Actual source code: linesearchbt.c

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

  4: typedef struct {
  5:   PetscReal alpha; /* sufficient decrease parameter */
  6: } SNESLineSearch_BT;

  8: /*@
  9:   SNESLineSearchBTSetAlpha - Sets the descent parameter, `alpha`, in the `SNESLINESEARCHBT` `SNESLineSearch` variant.

 11:   Input Parameters:
 12: + linesearch - linesearch context
 13: - alpha      - The descent parameter

 15:   Level: intermediate

 17: .seealso: [](ch_snes), `SNESLineSearch`, `SNESLineSearchSetLambda()`, `SNESLineSearchGetTolerances()`, `SNESLINESEARCHBT`, `SNESLineSearchBTGetAlpha()`
 18: @*/
 19: PetscErrorCode SNESLineSearchBTSetAlpha(SNESLineSearch linesearch, PetscReal alpha)
 20: {
 21:   SNESLineSearch_BT *bt = (SNESLineSearch_BT *)linesearch->data;

 23:   PetscFunctionBegin;
 25:   bt->alpha = alpha;
 26:   PetscFunctionReturn(PETSC_SUCCESS);
 27: }

 29: /*@
 30:   SNESLineSearchBTGetAlpha - Gets the descent parameter, `alpha`, in the `SNESLINESEARCHBT` variant that was set with `SNESLineSearchBTSetAlpha()`

 32:   Input Parameter:
 33: . linesearch - linesearch context

 35:   Output Parameter:
 36: . alpha - The descent parameter

 38:   Level: intermediate

 40: .seealso: [](ch_snes), `SNESLineSearch`, `SNESLineSearchGetLambda()`, `SNESLineSearchGetTolerances()`, `SNESLINESEARCHBT`, `SNESLineSearchBTSetAlpha()`
 41: @*/
 42: PetscErrorCode SNESLineSearchBTGetAlpha(SNESLineSearch linesearch, PetscReal *alpha)
 43: {
 44:   SNESLineSearch_BT *bt = (SNESLineSearch_BT *)linesearch->data;

 46:   PetscFunctionBegin;
 48:   *alpha = bt->alpha;
 49:   PetscFunctionReturn(PETSC_SUCCESS);
 50: }

 52: static PetscErrorCode SNESLineSearchApply_BT(SNESLineSearch linesearch)
 53: {
 54:   SNESLineSearch_BT *bt = (SNESLineSearch_BT *)linesearch->data;
 55:   PetscBool          changed_y, changed_w;
 56:   Vec                X, F, Y, W, G;
 57:   SNES               snes;
 58:   PetscReal          fnorm, xnorm, ynorm, gnorm;
 59:   PetscReal          lambda, lambdatemp, lambdaprev, minlambda, initslope, alpha, stol;
 60:   PetscReal          t1, t2, a, b, d;
 61:   PetscReal          f;
 62:   PetscReal          g, gprev;
 63:   PetscViewer        monitor;
 64:   PetscInt           max_it, count;
 65:   Mat                jac;
 66:   SNESObjectiveFn   *objective;
 67:   const char *const  ordStr[] = {"Linear", "Quadratic", "Cubic"};

 69:   PetscFunctionBegin;
 70:   PetscCall(SNESLineSearchGetVecs(linesearch, &X, &F, &Y, &W, &G));
 71:   PetscCall(SNESLineSearchGetNorms(linesearch, NULL, &fnorm, NULL));
 72:   PetscCall(SNESLineSearchGetLambda(linesearch, &lambda));
 73:   PetscCall(SNESLineSearchGetSNES(linesearch, &snes));
 74:   PetscCall(SNESLineSearchGetDefaultMonitor(linesearch, &monitor));
 75:   PetscCall(SNESLineSearchGetTolerances(linesearch, &minlambda, NULL, NULL, NULL, NULL, &max_it));
 76:   PetscCall(SNESGetTolerances(snes, NULL, NULL, &stol, NULL, NULL));
 77:   PetscCall(SNESGetObjective(snes, &objective, NULL));
 78:   alpha = bt->alpha;

 80:   PetscCall(SNESGetJacobian(snes, &jac, NULL, NULL, NULL));
 81:   PetscCheck(jac || objective, PetscObjectComm((PetscObject)linesearch), PETSC_ERR_USER, "SNESLineSearchBT requires a Jacobian matrix");

