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root/group/trunk/OOPSE/libmdtools/NPTf.cpp
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Comparing trunk/OOPSE/libmdtools/NPTf.cpp (file contents):
Revision 578 by gezelter, Wed Jul 9 02:15:29 2003 UTC vs.
Revision 855 by mmeineke, Thu Nov 6 22:01:37 2003 UTC

# Line 1 | Line 1
1 + #include <math.h>
2   #include "Atom.hpp"
3   #include "SRI.hpp"
4   #include "AbstractClasses.hpp"
# Line 6 | Line 7
7   #include "Thermo.hpp"
8   #include "ReadWrite.hpp"
9   #include "Integrator.hpp"
10 < #include "simError.h"
10 > #include "simError.h"
11  
12 + #ifdef IS_MPI
13 + #include "mpiSimulation.hpp"
14 + #endif
15  
16   // Basic non-isotropic thermostating and barostating via the Melchionna
17   // modification of the Hoover algorithm:
18   //
19   //    Melchionna, S., Ciccotti, G., and Holian, B. L., 1993,
20 < //       Molec. Phys., 78, 533.
20 > //       Molec. Phys., 78, 533.
21   //
22   //           and
23 < //
23 > //
24   //    Hoover, W. G., 1986, Phys. Rev. A, 34, 2499.
25  
26 < NPTf::NPTf ( SimInfo *theInfo, ForceFields* the_ff):
27 <  Integrator( theInfo, the_ff )
26 > template<typename T> NPTf<T>::NPTf ( SimInfo *theInfo, ForceFields* the_ff):
27 >  T( theInfo, the_ff )
28   {
29 <  int i;
30 <  chi = 0.0;
31 <  for(i = 0; i < 9; i++) eta[i] = 0.0;
32 <  have_tau_thermostat = 0;
33 <  have_tau_barostat = 0;
34 <  have_target_temp = 0;
35 <  have_target_pressure = 0;
29 >  GenericData* data;
30 >  DoubleArrayData * etaValue;
31 >  vector<double> etaArray;
32 >  int i,j;
33 >
34 >  for(i = 0; i < 3; i++){
35 >    for (j = 0; j < 3; j++){
36 >
37 >      eta[i][j] = 0.0;
38 >      oldEta[i][j] = 0.0;
39 >    }
40 >  }
41 >
42 >
43 >  if( theInfo->useInitXSstate ){
44 >    // retrieve eta array from simInfo if it exists
45 >    data = info->getProperty(ETAVALUE_ID);
46 >    if(data){
47 >      etaValue = dynamic_cast<DoubleArrayData*>(data);
48 >      
49 >      if(etaValue){
50 >        etaArray = etaValue->getData();
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 >      }
59 >    }
60 >  }
61 >
62   }
63  
64 < void NPTf::moveA() {
35 <  
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;
64 > template<typename T> NPTf<T>::~NPTf() {
65  
66 <  tt2 = tauThermostat * tauThermostat;
67 <  tb2 = tauBarostat * tauBarostat;
66 >  // empty for now
67 > }
68  
69 <  instaTemp = tStats->getTemperature();
56 <  tStats->getPressureTensor(press);
69 > template<typename T> void NPTf<T>::resetIntegrator() {
70  
71 <  for (i=0; i < 9; i++) press[i] *= p_convert;
71 >  int i, j;
72  
73 <  instaVol = tStats->getVolume();
74 <  
75 <  // 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;
79 <    
80 <    // velocity half step
81 <    
82 <    vx = vel[atomIndex];
83 <    vy = vel[atomIndex+1];
84 <    vz = vel[atomIndex+2];
85 <    
86 <    scx = (chi + eta[0])*vx + eta[1]*vy + eta[2]*vz;
87 <    scy = eta[3]*vx + (chi + eta[4])*vy + eta[5]*vz;
88 <    scz = eta[6]*vx + eta[7]*vy + (chi + eta[8])*vz;
89 <    
90 <    vx += dt2 * ((frc[atomIndex]  /atoms[i]->getMass())*eConvert - scx);
91 <    vy += dt2 * ((frc[atomIndex+1]/atoms[i]->getMass())*eConvert - scy);
92 <    vz += dt2 * ((frc[atomIndex+2]/atoms[i]->getMass())*eConvert - scz);
73 >  for(i = 0; i < 3; i++)
74 >    for (j = 0; j < 3; j++)
75 >      eta[i][j] = 0.0;
76  
77 <    vel[atomIndex] = vx;
78 <    vel[atomIndex+1] = vy;
96 <    vel[atomIndex+2] = vz;
77 >  T::resetIntegrator();
78 > }
79  
80 <    // position whole step    
80 > template<typename T> void NPTf<T>::evolveEtaA() {
81  
82 <    rj[0] = pos[atomIndex];
101 <    rj[1] = pos[atomIndex+1];
102 <    rj[2] = pos[atomIndex+2];
82 >  int i, j;
