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root/group/trunk/OOPSE/libmdtools/NPTf.cpp
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Comparing trunk/OOPSE/libmdtools/NPTf.cpp (file contents):
Revision 772 by gezelter, Fri Sep 19 16:01:07 2003 UTC vs.
Revision 857 by mmeineke, Fri Nov 7 17:09:48 2003 UTC

# Line 1 | Line 1
1 < #include <cmath>
1 > #include <math.h>
2 >
3   #include "Atom.hpp"
4   #include "SRI.hpp"
5   #include "AbstractClasses.hpp"
# Line 7 | Line 8
8   #include "Thermo.hpp"
9   #include "ReadWrite.hpp"
10   #include "Integrator.hpp"
11 < #include "simError.h"
11 > #include "simError.h"
12  
13   #ifdef IS_MPI
14   #include "mpiSimulation.hpp"
# Line 17 | Line 18
18   // modification of the Hoover algorithm:
19   //
20   //    Melchionna, S., Ciccotti, G., and Holian, B. L., 1993,
21 < //       Molec. Phys., 78, 533.
21 > //       Molec. Phys., 78, 533.
22   //
23   //           and
24 < //
24 > //
25   //    Hoover, W. G., 1986, Phys. Rev. A, 34, 2499.
26  
27   template<typename T> NPTf<T>::NPTf ( SimInfo *theInfo, ForceFields* the_ff):
28    T( theInfo, the_ff )
29   {
30 <  int i, j;
31 <  chi = 0.0;
32 <  integralOfChidt = 0.0;
30 >  GenericData* data;
31 >  DoubleArrayData * etaValue;
32 >  vector<double> etaArray;
33 >  int i,j;
34  
35 <  for(i = 0; i < 3; i++)
36 <    for (j = 0; j < 3; j++)
35 >  for(i = 0; i < 3; i++){
36 >    for (j = 0; j < 3; j++){
37 >
38        eta[i][j] = 0.0;
39 +      oldEta[i][j] = 0.0;
40 +    }
41 +  }
42  
37  have_tau_thermostat = 0;
38  have_tau_barostat = 0;
39  have_target_temp = 0;
40  have_target_pressure = 0;
43  
44 <  have_chi_tolerance = 0;
45 <  have_eta_tolerance = 0;
46 <  have_pos_iter_tolerance = 0;
44 >  if( theInfo->useInitXSstate ){
45 >    // retrieve eta array from simInfo if it exists
46 >    data = info->getProperty(ETAVALUE_ID);
47 >    if(data){
48 >      etaValue = dynamic_cast<DoubleArrayData*>(data);
49 >      
50 >      if(etaValue){
51 >        etaArray = etaValue->getData();
52 >        
53 >        for(i = 0; i < 3; i++){
54 >          for (j = 0; j < 3; j++){
55 >            eta[i][j] = etaArray[3*i+j];
56 >            oldEta[i][j] = eta[i][j];
57 >          }
58 >        }
59 >      }
60 >    }
61 >  }
62  
46  oldPos = new double[3*nAtoms];
47  oldVel = new double[3*nAtoms];
48  oldJi = new double[3*nAtoms];
49 #ifdef IS_MPI
50  Nparticles = mpiSim->getTotAtoms();
51 #else
52  Nparticles = theInfo->n_atoms;
53 #endif
54
63   }
64  
65   template<typename T> NPTf<T>::~NPTf() {
66 <  delete[] oldPos;
67 <  delete[] oldVel;
60 <  delete[] oldJi;
66 >
67 >  // empty for now
68   }
69  
70 < template<typename T> void NPTf<T>::moveA() {
70 > template<typename T> void NPTf<T>::resetIntegrator() {
71  
72 <  // new version of NPTf
66 <  int i, j, k;
67 <  DirectionalAtom* dAtom;
68 <  double Tb[3], ji[3];
69 <  double A[3][3], I[3][3];
70 <  double angle, mass;
71 <  double vel[3], pos[3], frc[3];
72 >  int i, j;
73  
74 <  double rj[3];
75 <  double instaTemp, instaPress, instaVol;
76 <  double tt2, tb2;
76 <  double sc[3];
77 <  double eta2ij;
78 <  double press[3][3], vScale[3][3], hm[3][3], hmnew[3][3], scaleMat[3][3];
79 <  double bigScale, smallScale, offDiagMax;
80 <  double COM[3];
74 >  for(i = 0; i < 3; i++)
