| 1 | gezelter | 578 | #include <cmath> | 
| 2 | gezelter | 574 | #include "Atom.hpp" | 
| 3 |  |  | #include "SRI.hpp" | 
| 4 |  |  | #include "AbstractClasses.hpp" | 
| 5 |  |  | #include "SimInfo.hpp" | 
| 6 |  |  | #include "ForceFields.hpp" | 
| 7 |  |  | #include "Thermo.hpp" | 
| 8 |  |  | #include "ReadWrite.hpp" | 
| 9 |  |  | #include "Integrator.hpp" | 
| 10 |  |  | #include "simError.h" | 
| 11 |  |  |  | 
| 12 | tim | 763 | #ifdef IS_MPI | 
| 13 |  |  | #include "mpiSimulation.hpp" | 
| 14 |  |  | #endif | 
| 15 | gezelter | 574 |  | 
| 16 |  |  | // Basic 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. | 
| 21 |  |  | // | 
| 22 |  |  | //           and | 
| 23 |  |  | // | 
| 24 |  |  | //    Hoover, W. G., 1986, Phys. Rev. A, 34, 2499. | 
| 25 |  |  |  | 
| 26 | tim | 645 | template<typename T> NPTi<T>::NPTi ( SimInfo *theInfo, ForceFields* the_ff): | 
| 27 |  |  | T( theInfo, the_ff ) | 
| 28 | gezelter | 574 | { | 
| 29 |  |  | chi = 0.0; | 
| 30 |  |  | eta = 0.0; | 
| 31 | tim | 763 | integralOfChidt = 0.0; | 
| 32 | gezelter | 574 | have_tau_thermostat = 0; | 
| 33 |  |  | have_tau_barostat = 0; | 
| 34 |  |  | have_target_temp = 0; | 
| 35 |  |  | have_target_pressure = 0; | 
| 36 | tim | 763 | have_chi_tolerance = 0; | 
| 37 |  |  | have_eta_tolerance = 0; | 
| 38 |  |  | have_pos_iter_tolerance = 0; | 
| 39 |  |  |  | 
| 40 |  |  | oldPos = new double[3*nAtoms]; | 
| 41 |  |  | oldVel = new double[3*nAtoms]; | 
| 42 |  |  | oldJi = new double[3*nAtoms]; | 
| 43 |  |  | #ifdef IS_MPI | 
| 44 |  |  | Nparticles = mpiSim->getTotAtoms(); | 
| 45 |  |  | #else | 
| 46 |  |  | Nparticles = theInfo->n_atoms; | 
| 47 |  |  | #endif | 
| 48 |  |  |  | 
| 49 | gezelter | 574 | } | 
| 50 |  |  |  | 
| 51 | tim | 763 | template<typename T> NPTi<T>::~NPTi() { | 
| 52 |  |  | delete[] oldPos; | 
| 53 |  |  | delete[] oldVel; | 
| 54 |  |  | delete[] oldJi; | 
| 55 |  |  | } | 
| 56 |  |  |  | 
| 57 | tim | 645 | template<typename T> void NPTi<T>::moveA() { | 
| 58 | tim | 763 |  | 
| 59 |  |  | //new version of NPTi | 
| 60 |  |  | int i, j, k; | 
| 61 | gezelter | 574 | DirectionalAtom* dAtom; | 
| 62 | gezelter | 600 | double Tb[3], ji[3]; | 
| 63 |  |  | double A[3][3], I[3][3]; | 
| 64 |  |  | double angle, mass; | 
| 65 |  |  | double vel[3], pos[3], frc[3]; | 
| 66 |  |  |  | 
| 67 | gezelter | 574 | double rj[3]; | 
| 68 |  |  | double instaTemp, instaPress, instaVol; | 
| 69 | gezelter | 611 | double tt2, tb2, scaleFactor; | 
| 70 | tim | 763 | double COM[3]; | 
| 71 | gezelter | 574 |  | 
| 72 |  |  | tt2 = tauThermostat * tauThermostat; | 
| 73 |  |  | tb2 = tauBarostat * tauBarostat; | 
| 74 |  |  |  | 
| 75 |  |  | instaTemp = tStats->getTemperature(); | 
| 76 |  |  | instaPress = tStats->getPressure(); | 
| 77 |  |  | instaVol = tStats->getVolume(); | 
| 78 |  |  |  | 