 83:   PetscCall(SNESLineSearchPreCheck(linesearch, X, Y, &changed_y));
 84:   PetscCall(SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_SUCCEEDED));

 86:   PetscCall(VecNormBegin(Y, NORM_2, &ynorm));
 87:   PetscCall(VecNormBegin(X, NORM_2, &xnorm));
 88:   PetscCall(VecNormEnd(Y, NORM_2, &ynorm));
 89:   PetscCall(VecNormEnd(X, NORM_2, &xnorm));

 91:   if (ynorm == 0.0) {
 92:     if (monitor) {
 93:       PetscCall(PetscViewerASCIIAddTab(monitor, ((PetscObject)linesearch)->tablevel));
 94:       PetscCall(PetscViewerASCIIPrintf(monitor, "    Line search: Initial direction and size is 0\n"));
 95:       PetscCall(PetscViewerASCIISubtractTab(monitor, ((PetscObject)linesearch)->tablevel));
 96:     }
 97:     PetscCall(VecCopy(X, W));
 98:     PetscCall(VecCopy(F, G));
 99:     PetscCall(SNESLineSearchSetNorms(linesearch, xnorm, fnorm, ynorm));
100:     PetscCall(SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_REDUCT));
101:     PetscFunctionReturn(PETSC_SUCCESS);
102:   }

104:   /* if the SNES has an objective set, use that instead of the function value */
105:   if (objective) {
106:     PetscCall(SNESComputeObjective(snes, X, &f));
107:   } else {
108:     f = 0.5 * PetscSqr(fnorm);
109:   }

111:   /* compute the initial slope */
112:   if (objective) {
113:     /* slope comes from the function (assumed to be the gradient of the objective) */
114:     PetscCall(VecDotRealPart(Y, F, &initslope));
115:   } else {
116:     /* slope comes from the normal equations */
117:     PetscCall(MatMult(jac, Y, W));
118:     PetscCall(VecDotRealPart(F, W, &initslope));
119:     if (initslope > 0.0) initslope = -initslope;
120:     if (initslope == 0.0) initslope = -1.0;
121:   }

123:   while (PETSC_TRUE) {
124:     PetscCall(VecWAXPY(W, -lambda, Y, X));
125:     if (linesearch->ops->viproject) PetscCall((*linesearch->ops->viproject)(snes, W));
126:     if (snes->nfuncs >= snes->max_funcs && snes->max_funcs >= 0) {
127:       PetscCall(PetscInfo(snes, "Exceeded maximum function evaluations, while checking full step length!\n"));
128:       snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
129:       PetscCall(SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_FUNCTION));
130:       PetscFunctionReturn(PETSC_SUCCESS);
131:     }

133:     if (objective) {
134:       PetscCall(SNESComputeObjective(snes, W, &g));
135:     } else {
136:       PetscCall((*linesearch->ops->snesfunc)(snes, W, G));
137:       if (linesearch->ops->vinorm) {
138:         gnorm = fnorm;
139:         PetscCall((*linesearch->ops->vinorm)(snes, G, W, &gnorm));
140:       } else {
141:         PetscCall(VecNorm(G, NORM_2, &gnorm));
142:       }
143:       g = 0.5 * PetscSqr(gnorm);
144:     }
145:     PetscCall(SNESLineSearchMonitor(linesearch));

147:     if (!PetscIsInfOrNanReal(g)) break;
148:     if (monitor) {
149:       PetscCall(PetscViewerASCIIAddTab(monitor, ((PetscObject)linesearch)->tablevel));
150:       PetscCall(PetscViewerASCIIPrintf(monitor, "    Line search: objective function at lambdas = %g is Inf or Nan, cutting lambda\n", (double)lambda));
151:       PetscCall(PetscViewerASCIISubtractTab(monitor, ((PetscObject)linesearch)->tablevel));
152:     }
153:     if (lambda <= minlambda) SNESCheckFunctionNorm(snes, g);
154:     lambda *= .5;
155:   }

