xref: /petsc/src/tao/bound/impls/bncg/bncg.c (revision 11eb65dca7891a9420bdee31b9ef32db58c1cdef) 
1 #include <petsctaolinesearch.h>
2 #include <../src/tao/bound/impls/bncg/bncg.h>
3 
4 #define CG_FletcherReeves       0
5 #define CG_PolakRibiere         1
6 #define CG_PolakRibierePlus     2
7 #define CG_HestenesStiefel      3
8 #define CG_DaiYuan              4
9 #define CG_Types                5
10 
11 static const char *CG_Table[64] = {"fr", "pr", "prp", "hs", "dy"};
12 
13 #define CG_AS_NONE       0
14 #define CG_AS_BERTSEKAS  1
15 #define CG_AS_SIZE       2
16 
17 static const char *CG_AS_TYPE[64] = {"none", "bertsekas"};
18 
19 PetscErrorCode TaoBNCGSetRecycleFlag(Tao tao, PetscBool recycle)
20 {
21   TAO_BNCG                     *cg = (TAO_BNCG*)tao->data;
22 
23   PetscFunctionBegin;
24   cg->recycle = recycle;
25   PetscFunctionReturn(0);
26 }
27 
28 PetscErrorCode TaoBNCGEstimateActiveSet(Tao tao, PetscInt asType)
29 {
30   PetscErrorCode               ierr;
31   TAO_BNCG                     *cg = (TAO_BNCG *)tao->data;
32 
33   PetscFunctionBegin;
34   ierr = ISDestroy(&cg->inactive_old);CHKERRQ(ierr);
35   if (cg->inactive_idx) {
36     ierr = ISDuplicate(cg->inactive_idx, &cg->inactive_old);CHKERRQ(ierr);
37     ierr = ISCopy(cg->inactive_idx, cg->inactive_old);CHKERRQ(ierr);
38   }
39   switch (asType) {
40   case CG_AS_NONE:
41     ierr = ISDestroy(&cg->inactive_idx);CHKERRQ(ierr);
42     ierr = VecWhichInactive(tao->XL, tao->solution, cg->unprojected_gradient, tao->XU, PETSC_TRUE, &cg->inactive_idx);CHKERRQ(ierr);
43     ierr = ISDestroy(&cg->active_idx);CHKERRQ(ierr);
44     ierr = ISComplementVec(cg->inactive_idx, tao->solution, &cg->active_idx);CHKERRQ(ierr);
45     break;
46 
47   case CG_AS_BERTSEKAS:
48     /* Use gradient descent to estimate the active set */
49     ierr = VecCopy(cg->unprojected_gradient, cg->W);CHKERRQ(ierr);
50     ierr = VecScale(cg->W, -1.0);CHKERRQ(ierr);
51     ierr = TaoEstimateActiveBounds(tao->solution, tao->XL, tao->XU, cg->unprojected_gradient, cg->W, cg->as_step, &cg->as_tol, &cg->active_lower, &cg->active_upper, &cg->active_fixed, &cg->active_idx, &cg->inactive_idx);CHKERRQ(ierr);
52 
53   default:
54     break;
55   }
56   PetscFunctionReturn(0);
57 }
58 
59 PetscErrorCode TaoBNCGBoundStep(Tao tao, Vec step)
60 {
61   PetscErrorCode               ierr;
62   TAO_BNCG                     *cg = (TAO_BNCG *)tao->data;
63 
64   PetscFunctionBegin;
65   switch (cg->as_type) {
66   case CG_AS_NONE:
67     if (cg->active_idx) {ierr = VecISSet(step, cg->active_idx, 0.0);CHKERRQ(ierr);}
68     break;
69 
70   case CG_AS_BERTSEKAS:
71     ierr = TaoBoundStep(tao->solution, tao->XL, tao->XU, cg->active_lower, cg->active_upper, cg->active_fixed, step);CHKERRQ(ierr);
72     break;
73 
74   default:
75     break;
76   }
77   PetscFunctionReturn(0);
78 }
79 
80 static PetscErrorCode TaoSolve_BNCG(Tao tao)
81 {
82   TAO_BNCG                     *cg = (TAO_BNCG*)tao->data;
83   PetscErrorCode               ierr;
84   TaoLineSearchConvergedReason ls_status = TAOLINESEARCH_CONTINUE_ITERATING;
85   PetscReal                    step=1.0,gnorm,gnorm2,delta,gd,ginner,beta,dnorm,resnorm;
86   PetscReal                    gd_old,gnorm2_old,f_old;
