Date: 2022-03-04T17:39:48+00:00

Actual source code: taosolver.c

      1: #define TAO_DLL

      3: #include <petsc/private/taoimpl.h>

      5: PetscBool TaoRegisterAllCalled = PETSC_FALSE;
      6: PetscFunctionList TaoList = NULL;

      8: PetscClassId TAO_CLASSID;

     10: PetscLogEvent TAO_Solve;
     11: PetscLogEvent TAO_ObjectiveEval;
     12: PetscLogEvent TAO_GradientEval;
     13: PetscLogEvent TAO_ObjGradEval;
     14: PetscLogEvent TAO_HessianEval;
     15: PetscLogEvent TAO_JacobianEval;
     16: PetscLogEvent TAO_ConstraintsEval;

     18: const char *TaoSubSetTypes[] = {"subvec","mask","matrixfree","TaoSubSetType","TAO_SUBSET_",NULL};

     20: struct _n_TaoMonitorDrawCtx {
     21:   PetscViewer viewer;
     22:   PetscInt    howoften;  /* when > 0 uses iteration % howoften, when negative only final solution plotted */
     23: };

     25: /*@
     26:   TaoCreate - Creates a TAO solver

     28:   Collective

     30:   Input Parameter:
     31: . comm - MPI communicator

     33:   Output Parameter:
     34: . newtao - the new Tao context

     36:   Available methods include:
     37: +    nls - Newton's method with line search for unconstrained minimization
     38: .    ntr - Newton's method with trust region for unconstrained minimization
     39: .    ntl - Newton's method with trust region, line search for unconstrained minimization
     40: .    lmvm - Limited memory variable metric method for unconstrained minimization
     41: .    cg - Nonlinear conjugate gradient method for unconstrained minimization
     42: .    nm - Nelder-Mead algorithm for derivate-free unconstrained minimization
     43: .    tron - Newton Trust Region method for bound constrained minimization
     44: .    gpcg - Newton Trust Region method for quadratic bound constrained minimization
     45: .    blmvm - Limited memory variable metric method for bound constrained minimization
     46: .    lcl - Linearly constrained Lagrangian method for pde-constrained minimization
     47: -    pounders - Model-based algorithm for nonlinear least squares

     49:    Options Database Keys:
     50: .   -tao_type - select which method TAO should use

     52:    Level: beginner

     54: .seealso: TaoSolve(), TaoDestroy()
     55: @*/
     56: PetscErrorCode TaoCreate(MPI_Comm comm, Tao *newtao)
     57: {
     59:   Tao            tao;

     63:   *newtao = NULL;

     65:   TaoInitializePackage();
     66:   TaoLineSearchInitializePackage();

     68:   PetscHeaderCreate(tao,TAO_CLASSID,"Tao","Optimization solver","Tao",comm,TaoDestroy,TaoView);
     69:   tao->ops->computeobjective = NULL;
     70:   tao->ops->computeobjectiveandgradient = NULL;
     71:   tao->ops->computegradient = NULL;
     72:   tao->ops->computehessian = NULL;
     73:   tao->ops->computeresidual = NULL;
     74:   tao->ops->computeresidualjacobian = NULL;
     75:   tao->ops->computeconstraints = NULL;
     76:   tao->ops->computejacobian = NULL;
     77:   tao->ops->computejacobianequality = NULL;
     78:   tao->ops->computejacobianinequality = NULL;
     79:   tao->ops->computeequalityconstraints = NULL;
     80:   tao->ops->computeinequalityconstraints = NULL;
     81:   tao->ops->convergencetest = TaoDefaultConvergenceTest;
     82:   tao->ops->convergencedestroy = NULL;
     83:   tao->ops->computedual = NULL;
     84:   tao->ops->setup = NULL;
     85:   tao->ops->solve = NULL;
     86:   tao->ops->view = NULL;
     87:   tao->ops->setfromoptions = NULL;
     88:   tao->ops->destroy = NULL;

     90:   tao->solution=NULL;
     91:   tao->gradient=NULL;
     92:   tao->ls_res = NULL;
     93:   tao->ls_jac = NULL;
     94:   tao->constraints=NULL;
     95:   tao->constraints_equality=NULL;
     96:   tao->constraints_inequality=NULL;
     97:   tao->res_weights_v=NULL;
     98:   tao->res_weights_w=NULL;
     99:   tao->stepdirection=NULL;
    100:   tao->niter=0;
    101:   tao->ntotalits=0;
    102:   tao->XL = NULL;
    103:   tao->XU = NULL;
    104:   tao->IL = NULL;
    105:   tao->IU = NULL;
    106:   tao->DI = NULL;
    107:   tao->DE = NULL;
    108:   tao->gradient_norm = NULL;
    109:   tao->gradient_norm_tmp = NULL;
    110:   tao->hessian = NULL;
    111:   tao->hessian_pre = NULL;
    112:   tao->jacobian = NULL;
    113:   tao->jacobian_pre = NULL;
    114:   tao->jacobian_state = NULL;
    115:   tao->jacobian_state_pre = NULL;
    116:   tao->jacobian_state_inv = NULL;
    117:   tao->jacobian_design = NULL;
    118:   tao->jacobian_design_pre = NULL;
    119:   tao->jacobian_equality = NULL;
    120:   tao->jacobian_equality_pre = NULL;
    121:   tao->jacobian_inequality = NULL;
    122:   tao->jacobian_inequality_pre = NULL;
    123:   tao->state_is = NULL;
    124:   tao->design_is = NULL;

    126:   tao->max_it     = 10000;
    127:   tao->max_funcs   = 10000;
    128: #if defined(PETSC_USE_REAL_SINGLE)
    129:   tao->gatol       = 1e-5;
    130:   tao->grtol       = 1e-5;
    131:   tao->crtol       = 1e-5;
    132:   tao->catol       = 1e-5;
    133: #else
    134:   tao->gatol       = 1e-8;
    135:   tao->grtol       = 1e-8;
    136:   tao->crtol       = 1e-8;
    137:   tao->catol       = 1e-8;
    138: #endif
    139:   tao->gttol       = 0.0;
    140:   tao->steptol     = 0.0;
    141:   tao->trust0      = PETSC_INFINITY;
    142:   tao->fmin        = PETSC_NINFINITY;
    143:   tao->hist_malloc = PETSC_FALSE;
    144:   tao->hist_reset = PETSC_TRUE;
    145:   tao->hist_max = 0;
    146:   tao->hist_len = 0;
    147:   tao->hist_obj = NULL;
    148:   tao->hist_resid = NULL;
    149:   tao->hist_cnorm = NULL;
    150:   tao->hist_lits = NULL;

    152:   tao->numbermonitors=0;
    153:   tao->viewsolution=PETSC_FALSE;
    154:   tao->viewhessian=PETSC_FALSE;
    155:   tao->viewgradient=PETSC_FALSE;
    156:   tao->viewjacobian=PETSC_FALSE;
    157:   tao->viewconstraints = PETSC_FALSE;

    159:   tao->bounded = PETSC_FALSE;
    160:   tao->constrained = PETSC_FALSE;
    161:   tao->eq_constrained = PETSC_FALSE;
    162:   tao->ineq_constrained = PETSC_FALSE;
    163:   tao->ineq_doublesided = PETSC_FALSE;

    165:   tao->recycle = PETSC_FALSE;

    167:   tao->header_printed = PETSC_FALSE;

    169:   /* These flags prevents algorithms from overriding user options */
    170:   tao->max_it_changed   =PETSC_FALSE;
    171:   tao->max_funcs_changed=PETSC_FALSE;
    172:   tao->gatol_changed    =PETSC_FALSE;
    173:   tao->grtol_changed    =PETSC_FALSE;
    174:   tao->gttol_changed    =PETSC_FALSE;
    175:   tao->steptol_changed  =PETSC_FALSE;
    176:   tao->trust0_changed   =PETSC_FALSE;
    177:   tao->fmin_changed     =PETSC_FALSE;
    178:   tao->catol_changed    =PETSC_FALSE;
    179:   tao->crtol_changed    =PETSC_FALSE;
    180:   TaoResetStatistics(tao);
    181:   *newtao = tao;
    182:   return(0);
    183: }

    185: /*@
    186:   TaoSolve - Solves an optimization problem min F(x) s.t. l <= x <= u

    188:   Collective on Tao

    190:   Input Parameters:
    191: . tao - the Tao context

    193:   Notes:
    194:   The user must set up the Tao with calls to TaoSetInitialVector(),
    195:   TaoSetObjectiveRoutine(),
    196:   TaoSetGradientRoutine(), and (if using 2nd order method) TaoSetHessianRoutine().

    198:   You should call TaoGetConvergedReason() or run with -tao_converged_reason to determine if the optimization algorithm actually succeeded or
    199:   why it failed.

    201:   Level: beginner

    203: .seealso: TaoCreate(), TaoSetObjectiveRoutine(), TaoSetGradientRoutine(), TaoSetHessianRoutine(), TaoGetConvergedReason()
    204:  @*/
    205: PetscErrorCode TaoSolve(Tao tao)
    206: {
    207:   PetscErrorCode   ierr;
    208:   static PetscBool set = PETSC_FALSE;

    212:   PetscCitationsRegister("@TechReport{tao-user-ref,\n"
    213:                                 "title   = {Toolkit for Advanced Optimization (TAO) Users Manual},\n"
    214:                                 "author  = {Todd Munson and Jason Sarich and Stefan Wild and Steve Benson and Lois Curfman McInnes},\n"
    215:                                 "Institution = {Argonne National Laboratory},\n"
    216:                                 "Year   = 2014,\n"
    217:                                 "Number = {ANL/MCS-TM-322 - Revision 3.5},\n"
    218:                                 "url    = {https://www.mcs.anl.gov/research/projects/tao/}\n}\n",&set);
    219:   tao->header_printed = PETSC_FALSE;
    220:   TaoSetUp(tao);
    221:   TaoResetStatistics(tao);
    222:   if (tao->linesearch) {
    223:     TaoLineSearchReset(tao->linesearch);
    224:   }

    226:   PetscLogEventBegin(TAO_Solve,tao,0,0,0);
    227:   if (tao->ops->solve) { (*tao->ops->solve)(tao); }
    228:   PetscLogEventEnd(TAO_Solve,tao,0,0,0);

    230:   VecViewFromOptions(tao->solution,(PetscObject)tao,"-tao_view_solution");

    232:   tao->ntotalits += tao->niter;
    233:   TaoViewFromOptions(tao,NULL,"-tao_view");

    235:   if (tao->printreason) {
    236:     if (tao->reason > 0) {
    237:       PetscPrintf(((PetscObject)tao)->comm,"TAO solve converged due to %s iterations %D\n",TaoConvergedReasons[tao->reason],tao->niter);
    238:     } else {
    239:       PetscPrintf(((PetscObject)tao)->comm,"TAO solve did not converge due to %s iteration %D\n",TaoConvergedReasons[tao->reason],tao->niter);
    240:     }
    241:   }
    242:   return(0);
    243: }

    245: /*@
    246:   TaoSetUp - Sets up the internal data structures for the later use
    247:   of a Tao solver

    249:   Collective on tao

    251:   Input Parameters:
    252: . tao - the TAO context

    254:   Notes:
    255:   The user will not need to explicitly call TaoSetUp(), as it will
    256:   automatically be called in TaoSolve().  However, if the user
    257:   desires to call it explicitly, it should come after TaoCreate()
    258:   and any TaoSetSomething() routines, but before TaoSolve().

    260:   Level: advanced

    262: .seealso: TaoCreate(), TaoSolve()
    263: @*/
    264: PetscErrorCode TaoSetUp(Tao tao)
    265: {

    270:   if (tao->setupcalled) return(0);

    272:   if (!tao->solution) SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_ARG_WRONGSTATE,"Must call TaoSetInitialVector");
    273:   if (tao->ops->setup) {
    274:     (*tao->ops->setup)(tao);
    275:   }
    276:   tao->setupcalled = PETSC_TRUE;
    277:   return(0);
    278: }

    280: /*@C
    281:   TaoDestroy - Destroys the TAO context that was created with
    282:   TaoCreate()

    284:   Collective on Tao

    286:   Input Parameter:
    287: . tao - the Tao context

    289:   Level: beginner

    291: .seealso: TaoCreate(), TaoSolve()
    292: @*/
    293: PetscErrorCode TaoDestroy(Tao *tao)
    294: {

    298:   if (!*tao) return(0);
    300:   if (--((PetscObject)*tao)->refct > 0) {*tao = NULL;return(0);}

    302:   if ((*tao)->ops->destroy) {
    303:     (*((*tao))->ops->destroy)(*tao);
    304:   }
    305:   KSPDestroy(&(*tao)->ksp);
    306:   TaoLineSearchDestroy(&(*tao)->linesearch);

    308:   if ((*tao)->ops->convergencedestroy) {
    309:     (*(*tao)->ops->convergencedestroy)((*tao)->cnvP);
    310:     if ((*tao)->jacobian_state_inv) {
    311:       MatDestroy(&(*tao)->jacobian_state_inv);
    312:     }
    313:   }
    314:   VecDestroy(&(*tao)->solution);
    315:   VecDestroy(&(*tao)->gradient);
    316:   VecDestroy(&(*tao)->ls_res);

    318:   if ((*tao)->gradient_norm) {
    319:     PetscObjectDereference((PetscObject)(*tao)->gradient_norm);
    320:     VecDestroy(&(*tao)->gradient_norm_tmp);
    321:   }

    323:   VecDestroy(&(*tao)->XL);
    324:   VecDestroy(&(*tao)->XU);
    325:   VecDestroy(&(*tao)->IL);
    326:   VecDestroy(&(*tao)->IU);
    327:   VecDestroy(&(*tao)->DE);
    328:   VecDestroy(&(*tao)->DI);
    329:   VecDestroy(&(*tao)->constraints_equality);
    330:   VecDestroy(&(*tao)->constraints_inequality);
    331:   VecDestroy(&(*tao)->stepdirection);
    332:   MatDestroy(&(*tao)->hessian_pre);
    333:   MatDestroy(&(*tao)->hessian);
    334:   MatDestroy(&(*tao)->ls_jac);
    335:   MatDestroy(&(*tao)->ls_jac_pre);
    336:   MatDestroy(&(*tao)->jacobian_pre);
    337:   MatDestroy(&(*tao)->jacobian);
    338:   MatDestroy(&(*tao)->jacobian_state_pre);
    339:   MatDestroy(&(*tao)->jacobian_state);
    340:   MatDestroy(&(*tao)->jacobian_state_inv);
    341:   MatDestroy(&(*tao)->jacobian_design);
    342:   MatDestroy(&(*tao)->jacobian_equality);
    343:   MatDestroy(&(*tao)->jacobian_equality_pre);
    344:   MatDestroy(&(*tao)->jacobian_inequality);
    345:   MatDestroy(&(*tao)->jacobian_inequality_pre);
    346:   ISDestroy(&(*tao)->state_is);
    347:   ISDestroy(&(*tao)->design_is);
    348:   VecDestroy(&(*tao)->res_weights_v);
    349:   TaoCancelMonitors(*tao);
    350:   if ((*tao)->hist_malloc) {
    351:     PetscFree4((*tao)->hist_obj,(*tao)->hist_resid,(*tao)->hist_cnorm,(*tao)->hist_lits);
    352:   }
    353:   if ((*tao)->res_weights_n) {
    354:     PetscFree((*tao)->res_weights_rows);
    355:     PetscFree((*tao)->res_weights_cols);
    356:     PetscFree((*tao)->res_weights_w);
    357:   }
    358:   PetscHeaderDestroy(tao);
    359:   return(0);
    360: }

    362: /*@
    363:   TaoSetFromOptions - Sets various Tao parameters from user
    364:   options.

