Actual source code: combustion3.c

  1: /*$Id: combustion.c,v 1.1 2002/08/08 9:39 lopezca@mauddib.mcs.anl.gov $*/

  3: /* Program usage: mpirun -np <proc> combustion [-help] [all TAO options] */

  5: /*
  6:   Include "tao.h" so we can use TAO solvers.
  7:   petscda.h for distributed array
  8:   ad_deriv.h for AD gradient
  9: */

 11: #include "petscda.h"
 12:  #include tao.h
 13:  #include taodaapplication.h

 15: static char help[] = "Steady-State Combustion.\n\
 16: We solve the Steady-State Combustion problem (MINPACK-2 test suite) in a 2D\n\
 17: rectangular domain, using distributed arrays (DAs) to partition the parallel grid.\n\
 18: The command line options include:\n\
 19:   -mx <xg>, where <xg> = number of grid points in the 1st coordinate direction\n\
 20:   -my <yg>, where <yg> = number of grid points in the 2nd coordinate direction\n\
 21:   -nlevels <nlevels>, where <nlevels> = number of levels in multigrid\n\
 22:   -byelement, if computation is made by functions on rectangular elements\n\
 23:   -adic, if AD is used (AD is not used by default)\n\
 24:   -par <parameter>, where <parameter> indicates the problem's nonlinearity\n\
 25:      parameter lambda (0 <= par <= 6.81)\n\n";

 27: /*T
 28:    Concepts: TAO - Solving a bounded minimization problem
 29:    Routines: TaoInitialize(); TaoFinalize();
 30:    Routines: TaoCreate(); TaoDestroy();
 31:    Routines: DAApplicationCreate(); DAApplicationDestroy();
 32:    Routines: DAAppSetVariableBoundsRoutine();
 33:    Routines: DAAppSetElementObjectiveAndGradientRoutine();
 34:    Routines: DAAppSetElementHessianRoutine();
 35:    Routines: DAAppSetObjectiveAndGradientRoutine();
 36:    Routines: DAAppSetADElementFunctionGradient();
 37:    Routines: DAAppSetHessianRoutine();
 38:    Routines: TaoAppSetOptions();
 39:    Routines: TaoGetSolutionStatus(); TaoDAAppSolve();
 40:    Routines: DAAppSetMonitor(); TaoView();
 41:    Routines: DAAppGetSolution();
 42:    Routines: DAAppGetInterpolationMatrix();
 43:    Processors: n
 44: T*/

 46: /*
 47:    User-defined application context - contains data needed by the
 48:    application-provided call-back routines.
 49: */

 51: typedef struct {
 52:   InactiveDouble      param;
 53:   InactiveDouble      hx, hy;        /* increment size in both directions */
 54:   InactiveDouble      area;          /* area of the triangles */
 55: } ADFGCtx;

 57: typedef struct {
 58:   PetscReal  param;          /* nonlinearity parameter */
 59:   double  hx, hy, area;   /* increments and area of the triangle */
 60:   int     mx, my;         /* discretization including boundaries */
 61:   ADFGCtx fgctx;          /* Used only when an ADIC generated gradient is used */
 62: } AppCtx;
 63: int ad_CombLocalFunction(int[2], DERIV_TYPE[4], DERIV_TYPE*, void*);

 65: /* User-defined routines foun in this file */
 66: static int AppCtxInitialize(void *ptr);
 67: static int FormInitialGuess(DA, Vec, AppCtx*);

 69: static int CombLocalFunctionGradient(int[3], double x[4], double *f, double g[4], void *ptr);
 70: static int WholeCombFunctionGradient(TAO_APPLICATION,DA,Vec,double *,Vec,void*);

 72: static int CombLocalHessian(int[3], double x[4], double H[4][4], void *ptr);
 73: static int WholeCombHessian(TAO_APPLICATION,DA,Vec,Mat,void*);

