Date: 2022-03-31T04:48:33+00:00

Actual source code: ex3.c

      1: static char help[] = "Newton methods to solve u'' + u^{2} = f in parallel.\n\
      2: This example employs a user-defined monitoring routine and optionally a user-defined\n\
      3: routine to check candidate iterates produced by line search routines.\n\
      4: The command line options include:\n\
      5:   -pre_check_iterates : activate checking of iterates\n\
      6:   -post_check_iterates : activate checking of iterates\n\
      7:   -check_tol <tol>: set tolerance for iterate checking\n\
      8:   -user_precond : activate a (trivial) user-defined preconditioner\n\n";

     10: /*T
     11:    Concepts: SNES^basic parallel example
     12:    Concepts: SNES^setting a user-defined monitoring routine
     13:    Processors: n
     14: T*/

     16: /*
     17:    Include "petscdm.h" so that we can use data management objects (DMs)
     18:    Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
     19:    Include "petscsnes.h" so that we can use SNES solvers.  Note that this
     20:    file automatically includes:
     21:      petscsys.h    - base PETSc routines
     22:      petscvec.h    - vectors
     23:      petscmat.h    - matrices
     24:      petscis.h     - index sets
     25:      petscksp.h    - Krylov subspace methods
     26:      petscviewer.h - viewers
     27:      petscpc.h     - preconditioners
     28:      petscksp.h    - linear solvers
     29: */

     31: #include <petscdm.h>
     32: #include <petscdmda.h>
     33: #include <petscsnes.h>

     35: /*
     36:    User-defined routines.
     37: */
     38: PetscErrorCode FormJacobian(SNES,Vec,Mat,Mat,void*);
     39: PetscErrorCode FormFunction(SNES,Vec,Vec,void*);
     40: PetscErrorCode FormInitialGuess(Vec);
     41: PetscErrorCode Monitor(SNES,PetscInt,PetscReal,void*);
     42: PetscErrorCode PreCheck(SNESLineSearch,Vec,Vec,PetscBool*,void*);
     43: PetscErrorCode PostCheck(SNESLineSearch,Vec,Vec,Vec,PetscBool*,PetscBool*,void*);
     44: PetscErrorCode PostSetSubKSP(SNESLineSearch,Vec,Vec,Vec,PetscBool*,PetscBool*,void*);
     45: PetscErrorCode MatrixFreePreconditioner(PC,Vec,Vec);

     47: /*
     48:    User-defined application context
     49: */
     50: typedef struct {
     51:   DM          da;      /* distributed array */
     52:   Vec         F;       /* right-hand-side of PDE */
     53:   PetscMPIInt rank;    /* rank of processor */
     54:   PetscMPIInt size;    /* size of communicator */
     55:   PetscReal   h;       /* mesh spacing */
     56:   PetscBool   sjerr;   /* if or not to test jacobian domain error */
     57: } ApplicationCtx;

     59: /*
     60:    User-defined context for monitoring
     61: */
     62: typedef struct {
     63:   PetscViewer viewer;
     64: } MonitorCtx;

     66: /*
     67:    User-defined context for checking candidate iterates that are
     68:    determined by line search methods
     69: */
     70: typedef struct {
     71:   Vec            last_step;  /* previous iterate */
     72:   PetscReal      tolerance;  /* tolerance for changes between successive iterates */
     73:   ApplicationCtx *user;
     74: } StepCheckCtx;

     76: typedef struct {
     77:   PetscInt its0; /* num of prevous outer KSP iterations */
     78: } SetSubKSPCtx;

