OPAL (Object Oriented Parallel Accelerator Library) 2024.2
OPAL
MultiBunchHandler.cpp
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1//
2// Class MultiBunchHandler
3// Helper class that stores bunch injection
4// information like azimuth, radius etc. of first
5// bunch in multi-bunch mode of ParallelCyclotronTracker.
6//
7// Copyright (c) 2007 - 2014, Jianjun Yang, Paul Scherrer Institut, Villigen PSI, Switzerland
8// Copyright (c) 2012 - 2023, Paul Scherrer Institut, Villigen PSI, Switzerland
9// All rights reserved
10//
11// Implemented as part of the PhD thesis
12// "Beam dynamics in high intensity cyclotrons including neighboring bunch effects"
13// and the paper
14// "Beam dynamics in high intensity cyclotrons including neighboring bunch effects:
15// Model, implementation, and application"
16// (https://journals.aps.org/prab/pdf/10.1103/PhysRevSTAB.13.064201)
17//
18// This file is part of OPAL.
19//
20// OPAL is free software: you can redistribute it and/or modify
21// it under the terms of the GNU General Public License as published by
22// the Free Software Foundation, either version 3 of the License, or
23// (at your option) any later version.
24//
25// You should have received a copy of the GNU General Public License
26// along with OPAL. If not, see <https://www.gnu.org/licenses/>.
27//
29
31#ifdef ENABLE_AMR
33#endif
35//FIXME Remove headers and dynamic_cast in
37#include "Physics/Units.h"
40
41#include <map>
42
43extern Inform *gmsg;
44
46 const int& numBunch,
47 const double& eta,
48 const double& para,
49 const std::string& mode,
50 const std::string& binning)
51 : onebunch_m(OpalData::getInstance()->getInputBasename() + "-onebunch.h5")
52 , numBunch_m(numBunch)
53 , eta_m(eta)
54 , coeffDBunches_m(para)
55 , radiusLastTurn_m(0.0)
56 , radiusThisTurn_m(0.0)
57 , bunchCount_m(1)
58{
59 PAssert_GT(numBunch, 1);
60
61 binfo_m.reserve(numBunch);
62 for (int i = 0; i < beam->getNumBunch(); ++i) {
63 binfo_m.push_back(beaminfo_t());
64 }
65
66 this->setBinning(binning);
67
68 // mode of generating new bunches:
69 // "FORCE" means generating one bunch after each revolution, until get "TURNS" bunches.
70 // "AUTO" means only when the distance between two neighbor bunches is below the limitation,
71 // then starts to generate new bunches after each revolution,until get "TURNS" bunches;
72 // otherwise, run single bunch track
73
74 *gmsg << "***-------------------- MULTI-BUNCHES MULTI-ENERGY-BINS MODE --------------------*** " << endl;
75
76 // only for regular run of multi bunches, instantiate the PartBins class
77 // note that for restart run of multi bunches, PartBins class is instantiated in function
78 // Distribution::doRestartOpalCycl()
79 if (!OpalData::getInstance()->inRestartRun()) {
80
81 // already exist bins number initially
82 const int BinCount = 1;
83 //allowed maximal bin
84 const int MaxBinNum = 1000;
85
86 // initialize particles number for each bin (both existed and not yet emmitted)
87 size_t partInBin[MaxBinNum] = {0};
88 partInBin[0] = beam->getTotalNum();
89
90 beam->setPBins(new PartBinsCyc(MaxBinNum, BinCount, partInBin));
91 // the allowed maximal bin number is set to 100
92 //beam->setPBins(new PartBins(100));
93
94 this->setMode(mode);
95
96 } else {
97 if (beam->pbin_m->getLastemittedBin() < 2) {
98 *gmsg << "In this restart job, the multi-bunches mode is forcely set to AUTO mode." << endl;
