Actual source code: taosolver.c

  1: #include <petsc/private/taoimpl.h>
  2: #include <petsc/private/snesimpl.h>

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

  7: PetscClassId TAO_CLASSID;

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

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

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

 24: static PetscErrorCode KSPPreSolve_TAOEW_Private(KSP ksp, Vec b, Vec x, Tao tao)
 25: {
 26:   SNES snes_ewdummy = tao->snes_ewdummy;

 28:   PetscFunctionBegin;
 29:   if (!snes_ewdummy) PetscFunctionReturn(PETSC_SUCCESS);
 30:   /* populate snes_ewdummy struct values used in KSPPreSolve_SNESEW */
 31:   snes_ewdummy->vec_func = b;
 32:   snes_ewdummy->rtol     = tao->gttol;
 33:   snes_ewdummy->iter     = tao->niter;
 34:   PetscCall(VecNorm(b, NORM_2, &snes_ewdummy->norm));
 35:   PetscCall(KSPPreSolve_SNESEW(ksp, b, x, snes_ewdummy));
 36:   snes_ewdummy->vec_func = NULL;
 37:   PetscFunctionReturn(PETSC_SUCCESS);
 38: }

 40: static PetscErrorCode KSPPostSolve_TAOEW_Private(KSP ksp, Vec b, Vec x, Tao tao)
 41: {
 42:   SNES snes_ewdummy = tao->snes_ewdummy;

 44:   PetscFunctionBegin;
 45:   if (!snes_ewdummy) PetscFunctionReturn(PETSC_SUCCESS);
 46:   PetscCall(KSPPostSolve_SNESEW(ksp, b, x, snes_ewdummy));
 47:   PetscFunctionReturn(PETSC_SUCCESS);
 48: }

 50: static PetscErrorCode TaoSetUpEW_Private(Tao tao)
 51: {
 52:   SNESKSPEW  *kctx;
 53:   const char *ewprefix;

 55:   PetscFunctionBegin;
 56:   if (!tao->ksp) PetscFunctionReturn(PETSC_SUCCESS);
 57:   if (tao->ksp_ewconv) {
 58:     if (!tao->snes_ewdummy) PetscCall(SNESCreate(PetscObjectComm((PetscObject)tao), &tao->snes_ewdummy));
 59:     tao->snes_ewdummy->ksp_ewconv = PETSC_TRUE;
 60:     PetscCall(KSPSetPreSolve(tao->ksp, (PetscErrorCode(*)(KSP, Vec, Vec, void *))KSPPreSolve_TAOEW_Private, tao));
 61:     PetscCall(KSPSetPostSolve(tao->ksp, (PetscErrorCode(*)(KSP, Vec, Vec, void *))KSPPostSolve_TAOEW_Private, tao));

 63:     PetscCall(KSPGetOptionsPrefix(tao->ksp, &ewprefix));
 64:     kctx = (SNESKSPEW *)tao->snes_ewdummy->kspconvctx;
 65:     PetscCall(SNESEWSetFromOptions_Private(kctx, PetscObjectComm((PetscObject)tao), ewprefix));
 66:   } else PetscCall(SNESDestroy(&tao->snes_ewdummy));
 67:   PetscFunctionReturn(PETSC_SUCCESS);
 68: }

 70: /*@
 71:   TaoCreate - Creates a Tao solver

 73:   Collective

 75:   Input Parameter:
 76: . comm - MPI communicator

 78:   Output Parameter:
 79: . newtao - the new `Tao` context

 81:    Options Database Key:
 82: .   -tao_type - select which method Tao should use

 84:    Level: beginner

 86: .seealso: [](chapter_tao), `Tao`, `TaoSolve()`, `TaoDestroy()`, `TAOSetFromOptions()`, `TAOSetType()`
 87: @*/
 88: PetscErrorCode TaoCreate(MPI_Comm comm, Tao *newtao)
 89: {
 90:   Tao tao;

 92:   PetscFunctionBegin;
 94:   PetscCall(TaoInitializePackage());
 95:   PetscCall(TaoLineSearchInitializePackage());
 96:   PetscCall(PetscHeaderCreate(tao, TAO_CLASSID, "Tao", "Optimization solver", "Tao", comm, TaoDestroy, TaoView));

 98:   /* Set non-NULL defaults */
 99:   tao->ops->convergencetest = TaoDefaultConvergenceTest;

101:   tao->max_it    = 10000;
102:   tao->max_funcs = -1;
103: #if defined(PETSC_USE_REAL_SINGLE)
104:   tao->gatol = 1e-5;
105:   tao->grtol = 1e-5;
106:   tao->crtol = 1e-5;
107:   tao->catol = 1e-5;
108: #else
109:   tao->gatol = 1e-8;
110:   tao->grtol = 1e-8;
111:   tao->crtol = 1e-8;
112:   tao->catol = 1e-8;
113: #endif
114:   tao->gttol   = 0.0;
115:   tao->steptol = 0.0;
116:   tao->trust0  = PETSC_INFINITY;
117:   tao->fmin    = PETSC_NINFINITY;

119:   tao->hist_reset = PETSC_TRUE;

121:   PetscCall(TaoResetStatistics(tao));
122:   *newtao = tao;
123:   PetscFunctionReturn(PETSC_SUCCESS);
124: }

126: /*@
127:   TaoSolve - Solves an optimization problem min F(x) s.t. l <= x <= u

129:   Collective

131:   Input Parameter:
132: . tao - the `Tao` context

134:   Level: beginner

136:   Notes:
137:   The user must set up the `Tao` object  with calls to `TaoSetSolution()`, `TaoSetObjective()`, `TaoSetGradient()`, and (if using 2nd order method) `TaoSetHessian()`.

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

142: .seealso: [](chapter_tao), `Tao`, `TaoCreate()`, `TaoSetObjective()`, `TaoSetGradient()`, `TaoSetHessian()`, `TaoGetConvergedReason()`, `TaoSetUp()`
143:  @*/
144: PetscErrorCode TaoSolve(Tao tao)
145: {
146:   static PetscBool set = PETSC_FALSE;

148:   PetscFunctionBegin;
150:   PetscCall(PetscCitationsRegister("@TechReport{tao-user-ref,\n"
151:                                    "title   = {Toolkit for Advanced Optimization (TAO) Users Manual},\n"
152:                                    "author  = {Todd Munson and Jason Sarich and Stefan Wild and Steve Benson and Lois Curfman McInnes},\n"
153:                                    "Institution = {Argonne National Laboratory},\n"
154:                                    "Year   = 2014,\n"
155:                                    "Number = {ANL/MCS-TM-322 - Revision 3.5},\n"
156:                                    "url    = {https://www.mcs.anl.gov/research/projects/tao/}\n}\n",
157:                                    &set));
158:   tao->header_printed = PETSC_FALSE;
159:   PetscCall(TaoSetUp(tao));
160:   PetscCall(TaoResetStatistics(tao));
161:   if (tao->linesearch) PetscCall(TaoLineSearchReset(tao->linesearch));

163:   PetscCall(PetscLogEventBegin(TAO_Solve, tao, 0, 0, 0));
164:   PetscTryTypeMethod(tao, solve);
165:   PetscCall(PetscLogEventEnd(TAO_Solve, tao, 0, 0, 0));

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

169:   tao->ntotalits += tao->niter;

171:   if (tao->printreason) {
172:     PetscViewer viewer = PETSC_VIEWER_STDOUT_(((PetscObject)tao)->comm);
173:     PetscCall(PetscViewerASCIIAddTab(viewer, ((PetscObject)tao)->tablevel));
174:     if (tao->reason > 0) {
175:       PetscCall(PetscViewerASCIIPrintf(viewer, "  TAO %s solve converged due to %s iterations %" PetscInt_FMT "\n", ((PetscObject)tao)->prefix ? ((PetscObject)tao)->prefix : "", TaoConvergedReasons[tao->reason], tao->niter));
176:     } else {
177:       PetscCall(PetscViewerASCIIPrintf(viewer, "  TAO %s solve did not converge due to %s iteration %" PetscInt_FMT "\n", ((PetscObject)tao)->prefix ? ((PetscObject)tao)->prefix : "", TaoConvergedReasons[tao->reason], tao->niter));
178:     }
179:     PetscCall(PetscViewerASCIISubtractTab(viewer, ((PetscObject)tao)->tablevel));
180:   }
181:   PetscCall(TaoViewFromOptions(tao, NULL, "-tao_view"));
182:   PetscFunctionReturn(PETSC_SUCCESS);
183: }

185: /*@
186:   TaoSetUp - Sets up the internal data structures for the later use
187:   of a Tao solver

189:   Collective

191:   Input Parameter:
192: . tao - the `Tao` context

194:   Level: advanced

196:   Note:
197:   The user will not need to explicitly call `TaoSetUp()`, as it will
198:   automatically be called in `TaoSolve()`.  However, if the user
199:   desires to call it explicitly, it should come after `TaoCreate()`
200:   and any TaoSetSomething() routines, but before `TaoSolve()`.

202: .seealso: [](chapter_tao), `Tao`, `TaoCreate()`, `TaoSolve()`
203: @*/
204: PetscErrorCode TaoSetUp(Tao tao)
205: {
206:   PetscFunctionBegin;
208:   if (tao->setupcalled) PetscFunctionReturn(PETSC_SUCCESS);
209:   PetscCall(TaoSetUpEW_Private(tao));
210:   PetscCheck(tao->solution, PetscObjectComm((PetscObject)tao), PETSC_ERR_ARG_WRONGSTATE, "Must call TaoSetSolution");
211:   PetscTryTypeMethod(tao, setup);
212:   tao->setupcalled = PETSC_TRUE;
213:   PetscFunctionReturn(PETSC_SUCCESS);
214: }

216: /*@C
217:   TaoDestroy - Destroys the `Tao` context that was created with `TaoCreate()`

219:   Collective

221:   Input Parameter:
222: . tao - the `Tao` context

224:   Level: beginner

226: .seealso: [](chapter_tao), `Tao`, `TaoCreate()`, `TaoSolve()`
227: @*/
228: PetscErrorCode TaoDestroy(Tao *tao)
229: {
230:   PetscFunctionBegin;
231:   if (!*tao) PetscFunctionReturn(PETSC_SUCCESS);
233:   if (--((PetscObject)*tao)->refct > 0) {
234:     *tao = NULL;
235:     PetscFunctionReturn(PETSC_SUCCESS);
236:   }

238:   if ((*tao)->ops->destroy) PetscCall((*((*tao))->ops->destroy)(*tao));
239:   PetscCall(KSPDestroy(&(*tao)->ksp));
240:   PetscCall(SNESDestroy(&(*tao)->snes_ewdummy));
241:   PetscCall(TaoLineSearchDestroy(&(*tao)->linesearch));

243:   if ((*tao)->ops->convergencedestroy) {
244:     PetscCall((*(*tao)->ops->convergencedestroy)((*tao)->cnvP));
245:     if ((*tao)->jacobian_state_inv) PetscCall(MatDestroy(&(*tao)->jacobian_state_inv));
246:   }
247:   PetscCall(VecDestroy(&(*tao)->solution));
248:   PetscCall(VecDestroy(&(*tao)->gradient));
249:   PetscCall(VecDestroy(&(*tao)->ls_res));

251:   if ((*tao)->gradient_norm) {
252:     PetscCall(PetscObjectDereference((PetscObject)(*tao)->gradient_norm));
253:     PetscCall(VecDestroy(&(*tao)->gradient_norm_tmp));
254:   }

256:   PetscCall(VecDestroy(&(*tao)->XL));
257:   PetscCall(VecDestroy(&(*tao)->XU));
258:   PetscCall(VecDestroy(&(*tao)->IL));
259:   PetscCall(VecDestroy(&(*tao)->IU));
260:   PetscCall(VecDestroy(&(*tao)->DE));
261:   PetscCall(VecDestroy(&(*tao)->DI));
262:   PetscCall(VecDestroy(&(*tao)->constraints));
263:   PetscCall(VecDestroy(&(*tao)->constraints_equality));
264:   PetscCall(VecDestroy(&(*tao)->constraints_inequality));
265:   PetscCall(VecDestroy(&(*tao)->stepdirection));
266:   PetscCall(MatDestroy(&(*tao)->hessian_pre));
267:   PetscCall(MatDestroy(&(*tao)->hessian));
268:   PetscCall(MatDestroy(&(*tao)->ls_jac));
269:   PetscCall(MatDestroy(&(*tao)->ls_jac_pre));
270:   PetscCall(MatDestroy(&(*tao)->jacobian_pre));
271:   PetscCall(MatDestroy(&(*tao)->jacobian));
272:   PetscCall(MatDestroy(&(*tao)->jacobian_state_pre));
273:   PetscCall(MatDestroy(&(*tao)->jacobian_state));
274:   PetscCall(MatDestroy(&(*tao)->jacobian_state_inv));
275:   PetscCall(MatDestroy(&(*tao)->jacobian_design));
276:   PetscCall(MatDestroy(&(*tao)->jacobian_equality));
277:   PetscCall(MatDestroy(&(*tao)->jacobian_equality_pre));
278:   PetscCall(MatDestroy(&(*tao)->jacobian_inequality));
279:   PetscCall(MatDestroy(&(*tao)->jacobian_inequality_pre));
280:   PetscCall(ISDestroy(&(*tao)->state_is));
281:   PetscCall(ISDestroy(&(*tao)->design_is));
282:   PetscCall(VecDestroy(&(*tao)->res_weights_v));
283:   PetscCall(TaoCancelMonitors(*tao));
284:   if ((*tao)->hist_malloc) PetscCall(PetscFree4((*tao)->hist_obj, (*tao)->hist_resid, (*tao)->hist_cnorm, (*tao)->hist_lits));
285:   if ((*tao)->res_weights_n) {
286:     PetscCall(PetscFree((*tao)->res_weights_rows));
287:     PetscCall(PetscFree((*tao)->res_weights_cols));
288:     PetscCall(PetscFree((*tao)->res_weights_w));
289:   }
290:   PetscCall(PetscHeaderDestroy(tao));
291:   PetscFunctionReturn(PETSC_SUCCESS);
292: }

294: /*@
295:    TaoKSPSetUseEW - Sets `SNES` use Eisenstat-Walker method for computing relative tolerance for linear solvers.

297:    Logically Collective

299:    Input Parameters:
300: +  tao - Tao context
301: -  flag - `PETSC_TRUE` or `PETSC_FALSE`

303:    Level: advanced

305:    Note:
306:    See `SNESKSPSetUseEW()` for customization details.

308:    Reference:
309: .  * - S. C. Eisenstat and H. F. Walker, "Choosing the forcing terms in an inexact Newton method", SISC 17 (1), pp.16-32, 1996.

