moldyn.c

   1 /*
   2  * moldyn.c - molecular dynamics library main file
   3  *
   4  * author: Frank Zirkelbach <frank.zirkelbach@physik.uni-augsburg.de>
   5  *
   6  */
   7
   8 #define _GNU_SOURCE
   9 #include <stdio.h>
  10 #include <stdlib.h>
  11 #include <string.h>
  12 #include <sys/types.h>
  13 #include <sys/stat.h>
  14 #include <fcntl.h>
  15 #include <unistd.h>
  16 #include <math.h>
  17
  18 #include "moldyn.h"
  19
  20 #include "math/math.h"
  21 #include "init/init.h"
  22 #include "random/random.h"
  23 #include "visual/visual.h"
  24 #include "list/list.h"
  25
  26
  27 int moldyn_init(t_moldyn *moldyn,int argc,char **argv) {
  28
  29         //int ret;
  30
  31         //ret=moldyn_parse_argv(moldyn,argc,argv);
  32         //if(ret<0) return ret;
  33
  34         memset(moldyn,0,sizeof(t_moldyn));
  35
  36         rand_init(&(moldyn->random),NULL,1);
  37         moldyn->random.status|=RAND_STAT_VERBOSE;
  38
  39         return 0;
  40 }
  41
  42 int moldyn_shutdown(t_moldyn *moldyn) {
  43
  44         printf("[moldyn] shutdown\n");
  45         moldyn_log_shutdown(moldyn);
  46         link_cell_shutdown(moldyn);
  47         rand_close(&(moldyn->random));
  48         free(moldyn->atom);
  49
  50         return 0;
  51 }
  52
  53 int set_int_alg(t_moldyn *moldyn,u8 algo) {
  54
  55         switch(algo) {
  56                 case MOLDYN_INTEGRATE_VERLET:
  57                         moldyn->integrate=velocity_verlet;
  58                         break;
  59                 default:
  60                         printf("unknown integration algorithm: %02x\n",algo);
  61                         return -1;
  62         }
  63
  64         return 0;
  65 }
  66
  67 int set_cutoff(t_moldyn *moldyn,double cutoff) {
  68
  69         moldyn->cutoff=cutoff;
  70
  71         return 0;
  72 }
  73
  74 int set_temperature(t_moldyn *moldyn,double t_ref) {
  75
  76         moldyn->t_ref=t_ref;
  77
  78         return 0;
  79 }
  80
  81 int set_pt_scale(t_moldyn *moldyn,u8 ptype,double ptc,u8 ttype,double ttc) {
  82
  83         moldyn->pt_scale=(ptype|ttype);
  84         moldyn->t_tc=ttc;
  85         moldyn->p_tc=ptc;
  86
  87         return 0;
  88 }
  89
  90 int set_dim(t_moldyn *moldyn,double x,double y,double z,u8 visualize) {
  91
  92         moldyn->dim.x=x;
  93         moldyn->dim.y=y;
  94         moldyn->dim.z=z;
  95
  96         if(visualize) {
  97                 moldyn->vis.dim.x=x;
  98                 moldyn->vis.dim.y=y;
  99                 moldyn->vis.dim.z=z;
 100         }
 101
 102         return 0;
 103 }
 104
 105 int set_nn_dist(t_moldyn *moldyn,double dist) {
 106
 107         moldyn->nnd=dist;
 108
 109         return 0;
 110 }
 111
 112 int set_pbc(t_moldyn *moldyn,u8 x,u8 y,u8 z) {
 113
 114         if(x)
 115                 moldyn->status|=MOLDYN_STAT_PBX;
 116
 117         if(y)
 118                 moldyn->status|=MOLDYN_STAT_PBY;
 119
 120         if(z)
 121                 moldyn->status|=MOLDYN_STAT_PBZ;
 122
 123         return 0;
 124 }
 125
 126 int set_potential1b(t_moldyn *moldyn,pf_func1b func,void *params) {
 127
 128         moldyn->func1b=func;
 129         moldyn->pot1b_params=params;
 130
 131         return 0;
 132 }
 133
 134 int set_potential2b(t_moldyn *moldyn,pf_func2b func,void *params) {
 135
 136         moldyn->func2b=func;
 137         moldyn->pot2b_params=params;
 138
 139         return 0;
 140 }
 141
 142 int set_potential2b_post(t_moldyn *moldyn,pf_func2b_post func,void *params) {
 143
 144         moldyn->func2b_post=func;
 145         moldyn->pot2b_params=params;
 146
 147         return 0;
 148 }
 149
 150 int set_potential3b(t_moldyn *moldyn,pf_func3b func,void *params) {
 151
 152         moldyn->func3b=func;
 153         moldyn->pot3b_params=params;
 154
 155         return 0;
 156 }
 157
 158 int moldyn_set_log(t_moldyn *moldyn,u8 type,char *fb,int timer) {
 159
 160         switch(type) {
 161                 case LOG_TOTAL_ENERGY:
 162                         moldyn->ewrite=timer;
 163                         moldyn->efd=open(fb,O_WRONLY|O_CREAT|O_TRUNC);
 164                         if(moldyn->efd<0) {
 165                                 perror("[moldyn] efd open");
 166                                 return moldyn->efd;
 167                         }
 168                         dprintf(moldyn->efd,"# total energy log file\n");
 169                         break;
 170                 case LOG_TOTAL_MOMENTUM:
 171                         moldyn->mwrite=timer;
 172                         moldyn->mfd=open(fb,O_WRONLY|O_CREAT|O_TRUNC);
 173                         if(moldyn->mfd<0) {
 174                                 perror("[moldyn] mfd open");
 175                                 return moldyn->mfd;
 176                         }
 177                         dprintf(moldyn->efd,"# total momentum log file\n");
 178                         break;
 179                 case SAVE_STEP:
 180                         moldyn->swrite=timer;
 181                         strncpy(moldyn->sfb,fb,63);
 182                         break;
 183                 case VISUAL_STEP:
 184                         moldyn->vwrite=timer;
 185                         strncpy(moldyn->vfb,fb,63);
 186                         visual_init(&(moldyn->vis),fb);
 187                         break;
 188                 default:
 189                         printf("unknown log mechanism: %02x\n",type);
 190                         return -1;
 191         }
 192
 193         return 0;
 194 }
 195
 196 int moldyn_log_shutdown(t_moldyn *moldyn) {
 197
 198         printf("[moldyn] log shutdown\n");
 199         if(moldyn->efd) close(moldyn->efd);
 200         if(moldyn->mfd) close(moldyn->mfd);
 201         if(&(moldyn->vis)) visual_tini(&(moldyn->vis));
 202