75 >    for (j = 0; j < 3; j++)
76 >      eta[i][j] = 0.0;
77  
78 <  tt2 = tauThermostat * tauThermostat;
79 <  tb2 = tauBarostat * tauBarostat;
78 >  T::resetIntegrator();
79 > }
80  
81 <  instaTemp = tStats->getTemperature();
86 <  tStats->getPressureTensor(press);
87 <  instaVol = tStats->getVolume();
88 <  
89 <  tStats->getCOM(COM);
81 > template<typename T> void NPTf<T>::evolveEtaA() {
82  
83 <  //calculate scale factor of veloity
84 <  for (i = 0; i < 3; i++ ) {
85 <    for (j = 0; j < 3; j++ ) {
86 <      vScale[i][j] = eta[i][j];
87 <      
88 <      if (i == j) {
89 <        vScale[i][j] += chi;          
90 <      }              
83 >  int i, j;
84 >
85 >  for(i = 0; i < 3; i ++){
86 >    for(j = 0; j < 3; j++){
87 >      if( i == j)
88 >        eta[i][j] += dt2 *  instaVol *
89 >          (press[i][j] - targetPressure/p_convert) / (NkBT*tb2);
90 >      else
91 >        eta[i][j] += dt2 * instaVol * press[i][j] / (NkBT*tb2);
92      }
93    }
101  
102  //evolve velocity half step
103  for( i=0; i<nAtoms; i++ ){
94  
95 <    atoms[i]->getVel( vel );
96 <    atoms[i]->getFrc( frc );
95 >  for(i = 0; i < 3; i++)
96 >    for (j = 0; j < 3; j++)
97 >      oldEta[i][j] = eta[i][j];
98 > }
99  
100 <    mass = atoms[i]->getMass();
109 <    
110 <    info->matVecMul3( vScale, vel, sc );
100 > template<typename T> void NPTf<T>::evolveEtaB() {
101  
102 <    for (j=0; j < 3; j++) {
113 <      // velocity half step
114 <      vel[j] += dt2 * ((frc[j]  / mass) * eConvert - sc[j]);
115 <    }
102 >  int i,j;
103  
104 <    atoms[i]->setVel( vel );
105 <  
106 <    if( atoms[i]->isDirectional() ){
104 >  for(i = 0; i < 3; i++)
105 >    for (j = 0; j < 3; j++)
106 >      prevEta[i][j] = eta[i][j];
107  
108 <      dAtom = (DirectionalAtom *)atoms[i];
108 >  for(i = 0; i < 3; i ++){
109 >    for(j = 0; j < 3; j++){
110 >      if( i == j) {
111 >        eta[i][j] = oldEta[i][j] + dt2 *  instaVol *
112 >          (press[i][j] - targetPressure/p_convert) / (NkBT*tb2);
113 >      } else {
114 >        eta[i][j] = oldEta[i][j] + dt2 * instaVol * press[i][j] / (NkBT*tb2);
115 >      }
116 >    }
117 >  }
118 > }
119  
120 <      // get and convert the torque to body frame
121 <      
125 <      dAtom->getTrq( Tb );
126 <      dAtom->lab2Body( Tb );
127 <      
128 <      // get the angular momentum, and propagate a half step
120 > template<typename T> void NPTf<T>::calcVelScale(void){
121 >  int i,j;
122  
123 <      dAtom->getJ( ji );
123 >  for (i = 0; i < 3; i++ ) {
124 >    for (j = 0; j < 3; j++ ) {
125 >      vScale[i][j] = eta[i][j];
126  
127 <      for (j=0; j < 3; j++)
128 <        ji[j] += dt2 * (Tb[j] * eConvert - ji[j]*chi);
129 <      
130 <      // use the angular velocities to propagate the rotation matrix a
136 <      // full time step
137 <
138 <      dAtom->getA(A);
139 <      dAtom->getI(I);
140 <    
141 <      // rotate about the x-axis      
142 <      angle = dt2 * ji[0] / I[0][0];
143 <      this->rotate( 1, 2, angle, ji, A );
144 <
145 <      // rotate about the y-axis
146 <      angle = dt2 * ji[1] / I[1][1];
147 <      this->rotate( 2, 0, angle, ji, A );
148 <      
149 <      // rotate about the z-axis
150 <      angle = dt * ji[2] / I[2][2];
151 <      this->rotate( 0, 1, angle, ji, A);
