source: trunk/MagicSoft/Mars/mextralgo/MExtralgoSpline.h@ 8538

Last change on this file since 8538 was 8524, checked in by tbretz, 18 years ago
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1#ifndef MARS_MExtralgoSpline
2#define MARS_MExtralgoSpline
3
4#ifndef ROOT_TROOT
5#include <TROOT.h>
6#endif
7
8class TComplex;
9
10class MExtralgoSpline
11{
12public:
13 enum ExtractionType_t { kAmplitude, kIntegralRel, kIntegralAbs }; //! Possible time and charge extraction types
14
15private:
16 ExtractionType_t fExtractionType;
17
18private:
19 //Bool_t fIsOwner; // Owner of derivatives....
20
21 // Input
22 Float_t const *fVal;
23 const Int_t fNum;
24
25 Float_t *fDer1;
26 Float_t *fDer2;
27
28 Float_t fRiseTime;
29 Float_t fFallTime;
30
31 Float_t fHeightTm;
32
33// Float_t fResolution;
34
35 // Result
36 Float_t fTime;
37 Float_t fTimeDev;
38 Float_t fWidth;
39 Float_t fWidthDev;
40 Float_t fSignal;
41 Float_t fSignalDev;
42 Float_t fHeight;
43
44 Double_t ReMul(const TComplex &c1, const TComplex &th) const;
45
46 inline Float_t Eval(Float_t val, Float_t a, Float_t deriv) const
47 {
48 return a*val + (a*a*a-a)*deriv;
49 }
50
51 // Evaluate value of spline in the interval i with x=[0;1[
52 inline Float_t Eval(const Int_t i, const Float_t x) const
53 {
54 // Eval(i,x) = (fDer2[i+1]-fDer2[i])*x*x*x + 3*fDer2[i]*x*x +
55 // (fVal[i+1]-fVal[i] -2*fDer2[i]-fDer2[i+1])*x + fVal[i];
56
57 // x := [0; 1[
58 return Eval(fVal[i], 1-x, fDer2[i]) + Eval(fVal[i+1], x, fDer2[i+1]);
59 }
60
61 // Evaluate first derivative of spline in the interval i with x=[0;1[
62 inline Double_t EvalDeriv1(const Float_t x, const Int_t i) const
63 {
64 // x := [0; 1[
65 const Double_t difval = fVal[i+1]-fVal[i];
66 const Double_t difder = fDer2[i+1]-fDer2[i];
67
68 return 3*difder*x*x + 6*fDer2[i]*x - 2*fDer2[i] - fDer2[i+1] + difval;
69 }
70
71 // Evaluate second derivative of spline in the interval i with x=[0;1[
72 inline Double_t EvalDeriv2(const Float_t x, const Int_t i) const
73 {
74 // x := [0; 1[
75 return 6*(fDer2[i+1]*x + fDer2[i]*(1-x));
76 }
77
78 Double_t FindY(Int_t i, Double_t y=0, Double_t min=0, Double_t max=1) const;
79 Double_t SearchY(Float_t maxpos, Float_t y) const;
80 Double_t SearchYup(Float_t maxpos, Float_t y) const;
81/*
82 // Evaluate first solution for a possible maximum (x|first deriv==0)
83 inline Double_t EvalDerivEq0S1(const Int_t i) const
84 {
85 // return the x value [0;1[ at which the derivative is zero (solution1)
86
87 Double_t sumder = fDer2[i]+fDer2[i+1];
88 Double_t difder = fDer2[i]-fDer2[i+1];
89
90 Double_t sqt1 = sumder*sumder - fDer2[i]*fDer2[i+1];
91 Double_t sqt2 = difder*(fVal[i+1]-fVal[i]);
92
93 Double_t x = 3*fDer2[i] - sqrt(3*sqt1 + 3*sqt2);
94
95 Double_t denom = 3*(fDer2[i+1]-fDer2[i]);
96
97 return -x/denom;
98 }
99
100 // Evaluate second solution for a possible maximum (x|first deriv==0)
101 inline Double_t EvalDerivEq0S2(const Int_t i) const
102 {
103 // return the x value [0;1[ at which the derivative is zero (solution2)
104
