 | 227 | for (int id1=nCLoc;id1--;) { |
5406439e | 228 | int id = id1+col0; |
1cf34ee8 | 229 | if (!(ncfRC=fCoefBound2D0[id])) { fTmpCf1[id1]=0; continue;} |
230 | if (dim1==2||dim2==2) fTmpCf1[id1] = same ? ChebEval1Deriv2(z,fCoefs + fCoefBound2D1[id], ncfRC) | |
231 | : ChebEval1Deriv(z,fCoefs + fCoefBound2D1[id], ncfRC); | |
232 | else fTmpCf1[id1] = ChebEval1D(z,fCoefs + fCoefBound2D1[id], ncfRC); | |
233 | } | |
234 | if (dim1==1||dim2==1) fTmpCf0[id0] = same ? ChebEval1Deriv2(y,fTmpCf1,nCLoc):ChebEval1Deriv(y,fTmpCf1,nCLoc); | |
235 | else fTmpCf0[id0] = ChebEval1D(y,fTmpCf1,nCLoc); | |
236 | } | |
237 | return (dim1==0||dim2==0) ? (same ? ChebEval1Deriv2(x,fTmpCf0,fNRows):ChebEval1Deriv(x,fTmpCf0,fNRows)) : ChebEval1D(x,fTmpCf0,fNRows); | |
238 | // | |
239 | } | |
240 | ||
99adacae | 241 | //_______________________________________________ |
242 | #ifdef _INC_CREATION_ALICHEB3D_ | |
243 | void AliCheb3DCalc::SaveData(const char* outfile,Bool_t append) const | |
244 | { | |
245 | // writes coefficients data to output text file, optionallt appending on the end of existing file | |
246 | TString strf = outfile; | |
247 | gSystem->ExpandPathName(strf); | |
248 | FILE* stream = fopen(strf,append ? "a":"w"); | |
249 | SaveData(stream); | |
250 | fclose(stream); | |
251 | // | |
252 | } | |
253 | #endif | |
254 | ||
255 | //_______________________________________________ | |
256 | #ifdef _INC_CREATION_ALICHEB3D_ | |
257 | void AliCheb3DCalc::SaveData(FILE* stream) const | |
258 | { | |
259 | // writes coefficients data to existing output stream | |
260 | // Note: fNCols, fNElemBound2D and fColAtRowBg is not stored, will be computed on fly during the loading of this file | |
261 | fprintf(stream,"#\nSTART %s\n",GetName()); | |
262 | fprintf(stream,"# Number of rows\n%d\n",fNRows); | |
263 | // | |
264 | fprintf(stream,"# Number of columns per row\n"); | |
265 | for (int i=0;i<fNRows;i++) fprintf(stream,"%d\n",fNColsAtRow[i]); | |
266 | // | |
267 | fprintf(stream,"# Number of Coefs in each significant block of third dimension\n"); | |
268 | for (int i=0;i<fNElemBound2D;i++) fprintf(stream,"%d\n",fCoefBound2D0[i]); | |
269 | // | |
270 | fprintf(stream,"# Coefficients\n"); | |
271 | for (int i=0;i<fNCoefs;i++) fprintf(stream,"%+.8e\n",fCoefs[i]); | |
272 | fprintf(stream,"END %s\n",GetName()); | |
273 | // | |
274 | } | |
275 | #endif | |
276 | ||
277 | //_______________________________________________ | |
278 | void AliCheb3DCalc::LoadData(FILE* stream) | |
279 | { | |
280 | // Load coefs. from the stream | |
281 | if (!stream) {Error("LoadData","No stream provided.\nStop"); exit(1);} | |
282 | TString buffs; | |
283 | Clear(); | |
284 | ReadLine(buffs,stream); | |
285 | if (!buffs.BeginsWith("START")) {Error("LoadData","Expected: \"START <fit_name>\", found \"%s\"\nStop\n",buffs.Data());exit(1);} | |
286 | if (buffs.First(' ')>0) SetName(buffs.Data()+buffs.First(' ')+1); | |
287 | // | |
288 | ReadLine(buffs,stream); // NRows | |
