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root/group/branches/new-templateless/OOPSE/libmdtools/NPTf.cpp
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Comparing:
trunk/OOPSE/libmdtools/NPTf.cpp (file contents), Revision 580 by gezelter, Wed Jul 9 13:56:36 2003 UTC vs.
branches/new-templateless/OOPSE/libmdtools/NPTf.cpp (file contents), Revision 852 by mmeineke, Thu Nov 6 18:20:47 2003 UTC

# Line 1 | Line 1
1 + #include <stdlib.h>
2 + #include <math.h>
3 + #include <string.h>
4 +
5   #include "Atom.hpp"
6   #include "SRI.hpp"
7   #include "AbstractClasses.hpp"
# Line 6 | Line 10
10   #include "Thermo.hpp"
11   #include "ReadWrite.hpp"
12   #include "Integrator.hpp"
13 < #include "simError.h"
13 > #include "simError.h"
14  
15 + #ifdef IS_MPI
16 + #include "mpiSimulation.hpp"
17 + #endif
18  
19   // Basic non-isotropic thermostating and barostating via the Melchionna
20   // modification of the Hoover algorithm:
21   //
22   //    Melchionna, S., Ciccotti, G., and Holian, B. L., 1993,
23 < //       Molec. Phys., 78, 533.
23 > //       Molec. Phys., 78, 533.
24   //
25   //           and
26 < //
26 > //
27   //    Hoover, W. G., 1986, Phys. Rev. A, 34, 2499.
28  
29   NPTf::NPTf ( SimInfo *theInfo, ForceFields* the_ff):
30 <  Integrator( theInfo, the_ff )
30 >  NPT( theInfo, the_ff )
31   {
32 <  int i;
33 <  chi = 0.0;
34 <  for(i = 0; i < 9; i++) eta[i] = 0.0;
28 <  have_tau_thermostat = 0;
29 <  have_tau_barostat = 0;
30 <  have_target_temp = 0;
31 <  have_target_pressure = 0;
32 < }
32 >  GenericData* data;
33 >  double *etaArray;
34 >  int i,j;
35  
36 < void NPTf::moveA() {
37 <  
36 <  int i,j,k;
37 <  int atomIndex, aMatIndex;
38 <  DirectionalAtom* dAtom;
39 <  double Tb[3];
40 <  double ji[3];
41 <  double rj[3];
42 <  double ident[3][3], eta1[3][3], eta2[3][3], hmnew[3][3];
43 <  double hm[9];
44 <  double vx, vy, vz;
45 <  double scx, scy, scz;
46 <  double instaTemp, instaPress, instaVol;
47 <  double tt2, tb2;
48 <  double angle;
49 <  double press[9];
50 <  const double p_convert = 1.63882576e8;
36 >  for(i = 0; i < 3; i++){
37 >    for (j = 0; j < 3; j++){
38  
39 <  tt2 = tauThermostat * tauThermostat;
40 <  tb2 = tauBarostat * tauBarostat;
39 >      eta[i][j] = 0.0;
40 >      oldEta[i][j] = 0.0;
41 >    }
42 >  }
43  
44 <  instaTemp = tStats->getTemperature();
45 <  tStats->getPressureTensor(press);
46 <
58 <  for (i=0; i < 9; i++) press[i] *= p_convert;
59 <
60 <  instaVol = tStats->getVolume();
61 <  
62 <  // first evolve chi a half step
63 <  
64 <  chi += dt2 * ( instaTemp / targetTemp - 1.0) / tt2;
65 <  
66 <  eta[0] += dt2 * instaVol * (press[0] - targetPressure) / (NkBT*tb2);
67 <  eta[1] += dt2 * instaVol * press[1] / (NkBT*tb2);
68 <  eta[2] += dt2 * instaVol * press[2] / (NkBT*tb2);
69 <  eta[3] += dt2 * instaVol * press[3] / (NkBT*tb2);
70 <  eta[4] += dt2 * instaVol * (press[4] - targetPressure) / (NkBT*tb2);
71 <  eta[5] += dt2 * instaVol * press[5] / (NkBT*tb2);
72 <  eta[6] += dt2 * instaVol * press[6] / (NkBT*tb2);
73 <  eta[7] += dt2 * instaVol * press[7] / (NkBT*tb2);
74 <  eta[8] += dt2 * instaVol * (press[8] - targetPressure) / (NkBT*tb2);
75 <  
