Actual source code: taosolver.c
petsc-3.13.6 2020-09-29
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      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_",0};

     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=0;
     70:   tao->ops->computeobjectiveandgradient=0;
     71:   tao->ops->computegradient=0;
     72:   tao->ops->computehessian=0;
     73:   tao->ops->computeresidual=0;
     74:   tao->ops->computeresidualjacobian=0;
     75:   tao->ops->computeconstraints=0;
     76:   tao->ops->computejacobian=0;
     77:   tao->ops->computejacobianequality=0;
     78:   tao->ops->computejacobianinequality=0;
     79:   tao->ops->computeequalityconstraints=0;
     80:   tao->ops->computeinequalityconstraints=0;
     81:   tao->ops->convergencetest=TaoDefaultConvergenceTest;
     82:   tao->ops->convergencedestroy=0;
     83:   tao->ops->computedual=0;
     84:   tao->ops->setup=0;
     85:   tao->ops->solve=0;
     86:   tao->ops->view=0;
     87:   tao->ops->setfromoptions=0;
     88:   tao->ops->destroy=0;

     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;

    162:   tao->header_printed = PETSC_FALSE;

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

    180: /*@
    181:   TaoSolve - Solves an optimization problem min F(x) s.t. l <= x <= u

    183:   Collective on Tao

    185:   Input Parameters:
    186: . tao - the Tao context

    188:   Notes:
    189:   The user must set up the Tao with calls to TaoSetInitialVector(),
    190:   TaoSetObjectiveRoutine(),
    191:   TaoSetGradientRoutine(), and (if using 2nd order method) TaoSetHessianRoutine().

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

    196:   Level: beginner

    198: .seealso: TaoCreate(), TaoSetObjectiveRoutine(), TaoSetGradientRoutine(), TaoSetHessianRoutine(), TaoGetConvergedReason()
    199:  @*/
    200: PetscErrorCode TaoSolve(Tao tao)
    201: {
    202:   PetscErrorCode   ierr;
    203:   static PetscBool set = PETSC_FALSE;

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

    221:   PetscLogEventBegin(TAO_Solve,tao,0,0,0);
    222:   if (tao->ops->solve){ (*tao->ops->solve)(tao); }
    223:   PetscLogEventEnd(TAO_Solve,tao,0,0,0);

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

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

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

    240: /*@
    241:   TaoSetUp - Sets up the internal data structures for the later use
    242:   of a Tao solver

    244:   Collective on tao

    246:   Input Parameters:
    247: . tao - the TAO context

    249:   Notes:
    250:   The user will not need to explicitly call TaoSetUp(), as it will
    251:   automatically be called in TaoSolve().  However, if the user
    252:   desires to call it explicitly, it should come after TaoCreate()
    253:   and any TaoSetSomething() routines, but before TaoSolve().

    255:   Level: advanced

    257: .seealso: TaoCreate(), TaoSolve()
    258: @*/
    259: PetscErrorCode TaoSetUp(Tao tao)
    260: {

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

    267:   if (!tao->solution) SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_ARG_WRONGSTATE,"Must call TaoSetInitialVector");
    268:   if (tao->ops->setup) {
    269:     (*tao->ops->setup)(tao);
    270:   }
    271:   tao->setupcalled = PETSC_TRUE;
    272:   return(0);
    273: }

    275: /*@
    276:   TaoDestroy - Destroys the TAO context that was created with
    277:   TaoCreate()

    279:   Collective on Tao

    281:   Input Parameter:
    282: . tao - the Tao context

    284:   Level: beginner

    286: .seealso: TaoCreate(), TaoSolve()
    287: @*/
    288: PetscErrorCode TaoDestroy(Tao *tao)
    289: {

    293:   if (!*tao) return(0);
    295:   if (--((PetscObject)*tao)->refct > 0) {*tao=0;return(0);}

    297:   if ((*tao)->ops->destroy) {
    298:     (*((*tao))->ops->destroy)(*tao);
    299:   }
    300:   KSPDestroy(&(*tao)->ksp);
    301:   TaoLineSearchDestroy(&(*tao)->linesearch);

    303:   if ((*tao)->ops->convergencedestroy) {
    304:     (*(*tao)->ops->convergencedestroy)((*tao)->cnvP);
    305:     if ((*tao)->jacobian_state_inv) {
    306:       MatDestroy(&(*tao)->jacobian_state_inv);
    307:     }
    308:   }
    309:   VecDestroy(&(*tao)->solution);
    310:   VecDestroy(&(*tao)->gradient);
    311:   VecDestroy(&(*tao)->ls_res);

    313:   if ((*tao)->gradient_norm) {
    314:     PetscObjectDereference((PetscObject)(*tao)->gradient_norm);
    315:     VecDestroy(&(*tao)->gradient_norm_tmp);
    316:   }

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

    357: /*@
    358:   TaoSetFromOptions - Sets various Tao parameters from user
    359:   options.

    361:   Collective on Tao

    363:   Input Paremeter:
    364: . tao - the Tao solver context

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

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

    397:   Level: beginner
    398: @*/
    399: PetscErrorCode TaoSetFromOptions(Tao tao)
    400: {
    402:   TaoType        default_type = TAOLMVM;
    403:   char           type[256], monfilename[PETSC_MAX_PATH_LEN];
    404:   PetscViewer    monviewer;
    405:   PetscBool      flg;
    406:   MPI_Comm       comm;

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

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

    415:   PetscObjectOptionsBegin((PetscObject)tao);
    416:   {
    417:     TaoRegisterAll();
    418:     if (((PetscObject)tao)->type_name) {
    419:       default_type = ((PetscObject)tao)->type_name;
    420:     }
    421:     /* Check for type from options */
    422:     PetscOptionsFList("-tao_type","Tao Solver type","TaoSetType",TaoList,default_type,type,256,&flg);
    423:     if (flg) {
    424:       TaoSetType(tao,type);
    425:     } else if (!((PetscObject)tao)->type_name) {
    426:       TaoSetType(tao,default_type);
    427:     }

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

    455:     PetscOptionsBool("-tao_converged_reason","Print reason for TAO converged","TaoSolve",tao->printreason,&tao->printreason,NULL);
    456:     PetscOptionsString("-tao_view_gradient","view gradient vector after each evaluation","TaoSetMonitor","stdout",monfilename,PETSC_MAX_PATH_LEN,&flg);
    457:     if (flg) {
    458:       PetscViewerASCIIOpen(comm,monfilename,&monviewer);
    459:       TaoSetMonitor(tao,TaoGradientMonitor,monviewer,(PetscErrorCode (*)(void**))PetscViewerDestroy);
    460:     }

    462:     PetscOptionsString("-tao_view_stepdirection","view step direction vector after each iteration","TaoSetMonitor","stdout",monfilename,PETSC_MAX_PATH_LEN,&flg);
    463:     if (flg) {
    464:       PetscViewerASCIIOpen(comm,monfilename,&monviewer);
    465:       TaoSetMonitor(tao,TaoStepDirectionMonitor,monviewer,(PetscErrorCode (*)(void**))PetscViewerDestroy);
    466:     }

    468:     PetscOptionsString("-tao_view_residual","view least-squares residual vector after each evaluation","TaoSetMonitor","stdout",monfilename,PETSC_MAX_PATH_LEN,&flg);
    469:     if (flg) {
    470:       PetscViewerASCIIOpen(comm,monfilename,&monviewer);
    471:       TaoSetMonitor(tao,TaoResidualMonitor,monviewer,(PetscErrorCode (*)(void**))PetscViewerDestroy);
    472:     }

    474:     PetscOptionsString("-tao_monitor","Use the default convergence monitor","TaoSetMonitor","stdout",monfilename,PETSC_MAX_PATH_LEN,&flg);
    475:     if (flg) {
    476:       PetscViewerASCIIOpen(comm,monfilename,&monviewer);
    477:       TaoSetMonitor(tao,TaoMonitorDefault,monviewer,(PetscErrorCode (*)(void**))PetscViewerDestroy);
    478:     }

    480:     PetscOptionsString("-tao_gmonitor","Use the convergence monitor with extra globalization info","TaoSetMonitor","stdout",monfilename,PETSC_MAX_PATH_LEN,&flg);
    481:     if (flg) {
    482:       PetscViewerASCIIOpen(comm,monfilename,&monviewer);
    483:       TaoSetMonitor(tao,TaoDefaultGMonitor,monviewer,(PetscErrorCode (*)(void**))PetscViewerDestroy);
    484:     }

    486:     PetscOptionsString("-tao_smonitor","Use the short convergence monitor","TaoSetMonitor","stdout",monfilename,PETSC_MAX_PATH_LEN,&flg);
    487:     if (flg) {
    488:       PetscViewerASCIIOpen(comm,monfilename,&monviewer);
    489:       TaoSetMonitor(tao,TaoDefaultSMonitor,monviewer,(PetscErrorCode (*)(void**))PetscViewerDestroy);
    490:     }

    492:     PetscOptionsString("-tao_cmonitor","Use the default convergence monitor with constraint norm","TaoSetMonitor","stdout",monfilename,PETSC_MAX_PATH_LEN,&flg);
    493:     if (flg) {
    494:       PetscViewerASCIIOpen(comm,monfilename,&monviewer);
    495:       TaoSetMonitor(tao,TaoDefaultCMonitor,monviewer,(PetscErrorCode (*)(void**))PetscViewerDestroy);
    496:     }

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

    503:     flg = PETSC_FALSE;
    504:     PetscOptionsBool("-tao_draw_solution","Plot solution vector at each iteration","TaoSetMonitor",flg,&flg,NULL);
    505:     if (flg) {
    506:       TaoMonitorDrawCtx drawctx;
    507:       PetscInt          howoften = 1;
    508:       TaoMonitorDrawCtxCreate(PetscObjectComm((PetscObject)tao),0,0,PETSC_DECIDE,PETSC_DECIDE,300,300,howoften,&drawctx);
    509:       TaoSetMonitor(tao,TaoDrawSolutionMonitor,drawctx,(PetscErrorCode (*)(void**))TaoMonitorDrawCtxDestroy);
    510:     }

    512:     flg = PETSC_FALSE;
    513:     PetscOptionsBool("-tao_draw_step","plots step direction at each iteration","TaoSetMonitor",flg,&flg,NULL);
    514:     if (flg) {
    515:       TaoSetMonitor(tao,TaoDrawStepMonitor,NULL,NULL);
    516:     }

    518:     flg = PETSC_FALSE;
    519:     PetscOptionsBool("-tao_draw_gradient","plots gradient at each iteration","TaoSetMonitor",flg,&flg,NULL);
    520:     if (flg) {
    521:       TaoMonitorDrawCtx drawctx;
    522:       PetscInt          howoften = 1;
    523:       TaoMonitorDrawCtxCreate(PetscObjectComm((PetscObject)tao),0,0,PETSC_DECIDE,PETSC_DECIDE,300,300,howoften,&drawctx);
    524:       TaoSetMonitor(tao,TaoDrawGradientMonitor,drawctx,(PetscErrorCode (*)(void**))TaoMonitorDrawCtxDestroy);
    525:     }
    526:     flg = PETSC_FALSE;
    527:     PetscOptionsBool("-tao_fd_gradient","compute gradient using finite differences","TaoDefaultComputeGradient",flg,&flg,NULL);
    528:     if (flg) {
    529:       TaoSetGradientRoutine(tao,TaoDefaultComputeGradient,NULL);
    530:     }
    531:     flg = PETSC_FALSE;
    532:     PetscOptionsBool("-tao_fd_hessian","compute hessian using finite differences","TaoDefaultComputeHessian",flg,&flg,NULL);
    533:     if (flg) {
    534:       Mat H;