    366:   Collective on Tao

    368:   Input Parameter:
    369: . tao - the Tao solver context

    371:   options Database Keys:
    372: + -tao_type <type> - The algorithm that TAO uses (lmvm, nls, etc.)
    373: . -tao_gatol <gatol> - absolute error tolerance for ||gradient||
    374: . -tao_grtol <grtol> - relative error tolerance for ||gradient||
    375: . -tao_gttol <gttol> - reduction of ||gradient|| relative to initial gradient
    376: . -tao_max_it <max> - sets maximum number of iterations
    377: . -tao_max_funcs <max> - sets maximum number of function evaluations
    378: . -tao_fmin <fmin> - stop if function value reaches fmin
    379: . -tao_steptol <tol> - stop if trust region radius less than <tol>
    380: . -tao_trust0 <t> - initial trust region radius
    381: . -tao_monitor - prints function value and residual at each iteration
    382: . -tao_smonitor - same as tao_monitor, but truncates very small values
    383: . -tao_cmonitor - prints function value, residual, and constraint norm at each iteration
    384: . -tao_view_solution - prints solution vector at each iteration
    385: . -tao_view_ls_residual - prints least-squares residual vector at each iteration
    386: . -tao_view_step - prints step direction vector at each iteration
    387: . -tao_view_gradient - prints gradient vector at each iteration
    388: . -tao_draw_solution - graphically view solution vector at each iteration
    389: . -tao_draw_step - graphically view step vector at each iteration
    390: . -tao_draw_gradient - graphically view gradient at each iteration
    391: . -tao_fd_gradient - use gradient computed with finite differences
    392: . -tao_fd_hessian - use hessian computed with finite differences
    393: . -tao_mf_hessian - use matrix-free hessian computed with finite differences
    394: . -tao_cancelmonitors - cancels all monitors (except those set with command line)
    395: . -tao_view - prints information about the Tao after solving
    396: - -tao_converged_reason - prints the reason TAO stopped iterating

    398:   Notes:
    399:   To see all options, run your program with the -help option or consult the
    400:   user's manual. Should be called after TaoCreate() but before TaoSolve()

    402:   Level: beginner
    403: @*/
    404: PetscErrorCode TaoSetFromOptions(Tao tao)
    405: {
    407:   TaoType        default_type = TAOLMVM;
    408:   char           type[256], monfilename[PETSC_MAX_PATH_LEN];
    409:   PetscViewer    monviewer;
    410:   PetscBool      flg;
    411:   MPI_Comm       comm;

    415:   PetscObjectGetComm((PetscObject)tao,&comm);

    417:   /* So no warnings are given about unused options */
    418:   PetscOptionsHasName(((PetscObject)tao)->options,((PetscObject)tao)->prefix,"-tao_ls_type",&flg);

    420:   PetscObjectOptionsBegin((PetscObject)tao);
    421:   {
    422:     TaoRegisterAll();
    423:     if (((PetscObject)tao)->type_name) {
    424:       default_type = ((PetscObject)tao)->type_name;
    425:     }
    426:     /* Check for type from options */
    427:     PetscOptionsFList("-tao_type","Tao Solver type","TaoSetType",TaoList,default_type,type,256,&flg);
    428:     if (flg) {
    429:       TaoSetType(tao,type);
    430:     } else if (!((PetscObject)tao)->type_name) {
    431:       TaoSetType(tao,default_type);
    432:     }

    434:     PetscOptionsReal("-tao_catol","Stop if constraints violations within","TaoSetConstraintTolerances",tao->catol,&tao->catol,&flg);
    435:     if (flg) tao->catol_changed=PETSC_TRUE;
    436:     PetscOptionsReal("-tao_crtol","Stop if relative contraint violations within","TaoSetConstraintTolerances",tao->crtol,&tao->crtol,&flg);
    437:     if (flg) tao->crtol_changed=PETSC_TRUE;
    438:     PetscOptionsReal("-tao_gatol","Stop if norm of gradient less than","TaoSetTolerances",tao->gatol,&tao->gatol,&flg);
    439:     if (flg) tao->gatol_changed=PETSC_TRUE;
    440:     PetscOptionsReal("-tao_grtol","Stop if norm of gradient divided by the function value is less than","TaoSetTolerances",tao->grtol,&tao->grtol,&flg);
    441:     if (flg) tao->grtol_changed=PETSC_TRUE;
    442:     PetscOptionsReal("-tao_gttol","Stop if the norm of the gradient is less than the norm of the initial gradient times tol","TaoSetTolerances",tao->gttol,&tao->gttol,&flg);
    443:     if (flg) tao->gttol_changed=PETSC_TRUE;
    444:     PetscOptionsInt("-tao_max_it","Stop if iteration number exceeds","TaoSetMaximumIterations",tao->max_it,&tao->max_it,&flg);
    445:     if (flg) tao->max_it_changed=PETSC_TRUE;
    446:     PetscOptionsInt("-tao_max_funcs","Stop if number of function evaluations exceeds","TaoSetMaximumFunctionEvaluations",tao->max_funcs,&tao->max_funcs,&flg);
    447:     if (flg) tao->max_funcs_changed=PETSC_TRUE;
    448:     PetscOptionsReal("-tao_fmin","Stop if function less than","TaoSetFunctionLowerBound",tao->fmin,&tao->fmin,&flg);
    449:     if (flg) tao->fmin_changed=PETSC_TRUE;
    450:     PetscOptionsReal("-tao_steptol","Stop if step size or trust region radius less than","",tao->steptol,&tao->steptol,&flg);
    451:     if (flg) tao->steptol_changed=PETSC_TRUE;
    452:     PetscOptionsReal("-tao_trust0","Initial trust region radius","TaoSetTrustRegionRadius",tao->trust0,&tao->trust0,&flg);
    453:     if (flg) tao->trust0_changed=PETSC_TRUE;
    454:     PetscOptionsString("-tao_view_solution","view solution vector after each evaluation","TaoSetMonitor","stdout",monfilename,sizeof(monfilename),&flg);
    455:     if (flg) {
    456:       PetscViewerASCIIOpen(comm,monfilename,&monviewer);
    457:       TaoSetMonitor(tao,TaoSolutionMonitor,monviewer,(PetscErrorCode (*)(void**))PetscViewerDestroy);
    458:     }

    460:     PetscOptionsBool("-tao_converged_reason","Print reason for TAO converged","TaoSolve",tao->printreason,&tao->printreason,NULL);
    461:     PetscOptionsString("-tao_view_gradient","view gradient vector after each evaluation","TaoSetMonitor","stdout",monfilename,sizeof(monfilename),&flg);
    462:     if (flg) {
    463:       PetscViewerASCIIOpen(comm,monfilename,&monviewer);
    464:       TaoSetMonitor(tao,TaoGradientMonitor,monviewer,(PetscErrorCode (*)(void**))PetscViewerDestroy);
    465:     }

    467:     PetscOptionsString("-tao_view_stepdirection","view step direction vector after each iteration","TaoSetMonitor","stdout",monfilename,sizeof(monfilename),&flg);
    468:     if (flg) {
    469:       PetscViewerASCIIOpen(comm,monfilename,&monviewer);
    470:       TaoSetMonitor(tao,TaoStepDirectionMonitor,monviewer,(PetscErrorCode (*)(void**))PetscViewerDestroy);
    471:     }

    473:     PetscOptionsString("-tao_view_residual","view least-squares residual vector after each evaluation","TaoSetMonitor","stdout",monfilename,sizeof(monfilename),&flg);
    474:     if (flg) {
    475:       PetscViewerASCIIOpen(comm,monfilename,&monviewer);
    476:       TaoSetMonitor(tao,TaoResidualMonitor,monviewer,(PetscErrorCode (*)(void**))PetscViewerDestroy);
    477:     }

    479:     PetscOptionsString("-tao_monitor","Use the default convergence monitor","TaoSetMonitor","stdout",monfilename,sizeof(monfilename),&flg);
    480:     if (flg) {
    481:       PetscViewerASCIIOpen(comm,monfilename,&monviewer);
    482:       TaoSetMonitor(tao,TaoMonitorDefault,monviewer,(PetscErrorCode (*)(void**))PetscViewerDestroy);
    483:     }

    485:     PetscOptionsString("-tao_gmonitor","Use the convergence monitor with extra globalization info","TaoSetMonitor","stdout",monfilename,sizeof(monfilename),&flg);
    486:     if (flg) {
    487:       PetscViewerASCIIOpen(comm,monfilename,&monviewer);
    488:       TaoSetMonitor(tao,TaoDefaultGMonitor,monviewer,(PetscErrorCode (*)(void**))PetscViewerDestroy);
    489:     }

    491:     PetscOptionsString("-tao_smonitor","Use the short convergence monitor","TaoSetMonitor","stdout",monfilename,sizeof(monfilename),&flg);
    492:     if (flg) {
    493:       PetscViewerASCIIOpen(comm,monfilename,&monviewer);
    494:       TaoSetMonitor(tao,TaoDefaultSMonitor,monviewer,(PetscErrorCode (*)(void**))PetscViewerDestroy);
    495:     }

    497:     PetscOptionsString("-tao_cmonitor","Use the default convergence monitor with constraint norm","TaoSetMonitor","stdout",monfilename,sizeof(monfilename),&flg);
    498:     if (flg) {
    499:       PetscViewerASCIIOpen(comm,monfilename,&monviewer);
    500:       TaoSetMonitor(tao,TaoDefaultCMonitor,monviewer,(PetscErrorCode (*)(void**))PetscViewerDestroy);
    501:     }

    503:     flg = PETSC_FALSE;
    504:     PetscOptionsBool("-tao_cancelmonitors","cancel all monitors and call any registered destroy routines","TaoCancelMonitors",flg,&flg,NULL);
    505:     if (flg) {TaoCancelMonitors(tao);}

    507:     flg = PETSC_FALSE;
    508:     PetscOptionsBool("-tao_draw_solution","Plot solution vector at each iteration","TaoSetMonitor",flg,&flg,NULL);
    509:     if (flg) {
    510:       TaoMonitorDrawCtx drawctx;
    511:       PetscInt          howoften = 1;
    512:       TaoMonitorDrawCtxCreate(PetscObjectComm((PetscObject)tao),NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,300,300,howoften,&drawctx);
    513:       TaoSetMonitor(tao,TaoDrawSolutionMonitor,drawctx,(PetscErrorCode (*)(void**))TaoMonitorDrawCtxDestroy);
    514:     }

    516:     flg = PETSC_FALSE;
    517:     PetscOptionsBool("-tao_draw_step","plots step direction at each iteration","TaoSetMonitor",flg,&flg,NULL);
    518:     if (flg) {
    519:       TaoSetMonitor(tao,TaoDrawStepMonitor,NULL,NULL);
    520:     }

    522:     flg = PETSC_FALSE;
    523:     PetscOptionsBool("-tao_draw_gradient","plots gradient at each iteration","TaoSetMonitor",flg,&flg,NULL);
    524:     if (flg) {
    525:       TaoMonitorDrawCtx drawctx;
    526:       PetscInt          howoften = 1;
    527:       TaoMonitorDrawCtxCreate(PetscObjectComm((PetscObject)tao),NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,300,300,howoften,&drawctx);
    528:       TaoSetMonitor(tao,TaoDrawGradientMonitor,drawctx,(PetscErrorCode (*)(void**))TaoMonitorDrawCtxDestroy);
    529:     }
    530:     flg = PETSC_FALSE;
    531:     PetscOptionsBool("-tao_fd_gradient","compute gradient using finite differences","TaoDefaultComputeGradient",flg,&flg,NULL);
    532:     if (flg) {
    533:       TaoSetGradientRoutine(tao,TaoDefaultComputeGradient,NULL);
    534:     }
    535:     flg = PETSC_FALSE;
    536:     PetscOptionsBool("-tao_fd_hessian","compute hessian using finite differences","TaoDefaultComputeHessian",flg,&flg,NULL);
    537:     if (flg) {
    538:       Mat H;

    540:       MatCreate(PetscObjectComm((PetscObject)tao),&H);
    541:       MatSetType(H,MATAIJ);
    542:       TaoSetHessianRoutine(tao,H,H,TaoDefaultComputeHessian,NULL);
    543:       MatDestroy(&H);
    544:     }
    545:     flg = PETSC_FALSE;
    546:     PetscOptionsBool("-tao_mf_hessian","compute matrix-free hessian using finite differences","TaoDefaultComputeHessianMFFD",flg,&flg,NULL);
    547:     if (flg) {
    548:       Mat H;

    550:       MatCreate(PetscObjectComm((PetscObject)tao),&H);
    551:       TaoSetHessianRoutine(tao,H,H,TaoDefaultComputeHessianMFFD,NULL);
    552:       MatDestroy(&H);
    553:     }
    554:     flg = PETSC_FALSE;
    555:     PetscOptionsBool("-tao_recycle_history","enable recycling/re-using information from the previous TaoSolve() call for some algorithms","TaoSetRecycleHistory",flg,&flg,NULL);
    556:     if (flg) {
    557:       TaoSetRecycleHistory(tao, PETSC_TRUE);
    558:     }
    559:     PetscOptionsEnum("-tao_subset_type","subset type","",TaoSubSetTypes,(PetscEnum)tao->subset_type,(PetscEnum*)&tao->subset_type,NULL);

    561:     if (tao->ops->setfromoptions) {
    562:       (*tao->ops->setfromoptions)(PetscOptionsObject,tao);
    563:     }
    564:   }
    565:   PetscOptionsEnd();
    566:   return(0);
    567: }

    569: /*@C
    570:    TaoViewFromOptions - View from Options

    572:    Collective on Tao

    574:    Input Parameters:
    575: +  A - the  Tao context
    576: .  obj - Optional object
    577: -  name - command line option

    579:    Level: intermediate
    580: .seealso:  Tao, TaoView, PetscObjectViewFromOptions(), TaoCreate()
    581: @*/
    582: PetscErrorCode  TaoViewFromOptions(Tao A,PetscObject obj,const char name[])
    583: {

    588:   PetscObjectViewFromOptions((PetscObject)A,obj,name);
    589:   return(0);
    590: }

    592: /*@C
    593:   TaoView - Prints information about the Tao

    595:   Collective on Tao

    597:   InputParameters:
    598: + tao - the Tao context
    599: - viewer - visualization context

    601:   Options Database Key:
    602: . -tao_view - Calls TaoView() at the end of TaoSolve()

    604:   Notes:
    605:   The available visualization contexts include
    606: +     PETSC_VIEWER_STDOUT_SELF - standard output (default)
    607: -     PETSC_VIEWER_STDOUT_WORLD - synchronized standard
    608:          output where only the first processor opens
    609:          the file.  All other processors send their
    610:          data to the first processor to print.