     80: int main(int argc,char **argv)
     81: {
     82:   SNES           snes;                 /* SNES context */
     83:   SNESLineSearch linesearch;           /* SNESLineSearch context */
     84:   Mat            J;                    /* Jacobian matrix */
     85:   ApplicationCtx ctx;                  /* user-defined context */
     86:   Vec            x,r,U,F;              /* vectors */
     87:   MonitorCtx     monP;                 /* monitoring context */
     88:   StepCheckCtx   checkP;               /* step-checking context */
     89:   SetSubKSPCtx   checkP1;
     90:   PetscBool      pre_check,post_check,post_setsubksp; /* flag indicating whether we're checking candidate iterates */
     91:   PetscScalar    xp,*FF,*UU,none = -1.0;
     92:   PetscInt       its,N = 5,i,maxit,maxf,xs,xm;
     93:   PetscReal      abstol,rtol,stol,norm;
     94:   PetscBool      flg,viewinitial = PETSC_FALSE;

     96:   PetscInitialize(&argc,&argv,(char*)0,help);
     97:   MPI_Comm_rank(PETSC_COMM_WORLD,&ctx.rank);
     98:   MPI_Comm_size(PETSC_COMM_WORLD,&ctx.size);
     99:   PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL);
    100:   ctx.h = 1.0/(N-1);
    101:   ctx.sjerr = PETSC_FALSE;
    102:   PetscOptionsGetBool(NULL,NULL,"-test_jacobian_domain_error",&ctx.sjerr,NULL);
    103:   PetscOptionsGetBool(NULL,NULL,"-view_initial",&viewinitial,NULL);

    105:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    106:      Create nonlinear solver context
    107:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    109:   SNESCreate(PETSC_COMM_WORLD,&snes);

    111:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    112:      Create vector data structures; set function evaluation routine
    113:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    115:   /*
    116:      Create distributed array (DMDA) to manage parallel grid and vectors
    117:   */
    118:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,N,1,1,NULL,&ctx.da);
    119:   DMSetFromOptions(ctx.da);
    120:   DMSetUp(ctx.da);

    122:   /*
    123:      Extract global and local vectors from DMDA; then duplicate for remaining
    124:      vectors that are the same types
    125:   */
    126:   DMCreateGlobalVector(ctx.da,&x);
    127:   VecDuplicate(x,&r);
    128:   VecDuplicate(x,&F); ctx.F = F;
    129:   VecDuplicate(x,&U);

    131:   /*
    132:      Set function evaluation routine and vector.  Whenever the nonlinear
    133:      solver needs to compute the nonlinear function, it will call this
    134:      routine.
    135:       - Note that the final routine argument is the user-defined
    136:         context that provides application-specific data for the
    137:         function evaluation routine.
    138:   */
    139:   SNESSetFunction(snes,r,FormFunction,&ctx);

    141:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    142:      Create matrix data structure; set Jacobian evaluation routine
    143:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    145:   MatCreate(PETSC_COMM_WORLD,&J);
    146:   MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,N,N);
    147:   MatSetFromOptions(J);
    148:   MatSeqAIJSetPreallocation(J,3,NULL);
    149:   MatMPIAIJSetPreallocation(J,3,NULL,3,NULL);

    151:   /*
    152:      Set Jacobian matrix data structure and default Jacobian evaluation
    153:      routine.  Whenever the nonlinear solver needs to compute the
    154:      Jacobian matrix, it will call this routine.
    155:       - Note that the final routine argument is the user-defined
    156:         context that provides application-specific data for the
    157:         Jacobian evaluation routine.
    158:   */
    159:   SNESSetJacobian(snes,J,J,FormJacobian,&ctx);

    161:   /*
    162:      Optionally allow user-provided preconditioner
    163:    */
    164:   PetscOptionsHasName(NULL,NULL,"-user_precond",&flg);
    165:   if (flg) {
    166:     KSP ksp;
    167:     PC  pc;
    168:     SNESGetKSP(snes,&ksp);
    169:     KSPGetPC(ksp,&pc);
    170:     PCSetType(pc,PCSHELL);
    171:     PCShellSetApply(pc,MatrixFreePreconditioner);
    172:   }

