ViewVC Help
View File | Revision Log | Show Annotations | View Changeset | Root Listing
root/group/branches/no-template-branch/OOPSE/libmdtools/NPTi.cpp
(Generate patch)

Comparing:
trunk/OOPSE/libmdtools/NPTi.cpp (file contents), Revision 763 by tim, Mon Sep 15 16:52:02 2003 UTC vs.
branches/no-template-branch/OOPSE/libmdtools/NPTi.cpp (file contents), Revision 831, Tue Oct 28 16:20:29 2003 UTC

# Line 1 | Line 1
1 < #include <cmath>
1 > #include <math.h>
2   #include "Atom.hpp"
3   #include "SRI.hpp"
4   #include "AbstractClasses.hpp"
# Line 13 | Line 13
13   #include "mpiSimulation.hpp"
14   #endif
15  
16 –
16   // Basic isotropic thermostating and barostating via the Melchionna
17   // modification of the Hoover algorithm:
18   //
# Line 27 | Line 26 | template<typename T> NPTi<T>::NPTi ( SimInfo *theInfo,
26   template<typename T> NPTi<T>::NPTi ( SimInfo *theInfo, ForceFields* the_ff):
27    T( theInfo, the_ff )
28   {
30 –  chi = 0.0;
29    eta = 0.0;
30 <  integralOfChidt = 0.0;
33 <  have_tau_thermostat = 0;
34 <  have_tau_barostat = 0;
35 <  have_target_temp = 0;
36 <  have_target_pressure = 0;
37 <  have_chi_tolerance = 0;
38 <  have_eta_tolerance = 0;
39 <  have_pos_iter_tolerance = 0;
40 <
41 <  oldPos = new double[3*nAtoms];
42 <  oldVel = new double[3*nAtoms];
43 <  oldJi = new double[3*nAtoms];
44 < #ifdef IS_MPI
45 <  Nparticles = mpiSim->getTotAtoms();
46 < #else
47 <  Nparticles = theInfo->n_atoms;
48 < #endif
49 <
30 >  oldEta = 0.0;
31   }
32  
33   template<typename T> NPTi<T>::~NPTi() {
34 <  delete[] oldPos;
54 <  delete[] oldVel;
55 <  delete[] oldJi;
34 >  //nothing for now
35   }
36  
37 < template<typename T> void NPTi<T>::moveA() {
37 > template<typename T> void NPTi<T>::resetIntegrator() {
38 >  eta = 0.0;
39 >  T::resetIntegrator();
40 > }
41  
42 <
43 < //   int i, j;
44 < //   DirectionalAtom* dAtom;
45 < //   double Tb[3], ji[3];
46 < //   double A[3][3], I[3][3];
65 < //   double angle, mass;
66 < //   double vel[3], pos[3], frc[3];
42 > template<typename T> void NPTi<T>::evolveEtaA() {
43 >  eta += dt2 * ( instaVol * (instaPress - targetPressure) /
44 >                 (p_convert*NkBT*tb2));
45 >  oldEta = eta;
46 > }
47  
48 < //   double rj[3];
69 < //   double instaTemp, instaPress, instaVol;
70 < //   double tt2, tb2, scaleFactor;
71 <
72 < //   tt2 = tauThermostat * tauThermostat;
73 < //   tb2 = tauBarostat * tauBarostat;
74 <
75 < //   instaTemp = tStats->getTemperature();
76 < //   instaPress = tStats->getPressure();
77 < //   instaVol = tStats->getVolume();
78 <  
79 < //    // first evolve chi a half step
48 > template<typename T> void NPTi<T>::evolveEtaB() {
49    
50 < //   chi += dt2 * ( instaTemp / targetTemp - 1.0) / tt2;
51 < //   eta += dt2 * ( instaVol * (instaPress - targetPressure) /
52 < //               (p_convert*NkBT*tb2));
50 >  prevEta = eta;
51 >  eta = oldEta + dt2 * ( instaVol * (instaPress - targetPressure) /
52 >                 (p_convert*NkBT*tb2));
53 > }
54  
55 < //   integralOfChidt += dt2* chi;
55 > template<typename T> void NPTi<T>::getVelScaleA(double sc[3], double vel[3]) {
56 >  int i;
57  
58 < //   for( i=0; i<nAtoms; i++ ){
59 < //     atoms[i]->getVel( vel );