    612:   Level: beginner

    614: .seealso: PetscViewerASCIIOpen()
    615: @*/
    616: PetscErrorCode TaoView(Tao tao, PetscViewer viewer)
    617: {
    618:   PetscErrorCode      ierr;
    619:   PetscBool           isascii,isstring;
    620:   TaoType             type;

    624:   if (!viewer) {
    625:     PetscViewerASCIIGetStdout(((PetscObject)tao)->comm,&viewer);
    626:   }

    630:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    631:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);
    632:   if (isascii) {
    633:     PetscObjectPrintClassNamePrefixType((PetscObject)tao,viewer);

    635:     if (tao->ops->view) {
    636:       PetscViewerASCIIPushTab(viewer);
    637:       (*tao->ops->view)(tao,viewer);
    638:       PetscViewerASCIIPopTab(viewer);
    639:     }
    640:     if (tao->linesearch) {
    641:       PetscViewerASCIIPushTab(viewer);
    642:       TaoLineSearchView(tao->linesearch,viewer);
    643:       PetscViewerASCIIPopTab(viewer);
    644:     }
    645:     if (tao->ksp) {
    646:       PetscViewerASCIIPushTab(viewer);
    647:       KSPView(tao->ksp,viewer);
    648:       PetscViewerASCIIPrintf(viewer,"total KSP iterations: %D\n",tao->ksp_tot_its);
    649:       PetscViewerASCIIPopTab(viewer);
    650:     }

    652:     PetscViewerASCIIPushTab(viewer);

    654:     if (tao->XL || tao->XU) {
    655:       PetscViewerASCIIPrintf(viewer,"Active Set subset type: %s\n",TaoSubSetTypes[tao->subset_type]);
    656:     }

    658:     PetscViewerASCIIPrintf(viewer,"convergence tolerances: gatol=%g,",(double)tao->gatol);
    659:     PetscViewerASCIIPrintf(viewer," steptol=%g,",(double)tao->steptol);
    660:     PetscViewerASCIIPrintf(viewer," gttol=%g\n",(double)tao->gttol);
    661:     PetscViewerASCIIPrintf(viewer,"Residual in Function/Gradient:=%g\n",(double)tao->residual);

    663:     if (tao->constrained) {
    664:       PetscViewerASCIIPrintf(viewer,"convergence tolerances:");
    665:       PetscViewerASCIIPrintf(viewer," catol=%g,",(double)tao->catol);
    666:       PetscViewerASCIIPrintf(viewer," crtol=%g\n",(double)tao->crtol);
    667:       PetscViewerASCIIPrintf(viewer,"Residual in Constraints:=%g\n",(double)tao->cnorm);
    668:     }

    670:     if (tao->trust < tao->steptol) {
    671:       PetscViewerASCIIPrintf(viewer,"convergence tolerances: steptol=%g\n",(double)tao->steptol);
    672:       PetscViewerASCIIPrintf(viewer,"Final trust region radius:=%g\n",(double)tao->trust);
    673:     }

    675:     if (tao->fmin>-1.e25) {
    676:       PetscViewerASCIIPrintf(viewer,"convergence tolerances: function minimum=%g\n",(double)tao->fmin);
    677:     }
    678:     PetscViewerASCIIPrintf(viewer,"Objective value=%g\n",(double)tao->fc);

    680:     PetscViewerASCIIPrintf(viewer,"total number of iterations=%D,          ",tao->niter);
    681:     PetscViewerASCIIPrintf(viewer,"              (max: %D)\n",tao->max_it);

    683:     if (tao->nfuncs>0) {
    684:       PetscViewerASCIIPrintf(viewer,"total number of function evaluations=%D,",tao->nfuncs);
    685:       PetscViewerASCIIPrintf(viewer,"                max: %D\n",tao->max_funcs);
    686:     }
    687:     if (tao->ngrads>0) {
    688:       PetscViewerASCIIPrintf(viewer,"total number of gradient evaluations=%D,",tao->ngrads);
    689:       PetscViewerASCIIPrintf(viewer,"                max: %D\n",tao->max_funcs);
    690:     }
    691:     if (tao->nfuncgrads>0) {
    692:       PetscViewerASCIIPrintf(viewer,"total number of function/gradient evaluations=%D,",tao->nfuncgrads);
    693:       PetscViewerASCIIPrintf(viewer,"    (max: %D)\n",tao->max_funcs);
    694:     }
    695:     if (tao->nhess>0) {
    696:       PetscViewerASCIIPrintf(viewer,"total number of Hessian evaluations=%D\n",tao->nhess);
    697:     }
    698:     /*  if (tao->linear_its>0) {
    699:      PetscViewerASCIIPrintf(viewer,"  total Krylov method iterations=%D\n",tao->linear_its);
    700:      }*/
    701:     if (tao->nconstraints>0) {
    702:       PetscViewerASCIIPrintf(viewer,"total number of constraint function evaluations=%D\n",tao->nconstraints);
    703:     }
    704:     if (tao->njac>0) {
    705:       PetscViewerASCIIPrintf(viewer,"total number of Jacobian evaluations=%D\n",tao->njac);
    706:     }

    708:     if (tao->reason>0) {
    709:       PetscViewerASCIIPrintf(viewer,    "Solution converged: ");
    710:       switch (tao->reason) {
    711:       case TAO_CONVERGED_GATOL:
    712:         PetscViewerASCIIPrintf(viewer," ||g(X)|| <= gatol\n");
    713:         break;
    714:       case TAO_CONVERGED_GRTOL:
    715:         PetscViewerASCIIPrintf(viewer," ||g(X)||/|f(X)| <= grtol\n");
    716:         break;
    717:       case TAO_CONVERGED_GTTOL:
    718:         PetscViewerASCIIPrintf(viewer," ||g(X)||/||g(X0)|| <= gttol\n");
    719:         break;
    720:       case TAO_CONVERGED_STEPTOL:
    721:         PetscViewerASCIIPrintf(viewer," Steptol -- step size small\n");
    722:         break;
    723:       case TAO_CONVERGED_MINF:
    724:         PetscViewerASCIIPrintf(viewer," Minf --  f < fmin\n");
    725:         break;
    726:       case TAO_CONVERGED_USER:
    727:         PetscViewerASCIIPrintf(viewer," User Terminated\n");
    728:         break;
    729:       default:
    730:         PetscViewerASCIIPrintf(viewer,"\n");
    731:         break;
    732:       }

    734:     } else {
    735:       PetscViewerASCIIPrintf(viewer,"Solver terminated: %d",tao->reason);
    736:       switch (tao->reason) {
    737:       case TAO_DIVERGED_MAXITS:
    738:         PetscViewerASCIIPrintf(viewer," Maximum Iterations\n");
    739:         break;
    740:       case TAO_DIVERGED_NAN:
    741:         PetscViewerASCIIPrintf(viewer," NAN or Inf encountered\n");
    742:         break;
    743:       case TAO_DIVERGED_MAXFCN:
    744:         PetscViewerASCIIPrintf(viewer," Maximum Function Evaluations\n");
    745:         break;
    746:       case TAO_DIVERGED_LS_FAILURE:
    747:         PetscViewerASCIIPrintf(viewer," Line Search Failure\n");
    748:         break;
    749:       case TAO_DIVERGED_TR_REDUCTION:
    750:         PetscViewerASCIIPrintf(viewer," Trust Region too small\n");
    751:         break;
    752:       case TAO_DIVERGED_USER:
    753:         PetscViewerASCIIPrintf(viewer," User Terminated\n");
    754:         break;
    755:       default:
    756:         PetscViewerASCIIPrintf(viewer,"\n");
    757:         break;
    758:       }
    759:     }
    760:     PetscViewerASCIIPopTab(viewer);
    761:   } else if (isstring) {
    762:     TaoGetType(tao,&type);
    763:     PetscViewerStringSPrintf(viewer," %-3.3s",type);
    764:   }
    765:   return(0);
    766: }

    768: /*@
    769:   TaoSetRecycleHistory - Sets the boolean flag to enable/disable re-using
    770:   iterate information from the previous TaoSolve(). This feature is disabled by
    771:   default.

    773:   For conjugate gradient methods (BNCG), this re-uses the latest search direction
    774:   from the previous TaoSolve() call when computing the first search direction in a
    775:   new solution. By default, CG methods set the first search direction to the
    776:   negative gradient.

    778:   For quasi-Newton family of methods (BQNLS, BQNKLS, BQNKTR, BQNKTL), this re-uses
    779:   the accumulated quasi-Newton Hessian approximation from the previous TaoSolve()
    780:   call. By default, QN family of methods reset the initial Hessian approximation to
    781:   the identity matrix.

    783:   For any other algorithm, this setting has no effect.

    785:   Logically collective on Tao

    787:   Input Parameters:
    788: + tao - the Tao context
    789: - recycle - boolean flag

    791:   Options Database Keys:
    792: . -tao_recycle_history

    794:   Level: intermediate

    796: .seealso: TaoSetRecycleHistory(), TAOBNCG, TAOBQNLS, TAOBQNKLS, TAOBQNKTR, TAOBQNKTL

    798: @*/
    799: PetscErrorCode TaoSetRecycleHistory(Tao tao, PetscBool recycle)
    800: {
    803:   tao->recycle = recycle;
    804:   return(0);
    805: }

    807: /*@
    808:   TaoGetRecycleHistory - Retrieve the boolean flag for re-using iterate information
    809:   from the previous TaoSolve(). This feature is disabled by default.

    811:   Logically collective on Tao

    813:   Input Parameters:
    814: , tao - the Tao context

    816:   Output Parameters:
    817: , recycle - boolean flag

    819:   Options Database Keys:
    820: . -tao_recycle_history

    822:   Level: intermediate

    824: .seealso: TaoGetRecycleHistory(), TAOBNCG, TAOBQNLS, TAOBQNKLS, TAOBQNKTR, TAOBQNKTL

    826: @*/
    827: PetscErrorCode TaoGetRecycleHistory(Tao tao, PetscBool *recycle)
    828: {
    831:   *recycle = tao->recycle;
    832:   return(0);
    833: }

    835: /*@
    836:   TaoSetTolerances - Sets parameters used in TAO convergence tests

    838:   Logically collective on Tao

    840:   Input Parameters:
    841: + tao - the Tao context
    842: . gatol - stop if norm of gradient is less than this
    843: . grtol - stop if relative norm of gradient is less than this
    844: - gttol - stop if norm of gradient is reduced by this factor

    846:   Options Database Keys:
    847: + -tao_gatol <gatol> - Sets gatol
    848: . -tao_grtol <grtol> - Sets grtol
    849: - -tao_gttol <gttol> - Sets gttol

    851:   Stopping Criteria:
    852: $ ||g(X)||                            <= gatol
    853: $ ||g(X)|| / |f(X)|                   <= grtol
    854: $ ||g(X)|| / ||g(X0)||                <= gttol

    856:   Notes:
    857:   Use PETSC_DEFAULT to leave one or more tolerances unchanged.

    859:   Level: beginner

    861: .seealso: TaoGetTolerances()

    863: @*/
    864: PetscErrorCode TaoSetTolerances(Tao tao, PetscReal gatol, PetscReal grtol, PetscReal gttol)
    865: {

    871:   if (gatol != PETSC_DEFAULT) {
    872:     if (gatol<0) {
    873:       PetscInfo(tao,"Tried to set negative gatol -- ignored.\n");
    874:     } else {
    875:       tao->gatol = PetscMax(0,gatol);
    876:       tao->gatol_changed=PETSC_TRUE;
    877:     }
    878:   }

    880:   if (grtol != PETSC_DEFAULT) {
    881:     if (grtol<0) {
    882:       PetscInfo(tao,"Tried to set negative grtol -- ignored.\n");
    883:     } else {
    884:       tao->grtol = PetscMax(0,grtol);
    885:       tao->grtol_changed=PETSC_TRUE;
    886:     }
    887:   }

    889:   if (gttol != PETSC_DEFAULT) {
    890:     if (gttol<0) {
    891:       PetscInfo(tao,"Tried to set negative gttol -- ignored.\n");
    892:     } else {
    893:       tao->gttol = PetscMax(0,gttol);
    894:       tao->gttol_changed=PETSC_TRUE;
    895:     }
    896:   }
    897:   return(0);
    898: }

    900: /*@
    901:   TaoSetConstraintTolerances - Sets constraint tolerance parameters used in TAO  convergence tests

    903:   Logically collective on Tao

    905:   Input Parameters:
    906: + tao - the Tao context
    907: . catol - absolute constraint tolerance, constraint norm must be less than catol for used for gatol convergence criteria
    908: - crtol - relative contraint tolerance, constraint norm must be less than crtol for used for gatol, gttol convergence criteria

    910:   Options Database Keys:
    911: + -tao_catol <catol> - Sets catol
    912: - -tao_crtol <crtol> - Sets crtol

    914:   Notes:
    915:   Use PETSC_DEFAULT to leave any tolerance unchanged.