 75: static int DAFixBoundary(TAO_APPLICATION, DA, Vec, Vec, void*);

 77: static int MyGridMonitorBefore(TAO_APPLICATION, DA, int, void *);


 82: int main( int argc, char **argv ) {

 84:   int             info,iter;           /* used to check for functions returning nonzeros */
 85:   int             Nx,Ny;
 86:   int             nlevels;                                           /* multigrid levels */
 87:   double          ff,gnorm;
 88:   DA              DAarray[20];
 89:   Vec             X;
 90:   PetscTruth      flg, PreLoad = PETSC_TRUE;                                    /* flags */
 91:   AppCtx          user;                                     /* user-defined work context */
 92:   TaoMethod       method = "tao_tron";                            /* minimization method */
 93:   TAO_SOLVER      tao;                                      /* TAO_SOLVER solver context */
 94:   TAO_APPLICATION CombApp;                                   /* The PETSc application */
 95:   TaoTerminateReason reason;

 97:   /* Initialize TAO */
 98:   PetscInitialize(&argc, &argv, (char *)0, help);
 99:   TaoInitialize(&argc, &argv, (char *)0, help);

101:   PreLoadBegin(PreLoad,"Solve");
102: 
103:   info = AppCtxInitialize((void*)&user); CHKERRQ(info);

105:   nlevels=5;
106:   info = PetscOptionsGetInt(PETSC_NULL,"-nlevels",&nlevels,&flg); CHKERRQ(info);
107:   if (PreLoadIt == 0) {
108:     nlevels = 1; user.mx = 11; user.my = 11;}

110:   PetscPrintf(MPI_COMM_WORLD,"\n---- Steady-State Combustion Problem -----\n\n");

112:   /* Let PETSc determine the vector distribution */
113:   Nx = PETSC_DECIDE; Ny = PETSC_DECIDE;

115:   /* Create distributed array (DA) to manage parallel grid and vectors  */
116:   info = DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_BOX,user.mx,
117:                     user.my,Nx,Ny,1,1,PETSC_NULL,PETSC_NULL,&DAarray[0]); CHKERRQ(info);
118:   for (iter=1;iter<nlevels;iter++){
119:     info = DARefine(DAarray[iter-1],PETSC_COMM_WORLD,&DAarray[iter]); CHKERRQ(info);
120:   }

122:   /* Create TAO solver and set desired solution method */
123:   info = TaoCreate(MPI_COMM_WORLD,method,&tao); CHKERRQ(info);

125:   info = TaoApplicationCreate(PETSC_COMM_WORLD, &CombApp); CHKERRQ(info);
126:   info = TaoAppSetDAApp(CombApp,DAarray,nlevels); CHKERRQ(info);

128:   /* Sets routines for function, gradient and bounds evaluation */
129:   info = DAAppSetVariableBoundsRoutine(CombApp,DAFixBoundary,(void *)&user); CHKERRQ(info);

131:   info = PetscOptionsHasName(TAO_NULL, "-byelement", &flg); CHKERRQ(info);
132:   if (flg) {

134:     /* Sets routines for function and gradient evaluation, element by element */
135:     info = PetscOptionsHasName(TAO_NULL, "-adic", &flg); CHKERRQ(info);
136:     if (flg) {
137:       info = DAAppSetADElementFunctionGradient(CombApp,ad_CombLocalFunction,228,(void *)&user.fgctx); CHKERRQ(info);
138:     } else {
139:       info = DAAppSetElementObjectiveAndGradientRoutine(CombApp,CombLocalFunctionGradient,51,(void *)&user); CHKERRQ(info);
140:     }
141:     /* Sets routines for Hessian evaluation, element by element */
142:     info = DAAppSetElementHessianRoutine(CombApp,CombLocalHessian,21,(void*)&user); CHKERRQ(info);