157:   if (!objective) PetscCall(PetscInfo(snes, "Initial fnorm %14.12e gnorm %14.12e\n", (double)fnorm, (double)gnorm));
158:   if (g <= f + lambda * alpha * initslope) { /* Sufficient reduction or step tolerance convergence */
159:     if (monitor) {
160:       PetscCall(PetscViewerASCIIAddTab(monitor, ((PetscObject)linesearch)->tablevel));
161:       if (!objective) {
162:         PetscCall(PetscViewerASCIIPrintf(monitor, "    Line search: Using full step: fnorm %14.12e gnorm %14.12e\n", (double)fnorm, (double)gnorm));
163:       } else {
164:         PetscCall(PetscViewerASCIIPrintf(monitor, "    Line search: Using full step: old obj %14.12e new obj %14.12e\n", (double)f, (double)g));
165:       }
166:       PetscCall(PetscViewerASCIISubtractTab(monitor, ((PetscObject)linesearch)->tablevel));
167:     }
168:   } else {
169:     if (stol * xnorm > ynorm) {
170:       /* Since the full step didn't give sufficient decrease and the step is tiny, exit */
171:       PetscCall(SNESLineSearchSetNorms(linesearch, xnorm, fnorm, ynorm));
172:       PetscCall(SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_SUCCEEDED));
173:       if (monitor) {
174:         PetscCall(PetscViewerASCIIAddTab(monitor, ((PetscObject)linesearch)->tablevel));
175:         PetscCall(PetscViewerASCIIPrintf(monitor, "    Line search: Ended due to ynorm < stol*xnorm (%14.12e < %14.12e).\n", (double)ynorm, (double)(stol * xnorm)));
176:         PetscCall(PetscViewerASCIISubtractTab(monitor, ((PetscObject)linesearch)->tablevel));
177:       }
178:       PetscFunctionReturn(PETSC_SUCCESS);
179:     }
180:     /* Here to avoid -Wmaybe-uninitiliazed warnings */
181:     lambdaprev = lambda;
182:     gprev      = g;
183:     if (linesearch->order != SNES_LINESEARCH_ORDER_LINEAR) {
184:       /* Fit points with quadratic */
185:       lambdatemp = -initslope * PetscSqr(lambda) / (2.0 * (g - f - lambda * initslope));
186:       lambda     = PetscClipInterval(lambdatemp, .1 * lambda, .5 * lambda);

