Actual source code: tr.c

  1: #include <../src/snes/impls/tr/trimpl.h>

  3: typedef struct {
  4:   SNES snes;
  5:   PetscErrorCode (*convtest)(KSP, PetscInt, PetscReal, KSPConvergedReason *, void *);
  6:   PetscErrorCode (*convdestroy)(void *);
  7:   void *convctx;
  8: } SNES_TR_KSPConverged_Ctx;

 10: const char *const SNESNewtonTRFallbackTypes[] = {"NEWTON", "CAUCHY", "DOGLEG", "SNESNewtonTRFallbackType", "SNES_TR_FALLBACK_", NULL};

 12: static PetscErrorCode SNESTR_KSPConverged_Private(KSP ksp, PetscInt n, PetscReal rnorm, KSPConvergedReason *reason, void *cctx)
 13: {
 14:   SNES_TR_KSPConverged_Ctx *ctx  = (SNES_TR_KSPConverged_Ctx *)cctx;
 15:   SNES                      snes = ctx->snes;
 16:   SNES_NEWTONTR            *neP  = (SNES_NEWTONTR *)snes->data;
 17:   Vec                       x;
 18:   PetscReal                 nrm;

 20:   PetscFunctionBegin;
 21:   PetscCall((*ctx->convtest)(ksp, n, rnorm, reason, ctx->convctx));
 22:   if (*reason) PetscCall(PetscInfo(snes, "Default or user provided convergence test KSP iterations=%" PetscInt_FMT ", rnorm=%g\n", n, (double)rnorm));
 23:   /* Determine norm of solution */
 24:   PetscCall(KSPBuildSolution(ksp, NULL, &x));
 25:   PetscCall(VecNorm(x, NORM_2, &nrm));
 26:   if (nrm >= neP->delta) {
 27:     PetscCall(PetscInfo(snes, "Ending linear iteration early, delta=%g, length=%g\n", (double)neP->delta, (double)nrm));
 28:     *reason = KSP_CONVERGED_STEP_LENGTH;
 29:   }
 30:   PetscFunctionReturn(PETSC_SUCCESS);
 31: }

 33: static PetscErrorCode SNESTR_KSPConverged_Destroy(void *cctx)
 34: {
 35:   SNES_TR_KSPConverged_Ctx *ctx = (SNES_TR_KSPConverged_Ctx *)cctx;

 37:   PetscFunctionBegin;
 38:   PetscCall((*ctx->convdestroy)(ctx->convctx));
 39:   PetscCall(PetscFree(ctx));
 40:   PetscFunctionReturn(PETSC_SUCCESS);
 41: }

 43: static PetscErrorCode SNESTR_Converged_Private(SNES snes, PetscInt it, PetscReal xnorm, PetscReal pnorm, PetscReal fnorm, SNESConvergedReason *reason, void *dummy)
 44: {
 45:   SNES_NEWTONTR *neP = (SNES_NEWTONTR *)snes->data;

 47:   PetscFunctionBegin;
 48:   *reason = SNES_CONVERGED_ITERATING;
 49:   if (neP->delta < snes->deltatol) {
 50:     PetscCall(PetscInfo(snes, "Diverged due to too small a trust region %g<%g\n", (double)neP->delta, (double)snes->deltatol));
 51:     *reason = SNES_DIVERGED_TR_DELTA;
 52:   } else if (snes->nfuncs >= snes->max_funcs && snes->max_funcs >= 0) {
 53:     PetscCall(PetscInfo(snes, "Exceeded maximum number of function evaluations: %" PetscInt_FMT "\n", snes->max_funcs));
 54:     *reason = SNES_DIVERGED_FUNCTION_COUNT;
 55:   }
 56:   PetscFunctionReturn(PETSC_SUCCESS);
 57: }

 59: /*@
 60:   SNESNewtonTRSetFallbackType - Set the type of fallback to use if the solution of the trust region subproblem is outside the radius

 62:   Input Parameters:
 63: + snes  - the nonlinear solver object
 64: - ftype - the fallback type, see `SNESNewtonTRFallbackType`

 66:   Level: intermediate

 68: .seealso: [](ch_snes), `SNESNEWTONTR`, `SNESNewtonTRPreCheck()`, `SNESNewtonTRGetPreCheck()`, `SNESNewtonTRSetPreCheck()`,
 69:           `SNESNewtonTRSetPostCheck()`, `SNESNewtonTRGetPostCheck()`
 70: @*/
 71: PetscErrorCode SNESNewtonTRSetFallbackType(SNES snes, SNESNewtonTRFallbackType ftype)
 72: {
 73:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
 74:   PetscBool      flg;

 76:   PetscFunctionBegin;
 79:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
 80:   if (flg) tr->fallback = ftype;
 81:   PetscFunctionReturn(PETSC_SUCCESS);
 82: }

 84: /*@C
 85:   SNESNewtonTRSetPreCheck - Sets a user function that is called before the search step has been determined.
 86:   Allows the user a chance to change or override the trust region decision.