    174:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    175:      Customize nonlinear solver; set runtime options
    176:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    178:   /*
    179:      Set an optional user-defined monitoring routine
    180:   */
    181:   PetscViewerDrawOpen(PETSC_COMM_WORLD,0,0,0,0,400,400,&monP.viewer);
    182:   SNESMonitorSet(snes,Monitor,&monP,0);

    184:   /*
    185:      Set names for some vectors to facilitate monitoring (optional)
    186:   */
    187:   PetscObjectSetName((PetscObject)x,"Approximate Solution");
    188:   PetscObjectSetName((PetscObject)U,"Exact Solution");

    190:   /*
    191:      Set SNES/KSP/KSP/PC runtime options, e.g.,
    192:          -snes_view -snes_monitor -ksp_type <ksp> -pc_type <pc>
    193:   */
    194:   SNESSetFromOptions(snes);

    196:   /*
    197:      Set an optional user-defined routine to check the validity of candidate
    198:      iterates that are determined by line search methods
    199:   */
    200:   SNESGetLineSearch(snes, &linesearch);
    201:   PetscOptionsHasName(NULL,NULL,"-post_check_iterates",&post_check);

    203:   if (post_check) {
    204:     PetscPrintf(PETSC_COMM_WORLD,"Activating post step checking routine\n");
    205:     SNESLineSearchSetPostCheck(linesearch,PostCheck,&checkP);
    206:     VecDuplicate(x,&(checkP.last_step));

    208:     checkP.tolerance = 1.0;
    209:     checkP.user      = &ctx;

    211:     PetscOptionsGetReal(NULL,NULL,"-check_tol",&checkP.tolerance,NULL);
    212:   }

    214:   PetscOptionsHasName(NULL,NULL,"-post_setsubksp",&post_setsubksp);
    215:   if (post_setsubksp) {
    216:     PetscPrintf(PETSC_COMM_WORLD,"Activating post setsubksp\n");
    217:     SNESLineSearchSetPostCheck(linesearch,PostSetSubKSP,&checkP1);
    218:   }

    220:   PetscOptionsHasName(NULL,NULL,"-pre_check_iterates",&pre_check);
    221:   if (pre_check) {
    222:     PetscPrintf(PETSC_COMM_WORLD,"Activating pre step checking routine\n");
    223:     SNESLineSearchSetPreCheck(linesearch,PreCheck,&checkP);
    224:   }

    226:   /*
    227:      Print parameters used for convergence testing (optional) ... just
    228:      to demonstrate this routine; this information is also printed with
    229:      the option -snes_view
    230:   */
    231:   SNESGetTolerances(snes,&abstol,&rtol,&stol,&maxit,&maxf);
    232:   PetscPrintf(PETSC_COMM_WORLD,"atol=%g, rtol=%g, stol=%g, maxit=%D, maxf=%D\n",(double)abstol,(double)rtol,(double)stol,maxit,maxf);

    234:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    235:      Initialize application:
    236:      Store right-hand-side of PDE and exact solution
    237:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    239:   /*
    240:      Get local grid boundaries (for 1-dimensional DMDA):
    241:        xs, xm - starting grid index, width of local grid (no ghost points)
    242:   */
    243:   DMDAGetCorners(ctx.da,&xs,NULL,NULL,&xm,NULL,NULL);

    245:   /*
    246:      Get pointers to vector data
    247:   */
    248:   DMDAVecGetArray(ctx.da,F,&FF);
    249:   DMDAVecGetArray(ctx.da,U,&UU);

    251:   /*
    252:      Compute local vector entries
    253:   */
    254:   xp = ctx.h*xs;
    255:   for (i=xs; i<xs+xm; i++) {
    256:     FF[i] = 6.0*xp + PetscPowScalar(xp+1.e-12,6.0); /* +1.e-12 is to prevent 0^6 */
    257:     UU[i] = xp*xp*xp;
    258:     xp   += ctx.h;
    259:   }

    261:   /*
    262:      Restore vectors
    263:   */
    264:   DMDAVecRestoreArray(ctx.da,F,&FF);
    265:   DMDAVecRestoreArray(ctx.da,U,&UU);
    266:   if (viewinitial) {
    267:     VecView(U,0);
    268:     VecView(F,0);
    269:   }