| 79 | tim | 763 | tStats->getCOM(COM); | 
| 80 |  |  |  | 
| 81 |  |  | //evolve velocity half step | 
| 82 |  |  | for( i=0; i<nAtoms; i++ ){ | 
| 83 | gezelter | 574 |  | 
| 84 | gezelter | 600 | atoms[i]->getVel( vel ); | 
| 85 |  |  | atoms[i]->getFrc( frc ); | 
| 86 | gezelter | 574 |  | 
| 87 | gezelter | 600 | mass = atoms[i]->getMass(); | 
| 88 | gezelter | 574 |  | 
| 89 | gezelter | 600 | for (j=0; j < 3; j++) { | 
| 90 | gezelter | 772 | // velocity half step | 
| 91 | tim | 763 | vel[j] += dt2 * ((frc[j] / mass ) * eConvert - vel[j]*(chi + eta)); | 
| 92 | gezelter | 600 | } | 
| 93 |  |  |  | 
| 94 |  |  | atoms[i]->setVel( vel ); | 
| 95 | tim | 763 |  | 
| 96 | gezelter | 574 | if( atoms[i]->isDirectional() ){ | 
| 97 |  |  |  | 
| 98 |  |  | dAtom = (DirectionalAtom *)atoms[i]; | 
| 99 | tim | 763 |  | 
| 100 | gezelter | 574 | // get and convert the torque to body frame | 
| 101 |  |  |  | 
| 102 | gezelter | 600 | dAtom->getTrq( Tb ); | 
| 103 | gezelter | 574 | dAtom->lab2Body( Tb ); | 
| 104 |  |  |  | 
| 105 |  |  | // get the angular momentum, and propagate a half step | 
| 106 |  |  |  | 
| 107 | gezelter | 600 | dAtom->getJ( ji ); | 
| 108 |  |  |  | 
| 109 |  |  | for (j=0; j < 3; j++) | 
| 110 |  |  | ji[j] += dt2 * (Tb[j] * eConvert - ji[j]*chi); | 
| 111 | gezelter | 574 |  | 
| 112 |  |  | // use the angular velocities to propagate the rotation matrix a | 
| 113 |  |  | // full time step | 
| 114 | gezelter | 600 |  | 
| 115 |  |  | dAtom->getA(A); | 
| 116 |  |  | dAtom->getI(I); | 
| 117 |  |  |  | 
| 118 | gezelter | 574 | // rotate about the x-axis | 
| 119 | gezelter | 600 | angle = dt2 * ji[0] / I[0][0]; | 
| 120 |  |  | this->rotate( 1, 2, angle, ji, A ); | 
| 121 |  |  |  | 
| 122 | gezelter | 574 | // rotate about the y-axis | 
| 123 | gezelter | 600 | angle = dt2 * ji[1] / I[1][1]; | 
| 124 |  |  | this->rotate( 2, 0, angle, ji, A ); | 
| 125 | gezelter | 574 |  | 
| 126 |  |  | // rotate about the z-axis | 
| 127 | gezelter | 600 | angle = dt * ji[2] / I[2][2]; | 
| 128 |  |  | this->rotate( 0, 1, angle, ji, A); | 
| 129 | gezelter | 574 |  | 
| 130 |  |  | // rotate about the y-axis | 
| 131 | gezelter | 600 | angle = dt2 * ji[1] / I[1][1]; | 
| 132 |  |  | this->rotate( 2, 0, angle, ji, A ); | 
| 133 | gezelter | 574 |  | 
| 134 |  |  | // rotate about the x-axis | 
| 135 | gezelter | 600 | angle = dt2 * ji[0] / I[0][0]; | 
| 136 |  |  | this->rotate( 1, 2, angle, ji, A ); | 
| 137 | gezelter | 574 |  | 
| 138 | gezelter | 600 | dAtom->setJ( ji ); | 
| 139 |  |  | dAtom->setA( A  ); | 
| 140 | tim | 763 | } | 
| 141 |  |  | } | 
| 142 | gezelter | 600 |  | 
| 143 | gezelter | 772 | // advance chi half step | 
| 144 | tim | 763 |  | 
| 145 |  |  | chi += dt2 * ( instaTemp / targetTemp - 1.0) / tt2; | 
| 146 |  |  |  | 
| 147 | gezelter | 772 | // calculate the integral of chidt | 