311: .seealso: [](chapter_tao), `Tao`, `SNESKSPSetUseEW()`
312: @*/
313: PetscErrorCode TaoKSPSetUseEW(Tao tao, PetscBool flag)
314: {
315:   PetscFunctionBegin;
318:   tao->ksp_ewconv = flag;
319:   PetscFunctionReturn(PETSC_SUCCESS);
320: }

322: /*@
323:   TaoSetFromOptions - Sets various Tao parameters from the options database

325:   Collective

327:   Input Parameter:
328: . tao - the `Tao` solver context

330:   Options Database Keys:
331: + -tao_type <type> - The algorithm that Tao uses (lmvm, nls, etc.)
332: . -tao_gatol <gatol> - absolute error tolerance for ||gradient||
333: . -tao_grtol <grtol> - relative error tolerance for ||gradient||
334: . -tao_gttol <gttol> - reduction of ||gradient|| relative to initial gradient
335: . -tao_max_it <max> - sets maximum number of iterations
336: . -tao_max_funcs <max> - sets maximum number of function evaluations
337: . -tao_fmin <fmin> - stop if function value reaches fmin
338: . -tao_steptol <tol> - stop if trust region radius less than <tol>
339: . -tao_trust0 <t> - initial trust region radius
340: . -tao_monitor - prints function value and residual norm at each iteration
341: . -tao_smonitor - same as tao_monitor, but truncates very small values
342: . -tao_cmonitor - prints function value, residual, and constraint norm at each iteration
343: . -tao_view_solution - prints solution vector at each iteration
344: . -tao_view_ls_residual - prints least-squares residual vector at each iteration
345: . -tao_view_stepdirection - prints step direction vector at each iteration
346: . -tao_view_gradient - prints gradient vector at each iteration
347: . -tao_draw_solution - graphically view solution vector at each iteration
348: . -tao_draw_step - graphically view step vector at each iteration
349: . -tao_draw_gradient - graphically view gradient at each iteration
350: . -tao_fd_gradient - use gradient computed with finite differences
351: . -tao_fd_hessian - use hessian computed with finite differences
352: . -tao_mf_hessian - use matrix-free hessian computed with finite differences
353: . -tao_cancelmonitors - cancels all monitors (except those set with command line)
354: . -tao_view - prints information about the Tao after solving
355: - -tao_converged_reason - prints the reason Tao stopped iterating

357:   Level: beginner

359:   Note:
360:   To see all options, run your program with the `-help` option or consult the
361:  user's manual. Should be called after `TaoCreate()` but before `TaoSolve()`

363: .seealso: [](chapter_tao), `Tao`, `TaoCreate()`, `TaoSolve()`
364: @*/
365: PetscErrorCode TaoSetFromOptions(Tao tao)
366: {
367:   TaoType     default_type = TAOLMVM;
368:   char        type[256], monfilename[PETSC_MAX_PATH_LEN];
369:   PetscViewer monviewer;
370:   PetscBool   flg;
371:   MPI_Comm    comm;

373:   PetscFunctionBegin;
375:   PetscCall(PetscObjectGetComm((PetscObject)tao, &comm));

377:   if (((PetscObject)tao)->type_name) default_type = ((PetscObject)tao)->type_name;

379:   PetscObjectOptionsBegin((PetscObject)tao);
380:   /* Check for type from options */
381:   PetscCall(PetscOptionsFList("-tao_type", "Tao Solver type", "TaoSetType", TaoList, default_type, type, 256, &flg));
382:   if (flg) {
383:     PetscCall(TaoSetType(tao, type));
384:   } else if (!((PetscObject)tao)->type_name) {
385:     PetscCall(TaoSetType(tao, default_type));
386:   }

388:   /* Tao solvers do not set the prefix, set it here if not yet done
389:      We do it after SetType since solver may have been changed */
390:   if (tao->linesearch) {
391:     const char *prefix;
392:     PetscCall(TaoLineSearchGetOptionsPrefix(tao->linesearch, &prefix));
393:     if (!prefix) PetscCall(TaoLineSearchSetOptionsPrefix(tao->linesearch, ((PetscObject)(tao))->prefix));
394:   }

396:   PetscCall(PetscOptionsReal("-tao_catol", "Stop if constraints violations within", "TaoSetConstraintTolerances", tao->catol, &tao->catol, &flg));
397:   if (flg) tao->catol_changed = PETSC_TRUE;
398:   PetscCall(PetscOptionsReal("-tao_crtol", "Stop if relative constraint violations within", "TaoSetConstraintTolerances", tao->crtol, &tao->crtol, &flg));
399:   if (flg) tao->crtol_changed = PETSC_TRUE;
400:   PetscCall(PetscOptionsReal("-tao_gatol", "Stop if norm of gradient less than", "TaoSetTolerances", tao->gatol, &tao->gatol, &flg));
401:   if (flg) tao->gatol_changed = PETSC_TRUE;
402:   PetscCall(PetscOptionsReal("-tao_grtol", "Stop if norm of gradient divided by the function value is less than", "TaoSetTolerances", tao->grtol, &tao->grtol, &flg));
403:   if (flg) tao->grtol_changed = PETSC_TRUE;
404:   PetscCall(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));
405:   if (flg) tao->gttol_changed = PETSC_TRUE;
406:   PetscCall(PetscOptionsInt("-tao_max_it", "Stop if iteration number exceeds", "TaoSetMaximumIterations", tao->max_it, &tao->max_it, &flg));
407:   if (flg) tao->max_it_changed = PETSC_TRUE;
408:   PetscCall(PetscOptionsInt("-tao_max_funcs", "Stop if number of function evaluations exceeds", "TaoSetMaximumFunctionEvaluations", tao->max_funcs, &tao->max_funcs, &flg));
409:   if (flg) tao->max_funcs_changed = PETSC_TRUE;
410:   PetscCall(PetscOptionsReal("-tao_fmin", "Stop if function less than", "TaoSetFunctionLowerBound", tao->fmin, &tao->fmin, &flg));
411:   if (flg) tao->fmin_changed = PETSC_TRUE;
412:   PetscCall(PetscOptionsReal("-tao_steptol", "Stop if step size or trust region radius less than", "", tao->steptol, &tao->steptol, &flg));
413:   if (flg) tao->steptol_changed = PETSC_TRUE;
414:   PetscCall(PetscOptionsReal("-tao_trust0", "Initial trust region radius", "TaoSetTrustRegionRadius", tao->trust0, &tao->trust0, &flg));
415:   if (flg) tao->trust0_changed = PETSC_TRUE;
416:   PetscCall(PetscOptionsString("-tao_view_solution", "view solution vector after each evaluation", "TaoSetMonitor", "stdout", monfilename, sizeof(monfilename), &flg));
417:   if (flg) {
418:     PetscCall(PetscViewerASCIIOpen(comm, monfilename, &monviewer));
419:     PetscCall(TaoSetMonitor(tao, TaoSolutionMonitor, monviewer, (PetscErrorCode(*)(void **))PetscViewerDestroy));
420:   }

422:   PetscCall(PetscOptionsBool("-tao_converged_reason", "Print reason for Tao converged", "TaoSolve", tao->printreason, &tao->printreason, NULL));
423:   PetscCall(PetscOptionsString("-tao_view_gradient", "view gradient vector after each evaluation", "TaoSetMonitor", "stdout", monfilename, sizeof(monfilename), &flg));
424:   if (flg) {
425:     PetscCall(PetscViewerASCIIOpen(comm, monfilename, &monviewer));
426:     PetscCall(TaoSetMonitor(tao, TaoGradientMonitor, monviewer, (PetscErrorCode(*)(void **))PetscViewerDestroy));
427:   }

429:   PetscCall(PetscOptionsString("-tao_view_stepdirection", "view step direction vector after each iteration", "TaoSetMonitor", "stdout", monfilename, sizeof(monfilename), &flg));
430:   if (flg) {
431:     PetscCall(PetscViewerASCIIOpen(comm, monfilename, &monviewer));
432:     PetscCall(TaoSetMonitor(tao, TaoStepDirectionMonitor, monviewer, (PetscErrorCode(*)(void **))PetscViewerDestroy));
433:   }

435:   PetscCall(PetscOptionsString("-tao_view_residual", "view least-squares residual vector after each evaluation", "TaoSetMonitor", "stdout", monfilename, sizeof(monfilename), &flg));
436:   if (flg) {
437:     PetscCall(PetscViewerASCIIOpen(comm, monfilename, &monviewer));
438:     PetscCall(TaoSetMonitor(tao, TaoResidualMonitor, monviewer, (PetscErrorCode(*)(void **))PetscViewerDestroy));
439:   }

441:   PetscCall(PetscOptionsString("-tao_monitor", "Use the default convergence monitor", "TaoSetMonitor", "stdout", monfilename, sizeof(monfilename), &flg));
442:   if (flg) {
443:     PetscCall(PetscViewerASCIIOpen(comm, monfilename, &monviewer));
444:     PetscCall(TaoSetMonitor(tao, TaoMonitorDefault, monviewer, (PetscErrorCode(*)(void **))PetscViewerDestroy));
445:   }

447:   PetscCall(PetscOptionsString("-tao_gmonitor", "Use the convergence monitor with extra globalization info", "TaoSetMonitor", "stdout", monfilename, sizeof(monfilename), &flg));
448:   if (flg) {
449:     PetscCall(PetscViewerASCIIOpen(comm, monfilename, &monviewer));
450:     PetscCall(TaoSetMonitor(tao, TaoDefaultGMonitor, monviewer, (PetscErrorCode(*)(void **))PetscViewerDestroy));
451:   }

453:   PetscCall(PetscOptionsString("-tao_smonitor", "Use the short convergence monitor", "TaoSetMonitor", "stdout", monfilename, sizeof(monfilename), &flg));
454:   if (flg) {
455:     PetscCall(PetscViewerASCIIOpen(comm, monfilename, &monviewer));
456:     PetscCall(TaoSetMonitor(tao, TaoDefaultSMonitor, monviewer, (PetscErrorCode(*)(void **))PetscViewerDestroy));
457:   }

459:   PetscCall(PetscOptionsString("-tao_cmonitor", "Use the default convergence monitor with constraint norm", "TaoSetMonitor", "stdout", monfilename, sizeof(monfilename), &flg));
460:   if (flg) {
461:     PetscCall(PetscViewerASCIIOpen(comm, monfilename, &monviewer));
462:     PetscCall(TaoSetMonitor(tao, TaoDefaultCMonitor, monviewer, (PetscErrorCode(*)(void **))PetscViewerDestroy));
463:   }

465:   flg = PETSC_FALSE;
466:   PetscCall(PetscOptionsBool("-tao_cancelmonitors", "cancel all monitors and call any registered destroy routines", "TaoCancelMonitors", flg, &flg, NULL));
467:   if (flg) PetscCall(TaoCancelMonitors(tao));

469:   flg = PETSC_FALSE;
470:   PetscCall(PetscOptionsBool("-tao_draw_solution", "Plot solution vector at each iteration", "TaoSetMonitor", flg, &flg, NULL));
471:   if (flg) {
472:     TaoMonitorDrawCtx drawctx;
473:     PetscInt          howoften = 1;
474:     PetscCall(TaoMonitorDrawCtxCreate(PetscObjectComm((PetscObject)tao), NULL, NULL, PETSC_DECIDE, PETSC_DECIDE, 300, 300, howoften, &drawctx));
475:     PetscCall(TaoSetMonitor(tao, TaoDrawSolutionMonitor, drawctx, (PetscErrorCode(*)(void **))TaoMonitorDrawCtxDestroy));
476:   }

478:   flg = PETSC_FALSE;
479:   PetscCall(PetscOptionsBool("-tao_draw_step", "plots step direction at each iteration", "TaoSetMonitor", flg, &flg, NULL));
480:   if (flg) PetscCall(TaoSetMonitor(tao, TaoDrawStepMonitor, NULL, NULL));

482:   flg = PETSC_FALSE;
483:   PetscCall(PetscOptionsBool("-tao_draw_gradient", "plots gradient at each iteration", "TaoSetMonitor", flg, &flg, NULL));
484:   if (flg) {
485:     TaoMonitorDrawCtx drawctx;
486:     PetscInt          howoften = 1;
487:     PetscCall(TaoMonitorDrawCtxCreate(PetscObjectComm((PetscObject)tao), NULL, NULL, PETSC_DECIDE, PETSC_DECIDE, 300, 300, howoften, &drawctx));
488:     PetscCall(TaoSetMonitor(tao, TaoDrawGradientMonitor, drawctx, (PetscErrorCode(*)(void **))TaoMonitorDrawCtxDestroy));
489:   }
490:   flg = PETSC_FALSE;
491:   PetscCall(PetscOptionsBool("-tao_fd_gradient", "compute gradient using finite differences", "TaoDefaultComputeGradient", flg, &flg, NULL));
492:   if (flg) PetscCall(TaoSetGradient(tao, NULL, TaoDefaultComputeGradient, NULL));
493:   flg = PETSC_FALSE;
494:   PetscCall(PetscOptionsBool("-tao_fd_hessian", "compute hessian using finite differences", "TaoDefaultComputeHessian", flg, &flg, NULL));
495:   if (flg) {
496:     Mat H;

498:     PetscCall(MatCreate(PetscObjectComm((PetscObject)tao), &H));
499:     PetscCall(MatSetType(H, MATAIJ));
500:     PetscCall(TaoSetHessian(tao, H, H, TaoDefaultComputeHessian, NULL));
501:     PetscCall(MatDestroy(&H));
502:   }
503:   flg = PETSC_FALSE;
504:   PetscCall(PetscOptionsBool("-tao_mf_hessian", "compute matrix-free hessian using finite differences", "TaoDefaultComputeHessianMFFD", flg, &flg, NULL));
505:   if (flg) {
506:     Mat H;

508:     PetscCall(MatCreate(PetscObjectComm((PetscObject)tao), &H));
509:     PetscCall(TaoSetHessian(tao, H, H, TaoDefaultComputeHessianMFFD, NULL));
510:     PetscCall(MatDestroy(&H));
511:   }
512:   flg = PETSC_FALSE;
513:   PetscCall(PetscOptionsBool("-tao_recycle_history", "enable recycling/re-using information from the previous TaoSolve() call for some algorithms", "TaoSetRecycleHistory", flg, &flg, NULL));
514:   if (flg) PetscCall(TaoSetRecycleHistory(tao, PETSC_TRUE));
515:   PetscCall(PetscOptionsEnum("-tao_subset_type", "subset type", "", TaoSubSetTypes, (PetscEnum)tao->subset_type, (PetscEnum *)&tao->subset_type, NULL));

