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CaloCondition.cc
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1 
14 // this class header
16 
17 // system include files
18 #include <iostream>
19 #include <iomanip>
20 
21 #include <string>
22 #include <vector>
23 #include <algorithm>
24 
25 // user include files
26 // base classes
29 
31 
33 
36 
37 // constructors
38 // default
41 
44 
45 }
46 
47 // from base template condition (from event setup usually)
49  const int nrL1EG,
50  const int nrL1Jet,
51  const int nrL1Tau,
52  const int ifCaloEtaNumberBits) :
54  m_gtCaloTemplate(static_cast<const CaloTemplate*>(caloTemplate)),
55  m_uGtB(ptrGTB),
56  m_ifCaloEtaNumberBits(ifCaloEtaNumberBits)
57 {
58 
60 
61  // maximum number of objects received for the evaluation of the condition
62  // retrieved before from event setup
63  // for a CondCalo, all objects ar of same type, hence it is enough to get the
64  // type for the first object
65 
66  switch ((m_gtCaloTemplate->objectType())[0]) {
67  case gtEG:
68  m_condMaxNumberObjects = nrL1EG;
69  break;
70 
71  case gtJet:
72  m_condMaxNumberObjects = nrL1Jet;
73  break;
74 
75  case gtTau:
76  m_condMaxNumberObjects = nrL1Tau;
77  break;
78  default:
80  break;
81  }
82 
83 }
84 
85 // copy constructor
87 
89  m_uGtB = cp.getuGtB();
90 
93 
97 
99 
100 }
101 
104 
105  copy(cp);
106 
107 }
108 
109 // destructor
111 
112  // empty
113 
114 }
115 
116 // equal operator
118  copy(cp);
119  return *this;
120 }
121 
122 // methods
124 
125  m_gtCaloTemplate = caloTempl;
126 
127 }
128 
131 
132  m_uGtB = ptrGTB;
133 
134 }
135 
136 // set the number of bits for eta of calorimeter objects
137 void l1t::CaloCondition::setGtIfCaloEtaNumberBits(const int& ifCaloEtaNumberBitsValue) {
138 
139  m_ifCaloEtaNumberBits = ifCaloEtaNumberBitsValue;
140 
141 }
142 
143 // set the maximum number of bins for the delta phi scales
145  const int& corrParDeltaPhiNrBins) {
146 
147  m_corrParDeltaPhiNrBins = corrParDeltaPhiNrBins;
148 
149 }
150 
151 // try all object permutations and check spatial correlations, if required
152 const bool l1t::CaloCondition::evaluateCondition(const int bxEval) const {
153 
154  // number of trigger objects in the condition
155  int nObjInCond = m_gtCaloTemplate->nrObjects();
156  //LogTrace("L1TGlobal") << " nObjInCond: " << nObjInCond
157  // << std::endl;
158 
159  // the candidates
160 
161  // objectType() gives the type for nrObjects() only,
162  // but in a CondCalo all objects have the same type
163  // take type from the type of the first object
164 
165  const BXVector<const l1t::L1Candidate*>* candVec;
166 
167  switch ((m_gtCaloTemplate->objectType())[0]) {
168  case gtEG:
169  candVec = m_uGtB->getCandL1EG();
170  break;
171 
172  case gtJet:
173  candVec = m_uGtB->getCandL1Jet();
174  break;
175 
176  case gtTau:
177  candVec = m_uGtB->getCandL1Tau();
178  break;
179 
180  default:
181  return false;
182  break;
183  }
184 
185  // Look at objects in bx = bx + relativeBx
186  int useBx = bxEval + m_gtCaloTemplate->condRelativeBx();
187 
188  // Fail condition if attempting to get Bx outside of range
189  if( ( useBx < candVec->getFirstBX() ) ||
190  ( useBx > candVec->getLastBX() ) ) {
191  return false;
192  }
193 
194 
195  int numberObjects = candVec->size(useBx);
196  //LogTrace("L1TGlobal") << " numberObjects: " << numberObjects
197  // << std::endl;
198  if (numberObjects < nObjInCond) {
199  return false;
200  }
201 
202  std::vector<int> index(numberObjects);
203 
204  for (int i = 0; i < numberObjects; ++i) {
205  index[i] = i;
206  }
207 
208  int totalLoops = 0;
209  int passLoops = 0;
210 
211  // condition result condResult set to true if at least one permutation