| 148 |  |  |  | 
| 149 | tim | 763 | integralOfChidt += dt2*chi; | 
| 150 |  |  |  | 
| 151 | gezelter | 772 | // advance eta half step | 
| 152 |  |  |  | 
| 153 |  |  | eta += dt2 * ( instaVol * (instaPress - targetPressure) / (p_convert*NkBT*tb2)); | 
| 154 |  |  |  | 
| 155 | tim | 763 | //save the old positions | 
| 156 |  |  | for(i = 0; i < nAtoms; i++){ | 
| 157 |  |  | atoms[i]->getPos(pos); | 
| 158 |  |  | for(j = 0; j < 3; j++) | 
| 159 |  |  | oldPos[i*3 + j] = pos[j]; | 
| 160 | gezelter | 574 | } | 
| 161 | tim | 763 |  | 
| 162 |  |  | //the first estimation of r(t+dt) is equal to  r(t) | 
| 163 |  |  |  | 
| 164 |  |  | for(k = 0; k < 4; k ++){ | 
| 165 | gezelter | 611 |  | 
| 166 | tim | 763 | for(i =0 ; i < nAtoms; i++){ | 
| 167 |  |  |  | 
| 168 |  |  | atoms[i]->getVel(vel); | 
| 169 |  |  | atoms[i]->getPos(pos); | 
| 170 |  |  |  | 
| 171 |  |  | for(j = 0; j < 3; j++) | 
| 172 | tim | 767 | rj[j] = (oldPos[i*3 + j] + pos[j])/2 - COM[j]; | 
| 173 | tim | 763 |  | 
| 174 |  |  | for(j = 0; j < 3; j++) | 
| 175 |  |  | pos[j] = oldPos[i*3 + j] + dt*(vel[j] + eta*rj[j]); | 
| 176 |  |  |  | 
| 177 |  |  | atoms[i]->setPos( pos ); | 
| 178 |  |  | } | 
| 179 | mmeineke | 768 |  | 
| 180 |  |  | if (nConstrained){ | 
| 181 |  |  | constrainA(); | 
| 182 |  |  | } | 
| 183 | tim | 763 | } | 
| 184 |  |  |  | 
| 185 |  |  |  | 
| 186 | gezelter | 577 | // Scale the box after all the positions have been moved: | 
| 187 | gezelter | 600 |  | 
| 188 | gezelter | 611 | scaleFactor = exp(dt*eta); | 
| 189 |  |  |  | 
| 190 | mmeineke | 614 | if ((scaleFactor > 1.1) || (scaleFactor < 0.9)) { | 
| 191 | gezelter | 611 | sprintf( painCave.errMsg, | 
| 192 |  |  | "NPTi error: Attempting a Box scaling of more than 10 percent" | 
| 193 |  |  | " check your tauBarostat, as it is probably too small!\n" | 
| 194 |  |  | " eta = %lf, scaleFactor = %lf\n", eta, scaleFactor | 
| 195 |  |  | ); | 
| 196 |  |  | painCave.isFatal = 1; | 
| 197 |  |  | simError(); | 
| 198 |  |  | } else { | 
| 199 | tim | 763 | info->scaleBox(scaleFactor); | 
| 200 |  |  | } | 
| 201 | mmeineke | 614 |  | 
| 202 | gezelter | 574 | } | 
| 203 |  |  |  | 
| 204 | tim | 645 | template<typename T> void NPTi<T>::moveB( void ){ | 
| 205 | gezelter | 574 |  | 
| 206 | tim | 763 | //new version of NPTi | 
| 207 |  |  | int i, j, k; | 
| 208 |  |  | DirectionalAtom* dAtom; | 
| 209 |  |  | double Tb[3], ji[3]; | 
| 210 |  |  | double vel[3], frc[3]; | 
| 211 |  |  | double mass; | 
| 212 |  |  |  | 
| 213 | gezelter | 772 | double instaTemp, instaPress, instaVol; | 
| 214 | tim | 763 | double tt2, tb2; | 
| 215 |  |  | double oldChi, prevChi; | 
| 216 | gezelter | 772 | double oldEta, prevEta; | 
| 217 | tim | 763 |  | 
| 218 |  |  | tt2 = tauThermostat * tauThermostat; | 
| 219 |  |  | tb2 = tauBarostat * tauBarostat; | 
