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root/group/trunk/OOPSE/libmdtools/SimInfo.cpp
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Comparing trunk/OOPSE/libmdtools/SimInfo.cpp (file contents):
Revision 458 by gezelter, Fri Apr 4 19:47:19 2003 UTC vs.
Revision 841 by mmeineke, Wed Oct 29 17:55:28 2003 UTC

# Line 1 | Line 1
1 < #include <cstdlib>
2 < #include <cstring>
1 > #include <stdlib.h>
2 > #include <string.h>
3 > #include <math.h>
4  
5 + #include <iostream>
6 + using namespace std;
7  
8   #include "SimInfo.hpp"
9   #define __C
# Line 9 | Line 12
12  
13   #include "fortranWrappers.hpp"
14  
15 + #ifdef IS_MPI
16 + #include "mpiSimulation.hpp"
17 + #endif
18 +
19 + inline double roundMe( double x ){
20 +  return ( x >= 0 ) ? floor( x + 0.5 ) : ceil( x - 0.5 );
21 + }
22 +          
23 +
24   SimInfo* currentInfo;
25  
26   SimInfo::SimInfo(){
27    excludes = NULL;
28    n_constraints = 0;
29 +  nZconstraints = 0;
30    n_oriented = 0;
31    n_dipoles = 0;
32    ndf = 0;
33    ndfRaw = 0;
34 +  nZconstraints = 0;
35    the_integrator = NULL;
36    setTemp = 0;
37    thermalTime = 0.0;
38 +  currentTime = 0.0;
39    rCut = 0.0;
40 +  origRcut = -1.0;
41 +  ecr = 0.0;
42 +  origEcr = -1.0;
43 +  est = 0.0;
44 +  oldEcr = 0.0;
45 +  oldRcut = 0.0;
46  
47 +  haveOrigRcut = 0;
48 +  haveOrigEcr = 0;
49 +  boxIsInit = 0;
50 +  
51 +  resetTime = 1e99;
52 +  
53 +
54    usePBC = 0;
55    useLJ = 0;
56    useSticky = 0;
# Line 31 | Line 59 | SimInfo::SimInfo(){
59    useGB = 0;
60    useEAM = 0;
61  
62 +  myConfiguration = new SimState();
63 +
64    wrapMeSimInfo( this );
65   }
66  
67 +
68 + SimInfo::~SimInfo(){
69 +
70 +  delete myConfiguration;
71 +
72 +  map<string, GenericData*>::iterator i;
73 +  
74 +  for(i = properties.begin(); i != properties.end(); i++)
75 +    delete (*i).second;
76 +    
77 + }
78 +
79   void SimInfo::setBox(double newBox[3]) {
80 <  box_x = newBox[0];
81 <  box_y = newBox[1];
82 <  box_z = newBox[2];
83 <  setFortranBoxSize(newBox);
80 >  
81 >  int i, j;
82 >  double tempMat[3][3];
83 >
84 >  for(i=0; i<3; i++)
85 >    for (j=0; j<3; j++) tempMat[i][j] = 0.0;;
86 >
87 >  tempMat[0][0] = newBox[0];
88 >  tempMat[1][1] = newBox[1];
89 >  tempMat[2][2] = newBox[2];
90 >
91 >  setBoxM( tempMat );
92 >
93   }
94  
95 < void SimInfo::getBox(double theBox[3]) {
96 <  theBox[0] = box_x;
97 <  theBox[1] = box_y;
98 <  theBox[2] = box_z;
95 > void SimInfo::setBoxM( double theBox[3][3] ){
96 >  
97 >  int i, j;
98 >  double FortranHmat[9]; // to preserve compatibility with Fortran the
99 >                         // ordering in the array is as follows:
100 >                         // [ 0 3 6 ]
101 >                         // [ 1 4 7 ]
102 >                         // [ 2 5 8 ]
103 >  double FortranHmatInv[9]; // the inverted Hmat (for Fortran);
104 >
105 >  
106 >  if( !boxIsInit ) boxIsInit = 1;
107 >
108 >  for(i=0; i < 3; i++)
109 >    for (j=0; j < 3; j++) Hmat[i][j] = theBox[i][j];
110 >  
111 >  calcBoxL();
112 >  calcHmatInv();
113 >
114 >  for(i=0; i < 3; i++) {
115 >    for (j=0; j < 3; j++) {