 88:   Logically Collective

 90:   Input Parameters:
 91: + snes - the nonlinear solver object
 92: . func - [optional] function evaluation routine, for the calling sequence see `SNESNewtonTRPreCheck()`
 93: - ctx  - [optional] user-defined context for private data for the function evaluation routine (may be `NULL`)

 95:   Level: deprecated (since 3.19)

 97:   Note:
 98:   This function is called BEFORE the function evaluation within the solver.

100: .seealso: [](ch_snes), `SNESNEWTONTR`, `SNESNewtonTRPreCheck()`, `SNESNewtonTRGetPreCheck()`, `SNESNewtonTRSetPostCheck()`, `SNESNewtonTRGetPostCheck()`,
101: @*/
102: PetscErrorCode SNESNewtonTRSetPreCheck(SNES snes, PetscErrorCode (*func)(SNES, Vec, Vec, PetscBool *, void *), void *ctx)
103: {
104:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
105:   PetscBool      flg;

107:   PetscFunctionBegin;
109:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
110:   if (flg) {
111:     if (func) tr->precheck = func;
112:     if (ctx) tr->precheckctx = ctx;
113:   }
114:   PetscFunctionReturn(PETSC_SUCCESS);
115: }

117: /*@C
118:   SNESNewtonTRGetPreCheck - Gets the pre-check function

120:   Deprecated use `SNESNEWTONDCTRDC`

122:   Not Collective

124:   Input Parameter:
125: . snes - the nonlinear solver context

127:   Output Parameters:
128: + func - [optional] function evaluation routine, for the calling sequence see `SNESNewtonTRPreCheck()`
129: - ctx  - [optional] user-defined context for private data for the function evaluation routine (may be `NULL`)

131:   Level: deprecated (since 3.19)

133: .seealso: [](ch_snes), `SNESNEWTONTR`, `SNESNewtonTRSetPreCheck()`, `SNESNewtonTRPreCheck()`
134: @*/
135: PetscErrorCode SNESNewtonTRGetPreCheck(SNES snes, PetscErrorCode (**func)(SNES, Vec, Vec, PetscBool *, void *), void **ctx)
136: {
137:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
138:   PetscBool      flg;

140:   PetscFunctionBegin;
142:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
143:   PetscAssert(flg, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONG, "Not for type %s", ((PetscObject)snes)->type_name);
144:   if (func) *func = tr->precheck;
145:   if (ctx) *ctx = tr->precheckctx;
146:   PetscFunctionReturn(PETSC_SUCCESS);
147: }

149: /*@C
150:   SNESNewtonTRSetPostCheck - Sets a user function that is called after the search step has been determined but before the next
151:   function evaluation. Allows the user a chance to change or override the internal decision of the solver

153:   Logically Collective

155:   Input Parameters:
156: + snes - the nonlinear solver object
157: . func - [optional] function evaluation routine, for the calling sequence see `SNESNewtonTRPostCheck()`
158: - ctx  - [optional] user-defined context for private data for the function evaluation routine (may be `NULL`)

160:   Level: deprecated (since 3.19)

162:   Note:
163:   This function is called BEFORE the function evaluation within the solver while the function set in
164:   `SNESLineSearchSetPostCheck()` is called AFTER the function evaluation.

166: .seealso: [](ch_snes), `SNESNEWTONTR`, `SNESNewtonTRPostCheck()`, `SNESNewtonTRGetPostCheck()`, `SNESNewtonTRSetPreCheck()`, `SNESNewtonTRGetPreCheck()`
167: @*/
168: PetscErrorCode SNESNewtonTRSetPostCheck(SNES snes, PetscErrorCode (*func)(SNES, Vec, Vec, Vec, PetscBool *, PetscBool *, void *), void *ctx)
169: {
170:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
171:   PetscBool      flg;

173:   PetscFunctionBegin;
175:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
176:   if (flg) {
177:     if (func) tr->postcheck = func;
178:     if (ctx) tr->postcheckctx = ctx;
179:   }
180:   PetscFunctionReturn(PETSC_SUCCESS);
181: }

183: /*@C
184:   SNESNewtonTRGetPostCheck - Gets the post-check function

186:   Not Collective

188:   Input Parameter:
189: . snes - the nonlinear solver context

191:   Output Parameters:
192: + func - [optional] function evaluation routine, for the calling sequence see `SNESNewtonTRPostCheck()`
193: - ctx  - [optional] user-defined context for private data for the function evaluation routine (may be `NULL`)

195:   Level: intermediate

197: .seealso: [](ch_snes), `SNESNEWTONTR`, `SNESNewtonTRSetPostCheck()`, `SNESNewtonTRPostCheck()`
198: @*/
199: PetscErrorCode SNESNewtonTRGetPostCheck(SNES snes, PetscErrorCode (**func)(SNES, Vec, Vec, Vec, PetscBool *, PetscBool *, void *), void **ctx)
200: {
201:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
202:   PetscBool      flg;

