Geant4 10.7.0
Toolkit for the simulation of the passage of particles through matter
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G4VCrossSectionHandler.cc
Go to the documentation of this file.
1//
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6// * the Geant4 Collaboration. It is provided under the terms and *
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19// * technical work of the GEANT4 collaboration. *
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25//
26//
27//
28// Author: Maria Grazia Pia ([email protected])
29//
30// History:
31// -----------
32// 1 Aug 2001 MGP Created
33// 09 Oct 2001 VI Add FindValue with 3 parameters
34// + NumberOfComponents
35// 19 Jul 2002 VI Create composite data set for material
36// 21 Jan 2003 VI Cut per region
37//
38// 15 Jul 2009 Nicolas A. Karakatsanis
39//
40// - LoadNonLogData method was created to load only the non-logarithmic data from G4EMLOW
41// dataset. It is essentially performing the data loading operations as in the past.
42//
43// - LoadData method was revised in order to calculate the logarithmic values of the data
44// It retrieves the data values from the G4EMLOW data files but, then, calculates the
45// respective log values and loads them to seperate data structures.
46// The EM data sets, initialized this way, contain both non-log and log values.
47// These initialized data sets can enhance the computing performance of data interpolation
48// operations
49//
50// - BuildMeanFreePathForMaterials method was also revised in order to calculate the
51// logarithmic values of the loaded data.
52// It generates the data values and, then, calculates the respective log values which
53// later load to seperate data structures.
54// The EM data sets, initialized this way, contain both non-log and log values.
55// These initialized data sets can enhance the computing performance of data interpolation
56// operations
57//
58// - LoadShellData method was revised in order to eliminate the presence of a potential
59// memory leak originally identified by Riccardo Capra.
60// Riccardo Capra Original Comment
61// Riccardo Capra <[email protected]>: PLEASE CHECK THE FOLLOWING PIECE OF CODE
62// "energies" AND "data" G4DataVector ARE ALLOCATED, FILLED IN AND NEVER USED OR
63// DELETED. WHATSMORE LOADING FILE OPERATIONS WERE DONE BY G4ShellEMDataSet
64// EVEN BEFORE THE CHANGES I DID ON THIS FILE. SO THE FOLLOWING CODE IN MY
65// OPINION SHOULD BE USELESS AND SHOULD PRODUCE A MEMORY LEAK.
66//
67//
68// -------------------------------------------------------------------
69
73#include "G4VEMDataSet.hh"
74#include "G4EMDataSet.hh"
76#include "G4ShellEMDataSet.hh"
78#include "G4Material.hh"
79#include "G4Element.hh"
80#include "Randomize.hh"
81#include <map>
82#include <vector>
83#include <fstream>
84#include <sstream>
85
86
88{
89 crossSections = 0;
90 interpolation = 0;
91 Initialise();
93}
94
95
97 G4double minE,
98 G4double maxE,
99 G4int bins,
100 G4double unitE,
101 G4double unitData,
102 G4int minZ,
103 G4int maxZ)
104 : interpolation(algorithm), eMin(minE), eMax(maxE), nBins(bins),
105 unit1(unitE), unit2(unitData), zMin(minZ), zMax(maxZ)
106{
107 crossSections = 0;
109}
110
112{
113 delete interpolation;
114 interpolation = 0;
115 std::map<G4int,G4VEMDataSet*,std::less<G4int> >::iterator pos;
116
117 for (pos = dataMap.begin(); pos != dataMap.end(); ++pos)
118 {
119 // The following is a workaround for STL ObjectSpace implementation,
120 // which does not support the standard and does not accept
121 // the syntax pos->second
122 // G4VEMDataSet* dataSet = pos->second;
123 G4VEMDataSet* dataSet = (*pos).second;
