Actual source code: eptorsion3.c

  1: /*$Id: eptorsion.c, v 1.1 2002/08/08 10:30 lopezca@mauddib.mcs.anl.gov $*/

  3: /* Program usage: mpirun -np <proc> eptorsion [-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[] = "This example is based on the Elastic-Plastic Torsion (dept)\n\
 16: problem from the MINPACK-2 test suite.\n\
 17: The command line options are:\n\
 18:   -mx <xg>, where <xg> = number of grid points in the 1st coordinate direction\n\
 19:   -my <yg>, where <yg> = number of grid points in the 2nd coordinate direction\n\
 20:   -nlevels <nlevels>, where <nlevels> = number of levels in multigrid\n\
 21:   -byelement, if computation is made by functions on rectangular elements\n\
 22:   -adic, if AD is used (AD is not used by default)\n\
 23:   -u1 <u1>, where <u1> = upper limit in the 1st coordinate direction\n\
 24:   -u2 <u2>, where <u2> = upper limit in the 2nd coordinate direction\n\
 25:   -par <param>, where <param> = angle of twist per unit length\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: TaoSetOptions();
 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: */
 50: typedef struct {
 51:   InactiveDouble      param;
 52:   InactiveDouble      hx, hy;        /* increment size in both directions */
 53:   InactiveDouble      area;          /* area of the triangles */
 54: } ADFGCtx;

 56: typedef struct {
 57:   PetscReal      param;          /* 'c' parameter */
 58:   PetscReal      u1, u2;         /* domain upper limits (lower limits = 0) */
 59:   double      hx, hy;        /* increment size in both directions */
 60:   double      area;          /* area of the triangles */
 61:   ADFGCtx     fgctx;         /* Used only when an ADIC generated gradient is used */
 62: } AppCtx;
 63: int ad_EPTorsLocalFunction(int[2], DERIV_TYPE[4], DERIV_TYPE*, void*);

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

 69: static int EPTorsLocalFunctionGradient(int[2], double x[4], double *f, double g[4], void *ptr);
 70: static int EPTorsLocalHessian(int[2], double x[4], double H[4][4], void *ptr);

 72: static int WholeEPTorsFunctionGradient(TAO_APPLICATION,DA,Vec,double *,Vec,void*);
 73: static int WholeEPTorsHessian(TAO_APPLICATION,DA,Vec,Mat,void*);

 75: static int DASetBounds(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;                           /* used to check for functions returning nonzeros */
 85:   int             mx,my,Nx,Ny;
 86:   double          ff,gnorm;
 87:   int             iter, nlevels;                                                /* multigrid levels */
 88:   DA              DAarray[20];
 89:   Vec             X;
 90:   PetscTruth      flg, PreLoad = PETSC_TRUE;                                               /* flags */
 91:   TaoMethod       method = "tao_gpcg";                                       /* minimization method */
 92:   AppCtx          user;                                                /* user-defined work context */
 93:   TAO_SOLVER      tao;                                                 /* TAO_SOLVER solver context */
 94:   TAO_APPLICATION EPTorsApp;                                            /* 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:   mx = my = 11;                               /* these correspond to 10 segments on each dimension */
108:   info = PetscOptionsGetInt(TAO_NULL, "-mx", &mx, &flg); CHKERRQ(info);
109:   info = PetscOptionsGetInt(TAO_NULL, "-my", &my, &flg); CHKERRQ(info);
110:   if (PreLoadIt == 0) {
111:     nlevels = 1; mx = 11; my = 11; }

113:   PetscPrintf(MPI_COMM_WORLD,"\n---- Elastic-Plastic Torsion Problem -----\n\n");

115:   /* Let PETSc determine the vector distribution */
116:   Nx = PETSC_DECIDE; Ny = PETSC_DECIDE;

118:   /* Create distributed array (DA) to manage parallel grid and vectors  */
119:   info = DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_BOX,mx,
120:                     my,Nx,Ny,1,1,PETSC_NULL,PETSC_NULL,&DAarray[0]); CHKERRQ(info);
121:   for (iter=1;iter<nlevels;iter++){
122:     info = DARefine(DAarray[iter-1],PETSC_COMM_WORLD,&DAarray[iter]); CHKERRQ(info);
123:   }