144:   } else {

146:     /* Sets routines for function and gradient evaluation, all in one routine */
147:     info = DAAppSetObjectiveAndGradientRoutine(CombApp,WholeCombFunctionGradient,(void *)&user); CHKERRQ(info);

149:     /* Sets routines for Hessian evaluation, all in one routine */
150:     info = DAAppSetHessianRoutine(CombApp,WholeCombHessian,(void*)&user); CHKERRQ(info);
151: 
152:   }

154:   info = DAAppSetBeforeMonitor(CombApp,MyGridMonitorBefore,(void*)&user); CHKERRQ(info);
155:   info = DAAppPrintStageTimes(CombApp); CHKERRQ(info);
156:   info = DAAppPrintInterpolationError(CombApp); CHKERRQ(info);

158:   info = TaoAppSetRelativeTolerance(CombApp,1.0e-8); CHKERRQ(info);
159:   info = TaoSetTolerances(tao,0,0,0,0); CHKERRQ(info);
160:   info = TaoSetGradientTolerances(tao,0,0,0); CHKERRQ(info);

162:   /* Check for any tao command line options */
163:   info = TaoSetOptions(CombApp, tao); CHKERRQ(info);

165:   info = DAAppGetSolution(CombApp,0,&X); CHKERRQ(info);
166:   info = FormInitialGuess(DAarray[0],X,&user); CHKERRQ(info);
167:   info = DAAppSetInitialSolution(CombApp,X); CHKERRQ(info);

169:   /* SOLVE THE APPLICATION */
170:   info = TaoDAAppSolve(CombApp, tao);  CHKERRQ(info);

172:   /* Get information on termination */
173:   info = TaoGetSolutionStatus(tao,&iter,&ff,&gnorm,0,0,&reason); CHKERRQ(info);
174:   if (reason <= 0 ){
175:     PetscPrintf(MPI_COMM_WORLD,"Try a different TAO method, adjust some parameters, or check the function evaluation routines\n");
176:     PetscPrintf(MPI_COMM_WORLD," Iterations: %d,  Function Value: %4.2e, Residual: %4.2e \n",iter,ff,gnorm);
177:   }

179:   info = PetscOptionsHasName(PETSC_NULL,"-view_sol",&flg); CHKERRQ(info);
180:   if (flg){
181:     info = DAAppGetSolution(CombApp,nlevels-1,&X); CHKERRQ(info);
182:     info=VecView(X,PETSC_VIEWER_STDOUT_WORLD); CHKERRQ(info);
183:   }

185:   /*  To View TAO solver information */
186:   // info = TaoView(tao); CHKERRQ(info);

188:   /* Free TAO data structures */
189:   info = TaoDestroy(tao); CHKERRQ(info);
190:   info = TaoAppDestroy(CombApp); CHKERRQ(info);

192:   /* Free PETSc data structures */
193:   for (iter=0;iter<nlevels;iter++){
194:     info = DADestroy(DAarray[iter]); CHKERRQ(info);
195:   }

197:   PreLoadEnd();

199:   /* Finalize TAO */
200:   TaoFinalize();
201:   PetscFinalize();

203:   return 0;
204: } /* main */



208: /*----- The following two routines
209:    
210:   MyGridMonitorBefore    MyGridMonitorAfter

212:   help diplay info of iterations at every grid level -------*/

216: static int MyGridMonitorBefore(TAO_APPLICATION myapp, DA da, int level, void *ctx) {

218:   AppCtx *user = (AppCtx*)ctx;
219:   int info,mx,my;

221:   info = DAGetInfo(da,PETSC_NULL,&mx,&my,PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL,
222:                    PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL);CHKERRQ(info);
223:   user->mx = mx;
224:   user->my = my;
225:   user->hx = 1.0 / (user->mx - 1);
226:   user->hy = 1.0 / (user->my - 1);
227:   user->area = 0.5 * user->hx * user->hy;
228:   user->fgctx.hx   = user->hx;
229:   user->fgctx.hy   = user->hy;
230:   user->fgctx.area = user->area;
231:   user->fgctx.param = user->param;