152 <      
153 <      // rotate about the y-axis
154 <      angle = dt2 * ji[1] / I[1][1];
155 <      this->rotate( 2, 0, angle, ji, A );
156 <      
157 <       // rotate about the x-axis
158 <      angle = dt2 * ji[0] / I[0][0];
159 <      this->rotate( 1, 2, angle, ji, A );
160 <      
161 <      dAtom->setJ( ji );
162 <      dAtom->setA( A  );    
163 <    }    
127 >      if (i == j) {
128 >        vScale[i][j] += chi;
129 >      }
130 >    }
131    }
132 + }
133  
134 <  // advance chi half step
135 <  chi += dt2 * ( instaTemp / targetTemp - 1.0) / tt2;
134 > template<typename T> void NPTf<T>::getVelScaleA(double sc[3], double vel[3]) {
135 >
136 >  info->matVecMul3( vScale, vel, sc );
137 > }
138  
139 <  // calculate the integral of chidt
140 <  integralOfChidt += dt2*chi;
139 > template<typename T> void NPTf<T>::getVelScaleB(double sc[3], int index ){
140 >  int j;
141 >  double myVel[3];
142 >  double vScale[3][3];
143  
144 <  // advance eta half step
144 >  for (j = 0; j < 3; j++)
145 >    myVel[j] = oldVel[3*index + j];
146  
147 <  for(i = 0; i < 3; i ++)
148 <    for(j = 0; j < 3; j++){
176 <      if( i == j)
177 <        eta[i][j] += dt2 *  instaVol *
178 <          (press[i][j] - targetPressure/p_convert) / (NkBT*tb2);
179 <      else
180 <        eta[i][j] += dt2 * instaVol * press[i][j] / (NkBT*tb2);
181 <    }
182 <    
183 <  //save the old positions
184 <  for(i = 0; i < nAtoms; i++){
185 <    atoms[i]->getPos(pos);
186 <    for(j = 0; j < 3; j++)
187 <      oldPos[i*3 + j] = pos[j];
188 <  }
189 <  
190 <  //the first estimation of r(t+dt) is equal to  r(t)
191 <    
192 <  for(k = 0; k < 4; k ++){
147 >  info->matVecMul3( vScale, myVel, sc );
148 > }
149  
150 <    for(i =0 ; i < nAtoms; i++){
150 > template<typename T> void NPTf<T>::getPosScale(double pos[3], double COM[3],
151 >                                               int index, double sc[3]){
152 >  int j;
153 >  double rj[3];
154  
155 <      atoms[i]->getVel(vel);
156 <      atoms[i]->getPos(pos);
155 >  for(j=0; j<3; j++)
156 >    rj[j] = ( oldPos[index*3+j] + pos[j]) / 2.0 - COM[j];
157  
158 <      for(j = 0; j < 3; j++)
159 <        rj[j] = (oldPos[i*3 + j] + pos[j])/2 - COM[j];
201 <      
202 <      info->matVecMul3( eta, rj, sc );
203 <      
204 <      for(j = 0; j < 3; j++)
205 <        pos[j] = oldPos[i*3 + j] + dt*(vel[j] + sc[j]);
158 >  info->matVecMul3( eta, rj, sc );
159 > }
160  
161 <      atoms[i]->setPos( pos );
161 > template<typename T> void NPTf<T>::scaleSimBox( void ){
162  
163 <    }
163 >  int i,j,k;
164 >  double scaleMat[3][3];
165 >  double eta2ij;
166 >  double bigScale, smallScale, offDiagMax;
167 >  double hm[3][3], hmnew[3][3];
168  
211    if (nConstrained) {
212      constrainA();
213    }
214  }  
169  
170 <
170 >
171    // Scale the box after all the positions have been moved:
172 <  
172 >
173    // Use a taylor expansion for eta products:  Hmat = Hmat . exp(dt * etaMat)
174    //  Hmat = Hmat . ( Ident + dt * etaMat  + dt^2 * etaMat*etaMat / 2)
175 <  
175 >
176    bigScale = 1.0;
177    smallScale = 1.0;
178    offDiagMax = 0.0;
179 <  
179 >
180    for(i=0; i<3; i++){
181      for(j=0; j<3; j++){
182 <      
182 >
183        // Calculate the matrix Product of the eta array (we only need