76 <  for( i=0; i<nAtoms; i++ ){
77 <    atomIndex = i * 3;
78 <    aMatIndex = i * 9;
44 >  // retrieve eta array from simInfo if it exists
45 >  data = info->getProperty(ETAVALUE_ID);
46 >  if(data != NULL){
47      
48 <    // velocity half step
48 >    int test = data->getDarray(etaArray);
49      
50 <    vx = vel[atomIndex];
51 <    vy = vel[atomIndex+1];
52 <    vz = vel[atomIndex+2];
53 <    
54 <    scx = (chi + eta[0])*vx + eta[1]*vy + eta[2]*vz;
55 <    scy = eta[3]*vx + (chi + eta[4])*vy + eta[5]*vz;
56 <    scz = eta[6]*vx + eta[7]*vy + (chi + eta[8])*vz;
57 <    
58 <    vx += dt2 * ((frc[atomIndex]  /atoms[i]->getMass())*eConvert - scx);
59 <    vy += dt2 * ((frc[atomIndex+1]/atoms[i]->getMass())*eConvert - scy);
60 <    vz += dt2 * ((frc[atomIndex+2]/atoms[i]->getMass())*eConvert - scz);
50 >    if( test == 9 ){
51 >      
52 >      for(i = 0; i < 3; i++){
53 >        for (j = 0; j < 3; j++){
54 >          eta[i][j] = etaArray[3*i+j];
55 >          oldEta[i][j] = eta[i][j];
56 >        }
57 >      }    
58 >      delete[] etaArray;
59 >    }
60 >    else
61 >      std::cerr << "NPTf error: etaArray is not length 9 (actual = " << test
62 >                << ").\n"
63 >                << "            Simulation wil proceed with eta = 0;\n";
64 >  }
65 > }
66  
67 <    vel[atomIndex] = vx;
95 <    vel[atomIndex+1] = vy;
96 <    vel[atomIndex+2] = vz;
67 > NPTf::~NPTf() {
68  
69 <    // position whole step    
69 >  // empty for now
70 > }
71  
72 <    rj[0] = pos[atomIndex];
101 <    rj[1] = pos[atomIndex+1];
102 <    rj[2] = pos[atomIndex+2];
72 > void NPTf::resetIntegrator() {
73  
74 <    info->wrapVector(rj);
74 >  int i, j;
75  
76 <    scx = eta[0]*rj[0] + eta[1]*rj[1] + eta[2]*rj[2];
77 <    scy = eta[3]*rj[0] + eta[4]*rj[1] + eta[5]*rj[2];
78 <    scz = eta[6]*rj[0] + eta[7]*rj[1] + eta[8]*rj[2];
76 >  for(i = 0; i < 3; i++)
77 >    for (j = 0; j < 3; j++)
78 >      eta[i][j] = 0.0;
79  
80 <    pos[atomIndex] += dt * (vel[atomIndex] + scx);
81 <    pos[atomIndex+1] += dt * (vel[atomIndex+1] + scy);
112 <    pos[atomIndex+2] += dt * (vel[atomIndex+2] + scz);
113 <  
114 <    if( atoms[i]->isDirectional() ){
80 >  NPT::resetIntegrator();
81 > }
82  
83 <      dAtom = (DirectionalAtom *)atoms[i];
117 <          
118 <      // get and convert the torque to body frame
119 <      
120 <      Tb[0] = dAtom->getTx();
121 <      Tb[1] = dAtom->getTy();
122 <      Tb[2] = dAtom->getTz();
123 <      
124 <      dAtom->lab2Body( Tb );
125 <      
126 <      // get the angular momentum, and propagate a half step
83 > void NPTf::evolveEtaA() {
84  
85 <      ji[0] = dAtom->getJx();
86 <      ji[1] = dAtom->getJy();
87 <      ji[2] = dAtom->getJz();
88 <      
89 <      ji[0] += dt2 * (Tb[0] * eConvert - ji[0]*chi);
90 <      ji[1] += dt2 * (Tb[1] * eConvert - ji[1]*chi);
91 <      ji[2] += dt2 * (Tb[2] * eConvert - ji[2]*chi);
92 <      
93 <      // use the angular velocities to propagate the rotation matrix a
137 <      // full time step
138 <      
139 <      // rotate about the x-axis      
140 <      angle = dt2 * ji[0] / dAtom->getIxx();
141 <      this->rotate( 1, 2, angle, ji, &Amat[aMatIndex] );
142 <      