87   PetscBool                    cg_restart;
88 
89   PetscFunctionBegin;
90   /*   Project the current point onto the feasible set */
91   ierr = TaoComputeVariableBounds(tao);CHKERRQ(ierr);
92   ierr = TaoLineSearchSetVariableBounds(tao->linesearch,tao->XL,tao->XU);CHKERRQ(ierr);
93 
94   /* Project the initial point onto the feasible region */
95   ierr = VecMedian(tao->XL,tao->solution,tao->XU,tao->solution);CHKERRQ(ierr);
96 
97   if (!cg->recycle) {
98     /*  Solver is not being recycled so just compute the objective function and criteria */
99     ierr = TaoComputeObjectiveAndGradient(tao, tao->solution, &cg->f, cg->unprojected_gradient);CHKERRQ(ierr);
100   } else {
101     /* We are recycling, so we have to compute ||g_old||^2 for use in the CG step calculation */
102     ierr = VecDot(cg->G_old, cg->G_old, &gnorm2_old);CHKERRQ(ierr);
103   }
104   ierr = VecNorm(cg->unprojected_gradient,NORM_2,&gnorm);CHKERRQ(ierr);
105   if (PetscIsInfOrNanReal(cg->f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
106 
107   /* Estimate the active set and compute the projected gradient */
108   ierr = VecCopy(cg->unprojected_gradient, cg->W);CHKERRQ(ierr);
109   ierr = VecScale(cg->W, -1.0);CHKERRQ(ierr);
110   ierr = TaoBNCGEstimateActiveSet(tao, cg->as_type);CHKERRQ(ierr);
111 
112   /* Project the gradient and calculate the norm */
113   ierr = VecCopy(cg->unprojected_gradient, tao->gradient);CHKERRQ(ierr);
114   ierr = VecISSet(tao->gradient, cg->active_idx, 0.0);CHKERRQ(ierr);
115   ierr = VecNorm(tao->gradient,NORM_2,&gnorm);CHKERRQ(ierr);
116   gnorm2 = gnorm*gnorm;
117 
118   /* Convergence check */
119   tao->niter = 0;
120   tao->reason = TAO_CONTINUE_ITERATING;
121   ierr = VecFischer(tao->solution, cg->unprojected_gradient, tao->XL, tao->XU, cg->W);CHKERRQ(ierr);
122   ierr = VecNorm(cg->W, NORM_2, &resnorm);CHKERRQ(ierr);
123   ierr = TaoLogConvergenceHistory(tao, cg->f, resnorm, 0.0, tao->ksp_its);CHKERRQ(ierr);
124   ierr = TaoMonitor(tao, tao->niter, cg->f, resnorm, 0.0, step);CHKERRQ(ierr);
125   ierr = (*tao->ops->convergencetest)(tao,tao->cnvP);CHKERRQ(ierr);
126   if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);
127 
128   /* Start optimization iterations */
129   cg->ls_fails = cg->broken_ortho = cg->descent_error = 0;
130   cg->resets = -1;
131   while (tao->reason == TAO_CONTINUE_ITERATING) {
132     /* Check restart conditions for using steepest descent */
133     cg_restart = PETSC_FALSE;
134     ierr = VecDot(tao->gradient, cg->G_old, &ginner);CHKERRQ(ierr);
135     ierr = VecNorm(tao->stepdirection, NORM_2, &dnorm);CHKERRQ(ierr);
136     if (tao->niter == 0 && !cg->recycle && dnorm != 0.0) {
137       /* 1) First iteration, with recycle disabled, and a non-zero previous step */
138       cg_restart = PETSC_TRUE;
139     } else if (PetscAbsScalar(ginner) >= cg->eta * gnorm2) {
140       /* 2) Gradients are far from orthogonal */
141       cg_restart = PETSC_TRUE;
142       cg->broken_ortho++;
143     }
144 
145     /* Compute CG step */
146     if (cg_restart) {
147       beta = 0.0;
148       cg->resets++;
149     } else {
150       switch (cg->cg_type) {
151       case CG_FletcherReeves:
152         beta = gnorm2 / gnorm2_old;