 203         return 0;
 204 }
 205
 206 int create_lattice(t_moldyn *moldyn,u8 type,double lc,int element,double mass,
 207                    u8 attr,u8 bnum,int a,int b,int c) {
 208
 209         int count;
 210         int ret;
 211         t_3dvec origin;
 212
 213         count=a*b*c;
 214
 215         if(type==FCC) count*=4;
 216
 217         if(type==DIAMOND) count*=8;
 218
 219         moldyn->atom=malloc(count*sizeof(t_atom));
 220         if(moldyn->atom==NULL) {
 221                 perror("malloc (atoms)");
 222                 return -1;
 223         }
 224
 225         v3_zero(&origin);
 226
 227         switch(type) {
 228                 case FCC:
 229                         ret=fcc_init(a,b,c,lc,moldyn->atom,&origin);
 230                         break;
 231                 case DIAMOND:
 232                         ret=diamond_init(a,b,c,lc,moldyn->atom,&origin);
 233                         break;
 234                 default:
 235                         printf("unknown lattice type (%02x)\n",type);
 236                         return -1;
 237         }
 238
 239         /* debug */
 240         if(ret!=count) {
 241                 printf("ok, there is something wrong ...\n");
 242                 printf("calculated -> %d atoms\n",count);
 243                 printf("created -> %d atoms\n",ret);
 244                 return -1;
 245         }
 246
 247         moldyn->count=count;
 248         printf("[moldyn] created lattice with %d atoms\n",count);
 249
 250         while(count) {
 251                 count-=1;
 252                 moldyn->atom[count].element=element;
 253                 moldyn->atom[count].mass=mass;
 254                 moldyn->atom[count].attr=attr;
 255                 moldyn->atom[count].bnum=bnum;
 256                 check_per_bound(moldyn,&(moldyn->atom[count].r));
 257         }
 258
 259
 260         return ret;
 261 }
 262
 263 int add_atom(t_moldyn *moldyn,int element,double mass,u8 bnum,u8 attr,
 264              t_3dvec *r,t_3dvec *v) {
 265
 266         t_atom *atom;
 267         void *ptr;
 268         int count;
 269
 270         atom=moldyn->atom;
 271         count=++(moldyn->count);
 272
 273         ptr=realloc(atom,count*sizeof(t_atom));
 274         if(!ptr) {
 275                 perror("[moldyn] realloc (add atom)");
 276                 return -1;
 277         }
 278         moldyn->atom=ptr;
 279
 280         atom=moldyn->atom;
 281         atom[count-1].r=*r;
 282         atom[count-1].v=*v;
 283         atom[count-1].element=element;
 284         atom[count-1].mass=mass;
 285         atom[count-1].bnum=bnum;
 286         atom[count-1].attr=attr;
 287
 288         return 0;
 289 }
 290
 291 int destroy_atoms(t_moldyn *moldyn) {
 292
 293         if(moldyn->atom) free(moldyn->atom);
 294
 295         return 0;
 296 }
 297
 298 int thermal_init(t_moldyn *moldyn,u8 equi_init) {
 299
 300         /*
 301          * - gaussian distribution of velocities
 302          * - zero total momentum
 303          * - velocity scaling (E = 3/2 N k T), E: kinetic energy
 304          */
 305
 306         int i;
 307         double v,sigma;
 308         t_3dvec p_total,delta;
 309         t_atom *atom;
 310         t_random *random;
 311
 312         atom=moldyn->atom;
 313         random=&(moldyn->random);
 314
 315         /* gaussian distribution of velocities */
 316         v3_zero(&p_total);
 317         for(i=0;i<moldyn->count;i++) {
 318                 sigma=sqrt(2.0*K_BOLTZMANN*moldyn->t_ref/atom[i].mass);
 319                 /* x direction */
 320                 v=sigma*rand_get_gauss(random);
 321                 atom[i].v.x=v;
 322                 p_total.x+=atom[i].mass*v;
 323                 /* y direction */
 324                 v=sigma*rand_get_gauss(random);
 325                 atom[i].v.y=v;
 326                 p_total.y+=atom[i].mass*v;
 327                 /* z direction */
 328                 v=sigma*rand_get_gauss(random);
 329                 atom[i].v.z=v;
 330                 p_total.z+=atom[i].mass*v;
 331         }
 332
 333         /* zero total momentum */
 334         v3_scale(&p_total,&p_total,1.0/moldyn->count);
 335         for(i=0;i<moldyn->count;i++) {
 336                 v3_scale(&delta,&p_total,1.0/atom[i].mass);
 337                 v3_sub(&(atom[i].v),&(atom[i].v),&delta);
 338         }
 339
 340         /* velocity scaling */
 341         scale_velocity(moldyn,equi_init);
 342
 343         return 0;
 344 }
 345
 346 int scale_velocity(t_moldyn *moldyn,u8 equi_init) {
 347
 348         int i;
 349         double e,scale;
 350         t_atom *atom;
 351         int count;
 352
 353         atom=moldyn->atom;
 354
 355         /*
 356          * - velocity scaling (E = 3/2 N k T), E: kinetic energy
 357          */
 358
 359         /* get kinetic energy / temperature & count involved atoms */
 360         e=0.0;
 361         count=0;
 362         for(i=0;i<moldyn->count;i++) {
 363                 if((equi_init&TRUE)||(atom[i].attr&ATOM_ATTR_HB)) {
 364                         e+=0.5*atom[i].mass*v3_absolute_square(&(atom[i].v));
 365                         count+=1;
 366                 }
 367         }
 368         if(count!=0) moldyn->t=(2.0*e)/(3.0*count*K_BOLTZMANN);
 369         else return 0;  /* no atoms involved in scaling! */
 370
 371         /* (temporary) hack for e,t = 0 */
 372         if(e==0.0) {
 373         moldyn->t=0.0;
 374                 if(moldyn->t_ref!=0.0)
 375                         thermal_init(moldyn,equi_init);
 376                 else
 377                         return 0; /* no scaling needed */
 378         }
 379
 380
 381         /* get scaling factor */
 382         scale=moldyn->t_ref/moldyn->t;
 383         if(equi_init&TRUE)
 384                 scale*=2.0;
 385         else