100 } else {
101 *gmsg << "In this restart job, the multi-bunches mode is forcely set to FORCE mode." << endl
102 << "If the existing bunch number is less than the specified number of TURN, "
103 << "readin the phase space of STEP#0 from h5 file consecutively" << endl;
105 }
106 }
107}
108
109
111
112 static IpplTimings::TimerRef saveBunchTimer = IpplTimings::getTimer("Save Bunch H5");
113 IpplTimings::startTimer(saveBunchTimer);
114 *gmsg << endl;
115 *gmsg << "* Store beam to H5 file for multibunch simulation ... ";
116
117 Ppos_t coord, momentum;
118 ParticleAttrib<double> mass, charge;
120
121 std::size_t localNum = beam->getLocalNum();
122
123 coord.create(localNum);
124 coord = beam->R;
125
126 momentum.create(localNum);
127 momentum = beam->P;
128
129 mass.create(localNum);
130 mass = beam->M;
131
132 charge.create(localNum);
133 charge = beam->Q;
134
135 porigin.create(localNum);
136 porigin = beam->POrigin;
137
138 std::map<std::string, double> additionalAttributes = {
139 std::make_pair("REFPR", 0.0),
140 std::make_pair("REFPT", 0.0),
141 std::make_pair("REFPZ", 0.0),
142 std::make_pair("REFR", 0.0),
143 std::make_pair("REFTHETA", 0.0),
144 std::make_pair("REFZ", 0.0),
145 std::make_pair("AZIMUTH", 0.0),
146 std::make_pair("ELEVATION", 0.0),
147 std::make_pair("B-ref_x", 0.0),
148 std::make_pair("B-ref_z", 0.0),
149 std::make_pair("B-ref_y", 0.0),
150 std::make_pair("E-ref_x", 0.0),
151 std::make_pair("E-ref_z", 0.0),
152 std::make_pair("E-ref_y", 0.0),
153 std::make_pair("B-head_x", 0.0),
154 std::make_pair("B-head_z", 0.0),
155 std::make_pair("B-head_y", 0.0),
156 std::make_pair("E-head_x", 0.0),
157 std::make_pair("E-head_z", 0.0),
158 std::make_pair("E-head_y", 0.0),
159 std::make_pair("B-tail_x", 0.0),
160 std::make_pair("B-tail_z", 0.0),
161 std::make_pair("B-tail_y", 0.0),
162 std::make_pair("E-tail_x", 0.0),
163 std::make_pair("E-tail_z", 0.0),
164 std::make_pair("E-tail_y", 0.0)
165 };
166
167 H5PartWrapperForPC h5wrapper(onebunch_m, H5_O_WRONLY);
168 h5wrapper.writeHeader();
169 h5wrapper.writeStep(beam, additionalAttributes);
170 h5wrapper.close();
171
172 *gmsg << "Done." << endl;
173 IpplTimings::stopTimer(saveBunchTimer);
174}
175
176
178
179 static IpplTimings::TimerRef readBunchTimer = IpplTimings::getTimer("Read Bunch H5");
180 IpplTimings::startTimer(readBunchTimer);
181 *gmsg << endl;
182 *gmsg << "* Read beam from H5 file for multibunch simulation ... ";
183
184 std::size_t localNum = beam->getLocalNum();
185
186 /*
187 * 2nd argument: 0 --> step zero is fine since the file has only this step
188 * 3rd argument: "" --> onebunch_m is used
189 * 4th argument: H5_O_RDONLY does not work with this constructor
190 */
191 H5PartWrapperForPC h5wrapper(onebunch_m, 0, "", H5_O_WRONLY);
192
193 size_t numParticles = h5wrapper.getNumParticles();
194
195 const int bunchNum = bunchCount_m - 1;
196
197 beam->setTotalNumPerBunch(numParticles, bunchNum);
198
199 if ( numParticles == 0 ) {
200 throw OpalException("MultiBunchHandler::readBunch()",
201 "No particles in file " + onebunch_m + ".");
202 }
203
204 size_t numParticlesPerNode = numParticles / Ippl::getNodes();
205
206 size_t firstParticle = numParticlesPerNode * Ippl::myNode();
207 size_t lastParticle = firstParticle + numParticlesPerNode - 1;
208 if (Ippl::myNode() == Ippl::getNodes() - 1)