517:   if (tao->ksp) {
518:     PetscCall(PetscOptionsBool("-tao_ksp_ew", "Use Eisentat-Walker linear system convergence test", "TaoKSPSetUseEW", tao->ksp_ewconv, &tao->ksp_ewconv, NULL));
519:     PetscCall(TaoKSPSetUseEW(tao, tao->ksp_ewconv));
520:   }

522:   PetscTryTypeMethod(tao, setfromoptions, PetscOptionsObject);

524:   /* process any options handlers added with PetscObjectAddOptionsHandler() */
525:   PetscCall(PetscObjectProcessOptionsHandlers((PetscObject)tao, PetscOptionsObject));
526:   PetscOptionsEnd();

528:   if (tao->linesearch) PetscCall(TaoLineSearchSetFromOptions(tao->linesearch));
529:   PetscFunctionReturn(PETSC_SUCCESS);
530: }

532: /*@C
533:    TaoViewFromOptions - View a `Tao` object based on values in the options database

535:    Collective

537:    Input Parameters:
538: +  A - the  `Tao` context
539: .  obj - Optional object that provides the prefix for the options database
540: -  name - command line option

542:    Level: intermediate

544: .seealso: [](chapter_tao), `Tao`, `TaoView`, `PetscObjectViewFromOptions()`, `TaoCreate()`
545: @*/
546: PetscErrorCode TaoViewFromOptions(Tao A, PetscObject obj, const char name[])
547: {
548:   PetscFunctionBegin;
550:   PetscCall(PetscObjectViewFromOptions((PetscObject)A, obj, name));
551:   PetscFunctionReturn(PETSC_SUCCESS);
552: }

554: /*@C
555:   TaoView - Prints information about the `Tao` object

557:   Collective

559:   InputParameters:
560: + tao - the `Tao` context
561: - viewer - visualization context

563:   Options Database Key:
564: . -tao_view - Calls `TaoView()` at the end of `TaoSolve()`

566:   Level: beginner

568:   Notes:
569:   The available visualization contexts include
570: +     `PETSC_VIEWER_STDOUT_SELF` - standard output (default)
571: -     `PETSC_VIEWER_STDOUT_WORLD` - synchronized standard
572:          output where only the first processor opens
573:          the file.  All other processors send their
574:          data to the first processor to print.

576: .seealso: [](chapter_tao), `Tao`, `PetscViewerASCIIOpen()`
577: @*/
578: PetscErrorCode TaoView(Tao tao, PetscViewer viewer)
579: {
580:   PetscBool isascii, isstring;
581:   TaoType   type;

583:   PetscFunctionBegin;
585:   if (!viewer) PetscCall(PetscViewerASCIIGetStdout(((PetscObject)tao)->comm, &viewer));
587:   PetscCheckSameComm(tao, 1, viewer, 2);

589:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
590:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSTRING, &isstring));
591:   if (isascii) {
592:     PetscCall(PetscObjectPrintClassNamePrefixType((PetscObject)tao, viewer));

594:     if (tao->ops->view) {
595:       PetscCall(PetscViewerASCIIPushTab(viewer));
596:       PetscUseTypeMethod(tao, view, viewer);
597:       PetscCall(PetscViewerASCIIPopTab(viewer));
598:     }
599:     if (tao->linesearch) {
600:       PetscCall(PetscViewerASCIIPushTab(viewer));
601:       PetscCall(TaoLineSearchView(tao->linesearch, viewer));
602:       PetscCall(PetscViewerASCIIPopTab(viewer));
603:     }
604:     if (tao->ksp) {
605:       PetscCall(PetscViewerASCIIPushTab(viewer));
606:       PetscCall(KSPView(tao->ksp, viewer));
607:       PetscCall(PetscViewerASCIIPrintf(viewer, "total KSP iterations: %" PetscInt_FMT "\n", tao->ksp_tot_its));
608:       PetscCall(PetscViewerASCIIPopTab(viewer));
609:     }

611:     PetscCall(PetscViewerASCIIPushTab(viewer));

613:     if (tao->XL || tao->XU) PetscCall(PetscViewerASCIIPrintf(viewer, "Active Set subset type: %s\n", TaoSubSetTypes[tao->subset_type]));

615:     PetscCall(PetscViewerASCIIPrintf(viewer, "convergence tolerances: gatol=%g,", (double)tao->gatol));
616:     PetscCall(PetscViewerASCIIPrintf(viewer, " steptol=%g,", (double)tao->steptol));
617:     PetscCall(PetscViewerASCIIPrintf(viewer, " gttol=%g\n", (double)tao->gttol));
618:     PetscCall(PetscViewerASCIIPrintf(viewer, "Residual in Function/Gradient:=%g\n", (double)tao->residual));

620:     if (tao->constrained) {
621:       PetscCall(PetscViewerASCIIPrintf(viewer, "convergence tolerances:"));
622:       PetscCall(PetscViewerASCIIPrintf(viewer, " catol=%g,", (double)tao->catol));
623:       PetscCall(PetscViewerASCIIPrintf(viewer, " crtol=%g\n", (double)tao->crtol));
624:       PetscCall(PetscViewerASCIIPrintf(viewer, "Residual in Constraints:=%g\n", (double)tao->cnorm));
625:     }

627:     if (tao->trust < tao->steptol) {
628:       PetscCall(PetscViewerASCIIPrintf(viewer, "convergence tolerances: steptol=%g\n", (double)tao->steptol));
629:       PetscCall(PetscViewerASCIIPrintf(viewer, "Final trust region radius:=%g\n", (double)tao->trust));
630:     }

632:     if (tao->fmin > -1.e25) PetscCall(PetscViewerASCIIPrintf(viewer, "convergence tolerances: function minimum=%g\n", (double)tao->fmin));
633:     PetscCall(PetscViewerASCIIPrintf(viewer, "Objective value=%g\n", (double)tao->fc));

635:     PetscCall(PetscViewerASCIIPrintf(viewer, "total number of iterations=%" PetscInt_FMT ",          ", tao->niter));
636:     PetscCall(PetscViewerASCIIPrintf(viewer, "              (max: %" PetscInt_FMT ")\n", tao->max_it));

638:     if (tao->nfuncs > 0) {
639:       PetscCall(PetscViewerASCIIPrintf(viewer, "total number of function evaluations=%" PetscInt_FMT ",", tao->nfuncs));
640:       PetscCall(PetscViewerASCIIPrintf(viewer, "                max: %" PetscInt_FMT "\n", tao->max_funcs));
641:     }
642:     if (tao->ngrads > 0) {
643:       PetscCall(PetscViewerASCIIPrintf(viewer, "total number of gradient evaluations=%" PetscInt_FMT ",", tao->ngrads));
644:       PetscCall(PetscViewerASCIIPrintf(viewer, "                max: %" PetscInt_FMT "\n", tao->max_funcs));
645:     }
646:     if (tao->nfuncgrads > 0) {
647:       PetscCall(PetscViewerASCIIPrintf(viewer, "total number of function/gradient evaluations=%" PetscInt_FMT ",", tao->nfuncgrads));
648:       PetscCall(PetscViewerASCIIPrintf(viewer, "    (max: %" PetscInt_FMT ")\n", tao->max_funcs));
649:     }
650:     if (tao->nhess > 0) PetscCall(PetscViewerASCIIPrintf(viewer, "total number of Hessian evaluations=%" PetscInt_FMT "\n", tao->nhess));
651:     if (tao->nconstraints > 0) PetscCall(PetscViewerASCIIPrintf(viewer, "total number of constraint function evaluations=%" PetscInt_FMT "\n", tao->nconstraints));
652:     if (tao->njac > 0) PetscCall(PetscViewerASCIIPrintf(viewer, "total number of Jacobian evaluations=%" PetscInt_FMT "\n", tao->njac));

654:     if (tao->reason > 0) {
655:       PetscCall(PetscViewerASCIIPrintf(viewer, "Solution converged: "));
656:       switch (tao->reason) {
657:       case TAO_CONVERGED_GATOL:
658:         PetscCall(PetscViewerASCIIPrintf(viewer, " ||g(X)|| <= gatol\n"));
659:         break;
660:       case TAO_CONVERGED_GRTOL:
661:         PetscCall(PetscViewerASCIIPrintf(viewer, " ||g(X)||/|f(X)| <= grtol\n"));
662:         break;
663:       case TAO_CONVERGED_GTTOL:
664:         PetscCall(PetscViewerASCIIPrintf(viewer, " ||g(X)||/||g(X0)|| <= gttol\n"));
665:         break;
666:       case TAO_CONVERGED_STEPTOL:
667:         PetscCall(PetscViewerASCIIPrintf(viewer, " Steptol -- step size small\n"));
668:         break;
669:       case TAO_CONVERGED_MINF:
670:         PetscCall(PetscViewerASCIIPrintf(viewer, " Minf --  f < fmin\n"));
671:         break;
672:       case TAO_CONVERGED_USER:
673:         PetscCall(PetscViewerASCIIPrintf(viewer, " User Terminated\n"));
674:         break;
675:       default:
676:         PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
677:         break;
678:       }
679:     } else {
680:       PetscCall(PetscViewerASCIIPrintf(viewer, "Solver terminated: %d", tao->reason));
681:       switch (tao->reason) {
682:       case TAO_DIVERGED_MAXITS:
683:         PetscCall(PetscViewerASCIIPrintf(viewer, " Maximum Iterations\n"));
684:         break;
685:       case TAO_DIVERGED_NAN:
686:         PetscCall(PetscViewerASCIIPrintf(viewer, " NAN or Inf encountered\n"));
687:         break;
688:       case TAO_DIVERGED_MAXFCN:
689:         PetscCall(PetscViewerASCIIPrintf(viewer, " Maximum Function Evaluations\n"));
690:         break;
691:       case TAO_DIVERGED_LS_FAILURE:
692:         PetscCall(PetscViewerASCIIPrintf(viewer, " Line Search Failure\n"));
693:         break;
694:       case TAO_DIVERGED_TR_REDUCTION:
695:         PetscCall(PetscViewerASCIIPrintf(viewer, " Trust Region too small\n"));
696:         break;
697:       case TAO_DIVERGED_USER:
698:         PetscCall(PetscViewerASCIIPrintf(viewer, " User Terminated\n"));
699:         break;
700:       default:
701:         PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
702:         break;
703:       }
704:     }
705:     PetscCall(PetscViewerASCIIPopTab(viewer));
706:   } else if (isstring) {
707:     PetscCall(TaoGetType(tao, &type));
708:     PetscCall(PetscViewerStringSPrintf(viewer, " %-3.3s", type));
709:   }
710:   PetscFunctionReturn(PETSC_SUCCESS);
711: }

713: /*@
714:   TaoSetRecycleHistory - Sets the boolean flag to enable/disable re-using
715:   iterate information from the previous `TaoSolve()`. This feature is disabled by
716:   default.

718:   Logically Collective

720:   Input Parameters:
721: + tao - the `Tao` context
722: - recycle - boolean flag

724:   Options Database Key:
725: . -tao_recycle_history <true,false> - reuse the history

727:   Level: intermediate

729:   Notes:
730:   For conjugate gradient methods (`TAOBNCG`), this re-uses the latest search direction
731:   from the previous `TaoSolve()` call when computing the first search direction in a
732:   new solution. By default, CG methods set the first search direction to the
733:   negative gradient.

735:   For quasi-Newton family of methods (`TAOBQNLS`, `TAOBQNKLS`, `TAOBQNKTR`, `TAOBQNKTL`), this re-uses
736:   the accumulated quasi-Newton Hessian approximation from the previous `TaoSolve()`
737:   call. By default, QN family of methods reset the initial Hessian approximation to
738:   the identity matrix.

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

742: .seealso: [](chapter_tao), `Tao`, `TaoGetRecycleHistory()`, `TAOBNCG`, `TAOBQNLS`, `TAOBQNKLS`, `TAOBQNKTR`, `TAOBQNKTL`
743: @*/
744: PetscErrorCode TaoSetRecycleHistory(Tao tao, PetscBool recycle)
745: {
746:   PetscFunctionBegin;
749:   tao->recycle = recycle;
750:   PetscFunctionReturn(PETSC_SUCCESS);
751: }

753: /*@
754:   TaoGetRecycleHistory - Retrieve the boolean flag for re-using iterate information
755:   from the previous `TaoSolve()`. This feature is disabled by default.

757:   Logically Collective

759:   Input Parameter:
760: . tao - the `Tao` context

762:   Output Parameter:
763: . recycle - boolean flag

765:   Level: intermediate

767: .seealso: [](chapter_tao), `Tao`, `TaoSetRecycleHistory()`, `TAOBNCG`, `TAOBQNLS`, `TAOBQNKLS`, `TAOBQNKTR`, `TAOBQNKTL`
768: @*/
769: PetscErrorCode TaoGetRecycleHistory(Tao tao, PetscBool *recycle)
770: {
771:   PetscFunctionBegin;
774:   *recycle = tao->recycle;
775:   PetscFunctionReturn(PETSC_SUCCESS);
776: }

778: /*@
779:   TaoSetTolerances - Sets parameters used in `TaoSolve()` convergence tests

781:   Logically Collective

783:   Input Parameters:
784: + tao - the `Tao` context
785: . gatol - stop if norm of gradient is less than this
786: . grtol - stop if relative norm of gradient is less than this
787: - gttol - stop if norm of gradient is reduced by this factor

789:   Options Database Keys:
790: + -tao_gatol <gatol> - Sets gatol
791: . -tao_grtol <grtol> - Sets grtol
792: - -tao_gttol <gttol> - Sets gttol

794:   Stopping Criteria:
795: .vb
796:   ||g(X)||                            <= gatol
797:   ||g(X)|| / |f(X)|                   <= grtol
798:   ||g(X)|| / ||g(X0)||                <= gttol
799: .ve

801:   Level: beginner

803:   Note:
804:   Use `PETSC_DEFAULT` to leave one or more tolerances unchanged.