| 220 |  |  |  | 
| 221 |  |  | // Set things up for the iteration: | 
| 222 |  |  |  | 
| 223 |  |  | oldChi = chi; | 
| 224 |  |  | oldEta = eta; | 
| 225 |  |  |  | 
| 226 |  |  | for( i=0; i<nAtoms; i++ ){ | 
| 227 |  |  |  | 
| 228 |  |  | atoms[i]->getVel( vel ); | 
| 229 |  |  |  | 
| 230 |  |  | for (j=0; j < 3; j++) | 
| 231 |  |  | oldVel[3*i + j]  = vel[j]; | 
| 232 |  |  |  | 
| 233 |  |  | if( atoms[i]->isDirectional() ){ | 
| 234 |  |  |  | 
| 235 |  |  | dAtom = (DirectionalAtom *)atoms[i]; | 
| 236 |  |  |  | 
| 237 |  |  | dAtom->getJ( ji ); | 
| 238 |  |  |  | 
| 239 |  |  | for (j=0; j < 3; j++) | 
| 240 |  |  | oldJi[3*i + j] = ji[j]; | 
| 241 |  |  |  | 
| 242 |  |  | } | 
| 243 |  |  | } | 
| 244 |  |  |  | 
| 245 |  |  | // do the iteration: | 
| 246 |  |  |  | 
| 247 | gezelter | 772 | instaVol = tStats->getVolume(); | 
| 248 | tim | 763 |  | 
| 249 |  |  | for (k=0; k < 4; k++) { | 
| 250 |  |  |  | 
| 251 | gezelter | 772 | instaTemp = tStats->getTemperature(); | 
| 252 |  |  | instaPress = tStats->getPressure(); | 
| 253 | tim | 763 |  | 
| 254 |  |  | // evolve chi another half step using the temperature at t + dt/2 | 
| 255 |  |  |  | 
| 256 |  |  | prevChi = chi; | 
| 257 | gezelter | 772 | chi = oldChi + dt2 * ( instaTemp / targetTemp - 1.0) / tt2; | 
| 258 | tim | 763 |  | 
| 259 | gezelter | 772 | prevEta = eta; | 
| 260 |  |  |  | 
| 261 |  |  | // advance eta half step and calculate scale factor for velocity | 
| 262 |  |  |  | 
| 263 |  |  | eta = oldEta + dt2 * ( instaVol * (instaPress - targetPressure) / | 
| 264 | tim | 763 | (p_convert*NkBT*tb2)); | 
| 265 |  |  |  | 
| 266 |  |  |  | 
| 267 |  |  | for( i=0; i<nAtoms; i++ ){ | 
| 268 |  |  |  | 
| 269 |  |  | atoms[i]->getFrc( frc ); | 
| 270 |  |  | atoms[i]->getVel(vel); | 
| 271 |  |  |  | 
| 272 |  |  | mass = atoms[i]->getMass(); | 
| 273 |  |  |  | 
| 274 |  |  | // velocity half step | 
| 275 |  |  | for (j=0; j < 3; j++) | 
| 276 |  |  | vel[j] = oldVel[3*i+j] + dt2 * ((frc[j] / mass ) * eConvert - oldVel[3*i + j]*(chi + eta)); | 
| 277 |  |  |  | 
| 278 |  |  | atoms[i]->setVel( vel ); | 
| 279 |  |  |  | 
| 280 |  |  | if( atoms[i]->isDirectional() ){ | 
| 281 |  |  |  | 
| 282 |  |  | dAtom = (DirectionalAtom *)atoms[i]; | 
| 283 |  |  |  | 
| 284 |  |  | // get and convert the torque to body frame | 
| 285 |  |  |  | 
| 286 |  |  | dAtom->getTrq( Tb ); | 
| 287 |  |  | dAtom->lab2Body( Tb ); | 
| 288 |  |  |  | 
| 289 |  |  | for (j=0; j < 3; j++) | 
| 290 |  |  | ji[j] = oldJi[3*i + j] + dt2 * (Tb[j] * eConvert - oldJi[3*i+j]*chi); | 
| 291 |  |  |  | 
| 292 |  |  | dAtom->setJ( ji ); | 
| 293 |  |  | } | 
| 294 |  |  | } | 
| 295 | mmeineke | 768 |  | 
| 296 |  |  | if (nConstrained){ | 
| 297 |  |  | constrainB(); | 
| 298 |  |  | } | 
| 299 |  |  |  | 
| 300 |  |  | if (fabs(prevChi - chi) <= | 
