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(PetscCtxRt 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:   Calling sequence of `func`:
196: + snes    - the nonlinear solver object
197: . X       - the current solution value
198: . Y       - the tentative update step
199: . changed - output, flag indicating `Y` has been changed by the pre-check
200: - ctx     - the optional application context

202:   Level: intermediate

204:   Note:
205:   This function is called BEFORE the function evaluation within the solver.

207: .seealso: [](ch_snes), `SNESNEWTONTR`, `SNESNewtonTRPreCheck()`, `SNESNewtonTRGetPreCheck()`, `SNESNewtonTRSetPostCheck()`, `SNESNewtonTRGetPostCheck()`,
208: @*/
209: PetscErrorCode SNESNewtonTRSetPreCheck(SNES snes, PetscErrorCode (*func)(SNES snes, Vec X, Vec Y, PetscBool *changed, PetscCtx ctx), PetscCtx ctx)
210: {
211:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
212:   PetscBool      flg;

214:   PetscFunctionBegin;
216:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
217:   if (flg) {
218:     if (func) tr->precheck = func;
219:     if (ctx) tr->precheckctx = ctx;
220:   }
221:   PetscFunctionReturn(PETSC_SUCCESS);
222: }

224: /*@C
225:   SNESNewtonTRGetPreCheck - Gets the pre-check function

227:   Not Collective

229:   Input Parameter:
230: . snes - the nonlinear solver context

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

236:   Calling sequence of `func`:
237: + snes    - the nonlinear solver object
238: . X       - the current solution value
239: . Y       - the tentative update step
240: . changed - output, flag indicating `Y` has been changed by the pre-check
241: - ctx     - the optional application context

243:   Level: intermediate

245: .seealso: [](ch_snes), `SNESNEWTONTR`, `SNESNewtonTRSetPreCheck()`, `SNESNewtonTRPreCheck()`
246: @*/
247: PetscErrorCode SNESNewtonTRGetPreCheck(SNES snes, PetscErrorCode (**func)(SNES snes, Vec X, Vec Y, PetscBool *changed, PetscCtx ctx), PetscCtxRt ctx)
248: {
249:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
250:   PetscBool      flg;

252:   PetscFunctionBegin;
254:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
255:   PetscAssert(flg, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONG, "Not for type %s", ((PetscObject)snes)->type_name);
256:   if (func) *func = tr->precheck;
257:   if (ctx) *(void **)ctx = tr->precheckctx;
258:   PetscFunctionReturn(PETSC_SUCCESS);
259: }

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

265:   Logically Collective

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

272:   Calling sequence of `func`:
273: + snes      - the nonlinear solver object
274: . X         - the current solution value
275: . Y         - the tentative update step
276: . W         - the tentative new solution value
277: . changed_Y - output, flag indicated `Y` has been changed by the post-check
278: . changed_W - output, flag indicated `W` has been changed by the post-check
279: - ctx       - the optional application context

281:   Level: intermediate

283:   Note:
284:   This function is called BEFORE the function evaluation within the solver while the function set in
285:   `SNESLineSearchSetPostCheck()` is called AFTER the function evaluation.

287: .seealso: [](ch_snes), `SNESNEWTONTR`, `SNESNewtonTRPostCheck()`, `SNESNewtonTRGetPostCheck()`, `SNESNewtonTRSetPreCheck()`, `SNESNewtonTRGetPreCheck()`
288: @*/
289: PetscErrorCode SNESNewtonTRSetPostCheck(SNES snes, PetscErrorCode (*func)(SNES snes, Vec X, Vec Y, Vec W, PetscBool *changed_Y, PetscBool *changed_W, PetscCtx ctx), PetscCtx ctx)
290: {
291:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
292:   PetscBool      flg;

294:   PetscFunctionBegin;
296:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
297:   if (flg) {
298:     if (func) tr->postcheck = func;
299:     if (ctx) tr->postcheckctx = ctx;
300:   }
301:   PetscFunctionReturn(PETSC_SUCCESS);
302: }

304: /*@C
305:   SNESNewtonTRGetPostCheck - Gets the post-check function

307:   Not Collective

309:   Input Parameter:
310: . snes - the nonlinear solver context

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

316:   Calling sequence of `func`:
317: + snes      - the nonlinear solver object
318: . X         - the current solution value
319: . Y         - the tentative update step
320: . W         - the tentative new solution value
321: . changed_Y - output, flag indicated `Y` has been changed by the post-check
322: . changed_W - output, flag indicated `W` has been changed by the post-check
323: - ctx       - the optional application context

325:   Level: intermediate

327: .seealso: [](ch_snes), `SNESNEWTONTR`, `SNESNewtonTRSetPostCheck()`, `SNESNewtonTRPostCheck()`
328: @*/
329: PetscErrorCode SNESNewtonTRGetPostCheck(SNES snes, PetscErrorCode (**func)(SNES snes, Vec X, Vec Y, Vec W, PetscBool *changed_Y, PetscBool *changed_W, PetscCtx ctx), PetscCtxRt ctx)
330: {
331:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
332:   PetscBool      flg;

334:   PetscFunctionBegin;
336:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
337:   PetscAssert(flg, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONG, "Not for type %s", ((PetscObject)snes)->type_name);
338:   if (func) *func = tr->postcheck;
339:   if (ctx) *(void **)ctx = tr->postcheckctx;
340:   PetscFunctionReturn(PETSC_SUCCESS);
341: }

343: /*@C
344:   SNESNewtonTRPreCheck - Runs the precheck routine

346:   Logically Collective

348:   Input Parameters:
349: + snes - the solver
350: . X    - The last solution
351: - Y    - The step direction

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

356:   Level: intermediate

358: .seealso: [](ch_snes), `SNESNEWTONTR`, `SNESNewtonTRSetPreCheck()`, `SNESNewtonTRGetPreCheck()`, `SNESNewtonTRPostCheck()`
359: @*/
360: PetscErrorCode SNESNewtonTRPreCheck(SNES snes, Vec X, Vec Y, PetscBool *changed_Y)
361: {
362:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
363:   PetscBool      flg;

365:   PetscFunctionBegin;
367:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
368:   PetscAssert(flg, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONG, "Not for type %s", ((PetscObject)snes)->type_name);
369:   *changed_Y = PETSC_FALSE;
370:   if (tr->precheck) {
371:     PetscCall((*tr->precheck)(snes, X, Y, changed_Y, tr->precheckctx));
373:   }
374:   PetscFunctionReturn(PETSC_SUCCESS);
375: }

377: /*@C
378:   SNESNewtonTRPostCheck - Runs the postcheck routine

380:   Logically Collective

382:   Input Parameters:
383: + snes - the solver
384: . X    - The last solution
385: . Y    - The full step direction
386: - W    - The updated solution, W = X - Y

388:   Output Parameters:
389: + changed_Y - indicator if step has been changed
390: - changed_W - Indicator if the new candidate solution W has been changed.