233:   PetscPrintf(MPI_COMM_WORLD,"Grid: %d,    mx: %d     my: %d   \n",level,mx,my);

235:   return 0;
236: }

238: /*------- USER-DEFINED: initialize the application context information -------*/

242: /*
243:   AppCtxInitialize - Sets initial values for the application context parameters

245:   Input:
246:     ptr - void user-defined application context

248:   Output:
249:     ptr - user-defined application context with the default or user-provided
250:              parameters
251: */
252: static int AppCtxInitialize(void *ptr) {

254:   AppCtx *user = (AppCtx*)ptr;
255:   PetscReal     LambdaMax = 6.81, LambdaMin = 0.0;  /* bounds on parameter lambda */
256:   PetscTruth    flg;            /* flag for PETSc calls */
257:   int info;

259:   /* Specify dimension of the problem */
260:   user->param = 5.0;
261:   user->mx = 11;
262:   user->my = 11;

264:   /* Check for any command line arguments that override defaults */
265:   info = PetscOptionsGetReal(TAO_NULL, "-par", &user->param, &flg); CHKERRQ(info);
266:   if (user->param >= LambdaMax || user->param <= LambdaMin) {
267:     SETERRQ(1,"Lambda is out of range.");
268:   }
269:   info = PetscOptionsGetInt(PETSC_NULL,"-mx",&user->mx,&flg); CHKERRQ(info);
270:   info = PetscOptionsGetInt(PETSC_NULL,"-my",&user->my,&flg); CHKERRQ(info);

272:   user->hx = 1.0 / (user->mx - 1);
273:   user->hy = 1.0 / (user->my - 1);
274:   user->area = 0.5 * user->hx * user->hy;
275:   info = PetscLogFlops(6); CHKERRQ(info);

277:   return 0;
278: } /* AppCtxInitialize */



284: static int FormInitialGuess(DA da, Vec X, AppCtx *ctx)
285: {
286:   int    info, i, j, mx, my;
287:   int    xs, ys, xm, ym, xe, ye;
288:   PetscReal hx, hy, temp, val, lambda;
289:   double **x;

291:   lambda = ctx->param;
292:   lambda = lambda/(lambda+1.0);

294:   /* Get local mesh boundaries */
295:   info = DAGetInfo(da,PETSC_NULL,&mx,&my,PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL,
296:                    PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL);CHKERRQ(info);
297:   hx = 1.0/(mx-1);  hy = 1.0/(my-1);

299:   info = DAGetCorners(da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL); CHKERRQ(info);
300:   xe = xs+xm; ye = ys+ym;

302:   info = DAVecGetArray(da, X, (void**)&x); CHKERRQ(info);
303:   /* Compute initial guess over locally owned part of mesh */
304:   for (j=ys; j<ye; j++) {  /*  for (j=0; j<my; j++) */
305:     temp = PetscMin(j+1,my-j)*hy;
306:     for (i=xs; i<xe; i++) {  /*  for (i=0; i<mx; i++) */
307:       val = lambda*sqrt(PetscMin((PetscMin(i+1,mx-i))*hx,temp));
308:       x[j][i] = val;
309:     }
310:   }
311:   info = DAVecRestoreArray(da, X, (void**)&x); CHKERRQ(info);

313:   return 0;
314: }


317: /*------- USER-DEFINED: set the upper and lower bounds for the variables  -------*/

321: /*
322:   FormBounds - Forms bounds on the variables

324:   Input:
325:     user - user-defined application context

327:   Output:
328:     XL - vector of lower bounds
329:     XU - vector of upper bounds

331: */
332: static int DAFixBoundary(TAO_APPLICATION daapplication, DA da, Vec XL, Vec XU, void *ptr)
333: {
334:   AppCtx *user = (AppCtx*)ptr;
335:   int i, j, mx, my, info, xs, xm, ys, ym;
336:   double lb = -TAO_INFINITY;
337:   double ub = TAO_INFINITY;
338:   double **xl, **xu;