184        // the ij element right now):
185 <      
185 >
186        eta2ij = 0.0;
187        for(k=0; k<3; k++){
188          eta2ij += eta[i][k] * eta[k][j];
189        }
190 <      
190 >
191        scaleMat[i][j] = 0.0;
192        // identity matrix (see above):
193        if (i == j) scaleMat[i][j] = 1.0;
# Line 241 | Line 195 | template<typename T> void NPTf<T>::moveA() {
195        scaleMat[i][j] += dt*eta[i][j]  + 0.5*dt*dt*eta2ij;
196  
197        if (i != j)
198 <        if (fabs(scaleMat[i][j]) > offDiagMax)
198 >        if (fabs(scaleMat[i][j]) > offDiagMax)
199            offDiagMax = fabs(scaleMat[i][j]);
200      }
201  
202      if (scaleMat[i][i] > bigScale) bigScale = scaleMat[i][i];
203      if (scaleMat[i][i] < smallScale) smallScale = scaleMat[i][i];
204    }
205 <  
206 <  if ((bigScale > 1.1) || (smallScale < 0.9)) {
205 >
206 >  if ((bigScale > 1.01) || (smallScale < 0.99)) {
207      sprintf( painCave.errMsg,
208 <             "NPTf error: Attempting a Box scaling of more than 10 percent.\n"
208 >             "NPTf error: Attempting a Box scaling of more than 1 percent.\n"
209               " Check your tauBarostat, as it is probably too small!\n\n"
210               " scaleMat = [%lf\t%lf\t%lf]\n"
211               "            [%lf\t%lf\t%lf]\n"
# Line 261 | Line 215 | template<typename T> void NPTf<T>::moveA() {
215               scaleMat[2][0],scaleMat[2][1],scaleMat[2][2]);
216      painCave.isFatal = 1;
217      simError();
218 <  } else if (offDiagMax > 0.1) {
218 >  } else if (offDiagMax > 0.01) {
219      sprintf( painCave.errMsg,
220 <             "NPTf error: Attempting an off-diagonal Box scaling of more than 10 percent.\n"
220 >             "NPTf error: Attempting an off-diagonal Box scaling of more than 1 percent.\n"
221               " Check your tauBarostat, as it is probably too small!\n\n"
222               " scaleMat = [%lf\t%lf\t%lf]\n"
223               "            [%lf\t%lf\t%lf]\n"
# Line 278 | Line 232 | template<typename T> void NPTf<T>::moveA() {
232      info->matMul3(hm, scaleMat, hmnew);
233      info->setBoxM(hmnew);
234    }
281  
235   }
236  
237 < template<typename T> void NPTf<T>::moveB( void ){
237 > template<typename T> bool NPTf<T>::etaConverged() {
238 >  int i;
239 >  double diffEta, sumEta;
240  
241 <  //new version of NPTf
287 <  int i, j, k;
288 <  DirectionalAtom* dAtom;
289 <  double Tb[3], ji[3];
290 <  double vel[3], myVel[3], frc[3];
291 <  double mass;
292 <
293 <  double instaTemp, instaPress, instaVol;
294 <  double tt2, tb2;
295 <  double sc[3];
296 <  double press[3][3], vScale[3][3];
297 <  double oldChi, prevChi;
298 <  double oldEta[3][3], prevEta[3][3], diffEta;
299 <  
300 <  tt2 = tauThermostat * tauThermostat;
301 <  tb2 = tauBarostat * tauBarostat;
302 <
303 <  // Set things up for the iteration:
304 <
305 <  oldChi = chi;
306 <  
241 >  sumEta = 0;
242    for(i = 0; i < 3; i++)
243 <    for(j = 0; j < 3; j++)
309 <      oldEta[i][j] = eta[i][j];
243 >    sumEta += pow(prevEta[i][i] - eta[i][i], 2);
244  
245 <  for( i=0; i<nAtoms; i++ ){
245 >  diffEta = sqrt( sumEta / 3.0 );
246  
247 <    atoms[i]->getVel( vel );
314 <
315 <    for (j=0; j < 3; j++)
316 <      oldVel[3*i + j]  = vel[j];
317 <