116 >      FortranHmat[3*j + i] = Hmat[i][j];
117 >      FortranHmatInv[3*j + i] = HmatInv[i][j];
118 >    }
119 >  }
120 >
121 >  setFortranBoxSize(FortranHmat, FortranHmatInv, &orthoRhombic);
122 >
123   }
124  
125 +
126 + void SimInfo::getBoxM (double theBox[3][3]) {
127 +
128 +  int i, j;
129 +  for(i=0; i<3; i++)
130 +    for (j=0; j<3; j++) theBox[i][j] = Hmat[i][j];
131 + }
132 +
133 +
134 + void SimInfo::scaleBox(double scale) {
135 +  double theBox[3][3];
136 +  int i, j;
137 +
138 +  // cerr << "Scaling box by " << scale << "\n";
139 +
140 +  for(i=0; i<3; i++)
141 +    for (j=0; j<3; j++) theBox[i][j] = Hmat[i][j]*scale;
142 +
143 +  setBoxM(theBox);
144 +
145 + }
146 +
147 + void SimInfo::calcHmatInv( void ) {
148 +  
149 +  int i,j;
150 +  double smallDiag;
151 +  double tol;
152 +  double sanity[3][3];
153 +
154 +  invertMat3( Hmat, HmatInv );
155 +
156 +  // Check the inverse to make sure it is sane:
157 +
158 +  matMul3( Hmat, HmatInv, sanity );
159 +    
160 +  // check to see if Hmat is orthorhombic
161 +  
162 +  smallDiag = Hmat[0][0];
163 +  if(smallDiag > Hmat[1][1]) smallDiag = Hmat[1][1];
164 +  if(smallDiag > Hmat[2][2]) smallDiag = Hmat[2][2];
165 +  tol = smallDiag * 1E-6;
166 +
167 +  orthoRhombic = 1;
168 +  
169 +  for (i = 0; i < 3; i++ ) {
170 +    for (j = 0 ; j < 3; j++) {
171 +      if (i != j) {
172 +        if (orthoRhombic) {
173 +          if (Hmat[i][j] >= tol) orthoRhombic = 0;
174 +        }        
175 +      }
176 +    }
177 +  }
178 + }
179 +
180 + double SimInfo::matDet3(double a[3][3]) {
181 +  int i, j, k;
182 +  double determinant;
183 +
184 +  determinant = 0.0;
185 +
186 +  for(i = 0; i < 3; i++) {
187 +    j = (i+1)%3;
188 +    k = (i+2)%3;
189 +
190 +    determinant += a[0][i] * (a[1][j]*a[2][k] - a[1][k]*a[2][j]);
191 +  }
192 +
193 +  return determinant;
194 + }
195 +
196 + void SimInfo::invertMat3(double a[3][3], double b[3][3]) {
197 +  
198 +  int  i, j, k, l, m, n;
199 +  double determinant;
200 +
201 +  determinant = matDet3( a );
202 +
203 +  if (determinant == 0.0) {
204 +    sprintf( painCave.errMsg,
205 +             "Can't invert a matrix with a zero determinant!\n");
206 +    painCave.isFatal = 1;
207 +    simError();
208 +  }
209 +
210 +  for (i=0; i < 3; i++) {
211 +    j = (i+1)%3;
212 +    k = (i+2)%3;
213 +    for(l = 0; l < 3; l++) {
214 +      m = (l+1)%3;
215 +      n = (l+2)%3;
216 +      
217 +      b[l][i] = (a[j][m]*a[k][n] - a[j][n]*a[k][m]) / determinant;
218 +    }
219 +  }
220 + }
221 +
222 + void SimInfo::matMul3(double a[3][3], double b[3][3], double c[3][3]) {
223 +  double r00, r01, r02, r10, r11, r12, r20, r21, r22;
224 +
225 +  r00 = a[0][0]*b[0][0] + a[0][1]*b[1][0] + a[0][2]*b[2][0];
226 +  r01 = a[0][0]*b[0][1] + a[0][1]*b[1][1] + a[0][2]*b[2][1];
227 +  r02 = a[0][0]*b[0][2] + a[0][1]*b[1][2] + a[0][2]*b[2][2];
228 +  
229 +  r10 = a[1][0]*b[0][0] + a[1][1]*b[1][0] + a[1][2]*b[2][0];
230 +  r11 = a[1][0]*b[0][1] + a[1][1]*b[1][1] + a[1][2]*b[2][1];
231 +  r12 = a[1][0]*b[0][2] + a[1][1]*b[1][2] + a[1][2]*b[2][2];
232 +  
233 +  r20 = a[2][0]*b[0][0] + a[2][1]*b[1][0] + a[2][2]*b[2][0];