340:   mx = user->mx;  /* number of points including the boundary */
341:   my = user->my;

343:   info = DAVecGetArray(da, XL, (void**)&xl); CHKERRQ(info);
344:   info = DAVecGetArray(da, XU, (void**)&xu); CHKERRQ(info);
345:   info = DAGetCorners(da, &xs, &ys, TAO_NULL, &xm, &ym, TAO_NULL); CHKERRQ(info);

347:   /* Compute initial guess over locally owned part of the grid */
348:   for (j = ys; j < ys+ym; j++){
349:     for (i = xs; i < xs+xm; i++){
350:       if (i == 0 || j == 0 || i == mx - 1 || j == my - 1) {
351:         xl[j][i] = xu[j][i] = 0.0;
352:       } else {
353:         xl[j][i] = lb;
354:         xu[j][i] = ub;
355:       }
356:     }
357:   }

359:   info = DAVecRestoreArray(da, XL, (void**)&xl); CHKERRQ(info);
360:   info = DAVecRestoreArray(da, XU, (void**)&xu); CHKERRQ(info);

362:   return 0;
363: } /* DAFixBoundary */


366: /*------- USER-DEFINED: routine to evaluate the function and gradient
367:            at a local (rectangular element) level              -------*/

371: /*
372:   CombLocalFunctionGradient - Evaluates function and gradient over the 
373:       local rectangular element

375:   Input:
376:     coor - vector with the indices of the position of current element
377:              in the first, second and third directions
378:     x - current point (values over the current rectangular element)
379:     ptr - user-defined application context

381:   Output:
382:     f - value of the objective funtion at the local rectangular element
383:     g - gradient of the local function

385: */
386: static int CombLocalFunctionGradient(int coor[2], double x[4], double *f, double g[4], void *ptr) {

388:   AppCtx *user = (AppCtx*)ptr;

390:   double lambdad3, hx, hy, area;
391:   double fquad, fexp, dvdx, dvdy;

393:   lambdad3 = user->param / 3.0;
394:   hx = user->hx;
395:   hy = user->hy;
396:   area = user->area;

398:   /* lower triangle contribution */
399:   dvdx = (x[0] - x[1]) / hx;
400:   dvdy = (x[0] - x[2]) / hy;
401:   fquad = dvdx * dvdx + dvdy * dvdy;
402:   fexp = exp(x[0]) + exp(x[1]) + exp(x[2]);

404:   dvdx = 0.5 * dvdx * hy;
405:   dvdy = 0.5 * dvdy * hx;
406:   g[0] = dvdx + dvdy - exp(x[0]) * area * lambdad3;
407:   g[1] = -dvdx - 2.0 * exp(x[1]) * area * lambdad3;
408:   g[2] = -dvdy - 2.0 * exp(x[2]) * area * lambdad3;

410:   /* upper triangle contribution */
411:   dvdx = (x[3] - x[2]) / hx;
412:   dvdy = (x[3] - x[1]) / hy;
413:   fquad += dvdx * dvdx + dvdy * dvdy;
414:   fexp += exp(x[1]) + exp(x[2]) + exp(x[3]);

416:   dvdx = 0.5 * dvdx * hy;
417:   dvdy = 0.5 * dvdy * hx;
418:   g[1] += -dvdy;
419:   g[2] += -dvdx;
420:   g[3] = dvdx + dvdy - exp(x[3]) * area * lambdad3;


423:   *f = area * (0.5 * fquad - lambdad3 * fexp);

425:   return 0;
426: } /* CombLocalFunctionGradient */


429: /*------- USER-DEFINED: routine to evaluate the Hessian
430:            at a local (rectangular element) level       -------*/

