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root/group/trunk/OOPSE/libmdtools/SimInfo.cpp
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Comparing trunk/OOPSE/libmdtools/SimInfo.cpp (file contents):
Revision 482 by chuckv, Tue Apr 8 22:38:43 2003 UTC vs.
Revision 872 by chrisfen, Fri Nov 21 19:31:05 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 | SimInfo* currentInfo;
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 + inline double min( double a, double b ){
24 +  return (a < b ) ? a : b;
25 + }
26 +
27   SimInfo* currentInfo;
28  
29   SimInfo::SimInfo(){
30    excludes = NULL;
31    n_constraints = 0;
32 +  nZconstraints = 0;
33    n_oriented = 0;
34    n_dipoles = 0;
35    ndf = 0;
36    ndfRaw = 0;
37 +  nZconstraints = 0;
38    the_integrator = NULL;
39    setTemp = 0;
40    thermalTime = 0.0;
41 +  currentTime = 0.0;
42    rCut = 0.0;
43 +  ecr = 0.0;
44 +  est = 0.0;
45  
46 +  haveRcut = 0;
47 +  haveEcr = 0;
48 +  boxIsInit = 0;
49 +  
50 +  resetTime = 1e99;
51 +
52 +  orthoTolerance = 1E-6;
53 +  useInitXSstate = true;
54 +
55    usePBC = 0;
56    useLJ = 0;
57    useSticky = 0;
# Line 31 | Line 60 | SimInfo::SimInfo(){
60    useGB = 0;
61    useEAM = 0;
62  
63 +  myConfiguration = new SimState();
64 +
65    wrapMeSimInfo( this );
66   }
67  
68 +
69 + SimInfo::~SimInfo(){
70 +
71 +  delete myConfiguration;
72 +
73 +  map<string, GenericData*>::iterator i;
74 +  
75 +  for(i = properties.begin(); i != properties.end(); i++)
76 +    delete (*i).second;
77 +    
78 + }
79 +
80   void SimInfo::setBox(double newBox[3]) {
81 <  double smallestBox, maxCutoff;
82 <  int status;
83 <  box_x = newBox[0];
41 <  box_y = newBox[1];
42 <  box_z = newBox[2];
43 <  setFortranBoxSize(newBox);
81 >  
82 >  int i, j;
83 >  double tempMat[3][3];
84  
85 <  smallestBox = box_x;
86 <  if (box_y < smallestBox) smallestBox = box_y;
47 <  if (box_z < smallestBox) smallestBox = box_z;
85 >  for(i=0; i<3; i++)
86 >    for (j=0; j<3; j++) tempMat[i][j] = 0.0;;
87  
88 <  maxCutoff = smallestBox / 2.0;
88 >  tempMat[0][0] = newBox[0];
89 >  tempMat[1][1] = newBox[1];
90 >  tempMat[2][2] = newBox[2];
91  
92 <  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();
92 >  setBoxM( tempMat );
93  
94 <    rList = maxCutoff;
94 > }
95  
96 <    sprintf( painCave.errMsg,
97 <             "New Box size is forcing cutoff radius down to %lf\n",
98 <             maxCutoff - 1.0 );
99 <    painCave.isFatal = 0;
100 <    simError();
96 > void SimInfo::setBoxM( double theBox[3][3] ){
97 >  
98 >  int i, j;
99 >  double FortranHmat[9]; // to preserve compatibility with Fortran the
100 >                         // ordering in the array is as follows:
101 >                         // [ 0 3 6 ]
102 >                         // [ 1 4 7 ]
103 >                         // [ 2 5 8 ]
104 >  double FortranHmatInv[9]; // the inverted Hmat (for Fortran);
105  
106 <    rCut = rList - 1.0;
106 >  if( !boxIsInit ) boxIsInit = 1;
107  
108 <    // list radius changed so we have to refresh the simulation structure.
