xref: /petsc/src/tao/bound/impls/bnk/bnk.c (revision eb9107154965f6d42900b472f8cc894abc73f56d)
1 #include <petsctaolinesearch.h>
2 #include <../src/tao/bound/impls/bnk/bnk.h>
3 
4 #include <petscksp.h>
5 
6 /* Routine for BFGS preconditioner */
7 
8 PetscErrorCode MatLMVMSolveShell(PC pc, Vec b, Vec x)
9 {
10   PetscErrorCode ierr;
11   Mat            M;
12 
13   PetscFunctionBegin;
14   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
15   PetscValidHeaderSpecific(b,VEC_CLASSID,2);
16   PetscValidHeaderSpecific(x,VEC_CLASSID,3);
17   ierr = PCShellGetContext(pc,(void**)&M);CHKERRQ(ierr);
18   ierr = MatLMVMSolve(M, b, x);CHKERRQ(ierr);
19   PetscFunctionReturn(0);
20 }
21 
22 PetscErrorCode TaoBNKInitialize(Tao tao)
23 {
24   PetscErrorCode               ierr;
25   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
26   KSPType                      ksp_type;
27   PC                           pc;
28 
29   PetscReal                    fmin, ftrial, prered, actred, kappa, sigma;
30   PetscReal                    tau, tau_1, tau_2, tau_max, tau_min, max_radius;
31   PetscReal                    delta, step = 1.0;
32 
33   PetscInt                     n,N,needH = 1;
34 
35   PetscInt                     i_max = 5;
36   PetscInt                     j_max = 1;
37   PetscInt                     i, j;
38 
39   PetscFunctionBegin;
40   /* Number of times ksp stopped because of these reasons */
41   bnk->ksp_atol = 0;
42   bnk->ksp_rtol = 0;
43   bnk->ksp_dtol = 0;
44   bnk->ksp_ctol = 0;
45   bnk->ksp_negc = 0;
46   bnk->ksp_iter = 0;
47   bnk->ksp_othr = 0;
48 
49   /* Initialize trust-region radius when using nash, stcg, or gltr
50      Command automatically ignored for other methods
51      Will be reset during the first iteration
52   */
53   ierr = KSPGetType(tao->ksp,&ksp_type);CHKERRQ(ierr);
54   ierr = PetscStrcmp(ksp_type,KSPCGNASH,&bnk->is_nash);CHKERRQ(ierr);
55   ierr = PetscStrcmp(ksp_type,KSPCGSTCG,&bnk->is_stcg);CHKERRQ(ierr);
56   ierr = PetscStrcmp(ksp_type,KSPCGGLTR,&bnk->is_gltr);CHKERRQ(ierr);
57 
58   ierr = KSPCGSetRadius(tao->ksp,bnk->max_radius);CHKERRQ(ierr);
59 
60   if (bnk->is_nash || bnk->is_stcg || bnk->is_gltr) {
61     if (tao->trust0 < 0.0) SETERRQ(PETSC_COMM_SELF,1,"Initial radius negative");
62     tao->trust = tao->trust0;
63     tao->trust = PetscMax(tao->trust, bnk->min_radius);
64     tao->trust = PetscMin(tao->trust, bnk->max_radius);
65   }
66 
67   /* Get vectors we will need */
68   if (BNK_PC_BFGS == bnk->pc_type && !bnk->M) {
69     ierr = VecGetLocalSize(tao->solution,&n);CHKERRQ(ierr);
70     ierr = VecGetSize(tao->solution,&N);CHKERRQ(ierr);
71     ierr = MatCreateLMVM(((PetscObject)tao)->comm,n,N,&bnk->M);CHKERRQ(ierr);
72     ierr = MatLMVMAllocateVectors(bnk->M,tao->solution);CHKERRQ(ierr);
73   }
74 
75   /* create vectors for the limited memory preconditioner */
76   if ((BNK_PC_BFGS == bnk->pc_type) && (BFGS_SCALE_BFGS != bnk->bfgs_scale_type)) {
77     if (!bnk->Diag) {
78       ierr = VecDuplicate(tao->solution,&bnk->Diag);CHKERRQ(ierr);
79     }
80   }
81 
82   /* Modify the preconditioner to use the bfgs approximation */
83   ierr = KSPGetPC(tao->ksp, &pc);CHKERRQ(ierr);
84   switch(bnk->pc_type) {
85   case BNK_PC_NONE:
86     ierr = PCSetType(pc, PCNONE);CHKERRQ(ierr);
87     ierr = PCSetFromOptions(pc);CHKERRQ(ierr);
88     break;
89 
90   case BNK_PC_AHESS:
91     ierr = PCSetType(pc, PCJACOBI);CHKERRQ(ierr);
92     ierr = PCSetFromOptions(pc);CHKERRQ(ierr);
93     ierr = PCJacobiSetUseAbs(pc,PETSC_TRUE);CHKERRQ(ierr);
94     break;
95 
96   case BNK_PC_BFGS:
97     ierr = PCSetType(pc, PCSHELL);CHKERRQ(ierr);
98     ierr = PCSetFromOptions(pc);CHKERRQ(ierr);