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

    546:       MatCreate(PetscObjectComm((PetscObject)tao),&H);
    547:       TaoSetHessianRoutine(tao,H,H,TaoDefaultComputeHessianMFFD,NULL);
    548:       MatDestroy(&H);
    549:     }
    550:     PetscOptionsEnum("-tao_subset_type","subset type","",TaoSubSetTypes,(PetscEnum)tao->subset_type,(PetscEnum*)&tao->subset_type,NULL);

    552:     if (tao->ops->setfromoptions) {
    553:       (*tao->ops->setfromoptions)(PetscOptionsObject,tao);
    554:     }
    555:   }
    556:   PetscOptionsEnd();
    557:   return(0);
    558: }

    560: /*@C
    561:    TaoViewFromOptions - View from Options

    563:    Collective on Tao

    565:    Input Parameters:
    566: +  A - the  Tao context
    567: .  obj - Optional object
    568: -  name - command line option

    570:    Level: intermediate
    571: .seealso:  Tao, TaoView, PetscObjectViewFromOptions(), TaoCreate()
    572: @*/
    573: PetscErrorCode  TaoViewFromOptions(Tao A,PetscObject obj,const char name[])
    574: {

    579:   PetscObjectViewFromOptions((PetscObject)A,obj,name);
    580:   return(0);
    581: }

    583: /*@C
    584:   TaoView - Prints information about the Tao

    586:   Collective on Tao

    588:   InputParameters:
    589: + tao - the Tao context
    590: - viewer - visualization context

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

    595:   Notes:
    596:   The available visualization contexts include
    597: +     PETSC_VIEWER_STDOUT_SELF - standard output (default)
    598: -     PETSC_VIEWER_STDOUT_WORLD - synchronized standard
    599:          output where only the first processor opens
    600:          the file.  All other processors send their
    601:          data to the first processor to print.

    603:   Level: beginner

    605: .seealso: PetscViewerASCIIOpen()
    606: @*/
    607: PetscErrorCode TaoView(Tao tao, PetscViewer viewer)
    608: {
    609:   PetscErrorCode      ierr;
    610:   PetscBool           isascii,isstring;
    611:   TaoType             type;

    615:   if (!viewer) {
    616:     PetscViewerASCIIGetStdout(((PetscObject)tao)->comm,&viewer);
    617:   }

    621:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    622:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);
    623:   if (isascii) {
    624:     PetscObjectPrintClassNamePrefixType((PetscObject)tao,viewer);

    626:     if (tao->ops->view) {
    627:       PetscViewerASCIIPushTab(viewer);
    628:       (*tao->ops->view)(tao,viewer);
    629:       PetscViewerASCIIPopTab(viewer);
    630:     }
    631:     if (tao->linesearch) {
    632:       PetscViewerASCIIPushTab(viewer);
    633:       TaoLineSearchView(tao->linesearch,viewer);
    634:       PetscViewerASCIIPopTab(viewer);
    635:     }
    636:     if (tao->ksp) {
    637:       PetscViewerASCIIPushTab(viewer);
    638:       KSPView(tao->ksp,viewer);
    639:       PetscViewerASCIIPrintf(viewer,"total KSP iterations: %D\n",tao->ksp_tot_its);
    640:       PetscViewerASCIIPopTab(viewer);
    641:     }

    643:     PetscViewerASCIIPushTab(viewer);

    645:     if (tao->XL || tao->XU) {
    646:       PetscViewerASCIIPrintf(viewer,"Active Set subset type: %s\n",TaoSubSetTypes[tao->subset_type]);
    647:     }

    649:     PetscViewerASCIIPrintf(viewer,"convergence tolerances: gatol=%g,",(double)tao->gatol);
    650:     PetscViewerASCIIPrintf(viewer," steptol=%g,",(double)tao->steptol);
    651:     PetscViewerASCIIPrintf(viewer," gttol=%g\n",(double)tao->gttol);
    652:     PetscViewerASCIIPrintf(viewer,"Residual in Function/Gradient:=%g\n",(double)tao->residual);

    654:     if (tao->constrained){
    655:       ierr=PetscViewerASCIIPrintf(viewer,"convergence tolerances:");
    656:       ierr=PetscViewerASCIIPrintf(viewer," catol=%g,",(double)tao->catol);
    657:       ierr=PetscViewerASCIIPrintf(viewer," crtol=%g\n",(double)tao->crtol);
    658:       PetscViewerASCIIPrintf(viewer,"Residual in Constraints:=%g\n",(double)tao->cnorm);
    659:     }

    661:     if (tao->trust < tao->steptol){
    662:       ierr=PetscViewerASCIIPrintf(viewer,"convergence tolerances: steptol=%g\n",(double)tao->steptol);
    663:       ierr=PetscViewerASCIIPrintf(viewer,"Final trust region radius:=%g\n",(double)tao->trust);
    664:     }

    666:     if (tao->fmin>-1.e25){
    667:       ierr=PetscViewerASCIIPrintf(viewer,"convergence tolerances: function minimum=%g\n",(double)tao->fmin);
    668:     }
    669:     PetscViewerASCIIPrintf(viewer,"Objective value=%g\n",(double)tao->fc);

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

    674:     if (tao->nfuncs>0){
    675:       PetscViewerASCIIPrintf(viewer,"total number of function evaluations=%D,",tao->nfuncs);
    676:       PetscViewerASCIIPrintf(viewer,"                max: %D\n",tao->max_funcs);
    677:     }
    678:     if (tao->ngrads>0){
    679:       PetscViewerASCIIPrintf(viewer,"total number of gradient evaluations=%D,",tao->ngrads);
    680:       PetscViewerASCIIPrintf(viewer,"                max: %D\n",tao->max_funcs);
    681:     }
    682:     if (tao->nfuncgrads>0){
    683:       PetscViewerASCIIPrintf(viewer,"total number of function/gradient evaluations=%D,",tao->nfuncgrads);
    684:       PetscViewerASCIIPrintf(viewer,"    (max: %D)\n",tao->max_funcs);
    685:     }
    686:     if (tao->nhess>0){
    687:       PetscViewerASCIIPrintf(viewer,"total number of Hessian evaluations=%D\n",tao->nhess);
    688:     }
    689:     /*  if (tao->linear_its>0){
    690:      PetscViewerASCIIPrintf(viewer,"  total Krylov method iterations=%D\n",tao->linear_its);
    691:      }*/
    692:     if (tao->nconstraints>0){
    693:       PetscViewerASCIIPrintf(viewer,"total number of constraint function evaluations=%D\n",tao->nconstraints);
    694:     }
    695:     if (tao->njac>0){
    696:       PetscViewerASCIIPrintf(viewer,"total number of Jacobian evaluations=%D\n",tao->njac);
    697:     }

    699:     if (tao->reason>0){
    700:       PetscViewerASCIIPrintf(viewer,    "Solution converged: ");
    701:       switch (tao->reason) {
    702:       case TAO_CONVERGED_GATOL:
    703:         PetscViewerASCIIPrintf(viewer," ||g(X)|| <= gatol\n");
    704:         break;
    705:       case TAO_CONVERGED_GRTOL:
    706:         PetscViewerASCIIPrintf(viewer," ||g(X)||/|f(X)| <= grtol\n");
    707:         break;
    708:       case TAO_CONVERGED_GTTOL:
    709:         PetscViewerASCIIPrintf(viewer," ||g(X)||/||g(X0)|| <= gttol\n");
    710:         break;
    711:       case TAO_CONVERGED_STEPTOL:
    712:         PetscViewerASCIIPrintf(viewer," Steptol -- step size small\n");
    713:         break;
    714:       case TAO_CONVERGED_MINF:
    715:         PetscViewerASCIIPrintf(viewer," Minf --  f < fmin\n");
    716:         break;
    717:       case TAO_CONVERGED_USER:
    718:         PetscViewerASCIIPrintf(viewer," User Terminated\n");
    719:         break;
    720:       default:
    721:         PetscViewerASCIIPrintf(viewer,"\n");
    722:         break;
    723:       }

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

    759: /*@
    760:   TaoSetTolerances - Sets parameters used in TAO convergence tests

    762:   Logically collective on Tao

    764:   Input Parameters:
    765: + tao - the Tao context
    766: . gatol - stop if norm of gradient is less than this
    767: . grtol - stop if relative norm of gradient is less than this
    768: - gttol - stop if norm of gradient is reduced by this factor

    770:   Options Database Keys:
    771: + -tao_gatol <gatol> - Sets gatol
    772: . -tao_grtol <grtol> - Sets grtol
    773: - -tao_gttol <gttol> - Sets gttol

    775:   Stopping Criteria:
    776: $ ||g(X)||                            <= gatol
    777: $ ||g(X)|| / |f(X)|                   <= grtol
    778: $ ||g(X)|| / ||g(X0)||                <= gttol

    780:   Notes:
    781:   Use PETSC_DEFAULT to leave one or more tolerances unchanged.

    783:   Level: beginner

    785: .seealso: TaoGetTolerances()

    787: @*/
    788: PetscErrorCode TaoSetTolerances(Tao tao, PetscReal gatol, PetscReal grtol, PetscReal gttol)
    789: {

    795:   if (gatol != PETSC_DEFAULT) {
    796:     if (gatol<0) {
    797:       PetscInfo(tao,"Tried to set negative gatol -- ignored.\n");
    798:     } else {
    799:       tao->gatol = PetscMax(0,gatol);
    800:       tao->gatol_changed=PETSC_TRUE;
    801:     }
    802:   }

    804:   if (grtol != PETSC_DEFAULT) {
    805:     if (grtol<0) {
    806:       PetscInfo(tao,"Tried to set negative grtol -- ignored.\n");
    807:     } else {
    808:       tao->grtol = PetscMax(0,grtol);
    809:       tao->grtol_changed=PETSC_TRUE;
    810:     }
    811:   }

    813:   if (gttol != PETSC_DEFAULT) {
    814:     if (gttol<0) {
    815:       PetscInfo(tao,"Tried to set negative gttol -- ignored.\n");
    816:     } else {
    817:       tao->gttol = PetscMax(0,gttol);
    818:       tao->gttol_changed=PETSC_TRUE;
    819:     }
    820:   }
    821:   return(0);
    822: }

    824: /*@
    825:   TaoSetConstraintTolerances - Sets constraint tolerance parameters used in TAO  convergence tests

    827:   Logically collective on Tao

    829:   Input Parameters:
    830: + tao - the Tao context
    831: . catol - absolute constraint tolerance, constraint norm must be less than catol for used for gatol convergence criteria
    832: - crtol - relative contraint tolerance, constraint norm must be less than crtol for used for gatol, gttol convergence criteria

    834:   Options Database Keys:
    835: + -tao_catol <catol> - Sets catol
    836: - -tao_crtol <crtol> - Sets crtol

    838:   Notes:
    839:   Use PETSC_DEFAULT to leave any tolerance unchanged.