109 <    refreshSim();
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 <  if (rCut > maxCutoff) {
122 <    sprintf( painCave.errMsg,
123 <             "New Box size is forcing cutoff radius down to %lf\n",
124 <             maxCutoff );
76 <    painCave.isFatal = 0;
77 <    simError();
121 >  setFortranBoxSize(FortranHmat, FortranHmatInv, &orthoRhombic);
122 >
123 > }
124 >
125  
126 <    status = 0;
127 <    LJ_new_rcut(&rCut, &status);
128 <    if (status != 0) {
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 oldOrtho;
150 >  int i,j;
151 >  double smallDiag;
152 >  double tol;
153 >  double sanity[3][3];
154 >
155 >  invertMat3( Hmat, HmatInv );
156 >
157 >  // check to see if Hmat is orthorhombic
158 >  
159 >  oldOrtho = orthoRhombic;
160 >
161 >  smallDiag = fabs(Hmat[0][0]);
162 >  if(smallDiag > fabs(Hmat[1][1])) smallDiag = fabs(Hmat[1][1]);
163 >  if(smallDiag > fabs(Hmat[2][2])) smallDiag = fabs(Hmat[2][2]);
164 >  tol = smallDiag * orthoTolerance;
165 >
166 >  orthoRhombic = 1;
167 >  
168 >  for (i = 0; i < 3; i++ ) {
169 >    for (j = 0 ; j < 3; j++) {
170 >      if (i != j) {
171 >        if (orthoRhombic) {
172 >          if ( fabs(Hmat[i][j]) >= tol) orthoRhombic = 0;
173 >        }        
174 >      }
175 >    }
176 >  }
177 >
178 >  if( oldOrtho != orthoRhombic ){
179 >    
180 >    if( orthoRhombic ){
181        sprintf( painCave.errMsg,
182 <               "Error in recomputing LJ shifts based on new rcut\n");
183 <      painCave.isFatal = 1;
182 >               "Hmat is switching from Non-Orthorhombic to OrthoRhombic\n"
183 >               "       If this is a bad thing, change the orthoBoxTolerance( currently %G ).\n",
184 >               orthoTolerance);
185        simError();
186      }
187 +    else {
188 +      sprintf( painCave.errMsg,
189 +               "Hmat is switching from Orthorhombic to Non-OrthoRhombic\n"
190 +               "       If this is a bad thing, change the orthoBoxTolerance( currently %G ).\n",
191 +               orthoTolerance);
192 +      simError();
193 +    }
194    }
195   }
196  
197 < void SimInfo::getBox(double theBox[3]) {
198 <  theBox[0] = box_x;
199 <  theBox[1] = box_y;
200 <  theBox[2] = box_z;
197 > double SimInfo::matDet3(double a[3][3]) {
198 >  int i, j, k;
199 >  double determinant;
200 >
201 >  determinant = 0.0;
202 >
203 >  for(i = 0; i < 3; i++) {
204 >    j = (i+1)%3;
205 >    k = (i+2)%3;
206 >
207 >    determinant += a[0][i] * (a[1][j]*a[2][k] - a[1][k]*a[2][j]);
208 >  }
209 >
210 >  return determinant;
211   }
212 <
212 >
213 > void SimInfo::invertMat3(double a[3][3], double b[3][3]) {
214 >  
215 >  int  i, j, k, l, m, n;
216 >  double determinant;
217 >
218 >  determinant = matDet3( a );
219 >
220 >  if (determinant == 0.0) {