124 delete dataSet;
125 }
126
127 if (crossSections != 0)
128 {
129 size_t n = crossSections->size();
130 for (size_t i=0; i<n; i++)
131 {
132 delete (*crossSections)[i];
133 }
134 delete crossSections;
135 crossSections = 0;
136 }
137}
138
140 G4double minE, G4double maxE,
141 G4int numberOfBins,
142 G4double unitE, G4double unitData,
143 G4int minZ, G4int maxZ)
144{
145 if (algorithm != 0)
146 {
147 delete interpolation;
148 interpolation = algorithm;
149 }
150 else
151 {
152 delete interpolation;
153 interpolation = CreateInterpolation();
154 }
155
156 eMin = minE;
157 eMax = maxE;
158 nBins = numberOfBins;
159 unit1 = unitE;
160 unit2 = unitData;
161 zMin = minZ;
162 zMax = maxZ;
163}
164
166{
167 std::map<G4int,G4VEMDataSet*,std::less<G4int> >::const_iterator pos;
168
169 for (pos = dataMap.begin(); pos != dataMap.end(); pos++)
170 {
171 // The following is a workaround for STL ObjectSpace implementation,
172 // which does not support the standard and does not accept
173 // the syntax pos->first or pos->second
174 // G4int z = pos->first;
175 // G4VEMDataSet* dataSet = pos->second;
176 G4int z = (*pos).first;
177 G4VEMDataSet* dataSet = (*pos).second;
178 G4cout << "---- Data set for Z = "
179 << z
180 << G4endl;
181 dataSet->PrintData();
182 G4cout << "--------------------------------------------------" << G4endl;
183 }
184}
185
187{
188 size_t nZ = activeZ.size();
189 for (size_t i=0; i<nZ; i++)
190 {
191 G4int Z = (G4int) activeZ[i];
192
193 // Build the complete string identifying the file with the data set
194
195 char* path = std::getenv("G4LEDATA");
196 if (!path)
197 {
198 G4Exception("G4VCrossSectionHandler::LoadData",
199 "em0006",FatalException,"G4LEDATA environment variable not set");
200 return;
201 }
202
203 std::ostringstream ost;
204 ost << path << '/' << fileName << Z << ".dat";
205 std::ifstream file(ost.str().c_str());
206 std::filebuf* lsdp = file.rdbuf();
207
208 if (! (lsdp->is_open()) )
209 {
210 G4String excep = "data file: " + ost.str() + " not found";
211 G4Exception("G4VCrossSectionHandler::LoadData",
212 "em0003",FatalException,excep);
213 }
214 G4double a = 0;
215 G4int k = 0;
216 G4int nColumns = 2;
217
218 G4DataVector* orig_reg_energies = new G4DataVector;
219 G4DataVector* orig_reg_data = new G4DataVector;
220 G4DataVector* log_reg_energies = new G4DataVector;
221 G4DataVector* log_reg_data = new G4DataVector;
222
223 do
224 {
225 file >> a;
226
227 if (a==0.) a=1e-300;
228
229 // The file is organized into four columns:
230 // 1st column contains the values of energy
231 // 2nd column contains the corresponding data value
232 // The file terminates with the pattern: -1 -1
233 // -2 -2
234 //
235 if (a != -1 && a != -2)
236 {
237 if (k%nColumns == 0)
238 {
239 orig_reg_energies->push_back(a*unit1);
240 log_reg_energies->push_back(std::log10(a)+std::log10(unit1));
241 }
242 else if (k%nColumns == 1)
243 {
244 orig_reg_data->push_back(a*unit2);
245 log_reg_data->push_back(std::log10(a)+std::log10(unit2));
246 }
247 k++;
248 }
249 }
250 while (a != -2); // End of File
251
252 file.close();
253 G4VDataSetAlgorithm* algo = interpolation->Clone();
254
255 G4VEMDataSet* dataSet = new G4EMDataSet(Z,orig_reg_energies,orig_reg_data,log_reg_energies,log_reg_data,algo);
256
257 dataMap[Z] = dataSet;
258
259 }
260}
261
262
264{
265 size_t nZ = activeZ.size();
266 for (size_t i=0; i<nZ; i++)
267 {
268 G4int Z = (G4int) activeZ[i];
269
270 // Build the complete string identifying the file with the data set
271
272 char* path = std::getenv("G4LEDATA");
273 if (!path)
274 {
275 G4Exception("G4VCrossSectionHandler::LoadNonLogData",
