Actual source code: tr.c

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

  3: typedef struct {
  4:   SNES                  snes;
  5:   KSPConvergenceTestFn *convtest;
  6:   PetscCtxDestroyFn    *convdestroy;
  7:   void                 *convctx;
  8: } SNES_TR_KSPConverged_Ctx;

 10: const char *const SNESNewtonTRFallbackTypes[] = {"NEWTON", "CAUCHY", "DOGLEG", "SNESNewtonTRFallbackType", "SNES_TR_FALLBACK_", NULL};
 11: const char *const SNESNewtonTRQNTypes[]       = {"NONE", "SAME", "DIFFERENT", "SNESNewtonTRQNType", "SNES_TR_QN_", NULL};

 13: static PetscErrorCode SNESNewtonTRSetTolerances_TR(SNES snes, PetscReal delta_min, PetscReal delta_max, PetscReal delta_0)
 14: {
 15:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;

 17:   PetscFunctionBegin;
 18:   if (delta_min == PETSC_DETERMINE) delta_min = tr->default_deltam;
 19:   if (delta_max == PETSC_DETERMINE) delta_max = tr->default_deltaM;
 20:   if (delta_0 == PETSC_DETERMINE) delta_0 = tr->default_delta0;
 21:   if (delta_min != PETSC_CURRENT) tr->deltam = delta_min;
 22:   if (delta_max != PETSC_CURRENT) tr->deltaM = delta_max;
 23:   if (delta_0 != PETSC_CURRENT) tr->delta0 = delta_0;
 24:   PetscFunctionReturn(PETSC_SUCCESS);
 25: }

 27: static PetscErrorCode SNESNewtonTRGetTolerances_TR(SNES snes, PetscReal *delta_min, PetscReal *delta_max, PetscReal *delta_0)
 28: {
 29:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;

 31:   PetscFunctionBegin;
 32:   if (delta_min) *delta_min = tr->deltam;
 33:   if (delta_max) *delta_max = tr->deltaM;
 34:   if (delta_0) *delta_0 = tr->delta0;
 35:   PetscFunctionReturn(PETSC_SUCCESS);
 36: }

 38: static PetscErrorCode SNESComputeJacobian_MATLMVM(SNES snes, Vec X, Mat J, Mat B, void *dummy)
 39: {
 40:   PetscFunctionBegin;
 41:   // PetscCall(MatLMVMSymBroydenSetDelta(B, _some_delta));
 42:   PetscCall(MatLMVMUpdate(B, X, snes->vec_func));
 43:   PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
 44:   PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
 45:   if (J != B) {
 46:     // PetscCall(MatLMVMSymBroydenSetDelta(J, _some_delta));
 47:     PetscCall(MatLMVMUpdate(J, X, snes->vec_func));
 48:     PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY));
 49:     PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY));
 50:   }
 51:   PetscFunctionReturn(PETSC_SUCCESS);
 52: }

 54: static PetscErrorCode SNESTR_KSPConverged_Private(KSP ksp, PetscInt n, PetscReal rnorm, KSPConvergedReason *reason, void *cctx)
 55: {
 56:   SNES_TR_KSPConverged_Ctx *ctx  = (SNES_TR_KSPConverged_Ctx *)cctx;
 57:   SNES                      snes = ctx->snes;
 58:   SNES_NEWTONTR            *neP  = (SNES_NEWTONTR *)snes->data;
 59:   Vec                       x;
 60:   PetscReal                 nrm;

 62:   PetscFunctionBegin;
 63:   /* Determine norm of solution */
 64:   PetscCall(KSPBuildSolution(ksp, NULL, &x));
 65:   PetscCall(VecNorm(x, neP->norm, &nrm));
 66:   if (nrm >= neP->delta) {
 67:     PetscCall(PetscInfo(snes, "Ending linear iteration early due to exiting trust region, delta=%g, length=%g\n", (double)neP->delta, (double)nrm));
 68:     *reason = KSP_CONVERGED_STEP_LENGTH;
 69:     PetscFunctionReturn(PETSC_SUCCESS);
 70:   }
 71:   PetscCall((*ctx->convtest)(ksp, n, rnorm, reason, ctx->convctx));
 72:   if (*reason) PetscCall(PetscInfo(snes, "Default or user provided convergence test KSP iterations=%" PetscInt_FMT ", rnorm=%g\n", n, (double)rnorm));
 73:   PetscFunctionReturn(PETSC_SUCCESS);
 74: }

 76: static PetscErrorCode SNESTR_KSPConverged_Destroy(void **cctx)
 77: {
 78:   SNES_TR_KSPConverged_Ctx *ctx = (SNES_TR_KSPConverged_Ctx *)*cctx;

 80:   PetscFunctionBegin;
 81:   PetscCall((*ctx->convdestroy)(&ctx->convctx));
 82:   PetscCall(PetscFree(ctx));
 83:   PetscFunctionReturn(PETSC_SUCCESS);
 84: }

 86: static PetscErrorCode SNESTR_Converged_Private(SNES snes, PetscInt it, PetscReal xnorm, PetscReal pnorm, PetscReal fnorm, SNESConvergedReason *reason, void *dummy)
 87: {
 88:   SNES_NEWTONTR *neP = (SNES_NEWTONTR *)snes->data;

 90:   PetscFunctionBegin;
 91:   *reason = SNES_CONVERGED_ITERATING;
 92:   if (neP->delta < neP->deltam) {
 93:     PetscCall(PetscInfo(snes, "Diverged due to too small a trust region %g<%g\n", (double)neP->delta, (double)neP->deltam));
 94:     *reason = SNES_DIVERGED_TR_DELTA;
 95:   } else if (snes->nfuncs >= snes->max_funcs && snes->max_funcs >= 0) {
 96:     PetscCall(PetscInfo(snes, "Exceeded maximum number of function evaluations: %" PetscInt_FMT "\n", snes->max_funcs));
 97:     *reason = SNES_DIVERGED_FUNCTION_COUNT;
 98:   }
 99:   PetscFunctionReturn(PETSC_SUCCESS);
100: }

102: /*@
103:   SNESNewtonTRSetNormType - Specify the type of norm to use for the computation of the trust region.

105:   Input Parameters:
106: + snes - the nonlinear solver object
107: - norm - the norm type

109:   Level: intermediate

111: .seealso: `SNESNEWTONTR`, `NormType`
112: @*/
113: PetscErrorCode SNESNewtonTRSetNormType(SNES snes, NormType norm)
114: {
115:   PetscBool flg;

117:   PetscFunctionBegin;
120:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
121:   if (flg) {
122:     SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;

124:     tr->norm = norm;
125:   }
126:   PetscFunctionReturn(PETSC_SUCCESS);
127: }

129: /*@
130:   SNESNewtonTRSetQNType - Specify to use a quasi-Newton model.

132:   Input Parameters:
133: + snes - the nonlinear solver object
134: - use  - the type of approximations to be used

136:   Level: intermediate

138:   Notes:
139:   Options for the approximations can be set with the `snes_tr_qn_` and `snes_tr_qn_pre_` prefixes.