83  
84 <    info->wrapVector(rj);
84 >  for(i = 0; i < 3; i ++){
85 >    for(j = 0; j < 3; j++){
86 >      if( i == j)
87 >        eta[i][j] += dt2 *  instaVol *
88 >          (press[i][j] - targetPressure/p_convert) / (NkBT*tb2);
89 >      else
90 >        eta[i][j] += dt2 * instaVol * press[i][j] / (NkBT*tb2);
91 >    }
92 >  }
93  
94 <    scx = eta[0]*rj[0] + eta[1]*rj[1] + eta[2]*rj[2];
95 <    scy = eta[3]*rj[0] + eta[4]*rj[1] + eta[5]*rj[2];
96 <    scz = eta[6]*rj[0] + eta[7]*rj[1] + eta[8]*rj[2];
94 >  for(i = 0; i < 3; i++)
95 >    for (j = 0; j < 3; j++)
96 >      oldEta[i][j] = eta[i][j];
97 > }
98  
99 <    pos[atomIndex] += dt * (vel[atomIndex] + scx);
111 <    pos[atomIndex+1] += dt * (vel[atomIndex+1] + scy);
112 <    pos[atomIndex+2] += dt * (vel[atomIndex+2] + scz);
113 <  
114 <    if( atoms[i]->isDirectional() ){
99 > template<typename T> void NPTf<T>::evolveEtaB() {
100  
101 <      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
101 >  int i,j;
102  
103 <      ji[0] = dAtom->getJx();
104 <      ji[1] = dAtom->getJy();
105 <      ji[2] = dAtom->getJz();
106 <      
107 <      ji[0] += dt2 * (Tb[0] * eConvert - ji[0]*chi);
108 <      ji[1] += dt2 * (Tb[1] * eConvert - ji[1]*chi);
109 <      ji[2] += dt2 * (Tb[2] * eConvert - ji[2]*chi);
110 <      
111 <      // use the angular velocities to propagate the rotation matrix a
112 <      // full time step
113 <      
114 <      // 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] );
103 >  for(i = 0; i < 3; i++)
104 >    for (j = 0; j < 3; j++)
105 >      prevEta[i][j] = eta[i][j];
106 >
107 >  for(i = 0; i < 3; i ++){
108 >    for(j = 0; j < 3; j++){
109 >      if( i == j) {
110 >        eta[i][j] = oldEta[i][j] + dt2 *  instaVol *
111 >          (press[i][j] - targetPressure/p_convert) / (NkBT*tb2);
112 >      } else {
113 >        eta[i][j] = oldEta[i][j] + dt2 * instaVol * press[i][j] / (NkBT*tb2);
114 >      }
115      }
163 –    
116    }
117 + }
118  
119 + template<typename T> void NPTf<T>::getVelScaleA(double sc[3], double vel[3]) {
120 +  int i,j;
121 +  double vScale[3][3];
122 +
123 +  for (i = 0; i < 3; i++ ) {
124 +    for (j = 0; j < 3; j++ ) {
125 +      vScale[i][j] = eta[i][j];
126 +
127 +      if (i == j) {
128 +        vScale[i][j] += chi;
129 +      }
130 +    }
131 +  }
132 +
133 +  info->matVecMul3( vScale, vel, sc );
134 + }
135 +
136 + template<typename T> void NPTf<T>::getVelScaleB(double sc[3], int index ){
137 +  int i,j;
138 +  double myVel[3];
139 +  double vScale[3][3];
140 +
141 +  for (i = 0; i < 3; i++ ) {
142 +    for (j = 0; j < 3; j++ ) {
143 +      vScale[i][j] = eta[i][j];
144 +
145 +      if (i == j) {
146 +        vScale[i][j] += chi;
147 +      }
148 +    }
149 +  }
150 +
151 +  for (j = 0; j < 3; j++)
152 +    myVel[j] = oldVel[3*index + j];
153 +
154 +  info->matVecMul3( vScale, myVel, sc );
155 + }
156 +
157 + template<typename T> void NPTf<T>::getPosScale(double pos[3], double COM[3],
158 +                                               int index, double sc[3]){
159 +  int j;
160 +  double rj[3];
161 +
162 +  for(j=0; j<3; j++)
163 +    rj[j] = ( oldPos[index*3+j] + pos[j]) / 2.0 - COM[j];
164 +
165 +  info->matVecMul3( eta, rj, sc );
166 + }
167 +
168 + template<typename T> void NPTf<T>::scaleSimBox( void ){
169 +
170 +  int i,j,k;
171 +  double scaleMat[3][3];
172 +  double eta2ij;
173 +  double bigScale, smallScale, offDiagMax;
174 +  double hm[3][3], hmnew[3][3];
175 +
176 +
177 +
178    // Scale the box after all the positions have been moved:
179  
180    // Use a taylor expansion for eta products:  Hmat = Hmat . exp(dt * etaMat)
181    //  Hmat = Hmat . ( Ident + dt * etaMat  + dt^2 * etaMat*etaMat / 2)