143 <      // rotate about the y-axis
144 <      angle = dt2 * ji[1] / dAtom->getIyy();
145 <      this->rotate( 2, 0, angle, ji, &Amat[aMatIndex] );
146 <      
147 <      // rotate about the z-axis
148 <      angle = dt * ji[2] / dAtom->getIzz();
149 <      this->rotate( 0, 1, angle, ji, &Amat[aMatIndex] );
150 <      
151 <      // rotate about the y-axis
152 <      angle = dt2 * ji[1] / dAtom->getIyy();
153 <      this->rotate( 2, 0, angle, ji, &Amat[aMatIndex] );
154 <      
155 <       // rotate about the x-axis
156 <      angle = dt2 * ji[0] / dAtom->getIxx();
157 <      this->rotate( 1, 2, angle, ji, &Amat[aMatIndex] );
158 <      
159 <      dAtom->setJx( ji[0] );
160 <      dAtom->setJy( ji[1] );
161 <      dAtom->setJz( ji[2] );
85 >  int i, j;
86 >
87 >  for(i = 0; i < 3; i ++){
88 >    for(j = 0; j < 3; j++){
89 >      if( i == j)
90 >        eta[i][j] += dt2 *  instaVol *
91 >          (press[i][j] - targetPressure/p_convert) / (NkBT*tb2);
92 >      else
93 >        eta[i][j] += dt2 * instaVol * press[i][j] / (NkBT*tb2);
94      }
163    
95    }
96  
97 <  // Scale the box after all the positions have been moved:
97 >  for(i = 0; i < 3; i++)
98 >    for (j = 0; j < 3; j++)
99 >      oldEta[i][j] = eta[i][j];
100 > }
101  
102 <  // Use a taylor expansion for eta products:  Hmat = Hmat . exp(dt * etaMat)
169 <  //  Hmat = Hmat . ( Ident + dt * etaMat  + dt^2 * etaMat*etaMat / 2)
102 > void NPTf::evolveEtaB() {
103  
104 +  int i,j;
105  
106 <  for(i=0; i<3; i++){
107 <    for(j=0; j<3; j++){
108 <      ident[i][j] = 0.0;
109 <      eta1[i][j] = eta[3*i+j];
110 <      eta2[i][j] = 0.0;
111 <      for(k=0; k<3; k++){
112 <        eta2[i][j] += eta[3*i+k] * eta[3*k+j];
106 >  for(i = 0; i < 3; i++)
107 >    for (j = 0; j < 3; j++)
108 >      prevEta[i][j] = eta[i][j];
109 >
110 >  for(i = 0; i < 3; i ++){
111 >    for(j = 0; j < 3; j++){
112 >      if( i == j) {
113 >        eta[i][j] = oldEta[i][j] + dt2 *  instaVol *
114 >          (press[i][j] - targetPressure/p_convert) / (NkBT*tb2);
115 >      } else {
116 >        eta[i][j] = oldEta[i][j] + dt2 * instaVol * press[i][j] / (NkBT*tb2);
117        }
118      }
181    ident[i][i] = 1.0;
119    }
120 + }
121  
122 <  
123 <  info->getBoxM(hm);
124 <
125 <  for(i=0; i<3; i++){
126 <    for(j=0; j<3; j++){      
127 <      hmnew[i][j] = 0.0;
128 <      for(k=0; k<3; k++){
129 <        // remember that hmat has transpose ordering for Fortran compat:
130 <        hmnew[i][j] += hm[3*k+i] * (ident[k][j]
131 <                                    + dt * eta1[k][j]
194 <                                    + 0.5 * dt * dt * eta2[k][j]);
122 > void NPTf::getVelScaleA(double sc[3], double vel[3]) {
123 >  int i,j;
124 >  double vScale[3][3];
125 >
126 >  for (i = 0; i < 3; i++ ) {
127 >    for (j = 0; j < 3; j++ ) {
128 >      vScale[i][j] = eta[i][j];
129 >
130 >      if (i == j) {
131 >        vScale[i][j] += chi;
132        }
133      }
134    }
198  
199  for (i = 0; i < 3; i++) {
200    for (j = 0; j < 3; j++) {
201      // remember that hmat has transpose ordering for Fortran compat:
202      hm[3*j + 1] = hmnew[i][j];
203    }
204  }
135  
136 <  info->setBoxM(hm);
207 <  