    271:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    272:      Evaluate initial guess; then solve nonlinear system
    273:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    275:   /*
    276:      Note: The user should initialize the vector, x, with the initial guess
    277:      for the nonlinear solver prior to calling SNESSolve().  In particular,
    278:      to employ an initial guess of zero, the user should explicitly set
    279:      this vector to zero by calling VecSet().
    280:   */
    281:   FormInitialGuess(x);
    282:   SNESSolve(snes,NULL,x);
    283:   SNESGetIterationNumber(snes,&its);
    284:   PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %D\n",its);

    286:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    287:      Check solution and clean up
    288:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    290:   /*
    291:      Check the error
    292:   */
    293:   VecAXPY(x,none,U);
    294:   VecNorm(x,NORM_2,&norm);
    295:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g Iterations %D\n",(double)norm,its);
    296:   if (ctx.sjerr) {
    297:     SNESType       snestype;
    298:     SNESGetType(snes,&snestype);
    299:     PetscPrintf(PETSC_COMM_WORLD,"SNES Type %s\n",snestype);
    300:   }

    302:   /*
    303:      Free work space.  All PETSc objects should be destroyed when they
    304:      are no longer needed.
    305:   */
    306:   PetscViewerDestroy(&monP.viewer);
    307:   if (post_check) VecDestroy(&checkP.last_step);
    308:   VecDestroy(&x);
    309:   VecDestroy(&r);
    310:   VecDestroy(&U);
    311:   VecDestroy(&F);
    312:   MatDestroy(&J);
    313:   SNESDestroy(&snes);
    314:   DMDestroy(&ctx.da);
    315:   PetscFinalize();
    316:   return 0;
    317: }

    319: /* ------------------------------------------------------------------- */
    320: /*
    321:    FormInitialGuess - Computes initial guess.

    323:    Input/Output Parameter:
    324: .  x - the solution vector
    325: */
    326: PetscErrorCode FormInitialGuess(Vec x)
    327: {
    328:   PetscScalar    pfive = .50;

    331:   VecSet(x,pfive);
    332:   return 0;
    333: }

    335: /* ------------------------------------------------------------------- */
    336: /*
    337:    FormFunction - Evaluates nonlinear function, F(x).

    339:    Input Parameters:
    340: .  snes - the SNES context
    341: .  x - input vector
    342: .  ctx - optional user-defined context, as set by SNESSetFunction()

    344:    Output Parameter:
    345: .  f - function vector

    347:    Note:
    348:    The user-defined context can contain any application-specific
    349:    data needed for the function evaluation.
    350: */
    351: PetscErrorCode FormFunction(SNES snes,Vec x,Vec f,void *ctx)
    352: {
    353:   ApplicationCtx *user = (ApplicationCtx*) ctx;
    354:   DM             da    = user->da;
    355:   PetscScalar    *xx,*ff,*FF,d;
    356:   PetscInt       i,M,xs,xm;
    357:   Vec            xlocal;

    360:   DMGetLocalVector(da,&xlocal);
    361:   /*
    362:      Scatter ghost points to local vector, using the 2-step process
    363:         DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
    364:      By placing code between these two statements, computations can
    365:      be done while messages are in transition.
    366:   */
    367:   DMGlobalToLocalBegin(da,x,INSERT_VALUES,xlocal);
    368:   DMGlobalToLocalEnd(da,x,INSERT_VALUES,xlocal);

    370:   /*
    371:      Get pointers to vector data.
    372:        - The vector xlocal includes ghost point; the vectors x and f do
    373:          NOT include ghost points.
    374:        - Using DMDAVecGetArray() allows accessing the values using global ordering
    375:   */
    376:   DMDAVecGetArray(da,xlocal,&xx);
    377:   DMDAVecGetArray(da,f,&ff);
    378:   DMDAVecGetArray(da,user->F,&FF);

