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root/group/branches/new-templateless/OOPSE/libmdtools/SimInfo.cpp
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Comparing:
trunk/OOPSE/libmdtools/SimInfo.cpp (file contents), Revision 483 by gezelter, Wed Apr 9 04:06:43 2003 UTC vs.
branches/new-templateless/OOPSE/libmdtools/SimInfo.cpp (file contents), Revision 850 by mmeineke, Mon Nov 3 22:07:17 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 +  properties = new GenericData();
65 +
66    wrapMeSimInfo( this );
67   }
68  
69 +
70 + SimInfo::~SimInfo(){
71 +
72 +  delete myConfiguration;
73 +  delete properties;    
74 + }
75 +
76   void SimInfo::setBox(double newBox[3]) {
77 <  double smallestBox, maxCutoff;
78 <  int status;
79 <  box_x = newBox[0];
41 <  box_y = newBox[1];
42 <  box_z = newBox[2];
43 <  setFortranBoxSize(newBox);
77 >  
78 >  int i, j;
79 >  double tempMat[3][3];
80  
81 <  smallestBox = box_x;
82 <  if (box_y < smallestBox) smallestBox = box_y;
47 <  if (box_z < smallestBox) smallestBox = box_z;
81 >  for(i=0; i<3; i++)
82 >    for (j=0; j<3; j++) tempMat[i][j] = 0.0;;
83  
84 <  maxCutoff = smallestBox / 2.0;
84 >  tempMat[0][0] = newBox[0];
85 >  tempMat[1][1] = newBox[1];
86 >  tempMat[2][2] = newBox[2];
87  
88 <  if (rList > maxCutoff) {
52 <    sprintf( painCave.errMsg,
53 <             "New Box size is forcing neighborlist radius down to %lf\n",
54 <             maxCutoff );
55 <    painCave.isFatal = 0;
56 <    simError();
88 >  setBoxM( tempMat );
89  
90 <    rList = maxCutoff;
90 > }
91  
92 <    sprintf( painCave.errMsg,
93 <             "New Box size is forcing cutoff radius down to %lf\n",
94 <             maxCutoff - 1.0 );
95 <    painCave.isFatal = 0;
96 <    simError();
92 > void SimInfo::setBoxM( double theBox[3][3] ){
93 >  
94 >  int i, j;
95 >  double FortranHmat[9]; // to preserve compatibility with Fortran the
96 >                         // ordering in the array is as follows:
97 >                         // [ 0 3 6 ]
98 >                         // [ 1 4 7 ]
99 >                         // [ 2 5 8 ]
100 >  double FortranHmatInv[9]; // the inverted Hmat (for Fortran);
101  
102 <    rCut = rList - 1.0;
102 >  
103 >  if( !boxIsInit ) boxIsInit = 1;
104  
105 <    // list radius changed so we have to refresh the simulation structure.