204:   PetscFunctionBegin;
206:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
207:   PetscAssert(flg, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONG, "Not for type %s", ((PetscObject)snes)->type_name);
208:   if (func) *func = tr->postcheck;
209:   if (ctx) *ctx = tr->postcheckctx;
210:   PetscFunctionReturn(PETSC_SUCCESS);
211: }

213: /*@C
214:   SNESNewtonTRPreCheck - Runs the precheck routine

216:   Logically Collective

218:   Input Parameters:
219: + snes - the solver
220: . X    - The last solution
221: - Y    - The step direction

223:   Output Parameter:
224: . changed_Y - Indicator that the step direction `Y` has been changed.

226:   Level: intermediate

228: .seealso: [](ch_snes), `SNESNEWTONTR`, `SNESNewtonTRSetPreCheck()`, `SNESNewtonTRGetPreCheck()`, `SNESNewtonTRPostCheck()`
229: @*/
230: PetscErrorCode SNESNewtonTRPreCheck(SNES snes, Vec X, Vec Y, PetscBool *changed_Y)
231: {
232:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
233:   PetscBool      flg;

235:   PetscFunctionBegin;
237:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
238:   PetscAssert(flg, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONG, "Not for type %s", ((PetscObject)snes)->type_name);
239:   *changed_Y = PETSC_FALSE;
240:   if (tr->precheck) {
241:     PetscCall((*tr->precheck)(snes, X, Y, changed_Y, tr->precheckctx));
243:   }
244:   PetscFunctionReturn(PETSC_SUCCESS);
245: }

247: /*@C
248:   SNESNewtonTRPostCheck - Runs the postcheck routine

250:   Logically Collective

252:   Input Parameters:
253: + snes - the solver
254: . X    - The last solution
255: . Y    - The full step direction
256: - W    - The updated solution, W = X - Y

258:   Output Parameters:
259: + changed_Y - indicator if step has been changed
260: - changed_W - Indicator if the new candidate solution W has been changed.

262:   Note:
263:   If Y is changed then W is recomputed as X - Y

265:   Level: intermediate

267: .seealso: [](ch_snes), `SNESNEWTONTR`, `SNESNewtonTRSetPostCheck()`, `SNESNewtonTRGetPostCheck()`, `SNESNewtonTRPreCheck()`
268: @*/
269: PetscErrorCode SNESNewtonTRPostCheck(SNES snes, Vec X, Vec Y, Vec W, PetscBool *changed_Y, PetscBool *changed_W)
270: {
271:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
272:   PetscBool      flg;

274:   PetscFunctionBegin;
276:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
277:   PetscAssert(flg, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONG, "Not for type %s", ((PetscObject)snes)->type_name);
278:   *changed_Y = PETSC_FALSE;
279:   *changed_W = PETSC_FALSE;
280:   if (tr->postcheck) {
281:     PetscCall((*tr->postcheck)(snes, X, Y, W, changed_Y, changed_W, tr->postcheckctx));
284:   }
285:   PetscFunctionReturn(PETSC_SUCCESS);
286: }

288: static inline void PetscQuadraticRoots(PetscReal a, PetscReal b, PetscReal c, PetscReal *xm, PetscReal *xp)
289: {
290:   PetscReal temp = -0.5 * (b + PetscCopysignReal(1.0, b) * PetscSqrtReal(b * b - 4 * a * c));
291:   PetscReal x1   = temp / a;
292:   PetscReal x2   = c / temp;
293:   *xm            = PetscMin(x1, x2);
294:   *xp            = PetscMax(x1, x2);
295: }

297: /* Computes the quadratic model difference */
298: static PetscErrorCode SNESNewtonTRQuadraticDelta(SNES snes, PetscBool has_objective, Vec Y, Vec GradF, Vec W, PetscReal *yTHy, PetscReal *gTy, PetscReal *deltaqm)
299: {
300:   PetscFunctionBegin;
301:   PetscCall(MatMult(snes->jacobian, Y, W));
302:   if (has_objective) PetscCall(VecDotRealPart(Y, W, yTHy));
303:   else PetscCall(VecDotRealPart(W, W, yTHy)); /* Gauss-Newton approximation J^t * J */
304:   PetscCall(VecDotRealPart(GradF, Y, gTy));
305:   *deltaqm = -(-(*gTy) + 0.5 * (*yTHy)); /* difference in quadratic model, -gTy because SNES solves it this way */
306:   PetscFunctionReturn(PETSC_SUCCESS);
307: }

309: /*
310:    SNESSolve_NEWTONTR - Implements Newton's Method with trust-region subproblem and adds dogleg Cauchy
311:    (Steepest Descent direction) step and direction if the trust region is not satisfied for solving system of
312:    nonlinear equations