89 < //     atoms[i]->getPos( pos );
90 < //     atoms[i]->getFrc( frc );
58 >  for(i=0; i<3; i++) sc[i] = vel[i] * ( chi + eta );
59 > }
60  
61 < //     mass = atoms[i]->getMass();
61 > template<typename T> void NPTi<T>::getVelScaleB(double sc[3], int index ){
62 >  int i;
63  
64 < //     for (j=0; j < 3; j++) {
65 < //       vel[j] += dt2 * ((frc[j] / mass ) * eConvert - vel[j]*(chi+eta));
96 < //       rj[j] = pos[j];
97 < //     }
64 >  for(i=0; i<3; i++) sc[i] = oldVel[index*3 + i] * ( chi + eta );
65 > }
66  
99 – //     atoms[i]->setVel( vel );
67  
68 < //     info->wrapVector(rj);
68 > template<typename T> void NPTi<T>::getPosScale(double pos[3], double COM[3],
69 >                                               int index, double sc[3]){
70 >  int j;
71  
72 < //     for (j = 0; j < 3; j++)
73 < //       pos[j] += dt * (vel[j] + eta*rj[j]);
72 >  for(j=0; j<3; j++)
73 >    sc[j] = ( oldPos[index*3+j] + pos[j]) / 2.0 - COM[j];
74  
75 < //     atoms[i]->setPos( pos );
75 >  for(j=0; j<3; j++)
76 >    sc[j] *= eta;
77 > }
78  
79 < //     if( atoms[i]->isDirectional() ){
79 > template<typename T> void NPTi<T>::scaleSimBox( void ){
80  
81 < //       dAtom = (DirectionalAtom *)atoms[i];
111 <          
112 < //       // get and convert the torque to body frame
113 <      
114 < //       dAtom->getTrq( Tb );
115 < //       dAtom->lab2Body( Tb );
116 <      
117 < //       // get the angular momentum, and propagate a half step
81 >  double scaleFactor;
82  
119 – //       dAtom->getJ( ji );
120 –
121 – //       for (j=0; j < 3; j++)
122 – //         ji[j] += dt2 * (Tb[j] * eConvert - ji[j]*chi);
123 –      
124 – //       // use the angular velocities to propagate the rotation matrix a
125 – //       // full time step
126 –
127 – //       dAtom->getA(A);
128 – //       dAtom->getI(I);
129 –    
130 – //       // rotate about the x-axis      
131 – //       angle = dt2 * ji[0] / I[0][0];
132 – //       this->rotate( 1, 2, angle, ji, A );
133 –
134 – //       // rotate about the y-axis
135 – //       angle = dt2 * ji[1] / I[1][1];
136 – //       this->rotate( 2, 0, angle, ji, A );
137 –      
138 – //       // rotate about the z-axis
139 – //       angle = dt * ji[2] / I[2][2];
140 – //       this->rotate( 0, 1, angle, ji, A);
141 –      
142 – //       // rotate about the y-axis
143 – //       angle = dt2 * ji[1] / I[1][1];
144 – //       this->rotate( 2, 0, angle, ji, A );
145 –      
146 – //        // rotate about the x-axis
147 – //       angle = dt2 * ji[0] / I[0][0];
148 – //       this->rotate( 1, 2, angle, ji, A );
149 –      
150 – //       dAtom->setJ( ji );
151 – //       dAtom->setA( A  );    
152 – //     }                
153 –
154 – //   }
155 –
156 – //   // Scale the box after all the positions have been moved:
157 –  
158 – //   scaleFactor = exp(dt*eta);
159 –
160 – //   if ((scaleFactor > 1.1) || (scaleFactor < 0.9)) {
161 – //     sprintf( painCave.errMsg,
162 – //              "NPTi error: Attempting a Box scaling of more than 10 percent"
163 – //              " check your tauBarostat, as it is probably too small!\n"
164 – //              " eta = %lf, scaleFactor = %lf\n", eta, scaleFactor
165 – //              );
166 – //     painCave.isFatal = 1;