    841:   Level: intermediate

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

    845: @*/
    846: PetscErrorCode TaoSetConstraintTolerances(Tao tao, PetscReal catol, PetscReal crtol)
    847: {

    853:   if (catol != PETSC_DEFAULT) {
    854:     if (catol<0) {
    855:       PetscInfo(tao,"Tried to set negative catol -- ignored.\n");
    856:     } else {
    857:       tao->catol = PetscMax(0,catol);
    858:       tao->catol_changed=PETSC_TRUE;
    859:     }
    860:   }

    862:   if (crtol != PETSC_DEFAULT) {
    863:     if (crtol<0) {
    864:       PetscInfo(tao,"Tried to set negative crtol -- ignored.\n");
    865:     } else {
    866:       tao->crtol = PetscMax(0,crtol);
    867:       tao->crtol_changed=PETSC_TRUE;
    868:     }
    869:   }
    870:   return(0);
    871: }

    873: /*@
    874:   TaoGetConstraintTolerances - Gets constraint tolerance parameters used in TAO  convergence tests

    876:   Not ollective

    878:   Input Parameter:
    879: . tao - the Tao context

    881:   Output Parameter:
    882: + catol - absolute constraint tolerance, constraint norm must be less than catol for used for gatol convergence criteria
    883: - crtol - relative contraint tolerance, constraint norm must be less than crtol for used for gatol, gttol convergence criteria

    885:   Level: intermediate

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

    889: @*/
    890: PetscErrorCode TaoGetConstraintTolerances(Tao tao, PetscReal *catol, PetscReal *crtol)
    891: {
    894:   if (catol) *catol = tao->catol;
    895:   if (crtol) *crtol = tao->crtol;
    896:   return(0);
    897: }

    899: /*@
    900:    TaoSetFunctionLowerBound - Sets a bound on the solution objective value.
    901:    When an approximate solution with an objective value below this number
    902:    has been found, the solver will terminate.

    904:    Logically Collective on Tao

    906:    Input Parameters:
    907: +  tao - the Tao solver context
    908: -  fmin - the tolerance

    910:    Options Database Keys:
    911: .    -tao_fmin <fmin> - sets the minimum function value

    913:    Level: intermediate

    915: .seealso: TaoSetTolerances()
    916: @*/
    917: PetscErrorCode TaoSetFunctionLowerBound(Tao tao,PetscReal fmin)
    918: {
    921:   tao->fmin = fmin;
    922:   tao->fmin_changed=PETSC_TRUE;
    923:   return(0);
    924: }

    926: /*@
    927:    TaoGetFunctionLowerBound - Gets the bound on the solution objective value.
    928:    When an approximate solution with an objective value below this number
    929:    has been found, the solver will terminate.

    931:    Not collective on Tao

    933:    Input Parameters:
    934: .  tao - the Tao solver context

    936:    OutputParameters:
    937: .  fmin - the minimum function value

    939:    Level: intermediate

    941: .seealso: TaoSetFunctionLowerBound()
    942: @*/
    943: PetscErrorCode TaoGetFunctionLowerBound(Tao tao,PetscReal *fmin)
    944: {
    947:   *fmin = tao->fmin;
    948:   return(0);
    949: }

    951: /*@
    952:    TaoSetMaximumFunctionEvaluations - Sets a maximum number of
    953:    function evaluations.

    955:    Logically Collective on Tao

    957:    Input Parameters:
    958: +  tao - the Tao solver context
    959: -  nfcn - the maximum number of function evaluations (>=0)

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

    964:    Level: intermediate

    966: .seealso: TaoSetTolerances(), TaoSetMaximumIterations()
    967: @*/

    969: PetscErrorCode TaoSetMaximumFunctionEvaluations(Tao tao,PetscInt nfcn)
    970: {
    973:   tao->max_funcs = PetscMax(0,nfcn);
    974:   tao->max_funcs_changed=PETSC_TRUE;
    975:   return(0);
    976: }

    978: /*@
    979:    TaoGetMaximumFunctionEvaluations - Sets a maximum number of
    980:    function evaluations.

    982:    Not Collective

    984:    Input Parameters:
    985: .  tao - the Tao solver context

    987:    Output Parameters:
    988: .  nfcn - the maximum number of function evaluations

    990:    Level: intermediate

    992: .seealso: TaoSetMaximumFunctionEvaluations(), TaoGetMaximumIterations()
    993: @*/

    995: PetscErrorCode TaoGetMaximumFunctionEvaluations(Tao tao,PetscInt *nfcn)
    996: {
    999:   *nfcn = tao->max_funcs;
    1000:   return(0);
    1001: }

    1003: /*@
    1004:    TaoGetCurrentFunctionEvaluations - Get current number of
    1005:    function evaluations.

    1007:    Not Collective

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

    1012:    Output Parameters:
    1013: .  nfuncs - the current number of function evaluations

    1015:    Level: intermediate

    1017: .seealso: TaoSetMaximumFunctionEvaluations(), TaoGetMaximumFunctionEvaluations(), TaoGetMaximumIterations()
    1018: @*/

    1020: PetscErrorCode TaoGetCurrentFunctionEvaluations(Tao tao,PetscInt *nfuncs)
    1021: {
    1024:   *nfuncs=PetscMax(tao->nfuncs,tao->nfuncgrads);
    1025:   return(0);
    1026: }

    1028: /*@
    1029:    TaoSetMaximumIterations - Sets a maximum number of iterates.

    1031:    Logically Collective on Tao

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

    1037:    Options Database Keys:
    1038: .    -tao_max_it <its> - sets the maximum number of iterations

    1040:    Level: intermediate

    1042: .seealso: TaoSetTolerances(), TaoSetMaximumFunctionEvaluations()
    1043: @*/
    1044: PetscErrorCode TaoSetMaximumIterations(Tao tao,PetscInt maxits)
    1045: {
    1048:   tao->max_it = PetscMax(0,maxits);
    1049:   tao->max_it_changed=PETSC_TRUE;
    1050:   return(0);
    1051: }

    1053: /*@
    1054:    TaoGetMaximumIterations - Sets a maximum number of iterates.

    1056:    Not Collective

    1058:    Input Parameters:
    1059: .  tao - the Tao solver context

    1061:    Output Parameters:
    1062: .  maxits - the maximum number of iterates

    1064:    Level: intermediate

    1066: .seealso: TaoSetMaximumIterations(), TaoGetMaximumFunctionEvaluations()
    1067: @*/
    1068: PetscErrorCode TaoGetMaximumIterations(Tao tao,PetscInt *maxits)
    1069: {
    1072:   *maxits = tao->max_it;
    1073:   return(0);
    1074: }

    1076: /*@
    1077:    TaoSetInitialTrustRegionRadius - Sets the initial trust region radius.

    1079:    Logically collective on Tao

    1081:    Input Parameter:
    1082: +  tao - a TAO optimization solver
    1083: -  radius - the trust region radius

    1085:    Level: intermediate

    1087:    Options Database Key:
    1088: .  -tao_trust0 <t0> - sets initial trust region radius

    1090: .seealso: TaoGetTrustRegionRadius(), TaoSetTrustRegionTolerance()
    1091: @*/
    1092: PetscErrorCode TaoSetInitialTrustRegionRadius(Tao tao, PetscReal radius)
    1093: {
    1096:   tao->trust0 = PetscMax(0.0,radius);
    1097:   tao->trust0_changed=PETSC_TRUE;
    1098:   return(0);
    1099: }

    1101: /*@
    1102:    TaoGetInitialTrustRegionRadius - Sets the initial trust region radius.

    1104:    Not Collective

    1106:    Input Parameter:
    1107: .  tao - a TAO optimization solver

    1109:    Output Parameter:
    1110: .  radius - the trust region radius

    1112:    Level: intermediate

    1114: .seealso: TaoSetInitialTrustRegionRadius(), TaoGetCurrentTrustRegionRadius()
    1115: @*/
    1116: PetscErrorCode TaoGetInitialTrustRegionRadius(Tao tao, PetscReal *radius)
    1117: {
    1120:   *radius = tao->trust0;
    1121:   return(0);
    1122: }

    1124: /*@
    1125:    TaoGetCurrentTrustRegionRadius - Gets the current trust region radius.

    1127:    Not Collective

    1129:    Input Parameter:
    1130: .  tao - a TAO optimization solver

    1132:    Output Parameter:
    1133: .  radius - the trust region radius

    1135:    Level: intermediate

    1137: .seealso: TaoSetInitialTrustRegionRadius(), TaoGetInitialTrustRegionRadius()
    1138: @*/
    1139: PetscErrorCode TaoGetCurrentTrustRegionRadius(Tao tao, PetscReal *radius)
    1140: {
    1143:   *radius = tao->trust;
    1144:   return(0);
    1145: }

    1147: /*@
    1148:   TaoGetTolerances - gets the current values of tolerances

    1150:   Not Collective

    1152:   Input Parameters:
    1153: . tao - the Tao context

    1155:   Output Parameters:
    1156: + gatol - stop if norm of gradient is less than this
    1157: . grtol - stop if relative norm of gradient is less than this
    1158: - gttol - stop if norm of gradient is reduced by a this factor

    1160:   Note: NULL can be used as an argument if not all tolerances values are needed

    1162: .seealso TaoSetTolerances()

    1164:   Level: intermediate
    1165: @*/
    1166: PetscErrorCode TaoGetTolerances(Tao tao, PetscReal *gatol, PetscReal *grtol, PetscReal *gttol)
    1167: {
    1170:   if (gatol) *gatol=tao->gatol;
    1171:   if (grtol) *grtol=tao->grtol;
    1172:   if (gttol) *gttol=tao->gttol;
    1173:   return(0);
    1174: }

    1176: /*@
    1177:   TaoGetKSP - Gets the linear solver used by the optimization solver.
    1178:   Application writers should use TaoGetKSP if they need direct access
    1179:   to the PETSc KSP object.

    1181:   Not Collective

    1183:    Input Parameters:
    1184: .  tao - the TAO solver

    1186:    Output Parameters:
    1187: .  ksp - the KSP linear solver used in the optimization solver

    1189:    Level: intermediate

    1191: @*/
    1192: PetscErrorCode TaoGetKSP(Tao tao, KSP *ksp)
    1193: {
    1195:   *ksp = tao->ksp;
    1196:   return(0);
    1197: }

    1199: /*@
    1200:    TaoGetLinearSolveIterations - Gets the total number of linear iterations
    1201:    used by the TAO solver

    1203:    Not Collective

    1205:    Input Parameter:
    1206: .  tao - TAO context

    1208:    Output Parameter:
    1209: .  lits - number of linear iterations

    1211:    Notes:
    1212:    This counter is reset to zero for each successive call to TaoSolve()

    1214:    Level: intermediate

    1216: .seealso:  TaoGetKSP()
    1217: @*/
    1218: PetscErrorCode  TaoGetLinearSolveIterations(Tao tao,PetscInt *lits)
    1219: {
    1223:   *lits = tao->ksp_tot_its;
    1224:   return(0);
    1225: }

    1227: /*@
    1228:   TaoGetLineSearch - Gets the line search used by the optimization solver.
    1229:   Application writers should use TaoGetLineSearch if they need direct access
    1230:   to the TaoLineSearch object.

    1232:   Not Collective

    1234:    Input Parameters:
    1235: .  tao - the TAO solver

    1237:    Output Parameters:
    1238: .  ls - the line search used in the optimization solver

    1240:    Level: intermediate

    1242: @*/
    1243: PetscErrorCode TaoGetLineSearch(Tao tao, TaoLineSearch *ls)
    1244: {
    1246:   *ls = tao->linesearch;
    1247:   return(0);
    1248: }

    1250: /*@
    1251:   TaoAddLineSearchCounts - Adds the number of function evaluations spent
    1252:   in the line search to the running total.

