Actual source code: jbearing2.c

  1: /*
  2:   Include "petsctao.h" so we can use TAO solvers
  3:   Include "petscdmda.h" so that we can use distributed arrays (DMs) for managing
  4:   Include "petscksp.h" so we can set KSP type
  5:   the parallel mesh.
  6: */

  8: #include <petsctao.h>
  9: #include <petscdmda.h>

 11: static  char help[]=
 12: "This example demonstrates use of the TAO package to \n\
 13: solve a bound constrained minimization problem.  This example is based on \n\
 14: the problem DPJB from the MINPACK-2 test suite.  This pressure journal \n\
 15: bearing problem is an example of elliptic variational problem defined over \n\
 16: a two dimensional rectangle.  By discretizing the domain into triangular \n\
 17: elements, the pressure surrounding the journal bearing is defined as the \n\
 18: minimum of a quadratic function whose variables are bounded below by zero.\n\
 19: The command line options are:\n\
 20:   -mx <xg>, where <xg> = number of grid points in the 1st coordinate direction\n\
 21:   -my <yg>, where <yg> = number of grid points in the 2nd coordinate direction\n\
 22:  \n";

 24: /*T
 25:    Concepts: TAO^Solving a bound constrained minimization problem
 26:    Routines: TaoCreate();
 27:    Routines: TaoSetType(); TaoSetObjectiveAndGradientRoutine();
 28:    Routines: TaoSetHessianRoutine();
 29:    Routines: TaoSetVariableBounds();
 30:    Routines: TaoSetMonitor(); TaoSetConvergenceTest();
 31:    Routines: TaoSetInitialVector();
 32:    Routines: TaoSetFromOptions();
 33:    Routines: TaoSolve();
 34:    Routines: TaoDestroy();
 35:    Processors: n
 36: T*/

 38: /*
 39:    User-defined application context - contains data needed by the
 40:    application-provided call-back routines, FormFunctionGradient(),
 41:    FormHessian().
 42: */
 43: typedef struct {
 44:   /* problem parameters */
 45:   PetscReal      ecc;          /* test problem parameter */
 46:   PetscReal      b;            /* A dimension of journal bearing */
 47:   PetscInt       nx,ny;        /* discretization in x, y directions */

 49:   /* Working space */
 50:   DM          dm;           /* distributed array data structure */
 51:   Mat         A;            /* Quadratic Objective term */
 52:   Vec         B;            /* Linear Objective term */
 53: } AppCtx;

 55: /* User-defined routines */
 56: static PetscReal p(PetscReal xi, PetscReal ecc);
 57: static PetscErrorCode FormFunctionGradient(Tao, Vec, PetscReal *,Vec,void *);
 58: static PetscErrorCode FormHessian(Tao,Vec,Mat, Mat, void *);
 59: static PetscErrorCode ComputeB(AppCtx*);
 60: static PetscErrorCode Monitor(Tao, void*);
 61: static PetscErrorCode ConvergenceTest(Tao, void*);

 63: int main(int argc, char **argv)
 64: {
 65:   PetscErrorCode     ierr;            /* used to check for functions returning nonzeros */
 66:   PetscInt           Nx, Ny;          /* number of processors in x- and y- directions */
 67:   PetscInt           m;               /* number of local elements in vectors */
 68:   Vec                x;               /* variables vector */
 69:   Vec                xl,xu;           /* bounds vectors */
 70:   PetscReal          d1000 = 1000;
 71:   PetscBool          flg,testgetdiag; /* A return variable when checking for user options */
 72:   Tao                tao;             /* Tao solver context */
 73:   KSP                ksp;
 74:   AppCtx             user;            /* user-defined work context */
 75:   PetscReal          zero = 0.0;      /* lower bound on all variables */

 77:   /* Initialize PETSC and TAO */
 78:   PetscInitialize(&argc, &argv,(char *)0,help);if (ierr) return ierr;