125:   /* Create TAO solver and set desired solution method */
126:   info = TaoCreate(MPI_COMM_WORLD,method,&tao); CHKERRQ(info);
127:   info = TaoApplicationCreate(PETSC_COMM_WORLD,&EPTorsApp); CHKERRQ(info);
128:   info = TaoAppSetDAApp(EPTorsApp, DAarray, nlevels ); CHKERRQ(info);
129:   /* Sets routines for function, gradient and bounds evaluation */
130:   info = DAAppSetVariableBoundsRoutine(EPTorsApp,DASetBounds,(void *)&user); CHKERRQ(info);

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

135:     /* Sets routines for function and gradient evaluation, element by element */
136:     info = PetscOptionsHasName(TAO_NULL, "-adic", &flg); CHKERRQ(info);
137:     if (flg) {
138:       info = DAAppSetADElementFunctionGradient(EPTorsApp,ad_EPTorsLocalFunction,192,(void *)&user.fgctx); CHKERRQ(info);
139:     } else {
140:       info = DAAppSetElementObjectiveAndGradientRoutine(EPTorsApp,EPTorsLocalFunctionGradient,42,(void *)&user); CHKERRQ(info);
141:     }
142:     /* Sets routines for Hessian evaluation, element by element */
143:     info = DAAppSetElementHessianRoutine(EPTorsApp,EPTorsLocalHessian,6,(void*)&user); CHKERRQ(info);

145:   } else {

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

150:     /* Sets routines for Hessian evaluation, all in one routine */
151:     info = DAAppSetHessianRoutine(EPTorsApp,WholeEPTorsHessian,(void*)&user); CHKERRQ(info);
152: 
153:   }

155:   info = DAAppSetBeforeMonitor(EPTorsApp,MyGridMonitorBefore,(void*)&user); CHKERRQ(info);
156:   info = PetscOptionsHasName(TAO_NULL,"-tao_monitor", &flg); CHKERRQ(info);
157:   if (flg){
158:     info = DAAppPrintStageTimes(EPTorsApp); CHKERRQ(info);
159:     info = DAAppPrintInterpolationError(EPTorsApp); CHKERRQ(info);
160:   }
161:   info = TaoAppSetRelativeTolerance(EPTorsApp,1.0e-8); CHKERRQ(info);
162:   info = TaoSetTolerances(tao,0,0,0,0); CHKERRQ(info);
163:   info = TaoSetGradientTolerances(tao,0,0,0); CHKERRQ(info);

165:   /* Check for any tao command line options */
166:   info = TaoSetOptions(EPTorsApp, tao); CHKERRQ(info);

168:   info = DAAppGetSolution(EPTorsApp,0,&X); CHKERRQ(info);
169:   info = FormInitialGuess(DAarray[0],X); CHKERRQ(info);
170:   info = DAAppSetInitialSolution(EPTorsApp,X); CHKERRQ(info);
171: 
172:   /* SOLVE THE APPLICATION */
173:   info = TaoDAAppSolve(EPTorsApp, tao);  CHKERRQ(info);

175:   /* Get information on termination */
176:   info = TaoGetSolutionStatus(tao,&iter,&ff,&gnorm,0,0,&reason); CHKERRQ(info);
177:   if (reason <= 0 ){
178:     PetscPrintf(MPI_COMM_WORLD,"Try a different TAO method, adjust some parameters, or check the function evaluation routines\n");
179:     PetscPrintf(MPI_COMM_WORLD," Iterations: %d,  Function Value: %4.2e, Residual: %4.2e \n",iter,ff,gnorm);
180:   }

182:   info = PetscOptionsHasName(PETSC_NULL,"-view_sol",&flg); CHKERRQ(info);
183:   if (flg){
184:     info = DAAppGetSolution(EPTorsApp,nlevels-1,&X); CHKERRQ(info);
185:     info=VecView(X,PETSC_VIEWER_STDOUT_WORLD); CHKERRQ(info);
186:   }