209 lastParticle = numParticles - 1;
210
211 PAssert_LT(firstParticle, lastParticle +1);
212
213 numParticles = lastParticle - firstParticle + 1;
214
215 beam->setLocalNumPerBunch(numParticles, bunchNum);
216
217 //FIXME
218 std::unique_ptr<PartBunchBase<double, 3> > tmpBunch = nullptr;
219#ifdef ENABLE_AMR
220 AmrPartBunch* amrbunch_p = dynamic_cast<AmrPartBunch*>(beam);
221 if ( amrbunch_p != nullptr ) {
222 tmpBunch.reset(new AmrPartBunch(&ref,
223 amrbunch_p->getAmrParticleBase()));
224 } else
225#endif
226 tmpBunch.reset(new PartBunch(&ref));
227
228 tmpBunch->create(numParticles);
229
230 h5wrapper.readStep(tmpBunch.get(), firstParticle, lastParticle);
231 h5wrapper.close();
232
233 beam->create(numParticles);
234
235 for(size_t ii = 0; ii < numParticles; ++ ii, ++ localNum) {
236 beam->R[localNum] = tmpBunch->R[ii];
237 beam->P[localNum] = tmpBunch->P[ii];
238 beam->M[localNum] = tmpBunch->M[ii];
239 beam->Q[localNum] = tmpBunch->Q[ii];
240 beam->POrigin[localNum] = ParticleOrigin::REGULAR;
241 beam->Bin[localNum] = bunchNum;
242 beam->bunchNum[localNum] = bunchNum;
243 }
244
245 beam->boundp();
246
247 binfo_m.push_back(beaminfo_t(injection_m));
248
249 *gmsg << "Done." << endl;
250
251 IpplTimings::stopTimer(readBunchTimer);
252 return true;
253}
254
255
257 const PartData& ref,
258 bool& flagTransition) {
259 short result = 0;
260 if ((bunchCount_m == 1) && (mode_m == MultiBunchMode::AUTO) && (!flagTransition)) {
261
262 // we have still a single bunch
263 beam->setTotalNumPerBunch(beam->getTotalNum(), 0);
264 beam->setLocalNumPerBunch(beam->getLocalNum(), 0);
265
266 // If all of the following conditions are met, this code will be executed
267 // to check the distance between two neighboring bunches:
268 // 1. Only one bunch exists (bunchCount_m == 1)
269 // 2. We are in multi-bunch mode, AUTO sub-mode (mode_m == 2)
270 // 3. It has been a full revolution since the last check (stepsNextCheck)
271
272 *gmsg << "* MBM: Checking for automatically injecting new bunch ..." << endl;
273
274 beam->calcBeamParameters();
275
276 Vector_t Rmean = beam->get_centroid(); // m
277
278 radiusThisTurn_m = std::hypot(Rmean[0],Rmean[1]);
279
280 Vector_t Rrms = beam->get_rrms(); // m
281
282 double XYrms = std::hypot(Rrms[0], Rrms[1]);
283
284 // If the distance between two neighboring bunches is less than 5 times of its 2D rms size
285 // start multi-bunch simulation, fill current phase space to initialR and initialP arrays
287 // since next turn, start multi-bunches
288 saveBunch(beam);
289 flagTransition = true;
290 }
291
292 *gmsg << "* MBM: RLastTurn = " << radiusLastTurn_m << " [m]" << endl;
293 *gmsg << "* MBM: RThisTurn = " << radiusThisTurn_m << " [m]" << endl;
294 *gmsg << "* MBM: XYrms = " << XYrms << " [m]" << endl;
295
297 result = 1;
298
299 } else if (bunchCount_m < numBunch_m) {
300 // Matthias: SteptoLastInj was used in MtsTracker, removed by DW in GenericTracker
301
302 // If all of the following conditions are met, this code will be executed
303 // to read new bunch from hdf5 format file:
304 // 1. We are in multi-bunch mode (numBunch_m > 1)
305 // 2. It has been a full revolution since the last check
306 // 3. Number of existing bunches is less than the desired number of bunches
307 // 4. FORCE mode, or AUTO mode with flagTransition = true
308 // Note: restart from 1 < BunchCount < numBunch_m must be avoided.