136 >  info->matVecMul3( vScale, vel, sc );
137   }
138  
139 < void NPTf::moveB( void ){
140 <  int i,j,k;
141 <  int atomIndex;
142 <  DirectionalAtom* dAtom;
214 <  double Tb[3];
215 <  double ji[3];
216 <  double press[9];
217 <  double instaTemp, instaVol;
218 <  double tt2, tb2;
219 <  double vx, vy, vz;
220 <  double scx, scy, scz;
221 <  const double p_convert = 1.63882576e8;
222 <  
223 <  tt2 = tauThermostat * tauThermostat;
224 <  tb2 = tauBarostat * tauBarostat;
139 > void NPTf::getVelScaleB(double sc[3], int index ){
140 >  int i,j;
141 >  double myVel[3];
142 >  double vScale[3][3];
143  
144 <  instaTemp = tStats->getTemperature();
227 <  tStats->getPressureTensor(press);
144 > //   std::cerr << "velScaleB chi = " << chi << "\n";
145  
146 <  for (i=0; i < 9; i++) press[i] *= p_convert;
146 >  for (i = 0; i < 3; i++ ) {
147 >    for (j = 0; j < 3; j++ ) {
148 >      vScale[i][j] = eta[i][j];
149  
150 <  instaVol = tStats->getVolume();
151 <  
152 <  // first evolve chi a half step
153 <  
154 <  chi += dt2 * ( instaTemp / targetTemp - 1.0) / tt2;
236 <  
237 <  eta[0] += dt2 * instaVol * (press[0] - targetPressure) / (NkBT*tb2);
238 <  eta[1] += dt2 * instaVol * press[1] / (NkBT*tb2);
239 <  eta[2] += dt2 * instaVol * press[2] / (NkBT*tb2);
240 <  eta[3] += dt2 * instaVol * press[3] / (NkBT*tb2);
241 <  eta[4] += dt2 * instaVol * (press[4] - targetPressure) / (NkBT*tb2);
242 <  eta[5] += dt2 * instaVol * press[5] / (NkBT*tb2);
243 <  eta[6] += dt2 * instaVol * press[6] / (NkBT*tb2);
244 <  eta[7] += dt2 * instaVol * press[7] / (NkBT*tb2);
245 <  eta[8] += dt2 * instaVol * (press[8] - targetPressure) / (NkBT*tb2);
150 >      if (i == j) {
151 >        vScale[i][j] += chi;
152 >      }
153 >    }
154 >  }
155  
156 <  for( i=0; i<nAtoms; i++ ){
157 <    atomIndex = i * 3;
156 >  for (j = 0; j < 3; j++)
157 >    myVel[j] = oldVel[3*index + j];
158  
159 <    // velocity half step
160 <    
252 <    vx = vel[atomIndex];
253 <    vy = vel[atomIndex+1];
254 <    vz = vel[atomIndex+2];
255 <    
256 <    scx = (chi + eta[0])*vx + eta[1]*vy + eta[2]*vz;
257 <    scy = eta[3]*vx + (chi + eta[4])*vy + eta[5]*vz;
258 <    scz = eta[6]*vx + eta[7]*vy + (chi + eta[8])*vz;
259 <    
260 <    vx += dt2 * ((frc[atomIndex]  /atoms[i]->getMass())*eConvert - scx);
261 <    vy += dt2 * ((frc[atomIndex+1]/atoms[i]->getMass())*eConvert - scy);
262 <    vz += dt2 * ((frc[atomIndex+2]/atoms[i]->getMass())*eConvert - scz);
159 >  info->matVecMul3( vScale, myVel, sc );
160 > }
161  
162 <    vel[atomIndex] = vx;
163 <    vel[atomIndex+1] = vy;
164 <    vel[atomIndex+2] = vz;
165 <    
166 <    if( atoms[i]->isDirectional() ){
167 <      
168 <      dAtom = (DirectionalAtom *)atoms[i];
169 <      
170 <      // get and convert the torque to body frame
273 <      
274 <      Tb[0] = dAtom->getTx();
275 <      Tb[1] = dAtom->getTy();
276 <      Tb[2] = dAtom->getTz();
277 <      
278 <      dAtom->lab2Body( Tb );
279 <      
280 <      // get the angular momentum, and complete the angular momentum
281 <      // half step
282 <      
283 <      ji[0] = dAtom->getJx();
284 <      ji[1] = dAtom->getJy();
285 <      ji[2] = dAtom->getJz();