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

191:   /* Free TAO data structures */
192:   info = TaoDestroy(tao); CHKERRQ(info);
193:   info = TaoAppDestroy(EPTorsApp); CHKERRQ(info);

195:   /* Free PETSc data structures */
196:   for (iter=0;iter<nlevels;iter++){
197:     info = DADestroy(DAarray[iter]); CHKERRQ(info);
198:   }

200:   PreLoadEnd();

202:   /* Finalize TAO */
203:   TaoFinalize();
204:   PetscFinalize();

206:   return 0;
207: } /* main */



211: /*----- The following two routines
212:   MyGridMonitorBefore    MyGridMonitorAfter
213:   help diplay info of iterations at every grid level
214: */
217: static int MyGridMonitorBefore(TAO_APPLICATION myapp, DA da, int level, void *ctx) {

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

222:   info = DAGetInfo(da,PETSC_NULL,&mx,&my,PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL,
223:                    PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL);CHKERRQ(info);
224:   user->hx = user->u1 / (mx - 1);
225:   user->hy = user->u2 / (my - 1);
226:   user->area = 0.5 * user->hx * user->hy;
227:   user->fgctx.hx   = user->hx;
228:   user->fgctx.hy   = user->hy;
229:   user->fgctx.area = user->area;
230:   user->fgctx.param = user->param;

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

234:   return 0;
235: }


238: /*------- USER-DEFINED: initialize the application context information -------*/
241: /*
242:   AppCtxInitialize - Sets initial values for the application context parameters

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

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

253:   AppCtx *user = (AppCtx*)ptr;
254:   PetscTruth    flg;            /* flag for PETSc calls */
255:   int info;

257:   /* Specify default parameters */
258:   user->param = 25.0;
259:   user->u1 = user->u2 = 1.0;

261:   /* Check for command line arguments that override defaults */
262:   info = PetscOptionsGetReal(TAO_NULL, "-par", &user->param, &flg); CHKERRQ(info);
263:   info = PetscOptionsGetReal(TAO_NULL, "-u1", &user->u1, &flg); CHKERRQ(info);
264:   info = PetscOptionsGetReal(TAO_NULL, "-u2", &user->u2, &flg); CHKERRQ(info);

266:   return 0;
267: } /* AppCtxInitialize */

271: static int FormInitialGuess(DA da, Vec X)
272: {
273:   int    info, i, j, mx, my;
274:   int    xs, ys, xm, ym, xe, ye;
275:   PetscReal hx, hy, temp, val;
276:   double **x;

278:   /* Get local mesh boundaries */
279:   info = DAGetInfo(da,PETSC_NULL,&mx,&my,PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL,
280:                    PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL);CHKERRQ(info);
281:   hx = 1.0/(mx-1);  hy = 1.0/(my-1);

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

286:   info = DAVecGetArray(da, X, (void**)&x); CHKERRQ(info);
287:   /* Compute initial guess over locally owned part of mesh */
288:   for (j=ys; j<ye; j++) {  /*  for (j=0; j<my; j++) */
289:     temp = PetscMin(j+1,my-j)*hy;
290:     for (i=xs; i<xe; i++) {  /*  for (i=0; i<mx; i++) */
291:       val = PetscMin((PetscMin(i+1,mx-i))*hx,temp);
292:       x[j][i] = val;
293:     }
294:   }
295:   info = DAVecRestoreArray(da, X, (void**)&x); CHKERRQ(info);

297:   return 0;
298: }


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

305: /*
306:   FormBounds - Forms bounds on the variables

308:   Input:
309:     user - user-defined application context

311:   Output:
312:     XL - vector of lower bounds
313:     XU - vector of upper bounds
314: */
315: static int DASetBounds(TAO_APPLICATION daapplication, DA da, Vec XL, Vec XU, void *ptr)
316: {
317:   AppCtx *user = (AppCtx*)ptr;
318:   int i, j, info, xs, xm, ys, ym;
319:   double hx, hy, u1, u2, dist, d1, d2, hd, vd;
320:   double **xl, **xu;