106 <    refreshSim();
105 >  for(i=0; i < 3; i++)
106 >    for (j=0; j < 3; j++) Hmat[i][j] = theBox[i][j];
107 >  
108 >  calcBoxL();
109 >  calcHmatInv();
110 >
111 >  for(i=0; i < 3; i++) {
112 >    for (j=0; j < 3; j++) {
113 >      FortranHmat[3*j + i] = Hmat[i][j];
114 >      FortranHmatInv[3*j + i] = HmatInv[i][j];
115 >    }
116    }
117  
118 <  if (rCut > maxCutoff) {
118 >  setFortranBoxSize(FortranHmat, FortranHmatInv, &orthoRhombic);
119 >
120 > }
121 >
122 >
123 > void SimInfo::getBoxM (double theBox[3][3]) {
124 >
125 >  int i, j;
126 >  for(i=0; i<3; i++)
127 >    for (j=0; j<3; j++) theBox[i][j] = Hmat[i][j];
128 > }
129 >
130 >
131 > void SimInfo::scaleBox(double scale) {
132 >  double theBox[3][3];
133 >  int i, j;
134 >
135 >  // cerr << "Scaling box by " << scale << "\n";
136 >
137 >  for(i=0; i<3; i++)
138 >    for (j=0; j<3; j++) theBox[i][j] = Hmat[i][j]*scale;
139 >
140 >  setBoxM(theBox);
141 >
142 > }
143 >
144 > void SimInfo::calcHmatInv( void ) {
145 >  
146 >  int i,j;
147 >  double smallDiag;
148 >  double tol;
149 >  double sanity[3][3];
150 >
151 >  invertMat3( Hmat, HmatInv );
152 >
153 >  // Check the inverse to make sure it is sane:
154 >
155 >  matMul3( Hmat, HmatInv, sanity );
156 >    
157 >  // check to see if Hmat is orthorhombic
158 >  
159 >  smallDiag = Hmat[0][0];
160 >  if(smallDiag > Hmat[1][1]) smallDiag = Hmat[1][1];
161 >  if(smallDiag > Hmat[2][2]) smallDiag = Hmat[2][2];
162 >  tol = smallDiag * 1E-6;
163 >
164 >  orthoRhombic = 1;
165 >  
166 >  for (i = 0; i < 3; i++ ) {
167 >    for (j = 0 ; j < 3; j++) {
168 >      if (i != j) {
169 >        if (orthoRhombic) {
170 >          if (Hmat[i][j] >= tol) orthoRhombic = 0;
171 >        }        
172 >      }
173 >    }
174 >  }
175 > }
176 >
177 > double SimInfo::matDet3(double a[3][3]) {
178 >  int i, j, k;
179 >  double determinant;
180 >
181 >  determinant = 0.0;
182 >
183 >  for(i = 0; i < 3; i++) {
184 >    j = (i+1)%3;
185 >    k = (i+2)%3;
186 >
187 >    determinant += a[0][i] * (a[1][j]*a[2][k] - a[1][k]*a[2][j]);
188 >  }
189 >
190 >  return determinant;
191 > }
192 >
193 > void SimInfo::invertMat3(double a[3][3], double b[3][3]) {
194 >  
195 >  int  i, j, k, l, m, n;
196 >  double determinant;
197 >
198 >  determinant = matDet3( a );
199 >
200 >  if (determinant == 0.0) {
201      sprintf( painCave.errMsg,
202 <             "New Box size is forcing cutoff radius down to %lf\n",
203 <             maxCutoff );
76 <    painCave.isFatal = 0;
202 >             "Can't invert a matrix with a zero determinant!\n");
203 >    painCave.isFatal = 1;
204      simError();
205 +  }
206  
207 <    status = 0;
208 <    LJ_new_rcut(&rCut, &status);
209 <    if (status != 0) {
210 <      sprintf( painCave.errMsg,