    1254:    Input Parameters:
    1255: +  tao - the TAO solver
    1256: -  ls - the line search used in the optimization solver

    1258:    Level: developer

    1260: .seealso: TaoLineSearchApply()
    1261: @*/
    1262: PetscErrorCode TaoAddLineSearchCounts(Tao tao)
    1263: {
    1265:   PetscBool      flg;
    1266:   PetscInt       nfeval,ngeval,nfgeval;

    1270:   if (tao->linesearch) {
    1271:     TaoLineSearchIsUsingTaoRoutines(tao->linesearch,&flg);
    1272:     if (!flg) {
    1273:       TaoLineSearchGetNumberFunctionEvaluations(tao->linesearch,&nfeval,&ngeval,&nfgeval);
    1274:       tao->nfuncs+=nfeval;
    1275:       tao->ngrads+=ngeval;
    1276:       tao->nfuncgrads+=nfgeval;
    1277:     }
    1278:   }
    1279:   return(0);
    1280: }

    1282: /*@
    1283:   TaoGetSolutionVector - Returns the vector with the current TAO solution

    1285:   Not Collective

    1287:   Input Parameter:
    1288: . tao - the Tao context

    1290:   Output Parameter:
    1291: . X - the current solution

    1293:   Level: intermediate

    1295:   Note:  The returned vector will be the same object that was passed into TaoSetInitialVector()
    1296: @*/
    1297: PetscErrorCode TaoGetSolutionVector(Tao tao, Vec *X)
    1298: {
    1301:   *X = tao->solution;
    1302:   return(0);
    1303: }

    1305: /*@
    1306:   TaoGetGradientVector - Returns the vector with the current TAO gradient

    1308:   Not Collective

    1310:   Input Parameter:
    1311: . tao - the Tao context

    1313:   Output Parameter:
    1314: . G - the current solution

    1316:   Level: intermediate
    1317: @*/
    1318: PetscErrorCode TaoGetGradientVector(Tao tao, Vec *G)
    1319: {
    1322:   *G = tao->gradient;
    1323:   return(0);
    1324: }

    1326: /*@
    1327:    TaoResetStatistics - Initialize the statistics used by TAO for all of the solvers.
    1328:    These statistics include the iteration number, residual norms, and convergence status.
    1329:    This routine gets called before solving each optimization problem.

    1331:    Collective on Tao

    1333:    Input Parameters:
    1334: .  solver - the Tao context

    1336:    Level: developer

    1338: .seealso: TaoCreate(), TaoSolve()
    1339: @*/
    1340: PetscErrorCode TaoResetStatistics(Tao tao)
    1341: {
    1344:   tao->niter        = 0;
    1345:   tao->nfuncs       = 0;
    1346:   tao->nfuncgrads   = 0;
    1347:   tao->ngrads       = 0;
    1348:   tao->nhess        = 0;
    1349:   tao->njac         = 0;
    1350:   tao->nconstraints = 0;
    1351:   tao->ksp_its      = 0;
    1352:   tao->ksp_tot_its  = 0;
    1353:   tao->reason       = TAO_CONTINUE_ITERATING;
    1354:   tao->residual     = 0.0;
    1355:   tao->cnorm        = 0.0;
    1356:   tao->step         = 0.0;
    1357:   tao->lsflag       = PETSC_FALSE;
    1358:   if (tao->hist_reset) tao->hist_len=0;
    1359:   return(0);
    1360: }

    1362: /*@C
    1363:   TaoSetUpdate - Sets the general-purpose update function called
    1364:   at the beginning of every iteration of the nonlinear solve. Specifically
    1365:   it is called at the top of every iteration, after the new solution and the gradient
    1366:   is determined, but before the Hessian is computed (if applicable).

    1368:   Logically Collective on Tao

    1370:   Input Parameters:
    1371: + tao - The tao solver context
    1372: - func - The function

    1374:   Calling sequence of func:
    1375: $ func (Tao tao, PetscInt step);

    1377: . step - The current step of the iteration

    1379:   Level: advanced

    1381: .seealso TaoSolve()
    1382: @*/
    1383: PetscErrorCode  TaoSetUpdate(Tao tao, PetscErrorCode (*func)(Tao, PetscInt,void*), void *ctx)
    1384: {
    1387:   tao->ops->update = func;
    1388:   tao->user_update = ctx;
    1389:   return(0);
    1390: }

    1392: /*@C
    1393:   TaoSetConvergenceTest - Sets the function that is to be used to test
    1394:   for convergence o fthe iterative minimization solution.  The new convergence
    1395:   testing routine will replace TAO's default convergence test.

    1397:   Logically Collective on Tao

    1399:   Input Parameters:
    1400: + tao - the Tao object
    1401: . conv - the routine to test for convergence
    1402: - ctx - [optional] context for private data for the convergence routine
    1403:         (may be NULL)

    1405:   Calling sequence of conv:
    1406: $   PetscErrorCode conv(Tao tao, void *ctx)

    1408: + tao - the Tao object
    1409: - ctx - [optional] convergence context

    1411:   Note: The new convergence testing routine should call TaoSetConvergedReason().

    1413:   Level: advanced

    1415: .seealso: TaoSetConvergedReason(), TaoGetSolutionStatus(), TaoGetTolerances(), TaoSetMonitor

    1417: @*/
    1418: PetscErrorCode TaoSetConvergenceTest(Tao tao, PetscErrorCode (*conv)(Tao,void*), void *ctx)
    1419: {
    1422:   (tao)->ops->convergencetest = conv;
    1423:   (tao)->cnvP = ctx;
    1424:   return(0);
    1425: }

    1427: /*@C
    1428:    TaoSetMonitor - Sets an ADDITIONAL function that is to be used at every
    1429:    iteration of the solver to display the iteration's
    1430:    progress.

    1432:    Logically Collective on Tao

    1434:    Input Parameters:
    1435: +  tao - the Tao solver context
    1436: .  mymonitor - monitoring routine
    1437: -  mctx - [optional] user-defined context for private data for the
    1438:           monitor routine (may be NULL)

    1440:    Calling sequence of mymonitor:
    1441: $     PetscErrorCode mymonitor(Tao tao,void *mctx)

    1443: +    tao - the Tao solver context
    1444: -    mctx - [optional] monitoring context

    1447:    Options Database Keys:
    1448: +    -tao_monitor        - sets TaoMonitorDefault()
    1449: .    -tao_smonitor       - sets short monitor
    1450: .    -tao_cmonitor       - same as smonitor plus constraint norm
    1451: .    -tao_view_solution   - view solution at each iteration
    1452: .    -tao_view_gradient   - view gradient at each iteration
    1453: .    -tao_view_ls_residual - view least-squares residual vector at each iteration
    1454: -    -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.

    1457:    Notes:
    1458:    Several different monitoring routines may be set by calling
    1459:    TaoSetMonitor() multiple times; all will be called in the
    1460:    order in which they were set.

    1462:    Fortran Notes:
    1463:     Only one monitor function may be set

    1465:    Level: intermediate

    1467: .seealso: TaoMonitorDefault(), TaoCancelMonitors(),  TaoSetDestroyRoutine()
    1468: @*/
    1469: PetscErrorCode TaoSetMonitor(Tao tao, PetscErrorCode (*func)(Tao, void*), void *ctx,PetscErrorCode (*dest)(void**))
    1470: {
    1472:   PetscInt       i;
    1473:   PetscBool      identical;

    1477:   if (tao->numbermonitors >= MAXTAOMONITORS) SETERRQ1(PetscObjectComm((PetscObject)tao),1,"Cannot attach another monitor -- max=",MAXTAOMONITORS);

    1479:   for (i=0; i<tao->numbermonitors;i++) {
    1480:     PetscMonitorCompare((PetscErrorCode (*)(void))func,ctx,dest,(PetscErrorCode (*)(void))tao->monitor[i],tao->monitorcontext[i],tao->monitordestroy[i],&identical);
    1481:     if (identical) return(0);
    1482:   }
    1483:   tao->monitor[tao->numbermonitors] = func;
    1484:   tao->monitorcontext[tao->numbermonitors] = (void*)ctx;
    1485:   tao->monitordestroy[tao->numbermonitors] = dest;
    1486:   ++tao->numbermonitors;
    1487:   return(0);
    1488: }

    1490: /*@
    1491:    TaoCancelMonitors - Clears all the monitor functions for a Tao object.

    1493:    Logically Collective on Tao

    1495:    Input Parameters:
    1496: .  tao - the Tao solver context

    1498:    Options Database:
    1499: .  -tao_cancelmonitors - cancels all monitors that have been hardwired
    1500:     into a code by calls to TaoSetMonitor(), but does not cancel those
    1501:     set via the options database

    1503:    Notes:
    1504:    There is no way to clear one specific monitor from a Tao object.

    1506:    Level: advanced

    1508: .seealso: TaoMonitorDefault(), TaoSetMonitor()
    1509: @*/
    1510: PetscErrorCode TaoCancelMonitors(Tao tao)
    1511: {
    1512:   PetscInt       i;

    1517:   for (i=0;i<tao->numbermonitors;i++) {
    1518:     if (tao->monitordestroy[i]) {
    1519:       (*tao->monitordestroy[i])(&tao->monitorcontext[i]);
    1520:     }
    1521:   }
    1522:   tao->numbermonitors=0;
    1523:   return(0);
    1524: }

    1526: /*@
    1527:    TaoMonitorDefault - Default routine for monitoring progress of the
    1528:    Tao solvers (default).  This monitor prints the function value and gradient
    1529:    norm at each iteration.  It can be turned on from the command line using the
    1530:    -tao_monitor option

    1532:    Collective on Tao

    1534:    Input Parameters:
    1535: +  tao - the Tao context
    1536: -  ctx - PetscViewer context or NULL

    1538:    Options Database Keys:
    1539: .  -tao_monitor

    1541:    Level: advanced

    1543: .seealso: TaoDefaultSMonitor(), TaoSetMonitor()
    1544: @*/
    1545: PetscErrorCode TaoMonitorDefault(Tao tao, void *ctx)
    1546: {
    1548:   PetscInt       its, tabs;
    1549:   PetscReal      fct,gnorm;
    1550:   PetscViewer    viewer = (PetscViewer)ctx;

    1554:   its=tao->niter;
    1555:   fct=tao->fc;
    1556:   gnorm=tao->residual;
    1557:   PetscViewerASCIIGetTab(viewer, &tabs);
    1558:   PetscViewerASCIISetTab(viewer, ((PetscObject)tao)->tablevel);
    1559:   if (its == 0 && ((PetscObject)tao)->prefix && !tao->header_printed) {
    1560:      PetscViewerASCIIPrintf(viewer,"  Iteration information for %s solve.\n",((PetscObject)tao)->prefix);
    1561:      tao->header_printed = PETSC_TRUE;
    1562:    }
    1563:   ierr=PetscViewerASCIIPrintf(viewer,"%3D TAO,",its);
    1564:   ierr=PetscViewerASCIIPrintf(viewer,"  Function value: %g,",(double)fct);
    1565:   if (gnorm >= PETSC_INFINITY) {
    1566:     ierr=PetscViewerASCIIPrintf(viewer,"  Residual: Inf \n");
    1567:   } else {
    1568:     ierr=PetscViewerASCIIPrintf(viewer,"  Residual: %g \n",(double)gnorm);
    1569:   }
    1570:   PetscViewerASCIISetTab(viewer, tabs);
    1571:   return(0);
    1572: }

    1574: /*@
    1575:    TaoDefaultGMonitor - Default routine for monitoring progress of the
    1576:    Tao solvers (default) with extra detail on the globalization method.
    1577:    This monitor prints the function value and gradient norm at each
    1578:    iteration, as well as the step size and trust radius. Note that the
    1579:    step size and trust radius may be the same for some algorithms.
    1580:    It can be turned on from the command line using the
    1581:    -tao_gmonitor option

    1583:    Collective on Tao

    1585:    Input Parameters:
    1586: +  tao - the Tao context
    1587: -  ctx - PetscViewer context or NULL