806: .seealso: [](chapter_tao), `Tao`, `TaoConvergedReason`, `TaoGetTolerances()`
807: @*/
808: PetscErrorCode TaoSetTolerances(Tao tao, PetscReal gatol, PetscReal grtol, PetscReal gttol)
809: {
810:   PetscFunctionBegin;

816:   if (gatol != PETSC_DEFAULT) {
817:     if (gatol < 0) {
818:       PetscCall(PetscInfo(tao, "Tried to set negative gatol -- ignored.\n"));
819:     } else {
820:       tao->gatol         = PetscMax(0, gatol);
821:       tao->gatol_changed = PETSC_TRUE;
822:     }
823:   }

825:   if (grtol != PETSC_DEFAULT) {
826:     if (grtol < 0) {
827:       PetscCall(PetscInfo(tao, "Tried to set negative grtol -- ignored.\n"));
828:     } else {
829:       tao->grtol         = PetscMax(0, grtol);
830:       tao->grtol_changed = PETSC_TRUE;
831:     }
832:   }

834:   if (gttol != PETSC_DEFAULT) {
835:     if (gttol < 0) {
836:       PetscCall(PetscInfo(tao, "Tried to set negative gttol -- ignored.\n"));
837:     } else {
838:       tao->gttol         = PetscMax(0, gttol);
839:       tao->gttol_changed = PETSC_TRUE;
840:     }
841:   }
842:   PetscFunctionReturn(PETSC_SUCCESS);
843: }

845: /*@
846:   TaoSetConstraintTolerances - Sets constraint tolerance parameters used in `TaoSolve()` convergence tests

848:   Logically Collective

850:   Input Parameters:
851: + tao - the `Tao` context
852: . catol - absolute constraint tolerance, constraint norm must be less than `catol` for used for gatol convergence criteria
853: - crtol - relative constraint tolerance, constraint norm must be less than `crtol` for used for gatol, gttol convergence criteria

855:   Options Database Keys:
856: + -tao_catol <catol> - Sets catol
857: - -tao_crtol <crtol> - Sets crtol

859:   Level: intermediate

861:   Notes:
862:   Use `PETSC_DEFAULT` to leave any tolerance unchanged.

864: .seealso: [](chapter_tao), `Tao`, `TaoConvergedReason`, `TaoGetTolerances()`, `TaoGetConstraintTolerances()`, `TaoSetTolerances()`
865: @*/
866: PetscErrorCode TaoSetConstraintTolerances(Tao tao, PetscReal catol, PetscReal crtol)
867: {
868:   PetscFunctionBegin;

873:   if (catol != PETSC_DEFAULT) {
874:     if (catol < 0) {
875:       PetscCall(PetscInfo(tao, "Tried to set negative catol -- ignored.\n"));
876:     } else {
877:       tao->catol         = PetscMax(0, catol);
878:       tao->catol_changed = PETSC_TRUE;
879:     }
880:   }

882:   if (crtol != PETSC_DEFAULT) {
883:     if (crtol < 0) {
884:       PetscCall(PetscInfo(tao, "Tried to set negative crtol -- ignored.\n"));
885:     } else {
886:       tao->crtol         = PetscMax(0, crtol);
887:       tao->crtol_changed = PETSC_TRUE;
888:     }
889:   }
890:   PetscFunctionReturn(PETSC_SUCCESS);
891: }

893: /*@
894:   TaoGetConstraintTolerances - Gets constraint tolerance parameters used in `TaoSolve()` convergence tests

896:   Not Collective

898:   Input Parameter:
899: . tao - the `Tao` context

901:   Output Parameters:
902: + catol - absolute constraint tolerance, constraint norm must be less than `catol` for used for gatol convergence criteria
903: - crtol - relative constraint tolerance, constraint norm must be less than `crtol` for used for gatol, gttol convergence criteria

905:   Level: intermediate

907: .seealso: [](chapter_tao), `Tao`, `TaoConvergedReasons`,`TaoGetTolerances()`, `TaoSetTolerances()`, `TaoSetConstraintTolerances()`
908: @*/
909: PetscErrorCode TaoGetConstraintTolerances(Tao tao, PetscReal *catol, PetscReal *crtol)
910: {
911:   PetscFunctionBegin;
913:   if (catol) *catol = tao->catol;
914:   if (crtol) *crtol = tao->crtol;
915:   PetscFunctionReturn(PETSC_SUCCESS);
916: }

918: /*@
919:    TaoSetFunctionLowerBound - Sets a bound on the solution objective value.
920:    When an approximate solution with an objective value below this number
921:    has been found, the solver will terminate.

923:    Logically Collective

925:    Input Parameters:
926: +  tao - the Tao solver context
927: -  fmin - the tolerance

929:    Options Database Key:
930: .    -tao_fmin <fmin> - sets the minimum function value

932:    Level: intermediate

934: .seealso: [](chapter_tao), `Tao`, `TaoConvergedReason`, `TaoSetTolerances()`
935: @*/
936: PetscErrorCode TaoSetFunctionLowerBound(Tao tao, PetscReal fmin)
937: {
938:   PetscFunctionBegin;
941:   tao->fmin         = fmin;
942:   tao->fmin_changed = PETSC_TRUE;
943:   PetscFunctionReturn(PETSC_SUCCESS);
944: }

946: /*@
947:    TaoGetFunctionLowerBound - Gets the bound on the solution objective value.
948:    When an approximate solution with an objective value below this number
949:    has been found, the solver will terminate.

951:    Not Collective

953:    Input Parameter:
954: .  tao - the `Tao` solver context

956:    OutputParameter:
957: .  fmin - the minimum function value

959:    Level: intermediate

961: .seealso: [](chapter_tao), `Tao`, `TaoConvergedReason`, `TaoSetFunctionLowerBound()`
962: @*/
963: PetscErrorCode TaoGetFunctionLowerBound(Tao tao, PetscReal *fmin)
964: {
965:   PetscFunctionBegin;
968:   *fmin = tao->fmin;
969:   PetscFunctionReturn(PETSC_SUCCESS);
970: }

972: /*@
973:    TaoSetMaximumFunctionEvaluations - Sets a maximum number of function evaluations allowed for a `TaoSolve()`.

975:    Logically Collective

977:    Input Parameters:
978: +  tao - the `Tao` solver context
979: -  nfcn - the maximum number of function evaluations (>=0)

981:    Options Database Key:
982: .    -tao_max_funcs <nfcn> - sets the maximum number of function evaluations

984:    Level: intermediate

986: .seealso: [](chapter_tao), `Tao`, `TaoSetTolerances()`, `TaoSetMaximumIterations()`
987: @*/
988: PetscErrorCode TaoSetMaximumFunctionEvaluations(Tao tao, PetscInt nfcn)
989: {
990:   PetscFunctionBegin;
993:   if (nfcn >= 0) {
994:     tao->max_funcs = PetscMax(0, nfcn);
995:   } else {
996:     tao->max_funcs = -1;
997:   }
998:   tao->max_funcs_changed = PETSC_TRUE;
999:   PetscFunctionReturn(PETSC_SUCCESS);
1000: }

1002: /*@
1003:    TaoGetMaximumFunctionEvaluations - Gets a maximum number of function evaluations allowed for a `TaoSolve()`

1005:    Logically Collective

1007:    Input Parameter:
1008: .  tao - the `Tao` solver context

1010:    Output Parameter:
1011: .  nfcn - the maximum number of function evaluations

1013:    Level: intermediate

1015: .seealso: [](chapter_tao), `Tao`, `TaoSetMaximumFunctionEvaluations()`, `TaoGetMaximumIterations()`
1016: @*/
1017: PetscErrorCode TaoGetMaximumFunctionEvaluations(Tao tao, PetscInt *nfcn)
1018: {
1019:   PetscFunctionBegin;
1022:   *nfcn = tao->max_funcs;
1023:   PetscFunctionReturn(PETSC_SUCCESS);
1024: }

1026: /*@
1027:    TaoGetCurrentFunctionEvaluations - Get current number of function evaluations used by a `Tao` object

1029:    Not Collective

1031:    Input Parameter:
1032: .  tao - the `Tao` solver context

1034:    Output Parameter:
1035: .  nfuncs - the current number of function evaluations (maximum between gradient and function evaluations)

1037:    Level: intermediate

1039: .seealso: [](chapter_tao), `Tao`, `TaoSetMaximumFunctionEvaluations()`, `TaoGetMaximumFunctionEvaluations()`, `TaoGetMaximumIterations()`
1040: @*/
1041: PetscErrorCode TaoGetCurrentFunctionEvaluations(Tao tao, PetscInt *nfuncs)
1042: {
1043:   PetscFunctionBegin;
1046:   *nfuncs = PetscMax(tao->nfuncs, tao->nfuncgrads);
1047:   PetscFunctionReturn(PETSC_SUCCESS);
1048: }

1050: /*@
1051:    TaoSetMaximumIterations - Sets a maximum number of iterates to be used in `TaoSolve()`

1053:    Logically Collective

1055:    Input Parameters:
1056: +  tao - the `Tao` solver context
1057: -  maxits - the maximum number of iterates (>=0)

1059:    Options Database Key:
1060: .  -tao_max_it <its> - sets the maximum number of iterations

1062:    Level: intermediate

1064: .seealso: [](chapter_tao), `Tao`, `TaoSetTolerances()`, `TaoSetMaximumFunctionEvaluations()`
1065: @*/
1066: PetscErrorCode TaoSetMaximumIterations(Tao tao, PetscInt maxits)
1067: {
1068:   PetscFunctionBegin;
1071:   tao->max_it         = PetscMax(0, maxits);
1072:   tao->max_it_changed = PETSC_TRUE;
1073:   PetscFunctionReturn(PETSC_SUCCESS);
1074: }

1076: /*@
1077:    TaoGetMaximumIterations - Gets a maximum number of iterates that will be used

1079:    Not Collective

1081:    Input Parameter:
1082: .  tao - the `Tao` solver context

1084:    Output Parameter:
1085: .  maxits - the maximum number of iterates

1087:    Level: intermediate

1089: .seealso: [](chapter_tao), `Tao`, `TaoSetMaximumIterations()`, `TaoGetMaximumFunctionEvaluations()`
1090: @*/
1091: PetscErrorCode TaoGetMaximumIterations(Tao tao, PetscInt *maxits)
1092: {
1093:   PetscFunctionBegin;
1096:   *maxits = tao->max_it;
1097:   PetscFunctionReturn(PETSC_SUCCESS);
1098: }

1100: /*@
1101:    TaoSetInitialTrustRegionRadius - Sets the initial trust region radius.

1103:    Logically Collective

1105:    Input Parameters:
1106: +  tao - a `Tao` optimization solver
1107: -  radius - the trust region radius

1109:    Options Database Key:
1110: .  -tao_trust0 <t0> - sets initial trust region radius

1112:    Level: intermediate

1114: .seealso: [](chapter_tao), `Tao`, `TaoGetTrustRegionRadius()`, `TaoSetTrustRegionTolerance()`, `TAONTR`
1115: @*/
1116: PetscErrorCode TaoSetInitialTrustRegionRadius(Tao tao, PetscReal radius)
1117: {
1118:   PetscFunctionBegin;
1121:   tao->trust0         = PetscMax(0.0, radius);
1122:   tao->trust0_changed = PETSC_TRUE;
1123:   PetscFunctionReturn(PETSC_SUCCESS);
1124: }

1126: /*@
1127:    TaoGetInitialTrustRegionRadius - Gets the initial trust region radius.

1129:    Not Collective

1131:    Input Parameter:
1132: .  tao - a `Tao` optimization solver

1134:    Output Parameter:
1135: .  radius - the trust region radius

1137:    Level: intermediate

1139: .seealso: [](chapter_tao), `Tao`, `TaoSetInitialTrustRegionRadius()`, `TaoGetCurrentTrustRegionRadius()`, `TAONTR`
1140: @*/
1141: PetscErrorCode TaoGetInitialTrustRegionRadius(Tao tao, PetscReal *radius)
1142: {
1143:   PetscFunctionBegin;
1146:   *radius = tao->trust0;
1147:   PetscFunctionReturn(PETSC_SUCCESS);
1148: }

1150: /*@
1151:    TaoGetCurrentTrustRegionRadius - Gets the current trust region radius.

1153:    Not Collective

1155:    Input Parameter:
1156: .  tao - a `Tao` optimization solver

1158:    Output Parameter:
1159: .  radius - the trust region radius

1161:    Level: intermediate

1163: .seealso: [](chapter_tao), `Tao`, `TaoSetInitialTrustRegionRadius()`, `TaoGetInitialTrustRegionRadius()`, `TAONTR`
1164: @*/
1165: PetscErrorCode TaoGetCurrentTrustRegionRadius(Tao tao, PetscReal *radius)
1166: {
1167:   PetscFunctionBegin;
1170:   *radius = tao->trust;
1171:   PetscFunctionReturn(PETSC_SUCCESS);
1172: }

1174: /*@
1175:   TaoGetTolerances - gets the current values of some tolerances used for the convergence testing of `TaoSolve()`

1177:   Not Collective

1179:   Input Parameter:
1180: . tao - the `Tao` context

1182:   Output Parameters:
1183: + gatol - stop if norm of gradient is less than this
1184: . grtol - stop if relative norm of gradient is less than this
1185: - gttol - stop if norm of gradient is reduced by a this factor

1187:   Level: intermediate

1189:   Note:
1190:   `NULL` can be used as an argument if not all tolerances values are needed

1192: .seealso: [](chapter_tao), `Tao`, `TaoSetTolerances()`
1193: @*/
1194: PetscErrorCode TaoGetTolerances(Tao tao, PetscReal *gatol, PetscReal *grtol, PetscReal *gttol)
1195: {
1196:   PetscFunctionBegin;
1198:   if (gatol) *gatol = tao->gatol;
1199:   if (grtol) *grtol = tao->grtol;
1200:   if (gttol) *gttol = tao->gttol;
1201:   PetscFunctionReturn(PETSC_SUCCESS);
1202: }

1204: /*@
1205:   TaoGetKSP - Gets the linear solver used by the optimization solver.

1207:   Not Collective

1209:    Input Parameter:
1210: .  tao - the `Tao` solver

1212:    Output Parameter:
1213: .  ksp - the `KSP` linear solver used in the optimization solver

1215:    Level: intermediate

1217: .seealso: [](chapter_tao), `Tao`, `KSP`
1218: @*/
1219: PetscErrorCode TaoGetKSP(Tao tao, KSP *ksp)
1220: {
1221:   PetscFunctionBegin;
1224:   *ksp = tao->ksp;
1225:   PetscFunctionReturn(PETSC_SUCCESS);
1226: }

1228: /*@
1229:    TaoGetLinearSolveIterations - Gets the total number of linear iterations
1230:    used by the `Tao` solver

1232:    Not Collective

1234:    Input Parameter:
1235: .  tao - the `Tao` context

1237:    Output Parameter:
1238: .  lits - number of linear iterations

1240:    Level: intermediate

1242:    Note:
1243:    This counter is reset to zero for each successive call to `TaoSolve()`

1245: .seealso: [](chapter_tao), `Tao`, `TaoGetKSP()`
1246: @*/
1247: PetscErrorCode TaoGetLinearSolveIterations(Tao tao, PetscInt *lits)
1248: {
1249:   PetscFunctionBegin;
1252:   *lits = tao->ksp_tot_its;
1253:   PetscFunctionReturn(PETSC_SUCCESS);
1254: }

1256: /*@
1257:   TaoGetLineSearch - Gets the line search used by the optimization solver.