211 <               "Error in recomputing LJ shifts based on new rcut\n");
212 <      painCave.isFatal = 1;
213 <      simError();
207 >  for (i=0; i < 3; i++) {
208 >    j = (i+1)%3;
209 >    k = (i+2)%3;
210 >    for(l = 0; l < 3; l++) {
211 >      m = (l+1)%3;
212 >      n = (l+2)%3;
213 >      
214 >      b[l][i] = (a[j][m]*a[k][n] - a[j][n]*a[k][m]) / determinant;
215      }
216    }
217   }
218  
219 < void SimInfo::getBox(double theBox[3]) {
220 <  theBox[0] = box_x;
221 <  theBox[1] = box_y;
222 <  theBox[2] = box_z;
219 > void SimInfo::matMul3(double a[3][3], double b[3][3], double c[3][3]) {
220 >  double r00, r01, r02, r10, r11, r12, r20, r21, r22;
221 >
222 >  r00 = a[0][0]*b[0][0] + a[0][1]*b[1][0] + a[0][2]*b[2][0];
223 >  r01 = a[0][0]*b[0][1] + a[0][1]*b[1][1] + a[0][2]*b[2][1];
224 >  r02 = a[0][0]*b[0][2] + a[0][1]*b[1][2] + a[0][2]*b[2][2];
225 >  
226 >  r10 = a[1][0]*b[0][0] + a[1][1]*b[1][0] + a[1][2]*b[2][0];
227 >  r11 = a[1][0]*b[0][1] + a[1][1]*b[1][1] + a[1][2]*b[2][1];
228 >  r12 = a[1][0]*b[0][2] + a[1][1]*b[1][2] + a[1][2]*b[2][2];
229 >  
230 >  r20 = a[2][0]*b[0][0] + a[2][1]*b[1][0] + a[2][2]*b[2][0];
231 >  r21 = a[2][0]*b[0][1] + a[2][1]*b[1][1] + a[2][2]*b[2][1];
232 >  r22 = a[2][0]*b[0][2] + a[2][1]*b[1][2] + a[2][2]*b[2][2];
233 >  
234 >  c[0][0] = r00; c[0][1] = r01; c[0][2] = r02;
235 >  c[1][0] = r10; c[1][1] = r11; c[1][2] = r12;
236 >  c[2][0] = r20; c[2][1] = r21; c[2][2] = r22;
237   }
238 <
238 >
239 > void SimInfo::matVecMul3(double m[3][3], double inVec[3], double outVec[3]) {
240 >  double a0, a1, a2;
241 >
242 >  a0 = inVec[0];  a1 = inVec[1];  a2 = inVec[2];
243 >
244 >  outVec[0] = m[0][0]*a0 + m[0][1]*a1 + m[0][2]*a2;
245 >  outVec[1] = m[1][0]*a0 + m[1][1]*a1 + m[1][2]*a2;
246 >  outVec[2] = m[2][0]*a0 + m[2][1]*a1 + m[2][2]*a2;
247 > }
248 >
249 > void SimInfo::transposeMat3(double in[3][3], double out[3][3]) {
250 >  double temp[3][3];
251 >  int i, j;
252 >
253 >  for (i = 0; i < 3; i++) {
254 >    for (j = 0; j < 3; j++) {
255 >      temp[j][i] = in[i][j];
256 >    }
257 >  }
258 >  for (i = 0; i < 3; i++) {
259 >    for (j = 0; j < 3; j++) {
260 >      out[i][j] = temp[i][j];
261 >    }
262 >  }
263 > }
264 >  
265 > void SimInfo::printMat3(double A[3][3] ){
266 >
267 >  std::cerr
268 >            << "[ " << A[0][0] << ", " << A[0][1] << ", " << A[0][2] << " ]\n"
269 >            << "[ " << A[1][0] << ", " << A[1][1] << ", " << A[1][2] << " ]\n"
270 >            << "[ " << A[2][0] << ", " << A[2][1] << ", " << A[2][2] << " ]\n";
271 > }
272 >
273 > void SimInfo::printMat9(double A[9] ){
274 >
275 >  std::cerr
276 >            << "[ " << A[0] << ", " << A[1] << ", " << A[2] << " ]\n"
277 >            << "[ " << A[3] << ", " << A[4] << ", " << A[5] << " ]\n"
278 >            << "[ " << A[6] << ", " << A[7] << ", " << A[8] << " ]\n";