141: .seealso: `SNESNEWTONTR`, `SNESNewtonTRQNType`, `MATLMVM`
142: @*/
143: PetscErrorCode SNESNewtonTRSetQNType(SNES snes, SNESNewtonTRQNType use)
144: {
145:   PetscBool flg;

147:   PetscFunctionBegin;
150:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
151:   if (flg) {
152:     SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;

154:     tr->qn = use;
155:   }
156:   PetscFunctionReturn(PETSC_SUCCESS);
157: }

159: /*@
160:   SNESNewtonTRSetFallbackType - Set the type of fallback to use if the solution of the trust region subproblem is outside the radius

162:   Input Parameters:
163: + snes  - the nonlinear solver object
164: - ftype - the fallback type, see `SNESNewtonTRFallbackType`

166:   Level: intermediate

168: .seealso: [](ch_snes), `SNESNEWTONTR`, `SNESNewtonTRPreCheck()`, `SNESNewtonTRGetPreCheck()`, `SNESNewtonTRSetPreCheck()`,
169:           `SNESNewtonTRSetPostCheck()`, `SNESNewtonTRGetPostCheck()`
170: @*/
171: PetscErrorCode SNESNewtonTRSetFallbackType(SNES snes, SNESNewtonTRFallbackType ftype)
172: {
173:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
174:   PetscBool      flg;

176:   PetscFunctionBegin;
179:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
180:   if (flg) tr->fallback = ftype;
181:   PetscFunctionReturn(PETSC_SUCCESS);
182: }

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

188:   Logically Collective

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

195:   Level: intermediate

197:   Note:
198:   This function is called BEFORE the function evaluation within the solver.

200: .seealso: [](ch_snes), `SNESNEWTONTR`, `SNESNewtonTRPreCheck()`, `SNESNewtonTRGetPreCheck()`, `SNESNewtonTRSetPostCheck()`, `SNESNewtonTRGetPostCheck()`,
201: @*/
202: PetscErrorCode SNESNewtonTRSetPreCheck(SNES snes, PetscErrorCode (*func)(SNES, Vec, Vec, PetscBool *, void *), void *ctx)
203: {
204:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
205:   PetscBool      flg;

207:   PetscFunctionBegin;
209:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
210:   if (flg) {
211:     if (func) tr->precheck = func;
212:     if (ctx) tr->precheckctx = ctx;
213:   }
214:   PetscFunctionReturn(PETSC_SUCCESS);
215: }

217: /*@C
218:   SNESNewtonTRGetPreCheck - Gets the pre-check function

220:   Not Collective

222:   Input Parameter:
223: . snes - the nonlinear solver context

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

229:   Level: intermediate

231: .seealso: [](ch_snes), `SNESNEWTONTR`, `SNESNewtonTRSetPreCheck()`, `SNESNewtonTRPreCheck()`
232: @*/
233: PetscErrorCode SNESNewtonTRGetPreCheck(SNES snes, PetscErrorCode (**func)(SNES, Vec, Vec, PetscBool *, void *), void **ctx)
234: {
235:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
236:   PetscBool      flg;

238:   PetscFunctionBegin;
240:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
241:   PetscAssert(flg, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONG, "Not for type %s", ((PetscObject)snes)->type_name);
242:   if (func) *func = tr->precheck;
243:   if (ctx) *ctx = tr->precheckctx;
244:   PetscFunctionReturn(PETSC_SUCCESS);
245: }

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

251:   Logically Collective

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

258:   Level: intermediate

260:   Note:
261:   This function is called BEFORE the function evaluation within the solver while the function set in
262:   `SNESLineSearchSetPostCheck()` is called AFTER the function evaluation.

264: .seealso: [](ch_snes), `SNESNEWTONTR`, `SNESNewtonTRPostCheck()`, `SNESNewtonTRGetPostCheck()`, `SNESNewtonTRSetPreCheck()`, `SNESNewtonTRGetPreCheck()`
265: @*/
266: PetscErrorCode SNESNewtonTRSetPostCheck(SNES snes, PetscErrorCode (*func)(SNES, Vec, Vec, Vec, PetscBool *, PetscBool *, void *), void *ctx)
267: {
268:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
269:   PetscBool      flg;

271:   PetscFunctionBegin;
273:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
274:   if (flg) {
275:     if (func) tr->postcheck = func;
276:     if (ctx) tr->postcheckctx = ctx;
277:   }
278:   PetscFunctionReturn(PETSC_SUCCESS);
279: }

281: /*@C
282:   SNESNewtonTRGetPostCheck - Gets the post-check function

284:   Not Collective

286:   Input Parameter:
287: . snes - the nonlinear solver context

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

293:   Level: intermediate

295: .seealso: [](ch_snes), `SNESNEWTONTR`, `SNESNewtonTRSetPostCheck()`, `SNESNewtonTRPostCheck()`
296: @*/
297: PetscErrorCode SNESNewtonTRGetPostCheck(SNES snes, PetscErrorCode (**func)(SNES, Vec, Vec, Vec, PetscBool *, PetscBool *, void *), void **ctx)
298: {
299:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
300:   PetscBool      flg;

302:   PetscFunctionBegin;
304:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
305:   PetscAssert(flg, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONG, "Not for type %s", ((PetscObject)snes)->type_name);
306:   if (func) *func = tr->postcheck;
307:   if (ctx) *ctx = tr->postcheckctx;
308:   PetscFunctionReturn(PETSC_SUCCESS);
309: }

311: /*@C
312:   SNESNewtonTRPreCheck - Runs the precheck routine

314:   Logically Collective

316:   Input Parameters:
317: + snes - the solver
318: . X    - The last solution
319: - Y    - The step direction

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

324:   Level: intermediate

326: .seealso: [](ch_snes), `SNESNEWTONTR`, `SNESNewtonTRSetPreCheck()`, `SNESNewtonTRGetPreCheck()`, `SNESNewtonTRPostCheck()`
327: @*/
328: PetscErrorCode SNESNewtonTRPreCheck(SNES snes, Vec X, Vec Y, PetscBool *changed_Y)
329: {
330:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
331:   PetscBool      flg;

333:   PetscFunctionBegin;
335:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
336:   PetscAssert(flg, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONG, "Not for type %s", ((PetscObject)snes)->type_name);
337:   *changed_Y = PETSC_FALSE;
338:   if (tr->precheck) {
339:     PetscCall((*tr->precheck)(snes, X, Y, changed_Y, tr->precheckctx));
341:   }
342:   PetscFunctionReturn(PETSC_SUCCESS);
343: }

345: /*@C
346:   SNESNewtonTRPostCheck - Runs the postcheck routine

348:   Logically Collective

350:   Input Parameters:
351: + snes - the solver
352: . X    - The last solution
353: . Y    - The full step direction
354: - W    - The updated solution, W = X - Y

356:   Output Parameters:
357: + changed_Y - indicator if step has been changed
358: - changed_W - Indicator if the new candidate solution W has been changed.