 386                 if(moldyn->pt_scale&T_SCALE_BERENDSEN)
 387                         scale=1.0+moldyn->tau*(scale-1.0)/moldyn->t_tc;
 388         scale=sqrt(scale);
 389
 390         /* velocity scaling */
 391         for(i=0;i<moldyn->count;i++)
 392                 if((equi_init&TRUE)||(atom[i].attr&ATOM_ATTR_HB))
 393                         v3_scale(&(atom[i].v),&(atom[i].v),scale);
 394
 395         return 0;
 396 }
 397
 398 double get_e_kin(t_moldyn *moldyn) {
 399
 400         int i;
 401         t_atom *atom;
 402
 403         atom=moldyn->atom;
 404         moldyn->ekin=0.0;
 405
 406         for(i=0;i<moldyn->count;i++)
 407                 moldyn->ekin+=0.5*atom[i].mass*v3_absolute_square(&(atom[i].v));
 408
 409         return moldyn->ekin;
 410 }
 411
 412 double get_e_pot(t_moldyn *moldyn) {
 413
 414         return moldyn->energy;
 415 }
 416
 417 double update_e_kin(t_moldyn *moldyn) {
 418
 419         return(get_e_kin(moldyn));
 420 }
 421
 422 double get_total_energy(t_moldyn *moldyn) {
 423
 424         return(moldyn->ekin+moldyn->energy);
 425 }
 426
 427 t_3dvec get_total_p(t_moldyn *moldyn) {
 428
 429         t_3dvec p,p_total;
 430         int i;
 431         t_atom *atom;
 432
 433         atom=moldyn->atom;
 434
 435         v3_zero(&p_total);
 436         for(i=0;i<moldyn->count;i++) {
 437                 v3_scale(&p,&(atom[i].v),atom[i].mass);
 438                 v3_add(&p_total,&p_total,&p);
 439         }
 440
 441         return p_total;
 442 }
 443
 444 double estimate_time_step(t_moldyn *moldyn,double nn_dist) {
 445
 446         double tau;
 447
 448         /* nn_dist is the nearest neighbour distance */
 449
 450         if(moldyn->t==5.0) {
 451                 printf("[moldyn] i do not estimate timesteps below %f K!\n",
 452                        MOLDYN_CRITICAL_EST_TEMP);
 453                 return 23.42;
 454         }
 455
 456         tau=(0.05*nn_dist*moldyn->atom[0].mass)/sqrt(3.0*K_BOLTZMANN*moldyn->t);
 457
 458         return tau;
 459 }
 460
 461 /*
 462  * numerical tricks
 463  */
 464
 465 /* linked list / cell method */
 466
 467 int link_cell_init(t_moldyn *moldyn) {
 468
 469         t_linkcell *lc;
 470         int i;
 471         int fd;
 472
 473         fd=open("/dev/null",O_WRONLY);
 474
 475         lc=&(moldyn->lc);
 476
 477         /* partitioning the md cell */
 478         lc->nx=moldyn->dim.x/moldyn->cutoff;
 479         lc->x=moldyn->dim.x/lc->nx;
 480         lc->ny=moldyn->dim.y/moldyn->cutoff;
 481         lc->y=moldyn->dim.y/lc->ny;
 482         lc->nz=moldyn->dim.z/moldyn->cutoff;
 483         lc->z=moldyn->dim.z/lc->nz;
 484
 485         lc->cells=lc->nx*lc->ny*lc->nz;
 486         lc->subcell=malloc(lc->cells*sizeof(t_list));
 487
 488         printf("[moldyn] initializing linked cells (%d)\n",lc->cells);
 489
 490         for(i=0;i<lc->cells;i++)
 491                 //list_init(&(lc->subcell[i]),1);
 492                 list_init(&(lc->subcell[i]),fd);
 493
 494         link_cell_update(moldyn);
 495
 496         return 0;
 497 }
 498
 499 int link_cell_update(t_moldyn *moldyn) {
 500
 501         int count,i,j,k;
 502         int nx,ny,nz;
 503         t_atom *atom;
 504         t_linkcell *lc;
 505
 506         atom=moldyn->atom;
 507         lc=&(moldyn->lc);
 508
 509         nx=lc->nx;
 510         ny=lc->ny;
 511         nz=lc->nz;
 512
 513         for(i=0;i<lc->cells;i++)
 514                 list_destroy(&(moldyn->lc.subcell[i]));
 515
 516         for(count=0;count<moldyn->count;count++) {
 517                 i=(atom[count].r.x+(moldyn->dim.x/2))/lc->x;
 518                 j=(atom[count].r.y+(moldyn->dim.y/2))/lc->y;
 519                 k=(atom[count].r.z+(moldyn->dim.z/2))/lc->z;
 520                 list_add_immediate_ptr(&(moldyn->lc.subcell[i+j*nx+k*nx*ny]),
 521                                        &(atom[count]));
 522         }
 523
 524         return 0;
 525 }
 526
 527 int link_cell_neighbour_index(t_moldyn *moldyn,int i,int j,int k,t_list *cell) {
 528
 529         t_linkcell *lc;
 530         int a;
 531         int count1,count2;
 532         int ci,cj,ck;
 533         int nx,ny,nz;
 534         int x,y,z;
 535         u8 bx,by,bz;
 536
 537         lc=&(moldyn->lc);
 538         nx=lc->nx;
 539         ny=lc->ny;
 540         nz=lc->nz;
 541         count1=1;
 542         count2=27;
 543         a=nx*ny;
 544
 545         cell[0]=lc->subcell[i+j*nx+k*a];
 546         for(ci=-1;ci<=1;ci++) {
 547                 bx=0;
 548                 x=i+ci;
 549                 if((x<0)||(x>=nx)) {
 550                         x=(x+nx)%nx;
 551                         bx=1;
 552                 }
 553                 for(cj=-1;cj<=1;cj++) {
 554                         by=0;
 555                         y=j+cj;
 556                         if((y<0)||(y>=ny)) {
 557                                 y=(y+ny)%ny;
 558                                 by=1;
 559                         }
 560                         for(ck=-1;ck<=1;ck++) {
 561                                 bz=0;
 562                                 z=k+ck;
 563                                 if((z<0)||(z>=nz)) {
 564                                         z=(z+nz)%nz;
 565                                         bz=1;
 566                                 }
 567                                 if(!(ci|cj|ck)) continue;
 568                                 if(bx|by|bz) {
 569                                         cell[--count2]=lc->subcell[x+y*nx+z*a];
 570                                 }
 571                                 else {
 572                                         cell[count1++]=lc->subcell[x+y*nx+z*a];
 573                                 }
 574                         }
 575                 }
 576         }
 577
 578         lc->dnlc=count1;
 579
 580         return count1;
 581 }