212  // passes all requirements
213  // all possible permutations are checked
214  bool condResult = false;
215 
216  // store the indices of the calorimeter objects
217  // from the combination evaluated in the condition
218  SingleCombInCond objectsInComb;
219  objectsInComb.reserve(nObjInCond);
220 
221  // clear the m_combinationsInCond vector
222  combinationsInCond().clear();
223 
225  if( nObjInCond==1 ){
226 
227  // clear the indices in the combination
228  //objectsInComb.clear();
229 
230  for( int i=0; i<numberObjects; i++ ){
231 
232  // clear the indices in the combination
233  objectsInComb.clear();
234 
235  totalLoops++;
236  bool passCondition = checkObjectParameter(0, *(candVec->at(useBx,i)), index[i]);
237  if( passCondition ){
238  objectsInComb.push_back(i);
239  condResult = true;
240  passLoops++;
241  combinationsInCond().push_back(objectsInComb);
242  }
243  }
244  }
245  else if( nObjInCond==2 ){
246 
247  for( int i=0; i<numberObjects; i++ ){
248 
249  bool passCondition0i = checkObjectParameter(0, *(candVec->at(useBx,i)),index[i]);
250  bool passCondition1i = checkObjectParameter(1, *(candVec->at(useBx,i)),index[i]);
251 
252  if( !( passCondition0i || passCondition1i ) ) continue;
253 
254  for( int j=0; j<numberObjects; j++ ){
255  if( i==j ) continue;
256  totalLoops++;
257 
258  bool passCondition0j = checkObjectParameter(0, *(candVec->at(useBx,j)),index[i]);
259  bool passCondition1j = checkObjectParameter(1, *(candVec->at(useBx,j)),index[i]);
260 
261  bool pass = (
262  (passCondition0i && passCondition1j) ||
263  (passCondition0j && passCondition1i)
264  );
265 
266  if( pass ){
267 
268  if (m_gtCaloTemplate->wsc()) {
269 
270  // wsc requirements have always nObjInCond = 2
271  // one can use directly 0] and 1] to compute
272  // eta and phi differences
273  const int ObjInWscComb = 2;
274  if (nObjInCond != ObjInWscComb) {
275 
276  if (m_verbosity) {
277  edm::LogError("L1TGlobal")
278  << "\n Error: "
279  << "number of particles in condition with spatial correlation = "
280  << nObjInCond << "\n it must be = " << ObjInWscComb
281  << std::endl;
282  }
283 
284  continue;
285  }
286 
289 
290  // check delta eta
291  if( !checkRangeDeltaEta( (candVec->at(useBx,i))->hwEta(), (candVec->at(useBx,j))->hwEta(), corrPar.deltaEtaRangeLower, corrPar.deltaEtaRangeUpper, 7) ){
292  LogDebug("L1TGlobal") << "\t\t l1t::Candidate failed checkRangeDeltaEta" << std::endl;
293  continue;
294  }
295 
296  // check delta phi
297  if( !checkRangeDeltaPhi( (candVec->at(useBx,i))->hwPhi(), (candVec->at(useBx,j))->hwPhi(),
298  corrPar.deltaPhiRangeLower, corrPar.deltaPhiRangeUpper) ){
299  LogDebug("L1TGlobal") << "\t\t l1t::Candidate failed checkRangeDeltaPhi" << std::endl;
300  continue;
301  }
302 
303  } // end wsc check
304 
305 
306  objectsInComb.clear();
307  objectsInComb.push_back(i);
308  objectsInComb.push_back(j);
309  condResult = true;
310  passLoops++;
311  combinationsInCond().push_back(objectsInComb);
312  }
313  }
314  }
315  }
316  else if( nObjInCond==3 ){
317 
318  for( int i=0; i<numberObjects; i++ ){
319 
320 
321  bool passCondition0i = checkObjectParameter(0, *(candVec->at(useBx,i)),index[i]);
322  bool passCondition1i = checkObjectParameter(1, *(candVec->at(useBx,i)),index[i]);
323  bool passCondition2i = checkObjectParameter(2, *(candVec->at(useBx,i)),index[i]);
324 
325  if( !( passCondition0i || passCondition1i || passCondition2i ) ) continue;
326 
327  for( int j=0; j<numberObjects; j++ ){
328  if( i==j ) continue;
329 
330  bool passCondition0j = checkObjectParameter(0, *(candVec->at(useBx,j)),index[i]);
331  bool passCondition1j = checkObjectParameter(1, *(candVec->at(useBx,j)),index[i]);