234 +  r21 = a[2][0]*b[0][1] + a[2][1]*b[1][1] + a[2][2]*b[2][1];
235 +  r22 = a[2][0]*b[0][2] + a[2][1]*b[1][2] + a[2][2]*b[2][2];
236 +  
237 +  c[0][0] = r00; c[0][1] = r01; c[0][2] = r02;
238 +  c[1][0] = r10; c[1][1] = r11; c[1][2] = r12;
239 +  c[2][0] = r20; c[2][1] = r21; c[2][2] = r22;
240 + }
241 +
242 + void SimInfo::matVecMul3(double m[3][3], double inVec[3], double outVec[3]) {
243 +  double a0, a1, a2;
244 +
245 +  a0 = inVec[0];  a1 = inVec[1];  a2 = inVec[2];
246 +
247 +  outVec[0] = m[0][0]*a0 + m[0][1]*a1 + m[0][2]*a2;
248 +  outVec[1] = m[1][0]*a0 + m[1][1]*a1 + m[1][2]*a2;
249 +  outVec[2] = m[2][0]*a0 + m[2][1]*a1 + m[2][2]*a2;
250 + }
251 +
252 + void SimInfo::transposeMat3(double in[3][3], double out[3][3]) {
253 +  double temp[3][3];
254 +  int i, j;
255 +
256 +  for (i = 0; i < 3; i++) {
257 +    for (j = 0; j < 3; j++) {
258 +      temp[j][i] = in[i][j];
259 +    }
260 +  }
261 +  for (i = 0; i < 3; i++) {
262 +    for (j = 0; j < 3; j++) {
263 +      out[i][j] = temp[i][j];
264 +    }
265 +  }
266 + }
267 +  
268 + void SimInfo::printMat3(double A[3][3] ){
269 +
270 +  std::cerr
271 +            << "[ " << A[0][0] << ", " << A[0][1] << ", " << A[0][2] << " ]\n"
272 +            << "[ " << A[1][0] << ", " << A[1][1] << ", " << A[1][2] << " ]\n"
273 +            << "[ " << A[2][0] << ", " << A[2][1] << ", " << A[2][2] << " ]\n";
274 + }
275 +
276 + void SimInfo::printMat9(double A[9] ){
277 +
278 +  std::cerr
279 +            << "[ " << A[0] << ", " << A[1] << ", " << A[2] << " ]\n"
280 +            << "[ " << A[3] << ", " << A[4] << ", " << A[5] << " ]\n"
281 +            << "[ " << A[6] << ", " << A[7] << ", " << A[8] << " ]\n";
282 + }
283 +
284 +
285 + void SimInfo::crossProduct3(double a[3],double b[3], double out[3]){
286 +
287 +      out[0] = a[1] * b[2] - a[2] * b[1];
288 +      out[1] = a[2] * b[0] - a[0] * b[2] ;
289 +      out[2] = a[0] * b[1] - a[1] * b[0];
290 +      
291 + }
292 +
293 + double SimInfo::dotProduct3(double a[3], double b[3]){
294 +  return a[0]*b[0] + a[1]*b[1]+ a[2]*b[2];
295 + }
296 +
297 + double SimInfo::length3(double a[3]){
298 +  return sqrt(a[0]*a[0] + a[1]*a[1] + a[2]*a[2]);
299 + }
300 +
301 + void SimInfo::calcBoxL( void ){
302 +
303 +  double dx, dy, dz, dsq;
304 +
305 +  // boxVol = Determinant of Hmat
306 +
307 +  boxVol = matDet3( Hmat );
308 +
309 +  // boxLx
310 +  
311 +  dx = Hmat[0][0]; dy = Hmat[1][0]; dz = Hmat[2][0];
312 +  dsq = dx*dx + dy*dy + dz*dz;
313 +  boxL[0] = sqrt( dsq );
314 +  //maxCutoff = 0.5 * boxL[0];
315 +
316 +  // boxLy
317 +  
318 +  dx = Hmat[0][1]; dy = Hmat[1][1]; dz = Hmat[2][1];
319 +  dsq = dx*dx + dy*dy + dz*dz;
320 +  boxL[1] = sqrt( dsq );
321 +  //if( (0.5 * boxL[1]) < maxCutoff ) maxCutoff = 0.5 * boxL[1];
322 +
323 +
324 +  // boxLz
325 +  
326 +  dx = Hmat[0][2]; dy = Hmat[1][2]; dz = Hmat[2][2];
327 +  dsq = dx*dx + dy*dy + dz*dz;
328 +  boxL[2] = sqrt( dsq );
329 +  //if( (0.5 * boxL[2]) < maxCutoff ) maxCutoff = 0.5 * boxL[2];
330 +
331 +  //calculate the max cutoff
332 +  maxCutoff =  calcMaxCutOff();
333 +  
334 +  checkCutOffs();