318 <    if( atoms[i]->isDirectional() ){
319 <
320 <      dAtom = (DirectionalAtom *)atoms[i];
321 <
322 <      dAtom->getJ( ji );
323 <
324 <      for (j=0; j < 3; j++)
325 <        oldJi[3*i + j] = ji[j];
326 <
327 <    }
328 <  }
329 <
330 <  // do the iteration:
331 <
332 <  instaVol = tStats->getVolume();
333 <  
334 <  for (k=0; k < 4; k++) {
335 <    
336 <    instaTemp = tStats->getTemperature();
337 <    tStats->getPressureTensor(press);
338 <
339 <    // evolve chi another half step using the temperature at t + dt/2
340 <
341 <    prevChi = chi;
342 <    chi = oldChi + dt2 * ( instaTemp / targetTemp - 1.0) / tt2;
343 <    
344 <    for(i = 0; i < 3; i++)
345 <      for(j = 0; j < 3; j++)
346 <        prevEta[i][j] = eta[i][j];
347 <
348 <    //advance eta half step and calculate scale factor for velocity
349 <
350 <    for(i = 0; i < 3; i ++)
351 <      for(j = 0; j < 3; j++){
352 <        if( i == j) {
353 <          eta[i][j] = oldEta[i][j] + dt2 *  instaVol *
354 <            (press[i][j] - targetPressure/p_convert) / (NkBT*tb2);
355 <          vScale[i][j] = eta[i][j] + chi;
356 <        } else {
357 <          eta[i][j] = oldEta[i][j] + dt2 * instaVol * press[i][j] / (NkBT*tb2);
358 <          vScale[i][j] = eta[i][j];
359 <        }
360 <      }  
361 <    
362 <    for( i=0; i<nAtoms; i++ ){
363 <
364 <      atoms[i]->getFrc( frc );
365 <      atoms[i]->getVel(vel);
366 <      
367 <      mass = atoms[i]->getMass();
368 <    
369 <      for (j = 0; j < 3; j++)
370 <        myVel[j] = oldVel[3*i + j];
371 <      
372 <      info->matVecMul3( vScale, myVel, sc );
373 <      
374 <      // velocity half step
375 <      for (j=0; j < 3; j++) {
376 <        // velocity half step  (use chi from previous step here):
377 <        vel[j] = oldVel[3*i+j] + dt2 * ((frc[j]  / mass) * eConvert - sc[j]);
378 <      }
379 <      
380 <      atoms[i]->setVel( vel );
381 <      
382 <      if( atoms[i]->isDirectional() ){
383 <
384 <        dAtom = (DirectionalAtom *)atoms[i];
385 <  
386 <        // get and convert the torque to body frame      
387 <  
388 <        dAtom->getTrq( Tb );
389 <        dAtom->lab2Body( Tb );      
390 <            
391 <        for (j=0; j < 3; j++)
392 <          ji[j] = oldJi[3*i + j] + dt2 * (Tb[j] * eConvert - oldJi[3*i+j]*chi);
393 <      
394 <          dAtom->setJ( ji );
395 <      }
396 <    }
397 <
398 <    if (nConstrained) {
399 <      constrainB();
400 <    }
401 <    
402 <    diffEta = 0;
403 <    for(i = 0; i < 3; i++)
404 <      diffEta += pow(prevEta[i][i] - eta[i][i], 2);    
405 <    
406 <    if (fabs(prevChi - chi) <= chiTolerance && sqrt(diffEta / 3) <= etaTolerance)
407 <      break;
408 <  }
409 <
410 <  //calculate integral of chidt
411 <  integralOfChidt += dt2*chi;
412 <  
247 >  return ( diffEta <= etaTolerance );
248   }
249  
415 template<typename T> void NPTf<T>::resetIntegrator() {
416  int i,j;
417  
418  chi = 0.0;
419
420  for(i = 0; i < 3; i++)
421    for (j = 0; j < 3; j++)
422      eta[i][j] = 0.0;
423
424 }
425
426 template<typename T> int NPTf<T>::readyCheck() {
427
428  //check parent's readyCheck() first
429  if (T::readyCheck() == -1)
430    return -1;
431
432  // First check to see if we have a target temperature.
433  // Not having one is fatal.