 80:   /* Set the default values for the problem parameters */
 81:   user.nx = 50; user.ny = 50; user.ecc = 0.1; user.b = 10.0;
 82:   testgetdiag = PETSC_FALSE;

 84:   /* Check for any command line arguments that override defaults */
 85:   PetscOptionsGetInt(NULL,NULL,"-mx",&user.nx,&flg);
 86:   PetscOptionsGetInt(NULL,NULL,"-my",&user.ny,&flg);
 87:   PetscOptionsGetReal(NULL,NULL,"-ecc",&user.ecc,&flg);
 88:   PetscOptionsGetReal(NULL,NULL,"-b",&user.b,&flg);
 89:   PetscOptionsGetBool(NULL,NULL,"-test_getdiagonal",&testgetdiag,NULL);

 91:   PetscPrintf(PETSC_COMM_WORLD,"\n---- Journal Bearing Problem SHB-----\n");
 92:   PetscPrintf(PETSC_COMM_WORLD,"mx: %D,  my: %D,  ecc: %g \n\n",user.nx,user.ny,(double)user.ecc);

 94:   /* Let Petsc determine the grid division */
 95:   Nx = PETSC_DECIDE; Ny = PETSC_DECIDE;

 97:   /*
 98:      A two dimensional distributed array will help define this problem,
 99:      which derives from an elliptic PDE on two dimensional domain.  From
100:      the distributed array, Create the vectors.
101:   */
102:   DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,user.nx,user.ny,Nx,Ny,1,1,NULL,NULL,&user.dm);
103:   DMSetFromOptions(user.dm);
104:   DMSetUp(user.dm);

106:   /*
107:      Extract global and local vectors from DM; the vector user.B is
108:      used solely as work space for the evaluation of the function,
109:      gradient, and Hessian.  Duplicate for remaining vectors that are
110:      the same types.
111:   */
112:   DMCreateGlobalVector(user.dm,&x); /* Solution */
113:   VecDuplicate(x,&user.B); /* Linear objective */

115:   /*  Create matrix user.A to store quadratic, Create a local ordering scheme. */
116:   VecGetLocalSize(x,&m);
117:   DMCreateMatrix(user.dm,&user.A);

119:   if (testgetdiag) {
120:     MatSetOperation(user.A,MATOP_GET_DIAGONAL,NULL);
121:   }

123:   /* User defined function -- compute linear term of quadratic */
124:   ComputeB(&user);

126:   /* The TAO code begins here */

128:   /*
129:      Create the optimization solver
130:      Suitable methods: TAOGPCG, TAOBQPIP, TAOTRON, TAOBLMVM
131:   */
132:   TaoCreate(PETSC_COMM_WORLD,&tao);
133:   TaoSetType(tao,TAOBLMVM);

135:   /* Set the initial vector */
136:   VecSet(x, zero);
137:   TaoSetInitialVector(tao,x);

139:   /* Set the user function, gradient, hessian evaluation routines and data structures */
140:   TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void*) &user);

142:   TaoSetHessianRoutine(tao,user.A,user.A,FormHessian,(void*)&user);

144:   /* Set a routine that defines the bounds */
145:   VecDuplicate(x,&xl);
146:   VecDuplicate(x,&xu);
147:   VecSet(xl, zero);
148:   VecSet(xu, d1000);
149:   TaoSetVariableBounds(tao,xl,xu);

151:   TaoGetKSP(tao,&ksp);
152:   if (ksp) {
153:     KSPSetType(ksp,KSPCG);
154:   }

156:   PetscOptionsHasName(NULL,NULL,"-testmonitor",&flg);
157:   if (flg) {
158:     TaoSetMonitor(tao,Monitor,&user,NULL);
159:   }
160:   PetscOptionsHasName(NULL,NULL,"-testconvergence",&flg);
161:   if (flg) {
162:     TaoSetConvergenceTest(tao,ConvergenceTest,&user);
163:   }

165:   /* Check for any tao command line options */
166:   TaoSetFromOptions(tao);