360:   Note:
361:   If Y is changed then W is recomputed as X - Y

363:   Level: intermediate

365: .seealso: [](ch_snes), `SNESNEWTONTR`, `SNESNewtonTRSetPostCheck()`, `SNESNewtonTRGetPostCheck()`, `SNESNewtonTRPreCheck()`
366: @*/
367: PetscErrorCode SNESNewtonTRPostCheck(SNES snes, Vec X, Vec Y, Vec W, PetscBool *changed_Y, PetscBool *changed_W)
368: {
369:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
370:   PetscBool      flg;

372:   PetscFunctionBegin;
374:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
375:   PetscAssert(flg, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONG, "Not for type %s", ((PetscObject)snes)->type_name);
376:   *changed_Y = PETSC_FALSE;
377:   *changed_W = PETSC_FALSE;
378:   if (tr->postcheck) {
379:     PetscCall((*tr->postcheck)(snes, X, Y, W, changed_Y, changed_W, tr->postcheckctx));
382:   }
383:   PetscFunctionReturn(PETSC_SUCCESS);
384: }

386: /* stable implementation of roots of a*x^2 + b*x + c = 0 */
387: static inline void PetscQuadraticRoots(PetscReal a, PetscReal b, PetscReal c, PetscReal *xm, PetscReal *xp)
388: {
389:   PetscReal temp = -0.5 * (b + PetscCopysignReal(1.0, b) * PetscSqrtReal(b * b - 4 * a * c));
390:   PetscReal x1   = temp / a;
391:   PetscReal x2   = c / temp;
392:   *xm            = PetscMin(x1, x2);
393:   *xp            = PetscMax(x1, x2);
394: }

396: /* Computes the quadratic model difference */
397: static PetscErrorCode SNESNewtonTRQuadraticDelta(SNES snes, Mat J, PetscBool has_objective, Vec Y, Vec GradF, Vec W, PetscReal *yTHy_, PetscReal *gTy_, PetscReal *deltaqm)
398: {
399:   PetscReal yTHy, gTy;

401:   PetscFunctionBegin;
402:   PetscCall(MatMult(J, Y, W));
403:   if (has_objective) PetscCall(VecDotRealPart(Y, W, &yTHy));
404:   else PetscCall(VecDotRealPart(W, W, &yTHy)); /* Gauss-Newton approximation J^t * J */
405:   PetscCall(VecDotRealPart(GradF, Y, &gTy));
406:   *deltaqm = -(-(gTy) + 0.5 * (yTHy)); /* difference in quadratic model, -gTy because SNES solves it this way */
407:   if (yTHy_) *yTHy_ = yTHy;
408:   if (gTy_) *gTy_ = gTy;
409:   PetscFunctionReturn(PETSC_SUCCESS);
410: }

412: /* Computes the new objective given X = Xk, Y = direction
413:    W work vector, on output W = X - Y
414:    G work vector, on output G = SNESFunction(W) */
415: static PetscErrorCode SNESNewtonTRObjective(SNES snes, PetscBool has_objective, Vec X, Vec Y, Vec W, Vec G, PetscReal *gnorm, PetscReal *fkp1)
416: {
417:   PetscBool changed_y, changed_w;

419:   PetscFunctionBegin;
420:   /* TODO: we can add a linesearch here */
421:   PetscCall(SNESNewtonTRPreCheck(snes, X, Y, &changed_y));
422:   PetscCall(VecWAXPY(W, -1.0, Y, X)); /* Xkp1 */
423:   PetscCall(SNESNewtonTRPostCheck(snes, X, Y, W, &changed_y, &changed_w));
424:   if (changed_y && !changed_w) PetscCall(VecWAXPY(W, -1.0, Y, X));

426:   PetscCall(SNESComputeFunction(snes, W, G)); /*  F(Xkp1) = G */
427:   PetscCall(VecNorm(G, NORM_2, gnorm));
428:   SNESCheckFunctionDomainError(snes, *gnorm);
429:   if (has_objective) {
430:     PetscCall(SNESComputeObjective(snes, W, fkp1));
431:     SNESCheckObjectiveDomainError(snes, *fkp1);
432:   } else *fkp1 = 0.5 * PetscSqr(*gnorm);
433:   PetscFunctionReturn(PETSC_SUCCESS);
434: }

436: static PetscErrorCode SNESSetUpQN_NEWTONTR(SNES snes)
437: {
438:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;

440:   PetscFunctionBegin;
441:   PetscCall(MatDestroy(&tr->qnB));
442:   PetscCall(MatDestroy(&tr->qnB_pre));
443:   if (tr->qn) {
444:     PetscInt    n, N;
445:     const char *optionsprefix;
446:     Mat         B;

448:     PetscCall(MatCreate(PetscObjectComm((PetscObject)snes), &B));
449:     PetscCall(SNESGetOptionsPrefix(snes, &optionsprefix));
450:     PetscCall(MatSetOptionsPrefix(B, "snes_tr_qn_"));
451:     PetscCall(MatAppendOptionsPrefix(B, optionsprefix));
452:     PetscCall(MatSetType(B, MATLMVMBFGS));
453:     PetscCall(VecGetLocalSize(snes->vec_sol, &n));
454:     PetscCall(VecGetSize(snes->vec_sol, &N));
455:     PetscCall(MatSetSizes(B, n, n, N, N));
456:     PetscCall(MatSetUp(B));
457:     PetscCall(MatSetFromOptions(B));
458:     PetscCall(MatLMVMAllocate(B, snes->vec_sol, snes->vec_func));
459:     tr->qnB = B;
460:     if (tr->qn == SNES_TR_QN_DIFFERENT) {
461:       PetscCall(MatCreate(PetscObjectComm((PetscObject)snes), &B));
462:       PetscCall(SNESGetOptionsPrefix(snes, &optionsprefix));
463:       PetscCall(MatSetOptionsPrefix(B, "snes_tr_qn_pre_"));
464:       PetscCall(MatAppendOptionsPrefix(B, optionsprefix));
465:       PetscCall(MatSetType(B, MATLMVMBFGS));
466:       PetscCall(MatSetSizes(B, n, n, N, N));
467:       PetscCall(MatSetUp(B));
468:       PetscCall(MatSetFromOptions(B));
469:       PetscCall(MatLMVMAllocate(B, snes->vec_sol, snes->vec_func));
470:       tr->qnB_pre = B;
471:     } else {
472:       PetscCall(PetscObjectReference((PetscObject)tr->qnB));
473:       tr->qnB_pre = tr->qnB;
474:     }
475:   }
476:   PetscFunctionReturn(PETSC_SUCCESS);
477: }

479: /*
480:    SNESSolve_NEWTONTR - Implements Newton's Method with trust-region subproblem and adds dogleg Cauchy
481:    (Steepest Descent direction) step and direction if the trust region is not satisfied for solving system of
482:    nonlinear equations

484: */
485: static PetscErrorCode SNESSolve_NEWTONTR(SNES snes)
486: {
487:   SNES_NEWTONTR            *neP = (SNES_NEWTONTR *)snes->data;
488:   Vec                       X, F, Y, G, W, GradF, YU, Yc;
489:   PetscInt                  maxits, lits;
490:   PetscReal                 rho, fnorm, gnorm = 0.0, xnorm = 0.0, delta, ynorm;
491:   PetscReal                 fk, fkp1, deltaqm = 0.0, gTy = 0.0, yTHy = 0.0;
492:   PetscReal                 auk, tauk, gfnorm, gfnorm_k, ycnorm, gTBg, objmin = 0.0, beta_k = 1.0;
493:   PC                        pc;
494:   Mat                       J, Jp;
495:   PetscBool                 already_done = PETSC_FALSE, on_boundary, use_cauchy;
496:   PetscBool                 clear_converged_test, rho_satisfied, has_objective;
497:   SNES_TR_KSPConverged_Ctx *ctx;
498:   void                     *convctx;
499:   SNESObjectiveFn          *objective;
500:   KSPConvergenceTestFn     *convtest;
501:   PetscCtxDestroyFn        *convdestroy;

503:   PetscFunctionBegin;
504:   PetscCall(SNESGetObjective(snes, &objective, NULL));
505:   has_objective = objective ? PETSC_TRUE : PETSC_FALSE;