    917:   Level: intermediate

    919: .seealso: TaoGetTolerances(), TaoGetConstraintTolerances(), TaoSetTolerances()

    921: @*/
    922: PetscErrorCode TaoSetConstraintTolerances(Tao tao, PetscReal catol, PetscReal crtol)
    923: {

    929:   if (catol != PETSC_DEFAULT) {
    930:     if (catol<0) {
    931:       PetscInfo(tao,"Tried to set negative catol -- ignored.\n");
    932:     } else {
    933:       tao->catol = PetscMax(0,catol);
    934:       tao->catol_changed=PETSC_TRUE;
    935:     }
    936:   }

    938:   if (crtol != PETSC_DEFAULT) {
    939:     if (crtol<0) {
    940:       PetscInfo(tao,"Tried to set negative crtol -- ignored.\n");
    941:     } else {
    942:       tao->crtol = PetscMax(0,crtol);
    943:       tao->crtol_changed=PETSC_TRUE;
    944:     }
    945:   }
    946:   return(0);
    947: }

    949: /*@
    950:   TaoGetConstraintTolerances - Gets constraint tolerance parameters used in TAO  convergence tests

    952:   Not ollective

    954:   Input Parameter:
    955: . tao - the Tao context

    957:   Output Parameters:
    958: + catol - absolute constraint tolerance, constraint norm must be less than catol for used for gatol convergence criteria
    959: - crtol - relative contraint tolerance, constraint norm must be less than crtol for used for gatol, gttol convergence criteria

    961:   Level: intermediate

    963: .seealso: TaoGetTolerances(), TaoSetTolerances(), TaoSetConstraintTolerances()

    965: @*/
    966: PetscErrorCode TaoGetConstraintTolerances(Tao tao, PetscReal *catol, PetscReal *crtol)
    967: {
    970:   if (catol) *catol = tao->catol;
    971:   if (crtol) *crtol = tao->crtol;
    972:   return(0);
    973: }

    975: /*@
    976:    TaoSetFunctionLowerBound - Sets a bound on the solution objective value.
    977:    When an approximate solution with an objective value below this number
    978:    has been found, the solver will terminate.

    980:    Logically Collective on Tao

    982:    Input Parameters:
    983: +  tao - the Tao solver context
    984: -  fmin - the tolerance

    986:    Options Database Keys:
    987: .    -tao_fmin <fmin> - sets the minimum function value

    989:    Level: intermediate

    991: .seealso: TaoSetTolerances()
    992: @*/
    993: PetscErrorCode TaoSetFunctionLowerBound(Tao tao,PetscReal fmin)
    994: {
    997:   tao->fmin = fmin;
    998:   tao->fmin_changed=PETSC_TRUE;
    999:   return(0);
    1000: }

    1002: /*@
    1003:    TaoGetFunctionLowerBound - Gets the bound on the solution objective value.
    1004:    When an approximate solution with an objective value below this number
    1005:    has been found, the solver will terminate.

    1007:    Not collective on Tao

    1009:    Input Parameters:
    1010: .  tao - the Tao solver context

    1012:    OutputParameters:
    1013: .  fmin - the minimum function value

    1015:    Level: intermediate

    1017: .seealso: TaoSetFunctionLowerBound()
    1018: @*/
    1019: PetscErrorCode TaoGetFunctionLowerBound(Tao tao,PetscReal *fmin)
    1020: {
    1023:   *fmin = tao->fmin;
    1024:   return(0);
    1025: }

    1027: /*@
    1028:    TaoSetMaximumFunctionEvaluations - Sets a maximum number of
    1029:    function evaluations.

    1031:    Logically Collective on Tao

    1033:    Input Parameters:
    1034: +  tao - the Tao solver context
    1035: -  nfcn - the maximum number of function evaluations (>=0)

    1037:    Options Database Keys:
    1038: .    -tao_max_funcs <nfcn> - sets the maximum number of function evaluations

    1040:    Level: intermediate

    1042: .seealso: TaoSetTolerances(), TaoSetMaximumIterations()
    1043: @*/

    1045: PetscErrorCode TaoSetMaximumFunctionEvaluations(Tao tao,PetscInt nfcn)
    1046: {
    1049:   tao->max_funcs = PetscMax(0,nfcn);
    1050:   tao->max_funcs_changed=PETSC_TRUE;
    1051:   return(0);
    1052: }

    1054: /*@
    1055:    TaoGetMaximumFunctionEvaluations - Sets a maximum number of
    1056:    function evaluations.

    1058:    Not Collective

    1060:    Input Parameters:
    1061: .  tao - the Tao solver context

    1063:    Output Parameters:
    1064: .  nfcn - the maximum number of function evaluations

    1066:    Level: intermediate

    1068: .seealso: TaoSetMaximumFunctionEvaluations(), TaoGetMaximumIterations()
    1069: @*/

    1071: PetscErrorCode TaoGetMaximumFunctionEvaluations(Tao tao,PetscInt *nfcn)
    1072: {
    1075:   *nfcn = tao->max_funcs;
    1076:   return(0);
    1077: }

    1079: /*@
    1080:    TaoGetCurrentFunctionEvaluations - Get current number of
    1081:    function evaluations.

    1083:    Not Collective

    1085:    Input Parameters:
    1086: .  tao - the Tao solver context

    1088:    Output Parameters:
    1089: .  nfuncs - the current number of function evaluations

    1091:    Level: intermediate

    1093: .seealso: TaoSetMaximumFunctionEvaluations(), TaoGetMaximumFunctionEvaluations(), TaoGetMaximumIterations()
    1094: @*/

    1096: PetscErrorCode TaoGetCurrentFunctionEvaluations(Tao tao,PetscInt *nfuncs)
    1097: {
    1100:   *nfuncs=PetscMax(tao->nfuncs,tao->nfuncgrads);
    1101:   return(0);
    1102: }

    1104: /*@
    1105:    TaoSetMaximumIterations - Sets a maximum number of iterates.

    1107:    Logically Collective on Tao

    1109:    Input Parameters:
    1110: +  tao - the Tao solver context
    1111: -  maxits - the maximum number of iterates (>=0)

    1113:    Options Database Keys:
    1114: .    -tao_max_it <its> - sets the maximum number of iterations

    1116:    Level: intermediate

    1118: .seealso: TaoSetTolerances(), TaoSetMaximumFunctionEvaluations()
    1119: @*/
    1120: PetscErrorCode TaoSetMaximumIterations(Tao tao,PetscInt maxits)
    1121: {
    1124:   tao->max_it = PetscMax(0,maxits);
    1125:   tao->max_it_changed=PETSC_TRUE;
    1126:   return(0);
    1127: }

    1129: /*@
    1130:    TaoGetMaximumIterations - Sets a maximum number of iterates.

    1132:    Not Collective

    1134:    Input Parameters:
    1135: .  tao - the Tao solver context

    1137:    Output Parameters:
    1138: .  maxits - the maximum number of iterates

    1140:    Level: intermediate

    1142: .seealso: TaoSetMaximumIterations(), TaoGetMaximumFunctionEvaluations()
    1143: @*/
    1144: PetscErrorCode TaoGetMaximumIterations(Tao tao,PetscInt *maxits)
    1145: {
    1148:   *maxits = tao->max_it;
    1149:   return(0);
    1150: }

    1152: /*@
    1153:    TaoSetInitialTrustRegionRadius - Sets the initial trust region radius.

    1155:    Logically collective on Tao

    1157:    Input Parameters:
    1158: +  tao - a TAO optimization solver
    1159: -  radius - the trust region radius

    1161:    Level: intermediate

    1163:    Options Database Key:
    1164: .  -tao_trust0 <t0> - sets initial trust region radius

    1166: .seealso: TaoGetTrustRegionRadius(), TaoSetTrustRegionTolerance()
    1167: @*/
    1168: PetscErrorCode TaoSetInitialTrustRegionRadius(Tao tao, PetscReal radius)
    1169: {
    1172:   tao->trust0 = PetscMax(0.0,radius);
    1173:   tao->trust0_changed=PETSC_TRUE;
    1174:   return(0);
    1175: }

    1177: /*@
    1178:    TaoGetInitialTrustRegionRadius - Sets the initial trust region radius.

    1180:    Not Collective

    1182:    Input Parameter:
    1183: .  tao - a TAO optimization solver

    1185:    Output Parameter:
    1186: .  radius - the trust region radius

    1188:    Level: intermediate

    1190: .seealso: TaoSetInitialTrustRegionRadius(), TaoGetCurrentTrustRegionRadius()
    1191: @*/
    1192: PetscErrorCode TaoGetInitialTrustRegionRadius(Tao tao, PetscReal *radius)
    1193: {
    1196:   *radius = tao->trust0;
    1197:   return(0);
    1198: }

    1200: /*@
    1201:    TaoGetCurrentTrustRegionRadius - Gets the current trust region radius.

    1203:    Not Collective

    1205:    Input Parameter:
    1206: .  tao - a TAO optimization solver

    1208:    Output Parameter:
    1209: .  radius - the trust region radius

    1211:    Level: intermediate

    1213: .seealso: TaoSetInitialTrustRegionRadius(), TaoGetInitialTrustRegionRadius()
    1214: @*/
    1215: PetscErrorCode TaoGetCurrentTrustRegionRadius(Tao tao, PetscReal *radius)
    1216: {
    1219:   *radius = tao->trust;
    1220:   return(0);
    1221: }

    1223: /*@
    1224:   TaoGetTolerances - gets the current values of tolerances

    1226:   Not Collective

    1228:   Input Parameter:
    1229: . tao - the Tao context

    1231:   Output Parameters:
    1232: + gatol - stop if norm of gradient is less than this
    1233: . grtol - stop if relative norm of gradient is less than this
    1234: - gttol - stop if norm of gradient is reduced by a this factor

    1236:   Note: NULL can be used as an argument if not all tolerances values are needed

    1238: .seealso TaoSetTolerances()

    1240:   Level: intermediate
    1241: @*/
    1242: PetscErrorCode TaoGetTolerances(Tao tao, PetscReal *gatol, PetscReal *grtol, PetscReal *gttol)
    1243: {
    1246:   if (gatol) *gatol=tao->gatol;
    1247:   if (grtol) *grtol=tao->grtol;
    1248:   if (gttol) *gttol=tao->gttol;
    1249:   return(0);
    1250: }

    1252: /*@
    1253:   TaoGetKSP - Gets the linear solver used by the optimization solver.
    1254:   Application writers should use TaoGetKSP if they need direct access
    1255:   to the PETSc KSP object.

    1257:   Not Collective

    1259:    Input Parameters:
    1260: .  tao - the TAO solver

    1262:    Output Parameters:
    1263: .  ksp - the KSP linear solver used in the optimization solver

    1265:    Level: intermediate

    1267: @*/
    1268: PetscErrorCode TaoGetKSP(Tao tao, KSP *ksp)
    1269: {
    1271:   *ksp = tao->ksp;
    1272:   return(0);
    1273: }

    1275: /*@
    1276:    TaoGetLinearSolveIterations - Gets the total number of linear iterations
    1277:    used by the TAO solver

    1279:    Not Collective

    1281:    Input Parameter:
    1282: .  tao - TAO context

    1284:    Output Parameter:
    1285: .  lits - number of linear iterations

    1287:    Notes:
    1288:    This counter is reset to zero for each successive call to TaoSolve()

    1290:    Level: intermediate

    1292: .seealso:  TaoGetKSP()
    1293: @*/
    1294: PetscErrorCode  TaoGetLinearSolveIterations(Tao tao,PetscInt *lits)
    1295: {
    1299:   *lits = tao->ksp_tot_its;
    1300:   return(0);
    1301: }

    1303: /*@
    1304:   TaoGetLineSearch - Gets the line search used by the optimization solver.
    1305:   Application writers should use TaoGetLineSearch if they need direct access
    1306:   to the TaoLineSearch object.

    1308:   Not Collective

    1310:    Input Parameters:
    1311: .  tao - the TAO solver

    1313:    Output Parameters:
    1314: .  ls - the line search used in the optimization solver

    1316:    Level: intermediate

    1318: @*/
    1319: PetscErrorCode TaoGetLineSearch(Tao tao, TaoLineSearch *ls)
    1320: {
    1322:   *ls = tao->linesearch;
    1323:   return(0);
    1324: }

    1326: /*@
    1327:   TaoAddLineSearchCounts - Adds the number of function evaluations spent
    1328:   in the line search to the running total.

    1330:    Input Parameters:
    1331: +  tao - the TAO solver
    1332: -  ls - the line search used in the optimization solver

    1334:    Level: developer

    1336: .seealso: TaoLineSearchApply()
    1337: @*/
    1338: PetscErrorCode TaoAddLineSearchCounts(Tao tao)
    1339: {
    1341:   PetscBool      flg;
    1342:   PetscInt       nfeval,ngeval,nfgeval;

    1346:   if (tao->linesearch) {
    1347:     TaoLineSearchIsUsingTaoRoutines(tao->linesearch,&flg);
    1348:     if (!flg) {
    1349:       TaoLineSearchGetNumberFunctionEvaluations(tao->linesearch,&nfeval,&ngeval,&nfgeval);
    1350:       tao->nfuncs+=nfeval;
    1351:       tao->ngrads+=ngeval;
    1352:       tao->nfuncgrads+=nfgeval;
    1353:     }
    1354:   }
    1355:   return(0);
    1356: }

    1358: /*@
    1359:   TaoGetSolutionVector - Returns the vector with the current TAO solution

    1361:   Not Collective

    1363:   Input Parameter:
    1364: . tao - the Tao context

    1366:   Output Parameter:
    1367: . X - the current solution

    1369:   Level: intermediate

    1371:   Note:  The returned vector will be the same object that was passed into TaoSetInitialVector()
    1372: @*/
    1373: PetscErrorCode TaoGetSolutionVector(Tao tao, Vec *X)
    1374: {
    1377:   *X = tao->solution;
    1378:   return(0);
    1379: }

    1381: /*@
    1382:   TaoGetGradientVector - Returns the vector with the current TAO gradient

    1384:   Not Collective

    1386:   Input Parameter:
    1387: . tao - the Tao context

    1389:   Output Parameter:
    1390: . G - the current solution

    1392:   Level: intermediate
    1393: @*/
    1394: PetscErrorCode TaoGetGradientVector(Tao tao, Vec *G)
    1395: {
    1398:   *G = tao->gradient;
    1399:   return(0);
    1400: }

    1402: /*@
    1403:    TaoResetStatistics - Initialize the statistics used by TAO for all of the solvers.
    1404:    These statistics include the iteration number, residual norms, and convergence status.
    1405:    This routine gets called before solving each optimization problem.