332  bool passCondition2j = checkObjectParameter(2, *(candVec->at(useBx,j)),index[i]);
333 
334  if( !( passCondition0j || passCondition1j || passCondition2j ) ) continue;
335 
336  for( int k=0; k<numberObjects; k++ ){
337  if( k==i || k==j ) continue;
338  totalLoops++;
339 
340  bool passCondition0k = checkObjectParameter(0, *(candVec->at(useBx,k)),index[i]);
341  bool passCondition1k = checkObjectParameter(1, *(candVec->at(useBx,k)),index[i]);
342  bool passCondition2k = checkObjectParameter(2, *(candVec->at(useBx,k)),index[i]);
343 
344  bool pass = (
345  (passCondition0i && passCondition1j && passCondition2k) ||
346  (passCondition0i && passCondition1k && passCondition2j) ||
347  (passCondition0j && passCondition1k && passCondition2i) ||
348  (passCondition0j && passCondition1i && passCondition2k) ||
349  (passCondition0k && passCondition1i && passCondition2j) ||
350  (passCondition0k && passCondition1j && passCondition2i)
351  );
352  if( pass ){
353  condResult = true;
354  passLoops++;
355  objectsInComb.clear();
356  objectsInComb.push_back(i);
357  objectsInComb.push_back(j);
358  objectsInComb.push_back(k);
359  combinationsInCond().push_back(objectsInComb);
360  }
361  }// end loop on k
362  }// end loop on j
363  }// end loop on i
364  } // end if condition has 3 objects
365  else if( nObjInCond==4 ){
366 
367 
368  for( int i=0; i<numberObjects; i++ ){
369 
370  bool passCondition0i = checkObjectParameter(0, *(candVec->at(useBx,i)),index[i]);
371  bool passCondition1i = checkObjectParameter(1, *(candVec->at(useBx,i)),index[i]);
372  bool passCondition2i = checkObjectParameter(2, *(candVec->at(useBx,i)),index[i]);
373  bool passCondition3i = checkObjectParameter(3, *(candVec->at(useBx,i)),index[i]);
374 
375  if( !( passCondition0i || passCondition1i || passCondition2i || passCondition3i ) ) continue;
376 
377  for( int j=0; j<numberObjects; j++ ){
378  if( j==i ) continue;
379 
380  bool passCondition0j = checkObjectParameter(0, *(candVec->at(useBx,j)),index[i]);
381  bool passCondition1j = checkObjectParameter(1, *(candVec->at(useBx,j)),index[i]);
382  bool passCondition2j = checkObjectParameter(2, *(candVec->at(useBx,j)),index[i]);
383  bool passCondition3j = checkObjectParameter(3, *(candVec->at(useBx,j)),index[i]);
384 
385  if( !( passCondition0j || passCondition1j || passCondition2j || passCondition3j ) ) continue;
386 
387  for( int k=0; k<numberObjects; k++ ){
388  if( k==i || k==j ) continue;
389 
390  bool passCondition0k = checkObjectParameter(0, *(candVec->at(useBx,k)),index[i]);
391  bool passCondition1k = checkObjectParameter(1, *(candVec->at(useBx,k)),index[i]);
392  bool passCondition2k = checkObjectParameter(2, *(candVec->at(useBx,k)),index[i]);
393  bool passCondition3k = checkObjectParameter(3, *(candVec->at(useBx,k)),index[i]);
394 
395  if( !( passCondition0k || passCondition1k || passCondition2k || passCondition3k ) ) continue;
396 
397  for( int m=0; m<numberObjects; m++ ){
398  if( m==i || m==j || m==k ) continue;
399  totalLoops++;
400 
401  bool passCondition0m = checkObjectParameter(0, *(candVec->at(useBx,m)),index[i]);
402  bool passCondition1m = checkObjectParameter(1, *(candVec->at(useBx,m)),index[i]);
403  bool passCondition2m = checkObjectParameter(2, *(candVec->at(useBx,m)),index[i]);
404  bool passCondition3m = checkObjectParameter(3, *(candVec->at(useBx,m)),index[i]);
405 
406  bool pass = (
407  (passCondition0i && passCondition1j && passCondition2k && passCondition3m) ||
408  (passCondition0i && passCondition1j && passCondition2m && passCondition3k) ||
409  (passCondition0i && passCondition1k && passCondition2j && passCondition3m) ||
410  (passCondition0i && passCondition1k && passCondition2m && passCondition3j) ||