    1589:    Options Database Keys:
    1590: .  -tao_monitor

    1592:    Level: advanced

    1594: .seealso: TaoDefaultSMonitor(), TaoSetMonitor()
    1595: @*/
    1596: PetscErrorCode TaoDefaultGMonitor(Tao tao, void *ctx)
    1597: {
    1599:   PetscInt       its, tabs;
    1600:   PetscReal      fct,gnorm,stp,tr;
    1601:   PetscViewer    viewer = (PetscViewer)ctx;

    1605:   its=tao->niter;
    1606:   fct=tao->fc;
    1607:   gnorm=tao->residual;
    1608:   stp=tao->step;
    1609:   tr=tao->trust;
    1610:   PetscViewerASCIIGetTab(viewer, &tabs);
    1611:   PetscViewerASCIISetTab(viewer, ((PetscObject)tao)->tablevel);
    1612:   if (its == 0 && ((PetscObject)tao)->prefix && !tao->header_printed) {
    1613:      PetscViewerASCIIPrintf(viewer,"  Iteration information for %s solve.\n",((PetscObject)tao)->prefix);
    1614:      tao->header_printed = PETSC_TRUE;
    1615:    }
    1616:   ierr=PetscViewerASCIIPrintf(viewer,"%3D TAO,",its);
    1617:   ierr=PetscViewerASCIIPrintf(viewer,"  Function value: %g,",(double)fct);
    1618:   if (gnorm >= PETSC_INFINITY) {
    1619:     ierr=PetscViewerASCIIPrintf(viewer,"  Residual: Inf,");
    1620:   } else {
    1621:     ierr=PetscViewerASCIIPrintf(viewer,"  Residual: %g,",(double)gnorm);
    1622:   }
    1623:   PetscViewerASCIIPrintf(viewer,"  Step: %g,  Trust: %g\n",(double)stp,(double)tr);
    1624:   PetscViewerASCIISetTab(viewer, tabs);
    1625:   return(0);
    1626: }

    1628: /*@
    1629:    TaoDefaultSMonitor - Default routine for monitoring progress of the
    1630:    solver. Same as TaoMonitorDefault() except
    1631:    it prints fewer digits of the residual as the residual gets smaller.
    1632:    This is because the later digits are meaningless and are often
    1633:    different on different machines; by using this routine different
    1634:    machines will usually generate the same output. It can be turned on
    1635:    by using the -tao_smonitor option

    1637:    Collective on Tao

    1639:    Input Parameters:
    1640: +  tao - the Tao context
    1641: -  ctx - PetscViewer context of type ASCII

    1643:    Options Database Keys:
    1644: .  -tao_smonitor

    1646:    Level: advanced

    1648: .seealso: TaoMonitorDefault(), TaoSetMonitor()
    1649: @*/
    1650: PetscErrorCode TaoDefaultSMonitor(Tao tao, void *ctx)
    1651: {
    1653:   PetscInt       its, tabs;
    1654:   PetscReal      fct,gnorm;
    1655:   PetscViewer    viewer = (PetscViewer)ctx;

    1659:   its=tao->niter;
    1660:   fct=tao->fc;
    1661:   gnorm=tao->residual;
    1662:   PetscViewerASCIIGetTab(viewer, &tabs);
    1663:   PetscViewerASCIISetTab(viewer, ((PetscObject)tao)->tablevel);
    1664:   ierr=PetscViewerASCIIPrintf(viewer,"iter = %3D,",its);
    1665:   ierr=PetscViewerASCIIPrintf(viewer," Function value %g,",(double)fct);
    1666:   if (gnorm >= PETSC_INFINITY) {
    1667:     ierr=PetscViewerASCIIPrintf(viewer," Residual: Inf \n");
    1668:   } else if (gnorm > 1.e-6) {
    1669:     ierr=PetscViewerASCIIPrintf(viewer," Residual: %g \n",(double)gnorm);
    1670:   } else if (gnorm > 1.e-11) {
    1671:     ierr=PetscViewerASCIIPrintf(viewer," Residual: < 1.0e-6 \n");
    1672:   } else {
    1673:     ierr=PetscViewerASCIIPrintf(viewer," Residual: < 1.0e-11 \n");
    1674:   }
    1675:   PetscViewerASCIISetTab(viewer, tabs);
    1676:   return(0);
    1677: }

    1679: /*@
    1680:    TaoDefaultCMonitor - same as TaoMonitorDefault() except
    1681:    it prints the norm of the constraints function. It can be turned on
    1682:    from the command line using the -tao_cmonitor option

    1684:    Collective on Tao

    1686:    Input Parameters:
    1687: +  tao - the Tao context
    1688: -  ctx - PetscViewer context or NULL

    1690:    Options Database Keys:
    1691: .  -tao_cmonitor

    1693:    Level: advanced

    1695: .seealso: TaoMonitorDefault(), TaoSetMonitor()
    1696: @*/
    1697: PetscErrorCode TaoDefaultCMonitor(Tao tao, void *ctx)
    1698: {
    1700:   PetscInt       its, tabs;
    1701:   PetscReal      fct,gnorm;
    1702:   PetscViewer    viewer = (PetscViewer)ctx;

    1706:   its=tao->niter;
    1707:   fct=tao->fc;
    1708:   gnorm=tao->residual;
    1709:   PetscViewerASCIIGetTab(viewer, &tabs);
    1710:   PetscViewerASCIISetTab(viewer, ((PetscObject)tao)->tablevel);
    1711:   ierr=PetscViewerASCIIPrintf(viewer,"iter = %D,",its);
    1712:   ierr=PetscViewerASCIIPrintf(viewer," Function value: %g,",(double)fct);
    1713:   ierr=PetscViewerASCIIPrintf(viewer,"  Residual: %g ",(double)gnorm);
    1714:   PetscViewerASCIIPrintf(viewer,"  Constraint: %g \n",(double)tao->cnorm);
    1715:   PetscViewerASCIISetTab(viewer, tabs);
    1716:   return(0);
    1717: }

    1719: /*@C
    1720:    TaoSolutionMonitor - Views the solution at each iteration
    1721:    It can be turned on from the command line using the
    1722:    -tao_view_solution option

    1724:    Collective on Tao

    1726:    Input Parameters:
    1727: +  tao - the Tao context
    1728: -  ctx - PetscViewer context or NULL

    1730:    Options Database Keys:
    1731: .  -tao_view_solution

    1733:    Level: advanced

    1735: .seealso: TaoDefaultSMonitor(), TaoSetMonitor()
    1736: @*/
    1737: PetscErrorCode TaoSolutionMonitor(Tao tao, void *ctx)
    1738: {
    1740:   PetscViewer    viewer  = (PetscViewer)ctx;

    1744:   VecView(tao->solution, viewer);
    1745:   return(0);
    1746: }

    1748: /*@C
    1749:    TaoGradientMonitor - Views the gradient at each iteration
    1750:    It can be turned on from the command line using the
    1751:    -tao_view_gradient option

    1753:    Collective on Tao

    1755:    Input Parameters:
    1756: +  tao - the Tao context
    1757: -  ctx - PetscViewer context or NULL

    1759:    Options Database Keys:
    1760: .  -tao_view_gradient

    1762:    Level: advanced

    1764: .seealso: TaoDefaultSMonitor(), TaoSetMonitor()
    1765: @*/
    1766: PetscErrorCode TaoGradientMonitor(Tao tao, void *ctx)
    1767: {
    1769:   PetscViewer    viewer = (PetscViewer)ctx;

    1773:   VecView(tao->gradient, viewer);
    1774:   return(0);
    1775: }

    1777: /*@C
    1778:    TaoStepDirectionMonitor - Views the gradient at each iteration
    1779:    It can be turned on from the command line using the
    1780:    -tao_view_gradient option

    1782:    Collective on Tao

    1784:    Input Parameters:
    1785: +  tao - the Tao context
    1786: -  ctx - PetscViewer context or NULL

    1788:    Options Database Keys:
    1789: .  -tao_view_gradient

    1791:    Level: advanced

    1793: .seealso: TaoDefaultSMonitor(), TaoSetMonitor()
    1794: @*/
    1795: PetscErrorCode TaoStepDirectionMonitor(Tao tao, void *ctx)
    1796: {
    1798:   PetscViewer    viewer = (PetscViewer)ctx;

    1802:   VecView(tao->stepdirection, viewer);
    1803:   return(0);
    1804: }

    1806: /*@C
    1807:    TaoDrawSolutionMonitor - Plots the solution at each iteration
    1808:    It can be turned on from the command line using the
    1809:    -tao_draw_solution option

    1811:    Collective on Tao

    1813:    Input Parameters:
    1814: +  tao - the Tao context
    1815: -  ctx - TaoMonitorDraw context

    1817:    Options Database Keys:
    1818: .  -tao_draw_solution

    1820:    Level: advanced

    1822: .seealso: TaoSolutionMonitor(), TaoSetMonitor(), TaoDrawGradientMonitor
    1823: @*/
    1824: PetscErrorCode TaoDrawSolutionMonitor(Tao tao, void *ctx)
    1825: {
    1826:   PetscErrorCode    ierr;
    1827:   TaoMonitorDrawCtx ictx = (TaoMonitorDrawCtx)ctx;

    1830:   if (!(((ictx->howoften > 0) && (!(tao->niter % ictx->howoften))) || ((ictx->howoften == -1) && tao->reason))) return(0);
    1831:   VecView(tao->solution,ictx->viewer);
    1832:   return(0);
    1833: }

    1835: /*@C
    1836:    TaoDrawGradientMonitor - Plots the gradient at each iteration
    1837:    It can be turned on from the command line using the
    1838:    -tao_draw_gradient option

    1840:    Collective on Tao

    1842:    Input Parameters:
    1843: +  tao - the Tao context
    1844: -  ctx - PetscViewer context

    1846:    Options Database Keys:
    1847: .  -tao_draw_gradient

    1849:    Level: advanced

    1851: .seealso: TaoGradientMonitor(), TaoSetMonitor(), TaoDrawSolutionMonitor
    1852: @*/
    1853: PetscErrorCode TaoDrawGradientMonitor(Tao tao, void *ctx)
    1854: {
    1855:   PetscErrorCode    ierr;
    1856:   TaoMonitorDrawCtx ictx = (TaoMonitorDrawCtx)ctx;

    1859:   if (!(((ictx->howoften > 0) && (!(tao->niter % ictx->howoften))) || ((ictx->howoften == -1) && tao->reason))) return(0);
    1860:   VecView(tao->gradient,ictx->viewer);
    1861:   return(0);
    1862: }

    1864: /*@C
    1865:    TaoDrawStepMonitor - Plots the step direction at each iteration
    1866:    It can be turned on from the command line using the
    1867:    -tao_draw_step option

    1869:    Collective on Tao

    1871:    Input Parameters:
    1872: +  tao - the Tao context
    1873: -  ctx - PetscViewer context

    1875:    Options Database Keys:
    1876: .  -tao_draw_step

    1878:    Level: advanced

    1880: .seealso: TaoSetMonitor(), TaoDrawSolutionMonitor
    1881: @*/
    1882: PetscErrorCode TaoDrawStepMonitor(Tao tao, void *ctx)
    1883: {
    1885:   PetscViewer    viewer = (PetscViewer)(ctx);

    1888:   VecView(tao->stepdirection, viewer);
    1889:   return(0);
    1890: }

    1892: /*@C
    1893:    TaoResidualMonitor - Views the least-squares residual at each iteration
    1894:    It can be turned on from the command line using the
    1895:    -tao_view_ls_residual option

    1897:    Collective on Tao

    1899:    Input Parameters:
    1900: +  tao - the Tao context
    1901: -  ctx - PetscViewer context or NULL

    1903:    Options Database Keys:
    1904: .  -tao_view_ls_residual

    1906:    Level: advanced

    1908: .seealso: TaoDefaultSMonitor(), TaoSetMonitor()
    1909: @*/
    1910: PetscErrorCode TaoResidualMonitor(Tao tao, void *ctx)
    1911: {
    1913:   PetscViewer    viewer  = (PetscViewer)ctx;

    1917:   VecView(tao->ls_res,viewer);
    1918:   return(0);
    1919: }

    1921: /*@
    1922:    TaoDefaultConvergenceTest - Determines whether the solver should continue iterating
    1923:    or terminate.