314: */
315: static PetscErrorCode SNESSolve_NEWTONTR(SNES snes)
316: {
317:   SNES_NEWTONTR            *neP = (SNES_NEWTONTR *)snes->data;
318:   Vec                       X, F, Y, G, W, GradF, YU;
319:   PetscInt                  maxits, lits;
320:   PetscReal                 rho, fnorm, gnorm = 0.0, xnorm = 0.0, delta, ynorm;
321:   PetscReal                 deltaM, fk, fkp1, deltaqm, gTy, yTHy;
322:   PetscReal                 auk, gfnorm, ycnorm, gTBg, objmin = 0.0;
323:   KSP                       ksp;
324:   PetscBool                 already_done = PETSC_FALSE;
325:   PetscBool                 clear_converged_test, rho_satisfied, has_objective;
326:   SNES_TR_KSPConverged_Ctx *ctx;
327:   void                     *convctx;
328:   PetscErrorCode (*convtest)(KSP, PetscInt, PetscReal, KSPConvergedReason *, void *), (*convdestroy)(void *);
329:   PetscErrorCode (*objective)(SNES, Vec, PetscReal *, void *);

331:   PetscFunctionBegin;
332:   PetscCall(SNESGetObjective(snes, &objective, NULL));
333:   has_objective = objective ? PETSC_TRUE : PETSC_FALSE;

335:   maxits = snes->max_its;                                   /* maximum number of iterations */
336:   X      = snes->vec_sol;                                   /* solution vector */
337:   F      = snes->vec_func;                                  /* residual vector */
338:   Y      = snes->vec_sol_update;                            /* update vector */
339:   G      = snes->work[0];                                   /* updated residual */
340:   W      = snes->work[1];                                   /* temporary vector */
341:   GradF  = !has_objective ? snes->work[2] : snes->vec_func; /* grad f = J^T F */
342:   YU     = snes->work[3];                                   /* work vector for dogleg method */

344:   PetscCheck(!snes->xl && !snes->xu && !snes->ops->computevariablebounds, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONGSTATE, "SNES solver %s does not support bounds", ((PetscObject)snes)->type_name);

346:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
347:   snes->iter = 0;
348:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));

350:   /* Set the linear stopping criteria to use the More' trick if needed */
351:   clear_converged_test = PETSC_FALSE;
352:   PetscCall(SNESGetKSP(snes, &ksp));
353:   PetscCall(KSPGetConvergenceTest(ksp, &convtest, &convctx, &convdestroy));
354:   if (convtest != SNESTR_KSPConverged_Private) {
355:     clear_converged_test = PETSC_TRUE;
356:     PetscCall(PetscNew(&ctx));
357:     ctx->snes = snes;
358:     PetscCall(KSPGetAndClearConvergenceTest(ksp, &ctx->convtest, &ctx->convctx, &ctx->convdestroy));
359:     PetscCall(KSPSetConvergenceTest(ksp, SNESTR_KSPConverged_Private, ctx, SNESTR_KSPConverged_Destroy));
360:     PetscCall(PetscInfo(snes, "Using Krylov convergence test SNESTR_KSPConverged_Private\n"));
361:   }

363:   if (!snes->vec_func_init_set) {
364:     PetscCall(SNESComputeFunction(snes, X, F)); /* F(X) */
365:   } else snes->vec_func_init_set = PETSC_FALSE;

367:   PetscCall(VecNorm(F, NORM_2, &fnorm)); /* fnorm <- || F || */
368:   SNESCheckFunctionNorm(snes, fnorm);
369:   PetscCall(VecNorm(X, NORM_2, &xnorm)); /* xnorm <- || X || */

371:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
372:   snes->norm = fnorm;
373:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
374:   delta      = neP->delta0;
375:   deltaM     = neP->deltaM;
376:   neP->delta = delta;
377:   PetscCall(SNESLogConvergenceHistory(snes, fnorm, 0));

379:   /* test convergence */
380:   rho_satisfied = PETSC_FALSE;
381:   PetscCall(SNESConverged(snes, 0, 0.0, 0.0, fnorm));
382:   PetscCall(SNESMonitor(snes, 0, fnorm));
383:   if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS);

385:   if (has_objective) PetscCall(SNESComputeObjective(snes, X, &fk));
386:   else fk = 0.5 * PetscSqr(fnorm); /* obj(x) = 0.5 * ||F(x)||^2 */

388:   while (snes->iter < maxits) {
389:     PetscBool changed_y;
390:     PetscBool changed_w;

392:     /* calculating Jacobian and GradF of minimization function only once */
393:     if (!already_done) {
394:       /* Call general purpose update function */
395:       PetscTryTypeMethod(snes, update, snes->iter);

397:       /* apply the nonlinear preconditioner */
398:       if (snes->npc && snes->npcside == PC_RIGHT) {
399:         SNESConvergedReason reason;