    380:   /*
    381:      Get local grid boundaries (for 1-dimensional DMDA):
    382:        xs, xm  - starting grid index, width of local grid (no ghost points)
    383:   */
    384:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);
    385:   DMDAGetInfo(da,NULL,&M,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);

    387:   /*
    388:      Set function values for boundary points; define local interior grid point range:
    389:         xsi - starting interior grid index
    390:         xei - ending interior grid index
    391:   */
    392:   if (xs == 0) { /* left boundary */
    393:     ff[0] = xx[0];
    394:     xs++;xm--;
    395:   }
    396:   if (xs+xm == M) {  /* right boundary */
    397:     ff[xs+xm-1] = xx[xs+xm-1] - 1.0;
    398:     xm--;
    399:   }

    401:   /*
    402:      Compute function over locally owned part of the grid (interior points only)
    403:   */
    404:   d = 1.0/(user->h*user->h);
    405:   for (i=xs; i<xs+xm; i++) ff[i] = d*(xx[i-1] - 2.0*xx[i] + xx[i+1]) + xx[i]*xx[i] - FF[i];

    407:   /*
    408:      Restore vectors
    409:   */
    410:   DMDAVecRestoreArray(da,xlocal,&xx);
    411:   DMDAVecRestoreArray(da,f,&ff);
    412:   DMDAVecRestoreArray(da,user->F,&FF);
    413:   DMRestoreLocalVector(da,&xlocal);
    414:   return 0;
    415: }

    417: /* ------------------------------------------------------------------- */
    418: /*
    419:    FormJacobian - Evaluates Jacobian matrix.

    421:    Input Parameters:
    422: .  snes - the SNES context
    423: .  x - input vector
    424: .  dummy - optional user-defined context (not used here)

    426:    Output Parameters:
    427: .  jac - Jacobian matrix
    428: .  B - optionally different preconditioning matrix
    429: .  flag - flag indicating matrix structure
    430: */
    431: PetscErrorCode FormJacobian(SNES snes,Vec x,Mat jac,Mat B,void *ctx)
    432: {
    433:   ApplicationCtx *user = (ApplicationCtx*) ctx;
    434:   PetscScalar    *xx,d,A[3];
    435:   PetscInt       i,j[3],M,xs,xm;
    436:   DM             da = user->da;

    439:   if (user->sjerr) {
    440:     SNESSetJacobianDomainError(snes);
    441:     return 0;
    442:   }
    443:   /*
    444:      Get pointer to vector data
    445:   */
    446:   DMDAVecGetArrayRead(da,x,&xx);
    447:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);

    449:   /*
    450:     Get range of locally owned matrix
    451:   */
    452:   DMDAGetInfo(da,NULL,&M,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);

    454:   /*
    455:      Determine starting and ending local indices for interior grid points.
    456:      Set Jacobian entries for boundary points.
    457:   */

    459:   if (xs == 0) {  /* left boundary */
    460:     i = 0; A[0] = 1.0;

    462:     MatSetValues(jac,1,&i,1,&i,A,INSERT_VALUES);
    463:     xs++;xm--;
    464:   }
    465:   if (xs+xm == M) { /* right boundary */
    466:     i    = M-1;
    467:     A[0] = 1.0;
    468:     MatSetValues(jac,1,&i,1,&i,A,INSERT_VALUES);
    469:     xm--;
    470:   }

    472:   /*
    473:      Interior grid points
    474:       - Note that in this case we set all elements for a particular
    475:         row at once.
    476:   */
    477:   d = 1.0/(user->h*user->h);
    478:   for (i=xs; i<xs+xm; i++) {
    479:     j[0] = i - 1; j[1] = i; j[2] = i + 1;
    480:     A[0] = A[2] = d; A[1] = -2.0*d + 2.0*xx[i];
    481:     MatSetValues(jac,1,&i,3,j,A,INSERT_VALUES);
    482:   }

    484:   /*
    485:      Assemble matrix, using the 2-step process:
    486:        MatAssemblyBegin(), MatAssemblyEnd().
    487:      By placing code between these two statements, computations can be
    488:      done while messages are in transition.