188:       PetscCall(VecWAXPY(W, -lambda, Y, X));
189:       if (linesearch->ops->viproject) PetscCall((*linesearch->ops->viproject)(snes, W));
190:       if (snes->nfuncs >= snes->max_funcs && snes->max_funcs >= 0) {
191:         PetscCall(PetscInfo(snes, "Exceeded maximum function evaluations, while attempting quadratic backtracking! %" PetscInt_FMT " \n", snes->nfuncs));
192:         snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
193:         PetscCall(SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_FUNCTION));
194:         PetscFunctionReturn(PETSC_SUCCESS);
195:       }
196:       if (objective) {
197:         PetscCall(SNESComputeObjective(snes, W, &g));
198:       } else {
199:         PetscCall((*linesearch->ops->snesfunc)(snes, W, G));
200:         if (linesearch->ops->vinorm) {
201:           gnorm = fnorm;
202:           PetscCall((*linesearch->ops->vinorm)(snes, G, W, &gnorm));
203:         } else {
204:           PetscCall(VecNorm(G, NORM_2, &gnorm));
205:         }
206:         g = 0.5 * PetscSqr(gnorm);
207:       }
208:       if (PetscIsInfOrNanReal(g)) {
209:         PetscCall(SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_NANORINF));
210:         PetscCall(PetscInfo(snes, "Aborted due to Nan or Inf in function evaluation\n"));
211:         PetscFunctionReturn(PETSC_SUCCESS);
212:       }
213:       if (monitor) {
214:         PetscCall(PetscViewerASCIIAddTab(monitor, ((PetscObject)linesearch)->tablevel));
215:         if (!objective) {
216:           PetscCall(PetscViewerASCIIPrintf(monitor, "    Line search: gnorm after quadratic fit %14.12e\n", (double)gnorm));
217:         } else {
218:           PetscCall(PetscViewerASCIIPrintf(monitor, "    Line search: obj after quadratic fit %14.12e\n", (double)g));
219:         }
220:         PetscCall(PetscViewerASCIISubtractTab(monitor, ((PetscObject)linesearch)->tablevel));
221:       }
222:     }
223:     if (linesearch->order != SNES_LINESEARCH_ORDER_LINEAR && g <= f + lambda * alpha * initslope) { /* sufficient reduction */
224:       if (monitor) {
225:         PetscCall(PetscViewerASCIIAddTab(monitor, ((PetscObject)linesearch)->tablevel));
226:         PetscCall(PetscViewerASCIIPrintf(monitor, "    Line search: Quadratically determined step, lambda=%18.16e\n", (double)lambda));
227:         PetscCall(PetscViewerASCIISubtractTab(monitor, ((PetscObject)linesearch)->tablevel));
228:       }
229:     } else {
230:       for (count = 0; count < max_it; count++) {
231:         if (lambda <= minlambda) {
232:           if (monitor) {
233:             PetscCall(PetscViewerASCIIAddTab(monitor, ((PetscObject)linesearch)->tablevel));
234:             PetscCall(PetscViewerASCIIPrintf(monitor, "    Line search: unable to find good step length! After %" PetscInt_FMT " tries \n", count));
235:             if (!objective) {
236:               PetscCall(PetscViewerASCIIPrintf(monitor, "    Line search: fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, minlambda=%18.16e, lambda=%18.16e, initial slope=%18.16e\n", (double)fnorm, (double)gnorm, (double)ynorm, (double)minlambda, (double)lambda, (double)initslope));
237:             } else {
238:               PetscCall(PetscViewerASCIIPrintf(monitor, "    Line search: obj(0)=%18.16e, obj=%18.16e, ynorm=%18.16e, minlambda=%18.16e, lambda=%18.16e, initial slope=%18.16e\n", (double)f, (double)g, (double)ynorm, (double)minlambda, (double)lambda, (double)initslope));
239:             }
240:             PetscCall(PetscViewerASCIISubtractTab(monitor, ((PetscObject)linesearch)->tablevel));
241:           }
242:           PetscCall(SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_REDUCT));
243:           PetscFunctionReturn(PETSC_SUCCESS);
244:         }
245:         if (linesearch->order == SNES_LINESEARCH_ORDER_CUBIC) {
246:           /* Fit points with cubic */
247:           t1 = g - f - lambda * initslope;
248:           t2 = gprev - f - lambdaprev * initslope;
249:           a  = (t1 / (lambda * lambda) - t2 / (lambdaprev * lambdaprev)) / (lambda - lambdaprev);
250:           b  = (-lambdaprev * t1 / (lambda * lambda) + lambda * t2 / (lambdaprev * lambdaprev)) / (lambda - lambdaprev);
251:           d  = b * b - 3 * a * initslope;
252:           if (d < 0.0) d = 0.0;
253:           if (a == 0.0) lambdatemp = -initslope / (2.0 * b);
254:           else lambdatemp = (-b + PetscSqrtReal(d)) / (3.0 * a);
255:         } else if (linesearch->order == SNES_LINESEARCH_ORDER_QUADRATIC) {
256:           lambdatemp = -initslope * PetscSqr(lambda) / (2.0 * (g - f - lambda * initslope));
257:         } else if (linesearch->order == SNES_LINESEARCH_ORDER_LINEAR) { /* Just backtrack */
258:           lambdatemp = .5 * lambda;
259:         } else SETERRQ(PetscObjectComm((PetscObject)linesearch), PETSC_ERR_SUP, "Line search order %" PetscInt_FMT " for type bt", linesearch->order);
260:         lambdaprev = lambda;
261:         gprev      = g;