392:   Note:
393:   If Y is changed then W is recomputed as X - Y

395:   Level: intermediate

397: .seealso: [](ch_snes), `SNESNEWTONTR`, `SNESNewtonTRSetPostCheck()`, `SNESNewtonTRGetPostCheck()`, `SNESNewtonTRPreCheck()`
398: @*/
399: PetscErrorCode SNESNewtonTRPostCheck(SNES snes, Vec X, Vec Y, Vec W, PetscBool *changed_Y, PetscBool *changed_W)
400: {
401:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
402:   PetscBool      flg;

404:   PetscFunctionBegin;
406:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
407:   PetscAssert(flg, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONG, "Not for type %s", ((PetscObject)snes)->type_name);
408:   *changed_Y = PETSC_FALSE;
409:   *changed_W = PETSC_FALSE;
410:   if (tr->postcheck) {
411:     PetscCall((*tr->postcheck)(snes, X, Y, W, changed_Y, changed_W, tr->postcheckctx));
414:   }
415:   PetscFunctionReturn(PETSC_SUCCESS);
416: }

418: /* stable implementation of roots of a*x^2 + b*x + c = 0 */
419: static inline void PetscQuadraticRoots(PetscReal a, PetscReal b, PetscReal c, PetscReal *xm, PetscReal *xp)
420: {
421:   PetscReal temp = -0.5 * (b + PetscCopysignReal(1.0, b) * PetscSqrtReal(b * b - 4 * a * c));
422:   PetscReal x1   = temp / a;
423:   PetscReal x2   = c / temp;
424:   *xm            = PetscMin(x1, x2);
425:   *xp            = PetscMax(x1, x2);
426: }

428: /* Computes the quadratic model difference */
429: static PetscErrorCode SNESNewtonTRQuadraticDelta(SNES snes, Mat J, PetscBool has_objective, Vec Y, Vec GradF, Vec W, PetscReal *yTHy_, PetscReal *gTy_, PetscReal *deltaqm)
430: {
431:   PetscReal yTHy, gTy;

433:   PetscFunctionBegin;
434:   PetscCall(MatMult(J, Y, W));
435:   if (has_objective) PetscCall(VecDotRealPart(Y, W, &yTHy));
436:   else PetscCall(VecDotRealPart(W, W, &yTHy)); /* Gauss-Newton approximation J^t * J */
437:   PetscCall(VecDotRealPart(GradF, Y, &gTy));
438:   *deltaqm = -(-(gTy) + 0.5 * (yTHy)); /* difference in quadratic model, -gTy because SNES solves it this way */
439:   if (yTHy_) *yTHy_ = yTHy;
440:   if (gTy_) *gTy_ = gTy;
441:   PetscFunctionReturn(PETSC_SUCCESS);
442: }

444: /* Computes the new objective given X = Xk, Y = direction
445:    W work vector, on output W = X - Y
446:    G work vector, on output G = SNESFunction(W) */
447: static PetscErrorCode SNESNewtonTRObjective(SNES snes, PetscBool has_objective, Vec X, Vec Y, Vec W, Vec G, PetscReal *gnorm, PetscReal *fkp1)
448: {
449:   PetscBool changed_Y, changed_W;

451:   PetscFunctionBegin;
452:   /* TODO: we can add a linesearch here */
453:   PetscCall(SNESNewtonTRPreCheck(snes, X, Y, &changed_Y));
454:   PetscCall(VecWAXPY(W, -1.0, Y, X)); /* Xkp1 */
455:   PetscCall(SNESNewtonTRPostCheck(snes, X, Y, W, &changed_Y, &changed_W));
456:   if (changed_Y && !changed_W) PetscCall(VecWAXPY(W, -1.0, Y, X));

458:   PetscCall(SNESComputeFunction(snes, W, G)); /*  F(Xkp1) = G */
459:   PetscCall(VecNorm(G, NORM_2, gnorm));
460:   SNESCheckFunctionDomainError(snes, *gnorm);
461:   if (has_objective) {
462:     PetscCall(SNESComputeObjective(snes, W, fkp1));
463:     SNESCheckObjectiveDomainError(snes, *fkp1);
464:   } else *fkp1 = 0.5 * PetscSqr(*gnorm);
465:   PetscFunctionReturn(PETSC_SUCCESS);
466: }

468: static PetscErrorCode SNESSetUpQN_NEWTONTR(SNES snes)
469: {
470:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;

472:   PetscFunctionBegin;
473:   PetscCall(MatDestroy(&tr->qnB));
474:   PetscCall(MatDestroy(&tr->qnB_pre));
475:   if (tr->qn) {
476:     PetscInt    n, N;
477:     const char *optionsprefix;
478:     Mat         B;