411  (passCondition0i && passCondition1m && passCondition2j && passCondition3k) ||
412  (passCondition0i && passCondition1m && passCondition2k && passCondition3j) ||
413  (passCondition0j && passCondition1i && passCondition2k && passCondition3m) ||
414  (passCondition0j && passCondition1i && passCondition2m && passCondition3k) ||
415  (passCondition0j && passCondition1k && passCondition2i && passCondition3m) ||
416  (passCondition0j && passCondition1k && passCondition2m && passCondition3i) ||
417  (passCondition0j && passCondition1m && passCondition2i && passCondition3k) ||
418  (passCondition0j && passCondition1m && passCondition2k && passCondition3i) ||
419  (passCondition0k && passCondition1i && passCondition2j && passCondition3m) ||
420  (passCondition0k && passCondition1i && passCondition2m && passCondition3j) ||
421  (passCondition0k && passCondition1j && passCondition2i && passCondition3m) ||
422  (passCondition0k && passCondition1j && passCondition2m && passCondition3i) ||
423  (passCondition0k && passCondition1m && passCondition2i && passCondition3j) ||
424  (passCondition0k && passCondition1m && passCondition2j && passCondition3i) ||
425  (passCondition0m && passCondition1i && passCondition2j && passCondition3k) ||
426  (passCondition0m && passCondition1i && passCondition2k && passCondition3j) ||
427  (passCondition0m && passCondition1j && passCondition2i && passCondition3k) ||
428  (passCondition0m && passCondition1j && passCondition2k && passCondition3i) ||
429  (passCondition0m && passCondition1k && passCondition2i && passCondition3j) ||
430  (passCondition0m && passCondition1k && passCondition2j && passCondition3i)
431  );
432  if( pass ){
433  objectsInComb.clear();
434  objectsInComb.push_back(i);
435  objectsInComb.push_back(j);
436  objectsInComb.push_back(k);
437  objectsInComb.push_back(m);
438  condResult = true;
439  passLoops++;
440  combinationsInCond().push_back(objectsInComb);
441  }
442  }// end loop on m
443  }// end loop on k
444  }// end loop on j
445  }// end loop on i
446  } // end if condition has 4 objects
447 
448 
449  LogTrace("L1TGlobal")
450  << "\n CaloCondition: total number of permutations found: " << totalLoops
451  << "\n CaloCondition: number of permutations passing requirements: " << passLoops
452  << "\n" << std::endl;
453 
454  return condResult;
455 
456 }
457 
458 // load calo candidates
459 const l1t::L1Candidate* l1t::CaloCondition::getCandidate(const int bx, const int indexCand) const {
460 
461  // objectType() gives the type for nrObjects() only,
462  // but in a CondCalo all objects have the same type
463  // take type from the type of the first object
464  switch ((m_gtCaloTemplate->objectType())[0]) {
465  case gtEG:
466  return (m_uGtB->getCandL1EG())->at(bx,indexCand);
467  break;
468 
469  case gtJet:
470  return (m_uGtB->getCandL1Jet())->at(bx,indexCand);
471  break;
472 
473  case gtTau:
474  return (m_uGtB->getCandL1Tau())->at(bx,indexCand);
475  break;
476  default:
477  return nullptr;
478  break;
479  }
480 
481  return nullptr;
482 }
483 
493 const bool l1t::CaloCondition::checkObjectParameter(const int iCondition, const l1t::L1Candidate& cand, unsigned int index) const {
494 
495  // number of objects in condition
496  int nObjInCond = m_gtCaloTemplate->nrObjects();
497 
498  if (iCondition >= nObjInCond || iCondition < 0) {
499  return false;
500  }
501 
502  // empty candidates can not be compared
503 // if (cand.empty()) {
504 // return false;
505 // }
506 
507  const CaloTemplate::ObjectParameter objPar = ( *(m_gtCaloTemplate->objectParameter()) )[iCondition];
508 
509  LogDebug("L1TGlobal")
510  << "\n CaloTemplate: "
