Date: 2021-03-03T22:28:12+00:00

Actual source code: jbearing2.c
petsc-3.14.5 2021-03-03
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      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*/

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

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

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

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

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

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

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

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

     96:   /* Let Petsc determine the grid division */
     97:   Nx = PETSC_DECIDE; Ny = PETSC_DECIDE;

     99:   /*
    100:      A two dimensional distributed array will help define this problem,
    101:      which derives from an elliptic PDE on two dimensional domain.  From
    102:      the distributed array, Create the vectors.
    103:   */
    104:   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);
    105:   DMSetFromOptions(user.dm);
    106:   DMSetUp(user.dm);

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

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

    122:   if (testgetdiag) {
    123:     MatSetOperation(user.A,MATOP_GET_DIAGONAL,NULL);
    124:   }

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

    129:   /* The TAO code begins here */

    131:   /*
    132:      Create the optimization solver
    133:      Suitable methods: TAOGPCG, TAOBQPIP, TAOTRON, TAOBLMVM
    134:   */
    135:   TaoCreate(PETSC_COMM_WORLD,&tao);
    136:   TaoSetType(tao,TAOBLMVM);

    139:   /* Set the initial vector */
    140:   VecSet(x, zero);
    141:   TaoSetInitialVector(tao,x);

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

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

    148:   /* Set a routine that defines the bounds */
    149:   VecDuplicate(x,&xl);
    150:   VecDuplicate(x,&xu);
    151:   VecSet(xl, zero);
    152:   VecSet(xu, d1000);
    153:   TaoSetVariableBounds(tao,xl,xu);

    155:   TaoGetKSP(tao,&ksp);
    156:   if (ksp) {
    157:     KSPSetType(ksp,KSPCG);
    158:   }

    160:   PetscOptionsHasName(NULL,NULL,"-testmonitor",&flg);
    161:   if (flg) {
    162:     TaoSetMonitor(tao,Monitor,&user,NULL);
    163:   }
    164:   PetscOptionsHasName(NULL,NULL,"-testconvergence",&flg);
    165:   if (flg) {
    166:     TaoSetConvergenceTest(tao,ConvergenceTest,&user);
    167:   }

    169:   /* Check for any tao command line options */
    170:   TaoSetFromOptions(tao);

    172:   /* Solve the bound constrained problem */
    173:   TaoSolve(tao);

    175:   /* Free PETSc data structures */
    176:   VecDestroy(&x);
    177:   VecDestroy(&xl);
    178:   VecDestroy(&xu);
    179:   MatDestroy(&user.A);
    180:   VecDestroy(&user.B);

    182:   /* Free TAO data structures */
    183:   TaoDestroy(&tao);
    184:   DMDestroy(&user.dm);
    185:   PetscFinalize();
    186:   return ierr;
    187: }

    190: static PetscReal p(PetscReal xi, PetscReal ecc)
    191: {
    192:   PetscReal t=1.0+ecc*PetscCosScalar(xi);
    193:   return (t*t*t);
    194: }

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

    206:   nx=user->nx;
    207:   ny=user->ny;
    208:   hx=two*pi/(nx+1.0);
    209:   hy=two*user->b/(ny+1.0);
    210:   ehxhy = ecc*hx*hy;

    213:   /*
    214:      Get local grid boundaries
    215:   */
    216:   DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
    217:   DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);

    219:   /* Compute the linear term in the objective function */
    220:   VecGetArray(user->B,&b);
    221:   for (i=xs; i<xs+xm; i++){
    222:     temp=PetscSinScalar((i+1)*hx);
    223:     for (j=ys; j<ys+ym; j++){
    224:       k=xm*(j-ys)+(i-xs);
    225:       b[k]=  - ehxhy*temp;
    226:     }
    227:   }
    228:   VecRestoreArray(user->B,&b);
    229:   PetscLogFlops(5.0*xm*ym+3.0*xm);

    231:   return 0;
    232: }

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

    249:   nx=user->nx;
    250:   ny=user->ny;
    251:   hx=two*pi/(nx+1.0);
    252:   hy=two*user->b/(ny+1.0);
    253:   hxhy=hx*hy;
    254:   hxhx=one/(hx*hx);
    255:   hyhy=one/(hy*hy);