289 | fNRows = buffs.Atoi(); | |
290 | if (fNRows<1) {Error("LoadData","Expected: '<number_of_rows>', found \"%s\"\nStop\n",buffs.Data());exit(1);} | |
291 | // | |
292 | fNCols = 0; | |
293 | fNElemBound2D = 0; | |
294 | InitRows(fNRows); | |
295 | // | |
296 | for (int id0=0;id0<fNRows;id0++) { | |
297 | ReadLine(buffs,stream); // n.cols at this row | |
298 | fNColsAtRow[id0] = buffs.Atoi(); | |
299 | fColAtRowBg[id0] = fNElemBound2D; // begining of this row in 2D boundary surface | |
300 | fNElemBound2D += fNColsAtRow[id0]; | |
301 | if (fNCols<fNColsAtRow[id0]) fNCols = fNColsAtRow[id0]; | |
302 | } | |
303 | InitCols(fNCols); | |
304 | // | |
305 | fNCoefs = 0; | |
306 | InitElemBound2D(fNElemBound2D); | |
307 | // | |
308 | for (int i=0;i<fNElemBound2D;i++) { | |
309 | ReadLine(buffs,stream); // n.coeffs at 3-d dimension for the given column/row | |
310 | fCoefBound2D0[i] = buffs.Atoi(); | |
311 | fCoefBound2D1[i] = fNCoefs; | |
312 | fNCoefs += fCoefBound2D0[i]; | |
313 | } | |
314 | // | |
315 | if (fNCoefs<=0) {Error("LoadData","Negtive (%d) number of Chebychef coeffs. is obtained.\nStop\n",fNCoefs);exit(1);} | |
316 | // | |
317 | InitCoefs(fNCoefs); | |
318 | for (int i=0;i<fNCoefs;i++) { | |
319 | ReadLine(buffs,stream); | |
320 | fCoefs[i] = buffs.Atof(); | |
321 | } | |
322 | // check end_of_data record | |
323 | ReadLine(buffs,stream); | |
324 | if (!buffs.BeginsWith("END") || !buffs.Contains(GetName())) { | |
325 | Error("LoadData","Expected \"END %s\", found \"%s\".\nStop\n",GetName(),buffs.Data()); | |
326 | exit(1); | |
327 | } | |
328 | // | |
329 | } | |
330 | ||
331 | //_______________________________________________ | |
332 | void AliCheb3DCalc::ReadLine(TString& str,FILE* stream) | |
333 | { | |
334 | // read single line from the stream, skipping empty and commented lines. EOF is not expected | |
335 | while (str.Gets(stream)) { | |
336 | str = str.Strip(TString::kBoth,' '); | |
337 | if (str.IsNull()||str.BeginsWith("#")) continue; | |
338 | return; | |
339 | } | |
340 | fprintf(stderr,"AliCheb3D::ReadLine: Failed to read from stream.\nStop");exit(1); // normally, should not reach here | |
341 | } | |
342 | ||
343 | //_______________________________________________ | |
344 | void AliCheb3DCalc::InitCols(int nc) | |
345 | { | |
346 | // Set max.number of significant columns in the coefs matrix | |
347 | fNCols = nc; | |
348 | if (fTmpCf1) delete[] fTmpCf1; | |
349 | fTmpCf1 = new Float_t [fNCols]; | |
350 | } | |
351 | ||
352 | //_______________________________________________ | |
353 | void AliCheb3DCalc::InitRows(int nr) | |
354 | { | |
355 | // Set max.number of significant rows in the coefs matrix | |
356 | if (fNColsAtRow) delete[] fNColsAtRow; | |
357 | if (fColAtRowBg) delete[] fColAtRowBg; | |
358 | if (fTmpCf0) delete[] fTmpCf0; | |
359 | fNRows = nr; | |
360 | fNColsAtRow = new Int_t[fNRows]; | |
361 | fTmpCf0 = new Float_t [fNRows]; | |
362 | fColAtRowBg = new Int_t[fNRows]; | |