99     ierr = PCShellSetName(pc, "bfgs");CHKERRQ(ierr);
100     ierr = PCShellSetContext(pc, bnk->M);CHKERRQ(ierr);
101     ierr = PCShellSetApply(pc, MatLMVMSolveShell);CHKERRQ(ierr);
102     break;
103 
104   default:
105     /* Use the pc method set by pc_type */
106     break;
107   }
108 
109   /* Initialize trust-region radius.  The initialization is only performed
110      when we are using Nash, Steihaug-Toint or the Generalized Lanczos method. */
111   if (bnk->is_nash || bnk->is_stcg || bnk->is_gltr) {
112     switch(bnk->init_type) {
113     case BNK_INIT_CONSTANT:
114       /* Use the initial radius specified */
115       break;
116 
117     case BNK_INIT_INTERPOLATION:
118       /* Use the initial radius specified */
119       max_radius = 0.0;
120 
121       for (j = 0; j < j_max; ++j) {
122         fmin = bnk->f;
123         sigma = 0.0;
124 
125         if (needH) {
126           ierr  = TaoComputeHessian(tao, tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr);
127           needH = 0;
128         }
129 
130         for (i = 0; i < i_max; ++i) {
131           ierr = VecCopy(tao->solution,bnk->W);CHKERRQ(ierr);
132           ierr = VecAXPY(bnk->W,-tao->trust/bnk->gnorm,tao->gradient);CHKERRQ(ierr);
133           ierr = TaoComputeObjective(tao, bnk->W, &ftrial);CHKERRQ(ierr);
134           if (PetscIsInfOrNanReal(ftrial)) {
135             tau = bnk->gamma1_i;
136           } else {
137             if (ftrial < fmin) {
138               fmin = ftrial;
139               sigma = -tao->trust / bnk->gnorm;
140             }
141 
142             ierr = MatMult(tao->hessian, tao->gradient, bnk->D);CHKERRQ(ierr);
143             ierr = VecDot(tao->gradient, bnk->D, &prered);CHKERRQ(ierr);
144 
145             prered = tao->trust * (bnk->gnorm - 0.5 * tao->trust * prered / (bnk->gnorm * bnk->gnorm));
146             actred = bnk->f - ftrial;
147             if ((PetscAbsScalar(actred) <= bnk->epsilon) && (PetscAbsScalar(prered) <= bnk->epsilon)) {
148               kappa = 1.0;
149             } else {
150               kappa = actred / prered;
151             }
152 
153             tau_1 = bnk->theta_i * bnk->gnorm * tao->trust / (bnk->theta_i * bnk->gnorm * tao->trust + (1.0 - bnk->theta_i) * prered - actred);
154             tau_2 = bnk->theta_i * bnk->gnorm * tao->trust / (bnk->theta_i * bnk->gnorm * tao->trust - (1.0 + bnk->theta_i) * prered + actred);
155             tau_min = PetscMin(tau_1, tau_2);
156             tau_max = PetscMax(tau_1, tau_2);
157 
158             if (PetscAbsScalar(kappa - 1.0) <= bnk->mu1_i) {
159               /* Great agreement */
160               max_radius = PetscMax(max_radius, tao->trust);
161 
162               if (tau_max < 1.0) {
163                 tau = bnk->gamma3_i;
164               } else if (tau_max > bnk->gamma4_i) {
165                 tau = bnk->gamma4_i;
166               } else if (tau_1 >= 1.0 && tau_1 <= bnk->gamma4_i && tau_2 < 1.0) {
167                 tau = tau_1;
168               } else if (tau_2 >= 1.0 && tau_2 <= bnk->gamma4_i && tau_1 < 1.0) {
169                 tau = tau_2;
170               } else {
171                 tau = tau_max;
172               }
173             } else if (PetscAbsScalar(kappa - 1.0) <= bnk->mu2_i) {
174               /* Good agreement */
175               max_radius = PetscMax(max_radius, tao->trust);
176 
177               if (tau_max < bnk->gamma2_i) {
178                 tau = bnk->gamma2_i;
179               } else if (tau_max > bnk->gamma3_i) {
180                 tau = bnk->gamma3_i;
181               } else {
182                 tau = tau_max;
183               }
184             } else {