221 >    sprintf( painCave.errMsg,
222 >             "Can't invert a matrix with a zero determinant!\n");
223 >    painCave.isFatal = 1;
224 >    simError();
225 >  }
226 >
227 >  for (i=0; i < 3; i++) {
228 >    j = (i+1)%3;
229 >    k = (i+2)%3;
230 >    for(l = 0; l < 3; l++) {
231 >      m = (l+1)%3;
232 >      n = (l+2)%3;
233 >      
234 >      b[l][i] = (a[j][m]*a[k][n] - a[j][n]*a[k][m]) / determinant;
235 >    }
236 >  }
237 > }
238 >
239 > void SimInfo::matMul3(double a[3][3], double b[3][3], double c[3][3]) {
240 >  double r00, r01, r02, r10, r11, r12, r20, r21, r22;
241 >
242 >  r00 = a[0][0]*b[0][0] + a[0][1]*b[1][0] + a[0][2]*b[2][0];
243 >  r01 = a[0][0]*b[0][1] + a[0][1]*b[1][1] + a[0][2]*b[2][1];
244 >  r02 = a[0][0]*b[0][2] + a[0][1]*b[1][2] + a[0][2]*b[2][2];
245 >  
246 >  r10 = a[1][0]*b[0][0] + a[1][1]*b[1][0] + a[1][2]*b[2][0];
247 >  r11 = a[1][0]*b[0][1] + a[1][1]*b[1][1] + a[1][2]*b[2][1];
248 >  r12 = a[1][0]*b[0][2] + a[1][1]*b[1][2] + a[1][2]*b[2][2];
249 >  
250 >  r20 = a[2][0]*b[0][0] + a[2][1]*b[1][0] + a[2][2]*b[2][0];
251 >  r21 = a[2][0]*b[0][1] + a[2][1]*b[1][1] + a[2][2]*b[2][1];
252 >  r22 = a[2][0]*b[0][2] + a[2][1]*b[1][2] + a[2][2]*b[2][2];
253 >  
254 >  c[0][0] = r00; c[0][1] = r01; c[0][2] = r02;
255 >  c[1][0] = r10; c[1][1] = r11; c[1][2] = r12;
256 >  c[2][0] = r20; c[2][1] = r21; c[2][2] = r22;
257 > }
258 >
259 > void SimInfo::matVecMul3(double m[3][3], double inVec[3], double outVec[3]) {
260 >  double a0, a1, a2;
261 >
262 >  a0 = inVec[0];  a1 = inVec[1];  a2 = inVec[2];
263 >
264 >  outVec[0] = m[0][0]*a0 + m[0][1]*a1 + m[0][2]*a2;
265 >  outVec[1] = m[1][0]*a0 + m[1][1]*a1 + m[1][2]*a2;
266 >  outVec[2] = m[2][0]*a0 + m[2][1]*a1 + m[2][2]*a2;
267 > }
268 >
269 > void SimInfo::transposeMat3(double in[3][3], double out[3][3]) {
270 >  double temp[3][3];
271 >  int i, j;
272 >
273 >  for (i = 0; i < 3; i++) {
274 >    for (j = 0; j < 3; j++) {
275 >      temp[j][i] = in[i][j];
276 >    }
277 >  }
278 >  for (i = 0; i < 3; i++) {
279 >    for (j = 0; j < 3; j++) {
280 >      out[i][j] = temp[i][j];
281 >    }
282 >  }
283 > }
284 >  
285 > void SimInfo::printMat3(double A[3][3] ){
286 >
287 >  std::cerr
288 >            << "[ " << A[0][0] << ", " << A[0][1] << ", " << A[0][2] << " ]\n"
289 >            << "[ " << A[1][0] << ", " << A[1][1] << ", " << A[1][2] << " ]\n"
290 >            << "[ " << A[2][0] << ", " << A[2][1] << ", " << A[2][2] << " ]\n";
291 > }
292 >
293 > void SimInfo::printMat9(double A[9] ){
294 >
295 >  std::cerr
296 >            << "[ " << A[0] << ", " << A[1] << ", " << A[2] << " ]\n"
297 >            << "[ " << A[3] << ", " << A[4] << ", " << A[5] << " ]\n"
298 >            << "[ " << A[6] << ", " << A[7] << ", " << A[8] << " ]\n";