 582
 583 int link_cell_shutdown(t_moldyn *moldyn) {
 584
 585         int i;
 586         t_linkcell *lc;
 587
 588         lc=&(moldyn->lc);
 589
 590         for(i=0;i<lc->nx*lc->ny*lc->nz;i++)
 591                 list_shutdown(&(moldyn->lc.subcell[i]));
 592
 593         return 0;
 594 }
 595
 596 int moldyn_add_schedule(t_moldyn *moldyn,int runs,double tau) {
 597
 598         int count;
 599         void *ptr;
 600         t_moldyn_schedule *schedule;
 601
 602         schedule=&(moldyn->schedule);
 603         count=++(schedule->content_count);
 604
 605         ptr=realloc(moldyn->schedule.runs,count*sizeof(int));
 606         if(!ptr) {
 607                 perror("[moldyn] realloc (runs)");
 608                 return -1;
 609         }
 610         moldyn->schedule.runs=ptr;
 611         moldyn->schedule.runs[count-1]=runs;
 612
 613         ptr=realloc(schedule->tau,count*sizeof(double));
 614         if(!ptr) {
 615                 perror("[moldyn] realloc (tau)");
 616                 return -1;
 617         }
 618         moldyn->schedule.tau=ptr;
 619         moldyn->schedule.tau[count-1]=tau;
 620
 621         return 0;
 622 }
 623
 624 int moldyn_set_schedule_hook(t_moldyn *moldyn,void *hook,void *hook_params) {
 625
 626         moldyn->schedule.hook=hook;
 627         moldyn->schedule.hook_params=hook_params;
 628
 629         return 0;
 630 }
 631
 632 /*
 633  *
 634  * 'integration of newtons equation' - algorithms
 635  *
 636  */
 637
 638 /* start the integration */
 639
 640 int moldyn_integrate(t_moldyn *moldyn) {
 641
 642         int i,sched;
 643         unsigned int e,m,s,v;
 644         t_3dvec p;
 645         t_moldyn_schedule *schedule;
 646         t_atom *atom;
 647         int fd;
 648         char fb[128];
 649         double ds;
 650
 651         schedule=&(moldyn->schedule);
 652         atom=moldyn->atom;
 653
 654         /* initialize linked cell method */
 655         link_cell_init(moldyn);
 656
 657         /* logging & visualization */
 658         e=moldyn->ewrite;
 659         m=moldyn->mwrite;
 660         s=moldyn->swrite;
 661         v=moldyn->vwrite;
 662
 663         /* sqaure of some variables */
 664         moldyn->tau_square=moldyn->tau*moldyn->tau;
 665         moldyn->cutoff_square=moldyn->cutoff*moldyn->cutoff;
 666
 667         /* calculate initial forces */
 668         potential_force_calc(moldyn);
 669
 670         /* some stupid checks before we actually start calculating bullshit */
 671         if(moldyn->cutoff>0.5*moldyn->dim.x)
 672                 printf("[moldyn] warning: cutoff > 0.5 x dim.x\n");
 673         if(moldyn->cutoff>0.5*moldyn->dim.y)
 674                 printf("[moldyn] warning: cutoff > 0.5 x dim.y\n");
 675         if(moldyn->cutoff>0.5*moldyn->dim.z)
 676                 printf("[moldyn] warning: cutoff > 0.5 x dim.z\n");
 677         ds=0.5*atom[0].f.x*moldyn->tau_square/atom[0].mass;
 678         if(ds>0.05*moldyn->nnd)
 679                 printf("[moldyn] warning: forces too high / tau too small!\n");
 680
 681         /* zero absolute time */
 682         moldyn->time=0.0;
 683
 684         /* debugging, ignre */
 685         moldyn->debug=0;
 686
 687         /* executing the schedule */
 688         for(sched=0;sched<moldyn->schedule.content_count;sched++) {
 689
 690                 /* setting amount of runs and finite time step size */
 691                 moldyn->tau=schedule->tau[sched];
 692                 moldyn->tau_square=moldyn->tau*moldyn->tau;
 693                 moldyn->time_steps=schedule->runs[sched];
 694
 695         /* integration according to schedule */
 696
 697         for(i=0;i<moldyn->time_steps;i++) {
 698
 699                 /* integration step */
 700 printf("MOVE\n");
 701                 moldyn->integrate(moldyn);
 702
 703                 /* p/t scaling */
 704                 if(moldyn->pt_scale&(T_SCALE_BERENDSEN|T_SCALE_DIRECT))
 705                         scale_velocity(moldyn,FALSE);
 706
 707                 /* increase absolute time */
 708                 moldyn->time+=moldyn->tau;
 709
 710                 /* check for log & visualization */
 711                 if(e) {
 712                         if(!(i%e))
 713                                 dprintf(moldyn->efd,
 714                                         "%.15f %.45f %.45f %.45f\n",
 715                                         moldyn->time,update_e_kin(moldyn),
 716                                         moldyn->energy,
 717                                         get_total_energy(moldyn));
 718                 }
 719                 if(m) {
 720                         if(!(i%m)) {
 721                                 p=get_total_p(moldyn);
 722                                 dprintf(moldyn->mfd,
 723                                         "%.15f %.45f\n",moldyn->time,
 724                                         v3_norm(&p));
 725                         }
 726                 }
 727                 if(s) {
 728                         if(!(i%s)) {
 729                                 snprintf(fb,128,"%s-%f-%.15f.save",moldyn->sfb,
 730                                          moldyn->t,i*moldyn->tau);
 731                                 fd=open(fb,O_WRONLY|O_TRUNC|O_CREAT);
 732                                 if(fd<0) perror("[moldyn] save fd open");
 733                                 else {
 734                                         write(fd,moldyn,sizeof(t_moldyn));
 735                                         write(fd,moldyn->atom,
 736                                               moldyn->count*sizeof(t_atom));
 737                                 }
 738                                 close(fd);
 739                         }
 740                 }
 741                 if(v) {
 742                         if(!(i%v)) {