167 – //     simError();
168 – //   } else {        
169 – //     info->scaleBox(exp(dt*eta));      
170 – //   }
171 –  
172 –
173 –  //new version of NPTi
174 –  int i, j, k;
175 –  DirectionalAtom* dAtom;
176 –  double Tb[3], ji[3];
177 –  double A[3][3], I[3][3];
178 –  double angle, mass;
179 –  double vel[3], pos[3], frc[3];
180 –
181 –  double rj[3];
182 –  double instaTemp, instaPress, instaVol;
183 –  double tt2, tb2, scaleFactor;
184 –  double COM[3];
185 –
186 –  tt2 = tauThermostat * tauThermostat;
187 –  tb2 = tauBarostat * tauBarostat;
188 –
189 –  instaTemp = tStats->getTemperature();
190 –  instaPress = tStats->getPressure();
191 –  instaVol = tStats->getVolume();
192 –  
193 –  tStats->getCOM(COM);
194 –  
195 –  //evolve velocity half step
196 –  for( i=0; i<nAtoms; i++ ){
197 –
198 –    atoms[i]->getVel( vel );
199 –    atoms[i]->getFrc( frc );
200 –
201 –    mass = atoms[i]->getMass();
202 –
203 –    for (j=0; j < 3; j++) {
204 –      // velocity half step  (use chi from previous step here):
205 –      vel[j] += dt2 * ((frc[j] / mass ) * eConvert - vel[j]*(chi + eta));
206 –  
207 –    }
208 –
209 –    atoms[i]->setVel( vel );
210 –  
211 –    if( atoms[i]->isDirectional() ){
212 –
213 –      dAtom = (DirectionalAtom *)atoms[i];
214 –
215 –      // get and convert the torque to body frame
216 –      
217 –      dAtom->getTrq( Tb );
218 –      dAtom->lab2Body( Tb );
219 –      
220 –      // get the angular momentum, and propagate a half step
221 –
222 –      dAtom->getJ( ji );
223 –
224 –      for (j=0; j < 3; j++)
225 –        ji[j] += dt2 * (Tb[j] * eConvert - ji[j]*chi);
226 –      
227 –      // use the angular velocities to propagate the rotation matrix a
228 –      // full time step
229 –
230 –      dAtom->getA(A);
231 –      dAtom->getI(I);
232 –    
233 –      // rotate about the x-axis      
234 –      angle = dt2 * ji[0] / I[0][0];
235 –      this->rotate( 1, 2, angle, ji, A );
236 –
237 –      // rotate about the y-axis
238 –      angle = dt2 * ji[1] / I[1][1];
239 –      this->rotate( 2, 0, angle, ji, A );
240 –      
241 –      // rotate about the z-axis
242 –      angle = dt * ji[2] / I[2][2];
243 –      this->rotate( 0, 1, angle, ji, A);
244 –      
245 –      // rotate about the y-axis
246 –      angle = dt2 * ji[1] / I[1][1];
247 –      this->rotate( 2, 0, angle, ji, A );
248 –      
249 –       // rotate about the x-axis
250 –      angle = dt2 * ji[0] / I[0][0];
251 –      this->rotate( 1, 2, angle, ji, A );
252 –      
253 –      dAtom->setJ( ji );
254 –      dAtom->setA( A  );    
255 –    }    
256 –  }
257 –
258 –  // evolve chi and eta  half step
259 –  
260 –  chi += dt2 * ( instaTemp / targetTemp - 1.0) / tt2;
261 –  eta += dt2 * ( instaVol * (instaPress - targetPressure) / (p_convert*NkBT*tb2));
262 –
263 –  //calculate the integral of chidt
264 –  integralOfChidt += dt2*chi;
265 –
266 –  //save the old positions
267 –  for(i = 0; i < nAtoms; i++){
268 –    atoms[i]->getPos(pos);
269 –    for(j = 0; j < 3; j++)
270 –      oldPos[i*3 + j] = pos[j];
271 –  }
272 –  
273 –  //the first estimation of r(t+dt) is equal to  r(t)
274 –    
275 –  for(k = 0; k < 4; k ++){
276 –
277 –    for(i =0 ; i < nAtoms; i++){