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

    259:   DMGlobalToLocalBegin(user->dm,X,INSERT_VALUES,localX);
    260:   DMGlobalToLocalEnd(user->dm,X,INSERT_VALUES,localX);

    262:   VecSet(G, zero);
    263:   /*
    264:     Get local grid boundaries
    265:   */
    266:   DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
    267:   DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);

    269:   VecGetArray(localX,&x);
    270:   VecGetArray(G,&g);

    272:   for (i=xs; i< xs+xm; i++){
    273:     xi=(i+1)*hx;
    274:     trule1=hxhy*(p(xi,ecc) + p(xi+hx,ecc) + p(xi,ecc)) / six; /* L(i,j) */
    275:     trule2=hxhy*(p(xi,ecc) + p(xi-hx,ecc) + p(xi,ecc)) / six; /* U(i,j) */
    276:     trule3=hxhy*(p(xi,ecc) + p(xi+hx,ecc) + p(xi+hx,ecc)) / six; /* U(i+1,j) */
    277:     trule4=hxhy*(p(xi,ecc) + p(xi-hx,ecc) + p(xi-hx,ecc)) / six; /* L(i-1,j) */
    278:     trule5=trule1; /* L(i,j-1) */
    279:     trule6=trule2; /* U(i,j+1) */

    281:     vdown=-(trule5+trule2)*hyhy;
    282:     vleft=-hxhx*(trule2+trule4);
    283:     vright= -hxhx*(trule1+trule3);
    284:     vup=-hyhy*(trule1+trule6);
    285:     vmiddle=(hxhx)*(trule1+trule2+trule3+trule4)+hyhy*(trule1+trule2+trule5+trule6);

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

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

    292:        k=0;
    293:        if (j>gys){
    294:          v[k]=vdown; col[k]=row - gxm; k++;
    295:        }

    297:        if (i>gxs){
    298:          v[k]= vleft; col[k]=row - 1; k++;
    299:        }

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

    303:        if (i+1 < gxs+gxm){
    304:          v[k]= vright; col[k]=row+1; k++;
    305:        }

    307:        if (j+1 <gys+gym){
    308:          v[k]= vup; col[k] = row+gxm; k++;
    309:        }
    310:        tt=0;
    311:        for (kk=0;kk<k;kk++){
    312:          tt+=v[kk]*x[col[kk]];
    313:        }
    314:        row=(j-ys)*xm + (i-xs);
    315:        g[row]=tt;

    317:      }

    319:   }

    321:   VecRestoreArray(localX,&x);
    322:   VecRestoreArray(G,&g);

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

    326:   VecDot(X,G,&f1);
    327:   VecDot(user->B,X,&f2);
    328:   VecAXPY(G, one, user->B);
    329:   *fcn = f1/2.0 + f2;

    332:   PetscLogFlops((91 + 10.0*ym) * xm);
    333:   return 0;

    335: }

    338: /*
    339:    FormHessian computes the quadratic term in the quadratic objective function
    340:    Notice that the objective function in this problem is quadratic (therefore a constant
    341:    hessian).  If using a nonquadratic solver, then you might want to reconsider this function
    342: */
    343: PetscErrorCode FormHessian(Tao tao,Vec X,Mat hes, Mat Hpre, void *ptr)
    344: {
    345:   AppCtx*        user=(AppCtx*)ptr;
    347:   PetscInt       i,j,k;
    348:   PetscInt       col[5],row,nx,ny,xs,xm,gxs,gxm,ys,ym,gys,gym;
    349:   PetscReal      one=1.0, two=2.0, six=6.0,pi=4.0*atan(1.0);
    350:   PetscReal      hx,hy,hxhy,hxhx,hyhy;
    351:   PetscReal      xi,v[5];
    352:   PetscReal      ecc=user->ecc, trule1,trule2,trule3,trule4,trule5,trule6;
    353:   PetscReal      vmiddle, vup, vdown, vleft, vright;
    354:   PetscBool      assembled;

    356:   nx=user->nx;
    357:   ny=user->ny;
    358:   hx=two*pi/(nx+1.0);
    359:   hy=two*user->b/(ny+1.0);
    360:   hxhy=hx*hy;
    361:   hxhx=one/(hx*hx);
    362:   hyhy=one/(hy*hy);