    1925:    Collective on Tao

    1927:    Input Parameters:
    1928: +  tao - the Tao context
    1929: -  dummy - unused dummy context

    1931:    Output Parameter:
    1932: .  reason - for terminating

    1934:    Notes:
    1935:    This routine checks the residual in the optimality conditions, the
    1936:    relative residual in the optimity conditions, the number of function
    1937:    evaluations, and the function value to test convergence.  Some
    1938:    solvers may use different convergence routines.

    1940:    Level: developer

    1942: .seealso: TaoSetTolerances(),TaoGetConvergedReason(),TaoSetConvergedReason()
    1943: @*/

    1945: PetscErrorCode TaoDefaultConvergenceTest(Tao tao,void *dummy)
    1946: {
    1947:   PetscInt           niter=tao->niter, nfuncs=PetscMax(tao->nfuncs,tao->nfuncgrads);
    1948:   PetscInt           max_funcs=tao->max_funcs;
    1949:   PetscReal          gnorm=tao->residual, gnorm0=tao->gnorm0;
    1950:   PetscReal          f=tao->fc, steptol=tao->steptol,trradius=tao->step;
    1951:   PetscReal          gatol=tao->gatol,grtol=tao->grtol,gttol=tao->gttol;
    1952:   PetscReal          catol=tao->catol,crtol=tao->crtol;
    1953:   PetscReal          fmin=tao->fmin, cnorm=tao->cnorm;
    1954:   TaoConvergedReason reason=tao->reason;
    1955:   PetscErrorCode     ierr;

    1959:   if (reason != TAO_CONTINUE_ITERATING) {
    1960:     return(0);
    1961:   }

    1963:   if (PetscIsInfOrNanReal(f)) {
    1964:     PetscInfo(tao,"Failed to converged, function value is Inf or NaN\n");
    1965:     reason = TAO_DIVERGED_NAN;
    1966:   } else if (f <= fmin && cnorm <=catol) {
    1967:     PetscInfo2(tao,"Converged due to function value %g < minimum function value %g\n", (double)f,(double)fmin);
    1968:     reason = TAO_CONVERGED_MINF;
    1969:   } else if (gnorm<= gatol && cnorm <=catol) {
    1970:     PetscInfo2(tao,"Converged due to residual norm ||g(X)||=%g < %g\n",(double)gnorm,(double)gatol);
    1971:     reason = TAO_CONVERGED_GATOL;
    1972:   } else if ( f!=0 && PetscAbsReal(gnorm/f) <= grtol && cnorm <= crtol) {
    1973:     PetscInfo2(tao,"Converged due to residual ||g(X)||/|f(X)| =%g < %g\n",(double)(gnorm/f),(double)grtol);
    1974:     reason = TAO_CONVERGED_GRTOL;
    1975:   } else if (gnorm0 != 0 && ((gttol == 0 && gnorm == 0) || gnorm/gnorm0 < gttol) && cnorm <= crtol) {
    1976:     PetscInfo2(tao,"Converged due to relative residual norm ||g(X)||/||g(X0)|| = %g < %g\n",(double)(gnorm/gnorm0),(double)gttol);
    1977:     reason = TAO_CONVERGED_GTTOL;
    1978:   } else if (nfuncs > max_funcs){
    1979:     PetscInfo2(tao,"Exceeded maximum number of function evaluations: %D > %D\n", nfuncs,max_funcs);
    1980:     reason = TAO_DIVERGED_MAXFCN;
    1981:   } else if ( tao->lsflag != 0 ){
    1982:     PetscInfo(tao,"Tao Line Search failure.\n");
    1983:     reason = TAO_DIVERGED_LS_FAILURE;
    1984:   } else if (trradius < steptol && niter > 0){
    1985:     PetscInfo2(tao,"Trust region/step size too small: %g < %g\n", (double)trradius,(double)steptol);
    1986:     reason = TAO_CONVERGED_STEPTOL;
    1987:   } else if (niter >= tao->max_it) {
    1988:     PetscInfo2(tao,"Exceeded maximum number of iterations: %D > %D\n",niter,tao->max_it);
    1989:     reason = TAO_DIVERGED_MAXITS;
    1990:   } else {
    1991:     reason = TAO_CONTINUE_ITERATING;
    1992:   }
    1993:   tao->reason = reason;
    1994:   return(0);
    1995: }

    1997: /*@C
    1998:    TaoSetOptionsPrefix - Sets the prefix used for searching for all
    1999:    TAO options in the database.

    2002:    Logically Collective on Tao

    2004:    Input Parameters:
    2005: +  tao - the Tao context
    2006: -  prefix - the prefix string to prepend to all TAO option requests

    2008:    Notes:
    2009:    A hyphen (-) must NOT be given at the beginning of the prefix name.
    2010:    The first character of all runtime options is AUTOMATICALLY the hyphen.

    2012:    For example, to distinguish between the runtime options for two
    2013:    different TAO solvers, one could call
    2014: .vb
    2015:       TaoSetOptionsPrefix(tao1,"sys1_")
    2016:       TaoSetOptionsPrefix(tao2,"sys2_")
    2017: .ve

    2019:    This would enable use of different options for each system, such as
    2020: .vb
    2021:       -sys1_tao_method blmvm -sys1_tao_gtol 1.e-3
    2022:       -sys2_tao_method lmvm  -sys2_tao_gtol 1.e-4
    2023: .ve

    2026:    Level: advanced

    2028: .seealso: TaoAppendOptionsPrefix(), TaoGetOptionsPrefix()
    2029: @*/

    2031: PetscErrorCode TaoSetOptionsPrefix(Tao tao, const char p[])
    2032: {

    2036:   PetscObjectSetOptionsPrefix((PetscObject)tao,p);
    2037:   if (tao->linesearch) {
    2038:     TaoLineSearchSetOptionsPrefix(tao->linesearch,p);
    2039:   }
    2040:   if (tao->ksp) {
    2041:     KSPSetOptionsPrefix(tao->ksp,p);
    2042:   }
    2043:   return(0);
    2044: }

    2046: /*@C
    2047:    TaoAppendOptionsPrefix - Appends to the prefix used for searching for all
    2048:    TAO options in the database.

    2051:    Logically Collective on Tao

    2053:    Input Parameters:
    2054: +  tao - the Tao solver context
    2055: -  prefix - the prefix string to prepend to all TAO option requests

    2057:    Notes:
    2058:    A hyphen (-) must NOT be given at the beginning of the prefix name.
    2059:    The first character of all runtime options is AUTOMATICALLY the hyphen.

    2062:    Level: advanced

    2064: .seealso: TaoSetOptionsPrefix(), TaoGetOptionsPrefix()
    2065: @*/
    2066: PetscErrorCode TaoAppendOptionsPrefix(Tao tao, const char p[])
    2067: {

    2071:   PetscObjectAppendOptionsPrefix((PetscObject)tao,p);
    2072:   if (tao->linesearch) {
    2073:     TaoLineSearchSetOptionsPrefix(tao->linesearch,p);
    2074:   }
    2075:   if (tao->ksp) {
    2076:     KSPSetOptionsPrefix(tao->ksp,p);
    2077:   }
    2078:   return(0);
    2079: }

    2081: /*@C
    2082:   TaoGetOptionsPrefix - Gets the prefix used for searching for all
    2083:   TAO options in the database

    2085:   Not Collective

    2087:   Input Parameters:
    2088: . tao - the Tao context

    2090:   Output Parameters:
    2091: . prefix - pointer to the prefix string used is returned

    2093:   Notes:
    2094:     On the fortran side, the user should pass in a string 'prefix' of
    2095:   sufficient length to hold the prefix.

    2097:   Level: advanced

    2099: .seealso: TaoSetOptionsPrefix(), TaoAppendOptionsPrefix()
    2100: @*/
    2101: PetscErrorCode TaoGetOptionsPrefix(Tao tao, const char *p[])
    2102: {
    2103:    return PetscObjectGetOptionsPrefix((PetscObject)tao,p);
    2104: }

    2106: /*@C
    2107:    TaoSetType - Sets the method for the unconstrained minimization solver.

    2109:    Collective on Tao

    2111:    Input Parameters:
    2112: +  solver - the Tao solver context
    2113: -  type - a known method

    2115:    Options Database Key:
    2116: .  -tao_type <type> - Sets the method; use -help for a list
    2117:    of available methods (for instance, "-tao_type lmvm" or "-tao_type tron")

    2119:    Available methods include:
    2120: +    nls - Newton's method with line search for unconstrained minimization
    2121: .    ntr - Newton's method with trust region for unconstrained minimization
    2122: .    ntl - Newton's method with trust region, line search for unconstrained minimization
    2123: .    lmvm - Limited memory variable metric method for unconstrained minimization
    2124: .    cg - Nonlinear conjugate gradient method for unconstrained minimization
    2125: .    nm - Nelder-Mead algorithm for derivate-free unconstrained minimization
    2126: .    tron - Newton Trust Region method for bound constrained minimization
    2127: .    gpcg - Newton Trust Region method for quadratic bound constrained minimization
    2128: .    blmvm - Limited memory variable metric method for bound constrained minimization
    2129: -    pounders - Model-based algorithm pounder extended for nonlinear least squares

    2131:   Level: intermediate

    2133: .seealso: TaoCreate(), TaoGetType(), TaoType

    2135: @*/
    2136: PetscErrorCode TaoSetType(Tao tao, TaoType type)
    2137: {
    2139:   PetscErrorCode (*create_xxx)(Tao);
    2140:   PetscBool      issame;

    2145:   PetscObjectTypeCompare((PetscObject)tao,type,&issame);
    2146:   if (issame) return(0);

    2148:   PetscFunctionListFind(TaoList, type, (void(**)(void))&create_xxx);
    2149:   if (!create_xxx) SETERRQ1(PetscObjectComm((PetscObject)tao),PETSC_ERR_ARG_UNKNOWN_TYPE,"Unable to find requested Tao type %s",type);

    2151:   /* Destroy the existing solver information */
    2152:   if (tao->ops->destroy) {
    2153:     (*tao->ops->destroy)(tao);
    2154:   }
    2155:   KSPDestroy(&tao->ksp);
    2156:   TaoLineSearchDestroy(&tao->linesearch);
    2157:   VecDestroy(&tao->gradient);
    2158:   VecDestroy(&tao->stepdirection);

    2160:   tao->ops->setup = 0;
    2161:   tao->ops->solve = 0;
    2162:   tao->ops->view  = 0;
    2163:   tao->ops->setfromoptions = 0;
    2164:   tao->ops->destroy = 0;

    2166:   tao->setupcalled = PETSC_FALSE;

    2168:   (*create_xxx)(tao);
    2169:   PetscObjectChangeTypeName((PetscObject)tao,type);
    2170:   return(0);
    2171: }

    2173: /*MC
    2174:    TaoRegister - Adds a method to the TAO package for unconstrained minimization.