182  
183 +  bigScale = 1.0;
184 +  smallScale = 1.0;
185 +  offDiagMax = 0.0;
186  
187    for(i=0; i<3; i++){
188      for(j=0; j<3; j++){
189 <      ident[i][j] = 0.0;
190 <      eta1[i][j] = eta[3*i+j];
191 <      eta2[i][j] = 0.0;
189 >
190 >      // Calculate the matrix Product of the eta array (we only need
191 >      // the ij element right now):
192 >
193 >      eta2ij = 0.0;
194        for(k=0; k<3; k++){
195 <        eta2[i][j] += eta[3*i+k] * eta[3*k+j];
195 >        eta2ij += eta[i][k] * eta[k][j];
196        }
197 +
198 +      scaleMat[i][j] = 0.0;
199 +      // identity matrix (see above):
200 +      if (i == j) scaleMat[i][j] = 1.0;
201 +      // Taylor expansion for the exponential truncated at second order:
202 +      scaleMat[i][j] += dt*eta[i][j]  + 0.5*dt*dt*eta2ij;
203 +
204 +      if (i != j)
205 +        if (fabs(scaleMat[i][j]) > offDiagMax)
206 +          offDiagMax = fabs(scaleMat[i][j]);
207      }
208 <    ident[i][i] = 1.0;
208 >
209 >    if (scaleMat[i][i] > bigScale) bigScale = scaleMat[i][i];
210 >    if (scaleMat[i][i] < smallScale) smallScale = scaleMat[i][i];
211    }
212  
213 <  
214 <  info->getBoxM(hm);
215 <
216 <  for(i=0; i<3; i++){
217 <    for(j=0; j<3; j++){      
218 <      hmnew[i][j] = 0.0;
219 <      for(k=0; k<3; k++){
220 <        // remember that hmat has transpose ordering for Fortran compat:
221 <        hmnew[i][j] += hm[3*k+i] * (ident[k][j]
222 <                                    + dt * eta1[k][j]
223 <                                    + 0.5 * dt * dt * eta2[k][j]);
224 <      }
225 <    }
213 >  if ((bigScale > 1.01) || (smallScale < 0.99)) {
214 >    sprintf( painCave.errMsg,
215 >             "NPTf error: Attempting a Box scaling of more than 1 percent.\n"
216 >             " Check your tauBarostat, as it is probably too small!\n\n"
217 >             " scaleMat = [%lf\t%lf\t%lf]\n"
218 >             "            [%lf\t%lf\t%lf]\n"
219 >             "            [%lf\t%lf\t%lf]\n",
220 >             scaleMat[0][0],scaleMat[0][1],scaleMat[0][2],
221 >             scaleMat[1][0],scaleMat[1][1],scaleMat[1][2],
222 >             scaleMat[2][0],scaleMat[2][1],scaleMat[2][2]);
223 >    painCave.isFatal = 1;
224 >    simError();
225 >  } else if (offDiagMax > 0.01) {
226 >    sprintf( painCave.errMsg,
227 >             "NPTf error: Attempting an off-diagonal Box scaling of more than 1 percent.\n"
228 >             " Check your tauBarostat, as it is probably too small!\n\n"
229 >             " scaleMat = [%lf\t%lf\t%lf]\n"
230 >             "            [%lf\t%lf\t%lf]\n"
231 >             "            [%lf\t%lf\t%lf]\n",
232 >             scaleMat[0][0],scaleMat[0][1],scaleMat[0][2],
233 >             scaleMat[1][0],scaleMat[1][1],scaleMat[1][2],
234 >             scaleMat[2][0],scaleMat[2][1],scaleMat[2][2]);
235 >    painCave.isFatal = 1;
236 >    simError();
237 >  } else {
238 >    info->getBoxM(hm);
239 >    info->matMul3(hm, scaleMat, hmnew);
240 >    info->setBoxM(hmnew);
241    }
242 <  
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 <  }
242 > }
243  
244 <  info->setBoxM(hm);
245 <  
244 > template<typename T> bool NPTf<T>::etaConverged() {
245 >  int i;
246 >  double diffEta, sumEta;
247 >
248 >  sumEta = 0;
249 >  for(i = 0; i < 3; i++)
250 >    sumEta += pow(prevEta[i][i] - eta[i][i], 2);
251 >
252 >  diffEta = sqrt( sumEta / 3.0 );
253 >
254 >  return ( diffEta <= etaTolerance );
255   }
256  
257 < void NPTf::moveB( void ){
211 <  int i,j,k;
212 <  int atomIndex;
213 <  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;
257 > template<typename T> double NPTf<T>::getConservedQuantity(void){
258  
259 <  instaTemp = tStats->getTemperature();