185               /* Not good agreement */
186               if (tau_min > 1.0) {
187                 tau = bnk->gamma2_i;
188               } else if (tau_max < bnk->gamma1_i) {
189                 tau = bnk->gamma1_i;
190               } else if ((tau_min < bnk->gamma1_i) && (tau_max >= 1.0)) {
191                 tau = bnk->gamma1_i;
192               } else if ((tau_1 >= bnk->gamma1_i) && (tau_1 < 1.0) && ((tau_2 < bnk->gamma1_i) || (tau_2 >= 1.0))) {
193                 tau = tau_1;
194               } else if ((tau_2 >= bnk->gamma1_i) && (tau_2 < 1.0) && ((tau_1 < bnk->gamma1_i) || (tau_2 >= 1.0))) {
195                 tau = tau_2;
196               } else {
197                 tau = tau_max;
198               }
199             }
200           }
201           tao->trust = tau * tao->trust;
202         }
203 
204         if (fmin < bnk->f) {
205           bnk->f = fmin;
206           ierr = VecAXPY(tao->solution,sigma,tao->gradient);CHKERRQ(ierr);
207           ierr = TaoComputeGradient(tao,tao->solution,tao->gradient);CHKERRQ(ierr);
208 
209           ierr = TaoGradientNorm(tao, tao->gradient,NORM_2,&bnk->gnorm);CHKERRQ(ierr);
210           if (PetscIsInfOrNanReal(bnk->gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute gradient generated Inf or NaN");
211           needH = 1;
212 
213           ierr = TaoLogConvergenceHistory(tao,bnk->f,bnk->gnorm,0.0,tao->ksp_its);CHKERRQ(ierr);
214           ierr = TaoMonitor(tao,tao->niter,bnk->f,bnk->gnorm,0.0,step);CHKERRQ(ierr);
215           ierr = (*tao->ops->convergencetest)(tao,tao->cnvP);CHKERRQ(ierr);
216           if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);
217         }
218       }
219       tao->trust = PetscMax(tao->trust, max_radius);
220 
221       /* Modify the radius if it is too large or small */
222       tao->trust = PetscMax(tao->trust, bnk->min_radius);
223       tao->trust = PetscMin(tao->trust, bnk->max_radius);
224       break;
225 
226     default:
227       /* Norm of the first direction will initialize radius */
228       tao->trust = 0.0;
229       break;
230     }
231   }
232 
233   /* Set initial scaling for the BFGS preconditioner
234      This step is done after computing the initial trust-region radius
235      since the function value may have decreased */
236   if (BNK_PC_BFGS == bnk->pc_type) {
237     if (bnk->f != 0.0) {
238       delta = 2.0 * PetscAbsScalar(bnk->f) / (bnk->gnorm*bnk->gnorm);
239     } else {
240       delta = 2.0 / (bnk->gnorm*bnk->gnorm);
241     }
242     ierr = MatLMVMSetDelta(bnk->M,delta);CHKERRQ(ierr);
243   }
244 
245   /* Set counter for gradient/reset steps*/
246   bnk->newt = 0;
247   bnk->bfgs = 0;
248   bnk->sgrad = 0;
249   bnk->grad = 0;
250   PetscFunctionReturn(0);
251 }
252 
253 PetscErrorCode TaoBNKComputeStep(Tao tao, PetscInt *stepType)
254 {
255   PetscErrorCode               ierr;
256   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
257   KSPConvergedReason           ksp_reason;
258 
259   PetscReal                    gdx, delta;
260   PetscReal                    norm_d = 0.0, e_min;
261 
262   PetscInt                     bfgsUpdates = 0;
263   PetscInt                     kspits;
264   PetscInt                     needH = 1;
265 
266   PetscFunctionBegin;
267   /* Compute the Hessian */
268   if (needH) {
269     ierr = TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr);
270   }
271 
272   if ((BNK_PC_BFGS == bnk->pc_type) && (BFGS_SCALE_AHESS == bnk->bfgs_scale_type)) {
273     /* Obtain diagonal for the bfgs preconditioner  */
274     ierr = MatGetDiagonal(tao->hessian, bnk->Diag);CHKERRQ(ierr);
275     ierr = VecAbs(bnk->Diag);CHKERRQ(ierr);