    2176:    Synopsis:
    2177:    TaoRegister(char *name_solver,char *path,char *name_Create,PetscErrorCode (*routine_Create)(Tao))

    2179:    Not collective

    2181:    Input Parameters:
    2182: +  sname - name of a new user-defined solver
    2183: -  func - routine to Create method context

    2185:    Notes:
    2186:    TaoRegister() may be called multiple times to add several user-defined solvers.

    2188:    Sample usage:
    2189: .vb
    2190:    TaoRegister("my_solver",MySolverCreate);
    2191: .ve

    2193:    Then, your solver can be chosen with the procedural interface via
    2194: $     TaoSetType(tao,"my_solver")
    2195:    or at runtime via the option
    2196: $     -tao_type my_solver

    2198:    Level: advanced

    2200: .seealso: TaoRegisterAll(), TaoRegisterDestroy()
    2201: M*/
    2202: PetscErrorCode TaoRegister(const char sname[], PetscErrorCode (*func)(Tao))
    2203: {

    2207:   TaoInitializePackage();
    2208:   PetscFunctionListAdd(&TaoList,sname, (void (*)(void))func);
    2209:   return(0);
    2210: }

    2212: /*@C
    2213:    TaoRegisterDestroy - Frees the list of minimization solvers that were
    2214:    registered by TaoRegisterDynamic().

    2216:    Not Collective

    2218:    Level: advanced

    2220: .seealso: TaoRegisterAll(), TaoRegister()
    2221: @*/
    2222: PetscErrorCode TaoRegisterDestroy(void)
    2223: {
    2226:   PetscFunctionListDestroy(&TaoList);
    2227:   TaoRegisterAllCalled = PETSC_FALSE;
    2228:   return(0);
    2229: }

    2231: /*@
    2232:    TaoGetIterationNumber - Gets the number of Tao iterations completed
    2233:    at this time.

    2235:    Not Collective

    2237:    Input Parameter:
    2238: .  tao - Tao context

    2240:    Output Parameter:
    2241: .  iter - iteration number

    2243:    Notes:
    2244:    For example, during the computation of iteration 2 this would return 1.

    2247:    Level: intermediate

    2249: .seealso:   TaoGetLinearSolveIterations(), TaoGetResidualNorm(), TaoGetObjective()
    2250: @*/
    2251: PetscErrorCode  TaoGetIterationNumber(Tao tao,PetscInt *iter)
    2252: {
    2256:   *iter = tao->niter;
    2257:   return(0);
    2258: }

    2260: /*@
    2261:    TaoGetObjective - Gets the current value of the objective function
    2262:    at this time.

    2264:    Not Collective

    2266:    Input Parameter:
    2267: .  tao - Tao context

    2269:    Output Parameter:
    2270: .  value - the current value

    2272:    Level: intermediate

    2274: .seealso:   TaoGetLinearSolveIterations(), TaoGetIterationNumber(), TaoGetResidualNorm()
    2275: @*/
    2276: PetscErrorCode  TaoGetObjective(Tao tao,PetscReal *value)
    2277: {
    2281:   *value = tao->fc;
    2282:   return(0);
    2283: }

    2285: /*@
    2286:    TaoGetResidualNorm - Gets the current value of the norm of the residual
    2287:    at this time.

    2289:    Not Collective

    2291:    Input Parameter:
    2292: .  tao - Tao context

    2294:    Output Parameter:
    2295: .  value - the current value

    2297:    Level: intermediate

    2299:    Developer Note: This is the 2-norm of the residual, we cannot use TaoGetGradientNorm() because that has
    2300:                    a different meaning. For some reason Tao sometimes calls the gradient the residual.

    2302: .seealso:   TaoGetLinearSolveIterations(), TaoGetIterationNumber(), TaoGetObjective()
    2303: @*/
    2304: PetscErrorCode  TaoGetResidualNorm(Tao tao,PetscReal *value)
    2305: {
    2309:   *value = tao->residual;
    2310:   return(0);
    2311: }

    2313: /*@
    2314:    TaoSetIterationNumber - Sets the current iteration number.

    2316:    Not Collective

    2318:    Input Parameter:
    2319: +  tao - Tao context
    2320: -  iter - iteration number

    2322:    Level: developer

    2324: .seealso:   TaoGetLinearSolveIterations()
    2325: @*/
    2326: PetscErrorCode  TaoSetIterationNumber(Tao tao,PetscInt iter)
    2327: {

    2332:   PetscObjectSAWsTakeAccess((PetscObject)tao);
    2333:   tao->niter = iter;
    2334:   PetscObjectSAWsGrantAccess((PetscObject)tao);
    2335:   return(0);
    2336: }

    2338: /*@
    2339:    TaoGetTotalIterationNumber - Gets the total number of Tao iterations
    2340:    completed. This number keeps accumulating if multiple solves
    2341:    are called with the Tao object.

    2343:    Not Collective

    2345:    Input Parameter:
    2346: .  tao - Tao context

    2348:    Output Parameter:
    2349: .  iter - iteration number

    2351:    Notes:
    2352:    The total iteration count is updated after each solve, if there is a current
    2353:    TaoSolve() in progress then those iterations are not yet counted.

    2355:    Level: intermediate

    2357: .seealso:   TaoGetLinearSolveIterations()
    2358: @*/
    2359: PetscErrorCode  TaoGetTotalIterationNumber(Tao tao,PetscInt *iter)
    2360: {
    2364:   *iter = tao->ntotalits;
    2365:   return(0);
    2366: }

    2368: /*@
    2369:    TaoSetTotalIterationNumber - Sets the current total iteration number.

    2371:    Not Collective

    2373:    Input Parameter:
    2374: +  tao - Tao context
    2375: -  iter - iteration number

    2377:    Level: developer

    2379: .seealso:   TaoGetLinearSolveIterations()
    2380: @*/
    2381: PetscErrorCode  TaoSetTotalIterationNumber(Tao tao,PetscInt iter)
    2382: {

    2387:   PetscObjectSAWsTakeAccess((PetscObject)tao);
    2388:   tao->ntotalits = iter;
    2389:   PetscObjectSAWsGrantAccess((PetscObject)tao);
    2390:   return(0);
    2391: }

    2393: /*@
    2394:   TaoSetConvergedReason - Sets the termination flag on a Tao object

    2396:   Logically Collective on Tao

    2398:   Input Parameters:
    2399: + tao - the Tao context
    2400: - reason - one of
    2401: $     TAO_CONVERGED_ATOL (2),
    2402: $     TAO_CONVERGED_RTOL (3),
    2403: $     TAO_CONVERGED_STEPTOL (4),
    2404: $     TAO_CONVERGED_MINF (5),
    2405: $     TAO_CONVERGED_USER (6),
    2406: $     TAO_DIVERGED_MAXITS (-2),
    2407: $     TAO_DIVERGED_NAN (-4),
    2408: $     TAO_DIVERGED_MAXFCN (-5),
    2409: $     TAO_DIVERGED_LS_FAILURE (-6),
    2410: $     TAO_DIVERGED_TR_REDUCTION (-7),
    2411: $     TAO_DIVERGED_USER (-8),
    2412: $     TAO_CONTINUE_ITERATING (0)

    2414:    Level: intermediate

    2416: @*/
    2417: PetscErrorCode TaoSetConvergedReason(Tao tao, TaoConvergedReason reason)
    2418: {
    2421:   tao->reason = reason;
    2422:   return(0);
    2423: }

    2425: /*@
    2426:    TaoGetConvergedReason - Gets the reason the Tao iteration was stopped.

    2428:    Not Collective

    2430:    Input Parameter:
    2431: .  tao - the Tao solver context

    2433:    Output Parameter:
    2434: .  reason - one of
    2435: $  TAO_CONVERGED_GATOL (3)           ||g(X)|| < gatol
    2436: $  TAO_CONVERGED_GRTOL (4)           ||g(X)|| / f(X)  < grtol
    2437: $  TAO_CONVERGED_GTTOL (5)           ||g(X)|| / ||g(X0)|| < gttol
    2438: $  TAO_CONVERGED_STEPTOL (6)         step size small
    2439: $  TAO_CONVERGED_MINF (7)            F < F_min
    2440: $  TAO_CONVERGED_USER (8)            User defined
    2441: $  TAO_DIVERGED_MAXITS (-2)          its > maxits
    2442: $  TAO_DIVERGED_NAN (-4)             Numerical problems
    2443: $  TAO_DIVERGED_MAXFCN (-5)          fevals > max_funcsals
    2444: $  TAO_DIVERGED_LS_FAILURE (-6)      line search failure
    2445: $  TAO_DIVERGED_TR_REDUCTION (-7)    trust region failure
    2446: $  TAO_DIVERGED_USER(-8)             (user defined)
    2447:  $  TAO_CONTINUE_ITERATING (0)

    2449:    where
    2450: +  X - current solution
    2451: .  X0 - initial guess
    2452: .  f(X) - current function value
    2453: .  f(X*) - true solution (estimated)
    2454: .  g(X) - current gradient
    2455: .  its - current iterate number
    2456: .  maxits - maximum number of iterates
    2457: .  fevals - number of function evaluations
    2458: -  max_funcsals - maximum number of function evaluations

    2460:    Level: intermediate

    2462: .seealso: TaoSetConvergenceTest(), TaoSetTolerances()

    2464: @*/
    2465: PetscErrorCode TaoGetConvergedReason(Tao tao, TaoConvergedReason *reason)
    2466: {
    2470:   *reason = tao->reason;
    2471:   return(0);
    2472: }

    2474: /*@
    2475:   TaoGetSolutionStatus - Get the current iterate, objective value,
    2476:   residual, infeasibility, and termination

    2478:   Not Collective

    2480:    Input Parameters:
    2481: .  tao - the Tao context

    2483:    Output Parameters:
    2484: +  iterate - the current iterate number (>=0)
    2485: .  f - the current function value
    2486: .  gnorm - the square of the gradient norm, duality gap, or other measure indicating distance from optimality.
    2487: .  cnorm - the infeasibility of the current solution with regard to the constraints.
    2488: .  xdiff - the step length or trust region radius of the most recent iterate.
    2489: -  reason - The termination reason, which can equal TAO_CONTINUE_ITERATING

    2491:    Level: intermediate

    2493:    Note:
    2494:    TAO returns the values set by the solvers in the routine TaoMonitor().

    2496:    Note:
    2497:    If any of the output arguments are set to NULL, no corresponding value will be returned.

    2499: .seealso: TaoMonitor(), TaoGetConvergedReason()
    2500: @*/
    2501: PetscErrorCode TaoGetSolutionStatus(Tao tao, PetscInt *its, PetscReal *f, PetscReal *gnorm, PetscReal *cnorm, PetscReal *xdiff, TaoConvergedReason *reason)
    2502: {
    2504:   if (its) *its=tao->niter;
    2505:   if (f) *f=tao->fc;
    2506:   if (gnorm) *gnorm=tao->residual;
    2507:   if (cnorm) *cnorm=tao->cnorm;
    2508:   if (reason) *reason=tao->reason;
    2509:   if (xdiff) *xdiff=tao->step;
    2510:   return(0);
    2511: }

    2513: /*@C
    2514:    TaoGetType - Gets the current Tao algorithm.

    2516:    Not Collective

    2518:    Input Parameter:
    2519: .  tao - the Tao solver context

    2521:    Output Parameter:
    2522: .  type - Tao method

    2524:    Level: intermediate

    2526: @*/
    2527: PetscErrorCode TaoGetType(Tao tao,TaoType *type)
    2528: {
    2532:   *type=((PetscObject)tao)->type_name;
    2533:   return(0);
    2534: }

    2536: /*@C
    2537:   TaoMonitor - Monitor the solver and the current solution.  This
    2538:   routine will record the iteration number and residual statistics,
    2539:   call any monitors specified by the user, and calls the convergence-check routine.