480:     PetscCall(MatCreate(PetscObjectComm((PetscObject)snes), &B));
481:     PetscCall(SNESGetOptionsPrefix(snes, &optionsprefix));
482:     PetscCall(MatSetOptionsPrefix(B, "snes_tr_qn_"));
483:     PetscCall(MatAppendOptionsPrefix(B, optionsprefix));
484:     PetscCall(MatSetType(B, MATLMVMBFGS));
485:     PetscCall(VecGetLocalSize(snes->vec_sol, &n));
486:     PetscCall(VecGetSize(snes->vec_sol, &N));
487:     PetscCall(MatSetSizes(B, n, n, N, N));
488:     PetscCall(MatSetUp(B));
489:     PetscCall(MatSetFromOptions(B));
490:     PetscCall(MatLMVMAllocate(B, snes->vec_sol, snes->vec_func));
491:     tr->qnB = B;
492:     if (tr->qn == SNES_TR_QN_DIFFERENT) {
493:       PetscCall(MatCreate(PetscObjectComm((PetscObject)snes), &B));
494:       PetscCall(SNESGetOptionsPrefix(snes, &optionsprefix));
495:       PetscCall(MatSetOptionsPrefix(B, "snes_tr_qn_pre_"));
496:       PetscCall(MatAppendOptionsPrefix(B, optionsprefix));
497:       PetscCall(MatSetType(B, MATLMVMBFGS));
498:       PetscCall(MatSetSizes(B, n, n, N, N));
499:       PetscCall(MatSetUp(B));
500:       PetscCall(MatSetFromOptions(B));
501:       PetscCall(MatLMVMAllocate(B, snes->vec_sol, snes->vec_func));
502:       tr->qnB_pre = B;
503:     } else {
504:       PetscCall(PetscObjectReference((PetscObject)tr->qnB));
505:       tr->qnB_pre = tr->qnB;
506:     }
507:   }
508:   PetscFunctionReturn(PETSC_SUCCESS);
509: }

511: /*
512:    SNESSolve_NEWTONTR - Implements Newton's Method with trust-region subproblem and adds dogleg Cauchy
513:    (Steepest Descent direction) step and direction if the trust region is not satisfied for solving system of
514:    nonlinear equations

516: */
517: static PetscErrorCode SNESSolve_NEWTONTR(SNES snes)
518: {
519:   SNES_NEWTONTR            *neP = (SNES_NEWTONTR *)snes->data;
520:   Vec                       X, F, Y, G, W, GradF, YU, Yc;
521:   PetscInt                  maxits, lits;
522:   PetscReal                 rho, fnorm, gnorm = 0.0, xnorm = 0.0, delta, ynorm;
523:   PetscReal                 fk, fkp1, deltaqm = 0.0, gTy = 0.0, yTHy = 0.0;
524:   PetscReal                 auk, tauk, gfnorm, gfnorm_k, ycnorm, gTBg, objmin = 0.0, beta_k = 1.0;
525:   PC                        pc;
526:   Mat                       J, Jp;
527:   PetscBool                 already_done = PETSC_FALSE, on_boundary, use_cauchy;
528:   PetscBool                 clear_converged_test, rho_satisfied, has_objective;
529:   SNES_TR_KSPConverged_Ctx *ctx;
530:   void                     *convctx;
531:   SNESObjectiveFn          *objective;
532:   KSPConvergenceTestFn     *convtest;
533:   PetscCtxDestroyFn        *convdestroy;

535:   PetscFunctionBegin;
536:   PetscCall(SNESGetObjective(snes, &objective, NULL));
537:   has_objective = objective ? PETSC_TRUE : PETSC_FALSE;

539:   maxits = snes->max_its;                                   /* maximum number of iterations */
540:   X      = snes->vec_sol;                                   /* solution vector */
541:   F      = snes->vec_func;                                  /* residual vector */
542:   Y      = snes->vec_sol_update;                            /* update vector */
543:   G      = snes->work[0];                                   /* updated residual */
544:   W      = snes->work[1];                                   /* temporary vector */
545:   GradF  = !has_objective ? snes->work[2] : snes->vec_func; /* grad f = J^T F */
546:   YU     = snes->work[3];                                   /* work vector for dogleg method */
547:   Yc     = snes->work[4];                                   /* Cauchy point */

549:   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);

551:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
552:   snes->iter = 0;
553:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));

555:   /* setup QN matrices if needed */
556:   PetscCall(SNESSetUpQN_NEWTONTR(snes));

558:   /* Set the linear stopping criteria to use the More' trick if needed */
559:   clear_converged_test = PETSC_FALSE;
560:   PetscCall(SNESGetKSP(snes, &snes->ksp));
561:   PetscCall(KSPGetConvergenceTest(snes->ksp, &convtest, &convctx, &convdestroy));
562:   if (convtest != SNESTR_KSPConverged_Private) {
563:     clear_converged_test = PETSC_TRUE;
564:     PetscCall(PetscNew(&ctx));
565:     ctx->snes = snes;
566:     PetscCall(KSPGetAndClearConvergenceTest(snes->ksp, &ctx->convtest, &ctx->convctx, &ctx->convdestroy));
567:     PetscCall(KSPSetConvergenceTest(snes->ksp, SNESTR_KSPConverged_Private, ctx, SNESTR_KSPConverged_Destroy));
568:     PetscCall(PetscInfo(snes, "Using Krylov convergence test SNESTR_KSPConverged_Private\n"));
569:   }

571:   if (!snes->vec_func_init_set) {
572:     PetscCall(SNESComputeFunction(snes, X, F)); /* F(X) */
573:   } else snes->vec_func_init_set = PETSC_FALSE;

575:   PetscCall(VecNorm(F, NORM_2, &fnorm)); /* fnorm <- || F || */
576:   SNESCheckFunctionDomainError(snes, fnorm);
577:   PetscCall(VecNorm(X, NORM_2, &xnorm)); /* xnorm <- || X || */

579:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
580:   snes->norm = fnorm;
581:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
582:   delta      = neP->delta0;
583:   neP->delta = delta;
584:   PetscCall(SNESLogConvergenceHistory(snes, fnorm, 0));

586:   /* test convergence */
587:   rho_satisfied = PETSC_FALSE;
588:   PetscCall(SNESConverged(snes, 0, 0.0, 0.0, fnorm));
589:   PetscCall(SNESMonitor(snes, 0, fnorm));
590:   if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS);

592:   if (has_objective) {
593:     PetscCall(SNESComputeObjective(snes, X, &fk));
594:     SNESCheckObjectiveDomainError(snes, fk);
595:   } else fk = 0.5 * PetscSqr(fnorm); /* obj(x) = 0.5 * ||F(x)||^2 */

597:   /* hook state vector to BFGS preconditioner */
598:   PetscCall(KSPGetPC(snes->ksp, &pc));
599:   PetscCall(PCLMVMSetUpdateVec(pc, X));