299 > }
300 >
301 >
302 > void SimInfo::crossProduct3(double a[3],double b[3], double out[3]){
303 >
304 >      out[0] = a[1] * b[2] - a[2] * b[1];
305 >      out[1] = a[2] * b[0] - a[0] * b[2] ;
306 >      out[2] = a[0] * b[1] - a[1] * b[0];
307 >      
308 > }
309 >
310 > double SimInfo::dotProduct3(double a[3], double b[3]){
311 >  return a[0]*b[0] + a[1]*b[1]+ a[2]*b[2];
312 > }
313 >
314 > double SimInfo::length3(double a[3]){
315 >  return sqrt(a[0]*a[0] + a[1]*a[1] + a[2]*a[2]);
316 > }
317 >
318 > void SimInfo::calcBoxL( void ){
319 >
320 >  double dx, dy, dz, dsq;
321 >
322 >  // boxVol = Determinant of Hmat
323 >
324 >  boxVol = matDet3( Hmat );
325 >
326 >  // boxLx
327 >  
328 >  dx = Hmat[0][0]; dy = Hmat[1][0]; dz = Hmat[2][0];
329 >  dsq = dx*dx + dy*dy + dz*dz;
330 >  boxL[0] = sqrt( dsq );
331 >  //maxCutoff = 0.5 * boxL[0];
332 >
333 >  // boxLy
334 >  
335 >  dx = Hmat[0][1]; dy = Hmat[1][1]; dz = Hmat[2][1];
336 >  dsq = dx*dx + dy*dy + dz*dz;
337 >  boxL[1] = sqrt( dsq );
338 >  //if( (0.5 * boxL[1]) < maxCutoff ) maxCutoff = 0.5 * boxL[1];
339 >
340 >
341 >  // boxLz
342 >  
343 >  dx = Hmat[0][2]; dy = Hmat[1][2]; dz = Hmat[2][2];
344 >  dsq = dx*dx + dy*dy + dz*dz;
345 >  boxL[2] = sqrt( dsq );
346 >  //if( (0.5 * boxL[2]) < maxCutoff ) maxCutoff = 0.5 * boxL[2];
347 >
348 >  //calculate the max cutoff
349 >  maxCutoff =  calcMaxCutOff();
350 >  
351 >  checkCutOffs();
352 >
353 > }
354 >
355 >
356 > double SimInfo::calcMaxCutOff(){
357 >
358 >  double ri[3], rj[3], rk[3];
359 >  double rij[3], rjk[3], rki[3];
360 >  double minDist;
361 >
362 >  ri[0] = Hmat[0][0];
363 >  ri[1] = Hmat[1][0];
364 >  ri[2] = Hmat[2][0];
365 >
366 >  rj[0] = Hmat[0][1];
367 >  rj[1] = Hmat[1][1];
368 >  rj[2] = Hmat[2][1];
369 >
370 >  rk[0] = Hmat[0][2];
371 >  rk[1] = Hmat[1][2];
372 >  rk[2] = Hmat[2][2];
373 >  
374 >  crossProduct3(ri,rj, rij);
375 >  distXY = dotProduct3(rk,rij) / length3(rij);
376 >
377 >  crossProduct3(rj,rk, rjk);
378 >  distYZ = dotProduct3(ri,rjk) / length3(rjk);
379 >
380 >  crossProduct3(rk,ri, rki);
381 >  distZX = dotProduct3(rj,rki) / length3(rki);
382 >
383 >  minDist = min(min(distXY, distYZ), distZX);
384 >  return minDist/2;
385 >  
386 > }
387 >
388 > void SimInfo::wrapVector( double thePos[3] ){
389 >
390 >  int i;
391 >  double scaled[3];
392 >
393 >  if( !orthoRhombic ){
394 >    // calc the scaled coordinates.
395 >  
396 >
397 >    matVecMul3(HmatInv, thePos, scaled);
398 >    
399 >    for(i=0; i<3; i++)
400 >      scaled[i] -= roundMe(scaled[i]);
401 >    
402 >    // calc the wrapped real coordinates from the wrapped scaled coordinates
403 >    
404 >    matVecMul3(Hmat, scaled, thePos);
405 >
406 >  }
407 >  else{
408 >    // calc the scaled coordinates.