434: /*
435:   CombLocalHessian - Computes the Hessian of the local (partial) function
436:          defined over the current rectangle

438:   Input:
439:     coor - vector with the indices of the position of current element
440:              in the first, second and third directions
441:     x - current local solution (over the rectangle only)
442:     ptr - user-defined application context

444:   Output:
445:     H - Hessian matrix of the local function (wrt the four
446:            points of the rectangle only)

448: */
449: static int CombLocalHessian(int coor[2], double x[4], double H[4][4],void *ptr) {

451:   AppCtx *user = (AppCtx*)ptr;
452:   double hx, hy, lambdad3, area, dxdy, dydx;
453:   double diagxy, dexp, bandxy, bandyx;

455:   hx = user->hx;
456:   hy = user->hy;
457:   lambdad3 = user->param / 3.0;
458:   area = user->area;
459:   dxdy = hx/hy;
460:   dydx = hy/hx;
461:   diagxy = 0.5 * (dxdy + dydx);
462:   bandxy = -0.5 * dxdy;
463:   bandyx = -0.5 * dydx;

465:           /* Hessian contribution at 0,0 */
466:   dexp = exp(x[0]) * area * lambdad3;
467:   H[0][0] = diagxy - dexp;
468:   H[0][1] = H[1][0] = bandyx;
469:   H[0][2] = H[2][0] = bandxy;
470:   H[0][3] = H[3][0] = 0.0;

472:           /* Hessian contribution at 1,0 */
473:   dexp = exp(x[1]) * area * 2.0 * lambdad3;
474:   H[1][1] = diagxy - dexp;
475:   H[1][2] = H[2][1] = 0.0;
476:   H[1][3] = H[3][1] = bandxy;

478:           /* Hessian contribution at 0,1 */
479:   dexp = exp(x[2]) * area * 2.0 * lambdad3;
480:   H[2][2] = diagxy - dexp;
481:   H[2][3] = H[3][2] = bandyx;

483:           /* Hessian contribution at 1,1 */
484:   dexp = exp(x[3]) * area * lambdad3;
485:   H[3][3] = diagxy - dexp;

487:   return 0;
488: } /* CombLocalHessian */


491: /*------- USER-DEFINED: routine to evaluate the function 
492:           and gradient at the whole grid             -------*/

496: /*
497:   WholeCombFunctionGradient - Evaluates function and gradient over the 
498:       whole grid

500:   Input:
501:     daapplication - TAO application object
502:     da  - distributed array
503:     X   - the current point, at which the function and gradient are evaluated
504:     ptr - user-defined application context

506:   Output:
507:     f - value of the objective funtion at X
508:     G - gradient at X
509: */
510: static int WholeCombFunctionGradient(TAO_APPLICATION daapplication, DA da, Vec X, double *f, Vec G, void *ptr) {

512:   AppCtx *user = (AppCtx*)ptr;
513:   Vec localX, localG;
514:   int info, i, j;
515:   int xs, xm, gxs, gxm, xe, ys, ym, gys, gym, ye;
516:   double **x, **g;
517:   double floc = 0.0;
518:   PetscScalar zero = 0.0;

520:   double lambdad3, hx, hy, area;
521:   double fquad, fexp, dvdx, dvdy;

523:   lambdad3 = user->param / 3.0;
524:   hx = user->hx;
525:   hy = user->hy;
526:   area = user->area;

528:   info = DAGetLocalVector(da, &localX); CHKERRQ(info);
529:   info = DAGetLocalVector(da, &localG); CHKERRQ(info);
530:   info = VecSet(G, zero); CHKERRQ(info);
531:   info = VecSet(localG, zero); CHKERRQ(info);

533:   info = DAGlobalToLocalBegin(da, X, INSERT_VALUES, localX); CHKERRQ(info);
534:   info = DAGlobalToLocalEnd(da, X, INSERT_VALUES, localX); CHKERRQ(info);