168:   /* Solve the bound constrained problem */
169:   TaoSolve(tao);

171:   /* Free PETSc data structures */
172:   VecDestroy(&x);
173:   VecDestroy(&xl);
174:   VecDestroy(&xu);
175:   MatDestroy(&user.A);
176:   VecDestroy(&user.B);

178:   /* Free TAO data structures */
179:   TaoDestroy(&tao);
180:   DMDestroy(&user.dm);
181:   PetscFinalize();
182:   return ierr;
183: }

185: static PetscReal p(PetscReal xi, PetscReal ecc)
186: {
187:   PetscReal t=1.0+ecc*PetscCosScalar(xi);
188:   return (t*t*t);
189: }

191: PetscErrorCode ComputeB(AppCtx* user)
192: {
194:   PetscInt       i,j,k;
195:   PetscInt       nx,ny,xs,xm,gxs,gxm,ys,ym,gys,gym;
196:   PetscReal      two=2.0, pi=4.0*atan(1.0);
197:   PetscReal      hx,hy,ehxhy;
198:   PetscReal      temp,*b;
199:   PetscReal      ecc=user->ecc;

201:   nx=user->nx;
202:   ny=user->ny;
203:   hx=two*pi/(nx+1.0);
204:   hy=two*user->b/(ny+1.0);
205:   ehxhy = ecc*hx*hy;

207:   /*
208:      Get local grid boundaries
209:   */
210:   DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
211:   DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);

213:   /* Compute the linear term in the objective function */
214:   VecGetArray(user->B,&b);
215:   for (i=xs; i<xs+xm; i++) {
216:     temp=PetscSinScalar((i+1)*hx);
217:     for (j=ys; j<ys+ym; j++) {
218:       k=xm*(j-ys)+(i-xs);
219:       b[k]=  - ehxhy*temp;
220:     }
221:   }
222:   VecRestoreArray(user->B,&b);
223:   PetscLogFlops(5.0*xm*ym+3.0*xm);

225:   return 0;
226: }

228: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *fcn,Vec G,void *ptr)
229: {
230:   AppCtx*        user=(AppCtx*)ptr;
232:   PetscInt       i,j,k,kk;
233:   PetscInt       col[5],row,nx,ny,xs,xm,gxs,gxm,ys,ym,gys,gym;
234:   PetscReal      one=1.0, two=2.0, six=6.0,pi=4.0*atan(1.0);
235:   PetscReal      hx,hy,hxhy,hxhx,hyhy;
236:   PetscReal      xi,v[5];
237:   PetscReal      ecc=user->ecc, trule1,trule2,trule3,trule4,trule5,trule6;
238:   PetscReal      vmiddle, vup, vdown, vleft, vright;
239:   PetscReal      tt,f1,f2;
240:   PetscReal      *x,*g,zero=0.0;
241:   Vec            localX;

243:   nx=user->nx;
244:   ny=user->ny;
245:   hx=two*pi/(nx+1.0);
246:   hy=two*user->b/(ny+1.0);
247:   hxhy=hx*hy;
248:   hxhx=one/(hx*hx);
249:   hyhy=one/(hy*hy);

251:   DMGetLocalVector(user->dm,&localX);

253:   DMGlobalToLocalBegin(user->dm,X,INSERT_VALUES,localX);
254:   DMGlobalToLocalEnd(user->dm,X,INSERT_VALUES,localX);

256:   VecSet(G, zero);
257:   /*
258:     Get local grid boundaries
259:   */
260:   DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
261:   DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);

263:   VecGetArray(localX,&x);
264:   VecGetArray(G,&g);