 743                                 visual_atoms(&(moldyn->vis),moldyn->time,
 744                                              moldyn->atom,moldyn->count);
 745                                 printf("\rsched: %d, steps: %d, theta: %d",
 746                                        sched,i,moldyn->debug);
 747                                 fflush(stdout);
 748                         }
 749                 }
 750
 751         }
 752
 753                 /* check for hooks */
 754                 if(schedule->hook)
 755                         schedule->hook(moldyn,schedule->hook_params);
 756
 757                 /* get a new info line */
 758                 printf("\n");
 759
 760         }
 761
 762         return 0;
 763 }
 764
 765 /* velocity verlet */
 766
 767 int velocity_verlet(t_moldyn *moldyn) {
 768
 769         int i,count;
 770         double tau,tau_square;
 771         t_3dvec delta;
 772         t_atom *atom;
 773
 774         atom=moldyn->atom;
 775         count=moldyn->count;
 776         tau=moldyn->tau;
 777         tau_square=moldyn->tau_square;
 778
 779         for(i=0;i<count;i++) {
 780                 /* new positions */
 781                 v3_scale(&delta,&(atom[i].v),tau);
 782                 v3_add(&(atom[i].r),&(atom[i].r),&delta);
 783                 v3_scale(&delta,&(atom[i].f),0.5*tau_square/atom[i].mass);
 784                 v3_add(&(atom[i].r),&(atom[i].r),&delta);
 785                 check_per_bound(moldyn,&(atom[i].r));
 786
 787                 /* velocities */
 788                 v3_scale(&delta,&(atom[i].f),0.5*tau/atom[i].mass);
 789                 v3_add(&(atom[i].v),&(atom[i].v),&delta);
 790         }
 791
 792         /* neighbour list update */
 793         link_cell_update(moldyn);
 794
 795         /* forces depending on chosen potential */
 796         potential_force_calc(moldyn);
 797
 798         for(i=0;i<count;i++) {
 799                 /* again velocities */
 800                 v3_scale(&delta,&(atom[i].f),0.5*tau/atom[i].mass);
 801                 v3_add(&(atom[i].v),&(atom[i].v),&delta);
 802         }
 803
 804         return 0;
 805 }
 806
 807
 808 /*
 809  *
 810  * potentials & corresponding forces
 811  *
 812  */
 813
 814 /* generic potential and force calculation */
 815
 816 int potential_force_calc(t_moldyn *moldyn) {
 817
 818         int i,j,k,count;
 819         t_atom *itom,*jtom,*ktom;
 820         t_linkcell *lc;
 821         t_list neighbour_i[27];
 822         t_list neighbour_i2[27];
 823         //t_list neighbour_j[27];
 824         t_list *this,*that;
 825         u8 bc_ij,bc_ik;
 826         int dnlc;
 827
 828         count=moldyn->count;
 829         itom=moldyn->atom;
 830         lc=&(moldyn->lc);
 831
 832         /* reset energy */
 833         moldyn->energy=0.0;
 834
 835         /* get energy and force of every atom */
 836         for(i=0;i<count;i++) {
 837
 838                 /* reset force */
 839                 v3_zero(&(itom[i].f));
 840
 841                 /* single particle potential/force */
 842                 if(itom[i].attr&ATOM_ATTR_1BP)
 843                         moldyn->func1b(moldyn,&(itom[i]));
 844
 845                 /* 2 body pair potential/force */
 846                 if(itom[i].attr&(ATOM_ATTR_2BP|ATOM_ATTR_3BP)) {
 847
 848                         link_cell_neighbour_index(moldyn,
 849                                 (itom[i].r.x+moldyn->dim.x/2)/lc->x,
 850                                 (itom[i].r.y+moldyn->dim.y/2)/lc->y,
 851                                 (itom[i].r.z+moldyn->dim.z/2)/lc->z,
 852                                 neighbour_i);
 853
 854                         dnlc=lc->dnlc;
 855
 856                         for(j=0;j<27;j++) {
 857
 858                                 this=&(neighbour_i[j]);
 859                                 list_reset(this);
 860
 861                                 if(this->start==NULL)
 862                                         continue;
 863
 864                                 bc_ij=(j<dnlc)?0:1;
 865
 866                                 do {
 867                                         jtom=this->current->data;
 868
 869                                         if(jtom==&(itom[i]))
 870                                                 continue;
 871
 872                                         if((jtom->attr&ATOM_ATTR_2BP)&
 873                                            (itom[i].attr&ATOM_ATTR_2BP))
 874                                                 moldyn->func2b(moldyn,
 875                                                                &(itom[i]),
 876                                                                jtom,
 877                                                                bc_ij);
 878
 879                                         /* 3 body potential/force */
 880
 881                                         if(!(itom[i].attr&ATOM_ATTR_3BP)||
 882                                            !(jtom->attr&ATOM_ATTR_3BP))
 883                                                 continue;
 884
 885                                         /* copy the neighbour lists */
 886                                         memcpy(neighbour_i2,neighbour_i,
 887                                                27*sizeof(t_list));
 888
 889                                         /* get neighbours of i */
 890                                         for(k=0;k<27;k++) {
 891
 892                                                 that=&(neighbour_i2[k]);
 893                                                 list_reset(that);
 894
 895                                                 if(that->start==NULL)
 896                                                         continue;
 897
 898                                                 bc_ik=(k<dnlc)?0:1;
 899