1259:   Not Collective

1261:    Input Parameter:
1262: .  tao - the `Tao` solver

1264:    Output Parameter:
1265: .  ls - the line search used in the optimization solver

1267:    Level: intermediate

1269: .seealso: [](chapter_tao), `Tao`, `TaoLineSearch`, `TaoLineSearchType`
1270: @*/
1271: PetscErrorCode TaoGetLineSearch(Tao tao, TaoLineSearch *ls)
1272: {
1273:   PetscFunctionBegin;
1276:   *ls = tao->linesearch;
1277:   PetscFunctionReturn(PETSC_SUCCESS);
1278: }

1280: /*@
1281:   TaoAddLineSearchCounts - Adds the number of function evaluations spent
1282:   in the line search to the running total.

1284:    Input Parameters:
1285: +  tao - the `Tao` solver
1286: -  ls - the line search used in the optimization solver

1288:    Level: developer

1290: .seealso: [](chapter_tao), `Tao`, `TaoGetLineSearch()`, `TaoLineSearchApply()`
1291: @*/
1292: PetscErrorCode TaoAddLineSearchCounts(Tao tao)
1293: {
1294:   PetscBool flg;
1295:   PetscInt  nfeval, ngeval, nfgeval;

1297:   PetscFunctionBegin;
1299:   if (tao->linesearch) {
1300:     PetscCall(TaoLineSearchIsUsingTaoRoutines(tao->linesearch, &flg));
1301:     if (!flg) {
1302:       PetscCall(TaoLineSearchGetNumberFunctionEvaluations(tao->linesearch, &nfeval, &ngeval, &nfgeval));
1303:       tao->nfuncs += nfeval;
1304:       tao->ngrads += ngeval;
1305:       tao->nfuncgrads += nfgeval;
1306:     }
1307:   }
1308:   PetscFunctionReturn(PETSC_SUCCESS);
1309: }

1311: /*@
1312:   TaoGetSolution - Returns the vector with the current solution from the `Tao` object

1314:   Not Collective

1316:   Input Parameter:
1317: . tao - the `Tao` context

1319:   Output Parameter:
1320: . X - the current solution

1322:   Level: intermediate

1324:   Note:
1325:   The returned vector will be the same object that was passed into `TaoSetSolution()`

1327: .seealso: [](chapter_tao), `Tao`, `TaoSetSolution()`, `TaoSolve()`
1328: @*/
1329: PetscErrorCode TaoGetSolution(Tao tao, Vec *X)
1330: {
1331:   PetscFunctionBegin;
1334:   *X = tao->solution;
1335:   PetscFunctionReturn(PETSC_SUCCESS);
1336: }

1338: /*@
1339:    TaoResetStatistics - Initialize the statistics collected by the `Tao` object.
1340:    These statistics include the iteration number, residual norms, and convergence status.
1341:    This routine gets called before solving each optimization problem.

1343:    Collective

1345:    Input Parameter:
1346: .  solver - the `Tao` context

1348:    Level: developer

1350: .seealso: [](chapter_tao), `Tao`, `TaoCreate()`, `TaoSolve()`
1351: @*/
1352: PetscErrorCode TaoResetStatistics(Tao tao)
1353: {
1354:   PetscFunctionBegin;
1356:   tao->niter        = 0;
1357:   tao->nfuncs       = 0;
1358:   tao->nfuncgrads   = 0;
1359:   tao->ngrads       = 0;
1360:   tao->nhess        = 0;
1361:   tao->njac         = 0;
1362:   tao->nconstraints = 0;
1363:   tao->ksp_its      = 0;
1364:   tao->ksp_tot_its  = 0;
1365:   tao->reason       = TAO_CONTINUE_ITERATING;
1366:   tao->residual     = 0.0;
1367:   tao->cnorm        = 0.0;
1368:   tao->step         = 0.0;
1369:   tao->lsflag       = PETSC_FALSE;
1370:   if (tao->hist_reset) tao->hist_len = 0;
1371:   PetscFunctionReturn(PETSC_SUCCESS);
1372: }

1374: /*@C
1375:   TaoSetUpdate - Sets the general-purpose update function called
1376:   at the beginning of every iteration of the optimization algorithm. Specifically
1377:   it is called at the top of every iteration, after the new solution and the gradient
1378:   is determined, but before the Hessian is computed (if applicable).

1380:   Logically Collective

1382:   Input Parameters:
1383: + tao - The tao solver context
1384: - func - The function

1386:   Calling sequence of func:
1387: $ func (Tao tao, PetscInt step);

1389: . step - The current step of the iteration

1391:   Level: advanced

1393: .seealso: [](chapter_tao), `Tao`, `TaoSolve()`
1394: @*/
1395: PetscErrorCode TaoSetUpdate(Tao tao, PetscErrorCode (*func)(Tao, PetscInt, void *), void *ctx)
1396: {
1397:   PetscFunctionBegin;
1399:   tao->ops->update = func;
1400:   tao->user_update = ctx;
1401:   PetscFunctionReturn(PETSC_SUCCESS);
1402: }

1404: /*@C
1405:   TaoSetConvergenceTest - Sets the function that is to be used to test
1406:   for convergence o fthe iterative minimization solution.  The new convergence
1407:   testing routine will replace Tao's default convergence test.

1409:   Logically Collective

1411:   Input Parameters:
1412: + tao - the `Tao` object
1413: . conv - the routine to test for convergence
1414: - ctx - [optional] context for private data for the convergence routine
1415:         (may be `NULL`)

1417:   Calling sequence of conv:
1418: $   PetscErrorCode conv(Tao tao, void *ctx)

1420: + tao - the `Tao` object
1421: - ctx - [optional] convergence context

1423:   Level: advanced

1425:   Note:
1426:   The new convergence testing routine should call `TaoSetConvergedReason()`.

1428: .seealso: [](chapter_tao), `Tao`, `TaoSolve()`, `TaoSetConvergedReason()`, `TaoGetSolutionStatus()`, `TaoGetTolerances()`, `TaoSetMonitor`
1429: @*/
1430: PetscErrorCode TaoSetConvergenceTest(Tao tao, PetscErrorCode (*conv)(Tao, void *), void *ctx)
1431: {
1432:   PetscFunctionBegin;
1434:   tao->ops->convergencetest = conv;
1435:   tao->cnvP                 = ctx;
1436:   PetscFunctionReturn(PETSC_SUCCESS);
1437: }

1439: /*@C
1440:    TaoSetMonitor - Sets an additional function that is to be used at every
1441:    iteration of the solver to display the iteration's
1442:    progress.

1444:    Logically Collective

1446:    Input Parameters:
1447: +  tao - the `Tao` solver context
1448: .  mymonitor - monitoring routine
1449: -  mctx - [optional] user-defined context for private data for the
1450:           monitor routine (may be `NULL`)

1452:    Calling sequence of mymonitor:
1453: .vb
1454:      PetscErrorCode mymonitor(Tao tao,void *mctx)
1455: .ve

1457: +    tao - the `Tao` solver context
1458: -    mctx - [optional] monitoring context

1460:    Options Database Keys:
1461: +    -tao_monitor        - sets the default monitor `TaoMonitorDefault()`
1462: .    -tao_smonitor       - sets short monitor
1463: .    -tao_cmonitor       - same as smonitor plus constraint norm
1464: .    -tao_view_solution   - view solution at each iteration
1465: .    -tao_view_gradient   - view gradient at each iteration
1466: .    -tao_view_ls_residual - view least-squares residual vector at each iteration
1467: -    -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.

1469:    Level: intermediate

1471:    Notes:
1472:    Several different monitoring routines may be set by calling
1473:    `TaoSetMonitor()` multiple times; all will be called in the
1474:    order in which they were set.

1476:    Fortran Note:
1477:     Only one monitor function may be set

1479: .seealso: [](chapter_tao), `Tao`, `TaoSolve()`, `TaoMonitorDefault()`, `TaoCancelMonitors()`, `TaoSetDestroyRoutine()`, `TaoView()`
1480: @*/
1481: PetscErrorCode TaoSetMonitor(Tao tao, PetscErrorCode (*func)(Tao, void *), void *ctx, PetscErrorCode (*dest)(void **))
1482: {
1483:   PetscInt  i;
1484:   PetscBool identical;

1486:   PetscFunctionBegin;
1488:   PetscCheck(tao->numbermonitors < MAXTAOMONITORS, PetscObjectComm((PetscObject)tao), PETSC_ERR_SUP, "Cannot attach another monitor -- max=%d", MAXTAOMONITORS);

1490:   for (i = 0; i < tao->numbermonitors; i++) {
1491:     PetscCall(PetscMonitorCompare((PetscErrorCode(*)(void))func, ctx, dest, (PetscErrorCode(*)(void))tao->monitor[i], tao->monitorcontext[i], tao->monitordestroy[i], &identical));
1492:     if (identical) PetscFunctionReturn(PETSC_SUCCESS);
1493:   }
1494:   tao->monitor[tao->numbermonitors]        = func;
1495:   tao->monitorcontext[tao->numbermonitors] = (void *)ctx;
1496:   tao->monitordestroy[tao->numbermonitors] = dest;
1497:   ++tao->numbermonitors;
1498:   PetscFunctionReturn(PETSC_SUCCESS);
1499: }

1501: /*@
1502:    TaoCancelMonitors - Clears all the monitor functions for a `Tao` object.

1504:    Logically Collective

1506:    Input Parameter:
1507: .  tao - the `Tao` solver context

1509:    Options Database Key:
1510: .  -tao_cancelmonitors - cancels all monitors that have been hardwired
1511:     into a code by calls to `TaoSetMonitor()`, but does not cancel those
1512:     set via the options database

1514:    Level: advanced

1516:    Note:
1517:    There is no way to clear one specific monitor from a `Tao` object.

1519: .seealso: [](chapter_tao), `Tao`, `TaoMonitorDefault()`, `TaoSetMonitor()`
1520: @*/
1521: PetscErrorCode TaoCancelMonitors(Tao tao)
1522: {
1523:   PetscInt i;

1525:   PetscFunctionBegin;
1527:   for (i = 0; i < tao->numbermonitors; i++) {
1528:     if (tao->monitordestroy[i]) PetscCall((*tao->monitordestroy[i])(&tao->monitorcontext[i]));
1529:   }
1530:   tao->numbermonitors = 0;
1531:   PetscFunctionReturn(PETSC_SUCCESS);
1532: }

1534: /*@
1535:    TaoMonitorDefault - Default routine for monitoring progress of `TaoSolve()`

1537:    Collective

1539:    Input Parameters:
1540: +  tao - the `Tao` context
1541: -  ctx - `PetscViewer` context or `NULL`

1543:    Options Database Key:
1544: .  -tao_monitor - turn on default monitoring

1546:    Level: advanced

1548:    Note:
1549:    This monitor prints the function value and gradient
1550:    norm at each iteration.

1552: .seealso: [](chapter_tao), `Tao`, `TaoDefaultSMonitor()`, `TaoSetMonitor()`
1553: @*/
1554: PetscErrorCode TaoMonitorDefault(Tao tao, void *ctx)
1555: {
1556:   PetscInt    its, tabs;
1557:   PetscReal   fct, gnorm;
1558:   PetscViewer viewer = (PetscViewer)ctx;

1560:   PetscFunctionBegin;
1563:   its   = tao->niter;
1564:   fct   = tao->fc;
1565:   gnorm = tao->residual;
1566:   PetscCall(PetscViewerASCIIGetTab(viewer, &tabs));
1567:   PetscCall(PetscViewerASCIISetTab(viewer, ((PetscObject)tao)->tablevel));
1568:   if (its == 0 && ((PetscObject)tao)->prefix && !tao->header_printed) {
1569:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Iteration information for %s solve.\n", ((PetscObject)tao)->prefix));
1570:     tao->header_printed = PETSC_TRUE;
1571:   }
1572:   PetscCall(PetscViewerASCIIPrintf(viewer, "%3" PetscInt_FMT " TAO,", its));
1573:   PetscCall(PetscViewerASCIIPrintf(viewer, "  Function value: %g,", (double)fct));
1574:   if (gnorm >= PETSC_INFINITY) {
1575:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Residual: Inf \n"));
1576:   } else {
1577:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Residual: %g \n", (double)gnorm));
1578:   }
1579:   PetscCall(PetscViewerASCIISetTab(viewer, tabs));
1580:   PetscFunctionReturn(PETSC_SUCCESS);
1581: }

1583: /*@
1584:    TaoDefaultGMonitor - Default routine for monitoring progress of `TaoSolve()` with extra detail on the globalization method.

1586:    Collective

1588:    Input Parameters:
1589: +  tao - the `Tao` context
1590: -  ctx - `PetscViewer` context or `NULL`

1592:    Options Database Key:
1593: .  -tao_gmonitor - turn on monitoring with globalization information

1595:    Level: advanced

1597:    Note:
1598:    This monitor prints the function value and gradient norm at each
1599:    iteration, as well as the step size and trust radius. Note that the
1600:    step size and trust radius may be the same for some algorithms.

1602: .seealso: [](chapter_tao), `Tao`, `TaoDefaultSMonitor()`, `TaoSetMonitor()`
1603: @*/
1604: PetscErrorCode TaoDefaultGMonitor(Tao tao, void *ctx)
1605: {
1606:   PetscInt    its, tabs;
1607:   PetscReal   fct, gnorm, stp, tr;
1608:   PetscViewer viewer = (PetscViewer)ctx;

1610:   PetscFunctionBegin;
1613:   its   = tao->niter;
1614:   fct   = tao->fc;
1615:   gnorm = tao->residual;
1616:   stp   = tao->step;
1617:   tr    = tao->trust;
1618:   PetscCall(PetscViewerASCIIGetTab(viewer, &tabs));
1619:   PetscCall(PetscViewerASCIISetTab(viewer, ((PetscObject)tao)->tablevel));
1620:   if (its == 0 && ((PetscObject)tao)->prefix && !tao->header_printed) {
1621:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Iteration information for %s solve.\n", ((PetscObject)tao)->prefix));
1622:     tao->header_printed = PETSC_TRUE;
1623:   }
1624:   PetscCall(PetscViewerASCIIPrintf(viewer, "%3" PetscInt_FMT " TAO,", its));
1625:   PetscCall(PetscViewerASCIIPrintf(viewer, "  Function value: %g,", (double)fct));
1626:   if (gnorm >= PETSC_INFINITY) {
1627:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Residual: Inf,"));
1628:   } else {
1629:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Residual: %g,", (double)gnorm));
1630:   }
1631:   PetscCall(PetscViewerASCIIPrintf(viewer, "  Step: %g,  Trust: %g\n", (double)stp, (double)tr));
1632:   PetscCall(PetscViewerASCIISetTab(viewer, tabs));
1633:   PetscFunctionReturn(PETSC_SUCCESS);
1634: }

1636: /*@
1637:    TaoDefaultSMonitor - Default routine for monitoring progress of `TaoSolve()`

1639:    Collective

1641:    Input Parameters:
1642: +  tao - the `Tao` context
1643: -  ctx - `PetscViewer` context of type `PETSCVIEWERASCII`

1645:    Options Database Key:
1646: .  -tao_smonitor - turn on default short monitoring

1648:    Level: advanced

1650:    Note:
1651:    Same as `TaoMonitorDefault()` except
1652:    it prints fewer digits of the residual as the residual gets smaller.
1653:    This is because the later digits are meaningless and are often
1654:    different on different machines; by using this routine different
1655:    machines will usually generate the same output.