    364:   /*
    365:     Get local grid boundaries
    366:   */
    367:   DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
    368:   DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
    369:   MatAssembled(hes,&assembled);
    370:   if (assembled){MatZeroEntries(hes);}

    372:   for (i=xs; i< xs+xm; i++){
    373:     xi=(i+1)*hx;
    374:     trule1=hxhy*(p(xi,ecc) + p(xi+hx,ecc) + p(xi,ecc)) / six; /* L(i,j) */
    375:     trule2=hxhy*(p(xi,ecc) + p(xi-hx,ecc) + p(xi,ecc)) / six; /* U(i,j) */
    376:     trule3=hxhy*(p(xi,ecc) + p(xi+hx,ecc) + p(xi+hx,ecc)) / six; /* U(i+1,j) */
    377:     trule4=hxhy*(p(xi,ecc) + p(xi-hx,ecc) + p(xi-hx,ecc)) / six; /* L(i-1,j) */
    378:     trule5=trule1; /* L(i,j-1) */
    379:     trule6=trule2; /* U(i,j+1) */

    381:     vdown=-(trule5+trule2)*hyhy;
    382:     vleft=-hxhx*(trule2+trule4);
    383:     vright= -hxhx*(trule1+trule3);
    384:     vup=-hyhy*(trule1+trule6);
    385:     vmiddle=(hxhx)*(trule1+trule2+trule3+trule4)+hyhy*(trule1+trule2+trule5+trule6);
    386:     v[0]=0; v[1]=0; v[2]=0; v[3]=0; v[4]=0;

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

    391:       k=0;
    392:       if (j>gys){
    393:         v[k]=vdown; col[k]=row - gxm; k++;
    394:       }

    396:       if (i>gxs){
    397:         v[k]= vleft; col[k]=row - 1; k++;
    398:       }

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

    402:       if (i+1 < gxs+gxm){
    403:         v[k]= vright; col[k]=row+1; k++;
    404:       }

    406:       if (j+1 <gys+gym){
    407:         v[k]= vup; col[k] = row+gxm; k++;
    408:       }
    409:       MatSetValuesLocal(hes,1,&row,k,col,v,INSERT_VALUES);

    411:     }

    413:   }

    415:   /*
    416:      Assemble matrix, using the 2-step process:
    417:      MatAssemblyBegin(), MatAssemblyEnd().
    418:      By placing code between these two statements, computations can be
    419:      done while messages are in transition.
    420:   */
    421:   MatAssemblyBegin(hes,MAT_FINAL_ASSEMBLY);
    422:   MatAssemblyEnd(hes,MAT_FINAL_ASSEMBLY);

    424:   /*
    425:     Tell the matrix we will never add a new nonzero location to the
    426:     matrix. If we do it will generate an error.
    427:   */
    428:   MatSetOption(hes,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
    429:   MatSetOption(hes,MAT_SYMMETRIC,PETSC_TRUE);

    431:   PetscLogFlops(9.0*xm*ym+49.0*xm);
    432:   MatNorm(hes,NORM_1,&hx);
    433:   return 0;
    434: }

    436: PetscErrorCode Monitor(Tao tao, void *ctx)
    437: {
    438:   PetscErrorCode     ierr;
    439:   PetscInt           its;
    440:   PetscReal          f,gnorm,cnorm,xdiff;
    441:   TaoConvergedReason reason;

    444:   TaoGetSolutionStatus(tao, &its, &f, &gnorm, &cnorm, &xdiff, &reason);
    445:   if (!(its%5)) {
    446:     PetscPrintf(PETSC_COMM_WORLD,"iteration=%D\tf=%g\n",its,(double)f);
    447:   }
    448:   return(0);
    449: }

    451: PetscErrorCode ConvergenceTest(Tao tao, void *ctx)
    452: {
    453:   PetscErrorCode     ierr;
    454:   PetscInt           its;
    455:   PetscReal          f,gnorm,cnorm,xdiff;
    456:   TaoConvergedReason reason;

    459:   TaoGetSolutionStatus(tao, &its, &f, &gnorm, &cnorm, &xdiff, &reason);
    460:   if (its == 100) {
    461:     TaoSetConvergedReason(tao,TAO_DIVERGED_MAXITS);
    462:   }
    463:   return(0);