 900                                                 do {
 901
 902                         ktom=that->current->data;
 903
 904                         if(!(ktom->attr&ATOM_ATTR_3BP))
 905                                 continue;
 906
 907                         if(ktom==jtom)
 908                                 continue;
 909
 910                         if(ktom==&(itom[i]))
 911                                 continue;
 912
 913                         moldyn->func3b(moldyn,&(itom[i]),jtom,ktom,bc_ik|bc_ij);
 914
 915                                                 } while(list_next(that)!=\
 916                                                         L_NO_NEXT_ELEMENT);
 917
 918                                         }
 919
 920                                 } while(list_next(this)!=L_NO_NEXT_ELEMENT);
 921
 922                                 /* 2bp post function */
 923                                 if(moldyn->func2b_post) {
 924                                         moldyn->func2b_post(moldyn,
 925                                                             &(itom[i]),
 926                                                             jtom,bc_ij);
 927                                 }
 928
 929                         }
 930                 }
 931 printf("debug atom %d: %.15f %.15f %.15f\n",i,itom[i].r.x,itom[i].v.x,itom[i].f.x);
 932         }
 933
 934         return 0;
 935 }
 936
 937 /*
 938  * periodic boundayr checking
 939  */
 940
 941 int check_per_bound(t_moldyn *moldyn,t_3dvec *a) {
 942
 943         double x,y,z;
 944         t_3dvec *dim;
 945
 946         dim=&(moldyn->dim);
 947
 948         x=0.5*dim->x;
 949         y=0.5*dim->y;
 950         z=0.5*dim->z;
 951
 952         if(moldyn->status&MOLDYN_STAT_PBX) {
 953                 if(a->x>=x) a->x-=dim->x;
 954                 else if(-a->x>x) a->x+=dim->x;
 955         }
 956         if(moldyn->status&MOLDYN_STAT_PBY) {
 957                 if(a->y>=y) a->y-=dim->y;
 958                 else if(-a->y>y) a->y+=dim->y;
 959         }
 960         if(moldyn->status&MOLDYN_STAT_PBZ) {
 961                 if(a->z>=z) a->z-=dim->z;
 962                 else if(-a->z>z) a->z+=dim->z;
 963         }
 964
 965         return 0;
 966 }
 967
 968
 969 /*
 970  * example potentials
 971  */
 972
 973 /* harmonic oscillator potential and force */
 974
 975 int harmonic_oscillator(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
 976
 977         t_ho_params *params;
 978         t_3dvec force,distance;
 979         double d;
 980         double sc,equi_dist;
 981
 982         params=moldyn->pot2b_params;
 983         sc=params->spring_constant;
 984         equi_dist=params->equilibrium_distance;
 985
 986         v3_sub(&distance,&(ai->r),&(aj->r));
 987
 988         if(bc) check_per_bound(moldyn,&distance);
 989         d=v3_norm(&distance);
 990         if(d<=moldyn->cutoff) {
 991                 /* energy is 1/2 (d-d0)^2, but we will add this twice ... */
 992                 moldyn->energy+=(0.25*sc*(d-equi_dist)*(d-equi_dist));
 993                 v3_scale(&force,&distance,-sc*(1.0-(equi_dist/d)));
 994                 v3_add(&(ai->f),&(ai->f),&force);
 995         }
 996
 997         return 0;
 998 }
 999
1000 /* lennard jones potential & force for one sort of atoms */
1001
1002 int lennard_jones(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
1003
1004         t_lj_params *params;
1005         t_3dvec force,distance;
1006         double d,h1,h2;
1007         double eps,sig6,sig12;
1008
1009         params=moldyn->pot2b_params;
1010         eps=params->epsilon4;
1011         sig6=params->sigma6;
1012         sig12=params->sigma12;
1013
1014         v3_sub(&distance,&(ai->r),&(aj->r));
1015         if(bc) check_per_bound(moldyn,&distance);
1016         d=v3_absolute_square(&distance);        /* 1/r^2 */
1017         if(d<=moldyn->cutoff_square) {
1018                 d=1.0/d;                        /* 1/r^2 */
1019                 h2=d*d;                         /* 1/r^4 */
1020                 h2*=d;                          /* 1/r^6 */
1021                 h1=h2*h2;                       /* 1/r^12 */
1022                 /* energy is eps*..., but we will add this twice ... */
1023                 moldyn->energy+=0.5*eps*(sig12*h1-sig6*h2);
1024                 h2*=d;                          /* 1/r^8 */
1025                 h1*=d;                          /* 1/r^14 */
1026                 h2*=6*sig6;
1027                 h1*=12*sig12;
1028                 d=+h1-h2;
1029                 d*=eps;
1030                 v3_scale(&force,&distance,d);
1031                 v3_add(&(ai->f),&(ai->f),&force);
1032         }
1033
1034         return 0;
1035 }
1036
1037 /*
1038  * tersoff potential & force for 2 sorts of atoms
1039  */
1040
1041 /* create mixed terms from parameters and set them */
1042 int tersoff_mult_complete_params(t_tersoff_mult_params *p) {
1043
1044         printf("[moldyn] tersoff parameter completion\n");
1045         p->Smixed=sqrt(p->S[0]*p->S[1]);
1046         p->Rmixed=sqrt(p->R[0]*p->R[1]);
1047         p->Amixed=sqrt(p->A[0]*p->A[1]);
1048         p->Bmixed=sqrt(p->B[0]*p->B[1]);
1049         p->lambda_m=0.5*(p->lambda[0]+p->lambda[1]);
1050         p->mu_m=0.5*(p->mu[0]+p->mu[1]);
1051
1052         printf("[moldyn] tersoff mult parameter info:\n");
1053         printf("  S (m)  | %.12f | %.12f | %.12f\n",p->S[0],p->S[1],p->Smixed);
1054         printf("  R (m)  | %.12f | %.12f | %.12f\n",p->R[0],p->R[1],p->Rmixed);
1055         printf("  A (eV) | %f | %f | %f\n",p->A[0]/EV,p->A[1]/EV,p->Amixed/EV);
1056         printf("  B (eV) | %f | %f | %f\n",p->B[0]/EV,p->B[1]/EV,p->Bmixed/EV);
1057         printf("  lambda | %f | %f | %f\n",p->lambda[0],p->lambda[1],
1058                                           p->lambda_m);