    1407:    Collective on Tao

    1409:    Input Parameters:
    1410: .  solver - the Tao context

    1412:    Level: developer

    1414: .seealso: TaoCreate(), TaoSolve()
    1415: @*/
    1416: PetscErrorCode TaoResetStatistics(Tao tao)
    1417: {
    1420:   tao->niter        = 0;
    1421:   tao->nfuncs       = 0;
    1422:   tao->nfuncgrads   = 0;
    1423:   tao->ngrads       = 0;
    1424:   tao->nhess        = 0;
    1425:   tao->njac         = 0;
    1426:   tao->nconstraints = 0;
    1427:   tao->ksp_its      = 0;
    1428:   tao->ksp_tot_its  = 0;
    1429:   tao->reason       = TAO_CONTINUE_ITERATING;
    1430:   tao->residual     = 0.0;
    1431:   tao->cnorm        = 0.0;
    1432:   tao->step         = 0.0;
    1433:   tao->lsflag       = PETSC_FALSE;
    1434:   if (tao->hist_reset) tao->hist_len=0;
    1435:   return(0);
    1436: }

    1438: /*@C
    1439:   TaoSetUpdate - Sets the general-purpose update function called
    1440:   at the beginning of every iteration of the nonlinear solve. Specifically
    1441:   it is called at the top of every iteration, after the new solution and the gradient
    1442:   is determined, but before the Hessian is computed (if applicable).

    1444:   Logically Collective on Tao

    1446:   Input Parameters:
    1447: + tao - The tao solver context
    1448: - func - The function

    1450:   Calling sequence of func:
    1451: $ func (Tao tao, PetscInt step);

    1453: . step - The current step of the iteration

    1455:   Level: advanced

    1457: .seealso TaoSolve()
    1458: @*/
    1459: PetscErrorCode  TaoSetUpdate(Tao tao, PetscErrorCode (*func)(Tao, PetscInt,void*), void *ctx)
    1460: {
    1463:   tao->ops->update = func;
    1464:   tao->user_update = ctx;
    1465:   return(0);
    1466: }

    1468: /*@C
    1469:   TaoSetConvergenceTest - Sets the function that is to be used to test
    1470:   for convergence o fthe iterative minimization solution.  The new convergence
    1471:   testing routine will replace TAO's default convergence test.

    1473:   Logically Collective on Tao

    1475:   Input Parameters:
    1476: + tao - the Tao object
    1477: . conv - the routine to test for convergence
    1478: - ctx - [optional] context for private data for the convergence routine
    1479:         (may be NULL)

    1481:   Calling sequence of conv:
    1482: $   PetscErrorCode conv(Tao tao, void *ctx)

    1484: + tao - the Tao object
    1485: - ctx - [optional] convergence context

    1487:   Note: The new convergence testing routine should call TaoSetConvergedReason().

    1489:   Level: advanced

    1491: .seealso: TaoSetConvergedReason(), TaoGetSolutionStatus(), TaoGetTolerances(), TaoSetMonitor

    1493: @*/
    1494: PetscErrorCode TaoSetConvergenceTest(Tao tao, PetscErrorCode (*conv)(Tao,void*), void *ctx)
    1495: {
    1498:   (tao)->ops->convergencetest = conv;
    1499:   (tao)->cnvP = ctx;
    1500:   return(0);
    1501: }

    1503: /*@C
    1504:    TaoSetMonitor - Sets an ADDITIONAL function that is to be used at every
    1505:    iteration of the solver to display the iteration's
    1506:    progress.

    1508:    Logically Collective on Tao

    1510:    Input Parameters:
    1511: +  tao - the Tao solver context
    1512: .  mymonitor - monitoring routine
    1513: -  mctx - [optional] user-defined context for private data for the
    1514:           monitor routine (may be NULL)

    1516:    Calling sequence of mymonitor:
    1517: $     PetscErrorCode mymonitor(Tao tao,void *mctx)

    1519: +    tao - the Tao solver context
    1520: -    mctx - [optional] monitoring context

    1522:    Options Database Keys:
    1523: +    -tao_monitor        - sets TaoMonitorDefault()
    1524: .    -tao_smonitor       - sets short monitor
    1525: .    -tao_cmonitor       - same as smonitor plus constraint norm
    1526: .    -tao_view_solution   - view solution at each iteration
    1527: .    -tao_view_gradient   - view gradient at each iteration
    1528: .    -tao_view_ls_residual - view least-squares residual vector at each iteration
    1529: -    -tao_cancelmonitors - cancels all monitors that have been hardwired into a code by calls to TaoSetMonitor(), but does not cancel those set via the options database.

    1531:    Notes:
    1532:    Several different monitoring routines may be set by calling
    1533:    TaoSetMonitor() multiple times; all will be called in the
    1534:    order in which they were set.

    1536:    Fortran Notes:
    1537:     Only one monitor function may be set

    1539:    Level: intermediate

    1541: .seealso: TaoMonitorDefault(), TaoCancelMonitors(),  TaoSetDestroyRoutine()
    1542: @*/
    1543: PetscErrorCode TaoSetMonitor(Tao tao, PetscErrorCode (*func)(Tao, void*), void *ctx,PetscErrorCode (*dest)(void**))
    1544: {
    1546:   PetscInt       i;
    1547:   PetscBool      identical;

    1551:   if (tao->numbermonitors >= MAXTAOMONITORS) SETERRQ1(PetscObjectComm((PetscObject)tao),PETSC_ERR_SUP,"Cannot attach another monitor -- max=%d",MAXTAOMONITORS);

    1553:   for (i=0; i<tao->numbermonitors;i++) {
    1554:     PetscMonitorCompare((PetscErrorCode (*)(void))func,ctx,dest,(PetscErrorCode (*)(void))tao->monitor[i],tao->monitorcontext[i],tao->monitordestroy[i],&identical);
    1555:     if (identical) return(0);
    1556:   }
    1557:   tao->monitor[tao->numbermonitors] = func;
    1558:   tao->monitorcontext[tao->numbermonitors] = (void*)ctx;
    1559:   tao->monitordestroy[tao->numbermonitors] = dest;
    1560:   ++tao->numbermonitors;
    1561:   return(0);
    1562: }

    1564: /*@
    1565:    TaoCancelMonitors - Clears all the monitor functions for a Tao object.

    1567:    Logically Collective on Tao

    1569:    Input Parameters:
    1570: .  tao - the Tao solver context

    1572:    Options Database:
    1573: .  -tao_cancelmonitors - cancels all monitors that have been hardwired
    1574:     into a code by calls to TaoSetMonitor(), but does not cancel those
    1575:     set via the options database

    1577:    Notes:
    1578:    There is no way to clear one specific monitor from a Tao object.

    1580:    Level: advanced

    1582: .seealso: TaoMonitorDefault(), TaoSetMonitor()
    1583: @*/
    1584: PetscErrorCode TaoCancelMonitors(Tao tao)
    1585: {
    1586:   PetscInt       i;

    1591:   for (i=0;i<tao->numbermonitors;i++) {
    1592:     if (tao->monitordestroy[i]) {
    1593:       (*tao->monitordestroy[i])(&tao->monitorcontext[i]);
    1594:     }
    1595:   }
    1596:   tao->numbermonitors=0;
    1597:   return(0);
    1598: }

    1600: /*@
    1601:    TaoMonitorDefault - Default routine for monitoring progress of the
    1602:    Tao solvers (default).  This monitor prints the function value and gradient
    1603:    norm at each iteration.  It can be turned on from the command line using the
    1604:    -tao_monitor option

    1606:    Collective on Tao

    1608:    Input Parameters:
    1609: +  tao - the Tao context
    1610: -  ctx - PetscViewer context or NULL

    1612:    Options Database Keys:
    1613: .  -tao_monitor

    1615:    Level: advanced

    1617: .seealso: TaoDefaultSMonitor(), TaoSetMonitor()
    1618: @*/
    1619: PetscErrorCode TaoMonitorDefault(Tao tao, void *ctx)
    1620: {
    1622:   PetscInt       its, tabs;
    1623:   PetscReal      fct,gnorm;
    1624:   PetscViewer    viewer = (PetscViewer)ctx;

    1628:   its=tao->niter;
    1629:   fct=tao->fc;
    1630:   gnorm=tao->residual;
    1631:   PetscViewerASCIIGetTab(viewer, &tabs);
    1632:   PetscViewerASCIISetTab(viewer, ((PetscObject)tao)->tablevel);
    1633:   if (its == 0 && ((PetscObject)tao)->prefix && !tao->header_printed) {
    1634:      PetscViewerASCIIPrintf(viewer,"  Iteration information for %s solve.\n",((PetscObject)tao)->prefix);
    1635:      tao->header_printed = PETSC_TRUE;
    1636:    }
    1637:   PetscViewerASCIIPrintf(viewer,"%3D TAO,",its);
    1638:   PetscViewerASCIIPrintf(viewer,"  Function value: %g,",(double)fct);
    1639:   if (gnorm >= PETSC_INFINITY) {
    1640:     PetscViewerASCIIPrintf(viewer,"  Residual: Inf \n");
    1641:   } else {
    1642:     PetscViewerASCIIPrintf(viewer,"  Residual: %g \n",(double)gnorm);
    1643:   }
    1644:   PetscViewerASCIISetTab(viewer, tabs);
    1645:   return(0);
    1646: }

    1648: /*@
    1649:    TaoDefaultGMonitor - Default routine for monitoring progress of the
    1650:    Tao solvers (default) with extra detail on the globalization method.
    1651:    This monitor prints the function value and gradient norm at each
    1652:    iteration, as well as the step size and trust radius. Note that the
    1653:    step size and trust radius may be the same for some algorithms.
    1654:    It can be turned on from the command line using the
    1655:    -tao_gmonitor option

    1657:    Collective on Tao

    1659:    Input Parameters:
    1660: +  tao - the Tao context
    1661: -  ctx - PetscViewer context or NULL

    1663:    Options Database Keys:
    1664: .  -tao_monitor

    1666:    Level: advanced

    1668: .seealso: TaoDefaultSMonitor(), TaoSetMonitor()
    1669: @*/
    1670: PetscErrorCode TaoDefaultGMonitor(Tao tao, void *ctx)
    1671: {
    1673:   PetscInt       its, tabs;
    1674:   PetscReal      fct,gnorm,stp,tr;
    1675:   PetscViewer    viewer = (PetscViewer)ctx;

    1679:   its=tao->niter;
    1680:   fct=tao->fc;
    1681:   gnorm=tao->residual;
    1682:   stp=tao->step;
    1683:   tr=tao->trust;
    1684:   PetscViewerASCIIGetTab(viewer, &tabs);
    1685:   PetscViewerASCIISetTab(viewer, ((PetscObject)tao)->tablevel);
    1686:   if (its == 0 && ((PetscObject)tao)->prefix && !tao->header_printed) {
    1687:      PetscViewerASCIIPrintf(viewer,"  Iteration information for %s solve.\n",((PetscObject)tao)->prefix);
    1688:      tao->header_printed = PETSC_TRUE;
    1689:    }
    1690:   PetscViewerASCIIPrintf(viewer,"%3D TAO,",its);
    1691:   PetscViewerASCIIPrintf(viewer,"  Function value: %g,",(double)fct);
    1692:   if (gnorm >= PETSC_INFINITY) {
    1693:     PetscViewerASCIIPrintf(viewer,"  Residual: Inf,");
    1694:   } else {
    1695:     PetscViewerASCIIPrintf(viewer,"  Residual: %g,",(double)gnorm);
    1696:   }
    1697:   PetscViewerASCIIPrintf(viewer,"  Step: %g,  Trust: %g\n",(double)stp,(double)tr);
    1698:   PetscViewerASCIISetTab(viewer, tabs);
    1699:   return(0);
    1700: }

    1702: /*@
    1703:    TaoDefaultSMonitor - Default routine for monitoring progress of the
    1704:    solver. Same as TaoMonitorDefault() except
    1705:    it prints fewer digits of the residual as the residual gets smaller.
    1706:    This is because the later digits are meaningless and are often
    1707:    different on different machines; by using this routine different
    1708:    machines will usually generate the same output. It can be turned on
    1709:    by using the -tao_smonitor option

    1711:    Collective on Tao

    1713:    Input Parameters:
    1714: +  tao - the Tao context
    1715: -  ctx - PetscViewer context of type ASCII

    1717:    Options Database Keys:
    1718: .  -tao_smonitor

    1720:    Level: advanced

    1722: .seealso: TaoMonitorDefault(), TaoSetMonitor()
    1723: @*/
    1724: PetscErrorCode TaoDefaultSMonitor(Tao tao, void *ctx)
    1725: {
    1727:   PetscInt       its, tabs;
    1728:   PetscReal      fct,gnorm;
    1729:   PetscViewer    viewer = (PetscViewer)ctx;