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

603:   while (snes->iter < maxits) {
604:     /* calculating Jacobian and GradF of minimization function only once */
605:     if (!already_done) {
606:       /* Call general purpose update function */
607:       PetscTryTypeMethod(snes, update, snes->iter);

609:       /* apply the nonlinear preconditioner */
610:       if (snes->npc && snes->npcside == PC_RIGHT) {
611:         SNESConvergedReason reason;

613:         PetscCall(SNESSetInitialFunction(snes->npc, F));
614:         PetscCall(PetscLogEventBegin(SNES_NPCSolve, snes->npc, X, snes->vec_rhs, 0));
615:         PetscCall(SNESSolve(snes->npc, snes->vec_rhs, X));
616:         PetscCall(PetscLogEventEnd(SNES_NPCSolve, snes->npc, X, snes->vec_rhs, 0));
617:         PetscCall(SNESGetConvergedReason(snes->npc, &reason));
618:         if (reason < 0 && reason != SNES_DIVERGED_MAX_IT && reason != SNES_DIVERGED_TR_DELTA) {
619:           snes->reason = SNES_DIVERGED_INNER;
620:           PetscFunctionReturn(PETSC_SUCCESS);
621:         }
622:         // XXX
623:         PetscCall(SNESGetNPCFunction(snes, F, &fnorm));
624:       }

626:       /* Jacobian */
627:       J  = NULL;
628:       Jp = NULL;
629:       if (!neP->qnB) {
630:         PetscCall(SNESComputeJacobian(snes, X, snes->jacobian, snes->jacobian_pre));
631:         SNESCheckJacobianDomainError(snes);
632:         J  = snes->jacobian;
633:         Jp = snes->jacobian_pre;
634:       } else { /* QN model */
635:         PetscCall(SNESComputeJacobian_MATLMVM(snes, X, neP->qnB, neP->qnB_pre, NULL));
636:         J  = neP->qnB;
637:         Jp = neP->qnB_pre;
638:       }
639:       SNESCheckJacobianDomainError(snes);

641:       /* objective function */
642:       PetscCall(VecNorm(F, NORM_2, &fnorm));
643:       SNESCheckFunctionDomainError(snes, fnorm);
644:       if (has_objective) {
645:         PetscCall(SNESComputeObjective(snes, X, &fk));
646:         SNESCheckObjectiveDomainError(snes, fk);
647:       } else fk = 0.5 * PetscSqr(fnorm); /* obj(x) = 0.5 * ||F(x)||^2 */

649:       /* GradF */
650:       if (has_objective) gfnorm = fnorm;
651:       else {
652:         PetscCall(MatMultTranspose(J, F, GradF)); /* grad f = J^T F */
653:         PetscCall(VecNorm(GradF, NORM_2, &gfnorm));
654:       }
655:       PetscCall(VecNorm(GradF, neP->norm, &gfnorm_k));
656:     }
657:     already_done = PETSC_TRUE;

659:     /* solve trust-region subproblem */

661:     /* first compute Cauchy Point */
662:     PetscCall(MatMult(J, GradF, W));
663:     if (has_objective) PetscCall(VecDotRealPart(GradF, W, &gTBg));
664:     else PetscCall(VecDotRealPart(W, W, &gTBg)); /* B = J^t * J */
665:     /* Eqs 4.11 and 4.12 in Nocedal and Wright 2nd Edition (4.7 and 4.8 in 1st Edition) */
666:     auk = delta / gfnorm_k;
667:     if (gTBg < 0.0) tauk = 1.0;
668:     else tauk = PetscMin(gfnorm * gfnorm * gfnorm_k / (delta * gTBg), 1);
669:     auk *= tauk;
670:     ycnorm = auk * gfnorm;
671:     PetscCall(VecAXPBY(Yc, auk, 0.0, GradF));

673:     on_boundary = PETSC_FALSE;
674:     use_cauchy  = (PetscBool)(tauk == 1.0 && has_objective);
675:     if (!use_cauchy) {
676:       KSPConvergedReason reason;

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

683:       /* specify radius if looking for Newton step and trust region norm is the l2 norm */
684:       PetscCall(KSPCGSetRadius(snes->ksp, neP->fallback == SNES_TR_FALLBACK_NEWTON && neP->norm == NORM_2 ? delta : 0.0));
685:       PetscCall(KSPSetOperators(snes->ksp, J, Jp));
686:       PetscCall(KSPSolve(snes->ksp, F, Y));
687:       SNESCheckKSPSolve(snes);
688:       PetscCall(KSPGetIterationNumber(snes->ksp, &lits));
689:       PetscCall(KSPGetConvergedReason(snes->ksp, &reason));
690:       on_boundary = (PetscBool)(reason == KSP_CONVERGED_STEP_LENGTH);
691:       PetscCall(PetscInfo(snes, "iter=%" PetscInt_FMT ", linear solve iterations=%" PetscInt_FMT "\n", snes->iter, lits));
692:       if (neP->kmdc) { /* update estimated Hessian largest eigenvalue */
693:         PetscReal emax, emin;
694:         PetscCall(KSPComputeExtremeSingularValues(snes->ksp, &emax, &emin));
695:         if (emax > 0.0) beta_k = emax + 1;
696:       }
697:     } else { /* Cauchy point is on the boundary, accept it */
698:       on_boundary = PETSC_TRUE;
699:       PetscCall(VecCopy(Yc, Y));
700:       PetscCall(PetscInfo(snes, "CP evaluated on boundary. delta: %g, ycnorm: %g, gTBg: %g\n", (double)delta, (double)ycnorm, (double)gTBg));
701:     }
702:     PetscCall(VecNorm(Y, neP->norm, &ynorm));