335 +
336 + }
337 +
338 +
339 + double SimInfo::calcMaxCutOff(){
340 +
341 +  double ri[3], rj[3], rk[3];
342 +  double rij[3], rjk[3], rki[3];
343 +  double minDist;
344 +
345 +  ri[0] = Hmat[0][0];
346 +  ri[1] = Hmat[1][0];
347 +  ri[2] = Hmat[2][0];
348 +
349 +  rj[0] = Hmat[0][1];
350 +  rj[1] = Hmat[1][1];
351 +  rj[2] = Hmat[2][1];
352 +
353 +  rk[0] = Hmat[0][2];
354 +  rk[1] = Hmat[1][2];
355 +  rk[2] = Hmat[2][2];
356 +  
357 +  crossProduct3(ri,rj, rij);
358 +  distXY = dotProduct3(rk,rij) / length3(rij);
359 +
360 +  crossProduct3(rj,rk, rjk);
361 +  distYZ = dotProduct3(ri,rjk) / length3(rjk);
362 +
363 +  crossProduct3(rk,ri, rki);
364 +  distZX = dotProduct3(rj,rki) / length3(rki);
365 +
366 +  minDist = min(min(distXY, distYZ), distZX);
367 +  return minDist/2;
368 +  
369 + }
370 +
371 + void SimInfo::wrapVector( double thePos[3] ){
372 +
373 +  int i;
374 +  double scaled[3];
375 +
376 +  if( !orthoRhombic ){
377 +    // calc the scaled coordinates.
378 +  
379 +
380 +    matVecMul3(HmatInv, thePos, scaled);
381 +    
382 +    for(i=0; i<3; i++)
383 +      scaled[i] -= roundMe(scaled[i]);
384 +    
385 +    // calc the wrapped real coordinates from the wrapped scaled coordinates
386 +    
387 +    matVecMul3(Hmat, scaled, thePos);
388 +
389 +  }
390 +  else{
391 +    // calc the scaled coordinates.
392 +    
393 +    for(i=0; i<3; i++)
394 +      scaled[i] = thePos[i]*HmatInv[i][i];
395 +    
396 +    // wrap the scaled coordinates
397 +    
398 +    for(i=0; i<3; i++)
399 +      scaled[i] -= roundMe(scaled[i]);
400 +    
401 +    // calc the wrapped real coordinates from the wrapped scaled coordinates
402 +    
403 +    for(i=0; i<3; i++)
404 +      thePos[i] = scaled[i]*Hmat[i][i];
405 +  }
406 +    
407 + }
408 +
409 +
410   int SimInfo::getNDF(){
411 <  int ndf_local, ndf;
411 >  int ndf_local;
412    
413    ndf_local = 3 * n_atoms + 3 * n_oriented - n_constraints;
414  
# Line 58 | Line 418 | int SimInfo::getNDF(){
418    ndf = ndf_local;
419   #endif
420  
421 <  ndf = ndf - 3;
421 >  ndf = ndf - 3 - nZconstraints;
422  
423    return ndf;
424   }
425  
426   int SimInfo::getNDFraw() {
427 <  int ndfRaw_local, ndfRaw;
427 >  int ndfRaw_local;
428  
429    // Raw degrees of freedom that we have to set
430    ndfRaw_local = 3 * n_atoms + 3 * n_oriented;
# Line 77 | Line 437 | int SimInfo::getNDFraw() {
437  
438    return ndfRaw;
439   }
440 <
440 >
441 > int SimInfo::getNDFtranslational() {
442 >  int ndfTrans_local;
443 >
444 >  ndfTrans_local = 3 * n_atoms - n_constraints;
445 >
446 > #ifdef IS_MPI
447 >  MPI_Allreduce(&ndfTrans_local,&ndfTrans,1,MPI_INT,MPI_SUM, MPI_COMM_WORLD);
448 > #else
449 >  ndfTrans = ndfTrans_local;
450 > #endif
451 >
452 >  ndfTrans = ndfTrans - 3 - nZconstraints;
453 >
454 >  return ndfTrans;
455 > }
456 >
457   void SimInfo::refreshSim(){
458  
459    simtype fInfo;
460    int isError;
461 +  int n_global;
462    int* excl;
463  
464 <  fInfo.box[0] = box_x;
88 <  fInfo.box[1] = box_y;
89 <  fInfo.box[2] = box_z;
464 >  fInfo.dielect = 0.0;
465  
466 <  fInfo.rlist = rList;
467 <  fInfo.rcut = rCut;