507:   maxits = snes->max_its;                                   /* maximum number of iterations */
508:   X      = snes->vec_sol;                                   /* solution vector */
509:   F      = snes->vec_func;                                  /* residual vector */
510:   Y      = snes->vec_sol_update;                            /* update vector */
511:   G      = snes->work[0];                                   /* updated residual */
512:   W      = snes->work[1];                                   /* temporary vector */
513:   GradF  = !has_objective ? snes->work[2] : snes->vec_func; /* grad f = J^T F */
514:   YU     = snes->work[3];                                   /* work vector for dogleg method */
515:   Yc     = snes->work[4];                                   /* Cauchy point */

517:   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);

519:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
520:   snes->iter = 0;
521:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));

523:   /* setup QN matrices if needed */
524:   PetscCall(SNESSetUpQN_NEWTONTR(snes));

526:   /* Set the linear stopping criteria to use the More' trick if needed */
527:   clear_converged_test = PETSC_FALSE;
528:   PetscCall(SNESGetKSP(snes, &snes->ksp));
529:   PetscCall(KSPGetConvergenceTest(snes->ksp, &convtest, &convctx, &convdestroy));
530:   if (convtest != SNESTR_KSPConverged_Private) {
531:     clear_converged_test = PETSC_TRUE;
532:     PetscCall(PetscNew(&ctx));
533:     ctx->snes = snes;
534:     PetscCall(KSPGetAndClearConvergenceTest(snes->ksp, &ctx->convtest, &ctx->convctx, &ctx->convdestroy));
535:     PetscCall(KSPSetConvergenceTest(snes->ksp, SNESTR_KSPConverged_Private, ctx, SNESTR_KSPConverged_Destroy));
536:     PetscCall(PetscInfo(snes, "Using Krylov convergence test SNESTR_KSPConverged_Private\n"));
537:   }

539:   if (!snes->vec_func_init_set) {
540:     PetscCall(SNESComputeFunction(snes, X, F)); /* F(X) */
541:   } else snes->vec_func_init_set = PETSC_FALSE;

543:   PetscCall(VecNorm(F, NORM_2, &fnorm)); /* fnorm <- || F || */
544:   SNESCheckFunctionDomainError(snes, fnorm);
545:   PetscCall(VecNorm(X, NORM_2, &xnorm)); /* xnorm <- || X || */

547:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
548:   snes->norm = fnorm;
549:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
550:   delta      = neP->delta0;
551:   neP->delta = delta;
552:   PetscCall(SNESLogConvergenceHistory(snes, fnorm, 0));

554:   /* test convergence */
555:   rho_satisfied = PETSC_FALSE;
556:   PetscCall(SNESConverged(snes, 0, 0.0, 0.0, fnorm));
557:   PetscCall(SNESMonitor(snes, 0, fnorm));
558:   if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS);

560:   if (has_objective) {
561:     PetscCall(SNESComputeObjective(snes, X, &fk));
562:     SNESCheckObjectiveDomainError(snes, fk);
563:   } else fk = 0.5 * PetscSqr(fnorm); /* obj(x) = 0.5 * ||F(x)||^2 */

565:   /* hook state vector to BFGS preconditioner */
566:   PetscCall(KSPGetPC(snes->ksp, &pc));
567:   PetscCall(PCLMVMSetUpdateVec(pc, X));

569:   if (neP->kmdc) PetscCall(KSPSetComputeEigenvalues(snes->ksp, PETSC_TRUE));

571:   while (snes->iter < maxits) {
572:     /* calculating Jacobian and GradF of minimization function only once */
573:     if (!already_done) {
574:       /* Call general purpose update function */
575:       PetscTryTypeMethod(snes, update, snes->iter);

577:       /* apply the nonlinear preconditioner */
578:       if (snes->npc && snes->npcside == PC_RIGHT) {
579:         SNESConvergedReason reason;

581:         PetscCall(SNESSetInitialFunction(snes->npc, F));
582:         PetscCall(PetscLogEventBegin(SNES_NPCSolve, snes->npc, X, snes->vec_rhs, 0));
583:         PetscCall(SNESSolve(snes->npc, snes->vec_rhs, X));
584:         PetscCall(PetscLogEventEnd(SNES_NPCSolve, snes->npc, X, snes->vec_rhs, 0));
585:         PetscCall(SNESGetConvergedReason(snes->npc, &reason));
586:         if (reason < 0 && reason != SNES_DIVERGED_MAX_IT && reason != SNES_DIVERGED_TR_DELTA) {
587:           snes->reason = SNES_DIVERGED_INNER;
588:           PetscFunctionReturn(PETSC_SUCCESS);
589:         }
590:         // XXX
591:         PetscCall(SNESGetNPCFunction(snes, F, &fnorm));
592:       }

594:       /* Jacobian */
595:       J  = NULL;
596:       Jp = NULL;
597:       if (!neP->qnB) {
598:         PetscCall(SNESComputeJacobian(snes, X, snes->jacobian, snes->jacobian_pre));
599:         SNESCheckJacobianDomainError(snes);
600:         J  = snes->jacobian;
601:         Jp = snes->jacobian_pre;
602:       } else { /* QN model */
603:         PetscCall(SNESComputeJacobian_MATLMVM(snes, X, neP->qnB, neP->qnB_pre, NULL));
604:         J  = neP->qnB;
605:         Jp = neP->qnB_pre;
606:       }
607:       SNESCheckJacobianDomainError(snes);

609:       /* objective function */
610:       PetscCall(VecNorm(F, NORM_2, &fnorm));
611:       SNESCheckFunctionDomainError(snes, fnorm);
612:       if (has_objective) {
613:         PetscCall(SNESComputeObjective(snes, X, &fk));
614:         SNESCheckObjectiveDomainError(snes, fk);
615:       } else fk = 0.5 * PetscSqr(fnorm); /* obj(x) = 0.5 * ||F(x)||^2 */

617:       /* GradF */
618:       if (has_objective) gfnorm = fnorm;
619:       else {
620:         PetscCall(MatMultTranspose(J, F, GradF)); /* grad f = J^T F */
621:         PetscCall(VecNorm(GradF, NORM_2, &gfnorm));
622:       }
623:       PetscCall(VecNorm(GradF, neP->norm, &gfnorm_k));
624:     }
625:     already_done = PETSC_TRUE;

627:     /* solve trust-region subproblem */

629:     /* first compute Cauchy Point */
630:     PetscCall(MatMult(J, GradF, W));
631:     if (has_objective) PetscCall(VecDotRealPart(GradF, W, &gTBg));
632:     else PetscCall(VecDotRealPart(W, W, &gTBg)); /* B = J^t * J */
633:     /* Eqs 4.11 and 4.12 in Nocedal and Wright 2nd Edition (4.7 and 4.8 in 1st Edition) */
634:     auk = delta / gfnorm_k;
635:     if (gTBg < 0.0) tauk = 1.0;
636:     else tauk = PetscMin(gfnorm * gfnorm * gfnorm_k / (delta * gTBg), 1);
637:     auk *= tauk;
638:     ycnorm = auk * gfnorm;
639:     PetscCall(VecAXPBY(Yc, auk, 0.0, GradF));

641:     on_boundary = PETSC_FALSE;
642:     use_cauchy  = (PetscBool)(tauk == 1.0 && has_objective);
643:     if (!use_cauchy) {
644:       KSPConvergedReason reason;