| 301 | gezelter | 772 | chiTolerance && fabs(prevEta -eta) <= etaTolerance) | 
| 302 | tim | 763 | break; | 
| 303 |  |  | } | 
| 304 |  |  |  | 
| 305 | gezelter | 772 | //calculate integral of chidt | 
| 306 | tim | 763 | integralOfChidt += dt2*chi; | 
| 307 |  |  |  | 
| 308 | gezelter | 574 | } | 
| 309 |  |  |  | 
| 310 | mmeineke | 746 | template<typename T> void NPTi<T>::resetIntegrator() { | 
| 311 |  |  | chi = 0.0; | 
| 312 |  |  | eta = 0.0; | 
| 313 |  |  | } | 
| 314 |  |  |  | 
| 315 | tim | 645 | template<typename T> int NPTi<T>::readyCheck() { | 
| 316 | tim | 658 |  | 
| 317 |  |  | //check parent's readyCheck() first | 
| 318 |  |  | if (T::readyCheck() == -1) | 
| 319 |  |  | return -1; | 
| 320 | gezelter | 574 |  | 
| 321 |  |  | // First check to see if we have a target temperature. | 
| 322 |  |  | // Not having one is fatal. | 
| 323 |  |  |  | 
| 324 |  |  | if (!have_target_temp) { | 
| 325 |  |  | sprintf( painCave.errMsg, | 
| 326 |  |  | "NPTi error: You can't use the NPTi integrator\n" | 
| 327 |  |  | "   without a targetTemp!\n" | 
| 328 |  |  | ); | 
| 329 |  |  | painCave.isFatal = 1; | 
| 330 |  |  | simError(); | 
| 331 |  |  | return -1; | 
| 332 |  |  | } | 
| 333 |  |  |  | 
| 334 |  |  | if (!have_target_pressure) { | 
| 335 |  |  | sprintf( painCave.errMsg, | 
| 336 |  |  | "NPTi error: You can't use the NPTi integrator\n" | 
| 337 |  |  | "   without a targetPressure!\n" | 
| 338 |  |  | ); | 
| 339 |  |  | painCave.isFatal = 1; | 
| 340 |  |  | simError(); | 
| 341 |  |  | return -1; | 
| 342 |  |  | } | 
| 343 |  |  |  | 
| 344 |  |  | // We must set tauThermostat. | 
| 345 |  |  |  | 
| 346 |  |  | if (!have_tau_thermostat) { | 
| 347 |  |  | sprintf( painCave.errMsg, | 
| 348 |  |  | "NPTi error: If you use the NPTi\n" | 
| 349 |  |  | "   integrator, you must set tauThermostat.\n"); | 
| 350 |  |  | painCave.isFatal = 1; | 
| 351 |  |  | simError(); | 
| 352 |  |  | return -1; | 
| 353 |  |  | } | 
| 354 |  |  |  | 
| 355 |  |  | // We must set tauBarostat. | 
| 356 |  |  |  | 
| 357 |  |  | if (!have_tau_barostat) { | 
| 358 |  |  | sprintf( painCave.errMsg, | 
| 359 |  |  | "NPTi error: If you use the NPTi\n" | 
| 360 |  |  | "   integrator, you must set tauBarostat.\n"); | 
| 361 |  |  | painCave.isFatal = 1; | 
| 362 |  |  | simError(); | 
| 363 |  |  | return -1; | 
| 364 |  |  | } | 
| 365 |  |  |  | 
| 366 | tim | 763 | if (!have_chi_tolerance) { | 
| 367 |  |  | sprintf( painCave.errMsg, | 
| 368 |  |  | "NPTi warning: setting chi tolerance to 1e-6\n"); | 
| 369 |  |  | chiTolerance = 1e-6; | 
| 370 |  |  | have_chi_tolerance = 1; | 
| 371 |  |  | painCave.isFatal = 0; | 
| 372 |  |  | simError(); | 
| 373 |  |  | } | 
| 374 |  |  |  | 
| 375 | gezelter | 770 | if (!have_eta_tolerance) { | 
| 376 | tim | 763 | sprintf( painCave.errMsg, | 