278 –
279 –      atoms[i]->getVel(vel);
280 –      atoms[i]->getPos(pos);
281 –
282 –      for(j = 0; j < 3; j++)
283 –        rj[j] = (oldPos[i*3 + j] + pos[j])/2 - COM[j];
284 –
285 –      
286 –      //wrapVector(r(t)) = r(t)-R0
287 –      //info->wrapVector(rj);
288 –      
289 –      for(j = 0; j < 3; j++)
290 –        pos[j] = oldPos[i*3 + j] + dt*(vel[j] + eta*rj[j]);
291 –
292 –      atoms[i]->setPos( pos );
293 –
294 –    }
295 –
296 –  }
297 –    
298 –
299 –  // Scale the box after all the positions have been moved:
300 –  
83    scaleFactor = exp(dt*eta);
84  
85    if ((scaleFactor > 1.1) || (scaleFactor < 0.9)) {
# Line 312 | Line 94 | template<typename T> void NPTi<T>::moveA() {
94      info->scaleBox(scaleFactor);      
95    }  
96  
315 –  //advance volume;
316 –  volume = volume * exp(dt*eta);
97   }
98  
99 < template<typename T> void NPTi<T>::moveB( void ){
320 <
321 < /*
322 <  int i, j;
323 <  DirectionalAtom* dAtom;
324 <  double Tb[3], ji[3];
325 <  double vel[3], frc[3];
326 <  double mass;
327 <
328 <  double instaTemp, instaPress, instaVol;
329 <  double tt2, tb2;
330 <  
331 <  tt2 = tauThermostat * tauThermostat;
332 <  tb2 = tauBarostat * tauBarostat;
333 <
334 <  instaTemp = tStats->getTemperature();
335 <  instaPress = tStats->getPressure();
336 <  instaVol = tStats->getVolume();
337 <
338 <  chi += dt2 * ( instaTemp / targetTemp - 1.0) / tt2;
339 <  eta += dt2 * ( instaVol * (instaPress - targetPressure) /
340 <                 (p_convert*NkBT*tb2));
341 <  integralOfChidt += dt2*chi;
342 <  
343 <  for( i=0; i<nAtoms; i++ ){
99 > template<typename T> bool NPTi<T>::etaConverged() {
100  
101 <    atoms[i]->getVel( vel );
346 <    atoms[i]->getFrc( frc );
347 <
348 <    mass = atoms[i]->getMass();
349 <
350 <    // velocity half step
351 <    for (j=0; j < 3; j++)
352 <      vel[j] += dt2 * ((frc[j] / mass ) * eConvert - vel[j]*(chi+eta));
353 <    
354 <    atoms[i]->setVel( vel );
355 <
356 <    if( atoms[i]->isDirectional() ){
357 <
358 <      dAtom = (DirectionalAtom *)atoms[i];
359 <
360 <      // get and convert the torque to body frame      
361 <
362 <      dAtom->getTrq( Tb );
363 <      dAtom->lab2Body( Tb );
364 <
365 <      // get the angular momentum, and propagate a half step
366 <
367 <      dAtom->getJ( ji );
368 <
369 <      for (j=0; j < 3; j++)
370 <        ji[j] += dt2 * (Tb[j] * eConvert - ji[j]*chi);    
371 <
372 <      dAtom->setJ( ji );
373 <    }
374 <  }
375 <
376 < */
377 <  
378 <  //new version of NPTi
379 <  int i, j, k;
380 <  DirectionalAtom* dAtom;
381 <  double Tb[3], ji[3];
382 <  double vel[3], frc[3];
383 <  double mass;
384 <
385 <  double instTemp, instPress, instVol;
386 <  double tt2, tb2;
387 <  double oldChi, prevChi;
388 <  double oldEta, preEta;
389 <  
390 <  tt2 = tauThermostat * tauThermostat;
391 <  tb2 = tauBarostat * tauBarostat;
392 <
393 <
394 <  // Set things up for the iteration:
395 <
396 <  oldChi = chi;
397 <  oldEta = eta;
398 <
399 <  for( i=0; i<nAtoms; i++ ){
400 <
401 <    atoms[i]->getVel( vel );
402 <
403 <    for (j=0; j < 3; j++)
404 <      oldVel[3*i + j]  = vel[j];
405 <
406 <    if( atoms[i]->isDirectional() ){
407 <
408 <      dAtom = (DirectionalAtom *)atoms[i];