1657: .seealso: [](chapter_tao), `Tao`, `TaoMonitorDefault()`, `TaoSetMonitor()`
1658: @*/
1659: PetscErrorCode TaoDefaultSMonitor(Tao tao, void *ctx)
1660: {
1661:   PetscInt    its, tabs;
1662:   PetscReal   fct, gnorm;
1663:   PetscViewer viewer = (PetscViewer)ctx;

1665:   PetscFunctionBegin;
1668:   its   = tao->niter;
1669:   fct   = tao->fc;
1670:   gnorm = tao->residual;
1671:   PetscCall(PetscViewerASCIIGetTab(viewer, &tabs));
1672:   PetscCall(PetscViewerASCIISetTab(viewer, ((PetscObject)tao)->tablevel));
1673:   PetscCall(PetscViewerASCIIPrintf(viewer, "iter = %3" PetscInt_FMT ",", its));
1674:   PetscCall(PetscViewerASCIIPrintf(viewer, " Function value %g,", (double)fct));
1675:   if (gnorm >= PETSC_INFINITY) {
1676:     PetscCall(PetscViewerASCIIPrintf(viewer, " Residual: Inf \n"));
1677:   } else if (gnorm > 1.e-6) {
1678:     PetscCall(PetscViewerASCIIPrintf(viewer, " Residual: %g \n", (double)gnorm));
1679:   } else if (gnorm > 1.e-11) {
1680:     PetscCall(PetscViewerASCIIPrintf(viewer, " Residual: < 1.0e-6 \n"));
1681:   } else {
1682:     PetscCall(PetscViewerASCIIPrintf(viewer, " Residual: < 1.0e-11 \n"));
1683:   }
1684:   PetscCall(PetscViewerASCIISetTab(viewer, tabs));
1685:   PetscFunctionReturn(PETSC_SUCCESS);
1686: }

1688: /*@
1689:    TaoDefaultCMonitor - same as `TaoMonitorDefault()` except
1690:    it prints the norm of the constraint function.

1692:    Collective

1694:    Input Parameters:
1695: +  tao - the `Tao` context
1696: -  ctx - `PetscViewer` context or `NULL`

1698:    Options Database Key:
1699: .  -tao_cmonitor - monitor the constraints

1701:    Level: advanced

1703: .seealso: [](chapter_tao), `Tao`, `TaoMonitorDefault()`, `TaoSetMonitor()`
1704: @*/
1705: PetscErrorCode TaoDefaultCMonitor(Tao tao, void *ctx)
1706: {
1707:   PetscInt    its, tabs;
1708:   PetscReal   fct, gnorm;
1709:   PetscViewer viewer = (PetscViewer)ctx;

1711:   PetscFunctionBegin;
1714:   its   = tao->niter;
1715:   fct   = tao->fc;
1716:   gnorm = tao->residual;
1717:   PetscCall(PetscViewerASCIIGetTab(viewer, &tabs));
1718:   PetscCall(PetscViewerASCIISetTab(viewer, ((PetscObject)tao)->tablevel));
1719:   PetscCall(PetscViewerASCIIPrintf(viewer, "iter = %" PetscInt_FMT ",", its));
1720:   PetscCall(PetscViewerASCIIPrintf(viewer, " Function value: %g,", (double)fct));
1721:   PetscCall(PetscViewerASCIIPrintf(viewer, "  Residual: %g ", (double)gnorm));
1722:   PetscCall(PetscViewerASCIIPrintf(viewer, "  Constraint: %g \n", (double)tao->cnorm));
1723:   PetscCall(PetscViewerASCIISetTab(viewer, tabs));
1724:   PetscFunctionReturn(PETSC_SUCCESS);
1725: }

1727: /*@C
1728:    TaoSolutionMonitor - Views the solution at each iteration of `TaoSolve()`

1730:    Collective

1732:    Input Parameters:
1733: +  tao - the `Tao` context
1734: -  ctx - `PetscViewer` context or `NULL`

1736:    Options Database Key:
1737: .  -tao_view_solution - view the solution

1739:    Level: advanced

1741: .seealso: [](chapter_tao), `Tao`, `TaoDefaultSMonitor()`, `TaoSetMonitor()`
1742: @*/
1743: PetscErrorCode TaoSolutionMonitor(Tao tao, void *ctx)
1744: {
1745:   PetscViewer viewer = (PetscViewer)ctx;

1747:   PetscFunctionBegin;
1750:   PetscCall(VecView(tao->solution, viewer));
1751:   PetscFunctionReturn(PETSC_SUCCESS);
1752: }

1754: /*@C
1755:    TaoGradientMonitor - Views the gradient at each iteration of `TaoSolve()`

1757:    Collective

1759:    Input Parameters:
1760: +  tao - the `Tao` context
1761: -  ctx - `PetscViewer` context or `NULL`

1763:    Options Database Key:
1764: .  -tao_view_gradient - view the gradient at each iteration

1766:    Level: advanced

1768: .seealso: [](chapter_tao), `Tao`, `TaoDefaultSMonitor()`, `TaoSetMonitor()`
1769: @*/
1770: PetscErrorCode TaoGradientMonitor(Tao tao, void *ctx)
1771: {
1772:   PetscViewer viewer = (PetscViewer)ctx;

1774:   PetscFunctionBegin;
1777:   PetscCall(VecView(tao->gradient, viewer));
1778:   PetscFunctionReturn(PETSC_SUCCESS);
1779: }

1781: /*@C
1782:    TaoStepDirectionMonitor - Views the step-direction at each iteration of `TaoSolve()`

1784:    Collective

1786:    Input Parameters:
1787: +  tao - the `Tao` context
1788: -  ctx - `PetscViewer` context or `NULL`

1790:    Options Database Key:
1791: .  -tao_view_stepdirection - view the step direction vector at each iteration

1793:    Level: advanced

1795: .seealso: [](chapter_tao), `Tao`, `TaoDefaultSMonitor()`, `TaoSetMonitor()`
1796: @*/
1797: PetscErrorCode TaoStepDirectionMonitor(Tao tao, void *ctx)
1798: {
1799:   PetscViewer viewer = (PetscViewer)ctx;

1801:   PetscFunctionBegin;
1804:   PetscCall(VecView(tao->stepdirection, viewer));
1805:   PetscFunctionReturn(PETSC_SUCCESS);
1806: }

1808: /*@C
1809:    TaoDrawSolutionMonitor - Plots the solution at each iteration of `TaoSolve()`

1811:    Collective

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

1817:    Options Database Key:
1818: .  -tao_draw_solution - draw the solution at each iteration

1820:    Level: advanced

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

1828:   PetscFunctionBegin;
1830:   if (!(((ictx->howoften > 0) && (!(tao->niter % ictx->howoften))) || ((ictx->howoften == -1) && tao->reason))) PetscFunctionReturn(PETSC_SUCCESS);
1831:   PetscCall(VecView(tao->solution, ictx->viewer));
1832:   PetscFunctionReturn(PETSC_SUCCESS);
1833: }

1835: /*@C
1836:    TaoDrawGradientMonitor - Plots the gradient at each iteration of `TaoSolve()`

1838:    Collective

1840:    Input Parameters:
1841: +  tao - the `Tao` context
1842: -  ctx - `PetscViewer` context

1844:    Options Database Key:
1845: .  -tao_draw_gradient - draw the gradient at each iteration

1847:    Level: advanced

1849: .seealso: [](chapter_tao), `Tao`, `TaoGradientMonitor()`, `TaoSetMonitor()`, `TaoDrawSolutionMonitor`
1850: @*/
1851: PetscErrorCode TaoDrawGradientMonitor(Tao tao, void *ctx)
1852: {
1853:   TaoMonitorDrawCtx ictx = (TaoMonitorDrawCtx)ctx;

1855:   PetscFunctionBegin;
1857:   if (!(((ictx->howoften > 0) && (!(tao->niter % ictx->howoften))) || ((ictx->howoften == -1) && tao->reason))) PetscFunctionReturn(PETSC_SUCCESS);
1858:   PetscCall(VecView(tao->gradient, ictx->viewer));
1859:   PetscFunctionReturn(PETSC_SUCCESS);
1860: }

1862: /*@C
1863:    TaoDrawStepMonitor - Plots the step direction at each iteration of `TaoSolve()`

1865:    Collective

1867:    Input Parameters:
1868: +  tao - the `Tao` context
1869: -  ctx - the `PetscViewer` context

1871:    Options Database Key:
1872: .  -tao_draw_step - draw the step direction at each iteration

1874:    Level: advanced

1876: .seealso: [](chapter_tao), `Tao`, `TaoSetMonitor()`, `TaoDrawSolutionMonitor`
1877: @*/
1878: PetscErrorCode TaoDrawStepMonitor(Tao tao, void *ctx)
1879: {
1880:   PetscViewer viewer = (PetscViewer)ctx;

1882:   PetscFunctionBegin;
1885:   PetscCall(VecView(tao->stepdirection, viewer));
1886:   PetscFunctionReturn(PETSC_SUCCESS);
1887: }

1889: /*@C
1890:    TaoResidualMonitor - Views the least-squares residual at each iteration of `TaoSolve()`

1892:    Collective

1894:    Input Parameters:
1895: +  tao - the `Tao` context
1896: -  ctx - the `PetscViewer` context or `NULL`

1898:    Options Database Key:
1899: .  -tao_view_ls_residual - view the residual at each iteration

1901:    Level: advanced

1903: .seealso: [](chapter_tao), `Tao`, `TaoDefaultSMonitor()`, `TaoSetMonitor()`
1904: @*/
1905: PetscErrorCode TaoResidualMonitor(Tao tao, void *ctx)
1906: {
1907:   PetscViewer viewer = (PetscViewer)ctx;

1909:   PetscFunctionBegin;
1912:   PetscCall(VecView(tao->ls_res, viewer));
1913:   PetscFunctionReturn(PETSC_SUCCESS);
1914: }

1916: /*@
1917:    TaoDefaultConvergenceTest - Determines whether the solver should continue iterating
1918:    or terminate.

1920:    Collective

1922:    Input Parameters:
1923: +  tao - the `Tao` context
1924: -  dummy - unused dummy context

1926:    Output Parameter:
1927: .  reason - for terminating

1929:    Level: developer

1931:    Notes:
1932:    This routine checks the residual in the optimality conditions, the
1933:    relative residual in the optimity conditions, the number of function
1934:    evaluations, and the function value to test convergence.  Some
1935:    solvers may use different convergence routines.

1937: .seealso: [](chapter_tao), `Tao`, `TaoSetTolerances()`, `TaoGetConvergedReason()`, `TaoSetConvergedReason()`
1938: @*/
1939: PetscErrorCode TaoDefaultConvergenceTest(Tao tao, void *dummy)
1940: {
1941:   PetscInt           niter = tao->niter, nfuncs = PetscMax(tao->nfuncs, tao->nfuncgrads);
1942:   PetscInt           max_funcs = tao->max_funcs;
1943:   PetscReal          gnorm = tao->residual, gnorm0 = tao->gnorm0;
1944:   PetscReal          f = tao->fc, steptol = tao->steptol, trradius = tao->step;
1945:   PetscReal          gatol = tao->gatol, grtol = tao->grtol, gttol = tao->gttol;
1946:   PetscReal          catol = tao->catol, crtol = tao->crtol;
1947:   PetscReal          fmin = tao->fmin, cnorm = tao->cnorm;
1948:   TaoConvergedReason reason = tao->reason;

1950:   PetscFunctionBegin;
1952:   if (reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(PETSC_SUCCESS);

1954:   if (PetscIsInfOrNanReal(f)) {
1955:     PetscCall(PetscInfo(tao, "Failed to converged, function value is Inf or NaN\n"));
1956:     reason = TAO_DIVERGED_NAN;
1957:   } else if (f <= fmin && cnorm <= catol) {
1958:     PetscCall(PetscInfo(tao, "Converged due to function value %g < minimum function value %g\n", (double)f, (double)fmin));
1959:     reason = TAO_CONVERGED_MINF;
1960:   } else if (gnorm <= gatol && cnorm <= catol) {
1961:     PetscCall(PetscInfo(tao, "Converged due to residual norm ||g(X)||=%g < %g\n", (double)gnorm, (double)gatol));
1962:     reason = TAO_CONVERGED_GATOL;
1963:   } else if (f != 0 && PetscAbsReal(gnorm / f) <= grtol && cnorm <= crtol) {
1964:     PetscCall(PetscInfo(tao, "Converged due to residual ||g(X)||/|f(X)| =%g < %g\n", (double)(gnorm / f), (double)grtol));
1965:     reason = TAO_CONVERGED_GRTOL;
1966:   } else if (gnorm0 != 0 && ((gttol == 0 && gnorm == 0) || gnorm / gnorm0 < gttol) && cnorm <= crtol) {
1967:     PetscCall(PetscInfo(tao, "Converged due to relative residual norm ||g(X)||/||g(X0)|| = %g < %g\n", (double)(gnorm / gnorm0), (double)gttol));
1968:     reason = TAO_CONVERGED_GTTOL;
1969:   } else if (max_funcs >= 0 && nfuncs > max_funcs) {
1970:     PetscCall(PetscInfo(tao, "Exceeded maximum number of function evaluations: %" PetscInt_FMT " > %" PetscInt_FMT "\n", nfuncs, max_funcs));
1971:     reason = TAO_DIVERGED_MAXFCN;
1972:   } else if (tao->lsflag != 0) {
1973:     PetscCall(PetscInfo(tao, "Tao Line Search failure.\n"));
1974:     reason = TAO_DIVERGED_LS_FAILURE;
1975:   } else if (trradius < steptol && niter > 0) {
1976:     PetscCall(PetscInfo(tao, "Trust region/step size too small: %g < %g\n", (double)trradius, (double)steptol));
1977:     reason = TAO_CONVERGED_STEPTOL;
1978:   } else if (niter >= tao->max_it) {
1979:     PetscCall(PetscInfo(tao, "Exceeded maximum number of iterations: %" PetscInt_FMT " > %" PetscInt_FMT "\n", niter, tao->max_it));
1980:     reason = TAO_DIVERGED_MAXITS;
1981:   } else {
1982:     reason = TAO_CONTINUE_ITERATING;
1983:   }
1984:   tao->reason = reason;
1985:   PetscFunctionReturn(PETSC_SUCCESS);
1986: }

1988: /*@C
1989:    TaoSetOptionsPrefix - Sets the prefix used for searching for all
1990:    Tao options in the database.