276 "em0006",FatalException,"G4LEDATA environment variable not set");
277 return;
278 }
279
280 std::ostringstream ost;
281 ost << path << '/' << fileName << Z << ".dat";
282 std::ifstream file(ost.str().c_str());
283 std::filebuf* lsdp = file.rdbuf();
284
285 if (! (lsdp->is_open()) )
286 {
287 G4String excep = "data file: " + ost.str() + " not found";
288 G4Exception("G4VCrossSectionHandler::LoadNonLogData",
289 "em0003",FatalException,excep);
290 }
291 G4double a = 0;
292 G4int k = 0;
293 G4int nColumns = 2;
294
295 G4DataVector* orig_reg_energies = new G4DataVector;
296 G4DataVector* orig_reg_data = new G4DataVector;
297
298 do
299 {
300 file >> a;
301
302 // The file is organized into four columns:
303 // 1st column contains the values of energy
304 // 2nd column contains the corresponding data value
305 // The file terminates with the pattern: -1 -1
306 // -2 -2
307 //
308 if (a != -1 && a != -2)
309 {
310 if (k%nColumns == 0)
311 {
312 orig_reg_energies->push_back(a*unit1);
313 }
314 else if (k%nColumns == 1)
315 {
316 orig_reg_data->push_back(a*unit2);
317 }
318 k++;
319 }
320 }
321 while (a != -2); // End of File
322
323 file.close();
324 G4VDataSetAlgorithm* algo = interpolation->Clone();
325
326 G4VEMDataSet* dataSet = new G4EMDataSet(Z,orig_reg_energies,orig_reg_data,algo);
327
328 dataMap[Z] = dataSet;
329
330 }
331}
332
334{
335 size_t nZ = activeZ.size();
336 for (size_t i=0; i<nZ; i++)
337 {
338 G4int Z = (G4int) activeZ[i];
339
340 G4VDataSetAlgorithm* algo = interpolation->Clone();
341 G4VEMDataSet* dataSet = new G4ShellEMDataSet(Z, algo);
342
343 dataSet->LoadData(fileName);
344
345 dataMap[Z] = dataSet;
346 }
347}
348
349
350
351
353{
354 // Reset the map of data sets: remove the data sets from the map
355 std::map<G4int,G4VEMDataSet*,std::less<G4int> >::iterator pos;
356
357 if(! dataMap.empty())
358 {
359 for (pos = dataMap.begin(); pos != dataMap.end(); ++pos)
360 {
361 // The following is a workaround for STL ObjectSpace implementation,
362 // which does not support the standard and does not accept
363 // the syntax pos->first or pos->second
364 // G4VEMDataSet* dataSet = pos->second;
365 G4VEMDataSet* dataSet = (*pos).second;
366 delete dataSet;
367 dataSet = 0;
368 G4int i = (*pos).first;
369 dataMap[i] = 0;
370 }
371 dataMap.clear();
372 }
373
374 activeZ.clear();
376}
377
379{
380 G4double value = 0.;
381
382 std::map<G4int,G4VEMDataSet*,std::less<G4int> >::const_iterator pos;
383 pos = dataMap.find(Z);
384 if (pos!= dataMap.end())
385 {
386 // The following is a workaround for STL ObjectSpace implementation,
387 // which does not support the standard and does not accept
388 // the syntax pos->first or pos->second
389 // G4VEMDataSet* dataSet = pos->second;
390 G4VEMDataSet* dataSet = (*pos).second;
391 value = dataSet->FindValue(energy);
392 }
393 else
394 {
395 G4cout << "WARNING: G4VCrossSectionHandler::FindValue did not find Z = "
396 << Z << G4endl;
397 }
398 return value;
399}
400
402 G4int shellIndex) const
403{
404 G4double value = 0.;
405
406 std::map<G4int,G4VEMDataSet*,std::less<G4int> >::const_iterator pos;
407 pos = dataMap.find(Z);
408 if (pos!= dataMap.end())
409 {
410 // The following is a workaround for STL ObjectSpace implementation,
411 // which does not support the standard and does not accept
412 // the syntax pos->first or pos->second
413 // G4VEMDataSet* dataSet = pos->second;
414 G4VEMDataSet* dataSet = (*pos).second;
415 if (shellIndex >= 0)
416 {
417 G4int nComponents = dataSet->NumberOfComponents();
418 if(shellIndex < nComponents)
419 // - MGP - Why doesn't it use G4VEMDataSet::FindValue directly?