409 >    
410 >    for(i=0; i<3; i++)
411 >      scaled[i] = thePos[i]*HmatInv[i][i];
412 >    
413 >    // wrap the scaled coordinates
414 >    
415 >    for(i=0; i<3; i++)
416 >      scaled[i] -= roundMe(scaled[i]);
417 >    
418 >    // calc the wrapped real coordinates from the wrapped scaled coordinates
419 >    
420 >    for(i=0; i<3; i++)
421 >      thePos[i] = scaled[i]*Hmat[i][i];
422 >  }
423 >    
424 > }
425 >
426 >
427   int SimInfo::getNDF(){
428 <  int ndf_local, ndf;
428 >  int ndf_local;
429    
430    ndf_local = 3 * n_atoms + 3 * n_oriented - n_constraints;
431  
# Line 104 | Line 435 | int SimInfo::getNDF(){
435    ndf = ndf_local;
436   #endif
437  
438 <  ndf = ndf - 3;
438 >  ndf = ndf - 3 - nZconstraints;
439  
440    return ndf;
441   }
442  
443   int SimInfo::getNDFraw() {
444 <  int ndfRaw_local, ndfRaw;
444 >  int ndfRaw_local;
445  
446    // Raw degrees of freedom that we have to set
447    ndfRaw_local = 3 * n_atoms + 3 * n_oriented;
# Line 123 | Line 454 | int SimInfo::getNDFraw() {
454  
455    return ndfRaw;
456   }
457 <
457 >
458 > int SimInfo::getNDFtranslational() {
459 >  int ndfTrans_local;
460 >
461 >  ndfTrans_local = 3 * n_atoms - n_constraints;
462 >
463 > #ifdef IS_MPI
464 >  MPI_Allreduce(&ndfTrans_local,&ndfTrans,1,MPI_INT,MPI_SUM, MPI_COMM_WORLD);
465 > #else
466 >  ndfTrans = ndfTrans_local;
467 > #endif
468 >
469 >  ndfTrans = ndfTrans - 3 - nZconstraints;
470 >
471 >  return ndfTrans;
472 > }
473 >
474   void SimInfo::refreshSim(){
475  
476    simtype fInfo;
477    int isError;
478 +  int n_global;
479    int* excl;
480 <  
133 <  fInfo.rrf = 0.0;
134 <  fInfo.rt = 0.0;
480 >
481    fInfo.dielect = 0.0;
482  
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 –
483    if( useDipole ){
145 –    fInfo.rrf = ecr;
146 –    fInfo.rt = ecr - est;
484      if( useReactionField )fInfo.dielect = dielectric;
485    }
486  
# Line 161 | Line 498 | void SimInfo::refreshSim(){
498  
499    excl = Exclude::getArray();
500  
501 + #ifdef IS_MPI
502 +  n_global = mpiSim->getTotAtoms();
503 + #else
504 +  n_global = n_atoms;
505 + #endif
506 +
507    isError = 0;
508  
509 < //   fInfo;
510 < //   n_atoms;
511 < //   identArray;
169 < //   n_exclude;
170 < //   excludes;
171 < //   nGlobalExcludes;
172 < //   globalExcludes;
173 < //   isError;
509 >  setFsimulation( &fInfo, &n_global, &n_atoms, identArray, &n_exclude, excl,
510 >                  &nGlobalExcludes, globalExcludes, molMembershipArray,
511 >                  &isError );
512  
175 –  setFsimulation( &fInfo, &n_atoms, identArray, &n_exclude, excl,
176 –                  &nGlobalExcludes, globalExcludes, &isError );
177 –
513    if( isError ){
514  
515      sprintf( painCave.errMsg,
# Line 191 | Line 526 | void SimInfo::refreshSim(){
526  
527    this->ndf = this->getNDF();
528    this->ndfRaw = this->getNDFraw();
529 +  this->ndfTrans = this->getNDFtranslational();
530 + }
531  
532 + void SimInfo::setDefaultRcut( double theRcut ){
533 +
534 +  haveRcut = 1;
535 +  rCut = theRcut;