279 > }
280 >
281 >
282 > void SimInfo::crossProduct3(double a[3],double b[3], double out[3]){
283 >
284 >      out[0] = a[1] * b[2] - a[2] * b[1];
285 >      out[1] = a[2] * b[0] - a[0] * b[2] ;
286 >      out[2] = a[0] * b[1] - a[1] * b[0];
287 >      
288 > }
289 >
290 > double SimInfo::dotProduct3(double a[3], double b[3]){
291 >  return a[0]*b[0] + a[1]*b[1]+ a[2]*b[2];
292 > }
293 >
294 > double SimInfo::length3(double a[3]){
295 >  return sqrt(a[0]*a[0] + a[1]*a[1] + a[2]*a[2]);
296 > }
297 >
298 > void SimInfo::calcBoxL( void ){
299 >
300 >  double dx, dy, dz, dsq;
301 >
302 >  // boxVol = Determinant of Hmat
303 >
304 >  boxVol = matDet3( Hmat );
305 >
306 >  // boxLx
307 >  
308 >  dx = Hmat[0][0]; dy = Hmat[1][0]; dz = Hmat[2][0];
309 >  dsq = dx*dx + dy*dy + dz*dz;
310 >  boxL[0] = sqrt( dsq );
311 >  //maxCutoff = 0.5 * boxL[0];
312 >
313 >  // boxLy
314 >  
315 >  dx = Hmat[0][1]; dy = Hmat[1][1]; dz = Hmat[2][1];
316 >  dsq = dx*dx + dy*dy + dz*dz;
317 >  boxL[1] = sqrt( dsq );
318 >  //if( (0.5 * boxL[1]) < maxCutoff ) maxCutoff = 0.5 * boxL[1];
319 >
320 >
321 >  // boxLz
322 >  
323 >  dx = Hmat[0][2]; dy = Hmat[1][2]; dz = Hmat[2][2];
324 >  dsq = dx*dx + dy*dy + dz*dz;
325 >  boxL[2] = sqrt( dsq );
326 >  //if( (0.5 * boxL[2]) < maxCutoff ) maxCutoff = 0.5 * boxL[2];
327 >
328 >  //calculate the max cutoff
329 >  maxCutoff =  calcMaxCutOff();
330 >  
331 >  checkCutOffs();
332 >
333 > }
334 >
335 >
336 > double SimInfo::calcMaxCutOff(){
337 >
338 >  double ri[3], rj[3], rk[3];
339 >  double rij[3], rjk[3], rki[3];
340 >  double minDist;
341 >
342 >  ri[0] = Hmat[0][0];
343 >  ri[1] = Hmat[1][0];
344 >  ri[2] = Hmat[2][0];
345 >
346 >  rj[0] = Hmat[0][1];
347 >  rj[1] = Hmat[1][1];
348 >  rj[2] = Hmat[2][1];
349 >
350 >  rk[0] = Hmat[0][2];
351 >  rk[1] = Hmat[1][2];
352 >  rk[2] = Hmat[2][2];
353 >  
354 >  crossProduct3(ri,rj, rij);
355 >  distXY = dotProduct3(rk,rij) / length3(rij);
356 >
357 >  crossProduct3(rj,rk, rjk);
358 >  distYZ = dotProduct3(ri,rjk) / length3(rjk);
359 >
360 >  crossProduct3(rk,ri, rki);
361 >  distZX = dotProduct3(rj,rki) / length3(rki);
362 >
363 >  minDist = min(min(distXY, distYZ), distZX);
364 >  return minDist/2;
365 >  
366 > }
367 >
368 > void SimInfo::wrapVector( double thePos[3] ){
369 >
370 >  int i;
371 >  double scaled[3];
372 >
373 >  if( !orthoRhombic ){
374 >    // calc the scaled coordinates.
375 >  
376 >
377 >    matVecMul3(HmatInv, thePos, scaled);
378 >    
379 >    for(i=0; i<3; i++)
380 >      scaled[i] -= roundMe(scaled[i]);
381 >    
382 >    // calc the wrapped real coordinates from the wrapped scaled coordinates
383 >    
384 >    matVecMul3(Hmat, scaled, thePos);
385 >
386 >  }
387 >  else{
388 >    // calc the scaled coordinates.