420 value = dataSet->GetComponent(shellIndex)->FindValue(energy);
421 else
422 {
423 G4cout << "WARNING: G4VCrossSectionHandler::FindValue did not find"
424 << " shellIndex= " << shellIndex
425 << " for Z= "
426 << Z << G4endl;
427 }
428 } else {
429 value = dataSet->FindValue(energy);
430 }
431 }
432 else
433 {
434 G4cout << "WARNING: G4VCrossSectionHandler::FindValue did not find Z = "
435 << Z << G4endl;
436 }
437 return value;
438}
439
440
442 G4double energy) const
443{
444 G4double value = 0.;
445
446 const G4ElementVector* elementVector = material->GetElementVector();
447 const G4double* nAtomsPerVolume = material->GetVecNbOfAtomsPerVolume();
448 G4int nElements = material->GetNumberOfElements();
449
450 for (G4int i=0 ; i<nElements ; i++)
451 {
452 G4int Z = (G4int) (*elementVector)[i]->GetZ();
453 G4double elementValue = FindValue(Z,energy);
454 G4double nAtomsVol = nAtomsPerVolume[i];
455 value += nAtomsVol * elementValue;
456 }
457
458 return value;
459}
460
461
463{
464 // Builds a CompositeDataSet containing the mean free path for each material
465 // in the material table
466
467 G4DataVector energyVector;
468 G4double dBin = std::log10(eMax/eMin) / nBins;
469
470 for (G4int i=0; i<nBins+1; i++)
471 {
472 energyVector.push_back(std::pow(10., std::log10(eMin)+i*dBin));
473 }
474
475 // Factory method to build cross sections in derived classes,
476 // related to the type of physics process
477
478 if (crossSections != 0)
479 { // Reset the list of cross sections
480 std::vector<G4VEMDataSet*>::iterator mat;
481 if (! crossSections->empty())
482 {
483 for (mat = crossSections->begin(); mat!= crossSections->end(); ++mat)
484 {
485 G4VEMDataSet* set = *mat;
486 delete set;
487 set = 0;
488 }
489 crossSections->clear();
490 delete crossSections;
491 crossSections = 0;
492 }
493 }
494
495 crossSections = BuildCrossSectionsForMaterials(energyVector,energyCuts);
496
497 if (crossSections == 0)
498 {
499 G4Exception("G4VCrossSectionHandler::BuildMeanFreePathForMaterials",
500 "em1010",FatalException,"crossSections = 0");
501 return 0;
502 }
503
505 G4VEMDataSet* materialSet = new G4CompositeEMDataSet(algo);
506 //G4cout << "G4VCrossSectionHandler new dataset " << materialSet << G4endl;
507
508 G4DataVector* energies;
509 G4DataVector* data;
510 G4DataVector* log_energies;
511 G4DataVector* log_data;
512
513
514 const G4ProductionCutsTable* theCoupleTable=
516 size_t numOfCouples = theCoupleTable->GetTableSize();
517
518
519 for (size_t mLocal=0; mLocal<numOfCouples; mLocal++)
520 {
521 energies = new G4DataVector;
522 data = new G4DataVector;
523 log_energies = new G4DataVector;
524 log_data = new G4DataVector;
525 for (G4int bin=0; bin<nBins; bin++)
526 {
527 G4double energy = energyVector[bin];
528 energies->push_back(energy);
529 log_energies->push_back(std::log10(energy));
530 G4VEMDataSet* matCrossSet = (*crossSections)[mLocal];
531 G4double materialCrossSection = 0.0;
532 G4int nElm = matCrossSet->NumberOfComponents();
533 for(G4int j=0; j<nElm; j++) {
534 materialCrossSection += matCrossSet->GetComponent(j)->FindValue(energy);
535 }
536
537 if (materialCrossSection > 0.)