536 +
537 +  ( rCut > ecr )? rList = rCut + 1.0: rList = ecr + 1.0;
538 +
539 +  notifyFortranCutOffs( &rCut, &rList, &ecr, &est );
540   }
541  
542 + void SimInfo::setDefaultEcr( double theEcr ){
543 +
544 +  haveEcr = 1;
545 +  ecr = theEcr;
546 +  
547 +  ( rCut > ecr )? rList = rCut + 1.0: rList = ecr + 1.0;
548 +
549 +  notifyFortranCutOffs( &rCut, &rList, &ecr, &est );
550 + }
551 +
552 + void SimInfo::setDefaultEcr( double theEcr, double theEst ){
553 +
554 +  est = theEst;
555 +  setDefaultEcr( theEcr );
556 + }
557 +
558 +
559 + void SimInfo::checkCutOffs( void ){
560 +  
561 +  if( boxIsInit ){
562 +    
563 +    //we need to check cutOffs against the box
564 +    
565 +    if( rCut > maxCutoff ){
566 +      sprintf( painCave.errMsg,
567 +               "Box size is too small for the long range cutoff radius, "
568 +               "%lf, at time %lf\n",
569 +               rCut, currentTime );
570 +      painCave.isFatal = 1;
571 +      simError();
572 +    }
573 +    
574 +    if( haveEcr ){
575 +      if( ecr > maxCutoff ){
576 +        sprintf( painCave.errMsg,
577 +                 "Box size is too small for the electrostatic cutoff radius, "
578 +                 "%lf, at time %lf\n",
579 +                 ecr, currentTime );
580 +        painCave.isFatal = 1;
581 +        simError();
582 +      }
583 +    }
584 +  } else {
585 +    // initialize this stuff before using it, OK?
586 +    sprintf( painCave.errMsg,
587 +             "Trying to check cutoffs without a box. Be smarter.\n" );
588 +    painCave.isFatal = 1;
589 +    simError();      
590 +  }
591 +  
592 + }
593 +
594 + void SimInfo::addProperty(GenericData* prop){
595 +
596 +  map<string, GenericData*>::iterator result;
597 +  result = properties.find(prop->getID());
598 +  
599 +  //we can't simply use  properties[prop->getID()] = prop,
600 +  //it will cause memory leak if we already contain a propery which has the same name of prop
601 +  
602 +  if(result != properties.end()){
603 +    
604 +    delete (*result).second;
605 +    (*result).second = prop;
606 +      
607 +  }
608 +  else{
609 +
610 +    properties[prop->getID()] = prop;
611 +
612 +  }
613 +    
614 + }
615 +
616 + GenericData* SimInfo::getProperty(const string& propName){
617 +
618 +  map<string, GenericData*>::iterator result;
619 +  
620 +  //string lowerCaseName = ();
621 +  
622 +  result = properties.find(propName);
623 +  
624 +  if(result != properties.end())
625 +    return (*result).second;  
626 +  else  
627 +    return NULL;  
628 + }
629 +
630 + vector<GenericData*> SimInfo::getProperties(){
631 +
632 +  vector<GenericData*> result;
633 +  map<string, GenericData*>::iterator i;
634 +  
635 +  for(i = properties.begin(); i != properties.end(); i++)
636 +    result.push_back((*i).second);
637 +    
638 +  return result;
639 + }
640 +
641 + double SimInfo::matTrace3(double m[3][3]){
642 +  double trace;
643 +  trace = m[0][0] + m[1][1] + m[2][2];
644 +
645 +  return trace;
646 + }

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