105 Double_t sumder = fDer2[i]+fDer2[i+1];
106 Double_t difder = fDer2[i]-fDer2[i+1];
107
108 Double_t sqt1 = sumder*sumder - fDer2[i]*fDer2[i+1];
109 Double_t sqt2 = difder*(fVal[i+1]-fVal[i]);
110
111 Double_t x = 3*fDer2[i] + sqrt(3*sqt1 + 3*sqt2);
112
113 Double_t denom = 3*(fDer2[i+1]-fDer2[i]);
114
115 return -x/denom;
116 }
117 */
118
119 inline void EvalDerivEq0(const Int_t i, Float_t &rc1, Float_t &rc2) const
120 {
121 /* --- ORIGINAL CODE ---
122 Double_t sumder = fDer2[i]+fDer2[i+1];
123 Double_t difder = fDer2[i]-fDer2[i+1];
124
125 Double_t sqt1 = sumder*sumder - fDer2[i]*fDer2[i+1];
126 Double_t sqt2 = difder*(fVal[i+1]-fVal[i]);
127 Double_t sqt3 = sqrt(3*sqt1 + 3*sqt2);
128 Double_t denom = -3*(fDer2[i+1]-fDer2[i]);
129
130 rc1 = -(3*fDer2[i] + sqt3)/denom;
131 rc2 = -(3*fDer2[i] - sqt3)/denom;
132 */
133
134 Double_t sumder = fDer2[i]+fDer2[i+1];
135 Double_t difder = fDer2[i]-fDer2[i+1];
136
137 Double_t sqt1 = sumder*sumder - fDer2[i]*fDer2[i+1];
138 Double_t sqt2 = difder*(fVal[i+1]-fVal[i]);
139 Double_t sqt3 = sqt1+sqt2<0 ? 0 : sqrt((sqt1 + sqt2)/3);
140
141 rc1 = -(fDer2[i] + sqt3)/difder;
142 rc2 = -(fDer2[i] - sqt3)/difder;
143 }
144
145 // Calculate the "Stammfunktion" of the Eval-function
146 inline Double_t EvalPrimitive(Int_t i, Float_t x) const
147 {
148 Align(i, x);
149
150 if (x==0)
151 return -fDer2[i]/4;
152
153 if (x==1)
154 return (fVal[i+1] + fVal[i])/2 - fDer2[i+1]/4 - fDer2[i]/2;
155
156 const Double_t x2 = x*x;
157 const Double_t x4 = x2*x2;
158 const Double_t x1 = 1-x;
159 const Double_t x14 = x1*x1*x1*x1;
160
161 return x2*fVal[i+1]/2 + (x4/2-x2)*fDer2[i+1]/2 + (x-x2/2)*fVal[i] + (x2/2-x-x14/4)*fDer2[i];
162
163 }
164
165 inline void Align(Int_t &i, Float_t &x) const
166 {
167 if (i<0)
168 {
169 x += i;
170 i=0;
171 }
172 if (i>=fNum-1)
173 {
174 x += i-(fNum-2);
175 i=fNum-2;
176 }
177 }
178
179 // Calculate the intgeral of the Eval-function in
180 // bin i from a=[0;1[ to b=[0;1[
181 inline Double_t EvalInteg(Int_t i, Float_t a, Float_t b) const
182 {
183 return EvalPrimitive(i, b)-EvalPrimitive(i, a);
184 }
185
186 // Identical to EvalInteg(i, 0, 1) but much faster
187 // Be carefull: NO RANGECHECK!
188 inline Double_t EvalInteg(Int_t i) const
189 {
190 return (fVal[i+1] + fVal[i])/2 - (fDer2[i+1] + fDer2[i])/4;
191 }
192
193 // Identical to sum EvalInteg(i, 0, 1) for i=0 to i<b but much faster
194 // Be carefull: NO RANGECHECK!
195 inline Double_t EvalInteg(Int_t a, Int_t b) const
196 {
197 /*
198 Double_t sum = 0;
199 for (int i=a; i<b; i++)
200 sum += EvalInteg(i);
201
202 return sum;
203 */
204 Double_t sum=0;
205 for (const Float_t *ptr=fDer2+a+1; ptr<fDer2+b; ptr++)
206 sum -= *ptr;
207
208 sum -= (fDer2[a]+fDer2[b])/2;
209
210 sum /= 2;
211
212 for (const Float_t *ptr=fVal+a+1; ptr<fVal+b; ptr++)
213 sum += *ptr;
214
215 sum += (fVal[a]+fVal[b])/2;
216
217 return sum;
218 }
219
220 // Calculate the intgeral of the Eval-function betwen x0 and x1
221 inline Double_t EvalInteg(Float_t x0, Float_t x1) const
222 {
223 // RANGE CHECK MISSING!