538 {
539 data->push_back(1./materialCrossSection);
540 log_data->push_back(std::log10(1./materialCrossSection));
541 }
542 else
543 {
544 data->push_back(DBL_MAX);
545 log_data->push_back(std::log10(DBL_MAX));
546 }
547 }
549
550 //G4VEMDataSet* dataSet = new G4EMDataSet(m,energies,data,algo,1.,1.);
551
552 G4VEMDataSet* dataSet = new G4EMDataSet(mLocal,energies,data,log_energies,log_data,algoLocal,1.,1.);
553
554 materialSet->AddComponent(dataSet);
555 }
556
557 return materialSet;
558}
559
560
562 G4double e) const
563{
564 // Select randomly an element within the material, according to the weight
565 // determined by the cross sections in the data set
566
567 const G4Material* material = couple->GetMaterial();
568 G4int nElements = material->GetNumberOfElements();
569
570 // Special case: the material consists of one element
571 if (nElements == 1)
572 {
573 G4int Z = (G4int) material->GetZ();
574 return Z;
575 }
576
577 // Composite material
578
579 const G4ElementVector* elementVector = material->GetElementVector();
580 size_t materialIndex = couple->GetIndex();
581
582 G4VEMDataSet* materialSet = (*crossSections)[materialIndex];
583 G4double materialCrossSection0 = 0.0;
584 G4DataVector cross;
585 cross.clear();
586 for ( G4int i=0; i < nElements; i++ )
587 {
588 G4double cr = materialSet->GetComponent(i)->FindValue(e);
589 materialCrossSection0 += cr;
590 cross.push_back(materialCrossSection0);
591 }
592
593 G4double random = G4UniformRand() * materialCrossSection0;
594
595 for (G4int k=0 ; k < nElements ; k++ )
596 {
597 if (random <= cross[k]) return (G4int) (*elementVector)[k]->GetZ();
598 }
599 // It should never get here
600 return 0;
601}
602
604 G4double e) const
605{
606 // Select randomly an element within the material, according to the weight determined
607 // by the cross sections in the data set
608
609 const G4Material* material = couple->GetMaterial();
610 G4Element* nullElement = 0;
611 G4int nElements = material->GetNumberOfElements();
612 const G4ElementVector* elementVector = material->GetElementVector();
613
614 // Special case: the material consists of one element
615 if (nElements == 1)
616 {
617 G4Element* element = (*elementVector)[0];
618 return element;
619 }
620 else
621 {
622 // Composite material
623
624 size_t materialIndex = couple->GetIndex();
625
626 G4VEMDataSet* materialSet = (*crossSections)[materialIndex];
627 G4double materialCrossSection0 = 0.0;
628 G4DataVector cross;
629 cross.clear();
630 for (G4int i=0; i<nElements; i++)
631 {
632 G4double cr = materialSet->GetComponent(i)->FindValue(e);
633 materialCrossSection0 += cr;
634 cross.push_back(materialCrossSection0);
635 }
636
637 G4double random = G4UniformRand() * materialCrossSection0;
638
639 for (G4int k=0 ; k < nElements ; k++ )
640 {
641 if (random <= cross[k]) return (*elementVector)[k];
642 }
643 // It should never end up here
644 G4cout << "G4VCrossSectionHandler::SelectRandomElement - no element found" << G4endl;
645 return nullElement;
646 }
647}
648
650{
651 // Select randomly a shell, according to the weight determined by the cross sections
652 // in the data set
653
654 // Note for later improvement: it would be useful to add a cache mechanism for already
655 // used shells to improve performance
656
657 G4int shell = 0;
658
659 G4double totCrossSection = FindValue(Z,e);
660 G4double random = G4UniformRand() * totCrossSection;
661 G4double partialSum = 0.;
662
663 G4VEMDataSet* dataSet = 0;
664 std::map<G4int,G4VEMDataSet*,std::less<G4int> >::const_iterator pos;
665 pos = dataMap.find(Z);
666 // The following is a workaround for STL ObjectSpace implementation,
667 // which does not support the standard and does not accept
668 // the syntax pos->first or pos->second
669 // if (pos != dataMap.end()) dataSet = pos->second;
670 if (pos != dataMap.end())
671 dataSet = (*pos).second;
672 else
673 {
674 G4Exception("G4VCrossSectionHandler::SelectRandomShell",
675 "em1011",FatalException,"unable to load the dataSet");
676 return 0;
677 }
678
679 size_t nShells = dataSet->NumberOfComponents();