153         break;
154 
155       case CG_PolakRibiere:
156         beta = (gnorm2 - ginner) / gnorm2_old;
157         break;
158 
159       case CG_PolakRibierePlus:
160         beta = PetscMax((gnorm2-ginner)/gnorm2_old, 0.0);
161         break;
162 
163       case CG_HestenesStiefel:
164         ierr = VecDot(tao->gradient, tao->stepdirection, &gd);CHKERRQ(ierr);
165         ierr = VecDot(cg->G_old, tao->stepdirection, &gd_old);CHKERRQ(ierr);
166         beta = (gnorm2 - ginner) / (gd - gd_old);
167         break;
168 
169       case CG_DaiYuan:
170         ierr = VecDot(tao->gradient, tao->stepdirection, &gd);CHKERRQ(ierr);
171         ierr = VecDot(cg->G_old, tao->stepdirection, &gd_old);CHKERRQ(ierr);
172         beta = gnorm2 / (gd - gd_old);
173         break;
174 
175       default:
176         beta = 0.0;
177         break;
178       }
179     }
180 
181     /*  Compute the direction d=-g + beta*d */
182     ierr = VecAXPBY(tao->stepdirection, -1.0, beta, tao->gradient);CHKERRQ(ierr);
183     ierr = TaoBNCGBoundStep(tao, tao->stepdirection);CHKERRQ(ierr);
184     if (cg->inactive_old) {
185       /* Compute which new indexes that were active before became inactive this iteration */
186       ierr = ISDestroy(&cg->new_inactives);CHKERRQ(ierr);
187       ierr = ISDifference(cg->inactive_old, cg->inactive_idx, &cg->new_inactives);
188       /* Selectively reset the CG step those freshly inactive variables to be the gradient descent direction */
189       ierr = VecGetSubVector(tao->stepdirection, cg->new_inactives, &cg->inactive_step);CHKERRQ(ierr);
190       ierr = VecGetSubVector(tao->gradient, cg->new_inactives, &cg->inactive_grad);CHKERRQ(ierr);
191       ierr = VecCopy(cg->inactive_grad, cg->inactive_step);CHKERRQ(ierr);
192       ierr = VecScale(cg->inactive_step, -1.0);CHKERRQ(ierr);
193       ierr = VecRestoreSubVector(tao->stepdirection, cg->new_inactives, &cg->inactive_step);CHKERRQ(ierr);
194       ierr = VecRestoreSubVector(tao->gradient, cg->new_inactives, &cg->inactive_grad);CHKERRQ(ierr);
195     }
196 
197     /* Verify that this is a descent direction */
198     ierr = VecDot(tao->gradient, tao->stepdirection, &gd);CHKERRQ(ierr);
199     ierr = VecNorm(tao->stepdirection, NORM_2, &dnorm);
200     if (gd > -cg->rho*PetscPowReal(dnorm, cg->pow)) {
201       /* Not a descent direction, so we reset back to projected gradient descent */
202       ierr = VecAXPBY(tao->stepdirection, -1.0, 0.0, tao->gradient);CHKERRQ(ierr);
203       cg->resets++;
204       cg->descent_error++;
205     }
206 
207     /*  update initial steplength choice */
208     delta = 1.0;
209     delta = PetscMax(delta, cg->delta_min);
210     delta = PetscMin(delta, cg->delta_max);
211 
212     /* Store solution and gradient info before it changes */
213     ierr = VecCopy(tao->solution, cg->X_old);CHKERRQ(ierr);
214     ierr = VecCopy(tao->gradient, cg->G_old);CHKERRQ(ierr);
215     ierr = VecCopy(cg->unprojected_gradient, cg->unprojected_gradient_old);CHKERRQ(ierr);
216     gnorm2_old = gnorm2;
217     f_old = cg->f;
218 
219     /* Perform bounded line search */
220     ierr = TaoLineSearchSetInitialStepLength(tao->linesearch,delta);CHKERRQ(ierr);