401:         PetscCall(SNESSetInitialFunction(snes->npc, F));
402:         PetscCall(PetscLogEventBegin(SNES_NPCSolve, snes->npc, X, snes->vec_rhs, 0));
403:         PetscCall(SNESSolve(snes->npc, snes->vec_rhs, X));
404:         PetscCall(PetscLogEventEnd(SNES_NPCSolve, snes->npc, X, snes->vec_rhs, 0));
405:         PetscCall(SNESGetConvergedReason(snes->npc, &reason));
406:         if (reason < 0 && reason != SNES_DIVERGED_MAX_IT && reason != SNES_DIVERGED_TR_DELTA) {
407:           snes->reason = SNES_DIVERGED_INNER;
408:           PetscFunctionReturn(PETSC_SUCCESS);
409:         }
410:         // XXX
411:         PetscCall(SNESGetNPCFunction(snes, F, &fnorm));
412:         if (has_objective) PetscCall(SNESComputeObjective(snes, X, &fk));
413:         else fk = 0.5 * PetscSqr(fnorm); /* obj(x) = 0.5 * ||F(x)||^2 */
414:         // XXX
415:       } else if (snes->ops->update) { /* if update is present, recompute objective function and function norm */
416:         PetscCall(SNESComputeFunction(snes, X, F));
417:         PetscCall(VecNorm(F, NORM_2, &fnorm));
418:         if (has_objective) PetscCall(SNESComputeObjective(snes, X, &fk));
419:         else fk = 0.5 * PetscSqr(fnorm); /* obj(x) = 0.5 * ||F(x)||^2 */
420:       }

422:       /* Jacobian */
423:       PetscCall(SNESComputeJacobian(snes, X, snes->jacobian, snes->jacobian_pre));
424:       SNESCheckJacobianDomainerror(snes);

426:       /* GradF */
427:       if (has_objective) gfnorm = fnorm;
428:       else {
429:         PetscCall(MatMultTranspose(snes->jacobian, F, GradF)); /* grad f = J^T F */
430:         PetscCall(VecNorm(GradF, NORM_2, &gfnorm));
431:       }
432:     }
433:     already_done = PETSC_TRUE;

435:     /* solve trust-region subproblem */

437:     /* sufficient decrease (see 6.3.27 in Conn, Gould, Toint "Trust Region Methods")
438:        This is actually more relaxed, since they use include gnorm/beta_k, with
439:        beta_k the largest eigenvalue of the Hessian */
440:     objmin = -neP->kmdc * gnorm * PetscMin(gnorm, delta);
441:     PetscCall(KSPCGSetObjectiveTarget(snes->ksp, objmin));

443:     /* don't specify radius if not looking for Newton step only */
444:     PetscCall(KSPCGSetRadius(snes->ksp, neP->fallback == SNES_TR_FALLBACK_NEWTON ? delta : 0.0));

446:     PetscCall(KSPSetOperators(snes->ksp, snes->jacobian, snes->jacobian_pre));
447:     PetscCall(KSPSolve(snes->ksp, F, Y));
448:     SNESCheckKSPSolve(snes);
449:     PetscCall(KSPGetIterationNumber(snes->ksp, &lits));
450:     PetscCall(PetscInfo(snes, "iter=%" PetscInt_FMT ", linear solve iterations=%" PetscInt_FMT "\n", snes->iter, lits));

452:     /* decide what to do when the update is outside of trust region */
453:     PetscCall(VecNorm(Y, NORM_2, &ynorm));
454:     if (ynorm > delta || ynorm == 0.0) {
455:       SNESNewtonTRFallbackType fallback = ynorm > 0.0 ? neP->fallback : SNES_TR_FALLBACK_CAUCHY;

457:       switch (fallback) {
458:       case SNES_TR_FALLBACK_NEWTON:
459:         auk = delta / ynorm;
460:         PetscCall(VecScale(Y, auk));
461:         PetscCall(PetscInfo(snes, "SN evaluated. delta: %g, ynorm: %g\n", (double)delta, (double)ynorm));
462:         break;
463:       case SNES_TR_FALLBACK_CAUCHY:
464:       case SNES_TR_FALLBACK_DOGLEG:
465:         PetscCall(MatMult(snes->jacobian, GradF, W));
466:         if (has_objective) PetscCall(VecDotRealPart(GradF, W, &gTBg));
467:         else PetscCall(VecDotRealPart(W, W, &gTBg)); /* B = J^t * J */
468:         /* Eqs 4.7 and 4.8 in Nocedal and Wright */
469:         auk = delta / gfnorm;
470:         if (gTBg > 0.0) auk *= PetscMin(gfnorm * gfnorm * gfnorm / (delta * gTBg), 1);
471:         ycnorm = auk * gfnorm;
472:         if (fallback == SNES_TR_FALLBACK_CAUCHY || gTBg <= 0.0) {
473:           /* Cauchy solution */
474:           PetscCall(VecAXPBY(Y, auk, 0.0, GradF));
475:           PetscCall(PetscInfo(snes, "CP evaluated. delta: %g, ynorm: %g, ycnorm: %g, gTBg: %g\n", (double)delta, (double)ynorm, (double)ycnorm, (double)gTBg));
476:         } else { /* take linear combination of Cauchy and Newton direction and step */
477:           PetscReal c0, c1, c2, tau = 0.0, tpos, tneg;
478:           PetscBool noroots;