322:   hx = user->hx;
323:   hy = user->hy;
324:   u1 = user->u1;
325:   u2 = user->u2;

327:   info = DAVecGetArray(da, XL, (void**)&xl); CHKERRQ(info);
328:   info = DAVecGetArray(da, XU, (void**)&xu); CHKERRQ(info);
329:   info = DAGetCorners(da, &xs, &ys, TAO_NULL, &xm, &ym, TAO_NULL); CHKERRQ(info);

331:   for (j = ys; j < ys+ym; j++){
332:     for (i = xs; i < xs+xm; i++){
333:       d1 = i * hx; d2 = u1 - d1; hd = PetscMin(d1,d2);
334:       d1 = j * hy; d2 = u2 - d1; vd = PetscMin(d1,d2);
335:       dist = PetscMin(hd,vd);
336:       xl[j][i] = -dist;
337:       xu[j][i] = dist;
338:     }
339:   }

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

344:   info = PetscLogFlops(xm * ym * 4); CHKERRQ(info);
345:   return 0;

347: } /* DASetBounds */


352: /*
353:   EPTorsLocalFunctionGradient - Evaluates function and gradient over the 
354:       local rectangular element

356:   Input:
357:     coor - vector with the indices of the position of current element
358:              in the first, second and third directions
359:     x - current point (values over the current rectangular element)
360:     df - degrees of freedom at each point
361:     ptr - user-defined application context

363:   Output:
364:     f - value of the objective funtion at the local rectangular element
365:     g - gradient of the local function
366: */
367: static int EPTorsLocalFunctionGradient(int coor[2], double x[4], double *f, double g[4], void *ptr) {

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

371:   double fquad, flin;
372:   double hx, hy, dvdx, dvdy, area;
373:   double cdiv3, cnt;

375:   cdiv3 = user->param / 3.0;
376:   hx = user->hx;
377:   hy = user->hy;
378:   area = user->area;
379:   cnt = area * cdiv3;

381:   /* lower triangle contribution */
382:   dvdx = (x[0] - x[1]) / hx;
383:   dvdy = (x[0] - x[2]) / hy;
384:   fquad = dvdx * dvdx + dvdy * dvdy;
385:   flin = x[0] + x[1] + x[2];

387:   dvdx = 0.5 * dvdx * hy;
388:   dvdy = 0.5 * dvdy * hx;
389:   g[0] = dvdx + dvdy - cnt;
390:   g[1] = -dvdx - 2.0 * cnt;
391:   g[2] = -dvdy - 2.0 * cnt;

393:   /* upper triangle contribution */
394:   dvdx = (x[3] - x[2]) / hx;
395:   dvdy = (x[3] - x[1]) / hy;
396:   fquad += dvdx * dvdx + dvdy * dvdy;
397:   flin += x[1] + x[2] + x[3];

399:   dvdx = 0.5 * dvdx * hy;
400:   dvdy = 0.5 * dvdy * hx;
401:   g[1] += -dvdy;
402:   g[2] += -dvdx;
403:   g[3] = dvdx + dvdy - cnt;

405:   *f = area * (0.5 * fquad - flin * cdiv3);

407:   return 0;
408: } /* EPTorsLocalFunctionGradient */



412: /*------- USER-DEFINED: routine to evaluate the Hessian
413:            at a local (rectangular element) level       -------*/
416: /*
417:   EPTorsLocalHessian - Computes the Hessian of the local (partial) function
418:          defined over the current rectangle

420:   Input:
421:     coor - vector with the indices of the position of current element
422:              in the first, second and third directions
423:     x - current local solution (over the rectangle only)
424:     df - degrees of freedom at each point
425:     ptr - user-defined application context

427:   Output:
428:     H - Hessian matrix of the local function (wrt the four
429:            points of the rectangle only)
430: */
431: static int EPTorsLocalHessian(int coor[2], double x[4], double H[4][4], void *ptr) {

433:   AppCtx *user = (AppCtx*)ptr;
434:   double hx, hy, dxdy, dydx;
435:   double diagxy, bandxy, bandyx;