221     ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &cg->f, cg->unprojected_gradient, tao->stepdirection, &step, &ls_status);CHKERRQ(ierr);
222     ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);
223 
224     /*  Check linesearch failure */
225     if (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER) {
226       cg->ls_fails++;
227       /* Restore previous point */
228       gnorm2 = gnorm2_old;
229       cg->f = f_old;
230       ierr = VecCopy(cg->X_old, tao->solution);CHKERRQ(ierr);
231       ierr = VecCopy(cg->G_old, tao->gradient);CHKERRQ(ierr);
232       ierr = VecCopy(cg->unprojected_gradient_old, cg->unprojected_gradient);CHKERRQ(ierr);
233 
234       /* Fall back on the unscaled gradient step */
235       delta = 1.0;
236       ierr = VecCopy(tao->gradient, tao->stepdirection);CHKERRQ(ierr);
237       ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
238       ierr = TaoBoundStep(tao->solution, tao->XL, tao->XU, cg->active_lower, cg->active_upper, cg->active_fixed, tao->stepdirection);CHKERRQ(ierr);
239 
240       ierr = TaoLineSearchSetInitialStepLength(tao->linesearch,delta);CHKERRQ(ierr);
241       ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &cg->f, cg->unprojected_gradient, tao->stepdirection, &step, &ls_status);CHKERRQ(ierr);
242       ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);
243 
244       if (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER){
245         cg->ls_fails++;
246         /* Restore previous point */
247         gnorm2 = gnorm2_old;
248         cg->f = f_old;
249         ierr = VecCopy(cg->X_old, tao->solution);CHKERRQ(ierr);
250         ierr = VecCopy(cg->G_old, tao->gradient);CHKERRQ(ierr);
251         ierr = VecCopy(cg->unprojected_gradient_old, cg->unprojected_gradient);CHKERRQ(ierr);
252 
253         /* Nothing left to do but fail out of the optimization */
254         step = 0.0;
255         tao->reason = TAO_DIVERGED_LS_FAILURE;
256       }
257     }
258 
259     /* Estimate the active set at the new solution */
260     ierr = TaoBNCGEstimateActiveSet(tao, cg->as_type);CHKERRQ(ierr);
261 
262     /* Compute the projected gradient and its norm */
263     ierr = VecCopy(cg->unprojected_gradient, tao->gradient);CHKERRQ(ierr);
264     ierr = VecISSet(tao->gradient, cg->active_idx, 0.0);CHKERRQ(ierr);
265     ierr = VecNorm(tao->gradient,NORM_2,&gnorm);CHKERRQ(ierr);
266     gnorm2 = gnorm*gnorm;
267 
268     /* Convergence test */
269     tao->niter++;
270     ierr = VecFischer(tao->solution, cg->unprojected_gradient, tao->XL, tao->XU, cg->W);CHKERRQ(ierr);
271     ierr = VecNorm(cg->W, NORM_2, &resnorm);CHKERRQ(ierr);
272     ierr = TaoLogConvergenceHistory(tao, cg->f, resnorm, 0.0, tao->ksp_its);CHKERRQ(ierr);
273     ierr = TaoMonitor(tao, tao->niter, cg->f, resnorm, 0.0, step);CHKERRQ(ierr);
274     ierr = (*tao->ops->convergencetest)(tao,tao->cnvP);CHKERRQ(ierr);
275   }
276   PetscFunctionReturn(0);
277 }
278 
279 static PetscErrorCode TaoSetUp_BNCG(Tao tao)
280 {
281   TAO_BNCG         *cg = (TAO_BNCG*)tao->data;
282   PetscErrorCode ierr;
283 
284   PetscFunctionBegin;
285   if (!tao->gradient) {ierr = VecDuplicate(tao->solution,&tao->gradient);CHKERRQ(ierr);}