480:           auk = gfnorm * gfnorm / gTBg;
481:           PetscCall(VecAXPBY(YU, auk, 0.0, GradF));
482:           PetscCall(VecAXPY(Y, -1.0, YU));
483:           PetscCall(VecNorm(Y, NORM_2, &c0));
484:           PetscCall(VecDotRealPart(YU, Y, &c1));
485:           c0 = PetscSqr(c0);
486:           c2 = PetscSqr(ycnorm) - PetscSqr(delta);
487:           PetscQuadraticRoots(c0, c1, c2, &tneg, &tpos);

489:           noroots = PetscIsInfOrNanReal(tneg);
490:           if (noroots) { /*  No roots, select Cauchy point */
491:             auk = delta / gfnorm;
492:             auk *= PetscMin(gfnorm * gfnorm * gfnorm / (delta * gTBg), 1);
493:             PetscCall(VecAXPBY(Y, auk, 0.0, GradF));
494:           } else { /* Here roots corresponds to tau-1 in Nocedal and Wright */
495:             tpos += 1.0;
496:             tneg += 1.0;
497:             tau = PetscClipInterval(tpos, 0.0, 2.0); /* clip to tau [0,2] */
498:             if (tau < 1.0) {
499:               PetscCall(VecAXPBY(Y, tau, 0.0, YU));
500:             } else {
501:               PetscCall(VecAXPBY(Y, 1.0, tau - 1, YU));
502:             }
503:           }
504:           PetscCall(VecNorm(Y, NORM_2, &c0)); /* this norm will be cached and reused later */
505:           PetscCall(PetscInfo(snes, "%s evaluated. roots: (%g, %g), tau %g, ynorm: %g, ycnorm: %g, ydlnorm %g, gTBg: %g\n", noroots ? "CP" : "DL", (double)tneg, (double)tpos, (double)tau, (double)ynorm, (double)ycnorm, (double)c0, (double)gTBg));
506:         }
507:         break;
508:       default:
509:         SETERRQ(PetscObjectComm((PetscObject)snes), PETSC_ERR_SUP, "Unknown fallback mode");
510:         break;
511:       }
512:     }

514:     /* Evaluate the solution to meet the improvement ratio criteria */

516:     /* compute the final ynorm */
517:     PetscCall(SNESNewtonTRPreCheck(snes, X, Y, &changed_y));
518:     PetscCall(VecNorm(Y, NORM_2, &ynorm));

520:     /* compute the quadratic model difference */
521:     PetscCall(SNESNewtonTRQuadraticDelta(snes, has_objective, Y, GradF, W, &yTHy, &gTy, &deltaqm));

523:     /* update */
524:     PetscCall(VecWAXPY(W, -1.0, Y, X)); /* Xkp1 */
525:     PetscCall(SNESNewtonTRPostCheck(snes, X, Y, W, &changed_y, &changed_w));
526:     if (changed_y) {
527:       /* Need to recompute the quadratic model difference */
528:       PetscCall(SNESNewtonTRQuadraticDelta(snes, has_objective, Y, GradF, YU, &yTHy, &gTy, &deltaqm));
529:       /* User changed Y but not W */
530:       if (!changed_w) PetscCall(VecWAXPY(W, -1.0, Y, X));
531:     }

533:     /* Compute new objective function */
534:     PetscCall(SNESComputeFunction(snes, W, G)); /*  F(Xkp1) = G */
535:     PetscCall(VecNorm(G, NORM_2, &gnorm));
536:     if (has_objective) PetscCall(SNESComputeObjective(snes, W, &fkp1));
537:     else fkp1 = 0.5 * PetscSqr(gnorm);
538:     SNESCheckFunctionNorm(snes, fkp1);

540:     if (deltaqm > 0.0) rho = (fk - fkp1) / deltaqm; /* actual improvement over predicted improvement */
541:     else rho = -1.0;                                /*  no reduction in quadratic model, step must be rejected */
542:     PetscCall(PetscInfo(snes, "rho=%g, delta=%g, fk=%g, fkp1=%g, deltaqm=%g, gTy=%g, yTHy=%g\n", (double)rho, (double)delta, (double)fk, (double)fkp1, (double)deltaqm, (double)gTy, (double)yTHy));

544:     if (rho < neP->eta2) delta *= neP->t1;      /* shrink the region */
545:     else if (rho > neP->eta3) delta *= neP->t2; /* expand the region */
546:     delta = PetscMin(delta, deltaM);            /* but not greater than deltaM */