680 for (size_t i=0; i<nShells; i++)
681 {
682 const G4VEMDataSet* shellDataSet = dataSet->GetComponent(i);
683 if (shellDataSet != 0)
684 {
685 G4double value = shellDataSet->FindValue(e);
686 partialSum += value;
687 if (random <= partialSum) return i;
688 }
689 }
690 // It should never get here
691 return shell;
692}
693
695{
696 const G4MaterialTable* materialTable = G4Material::GetMaterialTable();
697 if (materialTable == 0)
698 G4Exception("G4VCrossSectionHandler::ActiveElements",
699 "em1001",FatalException,"no MaterialTable found");
700
702
703 for (G4int mLocal2=0; mLocal2<nMaterials; mLocal2++)
704 {
705 const G4Material* material= (*materialTable)[mLocal2];
706 const G4ElementVector* elementVector = material->GetElementVector();
707 const G4int nElements = material->GetNumberOfElements();
708
709 for (G4int iEl=0; iEl<nElements; iEl++)
710 {
711 G4Element* element = (*elementVector)[iEl];
712 G4double Z = element->GetZ();
713 if (!(activeZ.contains(Z)) && Z >= zMin && Z <= zMax)
714 {
715 activeZ.push_back(Z);
716 }
717 }
718 }
719}
720
722{
724 return algorithm;
725}
726
728{
729 G4int n = 0;
730
731 std::map<G4int,G4VEMDataSet*,std::less<G4int> >::const_iterator pos;
732 pos = dataMap.find(Z);
733 if (pos!= dataMap.end())
734 {
735 G4VEMDataSet* dataSet = (*pos).second;
736 n = dataSet->NumberOfComponents();
737 }
738 else
739 {
740 G4cout << "WARNING: G4VCrossSectionHandler::NumberOfComponents did not "
741 << "find Z = "
742 << Z << G4endl;
743 }
744 return n;
745}
746
747
std::vector< G4Element * > G4ElementVector
@ FatalException
void G4Exception(const char *originOfException, const char *exceptionCode, G4ExceptionSeverity severity, const char *description)
Definition: G4Exception.cc:35
std::vector< G4Material * > G4MaterialTable
double G4double
Definition: G4Types.hh:83
int G4int
Definition: G4Types.hh:85
#define G4endl
Definition: G4ios.hh:57
G4GLOB_DLL std::ostream G4cout
#define G4UniformRand()
Definition: Randomize.hh:52
G4bool contains(const G4double &) const
G4double GetZ() const
Definition: G4Element.hh:130
const G4Material * GetMaterial() const
const G4ElementVector * GetElementVector() const
Definition: G4Material.hh:188
static size_t GetNumberOfMaterials()
Definition: G4Material.cc:644
G4double GetZ() const
Definition: G4Material.cc:701
size_t GetNumberOfElements() const
Definition: G4Material.hh:184
const G4double * GetVecNbOfAtomsPerVolume() const
Definition: G4Material.hh:204
static G4MaterialTable * GetMaterialTable()
Definition: G4Material.cc:637
std::size_t GetTableSize() const
static G4ProductionCutsTable * GetProductionCutsTable()
G4VEMDataSet * BuildMeanFreePathForMaterials(const G4DataVector *energyCuts=0)
G4double ValueForMaterial(const G4Material *material, G4double e) const
void LoadShellData(const G4String &dataFile)
virtual std::vector< G4VEMDataSet * > * BuildCrossSectionsForMaterials(const G4DataVector &energyVector, const G4DataVector *energyCuts=0)=0
G4double FindValue(G4int Z, G4double e) const
G4int NumberOfComponents(G4int Z) const
void LoadData(const G4String &dataFile)
void LoadNonLogData(const G4String &dataFile)
G4int SelectRandomAtom(const G4MaterialCutsCouple *couple, G4double e) const
void Initialise(G4VDataSetAlgorithm *interpolation=0, G4double minE=250 *CLHEP::eV, G4double maxE=100 *CLHEP::GeV, G4int numberOfBins=200, G4double unitE=CLHEP::MeV, G4double unitData=CLHEP::barn, G4int minZ=1, G4int maxZ=99)
G4int SelectRandomShell(G4int Z, G4double e) const
const G4Element * SelectRandomElement(const G4MaterialCutsCouple *material, G4double e) const
virtual G4VDataSetAlgorithm * CreateInterpolation()
virtual G4VDataSetAlgorithm * Clone() const =0
virtual const G4VEMDataSet * GetComponent(G4int componentId) const =0
virtual G4double FindValue(G4double x, G4int componentId=0) const =0
virtual void AddComponent(G4VEMDataSet *dataSet)=0
virtual size_t NumberOfComponents(void) const =0
virtual G4bool LoadData(const G4String &fileName)=0
virtual void PrintData(void) const =0
#define DBL_MAX
Definition: templates.hh:62