1992:    Logically Collective

1994:    Input Parameters:
1995: +  tao - the `Tao` context
1996: -  prefix - the prefix string to prepend to all Tao option requests

1998:    Notes:
1999:    A hyphen (-) must NOT be given at the beginning of the prefix name.
2000:    The first character of all runtime options is AUTOMATICALLY the hyphen.

2002:    For example, to distinguish between the runtime options for two
2003:    different Tao solvers, one could call
2004: .vb
2005:       TaoSetOptionsPrefix(tao1,"sys1_")
2006:       TaoSetOptionsPrefix(tao2,"sys2_")
2007: .ve

2009:    This would enable use of different options for each system, such as
2010: .vb
2011:       -sys1_tao_method blmvm -sys1_tao_grtol 1.e-3
2012:       -sys2_tao_method lmvm  -sys2_tao_grtol 1.e-4
2013: .ve

2015:    Level: advanced

2017: .seealso: [](chapter_tao), `Tao`, `TaoSetFromOptions()`, `TaoAppendOptionsPrefix()`, `TaoGetOptionsPrefix()`
2018: @*/
2019: PetscErrorCode TaoSetOptionsPrefix(Tao tao, const char p[])
2020: {
2021:   PetscFunctionBegin;
2023:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)tao, p));
2024:   if (tao->linesearch) PetscCall(TaoLineSearchSetOptionsPrefix(tao->linesearch, p));
2025:   if (tao->ksp) PetscCall(KSPSetOptionsPrefix(tao->ksp, p));
2026:   PetscFunctionReturn(PETSC_SUCCESS);
2027: }

2029: /*@C
2030:    TaoAppendOptionsPrefix - Appends to the prefix used for searching for all Tao options in the database.

2032:    Logically Collective

2034:    Input Parameters:
2035: +  tao - the `Tao` solver context
2036: -  prefix - the prefix string to prepend to all `Tao` option requests

2038:    Note:
2039:    A hyphen (-) must NOT be given at the beginning of the prefix name.
2040:    The first character of all runtime options is automatically the hyphen.

2042:    Level: advanced

2044: .seealso: [](chapter_tao), `Tao`, `TaoSetFromOptions()`, `TaoSetOptionsPrefix()`, `TaoGetOptionsPrefix()`
2045: @*/
2046: PetscErrorCode TaoAppendOptionsPrefix(Tao tao, const char p[])
2047: {
2048:   PetscFunctionBegin;
2050:   PetscCall(PetscObjectAppendOptionsPrefix((PetscObject)tao, p));
2051:   if (tao->linesearch) PetscCall(PetscObjectAppendOptionsPrefix((PetscObject)tao->linesearch, p));
2052:   if (tao->ksp) PetscCall(KSPAppendOptionsPrefix(tao->ksp, p));
2053:   PetscFunctionReturn(PETSC_SUCCESS);
2054: }

2056: /*@C
2057:   TaoGetOptionsPrefix - Gets the prefix used for searching for all
2058:   Tao options in the database

2060:   Not Collective

2062:   Input Parameter:
2063: . tao - the `Tao` context

2065:   Output Parameter:
2066: . prefix - pointer to the prefix string used is returned

2068:   Fortran Note:
2069:   Pass in a string 'prefix' of sufficient length to hold the prefix.

2071:   Level: advanced

2073: .seealso: [](chapter_tao), `Tao`, `TaoSetFromOptions()`, `TaoSetOptionsPrefix()`, `TaoAppendOptionsPrefix()`
2074: @*/
2075: PetscErrorCode TaoGetOptionsPrefix(Tao tao, const char *p[])
2076: {
2077:   PetscFunctionBegin;
2079:   PetscCall(PetscObjectGetOptionsPrefix((PetscObject)tao, p));
2080:   PetscFunctionReturn(PETSC_SUCCESS);
2081: }

2083: /*@C
2084:    TaoSetType - Sets the `TaoType` for the minimization solver.

2086:    Collective

2088:    Input Parameters:
2089: +  solver - the `Tao` solver context
2090: -  type - a known method

2092:    Options Database Key:
2093: .  -tao_type <type> - Sets the method; use -help for a list
2094:    of available methods (for instance, "-tao_type lmvm" or "-tao_type tron")

2096:   Level: intermediate

2098: .seealso: [](chapter_tao), `Tao`, `TaoCreate()`, `TaoGetType()`, `TaoType`
2099: @*/
2100: PetscErrorCode TaoSetType(Tao tao, TaoType type)
2101: {
2102:   PetscErrorCode (*create_xxx)(Tao);
2103:   PetscBool issame;

2105:   PetscFunctionBegin;

2108:   PetscCall(PetscObjectTypeCompare((PetscObject)tao, type, &issame));
2109:   if (issame) PetscFunctionReturn(PETSC_SUCCESS);

2111:   PetscCall(PetscFunctionListFind(TaoList, type, (void (**)(void)) & create_xxx));
2112:   PetscCheck(create_xxx, PetscObjectComm((PetscObject)tao), PETSC_ERR_ARG_UNKNOWN_TYPE, "Unable to find requested Tao type %s", type);

2114:   /* Destroy the existing solver information */
2115:   PetscTryTypeMethod(tao, destroy);
2116:   PetscCall(KSPDestroy(&tao->ksp));
2117:   PetscCall(TaoLineSearchDestroy(&tao->linesearch));
2118:   tao->ops->setup          = NULL;
2119:   tao->ops->solve          = NULL;
2120:   tao->ops->view           = NULL;
2121:   tao->ops->setfromoptions = NULL;
2122:   tao->ops->destroy        = NULL;

2124:   tao->setupcalled = PETSC_FALSE;

2126:   PetscCall((*create_xxx)(tao));
2127:   PetscCall(PetscObjectChangeTypeName((PetscObject)tao, type));
2128:   PetscFunctionReturn(PETSC_SUCCESS);
2129: }

2131: /*@C
2132:    TaoRegister - Adds a method to the Tao package for minimization.

2134:    Synopsis:
2135:    TaoRegister(char *name_solver,char *path,char *name_Create,PetscErrorCode (*routine_Create)(Tao))

2137:    Not collective

2139:    Input Parameters:
2140: +  sname - name of a new user-defined solver
2141: -  func - routine to Create method context

2143:    Sample usage:
2144: .vb
2145:    TaoRegister("my_solver",MySolverCreate);
2146: .ve

2148:    Then, your solver can be chosen with the procedural interface via
2149: $     TaoSetType(tao,"my_solver")
2150:    or at runtime via the option
2151: $     -tao_type my_solver

2153:    Level: advanced

2155:    Note:
2156:    `TaoRegister()` may be called multiple times to add several user-defined solvers.

2158: .seealso: [](chapter_tao), `Tao`, `TaoSetType()`, `TaoRegisterAll()`, `TaoRegisterDestroy()`
2159: @*/
2160: PetscErrorCode TaoRegister(const char sname[], PetscErrorCode (*func)(Tao))
2161: {
2162:   PetscFunctionBegin;
2163:   PetscCall(TaoInitializePackage());
2164:   PetscCall(PetscFunctionListAdd(&TaoList, sname, (void (*)(void))func));
2165:   PetscFunctionReturn(PETSC_SUCCESS);
2166: }

2168: /*@C
2169:    TaoRegisterDestroy - Frees the list of minimization solvers that were
2170:    registered by `TaoRegister()`.

2172:    Not Collective

2174:    Level: advanced

2176: .seealso: [](chapter_tao), `Tao`, `TaoRegisterAll()`, `TaoRegister()`
2177: @*/
2178: PetscErrorCode TaoRegisterDestroy(void)
2179: {
2180:   PetscFunctionBegin;
2181:   PetscCall(PetscFunctionListDestroy(&TaoList));
2182:   TaoRegisterAllCalled = PETSC_FALSE;
2183:   PetscFunctionReturn(PETSC_SUCCESS);
2184: }

2186: /*@
2187:    TaoGetIterationNumber - Gets the number of `TaoSolve()` iterations completed
2188:    at this time.

2190:    Not Collective

2192:    Input Parameter:
2193: .  tao - the `Tao` context

2195:    Output Parameter:
2196: .  iter - iteration number

2198:    Notes:
2199:    For example, during the computation of iteration 2 this would return 1.

2201:    Level: intermediate

2203: .seealso: [](chapter_tao), `Tao`, `TaoGetLinearSolveIterations()`, `TaoGetResidualNorm()`, `TaoGetObjective()`
2204: @*/
2205: PetscErrorCode TaoGetIterationNumber(Tao tao, PetscInt *iter)
2206: {
2207:   PetscFunctionBegin;
2210:   *iter = tao->niter;
2211:   PetscFunctionReturn(PETSC_SUCCESS);
2212: }

2214: /*@
2215:    TaoGetResidualNorm - Gets the current value of the norm of the residual (gradient)
2216:    at this time.

2218:    Not Collective

2220:    Input Parameter:
2221: .  tao - the `Tao` context

2223:    Output Parameter:
2224: .  value - the current value

2226:    Level: intermediate

2228:    Developer Note:
2229:    This is the 2-norm of the residual, we cannot use `TaoGetGradientNorm()` because that has
2230:    a different meaning. For some reason `Tao` sometimes calls the gradient the residual.

2232: .seealso: [](chapter_tao), `Tao`, `TaoGetLinearSolveIterations()`, `TaoGetIterationNumber()`, `TaoGetObjective()`
2233: @*/
2234: PetscErrorCode TaoGetResidualNorm(Tao tao, PetscReal *value)
2235: {
2236:   PetscFunctionBegin;
2239:   *value = tao->residual;
2240:   PetscFunctionReturn(PETSC_SUCCESS);
2241: }

2243: /*@
2244:    TaoSetIterationNumber - Sets the current iteration number.

2246:    Logically Collective

2248:    Input Parameters:
2249: +  tao - the `Tao` context
2250: -  iter - iteration number

2252:    Level: developer

2254: .seealso: [](chapter_tao), `Tao`, `TaoGetLinearSolveIterations()`
2255: @*/
2256: PetscErrorCode TaoSetIterationNumber(Tao tao, PetscInt iter)
2257: {
2258:   PetscFunctionBegin;
2261:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)tao));
2262:   tao->niter = iter;
2263:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)tao));
2264:   PetscFunctionReturn(PETSC_SUCCESS);
2265: }

2267: /*@
2268:    TaoGetTotalIterationNumber - Gets the total number of `TaoSolve()` iterations
2269:    completed. This number keeps accumulating if multiple solves
2270:    are called with the `Tao` object.

2272:    Not Collective

2274:    Input Parameter:
2275: .  tao - the `Tao` context

2277:    Output Parameter:
2278: .  iter - number of iterations

2280:    Level: intermediate

2282:    Notes:
2283:    The total iteration count is updated after each solve, if there is a current
2284:    `TaoSolve()` in progress then those iterations are not included in the count

2286: .seealso: [](chapter_tao), `Tao`, `TaoGetLinearSolveIterations()`
2287: @*/
2288: PetscErrorCode TaoGetTotalIterationNumber(Tao tao, PetscInt *iter)
2289: {
2290:   PetscFunctionBegin;
2293:   *iter = tao->ntotalits;
2294:   PetscFunctionReturn(PETSC_SUCCESS);
2295: }

2297: /*@
2298:    TaoSetTotalIterationNumber - Sets the current total iteration number.

2300:    Logically Collective

2302:    Input Parameters:
2303: +  tao - the `Tao` context
2304: -  iter - the iteration number

2306:    Level: developer

2308: .seealso: [](chapter_tao), `Tao`, `TaoGetLinearSolveIterations()`
2309: @*/
2310: PetscErrorCode TaoSetTotalIterationNumber(Tao tao, PetscInt iter)
2311: {
2312:   PetscFunctionBegin;
2315:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)tao));
2316:   tao->ntotalits = iter;
2317:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)tao));
2318:   PetscFunctionReturn(PETSC_SUCCESS);
2319: }

2321: /*@
2322:   TaoSetConvergedReason - Sets the termination flag on a `Tao` object

2324:   Logically Collective

2326:   Input Parameters:
2327: + tao - the `Tao` context
2328: - reason - the `TaoConvergedReason`

2330:    Level: intermediate

2332: .seealso: [](chapter_tao), `Tao`, `TaoConvergedReason`
2333: @*/
2334: PetscErrorCode TaoSetConvergedReason(Tao tao, TaoConvergedReason reason)
2335: {
2336:   PetscFunctionBegin;
2339:   tao->reason = reason;
2340:   PetscFunctionReturn(PETSC_SUCCESS);
2341: }

2343: /*@
2344:    TaoGetConvergedReason - Gets the reason the `TaoSolve()` was stopped.

2346:    Not Collective

2348:    Input Parameter:
2349: .  tao - the `Tao` solver context

2351:    Output Parameter:
2352: .  reason - value of `TaoConvergedReason`

2354:    Level: intermediate

2356: .seealso: [](chapter_tao), `Tao`, `TaoConvergedReason`, `TaoSetConvergenceTest()`, `TaoSetTolerances()`
2357: @*/
2358: PetscErrorCode TaoGetConvergedReason(Tao tao, TaoConvergedReason *reason)
2359: {
2360:   PetscFunctionBegin;
2363:   *reason = tao->reason;
2364:   PetscFunctionReturn(PETSC_SUCCESS);
2365: }

2367: /*@
2368:    TaoGetSolutionStatus - Get the current iterate, objective value,
2369:    residual, infeasibility, and termination from a `Tao` object

2371:    Not Collective

2373:    Input Parameter:
2374: .  tao - the `Tao` context

2376:    Output Parameters:
2377: +  iterate - the current iterate number (>=0)
2378: .  f - the current function value
2379: .  gnorm - the square of the gradient norm, duality gap, or other measure indicating distance from optimality.
2380: .  cnorm - the infeasibility of the current solution with regard to the constraints.
2381: .  xdiff - the step length or trust region radius of the most recent iterate.
2382: -  reason - The termination reason, which can equal `TAO_CONTINUE_ITERATING`

2384:    Level: intermediate

2386:    Notes:
2387:    Tao returns the values set by the solvers in the routine `TaoMonitor()`.