309 *gmsg << "* MBM: Injecting a new bunch ..." << endl;
310
311 bunchCount_m++;
312
314
315 // read initial distribution from h5 file
316 switch ( mode_m ) {
319 readBunch(beam, ref);
320 updateParticleBins(beam);
322 break;
323 default:
324 throw OpalException("MultiBunchHandler::injectBunch()",
325 "We shouldn't be here in single bunch mode.");
326 }
327
328 Ippl::Comm->barrier();
329
330 *gmsg << "* MBM: Bunch " << bunchCount_m
331 << " injected, total particle number = "
332 << beam->getTotalNum() << endl;
333 result = 2;
334 }
335 return result;
336}
337
338
340 if (bunchCount_m < 2)
341 return;
342
343 static IpplTimings::TimerRef binningTimer = IpplTimings::getTimer("Particle Binning");
344 IpplTimings::startTimer(binningTimer);
345 switch (binning_m) {
347 beam->resetPartBinID2(eta_m);
348 break;
350 beam->resetPartBinBunch();
351 break;
352 default:
353 beam->resetPartBinID2(eta_m);
354 }
355 IpplTimings::stopTimer(binningTimer);
356}
357
358
359void MultiBunchHandler::setMode(const std::string& mbmode) {
360
361 static const std::map<std::string, MultiBunchMode> stringMBMode_s = {
362 {"FORCE", MultiBunchMode::FORCE},
363 {"AUTO", MultiBunchMode::AUTO},
364 };
365 mode_m = stringMBMode_s.at(mbmode);
366
367 switch (mode_m) {
369 *gmsg << "FORCE mode: The multi bunches will be injected consecutively" << endl
370 << " after each revolution, until get \"TURNS\" bunches." << endl;
371 break;
373 *gmsg << "AUTO mode: The multi bunches will be injected only when the" << endl
374 << " distance between two neighboring bunches is below" << endl
375 << " the limitation. The control parameter is set to "
376 << coeffDBunches_m << endl;
377 break;
378 default:
379 throw OpalException("MultiBunchHandler::setMode",
380 "Unknown \"MBMODE\" multi-bunch mode for OPAL-cycl");
381 }
382}
383
384
385void MultiBunchHandler::setBinning(const std::string& binning) {
386
387 static const std::map<std::string, MultiBunchBinning> stringMBBinning_s = {
388 {"BUNCH_BINNING", MultiBunchBinning::BUNCH},
389 {"GAMMA_BINNING", MultiBunchBinning::GAMMA},
390 };
391 binning_m = stringMBBinning_s.at(binning);
392
393 switch (binning_m) {
395 *gmsg << "\nUse 'BUNCH_BINNING' injection for binnning.\n" << endl;
396 break;
398 *gmsg << "\nUse 'GAMMA_BINNING' injection for binnning.\n" << endl;
399 break;
400 default:
401 throw OpalException("MultiBunchHandler::setBinning",
402 "Unknown \"MB_BINNING\" type of energy binning in multi-bunch mode");
403 }
404}
405
406
407void MultiBunchHandler::setRadiusTurns(const double& radius) {
409 return;
410
411 radiusLastTurn_m = radius;
413
414 if (OpalData::getInstance()->inRestartRun()) {
415 *gmsg << "Radial position at restart position = ";
416 } else {
417 *gmsg << "Initial radial position = ";
418 }
419 *gmsg << radiusThisTurn_m << " m" << endl;
420}
421
422
424 short bunchNr) {
425
426 if (!OpalData::getInstance()->isInOPALCyclMode()) {
427 return false;
428 }
429
430 const unsigned long localNum = beam->getLocalNum();
431
432 long int bunchTotalNum = 0;
433 unsigned long bunchLocalNum = 0;
434
435 /* container:
436 *
437 * ekin, <x>, <y>, <z>, <p_x>, <p_y>, <p_z>,
438 * <x^2>, <y^2>, <z^2>, <p_x^2>, <p_y^2>, <p_z^2>,
439 * <xp_x>, <y_py>, <zp_z>,
440 * <x^3>, <y^3>, <z^3>, <x^4>, <y^4>, <z^4>
441 */
442 const unsigned int dim = PartBunchBase<double, 3>::Dimension;
443 std::vector<double> local(7 * dim + 1);
444
445 beaminfo_t& binfo = getBunchInfo(bunchNr);
446
447 for(unsigned long k = 0; k < localNum; ++k) {
448 if ( beam->bunchNum[k] != bunchNr ) { //|| ID[k] == 0 ) {
449 continue;
450 }
451
452 ++bunchTotalNum;
453 ++bunchLocalNum;
454
455 // ekin
456 local[0] += std::sqrt(dot(beam->P[k], beam->P[k]) + 1.0);