    465: }

    468: /*TEST

    470:    build:
    471:       requires: !complex

    473:    test:
    474:       args: -tao_smonitor -mx 8 -my 12 -tao_type tron -tao_gatol 1.e-5
    475:       requires: !single

    477:    test:
    478:       suffix: 2
    479:       nsize: 2
    480:       args: -tao_smonitor -mx 50 -my 50 -ecc 0.99 -tao_type gpcg -tao_gatol 1.e-5
    481:       requires: !single

    483:    test:
    484:       suffix: 3
    485:       nsize: 2
    486:       args: -tao_smonitor -mx 10 -my 16 -ecc 0.9 -tao_type bqpip -tao_gatol 1.e-4
    487:       requires: !single

    489:    test:
    490:       suffix: 4
    491:       nsize: 2
    492:       args: -tao_smonitor -mx 10 -my 16 -ecc 0.9 -tao_type bqpip -tao_gatol 1.e-4 -test_getdiagonal
    493:       output_file: output/jbearing2_3.out
    494:       requires: !single

    496:    test:
    497:       suffix: 5
    498:       args: -tao_smonitor -mx 8 -my 12 -tao_type bncg -tao_bncg_type gd -tao_gatol 1e-4
    499:       requires: !single

    501:    test:
    502:       suffix: 6
    503:       args: -tao_smonitor -mx 8 -my 12 -tao_type bncg -tao_gatol 1e-4
    504:       requires: !single

    506:    test:
    507:       suffix: 7
    508:       args: -tao_smonitor -mx 8 -my 12 -tao_type bnls -tao_gatol 1e-5
    509:       requires: !single

    511:    test:
    512:       suffix: 8
    513:       args: -tao_smonitor -mx 8 -my 12 -tao_type bntr -tao_gatol 1e-5
    514:       requires: !single

    516:    test:
    517:       suffix: 9
    518:       args: -tao_smonitor -mx 8 -my 12 -tao_type bntl -tao_gatol 1e-5
    519:       requires: !single

    521:    test:
    522:       suffix: 10
    523:       args: -tao_smonitor -mx 8 -my 12 -tao_type bnls -tao_gatol 1e-5 -tao_bnk_max_cg_its 3
    524:       requires: !single

    526:    test:
    527:       suffix: 11
    528:       args: -tao_smonitor -mx 8 -my 12 -tao_type bntr -tao_gatol 1e-5 -tao_bnk_max_cg_its 3
    529:       requires: !single

    531:    test:
    532:       suffix: 12
    533:       args: -tao_smonitor -mx 8 -my 12 -tao_type bntl -tao_gatol 1e-5 -tao_bnk_max_cg_its 3
    534:       requires: !single

    536:    test:
    537:      suffix: 13
    538:      args: -tao_smonitor -mx 8 -my 12 -tao_gatol 1e-4 -tao_type bqnls
    539:      requires: !single

    541:    test:
    542:      suffix: 14
    543:      args: -tao_smonitor -mx 8 -my 12 -tao_gatol 1e-4 -tao_type blmvm
    544:      requires: !single

    546:    test:
    547:      suffix: 15
    548:      args: -tao_smonitor -mx 8 -my 12 -tao_gatol 1e-4 -tao_type bqnkls -tao_bqnk_mat_type lmvmbfgs
    549:      requires: !single

    551:    test:
    552:      suffix: 16
    553:      args: -tao_smonitor -mx 8 -my 12 -tao_gatol 1e-4 -tao_type bqnktr -tao_bqnk_mat_type lmvmsr1
    554:      requires: !single

    556:    test:
    557:      suffix: 17
    558:      args: -tao_smonitor -mx 8 -my 12 -tao_gatol 1e-4 -tao_type bqnls -tao_bqnls_mat_lmvm_scale_type scalar -tao_view
    559:      requires: !single

    561:    test:
    562:      suffix: 18
    563:      args: -tao_smonitor -mx 8 -my 12 -tao_gatol 1e-4 -tao_type bqnls -tao_bqnls_mat_lmvm_scale_type none -tao_view
    564:      requires: !single

    566: TEST*/