286 <      
287 <      ji[0] += dt2 * (Tb[0] * eConvert - ji[0]*chi);
288 <      ji[1] += dt2 * (Tb[1] * eConvert - ji[1]*chi);
289 <      ji[2] += dt2 * (Tb[2] * eConvert - ji[2]*chi);
290 <      
291 <      dAtom->setJx( ji[0] );
292 <      dAtom->setJy( ji[1] );
293 <      dAtom->setJz( ji[2] );
294 <    }
295 <  }
162 > void NPTf::getPosScale(double pos[3], double COM[3],
163 >                       int index, double sc[3]){
164 >  int j;
165 >  double rj[3];
166 >
167 >  for(j=0; j<3; j++)
168 >    rj[j] = ( oldPos[index*3+j] + pos[j]) / 2.0 - COM[j];
169 >
170 >  info->matVecMul3( eta, rj, sc );
171   }
172  
173 < int NPTf::readyCheck() {
174 <
175 <  // First check to see if we have a target temperature.
176 <  // Not having one is fatal.
177 <  
178 <  if (!have_target_temp) {
179 <    sprintf( painCave.errMsg,
180 <             "NPTf error: You can't use the NPTf integrator\n"
181 <             "   without a targetTemp!\n"
182 <             );
183 <    painCave.isFatal = 1;
184 <    simError();
185 <    return -1;
173 > void NPTf::scaleSimBox( void ){
174 >
175 >  int i,j,k;
176 >  double scaleMat[3][3];
177 >  double eta2ij;
178 >  double bigScale, smallScale, offDiagMax;
179 >  double hm[3][3], hmnew[3][3];
180 >
181 >
182 >
183 >  // Scale the box after all the positions have been moved:
184 >
185 >  // Use a taylor expansion for eta products:  Hmat = Hmat . exp(dt * etaMat)
186 >  //  Hmat = Hmat . ( Ident + dt * etaMat  + dt^2 * etaMat*etaMat / 2)
187 >
188 >  bigScale = 1.0;
189 >  smallScale = 1.0;
190 >  offDiagMax = 0.0;
191 >
192 >  for(i=0; i<3; i++){
193 >    for(j=0; j<3; j++){
194 >
195 >      // Calculate the matrix Product of the eta array (we only need
196 >      // the ij element right now):
197 >
198 >      eta2ij = 0.0;
199 >      for(k=0; k<3; k++){
200 >        eta2ij += eta[i][k] * eta[k][j];
201 >      }
202 >
203 >      scaleMat[i][j] = 0.0;
204 >      // identity matrix (see above):
205 >      if (i == j) scaleMat[i][j] = 1.0;
206 >      // Taylor expansion for the exponential truncated at second order:
207 >      scaleMat[i][j] += dt*eta[i][j]  + 0.5*dt*dt*eta2ij;
208 >
209 >      if (i != j)
210 >        if (fabs(scaleMat[i][j]) > offDiagMax)
211 >          offDiagMax = fabs(scaleMat[i][j]);
212 >    }
213 >
214 >    if (scaleMat[i][i] > bigScale) bigScale = scaleMat[i][i];
215 >    if (scaleMat[i][i] < smallScale) smallScale = scaleMat[i][i];
216    }
217  
218 <  if (!have_target_pressure) {
218 >  if ((bigScale > 1.01) || (smallScale < 0.99)) {
219      sprintf( painCave.errMsg,
220 <             "NPTf error: You can't use the NPTf integrator\n"
221 <             "   without a targetPressure!\n"
222 <             );
220 >             "NPTf error: Attempting a 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"
224 >             "            [%lf\t%lf\t%lf]\n",
225 >             scaleMat[0][0],scaleMat[0][1],scaleMat[0][2],
226 >             scaleMat[1][0],scaleMat[1][1],scaleMat[1][2],
227 >             scaleMat[2][0],scaleMat[2][1],scaleMat[2][2]);
228      painCave.isFatal = 1;
229      simError();
230 <    return -1;
321 <  }
322 <  
323 <  // We must set tauThermostat.