1059         printf("  mu     | %f | %f | %f\n",p->mu[0],p->mu[1],p->mu_m);
1060         printf("  beta   | %.10f | %.10f\n",p->beta[0],p->beta[1]);
1061         printf("  n      | %f | %f\n",p->n[0],p->n[1]);
1062         printf("  c      | %f | %f\n",p->c[0],p->c[1]);
1063         printf("  d      | %f | %f\n",p->d[0],p->d[1]);
1064         printf("  h      | %f | %f\n",p->h[0],p->h[1]);
1065         printf("  chi    | %f \n",p->chi);
1066
1067         return 0;
1068 }
1069
1070 /* tersoff 1 body part */
1071 int tersoff_mult_1bp(t_moldyn *moldyn,t_atom *ai) {
1072
1073         int num;
1074         t_tersoff_mult_params *params;
1075         t_tersoff_exchange *exchange;
1076
1077         num=ai->bnum;
1078         params=moldyn->pot1b_params;
1079         exchange=&(params->exchange);
1080
1081         /*
1082          * simple: point constant parameters only depending on atom i to
1083          *         their right values
1084          */
1085
1086         exchange->beta=&(params->beta[num]);
1087         exchange->n=&(params->n[num]);
1088         exchange->c=&(params->c[num]);
1089         exchange->d=&(params->d[num]);
1090         exchange->h=&(params->h[num]);
1091
1092         exchange->betan=pow(*(exchange->beta),*(exchange->n));
1093         exchange->n_betan=*(exchange->n)*exchange->betan;
1094         exchange->c2=params->c[num]*params->c[num];
1095         exchange->d2=params->d[num]*params->d[num];
1096         exchange->c2d2=exchange->c2/exchange->d2;
1097
1098         return 0;
1099 }
1100
1101 /* tersoff 2 body part */
1102 int tersoff_mult_2bp(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
1103
1104         t_tersoff_mult_params *params;
1105         t_tersoff_exchange *exchange;
1106         t_3dvec dist_ij,force;
1107         double d_ij;
1108         double A,B,R,S,lambda,mu;
1109         double f_r,df_r;
1110         double f_c,df_c;
1111         int num;
1112         double s_r;
1113         double arg;
1114         double scale;
1115
1116         params=moldyn->pot2b_params;
1117         num=ai->bnum;
1118         exchange=&(params->exchange);
1119
1120         exchange->run3bp=0;
1121         exchange->run2bp_post=0;
1122
1123         /*
1124          * we need: f_c, df_c, f_r, df_r
1125          *
1126          * therefore we need: R, S, A, lambda
1127          */
1128
1129         v3_sub(&dist_ij,&(ai->r),&(aj->r));
1130
1131         if(bc) check_per_bound(moldyn,&dist_ij);
1132
1133         d_ij=v3_norm(&dist_ij);
1134
1135         /* save for use in 3bp */
1136         exchange->d_ij=d_ij;
1137         exchange->dist_ij=dist_ij;
1138
1139         /* constants */
1140         if(num==aj->bnum) {
1141                 S=params->S[num];
1142                 R=params->R[num];
1143                 A=params->A[num];
1144                 B=params->B[num];
1145                 lambda=params->lambda[num];
1146                 mu=params->mu[num];
1147                 params->exchange.chi=1.0;
1148         }
1149         else {
1150                 S=params->Smixed;
1151                 R=params->Rmixed;
1152                 A=params->Amixed;
1153                 B=params->Bmixed;
1154                 lambda=params->lambda_m;
1155                 mu=params->mu_m;
1156                 params->exchange.chi=params->chi;
1157         }
1158         if(d_ij>S)
1159                 return 0;
1160
1161         f_r=A*exp(-lambda*d_ij);
1162         df_r=-lambda*f_r/d_ij;
1163
1164         /* f_a, df_a calc + save for later use */
1165         exchange->f_a=-B*exp(-mu*d_ij);
1166         exchange->df_a=-mu*exchange->f_a/d_ij;
1167
1168         if(d_ij<R) {
1169                 /* f_c = 1, df_c = 0 */
1170                 f_c=1.0;
1171                 df_c=0.0;
1172                 v3_scale(&force,&dist_ij,df_r);
1173         }
1174         else {
1175                 s_r=S-R;
1176                 arg=M_PI*(d_ij-R)/s_r;
1177                 f_c=0.5+0.5*cos(arg);
1178                 df_c=-0.5*sin(arg)*(M_PI/(s_r*d_ij));
1179                 scale=df_c*f_r+df_r*f_c;
1180                 v3_scale(&force,&dist_ij,scale);
1181         }
1182
1183         /* add forces */
1184         v3_add(&(ai->f),&(ai->f),&force);
1185         /* energy is 0.5 f_r f_c ... */
1186         moldyn->energy+=(0.5*f_r*f_c);
1187
1188         /* save for use in 3bp */
1189         exchange->f_c=f_c;
1190         exchange->df_c=df_c;
1191
1192         /* enable the run of 3bp function and 2bp post processing */
1193         exchange->run3bp=1;
1194         exchange->run2bp_post=1;
1195
1196         /* reset 3bp sums */
1197         exchange->zeta=0.0;
1198         v3_zero(&(exchange->db_ij));
1199
1200         return 0;
1201 }
1202
1203 /* tersoff 2 body post part */
1204
1205 int tersoff_mult_post_2bp(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
1206
1207         /* here we have to allow for the 3bp sums */
1208
1209         t_tersoff_mult_params *params;
1210         t_tersoff_exchange *exchange;
1211
1212         t_3dvec force,temp,*db_ij,*dist_ij;
1213         double db_ij_scale1,db_ij_scale2;
1214         double b_ij;
1215         double f_c,df_c,f_a,df_a;
1216         double chi,n,n_betan;
1217         double zeta;
1218
1219         params=moldyn->pot2b_params;
1220         exchange=&(params->exchange);
1221
1222         /* we do not run if f_c_ij was detected to be 0! */
1223         if(!(exchange->run2bp_post))
1224                 return 0;
1225
1226         db_ij=&(exchange->db_ij);
1227         f_c=exchange->f_c;
1228         df_c=exchange->df_c;
1229         f_a=exchange->f_a;
1230         df_a=exchange->df_a;
1231         n_betan=exchange->n_betan;
1232         n=*(exchange->n);
1233         chi=exchange->chi;
1234         dist_ij=&(exchange->dist_ij);
1235         zeta=exchange->zeta;
1236
1237         db_ij_scale2=pow(zeta,n-1.0);