266:   for (i=xs; i< xs+xm; i++) {
267:     xi=(i+1)*hx;
268:     trule1=hxhy*(p(xi,ecc) + p(xi+hx,ecc) + p(xi,ecc)) / six; /* L(i,j) */
269:     trule2=hxhy*(p(xi,ecc) + p(xi-hx,ecc) + p(xi,ecc)) / six; /* U(i,j) */
270:     trule3=hxhy*(p(xi,ecc) + p(xi+hx,ecc) + p(xi+hx,ecc)) / six; /* U(i+1,j) */
271:     trule4=hxhy*(p(xi,ecc) + p(xi-hx,ecc) + p(xi-hx,ecc)) / six; /* L(i-1,j) */
272:     trule5=trule1; /* L(i,j-1) */
273:     trule6=trule2; /* U(i,j+1) */

275:     vdown=-(trule5+trule2)*hyhy;
276:     vleft=-hxhx*(trule2+trule4);
277:     vright= -hxhx*(trule1+trule3);
278:     vup=-hyhy*(trule1+trule6);
279:     vmiddle=(hxhx)*(trule1+trule2+trule3+trule4)+hyhy*(trule1+trule2+trule5+trule6);

281:     for (j=ys; j<ys+ym; j++) {

283:       row=(j-gys)*gxm + (i-gxs);
284:        v[0]=0; v[1]=0; v[2]=0; v[3]=0; v[4]=0;

286:        k=0;
287:        if (j>gys) {
288:          v[k]=vdown; col[k]=row - gxm; k++;
289:        }

291:        if (i>gxs) {
292:          v[k]= vleft; col[k]=row - 1; k++;
293:        }

295:        v[k]= vmiddle; col[k]=row; k++;

297:        if (i+1 < gxs+gxm) {
298:          v[k]= vright; col[k]=row+1; k++;
299:        }

301:        if (j+1 <gys+gym) {
302:          v[k]= vup; col[k] = row+gxm; k++;
303:        }
304:        tt=0;
305:        for (kk=0;kk<k;kk++) {
306:          tt+=v[kk]*x[col[kk]];
307:        }
308:        row=(j-ys)*xm + (i-xs);
309:        g[row]=tt;

311:      }

313:   }

315:   VecRestoreArray(localX,&x);
316:   VecRestoreArray(G,&g);

318:   DMRestoreLocalVector(user->dm,&localX);

320:   VecDot(X,G,&f1);
321:   VecDot(user->B,X,&f2);
322:   VecAXPY(G, one, user->B);
323:   *fcn = f1/2.0 + f2;

325:   PetscLogFlops((91 + 10.0*ym) * xm);
326:   return 0;

328: }

330: /*
331:    FormHessian computes the quadratic term in the quadratic objective function
332:    Notice that the objective function in this problem is quadratic (therefore a constant
333:    hessian).  If using a nonquadratic solver, then you might want to reconsider this function
334: */
335: PetscErrorCode FormHessian(Tao tao,Vec X,Mat hes, Mat Hpre, void *ptr)
336: {
337:   AppCtx*        user=(AppCtx*)ptr;
339:   PetscInt       i,j,k;
340:   PetscInt       col[5],row,nx,ny,xs,xm,gxs,gxm,ys,ym,gys,gym;
341:   PetscReal      one=1.0, two=2.0, six=6.0,pi=4.0*atan(1.0);
342:   PetscReal      hx,hy,hxhy,hxhx,hyhy;
343:   PetscReal      xi,v[5];
344:   PetscReal      ecc=user->ecc, trule1,trule2,trule3,trule4,trule5,trule6;
345:   PetscReal      vmiddle, vup, vdown, vleft, vright;
346:   PetscBool      assembled;

348:   nx=user->nx;
349:   ny=user->ny;
350:   hx=two*pi/(nx+1.0);
351:   hy=two*user->b/(ny+1.0);
352:   hxhy=hx*hy;
353:   hxhx=one/(hx*hx);
354:   hyhy=one/(hy*hy);

356:   /*
357:     Get local grid boundaries
358:   */
359:   DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
360:   DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
361:   MatAssembled(hes,&assembled);
362:   if (assembled) {MatZeroEntries(hes);}