468 <  fInfo.rrf = ecr;
94 <  fInfo.rt = ecr - est;
95 <  fInfo.dielect = dielectric;
466 >  if( useDipole ){
467 >    if( useReactionField )fInfo.dielect = dielectric;
468 >  }
469  
470    fInfo.SIM_uses_PBC = usePBC;
471    //fInfo.SIM_uses_LJ = 0;
# Line 108 | Line 481 | void SimInfo::refreshSim(){
481  
482    excl = Exclude::getArray();
483  
484 + #ifdef IS_MPI
485 +  n_global = mpiSim->getTotAtoms();
486 + #else
487 +  n_global = n_atoms;
488 + #endif
489 +
490    isError = 0;
491  
492 < //   fInfo;
493 < //   n_atoms;
494 < //   identArray;
116 < //   n_exclude;
117 < //   excludes;
118 < //   nGlobalExcludes;
119 < //   globalExcludes;
120 < //   isError;
492 >  setFsimulation( &fInfo, &n_global, &n_atoms, identArray, &n_exclude, excl,
493 >                  &nGlobalExcludes, globalExcludes, molMembershipArray,
494 >                  &isError );
495  
122 –  setFsimulation( &fInfo, &n_atoms, identArray, &n_exclude, excl,
123 –                  &nGlobalExcludes, globalExcludes, &isError );
124 –
496    if( isError ){
497  
498      sprintf( painCave.errMsg,
# Line 136 | Line 507 | void SimInfo::refreshSim(){
507    MPIcheckPoint();
508   #endif // is_mpi
509  
510 <  ndf = this->getNDF();
511 <  ndfRaw = this->getNDFraw();
510 >  this->ndf = this->getNDF();
511 >  this->ndfRaw = this->getNDFraw();
512 >  this->ndfTrans = this->getNDFtranslational();
513 > }
514  
515 +
516 + void SimInfo::setRcut( double theRcut ){
517 +
518 +  rCut = theRcut;
519 +  checkCutOffs();
520   }
521  
522 + void SimInfo::setDefaultRcut( double theRcut ){
523 +
524 +  haveOrigRcut = 1;
525 +  origRcut = theRcut;
526 +  rCut = theRcut;
527 + }
528 +
529 + void SimInfo::setEcr( double theEcr ){
530 +
531 +  ecr = theEcr;
532 +  checkCutOffs();
533 + }
534 +
535 + void SimInfo::setDefaultEcr( double theEcr ){
536 +
537 +  haveOrigEcr = 1;
538 +  origEcr = theEcr;
539 +  
540 +  ecr = theEcr;
541 + }
542 +
543 + void SimInfo::setEcr( double theEcr, double theEst ){
544 +
545 +  est = theEst;
546 +  setEcr( theEcr );
547 + }
548 +
549 + void SimInfo::setDefaultEcr( double theEcr, double theEst ){
550 +
551 +  est = theEst;
552 +  setDefaultEcr( theEcr );
553 + }
554 +
555 +
556 + void SimInfo::checkCutOffs( void ){
557 +
558 +  int cutChanged = 0;
559 +  
560 +  if( boxIsInit ){
561 +    
562 +    //we need to check cutOffs against the box
563 +
564 +    //detect the change of rCut
565 +    if(( maxCutoff > rCut )&&(usePBC)){
566 +      if( rCut < origRcut ){
567 +        rCut = origRcut;
568 +        
569 +        if (rCut > maxCutoff)
570 +          rCut = maxCutoff;
571 +  
572 +          sprintf( painCave.errMsg,
573 +                    "New Box size is setting the long range cutoff radius "
574 +                    "to %lf at time %lf\n",
575 +                    rCut, currentTime );
576 +          painCave.isFatal = 0;
577 +          simError();
578 +      }
579 +    }
580 +    else if ((rCut > maxCutoff)&&(usePBC)) {
581 +      sprintf( painCave.errMsg,
582 +               "New Box size is setting the long range cutoff radius "
583 +               "to %lf at time %lf\n",