536:   info = DAVecGetArray(da, localX, (void**)&x); CHKERRQ(info);
537:   info = DAVecGetArray(da, localG, (void**)&g); CHKERRQ(info);

539:   info = DAGetCorners(da, &xs, &ys, TAO_NULL, &xm, &ym, TAO_NULL); CHKERRQ(info);
540:   info = DAGetGhostCorners(da, &gxs, &gys, TAO_NULL, &gxm, &gym, TAO_NULL); CHKERRQ(info);

542:   xe = gxs + gxm - 1;
543:   ye = gys + gym - 1;
544:   for (j = ys; j < ye; j++) {
545:     for (i = xs; i < xe; i++) {

547:       /* lower triangle contribution */
548:       dvdx = (x[j][i] - x[j][i+1]) / hx;
549:       dvdy = (x[j][i] - x[j+1][i]) / hy;
550:       fquad = dvdx * dvdx + dvdy * dvdy;
551:       fexp = exp(x[j][i]) + exp(x[j][i+1]) + exp(x[j+1][i]);

553:       dvdx = 0.5 * dvdx * hy;
554:       dvdy = 0.5 * dvdy * hx;
555:       g[j][i] += dvdx + dvdy - exp(x[j][i]) * area * lambdad3;
556:       g[j][i+1] += -dvdx - 2.0 * exp(x[j][i+1]) * area * lambdad3;
557:       g[j+1][i] += -dvdy - 2.0 * exp(x[j+1][i]) * area * lambdad3;

559:       /* upper triangle contribution */
560:       dvdx = (x[j+1][i+1] - x[j+1][i]) / hx;
561:       dvdy = (x[j+1][i+1] - x[j][i+1]) / hy;
562:       fquad += dvdx * dvdx + dvdy * dvdy;
563:       fexp += exp(x[j][i+1]) + exp(x[j+1][i]) + exp(x[j+1][i+1]);

565:       dvdx = 0.5 * dvdx * hy;
566:       dvdy = 0.5 * dvdy * hx;
567:       g[j][i+1] += -dvdy;
568:       g[j+1][i] += -dvdx;
569:       g[j+1][i+1] += dvdx + dvdy - exp(x[j+1][i+1]) * area * lambdad3;

571:       floc += area * (0.5 * fquad - fexp * lambdad3);

573:     }
574:   }

576:   info = MPI_Allreduce(&floc, f, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD); CHKERRQ(info);

578:   info = DAVecRestoreArray(da, localX, (void**)&x); CHKERRQ(info);
579:   info = DAVecRestoreArray(da, localG, (void**)&g); CHKERRQ(info);

581:   info = DALocalToGlobalBegin(da, localG, G); CHKERRQ(info);
582:   info = DALocalToGlobalEnd(da, localG, G); CHKERRQ(info);

584:   info = DARestoreLocalVector(da, &localX); CHKERRQ(info);
585:   info = DARestoreLocalVector(da, &localG); CHKERRQ(info);

587:   info = PetscLogFlops((xe-xs) * (ye-ys) * 55 + 1); CHKERRQ(info);
588:   return 0;

590: } /* WholeCombFunctionGradient */


593: /*------- USER-DEFINED: routine to evaluate the Hessian 
594:           at the whole grid             -------*/
597: /*
598:   WholeCombHessian - Evaluates Hessian over the whole grid

600:   Input:
601:     daapplication - TAO application object
602:     da  - distributed array
603:     X   - the current point, at which the function and gradient are evaluated
604:     ptr - user-defined application context

606:   Output:
607:     H - Hessian at X
608: */
609: static int WholeCombHessian(TAO_APPLICATION daapplication, DA da, Vec X, Mat H, void *ptr) {

611:   AppCtx *user = (AppCtx*)ptr;
612:   Vec localX;
613:   int info, i, j, ind[4];
614:   int xs, xm, gxs, gxm, xe, ys, ym, gys, gym, ye;
615:   double smallH[4][4];
616:   double **x;