548:     neP->delta = delta;
549:     if (rho >= neP->eta1) {
550:       rho_satisfied = PETSC_TRUE;
551:     } else {
552:       rho_satisfied = PETSC_FALSE;
553:       PetscCall(PetscInfo(snes, "Trying again in smaller region\n"));
554:       /* check to see if progress is hopeless */
555:       PetscCall(SNESTR_Converged_Private(snes, snes->iter, xnorm, ynorm, fnorm, &snes->reason, snes->cnvP));
556:       if (!snes->reason) PetscCall(SNESConverged(snes, snes->iter, xnorm, ynorm, fnorm));
557:       if (snes->reason == SNES_CONVERGED_SNORM_RELATIVE) snes->reason = SNES_DIVERGED_TR_DELTA;
558:       snes->numFailures++;
559:       /* We're not progressing, so return with the current iterate */
560:       if (snes->reason) break;
561:     }
562:     if (rho_satisfied) {
563:       /* Update function values */
564:       already_done = PETSC_FALSE;
565:       fnorm        = gnorm;
566:       fk           = fkp1;

568:       /* New residual and linearization point */
569:       PetscCall(VecCopy(G, F));
570:       PetscCall(VecCopy(W, X));

572:       /* Monitor convergence */
573:       PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
574:       snes->iter++;
575:       snes->norm  = fnorm;
576:       snes->xnorm = xnorm;
577:       snes->ynorm = ynorm;
578:       PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
579:       PetscCall(SNESLogConvergenceHistory(snes, snes->norm, lits));

581:       /* Test for convergence, xnorm = || X || */
582:       PetscCall(VecNorm(X, NORM_2, &xnorm));
583:       PetscCall(SNESConverged(snes, snes->iter, xnorm, ynorm, fnorm));
584:       PetscCall(SNESMonitor(snes, snes->iter, snes->norm));
585:       if (snes->reason) break;
586:     }
587:   }

589:   if (clear_converged_test) {
590:     PetscCall(KSPGetAndClearConvergenceTest(ksp, &ctx->convtest, &ctx->convctx, &ctx->convdestroy));
591:     PetscCall(PetscFree(ctx));
592:     PetscCall(KSPSetConvergenceTest(ksp, convtest, convctx, convdestroy));
593:   }
594:   PetscFunctionReturn(PETSC_SUCCESS);
595: }

597: static PetscErrorCode SNESSetUp_NEWTONTR(SNES snes)
598: {
599:   PetscFunctionBegin;
600:   PetscCall(SNESSetWorkVecs(snes, 4));
601:   PetscCall(SNESSetUpMatrices(snes));
602:   PetscFunctionReturn(PETSC_SUCCESS);
603: }

605: static PetscErrorCode SNESDestroy_NEWTONTR(SNES snes)
606: {
607:   PetscFunctionBegin;
608:   PetscCall(PetscFree(snes->data));
609:   PetscFunctionReturn(PETSC_SUCCESS);
610: }

612: static PetscErrorCode SNESSetFromOptions_NEWTONTR(SNES snes, PetscOptionItems *PetscOptionsObject)
613: {
614:   SNES_NEWTONTR *ctx = (SNES_NEWTONTR *)snes->data;

616:   PetscFunctionBegin;
617:   PetscOptionsHeadBegin(PetscOptionsObject, "SNES trust region options for nonlinear equations");
618:   PetscCall(PetscOptionsReal("-snes_tr_tol", "Trust region tolerance", "SNESSetTrustRegionTolerance", snes->deltatol, &snes->deltatol, NULL));
619:   PetscCall(PetscOptionsReal("-snes_tr_eta1", "eta1", "None", ctx->eta1, &ctx->eta1, NULL));
620:   PetscCall(PetscOptionsReal("-snes_tr_eta2", "eta2", "None", ctx->eta2, &ctx->eta2, NULL));
621:   PetscCall(PetscOptionsReal("-snes_tr_eta3", "eta3", "None", ctx->eta3, &ctx->eta3, NULL));
622:   PetscCall(PetscOptionsReal("-snes_tr_t1", "t1", "None", ctx->t1, &ctx->t1, NULL));
623:   PetscCall(PetscOptionsReal("-snes_tr_t2", "t2", "None", ctx->t2, &ctx->t2, NULL));
624:   PetscCall(PetscOptionsReal("-snes_tr_deltaM", "deltaM", "None", ctx->deltaM, &ctx->deltaM, NULL));
625:   PetscCall(PetscOptionsReal("-snes_tr_delta0", "delta0", "None", ctx->delta0, &ctx->delta0, NULL));
626:   PetscCall(PetscOptionsReal("-snes_tr_kmdc", "sufficient decrease parameter", "None", ctx->kmdc, &ctx->kmdc, NULL));
627:   PetscCall(PetscOptionsEnum("-snes_tr_fallback_type", "Type of fallback if subproblem solution is outside of the trust region", "SNESNewtonTRSetFallbackType", SNESNewtonTRFallbackTypes, (PetscEnum)ctx->fallback, (PetscEnum *)&ctx->fallback, NULL));
628:   PetscOptionsHeadEnd();
629:   PetscFunctionReturn(PETSC_SUCCESS);
630: }