286   if (!tao->stepdirection) {ierr = VecDuplicate(tao->solution,&tao->stepdirection);CHKERRQ(ierr);}
287   if (!cg->W) {ierr = VecDuplicate(tao->solution,&cg->W);CHKERRQ(ierr);}
288   if (!cg->X_old) {ierr = VecDuplicate(tao->solution,&cg->X_old);CHKERRQ(ierr);}
289   if (!cg->G_old) {ierr = VecDuplicate(tao->gradient,&cg->G_old);CHKERRQ(ierr);}
290   if (!cg->unprojected_gradient) {ierr = VecDuplicate(tao->gradient,&cg->unprojected_gradient);CHKERRQ(ierr);}
291   if (!cg->unprojected_gradient_old) {ierr = VecDuplicate(tao->gradient,&cg->unprojected_gradient_old);CHKERRQ(ierr);}
292   PetscFunctionReturn(0);
293 }
294 
295 static PetscErrorCode TaoDestroy_BNCG(Tao tao)
296 {
297   TAO_BNCG       *cg = (TAO_BNCG*) tao->data;
298   PetscErrorCode ierr;
299 
300   PetscFunctionBegin;
301   if (tao->setupcalled) {
302     ierr = VecDestroy(&cg->W);CHKERRQ(ierr);
303     ierr = VecDestroy(&cg->X_old);CHKERRQ(ierr);
304     ierr = VecDestroy(&cg->G_old);CHKERRQ(ierr);
305     ierr = VecDestroy(&cg->unprojected_gradient);CHKERRQ(ierr);
306     ierr = VecDestroy(&cg->unprojected_gradient_old);CHKERRQ(ierr);
307   }
308   ierr = PetscFree(tao->data);CHKERRQ(ierr);
309   PetscFunctionReturn(0);
310 }
311 
312 static PetscErrorCode TaoSetFromOptions_BNCG(PetscOptionItems *PetscOptionsObject,Tao tao)
313  {
314     TAO_BNCG       *cg = (TAO_BNCG*)tao->data;
315     PetscErrorCode ierr;
316 
317     PetscFunctionBegin;
318     ierr = TaoLineSearchSetFromOptions(tao->linesearch);CHKERRQ(ierr);
319     ierr = PetscOptionsHead(PetscOptionsObject,"Nonlinear Conjugate Gradient method for unconstrained optimization");CHKERRQ(ierr);
320     ierr = PetscOptionsReal("-tao_bncg_eta","restart tolerance", "", cg->eta,&cg->eta,NULL);CHKERRQ(ierr);
321     ierr = PetscOptionsReal("-tao_bncg_rho","descent direction tolerance", "", cg->rho,&cg->rho,NULL);CHKERRQ(ierr);
322     ierr = PetscOptionsReal("-tao_bncg_pow","descent direction exponent", "", cg->pow,&cg->pow,NULL);CHKERRQ(ierr);
323     ierr = PetscOptionsEList("-tao_bncg_type","cg formula", "", CG_Table, CG_Types, CG_Table[cg->cg_type], &cg->cg_type,NULL);CHKERRQ(ierr);
324     ierr = PetscOptionsEList("-tao_bncg_as_type","active set estimation method", "", CG_AS_TYPE, CG_AS_SIZE, CG_AS_TYPE[cg->cg_type], &cg->cg_type,NULL);CHKERRQ(ierr);
325     ierr = PetscOptionsReal("-tao_bncg_delta_min","minimum delta value", "", cg->delta_min,&cg->delta_min,NULL);CHKERRQ(ierr);
326     ierr = PetscOptionsReal("-tao_bncg_delta_max","maximum delta value", "", cg->delta_max,&cg->delta_max,NULL);CHKERRQ(ierr);
327     ierr = PetscOptionsBool("-tao_bncg_recycle","enable recycling the existing solution and gradient at the start of a new solve","",cg->recycle,&cg->recycle,NULL);CHKERRQ(ierr);
328     ierr = PetscOptionsReal("-tao_bncg_as_tol", "initial tolerance used when estimating actively bounded variables", "", cg->as_tol, &cg->as_tol,NULL);CHKERRQ(ierr);
329     ierr = PetscOptionsReal("-tao_bncg_as_step", "step length used when estimating actively bounded variables", "", cg->as_step, &cg->as_step,NULL);CHKERRQ(ierr);
330    ierr = PetscOptionsTail();CHKERRQ(ierr);
331    PetscFunctionReturn(0);
332 }
333 
334 static PetscErrorCode TaoView_BNCG(Tao tao, PetscViewer viewer)
335 {