    2541:    Input Parameters:
    2542: +  tao - the Tao context
    2543: .  its - the current iterate number (>=0)
    2544: .  f - the current objective function value
    2545: .  res - the gradient norm, square root of the duality gap, or other measure indicating distince from optimality.  This measure will be recorded and
    2546:           used for some termination tests.
    2547: .  cnorm - the infeasibility of the current solution with regard to the constraints.
    2548: -  steplength - multiple of the step direction added to the previous iterate.

    2550:    Output Parameters:
    2551: .  reason - The termination reason, which can equal TAO_CONTINUE_ITERATING

    2553:    Options Database Key:
    2554: .  -tao_monitor - Use the default monitor, which prints statistics to standard output

    2556: .seealso TaoGetConvergedReason(), TaoMonitorDefault(), TaoSetMonitor()

    2558:    Level: developer

    2560: @*/
    2561: PetscErrorCode TaoMonitor(Tao tao, PetscInt its, PetscReal f, PetscReal res, PetscReal cnorm, PetscReal steplength)
    2562: {
    2564:   PetscInt       i;

    2568:   tao->fc = f;
    2569:   tao->residual = res;
    2570:   tao->cnorm = cnorm;
    2571:   tao->step = steplength;
    2572:   if (!its) {
    2573:     tao->cnorm0 = cnorm; tao->gnorm0 = res;
    2574:   }
    2575:   if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(res)) SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_USER, "User provided compute function generated Inf or NaN");
    2576:   for (i=0;i<tao->numbermonitors;i++) {
    2577:     (*tao->monitor[i])(tao,tao->monitorcontext[i]);
    2578:   }
    2579:   return(0);
    2580: }

    2582: /*@
    2583:    TaoSetConvergenceHistory - Sets the array used to hold the convergence history.

    2585:    Logically Collective on Tao

    2587:    Input Parameters:
    2588: +  tao - the Tao solver context
    2589: .  obj   - array to hold objective value history
    2590: .  resid - array to hold residual history
    2591: .  cnorm - array to hold constraint violation history
    2592: .  lits - integer array holds the number of linear iterations for each Tao iteration
    2593: .  na  - size of obj, resid, and cnorm
    2594: -  reset - PetscTrue indicates each new minimization resets the history counter to zero,
    2595:            else it continues storing new values for new minimizations after the old ones

    2597:    Notes:
    2598:    If set, TAO will fill the given arrays with the indicated
    2599:    information at each iteration.  If 'obj','resid','cnorm','lits' are
    2600:    *all* NULL then space (using size na, or 1000 if na is PETSC_DECIDE or
    2601:    PETSC_DEFAULT) is allocated for the history.
    2602:    If not all are NULL, then only the non-NULL information categories
    2603:    will be stored, the others will be ignored.

    2605:    Any convergence information after iteration number 'na' will not be stored.

    2607:    This routine is useful, e.g., when running a code for purposes
    2608:    of accurate performance monitoring, when no I/O should be done
    2609:    during the section of code that is being timed.

    2611:    Level: intermediate

    2613: .seealso: TaoGetConvergenceHistory()

    2615: @*/
    2616: PetscErrorCode TaoSetConvergenceHistory(Tao tao, PetscReal obj[], PetscReal resid[], PetscReal cnorm[], PetscInt lits[], PetscInt na,PetscBool reset)
    2617: {

    2627:   if (na == PETSC_DECIDE || na == PETSC_DEFAULT) na = 1000;
    2628:   if (!obj && !resid && !cnorm && !lits) {
    2629:     PetscCalloc4(na,&obj,na,&resid,na,&cnorm,na,&lits);
    2630:     tao->hist_malloc = PETSC_TRUE;
    2631:   }

    2633:   tao->hist_obj = obj;
    2634:   tao->hist_resid = resid;
    2635:   tao->hist_cnorm = cnorm;
    2636:   tao->hist_lits = lits;
    2637:   tao->hist_max   = na;
    2638:   tao->hist_reset = reset;
    2639:   tao->hist_len = 0;
    2640:   return(0);
    2641: }

    2643: /*@C
    2644:    TaoGetConvergenceHistory - Gets the arrays used to hold the convergence history.

    2646:    Collective on Tao

    2648:    Input Parameter:
    2649: .  tao - the Tao context

    2651:    Output Parameters:
    2652: +  obj   - array used to hold objective value history
    2653: .  resid - array used to hold residual history
    2654: .  cnorm - array used to hold constraint violation history
    2655: .  lits  - integer array used to hold linear solver iteration count
    2656: -  nhist  - size of obj, resid, cnorm, and lits

    2658:    Notes:
    2659:     This routine must be preceded by calls to TaoSetConvergenceHistory()
    2660:     and TaoSolve(), otherwise it returns useless information.

    2662:     The calling sequence for this routine in Fortran is
    2663: $   call TaoGetConvergenceHistory(Tao tao, PetscInt nhist, PetscErrorCode ierr)

    2665:    This routine is useful, e.g., when running a code for purposes
    2666:    of accurate performance monitoring, when no I/O should be done
    2667:    during the section of code that is being timed.

    2669:    Level: advanced

    2671: .seealso: TaoSetConvergenceHistory()

    2673: @*/
    2674: PetscErrorCode TaoGetConvergenceHistory(Tao tao, PetscReal **obj, PetscReal **resid, PetscReal **cnorm, PetscInt **lits, PetscInt *nhist)
    2675: {
    2678:   if (obj)   *obj   = tao->hist_obj;
    2679:   if (cnorm) *cnorm = tao->hist_cnorm;
    2680:   if (resid) *resid = tao->hist_resid;
    2681:   if (nhist) *nhist = tao->hist_len;
    2682:   return(0);
    2683: }

    2685: /*@
    2686:    TaoSetApplicationContext - Sets the optional user-defined context for
    2687:    a solver.

    2689:    Logically Collective on Tao

    2691:    Input Parameters:
    2692: +  tao  - the Tao context
    2693: -  usrP - optional user context

    2695:    Level: intermediate

    2697: .seealso: TaoGetApplicationContext(), TaoSetApplicationContext()
    2698: @*/
    2699: PetscErrorCode  TaoSetApplicationContext(Tao tao,void *usrP)
    2700: {
    2703:   tao->user = usrP;
    2704:   return(0);
    2705: }

    2707: /*@
    2708:    TaoGetApplicationContext - Gets the user-defined context for a
    2709:    TAO solvers.

    2711:    Not Collective

    2713:    Input Parameter:
    2714: .  tao  - Tao context

    2716:    Output Parameter:
    2717: .  usrP - user context

    2719:    Level: intermediate

    2721: .seealso: TaoSetApplicationContext()
    2722: @*/
    2723: PetscErrorCode  TaoGetApplicationContext(Tao tao,void *usrP)
    2724: {
    2727:   *(void**)usrP = tao->user;
    2728:   return(0);
    2729: }

    2731: /*@
    2732:    TaoSetGradientNorm - Sets the matrix used to define the inner product that measures the size of the gradient.

    2734:    Collective on tao

    2736:    Input Parameters:
    2737: +  tao  - the Tao context
    2738: -  M    - gradient norm

    2740:    Level: beginner

    2742: .seealso: TaoGetGradientNorm(), TaoGradientNorm()
    2743: @*/
    2744: PetscErrorCode  TaoSetGradientNorm(Tao tao, Mat M)
    2745: {

    2750:   PetscObjectReference((PetscObject)M);
    2751:   MatDestroy(&tao->gradient_norm);
    2752:   VecDestroy(&tao->gradient_norm_tmp);
    2753:   tao->gradient_norm = M;
    2754:   MatCreateVecs(M, NULL, &tao->gradient_norm_tmp);
    2755:   return(0);
    2756: }

    2758: /*@
    2759:    TaoGetGradientNorm - Returns the matrix used to define the inner product for measuring the size of the gradient.

    2761:    Not Collective

    2763:    Input Parameter:
    2764: .  tao  - Tao context

    2766:    Output Parameter:
    2767: .  M - gradient norm

    2769:    Level: beginner

    2771: .seealso: TaoSetGradientNorm(), TaoGradientNorm()
    2772: @*/
    2773: PetscErrorCode  TaoGetGradientNorm(Tao tao, Mat *M)
    2774: {
    2777:   *M = tao->gradient_norm;
    2778:   return(0);
    2779: }

    2781: /*c
    2782:    TaoGradientNorm - Compute the norm with respect to the inner product the user has set.

    2784:    Collective on tao

    2786:    Input Parameter:
    2787: .  tao      - the Tao context
    2788: .  gradient - the gradient to be computed
    2789: .  norm     - the norm type

    2791:    Output Parameter:
    2792: .  gnorm    - the gradient norm

    2794:    Level: developer

    2796: .seealso: TaoSetGradientNorm(), TaoGetGradientNorm()
    2797: @*/
    2798: PetscErrorCode  TaoGradientNorm(Tao tao, Vec gradient, NormType type, PetscReal *gnorm)
    2799: {

    2807:   if (tao->gradient_norm) {
    2808:     PetscScalar gnorms;

    2810:     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.");
    2811:     MatMult(tao->gradient_norm, gradient, tao->gradient_norm_tmp);
    2812:     VecDot(gradient, tao->gradient_norm_tmp, &gnorms);
    2813:     *gnorm = PetscRealPart(PetscSqrtScalar(gnorms));
    2814:   } else {
    2815:     VecNorm(gradient, type, gnorm);
    2816:   }
    2817:   return(0);
    2818: }

    2820: /*@C
    2821:    TaoMonitorDrawCtxCreate - Creates the monitor context for TaoMonitorDrawCtx

    2823:    Collective on Tao

    2825:    Output Patameter:
    2826: .    ctx - the monitor context

    2828:    Options Database:
    2829: .   -tao_draw_solution_initial - show initial guess as well as current solution

    2831:    Level: intermediate

    2833: .seealso: TaoMonitorSet(), TaoMonitorDefault(), VecView(), TaoMonitorDrawCtx()
    2834: @*/
    2835: PetscErrorCode  TaoMonitorDrawCtxCreate(MPI_Comm comm,const char host[],const char label[],int x,int y,int m,int n,PetscInt howoften,TaoMonitorDrawCtx *ctx)
    2836: {
    2837:   PetscErrorCode   ierr;

    2840:   PetscNew(ctx);
    2841:   PetscViewerDrawOpen(comm,host,label,x,y,m,n,&(*ctx)->viewer);
    2842:   PetscViewerSetFromOptions((*ctx)->viewer);
    2843:   (*ctx)->howoften = howoften;
    2844:   return(0);
    2845: }

    2847: /*@C
    2848:    TaoMonitorDrawCtxDestroy - Destroys the monitor context for TaoMonitorDrawSolution()

    2850:    Collective on Tao

    2852:    Input Parameters:
    2853: .    ctx - the monitor context

    2855:    Level: intermediate

    2857: .seealso: TaoMonitorSet(), TaoMonitorDefault(), VecView(), TaoMonitorDrawSolution()
    2858: @*/
    2859: PetscErrorCode  TaoMonitorDrawCtxDestroy(TaoMonitorDrawCtx *ictx)
    2860: {

    2864:   PetscViewerDestroy(&(*ictx)->viewer);
    2865:   PetscFree(*ictx);
    2866:   return(0);
    2867: }