646:       /* sufficient decrease (see 6.3.27 in Conn, Gould, Toint "Trust Region Methods")
647:          beta_k the largest eigenvalue of the Hessian. Here we use the previous estimated value */
648:       objmin = -neP->kmdc * gnorm * PetscMin(gnorm / beta_k, delta);
649:       PetscCall(KSPCGSetObjectiveTarget(snes->ksp, objmin));

651:       /* specify radius if looking for Newton step and trust region norm is the l2 norm */
652:       PetscCall(KSPCGSetRadius(snes->ksp, neP->fallback == SNES_TR_FALLBACK_NEWTON && neP->norm == NORM_2 ? delta : 0.0));
653:       PetscCall(KSPSetOperators(snes->ksp, J, Jp));
654:       PetscCall(KSPSolve(snes->ksp, F, Y));
655:       SNESCheckKSPSolve(snes);
656:       PetscCall(KSPGetIterationNumber(snes->ksp, &lits));
657:       PetscCall(KSPGetConvergedReason(snes->ksp, &reason));
658:       on_boundary = (PetscBool)(reason == KSP_CONVERGED_STEP_LENGTH);
659:       PetscCall(PetscInfo(snes, "iter=%" PetscInt_FMT ", linear solve iterations=%" PetscInt_FMT "\n", snes->iter, lits));
660:       if (neP->kmdc) { /* update estimated Hessian largest eigenvalue */
661:         PetscReal emax, emin;
662:         PetscCall(KSPComputeExtremeSingularValues(snes->ksp, &emax, &emin));
663:         if (emax > 0.0) beta_k = emax + 1;
664:       }
665:     } else { /* Cauchy point is on the boundary, accept it */
666:       on_boundary = PETSC_TRUE;
667:       PetscCall(VecCopy(Yc, Y));
668:       PetscCall(PetscInfo(snes, "CP evaluated on boundary. delta: %g, ycnorm: %g, gTBg: %g\n", (double)delta, (double)ycnorm, (double)gTBg));
669:     }
670:     PetscCall(VecNorm(Y, neP->norm, &ynorm));

672:     /* decide what to do when the update is outside of trust region */
673:     if (!use_cauchy && (ynorm > delta || ynorm == 0.0)) {
674:       SNESNewtonTRFallbackType fallback = ynorm > 0.0 ? neP->fallback : SNES_TR_FALLBACK_CAUCHY;

676:       PetscCheck(neP->norm == NORM_2 || fallback != SNES_TR_FALLBACK_DOGLEG, PetscObjectComm((PetscObject)snes), PETSC_ERR_SUP, "DOGLEG without l2 norm not implemented");
677:       switch (fallback) {
678:       case SNES_TR_FALLBACK_NEWTON:
679:         auk = delta / ynorm;
680:         PetscCall(VecScale(Y, auk));
681:         PetscCall(PetscInfo(snes, "SN evaluated. delta: %g, ynorm: %g\n", (double)delta, (double)ynorm));
682:         break;
683:       case SNES_TR_FALLBACK_CAUCHY:
684:       case SNES_TR_FALLBACK_DOGLEG:
685:         if (fallback == SNES_TR_FALLBACK_CAUCHY || gTBg <= 0.0) {
686:           PetscCall(VecCopy(Yc, Y));
687:           PetscCall(PetscInfo(snes, "CP evaluated. delta: %g, ynorm: %g, ycnorm: %g, gTBg: %g\n", (double)delta, (double)ynorm, (double)ycnorm, (double)gTBg));
688:         } else { /* take linear combination of Cauchy and Newton direction and step */
689:           auk = gfnorm * gfnorm / gTBg;
690:           if (gfnorm_k * auk >= delta) { /* first leg: Cauchy point outside of trust region */
691:             PetscCall(VecAXPBY(Y, delta / gfnorm_k, 0.0, GradF));
692:             PetscCall(PetscInfo(snes, "CP evaluated (outside region). delta: %g, ynorm: %g, ycnorm: %g\n", (double)delta, (double)ynorm, (double)ycnorm));
693:           } else { /* second leg */
694:             PetscReal c0, c1, c2, tau = 0.0, tpos, tneg;
695:             PetscBool noroots;

697:             /* Find solutions of (Eq. 4.16 in Nocedal and Wright)
698:                  ||p_U + lambda * (p_B - p_U)||^2 - delta^2 = 0,
699:                where p_U  the Cauchy direction, p_B the Newton direction */
700:             PetscCall(VecAXPBY(YU, auk, 0.0, GradF));
701:             PetscCall(VecAXPY(Y, -1.0, YU));
702:             PetscCall(VecNorm(Y, NORM_2, &c0));
703:             PetscCall(VecDotRealPart(YU, Y, &c1));
704:             c0 = PetscSqr(c0);
705:             c2 = PetscSqr(ycnorm) - PetscSqr(delta);
706:             PetscQuadraticRoots(c0, 2 * c1, c2, &tneg, &tpos);

708:             /* In principle the DL strategy as a unique solution in [0,1]
709:                here we check that for some reason we numerically failed
710:                to compute it. In that case, we use the Cauchy point */
711:             noroots = PetscIsInfOrNanReal(tneg);
712:             if (!noroots) {
713:               if (tpos > 1) {
714:                 if (tneg >= 0 && tneg <= 1) {
715:                   tau = tneg;
716:                 } else noroots = PETSC_TRUE;
717:               } else if (tpos >= 0) {
718:                 tau = tpos;
719:               } else noroots = PETSC_TRUE;
720:             }
721:             if (noroots) { /* No roots, select Cauchy point */
722:               PetscCall(VecCopy(Yc, Y));
723:             } else {
724:               PetscCall(VecAXPBY(Y, 1.0, tau, YU));
725:             }
726:             PetscCall(PetscInfo(snes, "%s evaluated. roots: (%g, %g), tau %g, ynorm: %g, ycnorm: %g, gTBg: %g\n", noroots ? "CP" : "DL", (double)tneg, (double)tpos, (double)tau, (double)ynorm, (double)ycnorm, (double)gTBg));
727:           }
728:         }
729:         break;
730:       default:
731:         SETERRQ(PetscObjectComm((PetscObject)snes), PETSC_ERR_SUP, "Unknown fallback mode");
732:         break;
733:       }
734:     }

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

739:     /* Compute new objective function */
740:     PetscCall(SNESNewtonTRObjective(snes, has_objective, X, Y, W, G, &gnorm, &fkp1));
741:     if (PetscIsInfOrNanReal(fkp1)) rho = neP->eta1;
742:     else {
743:       if (deltaqm > 0.0) rho = (fk - fkp1) / deltaqm; /* actual improvement over predicted improvement */
744:       else rho = neP->eta1;                           /*  no reduction in quadratic model, step must be rejected */
745:     }

747:     PetscCall(VecNorm(Y, neP->norm, &ynorm));
748:     PetscCall(PetscInfo(snes, "rho=%g, delta=%g, fk=%g, fkp1=%g, deltaqm=%g, gTy=%g, yTHy=%g, ynormk=%g\n", (double)rho, (double)delta, (double)fk, (double)fkp1, (double)deltaqm, (double)gTy, (double)yTHy, (double)ynorm));