511  << "\n\t condRelativeBx = " << m_gtCaloTemplate->condRelativeBx()
512  << "\n ObjectParameter : "
513  << "\n\t etThreshold = " << objPar.etLowThreshold << " - " << objPar.etHighThreshold
514  << "\n\t indexRange = " << objPar.indexLow << " - " << objPar.indexHigh
515  << "\n\t etaRange = " << objPar.etaRange
516  << "\n\t phiRange = " << objPar.phiRange
517  << "\n\t isolationLUT= " << objPar.isolationLUT
518  << std::endl;
519 
520  LogDebug("L1TGlobal")
521  << "\n l1t::Candidate : "
522  << "\n\t hwPt = " << cand.hwPt()
523  << "\n\t hwEta = " << cand.hwEta()
524  << "\n\t hwPhi = " << cand.hwPhi()
525  << std::endl;
526 
527 
528  // check energy threshold
529  if ( !checkThreshold(objPar.etLowThreshold, objPar.etHighThreshold, cand.hwPt(), m_gtCaloTemplate->condGEq()) ) {
530  LogDebug("L1TGlobal") << "\t\t l1t::Candidate failed checkThreshold" << std::endl;
531  return false;
532  }
533 
534  // check index
535  if ( !checkIndex(objPar.indexLow, objPar.indexHigh, index) ) {
536  LogDebug("L1TGlobal") << "\t\t ilt::Candidate Failed checkIndex " << std::endl;
537  return false;
538  }
539 
540  // check eta
541  if( !checkRangeEta(cand.hwEta(), objPar.etaWindow1Lower, objPar.etaWindow1Upper, objPar.etaWindow2Lower, objPar.etaWindow2Upper, 7) ){
542  LogDebug("L1TGlobal") << "\t\t l1t::Candidate failed checkRange(eta)" << std::endl;
543  return false;
544  }
545 
546 // if (!checkBit(objPar.etaRange, cand.hwEta())) {
547 // return false;
548 // }
549 
550  // check phi
551  if( !checkRangePhi(cand.hwPhi(), objPar.phiWindow1Lower, objPar.phiWindow1Upper, objPar.phiWindow2Lower, objPar.phiWindow2Upper) ){
552  LogDebug("L1TGlobal") << "\t\t l1t::Candidate failed checkRange(phi)" << std::endl;
553  return false;
554  }
555 
556  // check isolation ( bit check ) with isolation LUT
557  // sanity check on candidate isolation
558  if( cand.hwIso()>4 ){
559  LogDebug("L1TGlobal") << "\t\t l1t::Candidate has out of range hwIso = " << cand.hwIso() << std::endl;
560  return false;
561  }
562  bool passIsoLUT = ( (objPar.isolationLUT >> cand.hwIso()) & 1 );
563  if( !passIsoLUT ){
564  LogDebug("L1TGlobal") << "\t\t l1t::Candidate failed isolation requirement" << std::endl;
565  return false;
566  }
567 // if (!checkBit(objPar.phiRange, cand.hwPhi())) {
568 // return false;
569 // }
570 
571  // particle matches if we get here
572  //LogTrace("L1TGlobal")
573  // << " checkObjectParameter: calorimeter object OK, passes all requirements\n"
574  // << std::endl;
575 
576  return true;
577 }
578 
579 void l1t::CaloCondition::print(std::ostream& myCout) const {
580 
581  m_gtCaloTemplate->print(myCout);
582 
583  myCout << " Number of bits for eta of calorimeter objects = "
584  << m_ifCaloEtaNumberBits << std::endl;
585  myCout << " Maximum number of bins for the delta phi scales = "
586  << m_corrParDeltaPhiNrBins << "\n " << std::endl;
587 
589 
590 }
591 
#define LogDebug(id)
const bool evaluateCondition(const int bxEval) const override
the core function to check if the condition matches
const int nrObjects() const
get number of trigger objects
const CaloTemplate * gtCaloTemplate() const
get / set the pointer to a Condition
Definition: CaloCondition.h:74
const BXVector< const l1t::L1Candidate * > * getCandL1Tau() const
pointer to Tau data list
Definition: GlobalBoard.h:162
const BXVector< const l1t::L1Candidate * > * getCandL1Jet() const
pointer to Jet data list
Definition: GlobalBoard.h:155
unsigned int m_corrParDeltaPhiNrBins
const std::vector< ObjectParameter > * objectParameter() const
Definition: CaloTemplate.h:102
unsigned size(int bx) const
CombinationsInCond const & getCombinationsInCond() const
get all the object combinations evaluated to true in the condition