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

708:       PetscCheck(neP->norm == NORM_2 || fallback != SNES_TR_FALLBACK_DOGLEG, PetscObjectComm((PetscObject)snes), PETSC_ERR_SUP, "DOGLEG without l2 norm not implemented");
709:       switch (fallback) {
710:       case SNES_TR_FALLBACK_NEWTON:
711:         auk = delta / ynorm;
712:         PetscCall(VecScale(Y, auk));
713:         PetscCall(PetscInfo(snes, "SN evaluated. delta: %g, ynorm: %g\n", (double)delta, (double)ynorm));
714:         break;
715:       case SNES_TR_FALLBACK_CAUCHY:
716:       case SNES_TR_FALLBACK_DOGLEG:
717:         if (fallback == SNES_TR_FALLBACK_CAUCHY || gTBg <= 0.0) {
718:           PetscCall(VecCopy(Yc, Y));
719:           PetscCall(PetscInfo(snes, "CP evaluated. delta: %g, ynorm: %g, ycnorm: %g, gTBg: %g\n", (double)delta, (double)ynorm, (double)ycnorm, (double)gTBg));
720:         } else { /* take linear combination of Cauchy and Newton direction and step */
721:           auk = gfnorm * gfnorm / gTBg;
722:           if (gfnorm_k * auk >= delta) { /* first leg: Cauchy point outside of trust region */
723:             PetscCall(VecAXPBY(Y, delta / gfnorm_k, 0.0, GradF));
724:             PetscCall(PetscInfo(snes, "CP evaluated (outside region). delta: %g, ynorm: %g, ycnorm: %g\n", (double)delta, (double)ynorm, (double)ycnorm));
725:           } else { /* second leg */
726:             PetscReal c0, c1, c2, tau = 0.0, tpos, tneg;
727:             PetscBool noroots;

729:             /* Find solutions of (Eq. 4.16 in Nocedal and Wright)
730:                  ||p_U + lambda * (p_B - p_U)||^2 - delta^2 = 0,
731:                where p_U  the Cauchy direction, p_B the Newton direction */
732:             PetscCall(VecAXPBY(YU, auk, 0.0, GradF));
733:             PetscCall(VecAXPY(Y, -1.0, YU));
734:             PetscCall(VecNorm(Y, NORM_2, &c0));
735:             PetscCall(VecDotRealPart(YU, Y, &c1));
736:             c0 = PetscSqr(c0);
737:             c2 = PetscSqr(ycnorm) - PetscSqr(delta);
738:             PetscQuadraticRoots(c0, 2 * c1, c2, &tneg, &tpos);

740:             /* In principle the DL strategy as a unique solution in [0,1]
741:                here we check that for some reason we numerically failed
742:                to compute it. In that case, we use the Cauchy point */
743:             noroots = PetscIsInfOrNanReal(tneg);
744:             if (!noroots) {
745:               if (tpos > 1) {
746:                 if (tneg >= 0 && tneg <= 1) {
747:                   tau = tneg;
748:                 } else noroots = PETSC_TRUE;
749:               } else if (tpos >= 0) {
750:                 tau = tpos;
751:               } else noroots = PETSC_TRUE;
752:             }
753:             if (noroots) { /* No roots, select Cauchy point */
754:               PetscCall(VecCopy(Yc, Y));
755:             } else {
756:               PetscCall(VecAXPBY(Y, 1.0, tau, YU));
757:             }
758:             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));
759:           }
760:         }
761:         break;
762:       default:
763:         SETERRQ(PetscObjectComm((PetscObject)snes), PETSC_ERR_SUP, "Unknown fallback mode");
764:         break;
765:       }
766:     }

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

771:     /* Compute new objective function */
772:     PetscCall(SNESNewtonTRObjective(snes, has_objective, X, Y, W, G, &gnorm, &fkp1));
773:     if (PetscIsInfOrNanReal(fkp1)) rho = neP->eta1;
774:     else {
775:       if (deltaqm > 0.0) rho = (fk - fkp1) / deltaqm; /* actual improvement over predicted improvement */
776:       else rho = neP->eta1;                           /*  no reduction in quadratic model, step must be rejected */
777:     }

779:     PetscCall(VecNorm(Y, neP->norm, &ynorm));
780:     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));

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

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

790:     /* decide on new step */
791:     neP->delta = delta;
792:     if (rho > neP->eta1) {
793:       rho_satisfied = PETSC_TRUE;
794:     } else {
795:       rho_satisfied = PETSC_FALSE;
796:       PetscCall(PetscInfo(snes, "Trying again in smaller region\n"));
797:       /* check to see if progress is hopeless */
798:       PetscCall(SNESTR_Converged_Private(snes, snes->iter, xnorm, ynorm, fnorm, &snes->reason, snes->cnvP));
799:       if (!snes->reason) PetscCall(SNESConverged(snes, snes->iter, xnorm, ynorm, fnorm));
800:       if (snes->reason == SNES_CONVERGED_SNORM_RELATIVE) snes->reason = SNES_DIVERGED_TR_DELTA;
801:       snes->numFailures++;
802:       /* We're not progressing, so return with the current iterate */
803:       if (snes->reason) break;
804:     }
805:     if (rho_satisfied) {
806:       /* Update function values */
807:       already_done = PETSC_FALSE;
808:       fnorm        = gnorm;
809:       fk           = fkp1;

811:       /* New residual and linearization point */
812:       PetscCall(VecCopy(G, F));
813:       PetscCall(VecCopy(W, X));

815:       /* Monitor convergence */
816:       PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes));
817:       snes->iter++;
818:       snes->norm  = fnorm;
819:       snes->xnorm = xnorm;
820:       snes->ynorm = ynorm;
821:       PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes));
822:       PetscCall(SNESLogConvergenceHistory(snes, snes->norm, lits));

824:       /* Test for convergence, xnorm = || X || */
825:       PetscCall(VecNorm(X, NORM_2, &xnorm));
826:       PetscCall(SNESConverged(snes, snes->iter, xnorm, ynorm, fnorm));
827:       PetscCall(SNESMonitor(snes, snes->iter, snes->norm));
828:       if (snes->reason) break;
829:     }
830:   }

832:   if (clear_converged_test) {
833:     PetscCall(KSPGetAndClearConvergenceTest(snes->ksp, &ctx->convtest, &ctx->convctx, &ctx->convdestroy));
834:     PetscCall(PetscFree(ctx));
835:     PetscCall(KSPSetConvergenceTest(snes->ksp, convtest, convctx, convdestroy));
836:   }
837:   PetscFunctionReturn(PETSC_SUCCESS);
838: }

840: static PetscErrorCode SNESSetUp_NEWTONTR(SNES snes)
841: {
842:   PetscFunctionBegin;
843:   PetscCall(SNESSetWorkVecs(snes, 5));
844:   PetscCall(SNESSetUpMatrices(snes));
845:   PetscFunctionReturn(PETSC_SUCCESS);
846: }