457
458 for (unsigned int i = 0; i < dim; ++i) {
459
460 double r = beam->R[k](i);
461 double p = beam->P[k](i);
462
463 // <x>, <y>, <z>
464 local[i + 1] += r;
465
466 // <p_x>, <p_y, <p_z>
467 local[i + dim + 1] += p;
468
469 // <x^2>, <y^2>, <z^2>
470 double r2 = r * r;
471 local[i + 2 * dim + 1] += r2;
472
473 // <p_x^2>, <p_y^2>, <p_z^2>
474 local[i + 3 * dim + 1] += p * p;
475
476 // <xp_x>, <y_py>, <zp_z>
477 local[i + 4 * dim + 1] += r * p;
478
479 // <x^3>, <y^3>, <z^3>
480 local[i + 5 * dim + 1] += r2 * r;
481
482 // <x^4>, <y^4>, <z^4>
483 local[i + 6 * dim + 1] += r2 * r2;
484 }
485 }
486
487 // inefficient
488 allreduce(bunchTotalNum, 1, std::plus<long int>());
489
490 // here we also update the number of particles of *this* bunch
491 if (bunchNr >= (short)beam->getNumBunch()) {
492 throw OpalException("MultiBunchHandler::calcBunchBeamParameters()",
493 "Bunch number " + std::to_string(bunchNr) +
494 " exceeds bunch index " + std::to_string(beam->getNumBunch() - 1));
495 }
496 beam->setTotalNumPerBunch(bunchTotalNum, bunchNr);
497 beam->setLocalNumPerBunch(bunchLocalNum, bunchNr);
498
499 if (bunchTotalNum == 0) {
500 return false;
501 }
502
503 // ekin
504 const double m0 = beam->getM() * Units::eV2MeV;
505 local[0] -= bunchLocalNum;
506 local[0] *= m0;
507
508 allreduce(local.data(), local.size(), std::plus<double>());
509
510 double invN = 1.0 / double(bunchTotalNum);
511 binfo.ekin = local[0] * invN;
512
513 binfo.time = beam->getT();
514 binfo.nParticles = bunchTotalNum;
515
516 for (unsigned int i = 0; i < dim; ++i) {
517
518 double w = local[i + 1] * invN;
519 double pw = local[i + dim + 1] * invN;
520 double w2 = local[i + 2 * dim + 1] * invN;
521 double pw2 = local[i + 3 * dim + 1] * invN;
522 double wpw = local[i + 4 * dim + 1] * invN;
523 double w3 = local[i + 5 * dim + 1] * invN;
524 double w4 = local[i + 6 * dim + 1] * invN;
525
526 // <x>, <y>, <z>
527 binfo.mean[i] = w;
528
529 // central: <p_w^2> - <p_w>^2 (w = x, y, z)
530 binfo.prms[i] = pw2 - pw * pw;
531 if ( binfo.prms[i] < 0 ) {
532 binfo.prms[i] = 0.0;
533 }
534
535 // central: <wp_w> - <w><p_w>
536 wpw = wpw - w * pw;
537
538 // central: <w^2> - <w>^2 (w = x, y, z)
539 binfo.rrms[i] = w2 - w * w;
540
541 // central: normalized emittance
542 binfo.emit[i] = (binfo.rrms[i] * binfo.prms[i] - wpw * wpw);
543 binfo.emit[i] = std::sqrt(std::max(binfo.emit[i], 0.0));
544
545 // central: <w^4> - 4 * <w> * <w^3> + 6 * <w>^2 * <w^2> - 3 * <w>^4
546 double tmp = w4
547 - 4.0 * w * w3
548 + 6.0 * w * w * w2
549 - 3.0 * w * w * w * w;
550 binfo.halo[i] = tmp / ( binfo.rrms[i] * binfo.rrms[i] );
551
552 // central: sqrt(<w^2> - <w>^2) (w = x, y, z)
553 binfo.rrms[i] = std::sqrt(binfo.rrms[i]);
554
555 // central: sqrt(<p_w^2> - <p_w>^2)
556 binfo.prms[i] = std::sqrt(binfo.prms[i]);
557
558 // central: rms correlation --> (<wp_w> - <w><p_w>) / sqrt(<w^2> * <p_w^2>)
559 double denom = 1.0 / (binfo.rrms[i] * binfo.prms[i]);
560 binfo.correlation[i] = (std::isfinite(denom)) ? wpw * denom : 0.0;
561 }
562
563 double tmp = 1.0 / std::pow(binfo.ekin / m0 + 1.0, 2.0);
564 binfo.dEkin = binfo.prms[1] * m0 * std::sqrt(1.0 - tmp);
565
566 return true;
567}
568
569
570void MultiBunchHandler::updateTime(const double& dt) {
571 for (short b = 0; b < bunchCount_m; ++b) {
572 binfo_m[b].time += dt;
573 }
574}
575
576
577void MultiBunchHandler::updatePathLength(const std::vector<double>& lpaths) {
578 PAssert_EQ(bunchCount_m, (short)lpaths.size() - 1);
579 for (short b = 0; b < bunchCount_m; ++b) {
580 binfo_m[b].pathlength += lpaths[b];
581 }
582}
double dot(const Vector3D &lhs, const Vector3D &rhs)
Vector dot product.