409 <
410 <      dAtom->getJ( ji );
411 <
412 <      for (j=0; j < 3; j++)
413 <        oldJi[3*i + j] = ji[j];
414 <
415 <    }
416 <  }
417 <
418 <  // do the iteration:
419 <
420 <  instVol = tStats->getVolume();
421 <  
422 <  for (k=0; k < 4; k++) {
423 <    
424 <    instTemp = tStats->getTemperature();
425 <    instPress = tStats->getPressure();
426 <
427 <    // evolve chi another half step using the temperature at t + dt/2
428 <
429 <    prevChi = chi;
430 <    chi = oldChi + dt2 * ( instTemp / targetTemp - 1.0) /
431 <      (tauThermostat*tauThermostat);
432 <
433 <    preEta = eta;
434 <    eta = oldEta + dt2 * ( instVol * (instPress - targetPressure) /
435 <       (p_convert*NkBT*tb2));
436 <
437 <  
438 <    for( i=0; i<nAtoms; i++ ){
439 <
440 <      atoms[i]->getFrc( frc );
441 <      atoms[i]->getVel(vel);
442 <      
443 <      mass = atoms[i]->getMass();
444 <      
445 <      // velocity half step
446 <      for (j=0; j < 3; j++)
447 <        vel[j] = oldVel[3*i+j] + dt2 * ((frc[j] / mass ) * eConvert - oldVel[3*i + j]*(chi + eta));
448 <      
449 <      atoms[i]->setVel( vel );
450 <      
451 <      if( atoms[i]->isDirectional() ){
452 <
453 <        dAtom = (DirectionalAtom *)atoms[i];
454 <  
455 <        // get and convert the torque to body frame      
456 <  
457 <        dAtom->getTrq( Tb );
458 <        dAtom->lab2Body( Tb );      
459 <            
460 <        for (j=0; j < 3; j++)
461 <          ji[j] = oldJi[3*i + j] + dt2 * (Tb[j] * eConvert - oldJi[3*i+j]*chi);
462 <      
463 <          dAtom->setJ( ji );
464 <      }
465 <    }
466 <
467 <    if (fabs(prevChi - chi) <= chiTolerance && fabs(preEta -eta) <= etaTolerance)
468 <      break;
469 <  }
470 <
471 <  //calculate integral of chida
472 <  integralOfChidt += dt2*chi;
473 <
474 <
101 >  return ( fabs(prevEta - eta) <= etaTolerance );
102   }
103  
477 – template<typename T> void NPTi<T>::resetIntegrator() {
478 –  chi = 0.0;
479 –  eta = 0.0;
480 – }
481 –
482 – template<typename T> int NPTi<T>::readyCheck() {
483 –
484 –  //check parent's readyCheck() first
485 –  if (T::readyCheck() == -1)
486 –    return -1;
487 –
488 –  // First check to see if we have a target temperature.
489 –  // Not having one is fatal.
490 –  
491 –  if (!have_target_temp) {
492 –    sprintf( painCave.errMsg,
493 –             "NPTi error: You can't use the NPTi integrator\n"
494 –             "   without a targetTemp!\n"
495 –             );
496 –    painCave.isFatal = 1;
497 –    simError();
498 –    return -1;
499 –  }
500 –
501 –  if (!have_target_pressure) {
502 –    sprintf( painCave.errMsg,
503 –             "NPTi error: You can't use the NPTi integrator\n"
504 –             "   without a targetPressure!\n"
505 –             );
506 –    painCave.isFatal = 1;
507 –    simError();
508 –    return -1;
509 –  }
510 –  
511 –  // We must set tauThermostat.
512 –  
513 –  if (!have_tau_thermostat) {
514 –    sprintf( painCave.errMsg,
515 –             "NPTi error: If you use the NPTi\n"
516 –             "   integrator, you must set tauThermostat.\n");
517 –    painCave.isFatal = 1;
518 –    simError();
519 –    return -1;
520 –  }    
521 –
522 –  // We must set tauBarostat.