389 >    
390 >    for(i=0; i<3; i++)
391 >      scaled[i] = thePos[i]*HmatInv[i][i];
392 >    
393 >    // wrap the scaled coordinates
394 >    
395 >    for(i=0; i<3; i++)
396 >      scaled[i] -= roundMe(scaled[i]);
397 >    
398 >    // calc the wrapped real coordinates from the wrapped scaled coordinates
399 >    
400 >    for(i=0; i<3; i++)
401 >      thePos[i] = scaled[i]*Hmat[i][i];
402 >  }
403 >    
404 > }
405 >
406 >
407   int SimInfo::getNDF(){
408 <  int ndf_local, ndf;
408 >  int ndf_local;
409    
410    ndf_local = 3 * n_atoms + 3 * n_oriented - n_constraints;
411  
# Line 104 | Line 415 | int SimInfo::getNDF(){
415    ndf = ndf_local;
416   #endif
417  
418 <  ndf = ndf - 3;
418 >  ndf = ndf - 3 - nZconstraints;
419  
420    return ndf;
421   }
422  
423   int SimInfo::getNDFraw() {
424 <  int ndfRaw_local, ndfRaw;
424 >  int ndfRaw_local;
425  
426    // Raw degrees of freedom that we have to set
427    ndfRaw_local = 3 * n_atoms + 3 * n_oriented;
# Line 123 | Line 434 | int SimInfo::getNDFraw() {
434  
435    return ndfRaw;
436   }
437 <
437 >
438 > int SimInfo::getNDFtranslational() {
439 >  int ndfTrans_local;
440 >
441 >  ndfTrans_local = 3 * n_atoms - n_constraints;
442 >
443 > #ifdef IS_MPI
444 >  MPI_Allreduce(&ndfTrans_local,&ndfTrans,1,MPI_INT,MPI_SUM, MPI_COMM_WORLD);
445 > #else
446 >  ndfTrans = ndfTrans_local;
447 > #endif
448 >
449 >  ndfTrans = ndfTrans - 3 - nZconstraints;
450 >
451 >  return ndfTrans;
452 > }
453 >
454   void SimInfo::refreshSim(){
455  
456    simtype fInfo;
457    int isError;
458 +  int n_global;
459    int* excl;
460 <  
133 <  fInfo.rrf = 0.0;
134 <  fInfo.rt = 0.0;
460 >
461    fInfo.dielect = 0.0;
462  
137 –  fInfo.box[0] = box_x;
138 –  fInfo.box[1] = box_y;
139 –  fInfo.box[2] = box_z;
140 –
141 –  fInfo.rlist = rList;
142 –  fInfo.rcut = rCut;
143 –
463    if( useDipole ){
145 –    fInfo.rrf = ecr;
146 –    fInfo.rt = ecr - est;
464      if( useReactionField )fInfo.dielect = dielectric;
465    }
466  
# Line 161 | Line 478 | void SimInfo::refreshSim(){
478  
479    excl = Exclude::getArray();
480  
481 + #ifdef IS_MPI
482 +  n_global = mpiSim->getTotAtoms();
483 + #else
484 +  n_global = n_atoms;
485 + #endif
486 +
487    isError = 0;
488  
489 <  setFsimulation( &fInfo, &n_atoms, identArray, &n_exclude, excl,
489 >  setFsimulation( &fInfo, &n_global, &n_atoms, identArray, &n_exclude, excl,
490                    &nGlobalExcludes, globalExcludes, molMembershipArray,
491                    &isError );
492  
# Line 183 | Line 506 | void SimInfo::refreshSim(){
506  
507    this->ndf = this->getNDF();
508    this->ndfRaw = this->getNDFraw();
509 +  this->ndfTrans = this->getNDFtranslational();
510 + }
511  
512 +
513 + void SimInfo::setRcut( double theRcut ){
514 +
515 +  rCut = theRcut;
516 +  checkCutOffs();
517   }
518  
519 + void SimInfo::setDefaultRcut( double theRcut ){
520 +
521 +  haveOrigRcut = 1;
522 +  origRcut = theRcut;
523 +  rCut = theRcut;
524 +
525 +  ( rCut > ecr )? rList = rCut + 1.0: rList = ecr + 1.0;
526 +
527 +  notifyFortranCutOffs( &rCut, &rList, &ecr, &est );
528 + }
529 +
530 + void SimInfo::setEcr( double theEcr ){
531 +
532 +  ecr = theEcr;
533 +  checkCutOffs();
534 + }
535 +
536 + void SimInfo::setDefaultEcr( double theEcr ){
537 +
538 +  haveOrigEcr = 1;
539 +  origEcr = theEcr;
540 +  