263:         lambda = PetscClipInterval(lambdatemp, .1 * lambda, .5 * lambda);
264:         PetscCall(VecWAXPY(W, -lambda, Y, X));
265:         if (linesearch->ops->viproject) PetscCall((*linesearch->ops->viproject)(snes, W));
266:         if (snes->nfuncs >= snes->max_funcs && snes->max_funcs >= 0) {
267:           PetscCall(PetscInfo(snes, "Exceeded maximum function evaluations, while looking for good step length! %" PetscInt_FMT " \n", count));
268:           if (!objective) PetscCall(PetscInfo(snes, "fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lambda=%18.16e, initial slope=%18.16e\n", (double)fnorm, (double)gnorm, (double)ynorm, (double)lambda, (double)initslope));
269:           PetscCall(SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_FUNCTION));
270:           snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
271:           PetscFunctionReturn(PETSC_SUCCESS);
272:         }
273:         if (objective) {
274:           PetscCall(SNESComputeObjective(snes, W, &g));
275:         } else {
276:           PetscCall((*linesearch->ops->snesfunc)(snes, W, G));
277:           if (linesearch->ops->vinorm) {
278:             gnorm = fnorm;
279:             PetscCall((*linesearch->ops->vinorm)(snes, G, W, &gnorm));
280:           } else {
281:             PetscCall(VecNorm(G, NORM_2, &gnorm));
282:           }
283:           g = 0.5 * PetscSqr(gnorm);
284:         }
285:         if (PetscIsInfOrNanReal(g)) {
286:           PetscCall(SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_NANORINF));
287:           PetscCall(PetscInfo(snes, "Aborted due to Nan or Inf in function evaluation\n"));
288:           PetscFunctionReturn(PETSC_SUCCESS);
289:         }
290:         if (g <= f + lambda * alpha * initslope) { /* is reduction enough? */
291:           if (monitor) {
292:             PetscCall(PetscViewerASCIIAddTab(monitor, ((PetscObject)linesearch)->tablevel));
293:             if (!objective) {
294:               PetscCall(PetscViewerASCIIPrintf(monitor, "    Line search: %s step, current gnorm %14.12e lambda=%18.16e\n", ordStr[linesearch->order - 1], (double)gnorm, (double)lambda));
295:               PetscCall(PetscViewerASCIISubtractTab(monitor, ((PetscObject)linesearch)->tablevel));
296:             } else {
297:               PetscCall(PetscViewerASCIIPrintf(monitor, "    Line search: %s step, obj %14.12e lambda=%18.16e\n", ordStr[linesearch->order - 1], (double)g, (double)lambda));
298:               PetscCall(PetscViewerASCIISubtractTab(monitor, ((PetscObject)linesearch)->tablevel));
299:             }
300:           }
301:           break;
302:         } else if (monitor) {
303:           PetscCall(PetscViewerASCIIAddTab(monitor, ((PetscObject)linesearch)->tablevel));
304:           if (!objective) {
305:             PetscCall(PetscViewerASCIIPrintf(monitor, "    Line search: %s step no good, shrinking lambda, current gnorm %12.12e lambda=%18.16e\n", ordStr[linesearch->order - 1], (double)gnorm, (double)lambda));
306:             PetscCall(PetscViewerASCIISubtractTab(monitor, ((PetscObject)linesearch)->tablevel));
307:           } else {
308:             PetscCall(PetscViewerASCIIPrintf(monitor, "    Line search: %s step no good, shrinking lambda, obj %12.12e lambda=%18.16e\n", ordStr[linesearch->order - 1], (double)g, (double)lambda));
309:             PetscCall(PetscViewerASCIISubtractTab(monitor, ((PetscObject)linesearch)->tablevel));
310:           }
311:         }
312:       }
313:     }
314:   }

316:   /* postcheck */
317:   PetscCall(SNESLineSearchSetLambda(linesearch, lambda));
318:   PetscCall(SNESLineSearchPostCheck(linesearch, X, Y, W, &changed_y, &changed_w));
319:   if (changed_y) {
320:     if (!changed_w) PetscCall(VecWAXPY(W, -lambda, Y, X));
321:     if (linesearch->ops->viproject) PetscCall((*linesearch->ops->viproject)(snes, W));
322:   }
323:   if (changed_y || changed_w || objective) { /* recompute the function norm if the step has changed or the objective isn't the norm */
324:     PetscCall((*linesearch->ops->snesfunc)(snes, W, G));
325:     if (linesearch->ops->vinorm) {
326:       gnorm = fnorm;
327:       PetscCall((*linesearch->ops->vinorm)(snes, G, W, &gnorm));
328:     } else {
329:       PetscCall(VecNorm(G, NORM_2, &gnorm));
330:     }
331:     PetscCall(VecNorm(Y, NORM_2, &ynorm));
332:     if (PetscIsInfOrNanReal(gnorm)) {
333:       PetscCall(SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_NANORINF));
334:       PetscCall(PetscInfo(snes, "Aborted due to Nan or Inf in function evaluation\n"));
335:       PetscFunctionReturn(PETSC_SUCCESS);
336:     }
337:   }

339:   /* copy the solution over */
340:   PetscCall(VecCopy(W, X));
341:   PetscCall(VecCopy(G, F));
342:   PetscCall(VecNorm(X, NORM_2, &xnorm));
343:   PetscCall(SNESLineSearchSetNorms(linesearch, xnorm, gnorm, ynorm));
344:   PetscFunctionReturn(PETSC_SUCCESS);
345: }