const bool checkRangeDeltaPhi(const unsigned int obj1Phi, const unsigned int obj2Phi, const Type1 &lowerR, const Type1 &upperR) const
check if a value is in a given range
const bool checkRangeEta(const unsigned int bitNumber, const Type1 &W1beginR, const Type1 &W1endR, const Type1 &W2beginR, const Type1 &W2endR, const unsigned int nEtaBits) const
check if a value is in a given range and outside of a veto range
void setGtCorrParDeltaPhiNrBins(const int &)
const bool checkObjectParameter(const int iCondition, const l1t::L1Candidate &cand, const unsigned int index) const
function to check a single object if it matches a condition
virtual void print(std::ostream &myCout) const
print condition
void setGtIfCaloEtaNumberBits(const int &)
std::vector< int > SingleCombInCond
typedefs
const bool wsc() const
const bool condGEq() const
get / set condition GEq flag
int hwPhi() const
Definition: L1Candidate.h:50
void print(std::ostream &myCout) const override
print the condition
Definition: CaloTemplate.cc:97
const bool checkThreshold(const Type1 &thresholdL, const Type1 &thresholdH, const Type2 &value, bool condGEqValue) const
typedef for a single object template
Definition: CaloTemplate.h:59
void setGtCaloTemplate(const CaloTemplate *)
int hwIso() const
Definition: L1Candidate.h:52
bool condLastResult() const
get the latest result for the condition
const int & condRelativeBx() const
get / set the condition relative bx
const BXVector< const l1t::L1Candidate * > * getCandL1EG() const
pointer to EG data list
Definition: GlobalBoard.h:149
const std::vector< l1t::GlobalObject > & objectType() const
get / set the trigger object type(s) in the condition
const int gtIfCaloEtaNumberBits() const
get / set the number of bits for eta of calorimeter objects
Definition: CaloCondition.h:89
int hwEta() const
Definition: L1Candidate.h:49
CombinationsInCond m_combinationsInCond
store all the object combinations evaluated to true in the condition
const GlobalBoard * m_uGtB
pointer to uGt GlobalBoard, to be able to get the trigger objects
#define LogTrace(id)
void setuGtB(const GlobalBoard *)
set the pointer to uGT GlobalBoard
~CaloCondition() override
int k[5][pyjets_maxn]
const l1t::L1Candidate * getCandidate(const int bx, const int indexCand) const
load calo candidates
int m_verbosity
verbosity level
int hwPt() const
Definition: L1Candidate.h:48
void print(std::ostream &myCout) const override
print condition
bool m_condLastResult
the last result of evaluateCondition()
CaloCondition & operator=(const CaloCondition &)
typedef for correlation parameters
Definition: CaloTemplate.h:84
void copy(const CaloCondition &cp)
copy function for copy constructor and operator=
const GlobalBoard * getuGtB() const
get / set the pointer to uGt GlobalBoard
Definition: CaloCondition.h:81
int m_ifCaloEtaNumberBits
number of bits for eta of calorimeter objects
int getLastBX() const
const bool checkRangeDeltaEta(const unsigned int obj1Eta, const unsigned int obj2Eta, const Type1 &lowerR, const Type1 &upperR, const unsigned int nEtaBits) const
check if a value is in a given range
const bool checkIndex(const Type1 &indexLo, const Type1 &indexHi, const unsigned int index) const
check if a index is in a given range
CombinationsInCond & combinationsInCond() const
get all the object combinations (to fill it...)
const bool checkRangePhi(const unsigned int bitNumber, const Type1 &W1beginR, const Type1 &W1endR, const Type1 &W2beginR, const Type1 &W2endR) const
check if a value is in a given range and outside of a veto range
const CaloTemplate * m_gtCaloTemplate
pointer to a CaloTemplate
const CorrelationParameter * correlationParameter() const
Definition: CaloTemplate.h:107
const T & at(int bx, unsigned i) const