224
225 const Int_t min = TMath::CeilNint(x0);
226 const Int_t max = TMath::FloorNint(x1);
227
228 // This happens if x0 and x1 are in the same interval
229 if (min>max)
230 return EvalInteg(max, x0-max, x1-max);
231
232 // Sum complete intervals
233 Double_t sum = EvalInteg(min, max);
234
235 // Sum the incomplete intervals at the beginning and end
236 sum += EvalInteg(min-1, 1-(min-x0), 1);
237 sum += EvalInteg(max, 0, x1-max);
238
239 // return result
240 return sum;
241 }
242
243 // We search for the maximum from x=i-1 to x=i+1
244 // (Remeber: i corresponds to the value in bin i, i+1 to the
245 // next bin and i-1 to the last bin)
246 inline void GetMaxAroundI(Int_t i, Float_t &xmax, Float_t &ymax) const
247 {
248 Float_t xmax1=0, xmax2=0;
249 Float_t ymax1=0, ymax2=0;
250
251 Bool_t rc1 = i>0 && GetMax(i-1, xmax1, ymax1);
252 Bool_t rc2 = i<fNum-1 && GetMax(i, xmax2, ymax2);
253
254 // In case the medium bin is the first or last bin
255 // take the lower or upper edge of the region into account.
256 if (i==0)
257 {
258 xmax1 = 0;
259 ymax1 = fVal[0];
260 rc1 = kTRUE;
261 }
262 if (i>=fNum-1)
263 {
264 xmax2 = fNum-1;
265 ymax2 = fVal[fNum-1];
266 rc2 = kTRUE;
267 }
268
269 // Take a default in case no maximum is found
270 // FIXME: Check THIS!!!
271 xmax=i;
272 ymax=fVal[i];
273
274 if (rc1)
275 {
276 ymax = ymax1;
277 xmax = xmax1;
278 }
279 else
280 if (rc2)
281 {
282 ymax = ymax2;
283 xmax = xmax2;
284 }
285
286 if (rc2 && ymax2>ymax)
287 {
288 ymax = ymax2;
289 xmax = xmax2;
290 }
291 /*
292 // Search real maximum in [i-0.5, i+1.5]
293 Float_t xmax1, xmax2, xmax3;
294 Float_t ymax1, ymax2, ymax3;
295
296 Bool_t rc1 = i>0 && GetMax(i-1, xmax1, ymax1, 0.5, 1.0);
297 Bool_t rc2 = GetMax(i, xmax2, ymax2, 0.0, 1.0);
298 Bool_t rc3 = i<fNum-1 && GetMax(i+1, xmax3, ymax3, 0.0, 0.5);
299
300 // In case the medium bin is the first or last bin
301 // take the lower or upper edge of the region into account.
302 if (i==0)
303 {
304 xmax1 = 0;
305 ymax1 = Eval(0, 0);
306 rc1 = kTRUE;
307 }
308 if (i==fNum-1)
309 {
310 xmax3 = fNum-1e-5;
311 ymax3 = Eval(fNum-1, 1);
312 rc3 = kTRUE;
313 }
314
315 // Take a real default in case no maximum is found
316 xmax=i+0.5;
317 ymax=Eval(i, 0.5);
318
319 //if (!rc1 && !rc2 && !rc3)
320 // cout << "!!!!!!!!!!!!!!!" << endl;
321
322 if (rc1)
323 {
324 ymax = ymax1;
325 xmax = xmax1;
326 }
327 else
328 if (rc2)
329 {
330 ymax = ymax2;
331 xmax = xmax2;
332 }
333 else
334 if (rc3)
335 {
336 ymax = ymax3;
337 xmax = xmax3;
338 }
339
340 if (rc2 && ymax2>ymax)
341 {
342 ymax = ymax2;
343 xmax = xmax2;
344 }
345 if (rc3 && ymax3>ymax)
346 {
347 ymax = ymax3;
348 xmax = xmax3;
349 }
350 */
351 }
352
353 inline Bool_t GetMax(Int_t i, Float_t &xmax, Float_t &ymax, Float_t min=0, Float_t max=1) const
354 {
355 // Find analytical maximum in the bin i in the interval [min,max[
356
357 Float_t x1, x2;
358 EvalDerivEq0(i, x1, x2);
359 // const Float_t x1 = EvalDerivEq0S1(i);
360 // const Float_t x2 = EvalDerivEq0S2(i);
361
362 const Bool_t ismax1 = x1>=min && x1<max && EvalDeriv2(x1, i)<0;
363 const Bool_t ismax2 = x2>=min && x2<max && EvalDeriv2(x2, i)<0;
364
365 if (!ismax1 && !ismax2)
366 return kFALSE;
367
368 if (ismax1 && !ismax2)
369 {
370 xmax = i+x1;
371 ymax = Eval(i, x1);
372 return kTRUE;
373 }
374
375 if (!ismax1 && ismax2)
376 {
377 xmax = i+x2;
378 ymax = Eval(i, x2);
379 return kTRUE;
380 }
381
382 // Somehting must be wrong...