    1733:   its=tao->niter;
    1734:   fct=tao->fc;
    1735:   gnorm=tao->residual;
    1736:   PetscViewerASCIIGetTab(viewer, &tabs);
    1737:   PetscViewerASCIISetTab(viewer, ((PetscObject)tao)->tablevel);
    1738:   PetscViewerASCIIPrintf(viewer,"iter = %3D,",its);
    1739:   PetscViewerASCIIPrintf(viewer," Function value %g,",(double)fct);
    1740:   if (gnorm >= PETSC_INFINITY) {
    1741:     PetscViewerASCIIPrintf(viewer," Residual: Inf \n");
    1742:   } else if (gnorm > 1.e-6) {
    1743:     PetscViewerASCIIPrintf(viewer," Residual: %g \n",(double)gnorm);
    1744:   } else if (gnorm > 1.e-11) {
    1745:     PetscViewerASCIIPrintf(viewer," Residual: < 1.0e-6 \n");
    1746:   } else {
    1747:     PetscViewerASCIIPrintf(viewer," Residual: < 1.0e-11 \n");
    1748:   }
    1749:   PetscViewerASCIISetTab(viewer, tabs);
    1750:   return(0);
    1751: }

    1753: /*@
    1754:    TaoDefaultCMonitor - same as TaoMonitorDefault() except
    1755:    it prints the norm of the constraints function. It can be turned on
    1756:    from the command line using the -tao_cmonitor option

    1758:    Collective on Tao

    1760:    Input Parameters:
    1761: +  tao - the Tao context
    1762: -  ctx - PetscViewer context or NULL

    1764:    Options Database Keys:
    1765: .  -tao_cmonitor

    1767:    Level: advanced

    1769: .seealso: TaoMonitorDefault(), TaoSetMonitor()
    1770: @*/
    1771: PetscErrorCode TaoDefaultCMonitor(Tao tao, void *ctx)
    1772: {
    1774:   PetscInt       its, tabs;
    1775:   PetscReal      fct,gnorm;
    1776:   PetscViewer    viewer = (PetscViewer)ctx;

    1780:   its=tao->niter;
    1781:   fct=tao->fc;
    1782:   gnorm=tao->residual;
    1783:   PetscViewerASCIIGetTab(viewer, &tabs);
    1784:   PetscViewerASCIISetTab(viewer, ((PetscObject)tao)->tablevel);
    1785:   PetscViewerASCIIPrintf(viewer,"iter = %D,",its);
    1786:   PetscViewerASCIIPrintf(viewer," Function value: %g,",(double)fct);
    1787:   PetscViewerASCIIPrintf(viewer,"  Residual: %g ",(double)gnorm);
    1788:   PetscViewerASCIIPrintf(viewer,"  Constraint: %g \n",(double)tao->cnorm);
    1789:   PetscViewerASCIISetTab(viewer, tabs);
    1790:   return(0);
    1791: }

    1793: /*@C
    1794:    TaoSolutionMonitor - Views the solution at each iteration
    1795:    It can be turned on from the command line using the
    1796:    -tao_view_solution option

    1798:    Collective on Tao

    1800:    Input Parameters:
    1801: +  tao - the Tao context
    1802: -  ctx - PetscViewer context or NULL

    1804:    Options Database Keys:
    1805: .  -tao_view_solution

    1807:    Level: advanced

    1809: .seealso: TaoDefaultSMonitor(), TaoSetMonitor()
    1810: @*/
    1811: PetscErrorCode TaoSolutionMonitor(Tao tao, void *ctx)
    1812: {
    1814:   PetscViewer    viewer  = (PetscViewer)ctx;

    1818:   VecView(tao->solution, viewer);
    1819:   return(0);
    1820: }

    1822: /*@C
    1823:    TaoGradientMonitor - Views the gradient at each iteration
    1824:    It can be turned on from the command line using the
    1825:    -tao_view_gradient option

    1827:    Collective on Tao

    1829:    Input Parameters:
    1830: +  tao - the Tao context
    1831: -  ctx - PetscViewer context or NULL

    1833:    Options Database Keys:
    1834: .  -tao_view_gradient

    1836:    Level: advanced

    1838: .seealso: TaoDefaultSMonitor(), TaoSetMonitor()
    1839: @*/
    1840: PetscErrorCode TaoGradientMonitor(Tao tao, void *ctx)
    1841: {
    1843:   PetscViewer    viewer = (PetscViewer)ctx;

    1847:   VecView(tao->gradient, viewer);
    1848:   return(0);
    1849: }

    1851: /*@C
    1852:    TaoStepDirectionMonitor - Views the gradient at each iteration
    1853:    It can be turned on from the command line using the
    1854:    -tao_view_gradient option

    1856:    Collective on Tao

    1858:    Input Parameters:
    1859: +  tao - the Tao context
    1860: -  ctx - PetscViewer context or NULL

    1862:    Options Database Keys:
    1863: .  -tao_view_gradient

    1865:    Level: advanced

    1867: .seealso: TaoDefaultSMonitor(), TaoSetMonitor()
    1868: @*/
    1869: PetscErrorCode TaoStepDirectionMonitor(Tao tao, void *ctx)
    1870: {
    1872:   PetscViewer    viewer = (PetscViewer)ctx;

    1876:   VecView(tao->stepdirection, viewer);
    1877:   return(0);
    1878: }

    1880: /*@C
    1881:    TaoDrawSolutionMonitor - Plots the solution at each iteration
    1882:    It can be turned on from the command line using the
    1883:    -tao_draw_solution option

    1885:    Collective on Tao

    1887:    Input Parameters:
    1888: +  tao - the Tao context
    1889: -  ctx - TaoMonitorDraw context

    1891:    Options Database Keys:
    1892: .  -tao_draw_solution

    1894:    Level: advanced

    1896: .seealso: TaoSolutionMonitor(), TaoSetMonitor(), TaoDrawGradientMonitor
    1897: @*/
    1898: PetscErrorCode TaoDrawSolutionMonitor(Tao tao, void *ctx)
    1899: {
    1900:   PetscErrorCode    ierr;
    1901:   TaoMonitorDrawCtx ictx = (TaoMonitorDrawCtx)ctx;

    1904:   if (!(((ictx->howoften > 0) && (!(tao->niter % ictx->howoften))) || ((ictx->howoften == -1) && tao->reason))) return(0);
    1905:   VecView(tao->solution,ictx->viewer);
    1906:   return(0);
    1907: }

    1909: /*@C
    1910:    TaoDrawGradientMonitor - Plots the gradient at each iteration
    1911:    It can be turned on from the command line using the
    1912:    -tao_draw_gradient option

    1914:    Collective on Tao

    1916:    Input Parameters:
    1917: +  tao - the Tao context
    1918: -  ctx - PetscViewer context

    1920:    Options Database Keys:
    1921: .  -tao_draw_gradient

    1923:    Level: advanced

    1925: .seealso: TaoGradientMonitor(), TaoSetMonitor(), TaoDrawSolutionMonitor
    1926: @*/
    1927: PetscErrorCode TaoDrawGradientMonitor(Tao tao, void *ctx)
    1928: {
    1929:   PetscErrorCode    ierr;
    1930:   TaoMonitorDrawCtx ictx = (TaoMonitorDrawCtx)ctx;

    1933:   if (!(((ictx->howoften > 0) && (!(tao->niter % ictx->howoften))) || ((ictx->howoften == -1) && tao->reason))) return(0);
    1934:   VecView(tao->gradient,ictx->viewer);
    1935:   return(0);
    1936: }

    1938: /*@C
    1939:    TaoDrawStepMonitor - Plots the step direction at each iteration
    1940:    It can be turned on from the command line using the
    1941:    -tao_draw_step option

    1943:    Collective on Tao

    1945:    Input Parameters:
    1946: +  tao - the Tao context
    1947: -  ctx - PetscViewer context

    1949:    Options Database Keys:
    1950: .  -tao_draw_step

    1952:    Level: advanced

    1954: .seealso: TaoSetMonitor(), TaoDrawSolutionMonitor
    1955: @*/
    1956: PetscErrorCode TaoDrawStepMonitor(Tao tao, void *ctx)
    1957: {
    1959:   PetscViewer    viewer = (PetscViewer)(ctx);

    1962:   VecView(tao->stepdirection, viewer);
    1963:   return(0);
    1964: }

    1966: /*@C
    1967:    TaoResidualMonitor - Views the least-squares residual at each iteration
    1968:    It can be turned on from the command line using the
    1969:    -tao_view_ls_residual option

    1971:    Collective on Tao

    1973:    Input Parameters:
    1974: +  tao - the Tao context
    1975: -  ctx - PetscViewer context or NULL

    1977:    Options Database Keys:
    1978: .  -tao_view_ls_residual

    1980:    Level: advanced

    1982: .seealso: TaoDefaultSMonitor(), TaoSetMonitor()
    1983: @*/
    1984: PetscErrorCode TaoResidualMonitor(Tao tao, void *ctx)
    1985: {
    1987:   PetscViewer    viewer  = (PetscViewer)ctx;

    1991:   VecView(tao->ls_res,viewer);
    1992:   return(0);
    1993: }

    1995: /*@
    1996:    TaoDefaultConvergenceTest - Determines whether the solver should continue iterating
    1997:    or terminate.

    1999:    Collective on Tao

    2001:    Input Parameters:
    2002: +  tao - the Tao context
    2003: -  dummy - unused dummy context

    2005:    Output Parameter:
    2006: .  reason - for terminating

    2008:    Notes:
    2009:    This routine checks the residual in the optimality conditions, the
    2010:    relative residual in the optimity conditions, the number of function
    2011:    evaluations, and the function value to test convergence.  Some
    2012:    solvers may use different convergence routines.

    2014:    Level: developer

    2016: .seealso: TaoSetTolerances(),TaoGetConvergedReason(),TaoSetConvergedReason()
    2017: @*/

    2019: PetscErrorCode TaoDefaultConvergenceTest(Tao tao,void *dummy)
    2020: {
    2021:   PetscInt           niter=tao->niter, nfuncs=PetscMax(tao->nfuncs,tao->nfuncgrads);
    2022:   PetscInt           max_funcs=tao->max_funcs;
    2023:   PetscReal          gnorm=tao->residual, gnorm0=tao->gnorm0;
    2024:   PetscReal          f=tao->fc, steptol=tao->steptol,trradius=tao->step;
    2025:   PetscReal          gatol=tao->gatol,grtol=tao->grtol,gttol=tao->gttol;
    2026:   PetscReal          catol=tao->catol,crtol=tao->crtol;
    2027:   PetscReal          fmin=tao->fmin, cnorm=tao->cnorm;
    2028:   TaoConvergedReason reason=tao->reason;
    2029:   PetscErrorCode     ierr;

    2033:   if (reason != TAO_CONTINUE_ITERATING) {
    2034:     return(0);
    2035:   }

    2037:   if (PetscIsInfOrNanReal(f)) {
    2038:     PetscInfo(tao,"Failed to converged, function value is Inf or NaN\n");
    2039:     reason = TAO_DIVERGED_NAN;
    2040:   } else if (f <= fmin && cnorm <=catol) {
    2041:     PetscInfo2(tao,"Converged due to function value %g < minimum function value %g\n", (double)f,(double)fmin);
    2042:     reason = TAO_CONVERGED_MINF;
    2043:   } else if (gnorm<= gatol && cnorm <=catol) {
    2044:     PetscInfo2(tao,"Converged due to residual norm ||g(X)||=%g < %g\n",(double)gnorm,(double)gatol);
    2045:     reason = TAO_CONVERGED_GATOL;
    2046:   } else if (f!=0 && PetscAbsReal(gnorm/f) <= grtol && cnorm <= crtol) {
    2047:     PetscInfo2(tao,"Converged due to residual ||g(X)||/|f(X)| =%g < %g\n",(double)(gnorm/f),(double)grtol);
    2048:     reason = TAO_CONVERGED_GRTOL;
    2049:   } else if (gnorm0 != 0 && ((gttol == 0 && gnorm == 0) || gnorm/gnorm0 < gttol) && cnorm <= crtol) {
    2050:     PetscInfo2(tao,"Converged due to relative residual norm ||g(X)||/||g(X0)|| = %g < %g\n",(double)(gnorm/gnorm0),(double)gttol);
    2051:     reason = TAO_CONVERGED_GTTOL;
    2052:   } else if (nfuncs > max_funcs) {
    2053:     PetscInfo2(tao,"Exceeded maximum number of function evaluations: %D > %D\n", nfuncs,max_funcs);
    2054:     reason = TAO_DIVERGED_MAXFCN;
    2055:   } else if (tao->lsflag != 0) {
    2056:     PetscInfo(tao,"Tao Line Search failure.\n");
    2057:     reason = TAO_DIVERGED_LS_FAILURE;
    2058:   } else if (trradius < steptol && niter > 0) {
    2059:     PetscInfo2(tao,"Trust region/step size too small: %g < %g\n", (double)trradius,(double)steptol);
    2060:     reason = TAO_CONVERGED_STEPTOL;
    2061:   } else if (niter >= tao->max_it) {
    2062:     PetscInfo2(tao,"Exceeded maximum number of iterations: %D > %D\n",niter,tao->max_it);
    2063:     reason = TAO_DIVERGED_MAXITS;
    2064:   } else {
    2065:     reason = TAO_CONTINUE_ITERATING;
    2066:   }
    2067:   tao->reason = reason;
    2068:   return(0);
    2069: }

    2071: /*@C
    2072:    TaoSetOptionsPrefix - Sets the prefix used for searching for all
    2073:    TAO options in the database.

    2075:    Logically Collective on Tao

    2077:    Input Parameters:
    2078: +  tao - the Tao context
    2079: -  prefix - the prefix string to prepend to all TAO option requests

    2081:    Notes:
    2082:    A hyphen (-) must NOT be given at the beginning of the prefix name.
    2083:    The first character of all runtime options is AUTOMATICALLY the hyphen.

    2085:    For example, to distinguish between the runtime options for two
    2086:    different TAO solvers, one could call
    2087: .vb
    2088:       TaoSetOptionsPrefix(tao1,"sys1_")
    2089:       TaoSetOptionsPrefix(tao2,"sys2_")
    2090: .ve

    2092:    This would enable use of different options for each system, such as
    2093: .vb
    2094:       -sys1_tao_method blmvm -sys1_tao_gtol 1.e-3
    2095:       -sys2_tao_method lmvm  -sys2_tao_gtol 1.e-4
    2096: .ve

    2098:    Level: advanced

    2100: .seealso: TaoAppendOptionsPrefix(), TaoGetOptionsPrefix()
    2101: @*/

    2103: PetscErrorCode TaoSetOptionsPrefix(Tao tao, const char p[])
    2104: {

    2108:   PetscObjectSetOptionsPrefix((PetscObject)tao,p);
    2109:   if (tao->linesearch) {
    2110:     TaoLineSearchSetOptionsPrefix(tao->linesearch,p);
    2111:   }
    2112:   if (tao->ksp) {
    2113:     KSPSetOptionsPrefix(tao->ksp,p);
    2114:   }
    2115:   return(0);
    2116: }

    2118: /*@C
    2119:    TaoAppendOptionsPrefix - Appends to the prefix used for searching for all
    2120:    TAO options in the database.