    490:      Also, restore vector.
    491:   */

    493:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    494:   DMDAVecRestoreArrayRead(da,x,&xx);
    495:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);

    497:   return 0;
    498: }

    500: /* ------------------------------------------------------------------- */
    501: /*
    502:    Monitor - Optional user-defined monitoring routine that views the
    503:    current iterate with an x-window plot. Set by SNESMonitorSet().

    505:    Input Parameters:
    506:    snes - the SNES context
    507:    its - iteration number
    508:    norm - 2-norm function value (may be estimated)
    509:    ctx - optional user-defined context for private data for the
    510:          monitor routine, as set by SNESMonitorSet()

    512:    Note:
    513:    See the manpage for PetscViewerDrawOpen() for useful runtime options,
    514:    such as -nox to deactivate all x-window output.
    515:  */
    516: PetscErrorCode Monitor(SNES snes,PetscInt its,PetscReal fnorm,void *ctx)
    517: {
    518:   MonitorCtx     *monP = (MonitorCtx*) ctx;
    519:   Vec            x;

    522:   PetscPrintf(PETSC_COMM_WORLD,"iter = %D,SNES Function norm %g\n",its,(double)fnorm);
    523:   SNESGetSolution(snes,&x);
    524:   VecView(x,monP->viewer);
    525:   return 0;
    526: }

    528: /* ------------------------------------------------------------------- */
    529: /*
    530:    PreCheck - Optional user-defined routine that checks the validity of
    531:    candidate steps of a line search method.  Set by SNESLineSearchSetPreCheck().

    533:    Input Parameters:
    534:    snes - the SNES context
    535:    xcurrent - current solution
    536:    y - search direction and length

    538:    Output Parameters:
    539:    y         - proposed step (search direction and length) (possibly changed)
    540:    changed_y - tells if the step has changed or not
    541:  */
    542: PetscErrorCode PreCheck(SNESLineSearch linesearch,Vec xcurrent,Vec y, PetscBool *changed_y, void * ctx)
    543: {
    545:   *changed_y = PETSC_FALSE;
    546:   return 0;
    547: }

    549: /* ------------------------------------------------------------------- */
    550: /*
    551:    PostCheck - Optional user-defined routine that checks the validity of
    552:    candidate steps of a line search method.  Set by SNESLineSearchSetPostCheck().

    554:    Input Parameters:
    555:    snes - the SNES context
    556:    ctx  - optional user-defined context for private data for the
    557:           monitor routine, as set by SNESLineSearchSetPostCheck()
    558:    xcurrent - current solution
    559:    y - search direction and length
    560:    x    - the new candidate iterate

    562:    Output Parameters:
    563:    y    - proposed step (search direction and length) (possibly changed)
    564:    x    - current iterate (possibly modified)

    566:  */
    567: PetscErrorCode PostCheck(SNESLineSearch linesearch,Vec xcurrent,Vec y,Vec x,PetscBool  *changed_y,PetscBool  *changed_x, void * ctx)
    568: {
    569:   PetscInt       i,iter,xs,xm;
    570:   StepCheckCtx   *check;
    571:   ApplicationCtx *user;
    572:   PetscScalar    *xa,*xa_last,tmp;
    573:   PetscReal      rdiff;
    574:   DM             da;
    575:   SNES           snes;

    578:   *changed_x = PETSC_FALSE;
    579:   *changed_y = PETSC_FALSE;

    581:   SNESLineSearchGetSNES(linesearch, &snes);
    582:   check = (StepCheckCtx*)ctx;
    583:   user  = check->user;
    584:   SNESGetIterationNumber(snes,&iter);