750:     /* update the size of the trust region */
751:     if (rho < neP->eta2) delta *= neP->t1;                     /* shrink the region */
752:     else if (rho > neP->eta3 && on_boundary) delta *= neP->t2; /* expand the region */
753:     delta = PetscMin(delta, neP->deltaM);                      /* but not greater than deltaM */

755:     /* log 2-norm of update for moniroting routines */
756:     PetscCall(VecNorm(Y, NORM_2, &ynorm));

758:     /* decide on new step */
759:     neP->delta = delta;
760:     if (rho > neP->eta1) {
761:       rho_satisfied = PETSC_TRUE;
762:     } else {
763:       rho_satisfied = PETSC_FALSE;
764:       PetscCall(PetscInfo(snes, "Trying again in smaller region\n"));
765:       /* check to see if progress is hopeless */
766:       PetscCall(SNESTR_Converged_Private(snes, snes->iter, xnorm, ynorm, fnorm, &snes->reason, snes->cnvP));
767:       if (!snes->reason) PetscCall(SNESConverged(snes, snes->iter, xnorm, ynorm, fnorm));
768:       if (snes->reason == SNES_CONVERGED_SNORM_RELATIVE) snes->reason = SNES_DIVERGED_TR_DELTA;
769:       snes->numFailures++;
770:       /* We're not progressing, so return with the current iterate */
771:       if (snes->reason) break;
772:     }
773:     if (rho_satisfied) {
774:       /* Update function values */
775:       already_done = PETSC_FALSE;
776:       fnorm        = gnorm;
777:       fk           = fkp1;

779:       /* New residual and linearization point */
780:       PetscCall(VecCopy(G, F));
781:       PetscCall(VecCopy(W, X));

783:       /* Monitor convergence */
784:       PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
785:       snes->iter++;
786:       snes->norm  = fnorm;
787:       snes->xnorm = xnorm;
788:       snes->ynorm = ynorm;
789:       PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
790:       PetscCall(SNESLogConvergenceHistory(snes, snes->norm, lits));

792:       /* Test for convergence, xnorm = || X || */
793:       PetscCall(VecNorm(X, NORM_2, &xnorm));
794:       PetscCall(SNESConverged(snes, snes->iter, xnorm, ynorm, fnorm));
795:       PetscCall(SNESMonitor(snes, snes->iter, snes->norm));
796:       if (snes->reason) break;
797:     }
798:   }

800:   if (clear_converged_test) {
801:     PetscCall(KSPGetAndClearConvergenceTest(snes->ksp, &ctx->convtest, &ctx->convctx, &ctx->convdestroy));
802:     PetscCall(PetscFree(ctx));
803:     PetscCall(KSPSetConvergenceTest(snes->ksp, convtest, convctx, convdestroy));
804:   }
805:   PetscFunctionReturn(PETSC_SUCCESS);
806: }

808: static PetscErrorCode SNESSetUp_NEWTONTR(SNES snes)
809: {
810:   PetscFunctionBegin;
811:   PetscCall(SNESSetWorkVecs(snes, 5));
812:   PetscCall(SNESSetUpMatrices(snes));
813:   PetscFunctionReturn(PETSC_SUCCESS);
814: }

816: static PetscErrorCode SNESReset_NEWTONTR(SNES snes)
817: {
818:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;

820:   PetscFunctionBegin;
821:   PetscCall(MatDestroy(&tr->qnB));
822:   PetscCall(MatDestroy(&tr->qnB_pre));
823:   PetscFunctionReturn(PETSC_SUCCESS);
824: }

826: static PetscErrorCode SNESDestroy_NEWTONTR(SNES snes)
827: {
828:   PetscFunctionBegin;
829:   PetscCall(SNESReset_NEWTONTR(snes));
830:   PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESNewtonTRSetTolerances_C", NULL));
831:   PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESNewtonTRGetTolerances_C", NULL));
832:   PetscCall(PetscFree(snes->data));
833:   PetscFunctionReturn(PETSC_SUCCESS);
834: }

836: static PetscErrorCode SNESSetFromOptions_NEWTONTR(SNES snes, PetscOptionItems PetscOptionsObject)
837: {
838:   SNES_NEWTONTR           *ctx = (SNES_NEWTONTR *)snes->data;
839:   SNESNewtonTRQNType       qn;
840:   SNESNewtonTRFallbackType fallback;
841:   NormType                 norm;
842:   PetscBool                flg;

844:   PetscFunctionBegin;
845:   PetscOptionsHeadBegin(PetscOptionsObject, "SNES trust region options for nonlinear equations");
846:   PetscCall(PetscOptionsDeprecated("-snes_tr_deltaM", "-snes_tr_deltamax", "3.22", NULL));
847:   PetscCall(PetscOptionsReal("-snes_tr_eta1", "eta1", "SNESNewtonTRSetUpdateParameters", ctx->eta1, &ctx->eta1, NULL));
848:   PetscCall(PetscOptionsReal("-snes_tr_eta2", "eta2", "SNESNewtonTRSetUpdateParameters", ctx->eta2, &ctx->eta2, NULL));
849:   PetscCall(PetscOptionsReal("-snes_tr_eta3", "eta3", "SNESNewtonTRSetUpdateParameters", ctx->eta3, &ctx->eta3, NULL));
850:   PetscCall(PetscOptionsReal("-snes_tr_t1", "t1", "SNESNewtonTRSetUpdateParameters", ctx->t1, &ctx->t1, NULL));
851:   PetscCall(PetscOptionsReal("-snes_tr_t2", "t2", "SNESNewtonTRSetUpdateParameters", ctx->t2, &ctx->t2, NULL));
852:   PetscCall(PetscOptionsReal("-snes_tr_delta0", "Initial trust region size", "SNESNewtonTRSetTolerances", ctx->delta0, &ctx->delta0, NULL));
853:   PetscCall(PetscOptionsReal("-snes_tr_deltamin", "Minimum allowed trust region size", "SNESNewtonTRSetTolerances", ctx->deltam, &ctx->deltam, NULL));
854:   PetscCall(PetscOptionsReal("-snes_tr_deltamax", "Maximum allowed trust region size", "SNESNewtonTRSetTolerances", ctx->deltaM, &ctx->deltaM, NULL));
855:   PetscCall(PetscOptionsReal("-snes_tr_kmdc", "sufficient decrease parameter", "None", ctx->kmdc, &ctx->kmdc, NULL));

857:   fallback = ctx->fallback;
858:   PetscCall(PetscOptionsEnum("-snes_tr_fallback_type", "Type of fallback if subproblem solution is outside of the trust region", "SNESNewtonTRSetFallbackType", SNESNewtonTRFallbackTypes, (PetscEnum)fallback, (PetscEnum *)&fallback, &flg));
859:   if (flg) PetscCall(SNESNewtonTRSetFallbackType(snes, fallback));

861:   qn = ctx->qn;
862:   PetscCall(PetscOptionsEnum("-snes_tr_qn", "Use Quasi-Newton approximations for the model", "SNESNewtonTRSetQNType", SNESNewtonTRQNTypes, (PetscEnum)qn, (PetscEnum *)&qn, &flg));
863:   if (flg) PetscCall(SNESNewtonTRSetQNType(snes, qn));

865:   norm = ctx->norm;
866:   PetscCall(PetscOptionsEnum("-snes_tr_norm_type", "Type of norm for trust region bounds", "SNESNewtonTRSetNormType", NormTypes, (PetscEnum)norm, (PetscEnum *)&norm, &flg));
867:   if (flg) PetscCall(SNESNewtonTRSetNormType(snes, norm));