848: static PetscErrorCode SNESReset_NEWTONTR(SNES snes)
849: {
850:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;

852:   PetscFunctionBegin;
853:   PetscCall(MatDestroy(&tr->qnB));
854:   PetscCall(MatDestroy(&tr->qnB_pre));
855:   PetscFunctionReturn(PETSC_SUCCESS);
856: }

858: static PetscErrorCode SNESDestroy_NEWTONTR(SNES snes)
859: {
860:   PetscFunctionBegin;
861:   PetscCall(SNESReset_NEWTONTR(snes));
862:   PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESNewtonTRSetTolerances_C", NULL));
863:   PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESNewtonTRGetTolerances_C", NULL));
864:   PetscCall(PetscFree(snes->data));
865:   PetscFunctionReturn(PETSC_SUCCESS);
866: }

868: static PetscErrorCode SNESSetFromOptions_NEWTONTR(SNES snes, PetscOptionItems PetscOptionsObject)
869: {
870:   SNES_NEWTONTR           *ctx = (SNES_NEWTONTR *)snes->data;
871:   SNESNewtonTRQNType       qn;
872:   SNESNewtonTRFallbackType fallback;
873:   NormType                 norm;
874:   PetscBool                flg;

876:   PetscFunctionBegin;
877:   PetscOptionsHeadBegin(PetscOptionsObject, "SNES trust region options for nonlinear equations");
878:   PetscCall(PetscOptionsDeprecated("-snes_tr_deltaM", "-snes_tr_deltamax", "3.22", NULL));
879:   PetscCall(PetscOptionsReal("-snes_tr_eta1", "eta1", "SNESNewtonTRSetUpdateParameters", ctx->eta1, &ctx->eta1, NULL));
880:   PetscCall(PetscOptionsReal("-snes_tr_eta2", "eta2", "SNESNewtonTRSetUpdateParameters", ctx->eta2, &ctx->eta2, NULL));
881:   PetscCall(PetscOptionsReal("-snes_tr_eta3", "eta3", "SNESNewtonTRSetUpdateParameters", ctx->eta3, &ctx->eta3, NULL));
882:   PetscCall(PetscOptionsReal("-snes_tr_t1", "t1", "SNESNewtonTRSetUpdateParameters", ctx->t1, &ctx->t1, NULL));
883:   PetscCall(PetscOptionsReal("-snes_tr_t2", "t2", "SNESNewtonTRSetUpdateParameters", ctx->t2, &ctx->t2, NULL));
884:   PetscCall(PetscOptionsReal("-snes_tr_delta0", "Initial trust region size", "SNESNewtonTRSetTolerances", ctx->delta0, &ctx->delta0, NULL));
885:   PetscCall(PetscOptionsReal("-snes_tr_deltamin", "Minimum allowed trust region size", "SNESNewtonTRSetTolerances", ctx->deltam, &ctx->deltam, NULL));
886:   PetscCall(PetscOptionsReal("-snes_tr_deltamax", "Maximum allowed trust region size", "SNESNewtonTRSetTolerances", ctx->deltaM, &ctx->deltaM, NULL));
887:   PetscCall(PetscOptionsReal("-snes_tr_kmdc", "sufficient decrease parameter", "None", ctx->kmdc, &ctx->kmdc, NULL));

889:   fallback = ctx->fallback;
890:   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));
891:   if (flg) PetscCall(SNESNewtonTRSetFallbackType(snes, fallback));

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

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

901:   PetscOptionsHeadEnd();
902:   PetscFunctionReturn(PETSC_SUCCESS);
903: }

905: static PetscErrorCode SNESView_NEWTONTR(SNES snes, PetscViewer viewer)
906: {
907:   SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;
908:   PetscBool      isascii;

910:   PetscFunctionBegin;
911:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
912:   if (isascii) {
913:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Trust region parameters:\n"));
914:     PetscCall(PetscViewerASCIIPrintf(viewer, "    eta1=%g, eta2=%g, eta3=%g\n", (double)tr->eta1, (double)tr->eta2, (double)tr->eta3));
915:     PetscCall(PetscViewerASCIIPrintf(viewer, "    t1=%g, t2=%g\n", (double)tr->t1, (double)tr->t2));
916:     PetscCall(PetscViewerASCIIPrintf(viewer, "    delta_min=%g, delta_0=%g, delta_max=%g\n", (double)tr->deltam, (double)tr->delta0, (double)tr->deltaM));
917:     PetscCall(PetscViewerASCIIPrintf(viewer, "    kmdc=%g\n", (double)tr->kmdc));
918:     PetscCall(PetscViewerASCIIPrintf(viewer, "    fallback=%s\n", SNESNewtonTRFallbackTypes[tr->fallback]));
919:     if (tr->qn) PetscCall(PetscViewerASCIIPrintf(viewer, "    qn=%s\n", SNESNewtonTRQNTypes[tr->qn]));
920:     if (tr->norm != NORM_2) PetscCall(PetscViewerASCIIPrintf(viewer, "    norm=%s\n", NormTypes[tr->norm]));
921:   }
922:   PetscFunctionReturn(PETSC_SUCCESS);
923: }

925: /*@
926:   SNESSetTrustRegionTolerance - Sets the trust region parameter tolerance.

928:   Logically Collective

930:   Input Parameters:
931: + snes - the `SNES` context
932: - tol  - tolerance

934:   Level: deprecated

936: .seealso: [](ch_snes), `SNES`, `SNESNEWTONTR`, `SNESSetTolerances()`
937: @*/
938: PetscErrorCode SNESSetTrustRegionTolerance(SNES snes, PetscReal tol)
939: {
940:   return SNESNewtonTRSetTolerances(snes, tol, PETSC_CURRENT, PETSC_CURRENT);
941: }

943: /*@
944:   SNESNewtonTRSetTolerances - Sets the trust region parameter tolerances.