    586:   /* iteration 1 indicates we are working on the second iteration */
    587:   if (iter > 0) {
    588:     da   = user->da;
    589:     PetscPrintf(PETSC_COMM_WORLD,"Checking candidate step at iteration %D with tolerance %g\n",iter,(double)check->tolerance);

    591:     /* Access local array data */
    592:     DMDAVecGetArray(da,check->last_step,&xa_last);
    593:     DMDAVecGetArray(da,x,&xa);
    594:     DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);

    596:     /*
    597:        If we fail the user-defined check for validity of the candidate iterate,
    598:        then modify the iterate as we like.  (Note that the particular modification
    599:        below is intended simply to demonstrate how to manipulate this data, not
    600:        as a meaningful or appropriate choice.)
    601:     */
    602:     for (i=xs; i<xs+xm; i++) {
    603:       if (!PetscAbsScalar(xa[i])) rdiff = 2*check->tolerance;
    604:       else rdiff = PetscAbsScalar((xa[i] - xa_last[i])/xa[i]);
    605:       if (rdiff > check->tolerance) {
    606:         tmp        = xa[i];
    607:         xa[i]      = .5*(xa[i] + xa_last[i]);
    608:         *changed_x = PETSC_TRUE;
    609:         PetscPrintf(PETSC_COMM_WORLD,"  Altering entry %D: x=%g, x_last=%g, diff=%g, x_new=%g\n",i,(double)PetscAbsScalar(tmp),(double)PetscAbsScalar(xa_last[i]),(double)rdiff,(double)PetscAbsScalar(xa[i]));
    610:       }
    611:     }
    612:     DMDAVecRestoreArray(da,check->last_step,&xa_last);
    613:     DMDAVecRestoreArray(da,x,&xa);
    614:   }
    615:   VecCopy(x,check->last_step);
    616:   return 0;
    617: }

    619: /* ------------------------------------------------------------------- */
    620: /*
    621:    PostSetSubKSP - Optional user-defined routine that reset SubKSP options when hierarchical bjacobi PC is used
    622:    e.g,
    623:      mpiexec -n 8 ./ex3 -nox -n 10000 -ksp_type fgmres -pc_type bjacobi -pc_bjacobi_blocks 4 -sub_ksp_type gmres -sub_ksp_max_it 3 -post_setsubksp -sub_ksp_rtol 1.e-16
    624:    Set by SNESLineSearchSetPostCheck().

    626:    Input Parameters:
    627:    linesearch - the LineSearch context
    628:    xcurrent - current solution
    629:    y - search direction and length
    630:    x    - the new candidate iterate

    632:    Output Parameters:
    633:    y    - proposed step (search direction and length) (possibly changed)
    634:    x    - current iterate (possibly modified)

    636:  */
    637: PetscErrorCode PostSetSubKSP(SNESLineSearch linesearch,Vec xcurrent,Vec y,Vec x,PetscBool  *changed_y,PetscBool  *changed_x, void * ctx)
    638: {
    639:   SetSubKSPCtx   *check;
    640:   PetscInt       iter,its,sub_its,maxit;
    641:   KSP            ksp,sub_ksp,*sub_ksps;
    642:   PC             pc;
    643:   PetscReal      ksp_ratio;
    644:   SNES           snes;

    647:   SNESLineSearchGetSNES(linesearch, &snes);
    648:   check   = (SetSubKSPCtx*)ctx;
    649:   SNESGetIterationNumber(snes,&iter);
    650:   SNESGetKSP(snes,&ksp);
    651:   KSPGetPC(ksp,&pc);
    652:   PCBJacobiGetSubKSP(pc,NULL,NULL,&sub_ksps);
    653:   sub_ksp = sub_ksps[0];
    654:   KSPGetIterationNumber(ksp,&its);      /* outer KSP iteration number */
    655:   KSPGetIterationNumber(sub_ksp,&sub_its); /* inner KSP iteration number */