618:   double hx, hy, lambdad3, area, dxdy, dydx;
619:   double diagxy, dexp, bandxy, bandyx;
620:   PetscTruth assembled;


623:   hx = user->hx;
624:   hy = user->hy;
625:   lambdad3 = user->param / 3.0;
626:   area = user->area;
627:   dxdy = hx/hy;
628:   dydx = hy/hx;
629:   diagxy = 0.5 * (dxdy + dydx);
630:   bandxy = -0.5 * dxdy;
631:   bandyx = -0.5 * dydx;

633:   info = DAGetLocalVector(da, &localX); CHKERRQ(info);
634:   info = MatAssembled(H,&assembled); CHKERRQ(info);
635:   if (assembled){info = MatZeroEntries(H);  CHKERRQ(info);}

637:   info = DAGlobalToLocalBegin(da, X, INSERT_VALUES, localX); CHKERRQ(info);
638:   info = DAGlobalToLocalEnd(da, X, INSERT_VALUES, localX); CHKERRQ(info);

640:   info = DAVecGetArray(da, localX, (void**)&x); CHKERRQ(info);

642:   info = DAGetCorners(da, &xs, &ys, TAO_NULL, &xm, &ym, TAO_NULL); CHKERRQ(info);
643:   info = DAGetGhostCorners(da, &gxs, &gys, TAO_NULL, &gxm, &gym, TAO_NULL); CHKERRQ(info);

645:   xe = gxs + gxm - 1;
646:   ye = gys + gym - 1;
647:   for (j = ys; j < ye; j++) {
648:     for (i = xs; i < xe; i++) {

650:           /* Hessian contribution at 0,0 */
651:       dexp = exp(x[j][i]) * area * lambdad3;
652:       smallH[0][0] = diagxy - dexp;
653:       smallH[0][1] = smallH[1][0] = bandyx;
654:       smallH[0][2] = smallH[2][0] = bandxy;
655:       smallH[0][3] = smallH[3][0] = 0.0;

657:           /* Hessian contribution at 1,0 */
658:       dexp = exp(x[j][i+1]) * area * 2.0 * lambdad3;
659:       smallH[1][1] = diagxy - dexp;
660:       smallH[1][2] = smallH[2][1] = 0.0;
661:       smallH[1][3] = smallH[3][1] = bandxy;

663:           /* Hessian contribution at 0,1 */
664:       dexp = exp(x[j+1][i]) * area * 2.0 * lambdad3;
665:       smallH[2][2] = diagxy - dexp;
666:       smallH[2][3] = smallH[3][2] = bandyx;

668:           /* Hessian contribution at 1,1 */
669:       dexp = exp(x[j+1][i+1]) * area * lambdad3;
670:       smallH[3][3] = diagxy - dexp;

672:       ind[0] = (j-gys) * gxm + (i-gxs);
673:       ind[1] = ind[0] + 1;
674:       ind[2] = ind[0] + gxm;
675:       ind[3] = ind[2] + 1;
676:       info = MatSetValuesLocal(H,4,ind,4,ind,(PetscScalar*)smallH,ADD_VALUES); CHKERRQ(info);

678:     }
679:   }

681:   info = DAVecRestoreArray(da, localX, (void**)&x); CHKERRQ(info);

683:   info = MatAssemblyBegin(H, MAT_FINAL_ASSEMBLY); CHKERRQ(info);
684:   info = MatAssemblyEnd(H, MAT_FINAL_ASSEMBLY); CHKERRQ(info);
685:   info = MatSetOption(H, MAT_SYMMETRIC); CHKERRQ(info);

687:   info = DARestoreLocalVector(da, &localX); CHKERRQ(info);

689:   info = PetscLogFlops((xe-xs) * (ye-ys) * 14 + 7); CHKERRQ(info);
690:   return 0;

692: } /* WholeCombHessian */