1238 printf("DEBUG: %.15f %.15f\n",zeta,db_ij_scale2);
1239         db_ij_scale1=db_ij_scale2*zeta;
1240         db_ij_scale2*=n_betan;
1241         db_ij_scale1=pow((1.0+n_betan*db_ij_scale1),-1.0/(2*n)-1);
1242         b_ij=chi*db_ij_scale1*(1.0+n_betan*db_ij_scale1);
1243         db_ij_scale1*=(-1.0*chi/(2*n));
1244
1245         /* db_ij part */
1246         v3_scale(db_ij,db_ij,(db_ij_scale1*db_ij_scale2));
1247         v3_scale(db_ij,db_ij,f_a);
1248
1249         /* df_a part */
1250         v3_scale(&temp,dist_ij,b_ij*df_a);
1251
1252         /* db_ij + df_a part */
1253         v3_add(&force,&temp,db_ij);
1254         v3_scale(&force,&force,f_c);
1255
1256         /* df_c part */
1257         v3_scale(&temp,dist_ij,f_a*b_ij*df_c);
1258
1259         /* add energy of 3bp sum */
1260         moldyn->energy+=(0.5*f_c*b_ij*f_a);
1261
1262         /* add force of 3bp calculation (all three parts) */
1263         v3_add(&(ai->f),&temp,&force);
1264
1265         return 0;
1266 }
1267
1268 /* tersoff 3 body part */
1269
1270 int tersoff_mult_3bp(t_moldyn *moldyn,t_atom *ai,t_atom *aj,t_atom *ak,u8 bc) {
1271
1272         t_tersoff_mult_params *params;
1273         t_tersoff_exchange *exchange;
1274         t_3dvec dist_ij,dist_ik;
1275         t_3dvec temp,force;
1276         double R,S,s_r;
1277         double d_ij,d_ik;
1278         double rijrik,dijdik;
1279         double f_c,df_c,f_a,df_a;
1280         double f_c_ik,df_c_ik,arg;
1281         double n,c,d,h;
1282         double c2,d2,c2d2;
1283         double cos_theta,d_costheta1,d_costheta2;
1284         double h_cos,d2_h_cos2;
1285         double frac;
1286         double g;
1287         int num;
1288
1289         params=moldyn->pot3b_params;
1290         num=ai->bnum;
1291         exchange=&(params->exchange);
1292
1293         if(!(exchange->run3bp))
1294                 return 0;
1295
1296         /*
1297          * we need: f_c, d_fc, b_ij, db_ij, f_a, df_a
1298          *
1299          * we got f_c, df_c, f_a, df_a from 2bp calculation
1300          */
1301
1302         d_ij=exchange->d_ij;
1303         dist_ij=exchange->dist_ij;
1304
1305         f_a=params->exchange.f_a;
1306         df_a=params->exchange.df_a;
1307
1308         f_c=exchange->f_c;
1309         df_c=exchange->df_c;
1310
1311         /* d_ij is <= S, as we didn't return so far! */
1312
1313         /*
1314          * calc of b_ij (scalar) and db_ij (vector)
1315          *
1316          * - for b_ij: chi, beta, f_c_ik, w(=1), c, d, h, n, cos_theta
1317          *
1318          * - for db_ij: d_costheta, cos_theta, f_c_ik, df_c_ik, w_ik
1319          *
1320          */
1321
1322         v3_sub(&dist_ik,&(ai->r),&(ak->r));
1323         if(bc) check_per_bound(moldyn,&dist_ik);
1324         d_ik=v3_norm(&dist_ik);
1325
1326         /* constants */
1327         if(num==ak->bnum) {
1328                 R=params->R[num];
1329                 S=params->S[num];
1330         }
1331         else {
1332                 R=params->Rmixed;
1333                 S=params->Smixed;
1334         }
1335
1336         /* there is no contribution if f_c_ik = 0 */
1337         if(d_ik>S)
1338                 return 0;
1339
1340         /* get exchange data */
1341         n=*(exchange->n);
1342         c=*(exchange->c);
1343         d=*(exchange->d);
1344         h=*(exchange->h);
1345         c2=exchange->c2;
1346         d2=exchange->d2;
1347         c2d2=exchange->c2d2;
1348
1349         /* cosine of theta by scalaproduct */
1350         rijrik=v3_scalar_product(&dist_ij,&dist_ik);
1351         dijdik=d_ij*d_ik;
1352         cos_theta=rijrik/dijdik;
1353
1354         /* hack - cos theta machine accuracy problems! */
1355         if(cos_theta>1.0||cos_theta<-1.0) {
1356                 printf("THETA CORRECTION\n");
1357                 moldyn->debug++;
1358                 if(fabs(cos_theta)>1.0+ACCEPTABLE_ERROR)
1359                         printf("[moldyn] WARNING: cos theta failure!\n");
1360                 if(cos_theta<0) {
1361                         cos_theta=-1.0;
1362                 }
1363                 else {
1364                         cos_theta=1.0;
1365                 }
1366         }
1367
1368         d_costheta1=dijdik-rijrik*d_ik/d_ij;
1369         d_costheta2=dijdik-rijrik*d_ij/d_ik;
1370
1371         h_cos=(h-cos_theta);
1372         d2_h_cos2=d2+(h_cos*h_cos);
1373
1374         frac=c2/(d2_h_cos2);
1375         g=1.0+c2d2-frac;
1376
1377         /* d_costheta contrib to db_ij (needed in all remaining cases) */
1378         v3_scale(&temp,&dist_ij,d_costheta1);
1379         v3_scale(&force,&dist_ik,d_costheta2);
1380         v3_add(&force,&force,&temp);
1381         v3_scale(&force,&force,-2.0*frac*h_cos/d2_h_cos2); /* f_c_ik missing */
1382
1383         if(d_ik<R) {
1384                 /* f_c_ik = 1, df_c_ik = 0 */
1385                 /* => only d_costheta contrib to db_ij */
1386                 // => do nothing ...
1387
1388                 /* zeta, f_c_ik = 1 */
1389                 exchange->zeta+=g;
1390         }
1391         else {
1392                 s_r=S-R;
1393                 arg=M_PI*(d_ik-R)/s_r;
1394                 f_c_ik=0.5+0.5*cos(arg);
1395                 df_c_ik=-0.5*sin(arg)*(M_PI/(s_r*d_ik));
1396
1397                 /* scale d_costheta contrib with f_c_ik */
1398                 v3_scale(&force,&force,f_c_ik);
1399
1400                 /* df_c_ik contrib to db_ij */
1401                 v3_scale(&temp,&dist_ik,df_c_ik*g);
1402
1403                 /* sum up both parts */
1404                 v3_add(&force,&force,&temp);
1405
1406                 /* zeta */
1407                 exchange->zeta+=f_c_ik*g;
1408         }
1409 printf("%.30f\n",exchange->zeta);
1410
1411         /* add to db_ij */
1412         v3_add(&(exchange->db_ij),&(exchange->db_ij),&force);
1413
1414         return 0;
1415 }
1416