383 return kFALSE;
384 /*
385 std::cout << "?????????????" << std::endl;
386
387 const Double_t y1 = Eval(i, x1);
388 const Double_t y2 = Eval(i, x2);
389
390 if (y1>y2)
391 {
392 xmax = i+x1;
393 ymax = Eval(i, x1);
394 return kTRUE;
395 }
396 else
397 {
398 xmax = i+x2;
399 ymax = Eval(i, x2);
400 return kTRUE;
401 }
402
403 return kFALSE;*/
404 }
405/*
406 inline Int_t GetMaxPos(Int_t i, Float_t &xmax, Float_t &ymax) const
407 {
408 Double_t x[3];
409
410 x[0] = 0;
411 // x[1] = 1; // This means we miss a possible maximum at the
412 // upper edge of the last interval...
413
414 x[1] = EvalDerivEq0S1(i);
415 x[2] = EvalDerivEq0S2(i);
416
417 //y[0] = Eval(i, x[0]);
418 //y[1] = Eval(i, x[1]);
419 //y[1] = Eval(i, x[1]);
420 //y[2] = Eval(i, x[2]);
421
422 Int_t rc = 0;
423 Double_t max = Eval(i, x[0]);
424
425 for (Int_t j=1; j<3; j++)
426 {
427 if (x[j]<=0 || x[j]>=1)
428 continue;
429
430 const Float_t y = Eval(i, x[j]);
431 if (y>max)
432 {
433 max = y;
434 rc = j;
435 }
436 }
437
438 if (max>ymax)
439 {
440 xmax = x[rc]+i;
441 ymax = max;
442 }
443
444 return rc;
445 }
446
447 inline void GetMaxPos(Int_t min, Int_t max, Float_t &xmax, Float_t &ymax) const
448 {
449 Float_t xmax=-1;
450 Float_t ymax=-FLT_MAX;
451
452 for (int i=min; i<max; i++)
453 GetMaxPos(i, xmax, ymax);
454
455 for (int i=min+1; i<max; i++)
456 {
457 Float_t y = Eval(i, 0);
458 if (y>ymax)
459 {
460 ymax = y;
461 xmax = i;
462 }
463 }
464
465 }*/
466
467
468 void InitDerivatives() const;
469 Float_t CalcIntegral(Float_t start) const;
470
471public:
472 MExtralgoSpline(const Float_t *val, Int_t n, Float_t *der1, Float_t *der2)
473 : fExtractionType(kIntegralRel), fVal(val), fNum(n), fDer1(der1), fDer2(der2), fHeightTm(0.5), fTime(0), fTimeDev(-1), fSignal(0), fSignalDev(-1)
474 {
475 InitDerivatives();
476 }
477
478 void SetRiseFallTime(Float_t rise, Float_t fall) { fRiseTime=rise; fFallTime=fall; }
479 void SetExtractionType(ExtractionType_t typ) { fExtractionType = typ; }
480 void SetHeightTm(Float_t h) { fHeightTm = h; }
481 // void SetResolution(Float_t res) { fResolution=res; }
482
483 Float_t GetTime() const { return fTime; }
484 Float_t GetWidth() const { return fWidth; }
485 Float_t GetSignal() const { return fSignal; }
486 Float_t GetHeight() const { return fHeight; }
487
488 Float_t GetTimeDev() const { return fTimeDev; }
489 Float_t GetWidthDev() const { return fWidthDev; }
490 Float_t GetSignalDev() const { return fSignalDev; }
491
492 void GetSignal(Float_t &sig, Float_t &dsig) const { sig=fSignal; dsig=fSignalDev; }
493 void GetWidth(Float_t &sig, Float_t &dsig) const { sig=fWidth; dsig=fWidthDev; }
494 void GetTime(Float_t &sig, Float_t &dsig) const { sig=fTime; dsig=fTimeDev; }
495
496 Float_t ExtractNoise(/*Int_t iter*/);
497 void Extract(Byte_t sat, Int_t maxpos, Bool_t width=kFALSE);
498
499 Float_t EvalAt(const Float_t x) const;
500};
501
502inline Float_t MExtralgoSpline::EvalAt(const Float_t x) const
503{
504 Int_t i = TMath::FloorNint(x);
505 Float_t f = x-i;
506
507 Align(i, f);
508
509 return Eval(i, f);
510}
511
512#endif
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