Definition Vector3D.cpp:118
ParticleSpatialLayout< double, 3 >::ParticlePos_t Ppos_t
Definition PBunchDefs.h:19
Inform * gmsg
Definition Main.cpp:70
void allreduce(const T *input, T *output, int count, Op op)
Inform & endl(Inform &inf)
Definition Inform.cpp:42
#define PAssert_LT(a, b)
Definition PAssert.h:106
#define PAssert_EQ(a, b)
Definition PAssert.h:104
#define PAssert_GT(a, b)
Definition PAssert.h:108
constexpr double eV2MeV
Definition Units.h:77
ParticlePos_t & R
ParticleAttrib< int > Bin
bool resetPartBinID2(const double eta)
reset Bin[] for each particle according to the method given in paper PAST-AB(064402) by G....
void setNumBunch(short n)
size_t getLocalNum() const
ParticleAttrib< double > M
size_t getTotalNum() const
ParticleAttrib< Vector_t > P
void setLocalNumPerBunch(size_t numpart, short n)
ParticleAttrib< ParticleOrigin > POrigin
Vector_t get_rrms() const
ParticleAttrib< double > Q
PartBins * pbin_m
short getNumBunch() const
static const unsigned Dimension
Vector_t get_centroid() const
ParticleAttrib< short > bunchNum
void setTotalNumPerBunch(size_t numpart, short n)
void setPBins(PartBins *pbin)
virtual void boundp()
void create(size_t M)
double getM() const
double getT() const
The global OPAL structure.
Definition OpalData.h:49
static OpalData * getInstance()
Definition OpalData.cpp:196
void saveBunch(PartBunchBase< double, 3 > *beam)
bool calcBunchBeamParameters(PartBunchBase< double, 3 > *beam, short bunchNr)
MultiBunchHandler(PartBunchBase< double, 3 > *beam, const int &numBunch, const double &eta, const double &para, const std::string &mode, const std::string &binning)
MultiBunchBinning binning_m
beaminfo_t & getBunchInfo(short bunchNr)
void setMode(const std::string &mbmode)
void updateTime(const double &dt)
void setBinning(const std::string &binning)
MultiBunchMode mode_m
void setRadiusTurns(const double &radius)
short numBunch_m
The number of bunches specified in TURNS of RUN command.
bool readBunch(PartBunchBase< double, 3 > *beam, const PartData &ref)
void updatePathLength(const std::vector< double > &lpaths)
short injectBunch(PartBunchBase< double, 3 > *beam, const PartData &ref, bool &flagTransition)
std::vector< beaminfo_t > binfo_m
void updateParticleBins(PartBunchBase< double, 3 > *beam)
pbase_t * getAmrParticleBase()
int getLastemittedBin()
Definition PartBins.h:136
size_t getNumParticles() const
virtual void writeStep(PartBunchBase< double, 3 > *, const std::map< std::string, double > &additionalStepAttributes)
virtual void readStep(PartBunchBase< double, 3 > *, h5_ssize_t firstParticle, h5_ssize_t lastParticle)
The base class for all OPAL exceptions.
virtual void create(size_t)
static int getNodes()
Definition IpplInfo.cpp:670
static int myNode()
Definition IpplInfo.cpp:691
static Communicate * Comm
Definition IpplInfo.h:84
Timing::TimerRef TimerRef
static TimerRef getTimer(const char *nm)
static void stopTimer(TimerRef t)
static void startTimer(TimerRef t)
Vektor< double, 3 > Vector_t