584 +               maxCutoff, currentTime );
585 +      painCave.isFatal = 0;
586 +      simError();
587 +      rCut = maxCutoff;
588 +    }
589 +
590 +
591 +    //detect the change of ecr
592 +    if( maxCutoff > ecr ){
593 +      if( ecr < origEcr ){
594 +        ecr = origEcr;
595 +        if (ecr > maxCutoff) ecr = maxCutoff;
596 +  
597 +          sprintf( painCave.errMsg,
598 +                    "New Box size is setting the electrostaticCutoffRadius "
599 +                    "to %lf at time %lf\n",
600 +                    ecr, currentTime );
601 +            painCave.isFatal = 0;
602 +            simError();
603 +      }
604 +    }
605 +    else if( ecr > maxCutoff){
606 +      sprintf( painCave.errMsg,
607 +               "New Box size is setting the electrostaticCutoffRadius "
608 +               "to %lf at time %lf\n",
609 +               maxCutoff, currentTime  );
610 +      painCave.isFatal = 0;
611 +      simError();      
612 +      ecr = maxCutoff;
613 +    }
614 +
615 +    if( (oldEcr != ecr) || ( oldRcut != rCut ) ) cutChanged = 1;
616 +    
617 +    // rlist is the 1.0 plus max( rcut, ecr )
618 +    
619 +    ( rCut > ecr )? rList = rCut + 1.0: rList = ecr + 1.0;
620 +    
621 +    if( cutChanged ){
622 +      
623 +      notifyFortranCutOffs( &rCut, &rList, &ecr, &est );
624 +    }
625 +    
626 +    oldEcr = ecr;
627 +    oldRcut = rCut;
628 +    
629 +  } else {
630 +    // initialize this stuff before using it, OK?
631 +    sprintf( painCave.errMsg,
632 +             "Trying to check cutoffs without a box. Be smarter.\n" );
633 +    painCave.isFatal = 1;
634 +    simError();      
635 +  }
636 +  
637 + }
638 +
639 + void SimInfo::addProperty(GenericData* prop){
640 +
641 +  map<string, GenericData*>::iterator result;
642 +  result = properties.find(prop->getID());
643 +  
644 +  //we can't simply use  properties[prop->getID()] = prop,
645 +  //it will cause memory leak if we already contain a propery which has the same name of prop
646 +  
647 +  if(result != properties.end()){
648 +    
649 +    delete (*result).second;
650 +    (*result).second = prop;
651 +      
652 +  }
653 +  else{
654 +
655 +    properties[prop->getID()] = prop;
656 +
657 +  }
658 +    
659 + }
660 +
661 + GenericData* SimInfo::getProperty(const string& propName){
662 +
663 +  map<string, GenericData*>::iterator result;
664 +  
665 +  //string lowerCaseName = ();
666 +  
667 +  result = properties.find(propName);
668 +  
669 +  if(result != properties.end())
670 +    return (*result).second;  
671 +  else  
672 +    return NULL;  
673 + }
674 +
675 + vector<GenericData*> SimInfo::getProperties(){
676 +
677 +  vector<GenericData*> result;
678 +  map<string, GenericData*>::iterator i;
679 +  
680 +  for(i = properties.begin(); i != properties.end(); i++)
681 +    result.push_back((*i).second);
682 +    
683 +  return result;
684 + }
685 +
686 + double SimInfo::matTrace3(double m[3][3]){
687 +  double trace;
688 +  trace = m[0][0] + m[1][1] + m[2][2];
689 +
690 +  return trace;
691 + }

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