| 377 |  |  | "NPTi warning: setting eta tolerance to 1e-6\n"); | 
| 378 |  |  | etaTolerance = 1e-6; | 
| 379 |  |  | have_eta_tolerance = 1; | 
| 380 |  |  | painCave.isFatal = 0; | 
| 381 |  |  | simError(); | 
| 382 |  |  | } | 
| 383 | gezelter | 770 |  | 
| 384 |  |  |  | 
| 385 |  |  | // We need NkBT a lot, so just set it here: This is the RAW number | 
| 386 |  |  | // of particles, so no subtraction or addition of constraints or | 
| 387 |  |  | // orientational degrees of freedom: | 
| 388 |  |  |  | 
| 389 | tim | 763 | NkBT = (double)Nparticles * kB * targetTemp; | 
| 390 | gezelter | 770 |  | 
| 391 |  |  | // fkBT is used because the thermostat operates on more degrees of freedom | 
| 392 |  |  | // than the barostat (when there are particles with orientational degrees | 
| 393 |  |  | // of freedom).  ndf = 3 * (n_atoms + n_oriented -1) - n_constraint - nZcons | 
| 394 |  |  |  | 
| 395 | tim | 763 | fkBT = (double)info->ndf * kB * targetTemp; | 
| 396 | gezelter | 574 |  | 
| 397 |  |  | return 1; | 
| 398 |  |  | } | 
| 399 | tim | 763 |  | 
| 400 |  |  | template<typename T> double NPTi<T>::getConservedQuantity(void){ | 
| 401 |  |  |  | 
| 402 |  |  | double conservedQuantity; | 
| 403 | gezelter | 770 | double Three_NkBT; | 
| 404 | tim | 769 | double Energy; | 
| 405 |  |  | double thermostat_kinetic; | 
| 406 |  |  | double thermostat_potential; | 
| 407 |  |  | double barostat_kinetic; | 
| 408 |  |  | double barostat_potential; | 
| 409 | tim | 763 | double tb2; | 
| 410 | gezelter | 770 | double eta2; | 
| 411 | tim | 763 |  | 
| 412 | tim | 769 | Energy = tStats->getTotalE(); | 
| 413 | tim | 763 |  | 
| 414 | tim | 769 | thermostat_kinetic = fkBT* tauThermostat * tauThermostat * chi * chi / | 
| 415 |  |  | (2.0 * eConvert); | 
| 416 | tim | 763 |  | 
| 417 | tim | 769 | thermostat_potential = fkBT* integralOfChidt / eConvert; | 
| 418 | tim | 763 |  | 
| 419 |  |  |  | 
| 420 | gezelter | 770 | barostat_kinetic = 3.0 * NkBT * tauBarostat * tauBarostat * eta * eta / | 
| 421 | tim | 769 | (2.0 * eConvert); | 
| 422 |  |  |  | 
| 423 |  |  | barostat_potential = (targetPressure * tStats->getVolume() / p_convert) / | 
| 424 |  |  | eConvert; | 
| 425 | tim | 767 |  | 
| 426 | tim | 769 | conservedQuantity = Energy + thermostat_kinetic + thermostat_potential + | 
| 427 |  |  | barostat_kinetic + barostat_potential; | 
| 428 |  |  |  | 
| 429 | tim | 763 | cout.width(8); | 
| 430 |  |  | cout.precision(8); | 
| 431 |  |  |  | 
| 432 | tim | 769 | cerr << info->getTime() << "\t" << Energy << "\t" << thermostat_kinetic << | 
| 433 |  |  | "\t" << thermostat_potential << "\t" << barostat_kinetic << | 
| 434 |  |  | "\t" << barostat_potential << "\t" << conservedQuantity << endl; | 
| 435 | tim | 763 |  | 
| 436 |  |  | return conservedQuantity; | 
| 437 |  |  | } |