    2122:    Logically Collective on Tao

    2124:    Input Parameters:
    2125: +  tao - the Tao solver context
    2126: -  prefix - the prefix string to prepend to all TAO option requests

    2128:    Notes:
    2129:    A hyphen (-) must NOT be given at the beginning of the prefix name.
    2130:    The first character of all runtime options is AUTOMATICALLY the hyphen.

    2132:    Level: advanced

    2134: .seealso: TaoSetOptionsPrefix(), TaoGetOptionsPrefix()
    2135: @*/
    2136: PetscErrorCode TaoAppendOptionsPrefix(Tao tao, const char p[])
    2137: {

    2141:   PetscObjectAppendOptionsPrefix((PetscObject)tao,p);
    2142:   if (tao->linesearch) {
    2143:     TaoLineSearchSetOptionsPrefix(tao->linesearch,p);
    2144:   }
    2145:   if (tao->ksp) {
    2146:     KSPSetOptionsPrefix(tao->ksp,p);
    2147:   }
    2148:   return(0);
    2149: }

    2151: /*@C
    2152:   TaoGetOptionsPrefix - Gets the prefix used for searching for all
    2153:   TAO options in the database

    2155:   Not Collective

    2157:   Input Parameters:
    2158: . tao - the Tao context

    2160:   Output Parameters:
    2161: . prefix - pointer to the prefix string used is returned

    2163:   Notes:
    2164:     On the fortran side, the user should pass in a string 'prefix' of
    2165:   sufficient length to hold the prefix.

    2167:   Level: advanced

    2169: .seealso: TaoSetOptionsPrefix(), TaoAppendOptionsPrefix()
    2170: @*/
    2171: PetscErrorCode TaoGetOptionsPrefix(Tao tao, const char *p[])
    2172: {
    2173:    return PetscObjectGetOptionsPrefix((PetscObject)tao,p);
    2174: }

    2176: /*@C
    2177:    TaoSetType - Sets the method for the unconstrained minimization solver.

    2179:    Collective on Tao

    2181:    Input Parameters:
    2182: +  solver - the Tao solver context
    2183: -  type - a known method

    2185:    Options Database Key:
    2186: .  -tao_type <type> - Sets the method; use -help for a list
    2187:    of available methods (for instance, "-tao_type lmvm" or "-tao_type tron")

    2189:    Available methods include:
    2190: +    nls - Newton's method with line search for unconstrained minimization
    2191: .    ntr - Newton's method with trust region for unconstrained minimization
    2192: .    ntl - Newton's method with trust region, line search for unconstrained minimization
    2193: .    lmvm - Limited memory variable metric method for unconstrained minimization
    2194: .    cg - Nonlinear conjugate gradient method for unconstrained minimization
    2195: .    nm - Nelder-Mead algorithm for derivate-free unconstrained minimization
    2196: .    tron - Newton Trust Region method for bound constrained minimization
    2197: .    gpcg - Newton Trust Region method for quadratic bound constrained minimization
    2198: .    blmvm - Limited memory variable metric method for bound constrained minimization
    2199: -    pounders - Model-based algorithm pounder extended for nonlinear least squares

    2201:   Level: intermediate

    2203: .seealso: TaoCreate(), TaoGetType(), TaoType

    2205: @*/
    2206: PetscErrorCode TaoSetType(Tao tao, TaoType type)
    2207: {
    2209:   PetscErrorCode (*create_xxx)(Tao);
    2210:   PetscBool      issame;

    2215:   PetscObjectTypeCompare((PetscObject)tao,type,&issame);
    2216:   if (issame) return(0);

    2218:   PetscFunctionListFind(TaoList, type, (void(**)(void))&create_xxx);
    2219:   if (!create_xxx) SETERRQ1(PetscObjectComm((PetscObject)tao),PETSC_ERR_ARG_UNKNOWN_TYPE,"Unable to find requested Tao type %s",type);

    2221:   /* Destroy the existing solver information */
    2222:   if (tao->ops->destroy) {
    2223:     (*tao->ops->destroy)(tao);
    2224:   }
    2225:   KSPDestroy(&tao->ksp);
    2226:   TaoLineSearchDestroy(&tao->linesearch);
    2227:   VecDestroy(&tao->gradient);
    2228:   VecDestroy(&tao->stepdirection);

    2230:   tao->ops->setup = NULL;
    2231:   tao->ops->solve = NULL;
    2232:   tao->ops->view  = NULL;
    2233:   tao->ops->setfromoptions = NULL;
    2234:   tao->ops->destroy = NULL;

    2236:   tao->setupcalled = PETSC_FALSE;

    2238:   (*create_xxx)(tao);
    2239:   PetscObjectChangeTypeName((PetscObject)tao,type);
    2240:   return(0);
    2241: }

    2243: /*MC
    2244:    TaoRegister - Adds a method to the TAO package for unconstrained minimization.

    2246:    Synopsis:
    2247:    TaoRegister(char *name_solver,char *path,char *name_Create,PetscErrorCode (*routine_Create)(Tao))

    2249:    Not collective

    2251:    Input Parameters:
    2252: +  sname - name of a new user-defined solver
    2253: -  func - routine to Create method context

    2255:    Notes:
    2256:    TaoRegister() may be called multiple times to add several user-defined solvers.

    2258:    Sample usage:
    2259: .vb
    2260:    TaoRegister("my_solver",MySolverCreate);
    2261: .ve

    2263:    Then, your solver can be chosen with the procedural interface via
    2264: $     TaoSetType(tao,"my_solver")
    2265:    or at runtime via the option
    2266: $     -tao_type my_solver

    2268:    Level: advanced

    2270: .seealso: TaoRegisterAll(), TaoRegisterDestroy()
    2271: M*/
    2272: PetscErrorCode TaoRegister(const char sname[], PetscErrorCode (*func)(Tao))
    2273: {

    2277:   TaoInitializePackage();
    2278:   PetscFunctionListAdd(&TaoList,sname, (void (*)(void))func);
    2279:   return(0);
    2280: }

    2282: /*@C
    2283:    TaoRegisterDestroy - Frees the list of minimization solvers that were
    2284:    registered by TaoRegisterDynamic().

    2286:    Not Collective

    2288:    Level: advanced

    2290: .seealso: TaoRegisterAll(), TaoRegister()
    2291: @*/
    2292: PetscErrorCode TaoRegisterDestroy(void)
    2293: {
    2296:   PetscFunctionListDestroy(&TaoList);
    2297:   TaoRegisterAllCalled = PETSC_FALSE;
    2298:   return(0);
    2299: }

    2301: /*@
    2302:    TaoGetIterationNumber - Gets the number of Tao iterations completed
    2303:    at this time.

    2305:    Not Collective

    2307:    Input Parameter:
    2308: .  tao - Tao context

    2310:    Output Parameter:
    2311: .  iter - iteration number

    2313:    Notes:
    2314:    For example, during the computation of iteration 2 this would return 1.

    2316:    Level: intermediate

    2318: .seealso:   TaoGetLinearSolveIterations(), TaoGetResidualNorm(), TaoGetObjective()
    2319: @*/
    2320: PetscErrorCode  TaoGetIterationNumber(Tao tao,PetscInt *iter)
    2321: {
    2325:   *iter = tao->niter;
    2326:   return(0);
    2327: }

    2329: /*@
    2330:    TaoGetObjective - Gets the current value of the objective function
    2331:    at this time.

    2333:    Not Collective

    2335:    Input Parameter:
    2336: .  tao - Tao context

    2338:    Output Parameter:
    2339: .  value - the current value

    2341:    Level: intermediate

    2343: .seealso:   TaoGetLinearSolveIterations(), TaoGetIterationNumber(), TaoGetResidualNorm()
    2344: @*/
    2345: PetscErrorCode  TaoGetObjective(Tao tao,PetscReal *value)
    2346: {
    2350:   *value = tao->fc;
    2351:   return(0);
    2352: }

    2354: /*@
    2355:    TaoGetResidualNorm - Gets the current value of the norm of the residual
    2356:    at this time.

    2358:    Not Collective

    2360:    Input Parameter:
    2361: .  tao - Tao context

    2363:    Output Parameter:
    2364: .  value - the current value

    2366:    Level: intermediate

    2368:    Developer Note: This is the 2-norm of the residual, we cannot use TaoGetGradientNorm() because that has
    2369:                    a different meaning. For some reason Tao sometimes calls the gradient the residual.

    2371: .seealso:   TaoGetLinearSolveIterations(), TaoGetIterationNumber(), TaoGetObjective()
    2372: @*/
    2373: PetscErrorCode  TaoGetResidualNorm(Tao tao,PetscReal *value)
    2374: {
    2378:   *value = tao->residual;
    2379:   return(0);
    2380: }

    2382: /*@
    2383:    TaoSetIterationNumber - Sets the current iteration number.

    2385:    Not Collective

    2387:    Input Parameters:
    2388: +  tao - Tao context
    2389: -  iter - iteration number

    2391:    Level: developer

    2393: .seealso:   TaoGetLinearSolveIterations()
    2394: @*/
    2395: PetscErrorCode  TaoSetIterationNumber(Tao tao,PetscInt iter)
    2396: {

    2401:   PetscObjectSAWsTakeAccess((PetscObject)tao);
    2402:   tao->niter = iter;
    2403:   PetscObjectSAWsGrantAccess((PetscObject)tao);
    2404:   return(0);
    2405: }

    2407: /*@
    2408:    TaoGetTotalIterationNumber - Gets the total number of Tao iterations
    2409:    completed. This number keeps accumulating if multiple solves
    2410:    are called with the Tao object.

    2412:    Not Collective

    2414:    Input Parameter:
    2415: .  tao - Tao context

    2417:    Output Parameter:
    2418: .  iter - iteration number

    2420:    Notes:
    2421:    The total iteration count is updated after each solve, if there is a current
    2422:    TaoSolve() in progress then those iterations are not yet counted.

    2424:    Level: intermediate

    2426: .seealso:   TaoGetLinearSolveIterations()
    2427: @*/
    2428: PetscErrorCode  TaoGetTotalIterationNumber(Tao tao,PetscInt *iter)
    2429: {
    2433:   *iter = tao->ntotalits;
    2434:   return(0);
    2435: }

    2437: /*@
    2438:    TaoSetTotalIterationNumber - Sets the current total iteration number.

    2440:    Not Collective

    2442:    Input Parameters:
    2443: +  tao - Tao context
    2444: -  iter - iteration number

    2446:    Level: developer

    2448: .seealso:   TaoGetLinearSolveIterations()
    2449: @*/
    2450: PetscErrorCode  TaoSetTotalIterationNumber(Tao tao,PetscInt iter)
    2451: {

    2456:   PetscObjectSAWsTakeAccess((PetscObject)tao);
    2457:   tao->ntotalits = iter;
    2458:   PetscObjectSAWsGrantAccess((PetscObject)tao);
    2459:   return(0);
    2460: }

    2462: /*@
    2463:   TaoSetConvergedReason - Sets the termination flag on a Tao object

    2465:   Logically Collective on Tao

    2467:   Input Parameters:
    2468: + tao - the Tao context
    2469: - reason - one of
    2470: $     TAO_CONVERGED_ATOL (2),
    2471: $     TAO_CONVERGED_RTOL (3),
    2472: $     TAO_CONVERGED_STEPTOL (4),
    2473: $     TAO_CONVERGED_MINF (5),
    2474: $     TAO_CONVERGED_USER (6),
    2475: $     TAO_DIVERGED_MAXITS (-2),
    2476: $     TAO_DIVERGED_NAN (-4),
    2477: $     TAO_DIVERGED_MAXFCN (-5),
    2478: $     TAO_DIVERGED_LS_FAILURE (-6),
    2479: $     TAO_DIVERGED_TR_REDUCTION (-7),
    2480: $     TAO_DIVERGED_USER (-8),
    2481: $     TAO_CONTINUE_ITERATING (0)

    2483:    Level: intermediate

    2485: @*/
    2486: PetscErrorCode TaoSetConvergedReason(Tao tao, TaoConvergedReason reason)
    2487: {
    2490:   tao->reason = reason;
    2491:   return(0);
    2492: }

    2494: /*@
    2495:    TaoGetConvergedReason - Gets the reason the Tao iteration was stopped.

    2497:    Not Collective

    2499:    Input Parameter:
    2500: .  tao - the Tao solver context

    2502:    Output Parameter:
    2503: .  reason - one of
    2504: $  TAO_CONVERGED_GATOL (3)           ||g(X)|| < gatol
    2505: $  TAO_CONVERGED_GRTOL (4)           ||g(X)|| / f(X)  < grtol
    2506: $  TAO_CONVERGED_GTTOL (5)           ||g(X)|| / ||g(X0)|| < gttol
    2507: $  TAO_CONVERGED_STEPTOL (6)         step size small
    2508: $  TAO_CONVERGED_MINF (7)            F < F_min
    2509: $  TAO_CONVERGED_USER (8)            User defined
    2510: $  TAO_DIVERGED_MAXITS (-2)          its > maxits
    2511: $  TAO_DIVERGED_NAN (-4)             Numerical problems
    2512: $  TAO_DIVERGED_MAXFCN (-5)          fevals > max_funcsals
    2513: $  TAO_DIVERGED_LS_FAILURE (-6)      line search failure
    2514: $  TAO_DIVERGED_TR_REDUCTION (-7)    trust region failure
    2515: $  TAO_DIVERGED_USER(-8)             (user defined)
    2516:  $  TAO_CONTINUE_ITERATING (0)

    2518:    where
    2519: +  X - current solution
    2520: .  X0 - initial guess
    2521: .  f(X) - current function value
    2522: .  f(X*) - true solution (estimated)
    2523: .  g(X) - current gradient
    2524: .  its - current iterate number
    2525: .  maxits - maximum number of iterates
    2526: .  fevals - number of function evaluations
    2527: -  max_funcsals - maximum number of function evaluations

    2529:    Level: intermediate

    2531: .seealso: TaoSetConvergenceTest(), TaoSetTolerances()

    2533: @*/
    2534: PetscErrorCode TaoGetConvergedReason(Tao tao, TaoConvergedReason *reason)
    2535: {
    2539:   *reason = tao->reason;
    2540:   return(0);
    2541: }

    2543: /*@
    2544:   TaoGetSolutionStatus - Get the current iterate, objective value,
    2545:   residual, infeasibility, and termination

    2547:   Not Collective

    2549:    Input Parameter:
    2550: .  tao - the Tao context

    2552:    Output Parameters:
    2553: +  iterate - the current iterate number (>=0)
    2554: .  f - the current function value
    2555: .  gnorm - the square of the gradient norm, duality gap, or other measure indicating distance from optimality.
    2556: .  cnorm - the infeasibility of the current solution with regard to the constraints.
    2557: .  xdiff - the step length or trust region radius of the most recent iterate.
    2558: -  reason - The termination reason, which can equal TAO_CONTINUE_ITERATING

    2560:    Level: intermediate

    2562:    Note:
    2563:    TAO returns the values set by the solvers in the routine TaoMonitor().