869:   PetscOptionsHeadEnd();
870:   PetscFunctionReturn(PETSC_SUCCESS);
871: }

873: static PetscErrorCode SNESView_NEWTONTR(SNES snes, PetscViewer viewer)
874: {
875:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
876:   PetscBool      isascii;

878:   PetscFunctionBegin;
879:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
880:   if (isascii) {
881:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Trust region parameters:\n"));
882:     PetscCall(PetscViewerASCIIPrintf(viewer, "    eta1=%g, eta2=%g, eta3=%g\n", (double)tr->eta1, (double)tr->eta2, (double)tr->eta3));
883:     PetscCall(PetscViewerASCIIPrintf(viewer, "    t1=%g, t2=%g\n", (double)tr->t1, (double)tr->t2));
884:     PetscCall(PetscViewerASCIIPrintf(viewer, "    delta_min=%g, delta_0=%g, delta_max=%g\n", (double)tr->deltam, (double)tr->delta0, (double)tr->deltaM));
885:     PetscCall(PetscViewerASCIIPrintf(viewer, "    kmdc=%g\n", (double)tr->kmdc));
886:     PetscCall(PetscViewerASCIIPrintf(viewer, "    fallback=%s\n", SNESNewtonTRFallbackTypes[tr->fallback]));
887:     if (tr->qn) PetscCall(PetscViewerASCIIPrintf(viewer, "    qn=%s\n", SNESNewtonTRQNTypes[tr->qn]));
888:     if (tr->norm != NORM_2) PetscCall(PetscViewerASCIIPrintf(viewer, "    norm=%s\n", NormTypes[tr->norm]));
889:   }
890:   PetscFunctionReturn(PETSC_SUCCESS);
891: }

893: /*@
894:   SNESSetTrustRegionTolerance - Sets the trust region parameter tolerance.

896:   Logically Collective

898:   Input Parameters:
899: + snes - the `SNES` context
900: - tol  - tolerance

902:   Level: deprecated

904: .seealso: [](ch_snes), `SNES`, `SNESNEWTONTR`, `SNESSetTolerances()`
905: @*/
906: PetscErrorCode SNESSetTrustRegionTolerance(SNES snes, PetscReal tol)
907: {
908:   return SNESNewtonTRSetTolerances(snes, tol, PETSC_CURRENT, PETSC_CURRENT);
909: }

911: /*@
912:   SNESNewtonTRSetTolerances - Sets the trust region parameter tolerances.

914:   Logically Collective

916:   Input Parameters:
917: + snes      - the `SNES` context
918: . delta_min - minimum allowed trust region size
919: . delta_max - maximum allowed trust region size
920: - delta_0   - initial trust region size

922:   Options Database Key:
923: + -snes_tr_deltamin <tol> - Set minimum size
924: . -snes_tr_deltamax <tol> - Set maximum size
925: - -snes_tr_delta0   <tol> - Set initial size

927:   Note:
928:   Use `PETSC_DETERMINE` to use the default value for the given `SNES`.
929:   Use `PETSC_CURRENT` to retain a value.

931:   Fortran Note:
932:   Use `PETSC_DETERMINE_REAL`, `PETSC_CURRENT_REAL`

934:   Level: intermediate

936: .seealso: [](ch_snes), `SNES`, `SNESNEWTONTR`, `SNESNewtonTRGetTolerances()`
937: @*/
938: PetscErrorCode SNESNewtonTRSetTolerances(SNES snes, PetscReal delta_min, PetscReal delta_max, PetscReal delta_0)
939: {
940:   PetscFunctionBegin;
945:   PetscTryMethod(snes, "SNESNewtonTRSetTolerances_C", (SNES, PetscReal, PetscReal, PetscReal), (snes, delta_min, delta_max, delta_0));
946:   PetscFunctionReturn(PETSC_SUCCESS);
947: }

949: /*@
950:   SNESNewtonTRGetTolerances - Gets the trust region parameter tolerances.

952:   Not Collective

954:   Input Parameter:
955: . snes - the `SNES` context

957:   Output Parameters:
958: + delta_min - minimum allowed trust region size or `NULL`
959: . delta_max - maximum allowed trust region size or `NULL`
960: - delta_0   - initial trust region size or `NULL`

962:   Level: intermediate

964: .seealso: [](ch_snes), `SNES`, `SNESNEWTONTR`, `SNESNewtonTRSetTolerances()`
965: @*/
966: PetscErrorCode SNESNewtonTRGetTolerances(SNES snes, PetscReal *delta_min, PetscReal *delta_max, PetscReal *delta_0)
967: {
968:   PetscFunctionBegin;
970:   if (delta_min) PetscAssertPointer(delta_min, 2);
971:   if (delta_max) PetscAssertPointer(delta_max, 3);
972:   if (delta_0) PetscAssertPointer(delta_0, 4);
973:   PetscUseMethod(snes, "SNESNewtonTRGetTolerances_C", (SNES, PetscReal *, PetscReal *, PetscReal *), (snes, delta_min, delta_max, delta_0));
974:   PetscFunctionReturn(PETSC_SUCCESS);
975: }

977: /*@
978:   SNESNewtonTRSetUpdateParameters - Sets the trust region update parameters.

980:   Logically Collective

982:   Input Parameters:
983: + snes - the `SNES` context
984: . eta1 - acceptance tolerance
985: . eta2 - shrinking tolerance
986: . eta3 - enlarging tolerance
987: . t1   - shrink factor
988: - t2   - enlarge factor

990:   Options Database Key:
991: + -snes_tr_eta1 <tol> - Set `eta1`
992: . -snes_tr_eta2 <tol> - Set `eta2`
993: . -snes_tr_eta3 <tol> - Set `eta3`
994: . -snes_tr_t1   <tol> - Set `t1`
995: - -snes_tr_t2   <tol> - Set `t2`

997:   Notes:
998:   Given the ratio $\rho = \frac{f(x_k) - f(x_k+s_k)}{m(0) - m(s_k)}$, with $x_k$ the current iterate,
999:   $s_k$ the computed step, $f$ the objective function, and $m$ the quadratic model, the trust region
1000:   radius is modified as follows

1002:   $
1003:   \delta =
1004:   \begin{cases}
1005:   \delta * t_1 ,& \rho < \eta_2 \\
1006:   \delta * t_2 ,& \rho > \eta_3 \\
1007:   \end{cases}
1008:   $

1010:   The step is accepted if $\rho > \eta_1$.
1011:   Use `PETSC_DETERMINE` to use the default value for the given `SNES`.
1012:   Use `PETSC_CURRENT` to retain a value.