276     ierr = VecReciprocal(bnk->Diag);CHKERRQ(ierr);
277     ierr = MatLMVMSetScale(bnk->M,bnk->Diag);CHKERRQ(ierr);
278   }
279 
280   /* Shift the Hessian matrix */
281   bnk->pert = bnk->sval;
282   if (bnk->pert > 0) {
283     ierr = MatShift(tao->hessian, bnk->pert);CHKERRQ(ierr);
284     if (tao->hessian != tao->hessian_pre) {
285       ierr = MatShift(tao->hessian_pre, bnk->pert);CHKERRQ(ierr);
286     }
287   }
288 
289   if (BNK_PC_BFGS == bnk->pc_type) {
290     if (BFGS_SCALE_PHESS == bnk->bfgs_scale_type) {
291       /* Obtain diagonal for the bfgs preconditioner  */
292       ierr = MatGetDiagonal(tao->hessian, bnk->Diag);CHKERRQ(ierr);
293       ierr = VecAbs(bnk->Diag);CHKERRQ(ierr);
294       ierr = VecReciprocal(bnk->Diag);CHKERRQ(ierr);
295       ierr = MatLMVMSetScale(bnk->M,bnk->Diag);CHKERRQ(ierr);
296     }
297     /* Update the limited memory preconditioner and get existing # of updates */
298     ierr = MatLMVMUpdate(bnk->M, tao->solution, tao->gradient);CHKERRQ(ierr);
299     ierr = MatLMVMGetUpdates(bnk->M, &bfgsUpdates);CHKERRQ(ierr);
300   }
301 
302   /* Solve the Newton system of equations */
303   ierr = KSPSetOperators(tao->ksp,tao->hessian,tao->hessian_pre);CHKERRQ(ierr);
304   if (bnk->is_nash || bnk->is_stcg || bnk->is_gltr) {
305     ierr = KSPCGSetRadius(tao->ksp,bnk->max_radius);CHKERRQ(ierr);
306     ierr = KSPSolve(tao->ksp, tao->gradient, bnk->D);CHKERRQ(ierr);
307     ierr = KSPGetIterationNumber(tao->ksp,&kspits);CHKERRQ(ierr);
308     tao->ksp_its+=kspits;
309     tao->ksp_tot_its+=kspits;
310     ierr = KSPCGGetNormD(tao->ksp,&norm_d);CHKERRQ(ierr);
311 
312     if (0.0 == tao->trust) {
313       /* Radius was uninitialized; use the norm of the direction */
314       if (norm_d > 0.0) {
315         tao->trust = norm_d;
316 
317         /* Modify the radius if it is too large or small */
318         tao->trust = PetscMax(tao->trust, bnk->min_radius);
319         tao->trust = PetscMin(tao->trust, bnk->max_radius);
320       } else {
321         /* The direction was bad; set radius to default value and re-solve
322            the trust-region subproblem to get a direction */
323         tao->trust = tao->trust0;
324 
325         /* Modify the radius if it is too large or small */
326         tao->trust = PetscMax(tao->trust, bnk->min_radius);
327         tao->trust = PetscMin(tao->trust, bnk->max_radius);
328 
329         ierr = KSPCGSetRadius(tao->ksp,bnk->max_radius);CHKERRQ(ierr);
330         ierr = KSPSolve(tao->ksp, tao->gradient, bnk->D);CHKERRQ(ierr);
331         ierr = KSPGetIterationNumber(tao->ksp,&kspits);CHKERRQ(ierr);
332         tao->ksp_its+=kspits;
333         tao->ksp_tot_its+=kspits;
334         ierr = KSPCGGetNormD(tao->ksp,&norm_d);CHKERRQ(ierr);
335 
336         if (norm_d == 0.0) SETERRQ(PETSC_COMM_SELF,1, "Initial direction zero");
337       }
338     }
339   } else {
340     ierr = KSPSolve(tao->ksp, tao->gradient, bnk->D);CHKERRQ(ierr);
341     ierr = KSPGetIterationNumber(tao->ksp, &kspits);CHKERRQ(ierr);
342     tao->ksp_its += kspits;
343     tao->ksp_tot_its+=kspits;
344   }
345   ierr = VecScale(bnk->D, -1.0);CHKERRQ(ierr);
346   ierr = KSPGetConvergedReason(tao->ksp, &ksp_reason);CHKERRQ(ierr);
347   if ((KSP_DIVERGED_INDEFINITE_PC == ksp_reason) &&  (BNK_PC_BFGS == bnk->pc_type) && (bfgsUpdates > 1)) {
348     /* Preconditioner is numerically indefinite; reset the
349        approximate if using BFGS preconditioning. */
350 
351     if (bnk->f != 0.0) {
352       delta = 2.0 * PetscAbsScalar(bnk->f) / (bnk->gnorm*bnk->gnorm);
353     } else {
354       delta = 2.0 / (bnk->gnorm*bnk->gnorm);
355     }
356     ierr = MatLMVMSetDelta(bnk->M,delta);CHKERRQ(ierr);