946:   Logically Collective

948:   Input Parameters:
949: + snes      - the `SNES` context
950: . delta_min - minimum allowed trust region size
951: . delta_max - maximum allowed trust region size
952: - delta_0   - initial trust region size

954:   Options Database Key:
955: + -snes_tr_deltamin <tol> - Set minimum size
956: . -snes_tr_deltamax <tol> - Set maximum size
957: - -snes_tr_delta0   <tol> - Set initial size

959:   Note:
960:   Use `PETSC_DETERMINE` to use the default value for the given `SNES`.
961:   Use `PETSC_CURRENT` to retain a value.

963:   Fortran Note:
964:   Use `PETSC_DETERMINE_REAL`, `PETSC_CURRENT_REAL`

966:   Level: intermediate

968: .seealso: [](ch_snes), `SNES`, `SNESNEWTONTR`, `SNESNewtonTRGetTolerances()`
969: @*/
970: PetscErrorCode SNESNewtonTRSetTolerances(SNES snes, PetscReal delta_min, PetscReal delta_max, PetscReal delta_0)
971: {
972:   PetscFunctionBegin;
977:   PetscTryMethod(snes, "SNESNewtonTRSetTolerances_C", (SNES, PetscReal, PetscReal, PetscReal), (snes, delta_min, delta_max, delta_0));
978:   PetscFunctionReturn(PETSC_SUCCESS);
979: }

981: /*@
982:   SNESNewtonTRGetTolerances - Gets the trust region parameter tolerances.

984:   Not Collective

986:   Input Parameter:
987: . snes - the `SNES` context

989:   Output Parameters:
990: + delta_min - minimum allowed trust region size or `NULL`
991: . delta_max - maximum allowed trust region size or `NULL`
992: - delta_0   - initial trust region size or `NULL`

994:   Level: intermediate

996: .seealso: [](ch_snes), `SNES`, `SNESNEWTONTR`, `SNESNewtonTRSetTolerances()`
997: @*/
998: PetscErrorCode SNESNewtonTRGetTolerances(SNES snes, PetscReal *delta_min, PetscReal *delta_max, PetscReal *delta_0)
999: {
1000:   PetscFunctionBegin;
1002:   if (delta_min) PetscAssertPointer(delta_min, 2);
1003:   if (delta_max) PetscAssertPointer(delta_max, 3);
1004:   if (delta_0) PetscAssertPointer(delta_0, 4);
1005:   PetscUseMethod(snes, "SNESNewtonTRGetTolerances_C", (SNES, PetscReal *, PetscReal *, PetscReal *), (snes, delta_min, delta_max, delta_0));
1006:   PetscFunctionReturn(PETSC_SUCCESS);
1007: }

1009: /*@
1010:   SNESNewtonTRSetUpdateParameters - Sets the trust region update parameters.

1012:   Logically Collective

1014:   Input Parameters:
1015: + snes - the `SNES` context
1016: . eta1 - acceptance tolerance
1017: . eta2 - shrinking tolerance
1018: . eta3 - enlarging tolerance
1019: . t1   - shrink factor
1020: - t2   - enlarge factor

1022:   Options Database Key:
1023: + -snes_tr_eta1 <tol> - Set `eta1`
1024: . -snes_tr_eta2 <tol> - Set `eta2`
1025: . -snes_tr_eta3 <tol> - Set `eta3`
1026: . -snes_tr_t1   <tol> - Set `t1`
1027: - -snes_tr_t2   <tol> - Set `t2`

1029:   Notes:
1030:   Given the ratio $\rho = \frac{f(x_k) - f(x_k+s_k)}{m(0) - m(s_k)}$, with $x_k$ the current iterate,
1031:   $s_k$ the computed step, $f$ the objective function, and $m$ the quadratic model, the trust region
1032:   radius is modified as follows

1034:   $
1035:   \delta =
1036:   \begin{cases}
1037:   \delta * t_1 ,& \rho < \eta_2 \\
1038:   \delta * t_2 ,& \rho > \eta_3 \\
1039:   \end{cases}
1040:   $

1042:   The step is accepted if $\rho > \eta_1$.
1043:   Use `PETSC_DETERMINE` to use the default value for the given `SNES`.
1044:   Use `PETSC_CURRENT` to retain a value.

1046:   Fortran Note:
1047:   Use `PETSC_DETERMINE_REAL`, `PETSC_CURRENT_REAL`

1049:   Level: intermediate

1051: .seealso: [](ch_snes), `SNES`, `SNESNEWTONTR`, `SNESSetObjective()`, `SNESNewtonTRGetUpdateParameters()`
1052: @*/
1053: PetscErrorCode SNESNewtonTRSetUpdateParameters(SNES snes, PetscReal eta1, PetscReal eta2, PetscReal eta3, PetscReal t1, PetscReal t2)
1054: {
1055:   PetscBool flg;

1057:   PetscFunctionBegin;
1064:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
1065:   if (flg) {
1066:     SNES_NEWTONTR *tr = (SNES_NEWTONTR *)snes->data;

1068:     if (eta1 == PETSC_DETERMINE) eta1 = tr->default_eta1;
1069:     if (eta2 == PETSC_DETERMINE) eta2 = tr->default_eta2;
1070:     if (eta3 == PETSC_DETERMINE) eta3 = tr->default_eta3;
1071:     if (t1 == PETSC_DETERMINE) t1 = tr->default_t1;
1072:     if (t2 == PETSC_DETERMINE) t2 = tr->default_t2;
1073:     if (eta1 != PETSC_CURRENT) tr->eta1 = eta1;
1074:     if (eta2 != PETSC_CURRENT) tr->eta2 = eta2;
1075:     if (eta3 != PETSC_CURRENT) tr->eta3 = eta3;
1076:     if (t1 != PETSC_CURRENT) tr->t1 = t1;
1077:     if (t2 != PETSC_CURRENT) tr->t2 = t2;
1078:   }
1079:   PetscFunctionReturn(PETSC_SUCCESS);
1080: }

1082: /*@
1083:   SNESNewtonTRGetUpdateParameters - Gets the trust region update parameters.