347: static PetscErrorCode SNESLineSearchView_BT(SNESLineSearch linesearch, PetscViewer viewer)
348: {
349:   PetscBool          isascii;
350:   SNESLineSearch_BT *bt = (SNESLineSearch_BT *)linesearch->data;

352:   PetscFunctionBegin;
353:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
354:   if (isascii) {
355:     if (linesearch->order == SNES_LINESEARCH_ORDER_CUBIC) {
356:       PetscCall(PetscViewerASCIIPrintf(viewer, "  interpolation: cubic\n"));
357:     } else if (linesearch->order == SNES_LINESEARCH_ORDER_QUADRATIC) {
358:       PetscCall(PetscViewerASCIIPrintf(viewer, "  interpolation: quadratic\n"));
359:     }
360:     PetscCall(PetscViewerASCIIPrintf(viewer, "  alpha=%e\n", (double)bt->alpha));
361:   }
362:   PetscFunctionReturn(PETSC_SUCCESS);
363: }

365: static PetscErrorCode SNESLineSearchDestroy_BT(SNESLineSearch linesearch)
366: {
367:   PetscFunctionBegin;
368:   PetscCall(PetscFree(linesearch->data));
369:   PetscFunctionReturn(PETSC_SUCCESS);
370: }

372: static PetscErrorCode SNESLineSearchSetFromOptions_BT(SNESLineSearch linesearch, PetscOptionItems PetscOptionsObject)
373: {
374:   SNESLineSearch_BT *bt = (SNESLineSearch_BT *)linesearch->data;

376:   PetscFunctionBegin;
377:   PetscOptionsHeadBegin(PetscOptionsObject, "SNESLineSearch BT options");
378:   PetscCall(PetscOptionsReal("-snes_linesearch_alpha", "Descent tolerance", "SNESLineSearchBT", bt->alpha, &bt->alpha, NULL));
379:   PetscOptionsHeadEnd();
380:   PetscFunctionReturn(PETSC_SUCCESS);
381: }

383: /*MC
384:    SNESLINESEARCHBT - Backtracking line search {cite}`dennis:83`.

386:    This line search finds the minimum of a polynomial fitting either $1/2 ||F(x_k + \lambda Y_k)||_2^2$,
387:    or the objective function $G(x_k + \lambda Y_k)$ if it is provided with `SNESSetObjective()`.
388:    If this fit does not satisfy the sufficient decrease conditions, the interval shrinks
389:    and the fit is reattempted at most `max_it` times or until $\lambda$ is below `minlambda`.

391:    Options Database Keys:
392: +  -snes_linesearch_alpha <1e\-4>      - slope descent parameter
393: .  -snes_linesearch_damping <1.0>      - initial `lambda` on entry to the line search
394: .  -snes_linesearch_max_it <40>        - maximum number of shrinking iterations in the line search
395: .  -snes_linesearch_minlambda <1e\-12> - minimum `lambda` (scaling of solution update) allowed
396: -  -snes_linesearch_order <3>          - order of the polynomial fit, must be 1, 2, or 3. With order 1, it performs a simple backtracking without any curve fitting

398:    Level: advanced

400:    Note:
401:    This line search will always produce a step that is less than or equal to, in length, the full step size.

403: .seealso: [](ch_snes), `SNESLineSearch`, `SNESLineSearchType`, `SNESLineSearchCreate()`, `SNESLineSearchSetType()`
404: M*/
405: PETSC_EXTERN PetscErrorCode SNESLineSearchCreate_BT(SNESLineSearch linesearch)
406: {
407:   SNESLineSearch_BT *bt;

409:   PetscFunctionBegin;
410:   linesearch->ops->apply          = SNESLineSearchApply_BT;
411:   linesearch->ops->destroy        = SNESLineSearchDestroy_BT;
412:   linesearch->ops->setfromoptions = SNESLineSearchSetFromOptions_BT;
413:   linesearch->ops->reset          = NULL;
414:   linesearch->ops->view           = SNESLineSearchView_BT;
415:   linesearch->ops->setup          = NULL;

417:   PetscCall(PetscNew(&bt));

419:   linesearch->data   = (void *)bt;
420:   linesearch->max_it = 40;
421:   linesearch->order  = SNES_LINESEARCH_ORDER_CUBIC;
422:   bt->alpha          = 1e-4;
423:   PetscFunctionReturn(PETSC_SUCCESS);
424: }