2389:    If any of the output arguments are set to `NULL`, no corresponding value will be returned.

2391: .seealso: [](chapter_tao), `TaoMonitor()`, `TaoGetConvergedReason()`
2392: @*/
2393: PetscErrorCode TaoGetSolutionStatus(Tao tao, PetscInt *its, PetscReal *f, PetscReal *gnorm, PetscReal *cnorm, PetscReal *xdiff, TaoConvergedReason *reason)
2394: {
2395:   PetscFunctionBegin;
2397:   if (its) *its = tao->niter;
2398:   if (f) *f = tao->fc;
2399:   if (gnorm) *gnorm = tao->residual;
2400:   if (cnorm) *cnorm = tao->cnorm;
2401:   if (reason) *reason = tao->reason;
2402:   if (xdiff) *xdiff = tao->step;
2403:   PetscFunctionReturn(PETSC_SUCCESS);
2404: }

2406: /*@C
2407:    TaoGetType - Gets the current `TaoType` being used in the `Tao` object

2409:    Not Collective

2411:    Input Parameter:
2412: .  tao - the `Tao` solver context

2414:    Output Parameter:
2415: .  type - the `TaoType`

2417:    Level: intermediate

2419: .seealso: [](chapter_tao), `Tao`, `TaoType`, `TaoSetType()`
2420: @*/
2421: PetscErrorCode TaoGetType(Tao tao, TaoType *type)
2422: {
2423:   PetscFunctionBegin;
2426:   *type = ((PetscObject)tao)->type_name;
2427:   PetscFunctionReturn(PETSC_SUCCESS);
2428: }

2430: /*@C
2431:   TaoMonitor - Monitor the solver and the current solution.  This
2432:   routine will record the iteration number and residual statistics,
2433:   and call any monitors specified by the user.

2435:    Input Parameters:
2436: +  tao - the `Tao` context
2437: .  its - the current iterate number (>=0)
2438: .  f - the current objective function value
2439: .  res - the gradient norm, square root of the duality gap, or other measure indicating distince from optimality.  This measure will be recorded and
2440:           used for some termination tests.
2441: .  cnorm - the infeasibility of the current solution with regard to the constraints.
2442: -  steplength - multiple of the step direction added to the previous iterate.

2444:    Output Parameter:
2445: .  reason - The termination reason, which can equal `TAO_CONTINUE_ITERATING`

2447:    Options Database Key:
2448: .  -tao_monitor - Use the default monitor, which prints statistics to standard output

2450:    Level: developer

2452: .seealso: [](chapter_tao), `Tao`, `TaoGetConvergedReason()`, `TaoMonitorDefault()`, `TaoSetMonitor()`
2453: @*/
2454: PetscErrorCode TaoMonitor(Tao tao, PetscInt its, PetscReal f, PetscReal res, PetscReal cnorm, PetscReal steplength)
2455: {
2456:   PetscInt i;

2458:   PetscFunctionBegin;
2460:   tao->fc       = f;
2461:   tao->residual = res;
2462:   tao->cnorm    = cnorm;
2463:   tao->step     = steplength;
2464:   if (!its) {
2465:     tao->cnorm0 = cnorm;
2466:     tao->gnorm0 = res;
2467:   }
2468:   PetscCheck(!PetscIsInfOrNanReal(f) && !PetscIsInfOrNanReal(res), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated Inf or NaN");
2469:   for (i = 0; i < tao->numbermonitors; i++) PetscCall((*tao->monitor[i])(tao, tao->monitorcontext[i]));
2470:   PetscFunctionReturn(PETSC_SUCCESS);
2471: }

2473: /*@
2474:    TaoSetConvergenceHistory - Sets the array used to hold the convergence history.

2476:    Logically Collective

2478:    Input Parameters:
2479: +  tao - the `Tao` solver context
2480: .  obj   - array to hold objective value history
2481: .  resid - array to hold residual history
2482: .  cnorm - array to hold constraint violation history
2483: .  lits - integer array holds the number of linear iterations for each Tao iteration
2484: .  na  - size of `obj`, `resid`, and `cnorm`
2485: -  reset - `PETSC_TRUE` indicates each new minimization resets the history counter to zero,
2486:            else it continues storing new values for new minimizations after the old ones

2488:    Level: intermediate

2490:    Notes:
2491:    If set, `Tao` will fill the given arrays with the indicated
2492:    information at each iteration.  If 'obj','resid','cnorm','lits' are
2493:    *all* `NULL` then space (using size `na`, or 1000 if na is `PETSC_DECIDE` or
2494:    `PETSC_DEFAULT`) is allocated for the history.
2495:    If not all are `NULL`, then only the non-`NULL` information categories
2496:    will be stored, the others will be ignored.

2498:    Any convergence information after iteration number 'na' will not be stored.

2500:    This routine is useful, e.g., when running a code for purposes
2501:    of accurate performance monitoring, when no I/O should be done
2502:    during the section of code that is being timed.

2504: .seealso: [](chapter_tao), `TaoGetConvergenceHistory()`
2505: @*/
2506: PetscErrorCode TaoSetConvergenceHistory(Tao tao, PetscReal obj[], PetscReal resid[], PetscReal cnorm[], PetscInt lits[], PetscInt na, PetscBool reset)
2507: {
2508:   PetscFunctionBegin;

2515:   if (na == PETSC_DECIDE || na == PETSC_DEFAULT) na = 1000;
2516:   if (!obj && !resid && !cnorm && !lits) {
2517:     PetscCall(PetscCalloc4(na, &obj, na, &resid, na, &cnorm, na, &lits));
2518:     tao->hist_malloc = PETSC_TRUE;
2519:   }

2521:   tao->hist_obj   = obj;
2522:   tao->hist_resid = resid;
2523:   tao->hist_cnorm = cnorm;
2524:   tao->hist_lits  = lits;
2525:   tao->hist_max   = na;
2526:   tao->hist_reset = reset;
2527:   tao->hist_len   = 0;
2528:   PetscFunctionReturn(PETSC_SUCCESS);
2529: }

2531: /*@C
2532:    TaoGetConvergenceHistory - Gets the arrays used that hold the convergence history.

2534:    Collective

2536:    Input Parameter:
2537: .  tao - the `Tao` context

2539:    Output Parameters:
2540: +  obj   - array used to hold objective value history
2541: .  resid - array used to hold residual history
2542: .  cnorm - array used to hold constraint violation history
2543: .  lits  - integer array used to hold linear solver iteration count
2544: -  nhist  - size of `obj`, `resid`, `cnorm`, and `lits`

2546:    Level: advanced

2548:    Notes:
2549:     This routine must be preceded by calls to `TaoSetConvergenceHistory()`
2550:     and `TaoSolve()`, otherwise it returns useless information.

2552:    This routine is useful, e.g., when running a code for purposes
2553:    of accurate performance monitoring, when no I/O should be done
2554:    during the section of code that is being timed.

2556:    Fortran Note:
2557:    The calling sequence is
2558: .vb
2559:    call TaoGetConvergenceHistory(Tao tao, PetscInt nhist, PetscErrorCode ierr)
2560: .ve

2562: .seealso: [](chapter_tao), `Tao`, `TaoSolve()`, `TaoSetConvergenceHistory()`
2563: @*/
2564: PetscErrorCode TaoGetConvergenceHistory(Tao tao, PetscReal **obj, PetscReal **resid, PetscReal **cnorm, PetscInt **lits, PetscInt *nhist)
2565: {
2566:   PetscFunctionBegin;
2568:   if (obj) *obj = tao->hist_obj;
2569:   if (cnorm) *cnorm = tao->hist_cnorm;
2570:   if (resid) *resid = tao->hist_resid;
2571:   if (lits) *lits = tao->hist_lits;
2572:   if (nhist) *nhist = tao->hist_len;
2573:   PetscFunctionReturn(PETSC_SUCCESS);
2574: }

2576: /*@
2577:    TaoSetApplicationContext - Sets the optional user-defined context for a `Tao` solver.

2579:    Logically Collective

2581:    Input Parameters:
2582: +  tao  - the `Tao` context
2583: -  usrP - optional user context

2585:    Level: intermediate

2587: .seealso: [](chapter_tao), `Tao`, `TaoGetApplicationContext()`, `TaoSetApplicationContext()`
2588: @*/
2589: PetscErrorCode TaoSetApplicationContext(Tao tao, void *usrP)
2590: {
2591:   PetscFunctionBegin;
2593:   tao->user = usrP;
2594:   PetscFunctionReturn(PETSC_SUCCESS);
2595: }

2597: /*@
2598:    TaoGetApplicationContext - Gets the user-defined context for a `Tao` solver

2600:    Not Collective

2602:    Input Parameter:
2603: .  tao  - the `Tao` context

2605:    Output Parameter:
2606: .  usrP - user context

2608:    Level: intermediate

2610: .seealso: [](chapter_tao), `Tao`, `TaoSetApplicationContext()`
2611: @*/
2612: PetscErrorCode TaoGetApplicationContext(Tao tao, void *usrP)
2613: {
2614:   PetscFunctionBegin;
2617:   *(void **)usrP = tao->user;
2618:   PetscFunctionReturn(PETSC_SUCCESS);
2619: }

2621: /*@
2622:    TaoSetGradientNorm - Sets the matrix used to define the norm that measures the size of the gradient.

2624:    Collective

2626:    Input Parameters:
2627: +  tao  - the `Tao` context
2628: -  M    - matrix that defines the norm

2630:    Level: beginner

2632: .seealso: [](chapter_tao), `Tao`, `TaoGetGradientNorm()`, `TaoGradientNorm()`
2633: @*/
2634: PetscErrorCode TaoSetGradientNorm(Tao tao, Mat M)
2635: {
2636:   PetscFunctionBegin;
2639:   PetscCall(PetscObjectReference((PetscObject)M));
2640:   PetscCall(MatDestroy(&tao->gradient_norm));
2641:   PetscCall(VecDestroy(&tao->gradient_norm_tmp));
2642:   tao->gradient_norm = M;
2643:   PetscCall(MatCreateVecs(M, NULL, &tao->gradient_norm_tmp));
2644:   PetscFunctionReturn(PETSC_SUCCESS);
2645: }

2647: /*@
2648:    TaoGetGradientNorm - Returns the matrix used to define the norm used for measuring the size of the gradient.

2650:    Not Collective

2652:    Input Parameter:
2653: .  tao  - the `Tao` context

2655:    Output Parameter:
2656: .  M - gradient norm

2658:    Level: beginner

2660: .seealso: [](chapter_tao), `Tao`, `TaoSetGradientNorm()`, `TaoGradientNorm()`
2661: @*/
2662: PetscErrorCode TaoGetGradientNorm(Tao tao, Mat *M)
2663: {
2664:   PetscFunctionBegin;
2667:   *M = tao->gradient_norm;
2668:   PetscFunctionReturn(PETSC_SUCCESS);
2669: }

2671: /*@C
2672:    TaoGradientNorm - Compute the norm using the `NormType`, the user has selected

2674:    Collective

2676:    Input Parameters:
2677: +  tao      - the `Tao` context
2678: .  gradient - the gradient to be computed
2679: -  norm     - the norm type

2681:    Output Parameter:
2682: .  gnorm    - the gradient norm

2684:    Level: advanced

2686: .seealso: [](chapter_tao), `Tao`, `TaoSetGradientNorm()`, `TaoGetGradientNorm()`
2687: @*/
2688: PetscErrorCode TaoGradientNorm(Tao tao, Vec gradient, NormType type, PetscReal *gnorm)
2689: {
2690:   PetscFunctionBegin;
2695:   if (tao->gradient_norm) {
2696:     PetscScalar gnorms;

2698:     PetscCheck(type == NORM_2, PetscObjectComm((PetscObject)gradient), PETSC_ERR_ARG_WRONG, "Norm type must be NORM_2 if an inner product for the gradient norm is set.");
2699:     PetscCall(MatMult(tao->gradient_norm, gradient, tao->gradient_norm_tmp));
2700:     PetscCall(VecDot(gradient, tao->gradient_norm_tmp, &gnorms));
2701:     *gnorm = PetscRealPart(PetscSqrtScalar(gnorms));
2702:   } else {
2703:     PetscCall(VecNorm(gradient, type, gnorm));
2704:   }
2705:   PetscFunctionReturn(PETSC_SUCCESS);
2706: }

2708: /*@C
2709:    TaoMonitorDrawCtxCreate - Creates the monitor context for `TaoMonitorDrawSolution()`

2711:    Collective

2713:    Output Parameter:
2714: .    ctx - the monitor context

2716:    Options Database Key:
2717: .   -tao_draw_solution_initial - show initial guess as well as current solution

2719:    Level: intermediate

2721: .seealso: [](chapter_tao), `Tao`, `TaoMonitorSet()`, `TaoMonitorDefault()`, `VecView()`, `TaoMonitorDrawCtx()`
2722: @*/
2723: PetscErrorCode TaoMonitorDrawCtxCreate(MPI_Comm comm, const char host[], const char label[], int x, int y, int m, int n, PetscInt howoften, TaoMonitorDrawCtx *ctx)
2724: {
2725:   PetscFunctionBegin;
2726:   PetscCall(PetscNew(ctx));
2727:   PetscCall(PetscViewerDrawOpen(comm, host, label, x, y, m, n, &(*ctx)->viewer));
2728:   PetscCall(PetscViewerSetFromOptions((*ctx)->viewer));
2729:   (*ctx)->howoften = howoften;
2730:   PetscFunctionReturn(PETSC_SUCCESS);
2731: }

2733: /*@C
2734:    TaoMonitorDrawCtxDestroy - Destroys the monitor context for `TaoMonitorDrawSolution()`

2736:    Collective

2738:    Input Parameter:
2739: .    ctx - the monitor context

2741:    Level: intermediate

2743: .seealso: [](chapter_tao), `Tao`, `TaoMonitorSet()`, `TaoMonitorDefault()`, `VecView()`, `TaoMonitorDrawSolution()`
2744: @*/
2745: PetscErrorCode TaoMonitorDrawCtxDestroy(TaoMonitorDrawCtx *ictx)
2746: {
2747:   PetscFunctionBegin;
2748:   PetscCall(PetscViewerDestroy(&(*ictx)->viewer));
2749:   PetscCall(PetscFree(*ictx));
2750:   PetscFunctionReturn(PETSC_SUCCESS);
2751: }