364:   for (i=xs; i< xs+xm; i++) {
365:     xi=(i+1)*hx;
366:     trule1=hxhy*(p(xi,ecc) + p(xi+hx,ecc) + p(xi,ecc)) / six; /* L(i,j) */
367:     trule2=hxhy*(p(xi,ecc) + p(xi-hx,ecc) + p(xi,ecc)) / six; /* U(i,j) */
368:     trule3=hxhy*(p(xi,ecc) + p(xi+hx,ecc) + p(xi+hx,ecc)) / six; /* U(i+1,j) */
369:     trule4=hxhy*(p(xi,ecc) + p(xi-hx,ecc) + p(xi-hx,ecc)) / six; /* L(i-1,j) */
370:     trule5=trule1; /* L(i,j-1) */
371:     trule6=trule2; /* U(i,j+1) */

373:     vdown=-(trule5+trule2)*hyhy;
374:     vleft=-hxhx*(trule2+trule4);
375:     vright= -hxhx*(trule1+trule3);
376:     vup=-hyhy*(trule1+trule6);
377:     vmiddle=(hxhx)*(trule1+trule2+trule3+trule4)+hyhy*(trule1+trule2+trule5+trule6);
378:     v[0]=0; v[1]=0; v[2]=0; v[3]=0; v[4]=0;

380:     for (j=ys; j<ys+ym; j++) {
381:       row=(j-gys)*gxm + (i-gxs);

383:       k=0;
384:       if (j>gys) {
385:         v[k]=vdown; col[k]=row - gxm; k++;
386:       }

388:       if (i>gxs) {
389:         v[k]= vleft; col[k]=row - 1; k++;
390:       }

392:       v[k]= vmiddle; col[k]=row; k++;

394:       if (i+1 < gxs+gxm) {
395:         v[k]= vright; col[k]=row+1; k++;
396:       }

398:       if (j+1 <gys+gym) {
399:         v[k]= vup; col[k] = row+gxm; k++;
400:       }
401:       MatSetValuesLocal(hes,1,&row,k,col,v,INSERT_VALUES);

403:     }

405:   }

407:   /*
408:      Assemble matrix, using the 2-step process:
409:      MatAssemblyBegin(), MatAssemblyEnd().
410:      By placing code between these two statements, computations can be
411:      done while messages are in transition.
412:   */
413:   MatAssemblyBegin(hes,MAT_FINAL_ASSEMBLY);
414:   MatAssemblyEnd(hes,MAT_FINAL_ASSEMBLY);

416:   /*
417:     Tell the matrix we will never add a new nonzero location to the
418:     matrix. If we do it will generate an error.
419:   */
420:   MatSetOption(hes,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
421:   MatSetOption(hes,MAT_SYMMETRIC,PETSC_TRUE);

423:   PetscLogFlops(9.0*xm*ym+49.0*xm);
424:   MatNorm(hes,NORM_1,&hx);
425:   return 0;
426: }

428: PetscErrorCode Monitor(Tao tao, void *ctx)
429: {
430:   PetscErrorCode     ierr;
431:   PetscInt           its;
432:   PetscReal          f,gnorm,cnorm,xdiff;
433:   TaoConvergedReason reason;

436:   TaoGetSolutionStatus(tao, &its, &f, &gnorm, &cnorm, &xdiff, &reason);
437:   if (!(its%5)) {
438:     PetscPrintf(PETSC_COMM_WORLD,"iteration=%D\tf=%g\n",its,(double)f);
439:   }
440:   return(0);
441: }

443: PetscErrorCode ConvergenceTest(Tao tao, void *ctx)
444: {
445:   PetscErrorCode     ierr;
446:   PetscInt           its;
447:   PetscReal          f,gnorm,cnorm,xdiff;
448:   TaoConvergedReason reason;

451:   TaoGetSolutionStatus(tao, &its, &f, &gnorm, &cnorm, &xdiff, &reason);
452:   if (its == 100) {
453:     TaoSetConvergedReason(tao,TAO_DIVERGED_MAXITS);
454:   }
455:   return(0);