    2565:    Note:
    2566:    If any of the output arguments are set to NULL, no corresponding value will be returned.

    2568: .seealso: TaoMonitor(), TaoGetConvergedReason()
    2569: @*/
    2570: PetscErrorCode TaoGetSolutionStatus(Tao tao, PetscInt *its, PetscReal *f, PetscReal *gnorm, PetscReal *cnorm, PetscReal *xdiff, TaoConvergedReason *reason)
    2571: {
    2573:   if (its) *its=tao->niter;
    2574:   if (f) *f=tao->fc;
    2575:   if (gnorm) *gnorm=tao->residual;
    2576:   if (cnorm) *cnorm=tao->cnorm;
    2577:   if (reason) *reason=tao->reason;
    2578:   if (xdiff) *xdiff=tao->step;
    2579:   return(0);
    2580: }

    2582: /*@C
    2583:    TaoGetType - Gets the current Tao algorithm.

    2585:    Not Collective

    2587:    Input Parameter:
    2588: .  tao - the Tao solver context

    2590:    Output Parameter:
    2591: .  type - Tao method

    2593:    Level: intermediate

    2595: @*/
    2596: PetscErrorCode TaoGetType(Tao tao,TaoType *type)
    2597: {
    2601:   *type=((PetscObject)tao)->type_name;
    2602:   return(0);
    2603: }

    2605: /*@C
    2606:   TaoMonitor - Monitor the solver and the current solution.  This
    2607:   routine will record the iteration number and residual statistics,
    2608:   call any monitors specified by the user, and calls the convergence-check routine.

    2610:    Input Parameters:
    2611: +  tao - the Tao context
    2612: .  its - the current iterate number (>=0)
    2613: .  f - the current objective function value
    2614: .  res - the gradient norm, square root of the duality gap, or other measure indicating distince from optimality.  This measure will be recorded and
    2615:           used for some termination tests.
    2616: .  cnorm - the infeasibility of the current solution with regard to the constraints.
    2617: -  steplength - multiple of the step direction added to the previous iterate.

    2619:    Output Parameters:
    2620: .  reason - The termination reason, which can equal TAO_CONTINUE_ITERATING

    2622:    Options Database Key:
    2623: .  -tao_monitor - Use the default monitor, which prints statistics to standard output

    2625: .seealso TaoGetConvergedReason(), TaoMonitorDefault(), TaoSetMonitor()

    2627:    Level: developer

    2629: @*/
    2630: PetscErrorCode TaoMonitor(Tao tao, PetscInt its, PetscReal f, PetscReal res, PetscReal cnorm, PetscReal steplength)
    2631: {
    2633:   PetscInt       i;

    2637:   tao->fc = f;
    2638:   tao->residual = res;
    2639:   tao->cnorm = cnorm;
    2640:   tao->step = steplength;
    2641:   if (!its) {
    2642:     tao->cnorm0 = cnorm; tao->gnorm0 = res;
    2643:   }
    2644:   if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(res)) SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_USER, "User provided compute function generated Inf or NaN");
    2645:   for (i=0;i<tao->numbermonitors;i++) {
    2646:     (*tao->monitor[i])(tao,tao->monitorcontext[i]);
    2647:   }
    2648:   return(0);
    2649: }

    2651: /*@
    2652:    TaoSetConvergenceHistory - Sets the array used to hold the convergence history.

    2654:    Logically Collective on Tao

    2656:    Input Parameters:
    2657: +  tao - the Tao solver context
    2658: .  obj   - array to hold objective value history
    2659: .  resid - array to hold residual history
    2660: .  cnorm - array to hold constraint violation history
    2661: .  lits - integer array holds the number of linear iterations for each Tao iteration
    2662: .  na  - size of obj, resid, and cnorm
    2663: -  reset - PetscTrue indicates each new minimization resets the history counter to zero,
    2664:            else it continues storing new values for new minimizations after the old ones

    2666:    Notes:
    2667:    If set, TAO will fill the given arrays with the indicated
    2668:    information at each iteration.  If 'obj','resid','cnorm','lits' are
    2669:    *all* NULL then space (using size na, or 1000 if na is PETSC_DECIDE or
    2670:    PETSC_DEFAULT) is allocated for the history.
    2671:    If not all are NULL, then only the non-NULL information categories
    2672:    will be stored, the others will be ignored.

    2674:    Any convergence information after iteration number 'na' will not be stored.

    2676:    This routine is useful, e.g., when running a code for purposes
    2677:    of accurate performance monitoring, when no I/O should be done
    2678:    during the section of code that is being timed.

    2680:    Level: intermediate

    2682: .seealso: TaoGetConvergenceHistory()

    2684: @*/
    2685: PetscErrorCode TaoSetConvergenceHistory(Tao tao, PetscReal obj[], PetscReal resid[], PetscReal cnorm[], PetscInt lits[], PetscInt na,PetscBool reset)
    2686: {

    2696:   if (na == PETSC_DECIDE || na == PETSC_DEFAULT) na = 1000;
    2697:   if (!obj && !resid && !cnorm && !lits) {
    2698:     PetscCalloc4(na,&obj,na,&resid,na,&cnorm,na,&lits);
    2699:     tao->hist_malloc = PETSC_TRUE;
    2700:   }

    2702:   tao->hist_obj = obj;
    2703:   tao->hist_resid = resid;
    2704:   tao->hist_cnorm = cnorm;
    2705:   tao->hist_lits = lits;
    2706:   tao->hist_max   = na;
    2707:   tao->hist_reset = reset;
    2708:   tao->hist_len = 0;
    2709:   return(0);
    2710: }

    2712: /*@C
    2713:    TaoGetConvergenceHistory - Gets the arrays used to hold the convergence history.

    2715:    Collective on Tao

    2717:    Input Parameter:
    2718: .  tao - the Tao context

    2720:    Output Parameters:
    2721: +  obj   - array used to hold objective value history
    2722: .  resid - array used to hold residual history
    2723: .  cnorm - array used to hold constraint violation history
    2724: .  lits  - integer array used to hold linear solver iteration count
    2725: -  nhist  - size of obj, resid, cnorm, and lits

    2727:    Notes:
    2728:     This routine must be preceded by calls to TaoSetConvergenceHistory()
    2729:     and TaoSolve(), otherwise it returns useless information.

    2731:     The calling sequence for this routine in Fortran is
    2732: $   call TaoGetConvergenceHistory(Tao tao, PetscInt nhist, PetscErrorCode ierr)

    2734:    This routine is useful, e.g., when running a code for purposes
    2735:    of accurate performance monitoring, when no I/O should be done
    2736:    during the section of code that is being timed.

    2738:    Level: advanced

    2740: .seealso: TaoSetConvergenceHistory()

    2742: @*/
    2743: PetscErrorCode TaoGetConvergenceHistory(Tao tao, PetscReal **obj, PetscReal **resid, PetscReal **cnorm, PetscInt **lits, PetscInt *nhist)
    2744: {
    2747:   if (obj)   *obj   = tao->hist_obj;
    2748:   if (cnorm) *cnorm = tao->hist_cnorm;
    2749:   if (resid) *resid = tao->hist_resid;
    2750:   if (nhist) *nhist = tao->hist_len;
    2751:   return(0);
    2752: }

    2754: /*@
    2755:    TaoSetApplicationContext - Sets the optional user-defined context for
    2756:    a solver.

    2758:    Logically Collective on Tao

    2760:    Input Parameters:
    2761: +  tao  - the Tao context
    2762: -  usrP - optional user context

    2764:    Level: intermediate

    2766: .seealso: TaoGetApplicationContext(), TaoSetApplicationContext()
    2767: @*/
    2768: PetscErrorCode  TaoSetApplicationContext(Tao tao,void *usrP)
    2769: {
    2772:   tao->user = usrP;
    2773:   return(0);
    2774: }

    2776: /*@
    2777:    TaoGetApplicationContext - Gets the user-defined context for a
    2778:    TAO solvers.

    2780:    Not Collective

    2782:    Input Parameter:
    2783: .  tao  - Tao context

    2785:    Output Parameter:
    2786: .  usrP - user context

    2788:    Level: intermediate

    2790: .seealso: TaoSetApplicationContext()
    2791: @*/
    2792: PetscErrorCode  TaoGetApplicationContext(Tao tao,void *usrP)
    2793: {
    2796:   *(void**)usrP = tao->user;
    2797:   return(0);
    2798: }

    2800: /*@
    2801:    TaoSetGradientNorm - Sets the matrix used to define the inner product that measures the size of the gradient.

    2803:    Collective on tao

    2805:    Input Parameters:
    2806: +  tao  - the Tao context
    2807: -  M    - gradient norm

    2809:    Level: beginner

    2811: .seealso: TaoGetGradientNorm(), TaoGradientNorm()
    2812: @*/
    2813: PetscErrorCode  TaoSetGradientNorm(Tao tao, Mat M)
    2814: {

    2819:   PetscObjectReference((PetscObject)M);
    2820:   MatDestroy(&tao->gradient_norm);
    2821:   VecDestroy(&tao->gradient_norm_tmp);
    2822:   tao->gradient_norm = M;
    2823:   MatCreateVecs(M, NULL, &tao->gradient_norm_tmp);
    2824:   return(0);
    2825: }

    2827: /*@
    2828:    TaoGetGradientNorm - Returns the matrix used to define the inner product for measuring the size of the gradient.

    2830:    Not Collective

    2832:    Input Parameter:
    2833: .  tao  - Tao context

    2835:    Output Parameter:
    2836: .  M - gradient norm

    2838:    Level: beginner

    2840: .seealso: TaoSetGradientNorm(), TaoGradientNorm()
    2841: @*/
    2842: PetscErrorCode  TaoGetGradientNorm(Tao tao, Mat *M)
    2843: {
    2846:   *M = tao->gradient_norm;
    2847:   return(0);
    2848: }

    2850: /*@C
    2851:    TaoGradientNorm - Compute the norm with respect to the inner product the user has set.

    2853:    Collective on tao

    2855:    Input Parameters:
    2856: +  tao      - the Tao context
    2857: .  gradient - the gradient to be computed
    2858: -  norm     - the norm type

    2860:    Output Parameter:
    2861: .  gnorm    - the gradient norm

    2863:    Level: developer

    2865: .seealso: TaoSetGradientNorm(), TaoGetGradientNorm()
    2866: @*/
    2867: PetscErrorCode  TaoGradientNorm(Tao tao, Vec gradient, NormType type, PetscReal *gnorm)
    2868: {

    2876:   if (tao->gradient_norm) {
    2877:     PetscScalar gnorms;

    2879:     if (type != NORM_2) SETERRQ(PetscObjectComm((PetscObject)gradient), PETSC_ERR_ARG_WRONG, "Norm type must be NORM_2 if an inner product for the gradient norm is set.");
    2880:     MatMult(tao->gradient_norm, gradient, tao->gradient_norm_tmp);
    2881:     VecDot(gradient, tao->gradient_norm_tmp, &gnorms);
    2882:     *gnorm = PetscRealPart(PetscSqrtScalar(gnorms));
    2883:   } else {
    2884:     VecNorm(gradient, type, gnorm);
    2885:   }
    2886:   return(0);
    2887: }

    2889: /*@C
    2890:    TaoMonitorDrawCtxCreate - Creates the monitor context for TaoMonitorDrawCtx

    2892:    Collective on Tao

    2894:    Output Patameter:
    2895: .    ctx - the monitor context

    2897:    Options Database:
    2898: .   -tao_draw_solution_initial - show initial guess as well as current solution

    2900:    Level: intermediate

    2902: .seealso: TaoMonitorSet(), TaoMonitorDefault(), VecView(), TaoMonitorDrawCtx()
    2903: @*/
    2904: PetscErrorCode  TaoMonitorDrawCtxCreate(MPI_Comm comm,const char host[],const char label[],int x,int y,int m,int n,PetscInt howoften,TaoMonitorDrawCtx *ctx)
    2905: {
    2906:   PetscErrorCode   ierr;

    2909:   PetscNew(ctx);
    2910:   PetscViewerDrawOpen(comm,host,label,x,y,m,n,&(*ctx)->viewer);
    2911:   PetscViewerSetFromOptions((*ctx)->viewer);
    2912:   (*ctx)->howoften = howoften;
    2913:   return(0);
    2914: }

    2916: /*@C
    2917:    TaoMonitorDrawCtxDestroy - Destroys the monitor context for TaoMonitorDrawSolution()

    2919:    Collective on Tao

    2921:    Input Parameters:
    2922: .    ctx - the monitor context

    2924:    Level: intermediate

    2926: .seealso: TaoMonitorSet(), TaoMonitorDefault(), VecView(), TaoMonitorDrawSolution()
    2927: @*/
    2928: PetscErrorCode  TaoMonitorDrawCtxDestroy(TaoMonitorDrawCtx *ictx)
    2929: {

    2933:   PetscViewerDestroy(&(*ictx)->viewer);
    2934:   PetscFree(*ictx);
    2935:   return(0);
    2936: }