523 –  
524 –  if (!have_tau_barostat) {
525 –    sprintf( painCave.errMsg,
526 –             "NPTi error: If you use the NPTi\n"
527 –             "   integrator, you must set tauBarostat.\n");
528 –    painCave.isFatal = 1;
529 –    simError();
530 –    return -1;
531 –  }    
532 –
533 –  if (!have_chi_tolerance) {
534 –    sprintf( painCave.errMsg,
535 –             "NPTi warning: setting chi tolerance to 1e-6\n");
536 –    chiTolerance = 1e-6;
537 –    have_chi_tolerance = 1;
538 –    painCave.isFatal = 0;
539 –    simError();
540 –  }
541 –
542 –    if (!have_eta_tolerance) {
543 –    sprintf( painCave.errMsg,
544 –             "NPTi warning: setting eta tolerance to 1e-6\n");
545 –    etaTolerance = 1e-6;
546 –    have_eta_tolerance = 1;
547 –    painCave.isFatal = 0;
548 –    simError();
549 –  }
550 –  // We need NkBT a lot, so just set it here:
551 –
552 –  NkBT = (double)Nparticles * kB * targetTemp;
553 –  fkBT = (double)info->ndf * kB * targetTemp;
554 –
555 –  return 1;
556 – }
557 –
104   template<typename T> double NPTi<T>::getConservedQuantity(void){
105  
106    double conservedQuantity;
107 <  double tb2;
108 <  double eta2;  
109 <  double E_NPT;
110 <  double U;
111 <  double TS;
112 <  double PV;
113 <  double extra;
107 >  double Energy;
108 >  double thermostat_kinetic;
109 >  double thermostat_potential;
110 >  double barostat_kinetic;
111 >  double barostat_potential;
112 >  
113 >  Energy = tStats->getTotalE();
114  
115 <  static double pre_U;
116 <  static double pre_TS;
571 <  static double pre_PV;
572 <  static double pre_extra;
573 <  static int hackCount = 0;
115 >  thermostat_kinetic = fkBT* tt2 * chi * chi /
116 >    (2.0 * eConvert);
117  
118 <  double delta_U;
576 <  double delta_TS;
577 <  double delta_PV;
578 <  double delta_extra;
118 >  thermostat_potential = fkBT* integralOfChidt / eConvert;
119  
580 –  U = tStats->getTotalE();
120  
121 <  TS = fkBT *
122 <    (integralOfChidt + tauThermostat * tauThermostat * chi * chi / 2.0) / eConvert;
121 >  barostat_kinetic = 3.0 * NkBT * tb2 * eta * eta /
122 >    (2.0 * eConvert);
123 >  
124 >  barostat_potential = (targetPressure * tStats->getVolume() / p_convert) /
125 >    eConvert;
126  
127 <  PV = (targetPressure * tStats->getVolume() / p_convert) / eConvert;
128 <
587 <  tb2 = tauBarostat * tauBarostat;
588 <  eta2 = eta * eta;
589 <
590 <  extra = (fkBT * tb2 * eta2 / 2.0 ) / eConvert;
591 <  /*
592 <  if(hackCount == 0){
593 <    pre_U = U;
594 <    pre_TS =TS;
595 <    pre_PV = PV;
596 <    pre_extra =extra;
597 <    hackCount ++;
598 <  }
599 <
600 <  delta_U = U - pre_U;
601 <  delta_TS = TS - pre_TS;
602 <  delta_PV = PV - pre_PV;
603 <  delta_extra = extra - pre_extra;
604 < */
605 <  cout.width(8);
606 <  cout.precision(8);
607 <
127 >  conservedQuantity = Energy + thermostat_kinetic + thermostat_potential +
128 >    barostat_kinetic + barostat_potential;
129    
130 <  cout << info->getTime() << "\t"
131 <       << chi << "\t"
611 <       << eta << "\t"
612 <       << U << "\t"
613 <       << TS << "\t"
614 <       << PV << "\t"
615 <       << extra << "\t"
616 <       << U+TS+PV+extra << endl;
130 > //   cout.width(8);
131 > //   cout.precision(8);
132  
133 < /*
134 <    pre_U = U;
135 <    pre_TS =TS;
621 <    pre_PV = PV;
622 <    pre_extra =extra;
623 <
624 <
625 <  cout << info->getTime() << "\t"
626 <       << U << "\t"
627 <       << U+TS << "\t"
628 <       << U+TS+PV << "\t"
629 <       << U+TS+PV+extra << endl;
630 < */
631 <  conservedQuantity = U+TS+PV+extra;
133 > //   cerr << info->getTime() << "\t" << Energy << "\t" << thermostat_kinetic <<
134 > //       "\t" << thermostat_potential << "\t" << barostat_kinetic <<
135 > //       "\t" << barostat_potential << "\t" << conservedQuantity << endl;
136    return conservedQuantity;
137   }

Diff Legend

– Removed lines
+ Added lines
< Changed lines
> Changed lines