541 +  ( rCut > ecr )? rList = rCut + 1.0: rList = ecr + 1.0;
542 +
543 +  ecr = theEcr;
544 +
545 +  notifyFortranCutOffs( &rCut, &rList, &ecr, &est );
546 + }
547 +
548 + void SimInfo::setEcr( double theEcr, double theEst ){
549 +
550 +  est = theEst;
551 +  setEcr( theEcr );
552 + }
553 +
554 + void SimInfo::setDefaultEcr( double theEcr, double theEst ){
555 +
556 +  est = theEst;
557 +  setDefaultEcr( theEcr );
558 + }
559 +
560 +
561 + void SimInfo::checkCutOffs( void ){
562 +
563 +  int cutChanged = 0;
564 +  
565 +  if( boxIsInit ){
566 +    
567 +    //we need to check cutOffs against the box
568 +
569 +    //detect the change of rCut
570 +    if(( maxCutoff > rCut )&&(usePBC)){
571 +      if( rCut < origRcut ){
572 +        rCut = origRcut;
573 +        
574 +        if (rCut > maxCutoff)
575 +          rCut = maxCutoff;
576 +  
577 +          sprintf( painCave.errMsg,
578 +                    "New Box size is setting the long range cutoff radius "
579 +                    "to %lf at time %lf\n",
580 +                    rCut, currentTime );
581 +          painCave.isFatal = 0;
582 +          simError();
583 +      }
584 +    }
585 +    else if ((rCut > maxCutoff)&&(usePBC)) {
586 +      sprintf( painCave.errMsg,
587 +               "New Box size is setting the long range cutoff radius "
588 +               "to %lf at time %lf\n",
589 +               maxCutoff, currentTime );
590 +      painCave.isFatal = 0;
591 +      simError();
592 +      rCut = maxCutoff;
593 +    }
594 +
595 +
596 +    //detect the change of ecr
597 +    if( maxCutoff > ecr ){
598 +      if( ecr < origEcr ){
599 +        ecr = origEcr;
600 +        if (ecr > maxCutoff) ecr = maxCutoff;
601 +  
602 +          sprintf( painCave.errMsg,
603 +                    "New Box size is setting the electrostaticCutoffRadius "
604 +                    "to %lf at time %lf\n",
605 +                    ecr, currentTime );
606 +            painCave.isFatal = 0;
607 +            simError();
608 +      }
609 +    }
610 +    else if( ecr > maxCutoff){
611 +      sprintf( painCave.errMsg,
612 +               "New Box size is setting the electrostaticCutoffRadius "
613 +               "to %lf at time %lf\n",
614 +               maxCutoff, currentTime  );
615 +      painCave.isFatal = 0;
616 +      simError();      
617 +      ecr = maxCutoff;
618 +    }
619 +
620 +    if( (oldEcr != ecr) || ( oldRcut != rCut ) ) cutChanged = 1;
621 +    
622 +    // rlist is the 1.0 plus max( rcut, ecr )
623 +    
624 +    ( rCut > ecr )? rList = rCut + 1.0: rList = ecr + 1.0;
625 +    
626 +    if( cutChanged ){
627 +      notifyFortranCutOffs( &rCut, &rList, &ecr, &est );
628 +    }
629 +    
630 +    oldEcr = ecr;
631 +    oldRcut = rCut;
632 +    
633 +  } else {
634 +    // initialize this stuff before using it, OK?
635 +    sprintf( painCave.errMsg,
636 +             "Trying to check cutoffs without a box. Be smarter.\n" );
637 +    painCave.isFatal = 1;
638 +    simError();      
639 +  }
640 +  
641 + }
642 +
643 + GenericData* SimInfo::getProperty(char* propName){
644 +
645 +  return properties->find( propName );
646 + }
647 +
648 + double SimInfo::matTrace3(double m[3][3]){
649 +  double trace;
650 +  trace = m[0][0] + m[1][1] + m[2][2];
651 +
652 +  return trace;
653 + }

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