260 <  tStats->getPressureTensor(press);
259 >  double conservedQuantity;
260 >  double totalEnergy;
261 >  double thermostat_kinetic;
262 >  double thermostat_potential;
263 >  double barostat_kinetic;
264 >  double barostat_potential;
265 >  double trEta;
266 >  double a[3][3], b[3][3];
267  
268 <  for (i=0; i < 9; i++) press[i] *= p_convert;
268 >  totalEnergy = tStats->getTotalE();
269  
270 <  instaVol = tStats->getVolume();
271 <  
233 <  // first evolve chi a half step
234 <  
235 <  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);
270 >  thermostat_kinetic = fkBT * tt2 * chi * chi /
271 >    (2.0 * eConvert);
272  
273 <  for( i=0; i<nAtoms; i++ ){
248 <    atomIndex = i * 3;
273 >  thermostat_potential = fkBT* integralOfChidt / eConvert;
274  
275 <    // velocity half step
276 <    
277 <    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);
275 >  info->transposeMat3(eta, a);
276 >  info->matMul3(a, eta, b);
277 >  trEta = info->matTrace3(b);
278  
279 <    vel[atomIndex] = vx;
280 <    vel[atomIndex+1] = vy;
266 <    vel[atomIndex+2] = vz;
267 <    
268 <    if( atoms[i]->isDirectional() ){
269 <      
270 <      dAtom = (DirectionalAtom *)atoms[i];
271 <      
272 <      // 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 <  }
296 < }
279 >  barostat_kinetic = NkBT * tb2 * trEta /
280 >    (2.0 * eConvert);
281  
282 < int NPTi::readyCheck() {
283 <
300 <  // First check to see if we have a target temperature.
301 <  // Not having one is fatal.
302 <  
303 <  if (!have_target_temp) {
304 <    sprintf( painCave.errMsg,
305 <             "NPTi error: You can't use the NPTi integrator\n"
306 <             "   without a targetTemp!\n"
307 <             );
308 <    painCave.isFatal = 1;
309 <    simError();
310 <    return -1;
311 <  }
282 >  barostat_potential = (targetPressure * tStats->getVolume() / p_convert) /
283 >    eConvert;
284  
285 <  if (!have_target_pressure) {
286 <    sprintf( painCave.errMsg,
315 <             "NPTi error: You can't use the NPTi integrator\n"
316 <             "   without a targetPressure!\n"
317 <             );
318 <    painCave.isFatal = 1;
319 <    simError();
320 <    return -1;
321 <  }
322 <  
323 <  // We must set tauThermostat.
324 <  
325 <  if (!have_tau_thermostat) {
326 <    sprintf( painCave.errMsg,
327 <             "NPTi error: If you use the NPTi\n"
328 <             "   integrator, you must set tauThermostat.\n");
329 <    painCave.isFatal = 1;
330 <    simError();
331 <    return -1;
332 <  }    
285 >  conservedQuantity = totalEnergy + thermostat_kinetic + thermostat_potential +
286 >    barostat_kinetic + barostat_potential;
287  
288 <  // We must set tauBarostat.
335 <  
336 <  if (!have_tau_barostat) {
337 <    sprintf( painCave.errMsg,
338 <             "NPTi error: If you use the NPTi\n"
339 <             "   integrator, you must set tauBarostat.\n");
340 <    painCave.isFatal = 1;
341 <    simError();
342 <    return -1;
343 <  }    
288 >  return conservedQuantity;
289  
290 <  // We need NkBT a lot, so just set it here:
290 > }
291  
292 <  NkBT = (double)info->ndf * kB * targetTemp;
292 > template<typename T> string NPTf<T>::getAdditionalParameters(void){
293 >  string parameters;
294 >  const int BUFFERSIZE = 2000; // size of the read buffer
295 >  char buffer[BUFFERSIZE];
296  
297 <  return 1;
297 >  sprintf(buffer,"\t%G\t%G;", chi, integralOfChidt);
298 >  parameters += buffer;
299 >
300 >  for(int i = 0; i < 3; i++){
301 >    sprintf(buffer,"\t%G\t%G\t%G;", eta[i][0], eta[i][1], eta[i][2]);
302 >    parameters += buffer;
303 >  }
304 >
305 >  return parameters;
306 >
307   }

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