1014:   Fortran Note:
1015:   Use `PETSC_DETERMINE_REAL`, `PETSC_CURRENT_REAL`

1017:   Level: intermediate

1019: .seealso: [](ch_snes), `SNES`, `SNESNEWTONTR`, `SNESSetObjective()`, `SNESNewtonTRGetUpdateParameters()`
1020: @*/
1021: PetscErrorCode SNESNewtonTRSetUpdateParameters(SNES snes, PetscReal eta1, PetscReal eta2, PetscReal eta3, PetscReal t1, PetscReal t2)
1022: {
1023:   PetscBool flg;

1025:   PetscFunctionBegin;
1032:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
1033:   if (flg) {
1034:     SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;

1036:     if (eta1 == PETSC_DETERMINE) eta1 = tr->default_eta1;
1037:     if (eta2 == PETSC_DETERMINE) eta2 = tr->default_eta2;
1038:     if (eta3 == PETSC_DETERMINE) eta3 = tr->default_eta3;
1039:     if (t1 == PETSC_DETERMINE) t1 = tr->default_t1;
1040:     if (t2 == PETSC_DETERMINE) t2 = tr->default_t2;
1041:     if (eta1 != PETSC_CURRENT) tr->eta1 = eta1;
1042:     if (eta2 != PETSC_CURRENT) tr->eta2 = eta2;
1043:     if (eta3 != PETSC_CURRENT) tr->eta3 = eta3;
1044:     if (t1 != PETSC_CURRENT) tr->t1 = t1;
1045:     if (t2 != PETSC_CURRENT) tr->t2 = t2;
1046:   }
1047:   PetscFunctionReturn(PETSC_SUCCESS);
1048: }

1050: /*@
1051:   SNESNewtonTRGetUpdateParameters - Gets the trust region update parameters.

1053:   Not Collective

1055:   Input Parameter:
1056: . snes - the `SNES` context

1058:   Output Parameters:
1059: + eta1 - acceptance tolerance
1060: . eta2 - shrinking tolerance
1061: . eta3 - enlarging tolerance
1062: . t1   - shrink factor
1063: - t2   - enlarge factor

1065:   Level: intermediate

1067: .seealso: [](ch_snes), `SNES`, `SNESNEWTONTR`, `SNESNewtonTRSetUpdateParameters()`
1068: @*/
1069: PetscErrorCode SNESNewtonTRGetUpdateParameters(SNES snes, PetscReal *eta1, PetscReal *eta2, PetscReal *eta3, PetscReal *t1, PetscReal *t2)
1070: {
1071:   SNES_NEWTONTR *tr;
1072:   PetscBool      flg;

1074:   PetscFunctionBegin;
1076:   if (eta1) PetscAssertPointer(eta1, 2);
1077:   if (eta2) PetscAssertPointer(eta2, 3);
1078:   if (eta3) PetscAssertPointer(eta3, 4);
1079:   if (t1) PetscAssertPointer(t1, 5);
1080:   if (t2) PetscAssertPointer(t2, 6);
1081:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
1082:   PetscAssert(flg, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONG, "Not for type %s", ((PetscObject)snes)->type_name);
1083:   tr = (SNES_NEWTONTR *)snes->data;
1084:   if (eta1) *eta1 = tr->eta1;
1085:   if (eta2) *eta2 = tr->eta2;
1086:   if (eta3) *eta3 = tr->eta3;
1087:   if (t1) *t1 = tr->t1;
1088:   if (t2) *t2 = tr->t2;
1089:   PetscFunctionReturn(PETSC_SUCCESS);
1090: }

1092: /*MC
1093:    SNESNEWTONTR - Newton based nonlinear solver that uses a trust-region strategy

1095:    Options Database Keys:
1096: +  -snes_tr_deltamin <deltamin>                  - trust region parameter, minimum size of trust region
1097: .  -snes_tr_deltamax <deltamax>                  - trust region parameter, max size of trust region (default: 1e10)
1098: .  -snes_tr_delta0 <delta0>                      - trust region parameter, initial size of trust region (default: 0.2)
1099: .  -snes_tr_eta1 <eta1>                          - trust region parameter $eta1 \le eta2$, $rho > eta1$ breaks out of the inner iteration (default: 0.001)
1100: .  -snes_tr_eta2 <eta2>                          - trust region parameter, $rho \le eta2$ shrinks the trust region (default: 0.25)
1101: .  -snes_tr_eta3 <eta3>                          - trust region parameter $eta3 > eta2$, $rho \ge eta3$ expands the trust region (default: 0.75)
1102: .  -snes_tr_t1 <t1>                              - trust region parameter, shrinking factor of trust region (default: 0.25)
1103: .  -snes_tr_t2 <t2>                              - trust region parameter, expanding factor of trust region (default: 2.0)
1104: .  -snes_tr_norm_type <1,2,infinity>             - Type of norm for trust region bounds (default: 2)
1105: -  -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.

1107:    Level: beginner

1109:    Notes:
1110:    The code is largely based on the book {cite}`nocedal2006numerical` and supports minimizing objective functions using a quadratic model.
1111:    Quasi-Newton models are also supported.

1113:    Default step computation uses the Newton direction, but a dogleg type update is also supported.
1114:    The 1- and infinity-norms are also supported when computing the trust region bounds.

1116: .seealso: [](ch_snes), `SNESCreate()`, `SNES`, `SNESSetType()`, `SNESSetObjective()`,
1117:           `SNESNewtonTRSetTolerances()`, `SNESNewtonTRSetUpdateParameters()`
1118:           `SNESNewtonTRSetNormType()`, `SNESNewtonTRSetFallbackType()`, `SNESNewtonTRSetQNType()`
1119:           `SNESNewtonTRSetPostCheck()`, `SNESNewtonTRSetPreCheck()`,
1120: M*/
1121: PETSC_EXTERN PetscErrorCode SNESCreate_NEWTONTR(SNES snes)
1122: {
1123:   SNES_NEWTONTR *neP;

1125:   PetscFunctionBegin;
1126:   snes->ops->setup          = SNESSetUp_NEWTONTR;
1127:   snes->ops->solve          = SNESSolve_NEWTONTR;
1128:   snes->ops->reset          = SNESReset_NEWTONTR;
1129:   snes->ops->destroy        = SNESDestroy_NEWTONTR;
1130:   snes->ops->setfromoptions = SNESSetFromOptions_NEWTONTR;
1131:   snes->ops->view           = SNESView_NEWTONTR;

1133:   PetscCall(SNESParametersInitialize(snes));
1134:   PetscObjectParameterSetDefault(snes, stol, 0.0);

1136:   snes->usesksp = PETSC_TRUE;
1137:   snes->npcside = PC_RIGHT;
1138:   snes->usesnpc = PETSC_TRUE;

1140:   snes->alwayscomputesfinalresidual = PETSC_TRUE;

1142:   PetscCall(PetscNew(&neP));
1143:   snes->data = (void *)neP;

1145:   PetscObjectParameterSetDefault(neP, eta1, 0.001);
1146:   PetscObjectParameterSetDefault(neP, eta2, 0.25);
1147:   PetscObjectParameterSetDefault(neP, eta3, 0.75);
1148:   PetscObjectParameterSetDefault(neP, t1, 0.25);
1149:   PetscObjectParameterSetDefault(neP, t2, 2.0);
1150:   PetscObjectParameterSetDefault(neP, deltam, PetscDefined(USE_REAL_SINGLE) ? 1.e-6 : 1.e-12);
1151:   PetscObjectParameterSetDefault(neP, delta0, 0.2);
1152:   PetscObjectParameterSetDefault(neP, deltaM, 1.e10);

1154:   neP->norm     = NORM_2;
1155:   neP->fallback = SNES_TR_FALLBACK_NEWTON;
1156:   neP->kmdc     = 0.0; /* by default do not use sufficient decrease */

1158:   PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESNewtonTRSetTolerances_C", SNESNewtonTRSetTolerances_TR));
1159:   PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESNewtonTRGetTolerances_C", SNESNewtonTRGetTolerances_TR));
1160:   PetscFunctionReturn(PETSC_SUCCESS);
1161: }