437:   hx = user->hx;
438:   hy = user->hy;
439:   dxdy = hx/hy;
440:   dydx = hy/hx;
441:   diagxy = 0.5 * (dxdy + dydx);
442:   bandxy = -0.5 * dxdy;
443:   bandyx = -0.5 * dydx;

445:           /* Hessian contribution at 0,0 */
446:   H[0][0] = diagxy;
447:   H[0][1] =  H[1][0] = bandyx;
448:   H[0][2] =  H[2][0] = bandxy;
449:   H[0][3] =  H[3][0] = 0.0;

451:           /* Hessian contribution at 1,0 */
452:   H[1][1] = diagxy;
453:   H[1][2] =  H[2][1] = 0.0;
454:   H[1][3] =  H[3][1] = bandxy;

456:           /* Hessian contribution at 0,1 */
457:   H[2][2] = diagxy;
458:   H[2][3] =  H[3][2] = bandyx;

460:           /* Hessian contribution at 1,1 */
461:   H[3][3] = diagxy;

463:   return 0;

465: } /* EPTorsLocalHessian */


468: /*------- USER-DEFINED: routine to evaluate the function 
469:           and gradient at the whole grid             -------*/
472: /*
473:   WholeEPTorsFunctionGradient - Evaluates function and gradient over the 
474:       whole grid

476:   Input:
477:     daapplication - TAO application object
478:     da  - distributed array
479:     X   - the current point, at which the function and gradient are evaluated
480:     ptr - user-defined application context

482:   Output:
483:     f - value of the objective funtion at X
484:     G - gradient at X
485: */
486: static int WholeEPTorsFunctionGradient(TAO_APPLICATION daapplication, DA da, Vec X, double *f, Vec G, void *ptr) {

488:   AppCtx *user = (AppCtx*)ptr;
489:   Vec localX, localG;
490:   int info, i, j;
491:   int xs, xm, gxs, gxm, xe, ys, ym, gys, gym, ye;
492:   double **x, **g;
493:   double floc = 0.0;
494:   PetscScalar zero = 0.0;

496:   double fquad, flin;
497:   double hx, hy, dvdx, dvdy, area;
498:   double cdiv3, cnt;

500:   cdiv3 = user->param / 3.0;
501:   hx = user->hx;
502:   hy = user->hy;
503:   area = user->area;
504:   cnt = area * cdiv3;

506:   info = DAGetLocalVector(da, &localX); CHKERRQ(info);
507:   info = DAGetLocalVector(da, &localG); CHKERRQ(info);
508:   info = VecSet(G, zero); CHKERRQ(info);
509:   info = VecSet(localG, zero); CHKERRQ(info);

511:   info = DAGlobalToLocalBegin(da, X, INSERT_VALUES, localX); CHKERRQ(info);
512:   info = DAGlobalToLocalEnd(da, X, INSERT_VALUES, localX); CHKERRQ(info);

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

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

520:   xe = gxs + gxm - 1;
521:   ye = gys + gym - 1;
522:   for (j = ys; j < ye; j++) {
523:     for (i = xs; i < xe; i++) {

525:       /* lower triangle contribution */
526:       dvdx = (x[j][i] - x[j][i+1]) / hx;
527:       dvdy = (x[j][i] - x[j+1][i]) / hy;
528:       fquad = dvdx * dvdx + dvdy * dvdy;
529:       flin = x[j][i] + x[j][i+1] + x[j+1][i];

531:       dvdx = 0.5 * dvdx * hy;
532:       dvdy = 0.5 * dvdy * hx;
533:       g[j][i] += dvdx + dvdy - cnt;
534:       g[j][i+1] += -dvdx - 2.0 * cnt;
535:       g[j+1][i] += -dvdy - 2.0 * cnt;

537:       /* upper triangle contribution */
538:       dvdx = (x[j+1][i+1] - x[j+1][i]) / hx;
539:       dvdy = (x[j+1][i+1] - x[j][i+1]) / hy;
540:       fquad += dvdx * dvdx + dvdy * dvdy;
541:       flin += x[j][i+1] + x[j+1][i] + x[j+1][i+1];