632: static PetscErrorCode SNESView_NEWTONTR(SNES snes, PetscViewer viewer)
633: {
634:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
635:   PetscBool      iascii;

637:   PetscFunctionBegin;
638:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
639:   if (iascii) {
640:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Trust region tolerance %g\n", (double)snes->deltatol));
641:     PetscCall(PetscViewerASCIIPrintf(viewer, "  eta1=%g, eta2=%g, eta3=%g\n", (double)tr->eta1, (double)tr->eta2, (double)tr->eta3));
642:     PetscCall(PetscViewerASCIIPrintf(viewer, "  delta0=%g, t1=%g, t2=%g, deltaM=%g\n", (double)tr->delta0, (double)tr->t1, (double)tr->t2, (double)tr->deltaM));
643:     PetscCall(PetscViewerASCIIPrintf(viewer, "  kmdc=%g\n", (double)tr->kmdc));
644:     PetscCall(PetscViewerASCIIPrintf(viewer, "  fallback=%s\n", SNESNewtonTRFallbackTypes[tr->fallback]));
645:   }
646:   PetscFunctionReturn(PETSC_SUCCESS);
647: }

649: /*MC
650:    SNESNEWTONTR - Newton based nonlinear solver that uses trust-region dogleg method with Cauchy direction {cite}`nocedal2006numerical`

652:    Options Database Keys:
653: +  -snes_tr_tol <tol>                            - trust region tolerance
654: .  -snes_tr_eta1 <eta1>                          - trust region parameter 0.0 <= eta1 <= eta2, rho >= eta1 breaks out of the inner iteration (default: eta1=0.001)
655: .  -snes_tr_eta2 <eta2>                          - trust region parameter 0.0 <= eta1 <= eta2, rho <= eta2 shrinks the trust region (default: eta2=0.25)
656: .  -snes_tr_eta3 <eta3>                          - trust region parameter eta3 > eta2, rho >= eta3 expands the trust region (default: eta3=0.75)
657: .  -snes_tr_t1 <t1>                              - trust region parameter, shrinking factor of trust region (default: 0.25)
658: .  -snes_tr_t2 <t2>                              - trust region parameter, expanding factor of trust region (default: 2.0)
659: .  -snes_tr_deltaM <deltaM>                      - trust region parameter, max size of trust region (default: MAX_REAL)
660: .  -snes_tr_delta0 <delta0>                      - trust region parameter, initial size of trust region (default: 0.2)
661: -  -snes_tr_fallback_type <newton,cauchy,dogleg> - Solution strategy to test reduction when step is outside of trust region. Can use scaled Newton direction, Cauchy point (Steepest Descent direction) or dogleg method.

663:    Level: deprecated (since 3.19)

665: .seealso: [](ch_snes), `SNESCreate()`, `SNES`, `SNESSetType()`, `SNESNEWTONLS`, `SNESSetTrustRegionTolerance()`,
666:           `SNESNewtonTRPreCheck()`, `SNESNewtonTRGetPreCheck()`, `SNESNewtonTRSetPostCheck()`, `SNESNewtonTRGetPostCheck()`,
667:           `SNESNewtonTRSetPreCheck()`, `SNESNewtonTRSetFallbackType()`
668: M*/
669: PETSC_EXTERN PetscErrorCode SNESCreate_NEWTONTR(SNES snes)
670: {
671:   SNES_NEWTONTR *neP;

673:   PetscFunctionBegin;
674:   snes->ops->setup          = SNESSetUp_NEWTONTR;
675:   snes->ops->solve          = SNESSolve_NEWTONTR;
676:   snes->ops->destroy        = SNESDestroy_NEWTONTR;
677:   snes->ops->setfromoptions = SNESSetFromOptions_NEWTONTR;
678:   snes->ops->view           = SNESView_NEWTONTR;

680:   snes->stol    = 0.0;
681:   snes->usesksp = PETSC_TRUE;
682:   snes->npcside = PC_RIGHT;
683:   snes->usesnpc = PETSC_TRUE;

685:   snes->alwayscomputesfinalresidual = PETSC_TRUE;

687:   PetscCall(PetscNew(&neP));
688:   snes->data    = (void *)neP;
689:   neP->delta    = 0.0;
690:   neP->delta0   = 0.2;
691:   neP->eta1     = 0.001;
692:   neP->eta2     = 0.25;
693:   neP->eta3     = 0.75;
694:   neP->t1       = 0.25;
695:   neP->t2       = 2.0;
696:   neP->deltaM   = 1.e10;
697:   neP->fallback = SNES_TR_FALLBACK_NEWTON;
698:   neP->kmdc     = 0.0; /* by default do not use sufficient decrease */
699:   PetscFunctionReturn(PETSC_SUCCESS);
700: }