457: }

459: /*TEST

461:    build:
462:       requires: !complex

464:    test:
465:       args: -tao_smonitor -mx 8 -my 12 -tao_type tron -tao_gatol 1.e-5
466:       requires: !single

468:    test:
469:       suffix: 2
470:       nsize: 2
471:       args: -tao_smonitor -mx 50 -my 50 -ecc 0.99 -tao_type gpcg -tao_gatol 1.e-5
472:       requires: !single

474:    test:
475:       suffix: 3
476:       nsize: 2
477:       args: -tao_smonitor -mx 10 -my 16 -ecc 0.9 -tao_type bqpip -tao_gatol 1.e-4
478:       requires: !single

480:    test:
481:       suffix: 4
482:       nsize: 2
483:       args: -tao_smonitor -mx 10 -my 16 -ecc 0.9 -tao_type bqpip -tao_gatol 1.e-4 -test_getdiagonal
484:       output_file: output/jbearing2_3.out
485:       requires: !single

487:    test:
488:       suffix: 5
489:       args: -tao_smonitor -mx 8 -my 12 -tao_type bncg -tao_bncg_type gd -tao_gatol 1e-4
490:       requires: !single

492:    test:
493:       suffix: 6
494:       args: -tao_smonitor -mx 8 -my 12 -tao_type bncg -tao_gatol 1e-4
495:       requires: !single

497:    test:
498:       suffix: 7
499:       args: -tao_smonitor -mx 8 -my 12 -tao_type bnls -tao_gatol 1e-5
500:       requires: !single

502:    test:
503:       suffix: 8
504:       args: -tao_smonitor -mx 8 -my 12 -tao_type bntr -tao_gatol 1e-5
505:       requires: !single

507:    test:
508:       suffix: 9
509:       args: -tao_smonitor -mx 8 -my 12 -tao_type bntl -tao_gatol 1e-5
510:       requires: !single

512:    test:
513:       suffix: 10
514:       args: -tao_smonitor -mx 8 -my 12 -tao_type bnls -tao_gatol 1e-5 -tao_bnk_max_cg_its 3
515:       requires: !single

517:    test:
518:       suffix: 11
519:       args: -tao_smonitor -mx 8 -my 12 -tao_type bntr -tao_gatol 1e-5 -tao_bnk_max_cg_its 3
520:       requires: !single

522:    test:
523:       suffix: 12
524:       args: -tao_smonitor -mx 8 -my 12 -tao_type bntl -tao_gatol 1e-5 -tao_bnk_max_cg_its 3
525:       requires: !single

527:    test:
528:      suffix: 13
529:      args: -tao_smonitor -mx 8 -my 12 -tao_gatol 1e-4 -tao_type bqnls
530:      requires: !single

532:    test:
533:      suffix: 14
534:      args: -tao_smonitor -mx 8 -my 12 -tao_gatol 1e-4 -tao_type blmvm
535:      requires: !single

537:    test:
538:      suffix: 15
539:      args: -tao_smonitor -mx 8 -my 12 -tao_gatol 1e-4 -tao_type bqnkls -tao_bqnk_mat_type lmvmbfgs
540:      requires: !single

542:    test:
543:      suffix: 16
544:      args: -tao_smonitor -mx 8 -my 12 -tao_gatol 1e-4 -tao_type bqnktr -tao_bqnk_mat_type lmvmsr1
545:      requires: !single

547:    test:
548:      suffix: 17
549:      args: -tao_smonitor -mx 8 -my 12 -tao_gatol 1e-4 -tao_type bqnls -tao_bqnls_mat_lmvm_scale_type scalar -tao_view
550:      requires: !single

552:    test:
553:      suffix: 18
554:      args: -tao_smonitor -mx 8 -my 12 -tao_gatol 1e-4 -tao_type bqnls -tao_bqnls_mat_lmvm_scale_type none -tao_view
555:      requires: !single

557: TEST*/