543:       dvdx = 0.5 * dvdx * hy;
544:       dvdy = 0.5 * dvdy * hx;
545:       g[j][i+1] += -dvdy;
546:       g[j+1][i] += -dvdx;
547:       g[j+1][i+1] += dvdx + dvdy - cnt;

549:       floc += area * (0.5 * fquad - flin * cdiv3);

551:     }
552:   }

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

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

559:   info = DALocalToGlobalBegin(da, localG, G); CHKERRQ(info);
560:   info = DALocalToGlobalEnd(da, localG, G); CHKERRQ(info);

562:   info = DARestoreLocalVector(da, &localX); CHKERRQ(info);
563:   info = DARestoreLocalVector(da, &localG); CHKERRQ(info);

565:   info = PetscLogFlops((xe-xs) * (ye-ys) * 47 + 2); CHKERRQ(info);
566:   return 0;
567: } /* WholeEPTorsFunctionGradient */


570: /*------- USER-DEFINED: routine to evaluate the Hessian 
571:           at the whole grid             -------*/
574: /*
575:   WholeEPTorsHessian - Evaluates Hessian over the whole grid

577:   Input:
578:     daapplication - TAO application object
579:     da  - distributed array
580:     X   - the current point, at which the function and gradient are evaluated
581:     ptr - user-defined application context

583:   Output:
584:     H - Hessian at X
585: */
586: static int WholeEPTorsHessian(TAO_APPLICATION daapplication, DA da, Vec X, Mat H, void *ptr) {

588:   AppCtx *user = (AppCtx*)ptr;
589:   int info, i, j, ind[4];
590:   int xs, xm, gxs, gxm, xe, ys, ym, gys, gym, ye;
591:   double smallH[4][4];

593:   double hx, hy, dxdy, dydx;
594:   double diagxy, bandxy, bandyx;
595:   PetscTruth assembled;

597:   hx = user->hx;
598:   hy = user->hy;
599:   dxdy = hx/hy;
600:   dydx = hy/hx;
601:   diagxy = 0.5 * (dxdy + dydx);
602:   bandxy = -0.5 * dxdy;
603:   bandyx = -0.5 * dydx;

605:   info = MatAssembled(H,&assembled); CHKERRQ(info);
606:   if (assembled){info = MatZeroEntries(H);  CHKERRQ(info);}


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

612:   xe = gxs + gxm - 1;
613:   ye = gys + gym - 1;
614:   for (j = ys; j < ye; j++) {
615:     for (i = xs; i < xe; i++) {

617:           /* Hessian contribution at 0,0 */
618:       smallH[0][0] = diagxy;
619:       smallH[0][1] = smallH[1][0] = bandyx;
620:       smallH[0][2] = smallH[2][0] = bandxy;
621:       smallH[0][3] = smallH[3][0] = 0.0;

623:           /* Hessian contribution at 1,0 */
624:       smallH[1][1] = diagxy;
625:       smallH[1][2] = smallH[2][1] = 0.0;
626:       smallH[1][3] = smallH[3][1] = bandxy;

628:           /* Hessian contribution at 0,1 */
629:       smallH[2][2] = diagxy;
630:       smallH[2][3] = smallH[3][2] = bandyx;

632:           /* Hessian contribution at 1,1 */
633:       smallH[3][3] = diagxy;

635:       ind[0] = (j-gys) * gxm + (i-gxs);
636:       ind[1] = ind[0] + 1;
637:       ind[2] = ind[0] + gxm;
638:       ind[3] = ind[2] + 1;
639:       info = MatSetValuesLocal(H,4,ind,4,ind,(PetscScalar*)smallH,ADD_VALUES); CHKERRQ(info);

641:     }
642:   }

644:   info = MatAssemblyBegin(H, MAT_FINAL_ASSEMBLY); CHKERRQ(info);
645:   info = MatAssemblyEnd(H, MAT_FINAL_ASSEMBLY); CHKERRQ(info);
646:   info = MatSetOption(H, MAT_SYMMETRIC); CHKERRQ(info);


649:   info = PetscLogFlops(6); CHKERRQ(info);
650:   return 0;

652: } /* WholeEPTorsHessian */