363 | for (int i=fNRows;i--;) fNColsAtRow[i] = fColAtRowBg[i] = 0; | |
364 | } | |
365 | ||
366 | //_______________________________________________ | |
367 | void AliCheb3DCalc::InitElemBound2D(int ne) | |
368 | { | |
369 | // Set max number of significant coefs for given row/column of coefs 3D matrix | |
370 | if (fCoefBound2D0) delete[] fCoefBound2D0; | |
371 | if (fCoefBound2D1) delete[] fCoefBound2D1; | |
372 | fNElemBound2D = ne; | |
373 | fCoefBound2D0 = new Int_t[fNElemBound2D]; | |
374 | fCoefBound2D1 = new Int_t[fNElemBound2D]; | |
375 | for (int i=fNElemBound2D;i--;) fCoefBound2D0[i] = fCoefBound2D1[i] = 0; | |
376 | } | |
377 | ||
378 | //_______________________________________________ | |
379 | void AliCheb3DCalc::InitCoefs(int nc) | |
380 | { | |
381 | // Set total number of significant coefs | |
382 | if (fCoefs) delete[] fCoefs; | |
383 | fNCoefs = nc; | |
384 | fCoefs = new Float_t [fNCoefs]; | |
385 | for (int i=fNCoefs;i--;) fCoefs[i] = 0.0; | |
386 | } | |
387 | ||
40389866 | 388 | //__________________________________________________________________________________________ |
389 | Float_t AliCheb3DCalc::ChebEval1Deriv(Float_t x, const Float_t * array, int ncf ) | |
390 | { | |
391 | // evaluate 1D Chebyshev parameterization's derivative. x is the argument mapped to [-1:1] interval | |
1cf34ee8 | 392 | if (--ncf<1) return 0; |
40389866 | 393 | Float_t b0, b1, b2; |
394 | Float_t x2 = x+x; | |
395 | b1 = b2 = 0; | |
396 | float dcf0=0,dcf1,dcf2=0; | |
397 | b0 = dcf1 = 2*ncf*array[ncf]; | |
1cf34ee8 | 398 | if (!(--ncf)) return b0/2; |
40389866 | 399 | // |
400 | for (int i=ncf;i--;) { | |
401 | b2 = b1; | |
402 | b1 = b0; | |
403 | dcf0 = dcf2 + 2*(i+1)*array[i+1]; | |
404 | b0 = dcf0 + x2*b1 -b2; | |
405 | dcf2 = dcf1; | |
406 | dcf1 = dcf0; | |
407 | } | |
408 | // | |
409 | return b0 - x*b1 - dcf0/2; | |
410 | } | |
1cf34ee8 | 411 | |
412 | //__________________________________________________________________________________________ | |
413 | Float_t AliCheb3DCalc::ChebEval1Deriv2(Float_t x, const Float_t * array, int ncf ) | |
414 | { | |
415 | // evaluate 1D Chebyshev parameterization's 2nd derivative. x is the argument mapped to [-1:1] interval | |
416 | if (--ncf<2) return 0; | |
417 | Float_t b0, b1, b2; | |
418 | Float_t x2 = x+x; | |
419 | b1 = b2 = 0; | |
420 | float dcf0=0,dcf1=0,dcf2=0; | |
421 | float ddcf0=0,ddcf1,ddcf2=0; | |
422 | // | |
423 | dcf2 = 2*ncf*array[ncf]; | |
424 | --ncf; | |
425 | ||
426 | dcf1 = 2*ncf*array[ncf]; | |
427 | b0 = ddcf1 = 2*ncf*dcf2; | |
428 | // | |
429 | if (!(--ncf)) return b0/2; | |
430 | // | |
431 | for (int i=ncf;i--;) { | |
432 | b2 = b1; | |
433 | b1 = b0; | |
434 | dcf0 = dcf2 + 2*(i+1)*array[i+1]; | |
435 | ddcf0 = ddcf2 + 2*(i+1)*dcf1; | |
436 | b0 = ddcf0 + x2*b1 -b2; | |
437 | // | |
438 | ddcf2 = ddcf1; | |
439 | ddcf1 = ddcf0; | |
440 | // | |
441 | dcf2 = dcf1; | |
442 | dcf1 = dcf0; | |
443 | // | |
444 | } | |
445 | // | |
446 | return b0 - x*b1 - ddcf0/2; | |
447 | } | |
448 |