324 <  
325 <  if (!have_tau_thermostat) {
230 >  } else if (offDiagMax > 0.01) {
231      sprintf( painCave.errMsg,
232 <             "NPTf error: If you use the NPTf\n"
233 <             "   integrator, you must set tauThermostat.\n");
232 >             "NPTf error: Attempting an off-diagonal Box scaling of more than 1 percent.\n"
233 >             " Check your tauBarostat, as it is probably too small!\n\n"
234 >             " scaleMat = [%lf\t%lf\t%lf]\n"
235 >             "            [%lf\t%lf\t%lf]\n"
236 >             "            [%lf\t%lf\t%lf]\n",
237 >             scaleMat[0][0],scaleMat[0][1],scaleMat[0][2],
238 >             scaleMat[1][0],scaleMat[1][1],scaleMat[1][2],
239 >             scaleMat[2][0],scaleMat[2][1],scaleMat[2][2]);
240      painCave.isFatal = 1;
241      simError();
242 <    return -1;
243 <  }    
242 >  } else {
243 >    info->getBoxM(hm);
244 >    info->matMul3(hm, scaleMat, hmnew);
245 >    info->setBoxM(hmnew);
246 >  }
247 > }
248  
249 <  // We must set tauBarostat.
250 <  
251 <  if (!have_tau_barostat) {
337 <    sprintf( painCave.errMsg,
338 <             "NPTf error: If you use the NPTf\n"
339 <             "   integrator, you must set tauBarostat.\n");
340 <    painCave.isFatal = 1;
341 <    simError();
342 <    return -1;
343 <  }    
249 > bool NPTf::etaConverged() {
250 >  int i;
251 >  double diffEta, sumEta;
252  
253 <  // We need NkBT a lot, so just set it here:
253 >  sumEta = 0;
254 >  for(i = 0; i < 3; i++)
255 >    sumEta += pow(prevEta[i][i] - eta[i][i], 2);
256  
257 <  NkBT = (double)info->ndf * kB * targetTemp;
257 >  diffEta = sqrt( sumEta / 3.0 );
258  
259 <  return 1;
259 >  return ( diffEta <= etaTolerance );
260   }
261 +
262 + double NPTf::getConservedQuantity(void){
263 +
264 +  double conservedQuantity;
265 +  double totalEnergy;
266 +  double thermostat_kinetic;
267 +  double thermostat_potential;
268 +  double barostat_kinetic;
269 +  double barostat_potential;
270 +  double trEta;
271 +  double a[3][3], b[3][3];
272 +
273 +  totalEnergy = tStats->getTotalE();
274 +
275 +  thermostat_kinetic = fkBT * tt2 * chi * chi /
276 +    (2.0 * eConvert);
277 +
278 +  thermostat_potential = fkBT* integralOfChidt / eConvert;
279 +
280 +  info->transposeMat3(eta, a);
281 +  info->matMul3(a, eta, b);
282 +  trEta = info->matTrace3(b);
283 +
284 +  barostat_kinetic = NkBT * tb2 * trEta /
285 +    (2.0 * eConvert);
286 +
287 +  barostat_potential = (targetPressure * tStats->getVolume() / p_convert) /
288 +    eConvert;
289 +
290 +  conservedQuantity = totalEnergy + thermostat_kinetic + thermostat_potential +
291 +    barostat_kinetic + barostat_potential;
292 +
293 +  return conservedQuantity;
294 +
295 + }
296 +
297 + char* NPTf::getAdditionalParameters(void){
298 +
299 +  sprintf(addParamBuffer,
300 +          "\t%G\t%G;"
301 +          "\t%G\t%G\t%G;"
302 +          "\t%G\t%G\t%G;"
303 +          "\t%G\t%G\t%G;",
304 +          chi, integralOfChidt,
305 +          eta[0][0], eta[0][1], eta[0][2],
306 +          eta[1][0], eta[1][1], eta[1][2],
307 +          eta[2][0], eta[2][1], eta[2][2]
308 +          );
309 +
310 +  return addParamBuffer;
311 + }

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