434  
435  if (!have_target_temp) {
436    sprintf( painCave.errMsg,
437             "NPTf error: You can't use the NPTf integrator\n"
438             "   without a targetTemp!\n"
439             );
440    painCave.isFatal = 1;
441    simError();
442    return -1;
443  }
444
445  if (!have_target_pressure) {
446    sprintf( painCave.errMsg,
447             "NPTf error: You can't use the NPTf integrator\n"
448             "   without a targetPressure!\n"
449             );
450    painCave.isFatal = 1;
451    simError();
452    return -1;
453  }
454  
455  // We must set tauThermostat.
456  
457  if (!have_tau_thermostat) {
458    sprintf( painCave.errMsg,
459             "NPTf error: If you use the NPTf\n"
460             "   integrator, you must set tauThermostat.\n");
461    painCave.isFatal = 1;
462    simError();
463    return -1;
464  }    
465
466  // We must set tauBarostat.
467  
468  if (!have_tau_barostat) {
469    sprintf( painCave.errMsg,
470             "NPTf error: If you use the NPTf\n"
471             "   integrator, you must set tauBarostat.\n");
472    painCave.isFatal = 1;
473    simError();
474    return -1;
475  }    
476
477  
478  // We need NkBT a lot, so just set it here: This is the RAW number
479  // of particles, so no subtraction or addition of constraints or
480  // orientational degrees of freedom:
481  
482  NkBT = (double)Nparticles * kB * targetTemp;
483  
484  // fkBT is used because the thermostat operates on more degrees of freedom
485  // than the barostat (when there are particles with orientational degrees
486  // of freedom).  ndf = 3 * (n_atoms + n_oriented -1) - n_constraint - nZcons
487  
488  fkBT = (double)info->ndf * kB * targetTemp;
489
490  return 1;
491 }
492
250   template<typename T> double NPTf<T>::getConservedQuantity(void){
251  
252    double conservedQuantity;
253 <  double Energy;
253 >  double totalEnergy;
254    double thermostat_kinetic;
255    double thermostat_potential;
256    double barostat_kinetic;
# Line 501 | Line 258 | template<typename T> double NPTf<T>::getConservedQuant
258    double trEta;
259    double a[3][3], b[3][3];
260  
261 <  Energy = tStats->getTotalE();
261 >  totalEnergy = tStats->getTotalE();
262  
263 <  thermostat_kinetic = fkBT* tauThermostat * tauThermostat * chi * chi /
263 >  thermostat_kinetic = fkBT * tt2 * chi * chi /
264      (2.0 * eConvert);
265  
266    thermostat_potential = fkBT* integralOfChidt / eConvert;
# Line 512 | Line 269 | template<typename T> double NPTf<T>::getConservedQuant
269    info->matMul3(a, eta, b);
270    trEta = info->matTrace3(b);
271  
272 <  barostat_kinetic = NkBT * tauBarostat * tauBarostat * trEta /
272 >  barostat_kinetic = NkBT * tb2 * trEta /
273      (2.0 * eConvert);
274 <  
275 <  barostat_potential = (targetPressure * tStats->getVolume() / p_convert) /
274 >
275 >  barostat_potential = (targetPressure * tStats->getVolume() / p_convert) /
276      eConvert;
277  
278 <  conservedQuantity = Energy + thermostat_kinetic + thermostat_potential +
278 >  conservedQuantity = totalEnergy + thermostat_kinetic + thermostat_potential +
279      barostat_kinetic + barostat_potential;
523  
524  cout.width(8);
525  cout.precision(8);
280  
281 <  cerr << info->getTime() << "\t" << Energy << "\t" << thermostat_kinetic <<
528 <      "\t" << thermostat_potential << "\t" << barostat_kinetic <<
529 <      "\t" << barostat_potential << "\t" << conservedQuantity << endl;
281 >  return conservedQuantity;
282  
531  return conservedQuantity;
283   }
284 +
285 + template<typename T> string NPTf<T>::getAdditionalParameters(void){
286 +  string parameters;
287 +  const int BUFFERSIZE = 2000; // size of the read buffer
288 +  char buffer[BUFFERSIZE];
289 +
290 +  sprintf(buffer,"\t%G\t%G;", chi, integralOfChidt);
291 +  parameters += buffer;
292 +
293 +  for(int i = 0; i < 3; i++){
294 +    sprintf(buffer,"\t%G\t%G\t%G;", eta[i][0], eta[i][1], eta[i][2]);
295 +    parameters += buffer;
296 +  }
297 +
298 +  return parameters;
299 +
300 + }

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