1085:   Not Collective

1087:   Input Parameter:
1088: . snes - the `SNES` context

1090:   Output Parameters:
1091: + eta1 - acceptance tolerance
1092: . eta2 - shrinking tolerance
1093: . eta3 - enlarging tolerance
1094: . t1   - shrink factor
1095: - t2   - enlarge factor

1097:   Level: intermediate

1099: .seealso: [](ch_snes), `SNES`, `SNESNEWTONTR`, `SNESNewtonTRSetUpdateParameters()`
1100: @*/
1101: PetscErrorCode SNESNewtonTRGetUpdateParameters(SNES snes, PetscReal *eta1, PetscReal *eta2, PetscReal *eta3, PetscReal *t1, PetscReal *t2)
1102: {
1103:   SNES_NEWTONTR *tr;
1104:   PetscBool      flg;

1106:   PetscFunctionBegin;
1108:   if (eta1) PetscAssertPointer(eta1, 2);
1109:   if (eta2) PetscAssertPointer(eta2, 3);
1110:   if (eta3) PetscAssertPointer(eta3, 4);
1111:   if (t1) PetscAssertPointer(t1, 5);
1112:   if (t2) PetscAssertPointer(t2, 6);
1113:   PetscCall(PetscObjectTypeCompare((PetscObject)snes, SNESNEWTONTR, &flg));
1114:   PetscAssert(flg, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONG, "Not for type %s", ((PetscObject)snes)->type_name);
1115:   tr = (SNES_NEWTONTR *)snes->data;
1116:   if (eta1) *eta1 = tr->eta1;
1117:   if (eta2) *eta2 = tr->eta2;
1118:   if (eta3) *eta3 = tr->eta3;
1119:   if (t1) *t1 = tr->t1;
1120:   if (t2) *t2 = tr->t2;
1121:   PetscFunctionReturn(PETSC_SUCCESS);
1122: }

1124: /*MC
1125:    SNESNEWTONTR - Newton based nonlinear solver that uses a trust-region strategy

1127:    Options Database Keys:
1128: +  -snes_tr_deltamin <deltamin>                  - trust region parameter, minimum size of trust region
1129: .  -snes_tr_deltamax <deltamax>                  - trust region parameter, max size of trust region (default: 1e10)
1130: .  -snes_tr_delta0 <delta0>                      - trust region parameter, initial size of trust region (default: 0.2)
1131: .  -snes_tr_eta1 <eta1>                          - trust region parameter $eta1 \le eta2$, $rho > eta1$ breaks out of the inner iteration (default: 0.001)
1132: .  -snes_tr_eta2 <eta2>                          - trust region parameter, $rho \le eta2$ shrinks the trust region (default: 0.25)
1133: .  -snes_tr_eta3 <eta3>                          - trust region parameter $eta3 > eta2$, $rho \ge eta3$ expands the trust region (default: 0.75)
1134: .  -snes_tr_t1 <t1>                              - trust region parameter, shrinking factor of trust region (default: 0.25)
1135: .  -snes_tr_t2 <t2>                              - trust region parameter, expanding factor of trust region (default: 2.0)
1136: .  -snes_tr_norm_type <1,2,infinity>             - Type of norm for trust region bounds (default: 2)
1137: -  -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.

1139:    Level: beginner

1141:    Notes:
1142:    The code is largely based on the book {cite}`nocedal2006numerical` and supports minimizing objective functions using a quadratic model.
1143:    Quasi-Newton models are also supported.

1145:    Default step computation uses the Newton direction, but a dogleg type update is also supported.
1146:    The 1- and infinity-norms are also supported when computing the trust region bounds.

1148: .seealso: [](ch_snes), `SNESCreate()`, `SNES`, `SNESSetType()`, `SNESSetObjective()`,
1149:           `SNESNewtonTRSetTolerances()`, `SNESNewtonTRSetUpdateParameters()`
1150:           `SNESNewtonTRSetNormType()`, `SNESNewtonTRSetFallbackType()`, `SNESNewtonTRSetQNType()`
1151:           `SNESNewtonTRSetPostCheck()`, `SNESNewtonTRSetPreCheck()`,
1152: M*/
1153: PETSC_EXTERN PetscErrorCode SNESCreate_NEWTONTR(SNES snes)
1154: {
1155:   SNES_NEWTONTR *neP;

1157:   PetscFunctionBegin;
1158:   snes->ops->setup          = SNESSetUp_NEWTONTR;
1159:   snes->ops->solve          = SNESSolve_NEWTONTR;
1160:   snes->ops->reset          = SNESReset_NEWTONTR;
1161:   snes->ops->destroy        = SNESDestroy_NEWTONTR;
1162:   snes->ops->setfromoptions = SNESSetFromOptions_NEWTONTR;
1163:   snes->ops->view           = SNESView_NEWTONTR;

1165:   PetscCall(SNESParametersInitialize(snes));
1166:   PetscObjectParameterSetDefault(snes, stol, 0.0);

1168:   snes->usesksp = PETSC_TRUE;
1169:   snes->npcside = PC_RIGHT;
1170:   snes->usesnpc = PETSC_TRUE;

1172:   snes->alwayscomputesfinalresidual = PETSC_TRUE;

1174:   PetscCall(PetscNew(&neP));
1175:   snes->data = (void *)neP;

1177:   PetscObjectParameterSetDefault(neP, eta1, 0.001);
1178:   PetscObjectParameterSetDefault(neP, eta2, 0.25);
1179:   PetscObjectParameterSetDefault(neP, eta3, 0.75);
1180:   PetscObjectParameterSetDefault(neP, t1, 0.25);
1181:   PetscObjectParameterSetDefault(neP, t2, 2.0);
1182:   PetscObjectParameterSetDefault(neP, deltam, PetscDefined(USE_REAL_SINGLE) ? 1.e-6 : 1.e-12);
1183:   PetscObjectParameterSetDefault(neP, delta0, 0.2);
1184:   PetscObjectParameterSetDefault(neP, deltaM, 1.e10);

1186:   neP->norm     = NORM_2;
1187:   neP->fallback = SNES_TR_FALLBACK_NEWTON;
1188:   neP->kmdc     = 0.0; /* by default do not use sufficient decrease */

1190:   PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESNewtonTRSetTolerances_C", SNESNewtonTRSetTolerances_TR));
1191:   PetscCall(PetscObjectComposeFunction((PetscObject)snes, "SNESNewtonTRGetTolerances_C", SNESNewtonTRGetTolerances_TR));
1192:   PetscFunctionReturn(PETSC_SUCCESS);
1193: }