    657:   if (iter) {
    658:     PetscPrintf(PETSC_COMM_WORLD,"    ...PostCheck snes iteration %D, ksp_it %D %D, subksp_it %D\n",iter,check->its0,its,sub_its);
    659:     ksp_ratio = ((PetscReal)(its))/check->its0;
    660:     maxit     = (PetscInt)(ksp_ratio*sub_its + 0.5);
    661:     if (maxit < 2) maxit = 2;
    662:     KSPSetTolerances(sub_ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,maxit);
    663:     PetscPrintf(PETSC_COMM_WORLD,"    ...ksp_ratio %g, new maxit %D\n\n",(double)ksp_ratio,maxit);
    664:   }
    665:   check->its0 = its; /* save current outer KSP iteration number */
    666:   return 0;
    667: }

    669: /* ------------------------------------------------------------------- */
    670: /*
    671:    MatrixFreePreconditioner - This routine demonstrates the use of a
    672:    user-provided preconditioner.  This code implements just the null
    673:    preconditioner, which of course is not recommended for general use.

    675:    Input Parameters:
    676: +  pc - preconditioner
    677: -  x - input vector

    679:    Output Parameter:
    680: .  y - preconditioned vector
    681: */
    682: PetscErrorCode MatrixFreePreconditioner(PC pc,Vec x,Vec y)
    683: {
    684:   VecCopy(x,y);
    685:   return 0;
    686: }

    688: /*TEST

    690:    test:
    691:       args: -nox -snes_monitor_cancel -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    693:    test:
    694:       suffix: 2
    695:       nsize: 3
    696:       args: -nox -pc_type asm -mat_type mpiaij -snes_monitor_cancel -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    698:    test:
    699:       suffix: 3
    700:       nsize: 2
    701:       args: -nox -snes_monitor_cancel -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    703:    test:
    704:       suffix: 4
    705:       args: -nox -pre_check_iterates -post_check_iterates

    707:    test:
    708:       suffix: 5
    709:       requires: double !complex !single
    710:       nsize: 2
    711:       args: -nox -snes_test_jacobian  -snes_test_jacobian_view

    713:    test:
    714:       suffix: 6
    715:       requires: double !complex !single
    716:       nsize: 4
    717:       args: -test_jacobian_domain_error -snes_converged_reason -snes_check_jacobian_domain_error 1

    719:    test:
    720:       suffix: 7
    721:       requires: double !complex !single
    722:       nsize: 4
    723:       args: -test_jacobian_domain_error -snes_converged_reason -snes_type newtontr -snes_check_jacobian_domain_error 1

    725:    test:
    726:       suffix: 8
    727:       requires: double !complex !single
    728:       nsize: 4
    729:       args: -test_jacobian_domain_error -snes_converged_reason -snes_type vinewtonrsls -snes_check_jacobian_domain_error 1

    731:    test:
    732:       suffix: 9
    733:       requires: double !complex !single
    734:       nsize: 4
    735:       args: -test_jacobian_domain_error -snes_converged_reason -snes_type vinewtonssls -snes_check_jacobian_domain_error 1

    737:    test:
    738:       suffix: 10
    739:       requires: double !complex !single
    740:       nsize: 4
    741:       args: -test_jacobian_domain_error -snes_converged_reason -snes_type qn -snes_qn_scale_type jacobian -snes_check_jacobian_domain_error 1

    743:    test:
    744:       suffix: 11
    745:       requires: double !complex !single
    746:       nsize: 4
    747:       args: -test_jacobian_domain_error -snes_converged_reason -snes_type ms -snes_ms_type m62 -snes_ms_damping 0.9 -snes_check_jacobian_domain_error 1

    749:    test:
    750:       suffix: 12
    751:       args: -view_initial
    752:       filter: grep -v "type:"

    754:    test:
    755:       suffix: 13
    756:       requires: double !complex !single
    757:       nsize: 4
    758:       args: -test_jacobian_domain_error -snes_converged_reason -snes_type newtontrdc -snes_check_jacobian_domain_error 1

    760: TEST*/