336   PetscBool      isascii;
337   TAO_BNCG       *cg = (TAO_BNCG*)tao->data;
338   PetscErrorCode ierr;
339 
340   PetscFunctionBegin;
341   ierr = PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii);CHKERRQ(ierr);
342   if (isascii) {
343     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
344     ierr = PetscViewerASCIIPrintf(viewer, "CG Type: %s\n", CG_Table[cg->cg_type]);CHKERRQ(ierr);
345     ierr = PetscViewerASCIIPrintf(viewer, "Resets: %i\n", cg->resets);CHKERRQ(ierr);
346     ierr = PetscViewerASCIIPrintf(viewer, "  Broken ortho: %i\n", cg->broken_ortho);CHKERRQ(ierr);
347     ierr = PetscViewerASCIIPrintf(viewer, "  Not a descent dir.: %i\n", cg->descent_error);CHKERRQ(ierr);
348     ierr = PetscViewerASCIIPrintf(viewer, "Line search fails: %i\n", cg->ls_fails);CHKERRQ(ierr);
349     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
350   }
351   PetscFunctionReturn(0);
352 }
353 
354 /*MC
355      TAOBNCG -   Bound-constrained Nonlinear Conjugate Gradient method.
356 
357    Options Database Keys:
358 +      -tao_bncg_eta <r> - restart tolerance
359 .      -tao_bncg_type <taocg_type> - cg formula
360 .      -tao_bncg_delta_min <r> - minimum delta value
361 -      -tao_bncg_delta_max <r> - maximum delta value
362 
363   Notes:
364      CG formulas are:
365          "fr" - Fletcher-Reeves
366          "pr" - Polak-Ribiere
367          "prp" - Polak-Ribiere-Plus
368          "hs" - Hestenes-Steifel
369          "dy" - Dai-Yuan
370   Level: beginner
371 M*/
372 
373 
374 PETSC_EXTERN PetscErrorCode TaoCreate_BNCG(Tao tao)
375 {
376   TAO_BNCG       *cg;
377   const char     *morethuente_type = TAOLINESEARCHMT;
378   PetscErrorCode ierr;
379 
380   PetscFunctionBegin;
381   tao->ops->setup = TaoSetUp_BNCG;
382   tao->ops->solve = TaoSolve_BNCG;
383   tao->ops->view = TaoView_BNCG;
384   tao->ops->setfromoptions = TaoSetFromOptions_BNCG;
385   tao->ops->destroy = TaoDestroy_BNCG;
386 
387   /* Override default settings (unless already changed) */
388   if (!tao->max_it_changed) tao->max_it = 2000;
389   if (!tao->max_funcs_changed) tao->max_funcs = 4000;
390 
391   /*  Note: nondefault values should be used for nonlinear conjugate gradient  */
392   /*  method.  In particular, gtol should be less that 0.5; the value used in  */
393   /*  Nocedal and Wright is 0.10.  We use the default values for the  */
394   /*  linesearch because it seems to work better. */
395   ierr = TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch);CHKERRQ(ierr);
396   ierr = PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1);CHKERRQ(ierr);
397   ierr = TaoLineSearchSetType(tao->linesearch, morethuente_type);CHKERRQ(ierr);
398   ierr = TaoLineSearchUseTaoRoutines(tao->linesearch, tao);CHKERRQ(ierr);
399   ierr = TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);CHKERRQ(ierr);
400 
401   ierr = PetscNewLog(tao,&cg);CHKERRQ(ierr);
402   tao->data = (void*)cg;
403   cg->rho = 1e-4;
404   cg->pow = 2.1;
405   cg->eta = 0.5;
406   cg->delta_min = 1e-7;
407   cg->delta_max = 100;
408   cg->as_step = 0.001;
409   cg->as_tol = 0.001;
410   cg->as_type = CG_AS_BERTSEKAS;
411   cg->cg_type = CG_DaiYuan;
412   cg->recycle = PETSC_FALSE;
413   PetscFunctionReturn(0);
414 }
415