357     ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr);
358     ierr = MatLMVMUpdate(bnk->M, tao->solution, tao->gradient);CHKERRQ(ierr);
359     bfgsUpdates = 1;
360   }
361 
362   if (KSP_CONVERGED_ATOL == ksp_reason) {
363     ++bnk->ksp_atol;
364   } else if (KSP_CONVERGED_RTOL == ksp_reason) {
365     ++bnk->ksp_rtol;
366   } else if (KSP_CONVERGED_CG_CONSTRAINED == ksp_reason) {
367     ++bnk->ksp_ctol;
368   } else if (KSP_CONVERGED_CG_NEG_CURVE == ksp_reason) {
369     ++bnk->ksp_negc;
370   } else if (KSP_DIVERGED_DTOL == ksp_reason) {
371     ++bnk->ksp_dtol;
372   } else if (KSP_DIVERGED_ITS == ksp_reason) {
373     ++bnk->ksp_iter;
374   } else {
375     ++bnk->ksp_othr;
376   }
377 
378   /* Check for success (descent direction) */
379   ierr = VecDot(bnk->D, tao->gradient, &gdx);CHKERRQ(ierr);
380   if ((gdx >= 0.0) || PetscIsInfOrNanReal(gdx)) {
381     /* Newton step is not descent or direction produced Inf or NaN
382        Update the perturbation for next time */
383     if (bnk->pert <= 0.0) {
384       /* Initialize the perturbation */
385       bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
386       if (bnk->is_gltr) {
387         ierr = KSPCGGLTRGetMinEig(tao->ksp,&e_min);CHKERRQ(ierr);
388         bnk->pert = PetscMax(bnk->pert, -e_min);
389       }
390     } else {
391       /* Increase the perturbation */
392       bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
393     }
394 
395     if (BNK_PC_BFGS != bnk->pc_type) {
396       /* We don't have the bfgs matrix around and updated
397          Must use gradient direction in this case */
398       ierr = VecCopy(tao->gradient, bnk->D);CHKERRQ(ierr);
399       ierr = VecScale(bnk->D, -1.0);CHKERRQ(ierr);
400       ++bnk->grad;
401       *stepType = BNK_GRADIENT;
402     } else {
403       /* Attempt to use the BFGS direction */
404       ierr = MatLMVMSolve(bnk->M, tao->gradient, bnk->D);CHKERRQ(ierr);
405       ierr = VecScale(bnk->D, -1.0);CHKERRQ(ierr);
406 
407       /* Check for success (descent direction) */
408       ierr = VecDot(tao->gradient, bnk->D, &gdx);CHKERRQ(ierr);
409       if ((gdx >= 0) || PetscIsInfOrNanReal(gdx)) {
410         /* BFGS direction is not descent or direction produced not a number
411            We can assert bfgsUpdates > 1 in this case because
412            the first solve produces the scaled gradient direction,
413            which is guaranteed to be descent */
414 
415         /* Use steepest descent direction (scaled) */
416 
417         if (bnk->f != 0.0) {
418           delta = 2.0 * PetscAbsScalar(bnk->f) / (bnk->gnorm*bnk->gnorm);
419         } else {
420           delta = 2.0 / (bnk->gnorm*bnk->gnorm);
421         }
422         ierr = MatLMVMSetDelta(bnk->M, delta);CHKERRQ(ierr);
423         ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr);
424         ierr = MatLMVMUpdate(bnk->M, tao->solution, tao->gradient);CHKERRQ(ierr);
425         ierr = MatLMVMSolve(bnk->M, tao->gradient, bnk->D);CHKERRQ(ierr);
426         ierr = VecScale(bnk->D, -1.0);CHKERRQ(ierr);
427 
428         bfgsUpdates = 1;
429         ++bnk->sgrad;
430         *stepType = BNK_SCALED_GRADIENT;
431       } else {
432         if (1 == bfgsUpdates) {
433           /* The first BFGS direction is always the scaled gradient */
434           ++bnk->sgrad;
435           *stepType = BNK_SCALED_GRADIENT;
436         } else {
437           ++bnk->bfgs;
438           *stepType = BNK_BFGS;
439         }
440       }
441     }
442   } else {
443     /* Computed Newton step is descent */
444     switch (ksp_reason) {
445     case KSP_DIVERGED_NANORINF:
446     case KSP_DIVERGED_BREAKDOWN:
447     case KSP_DIVERGED_INDEFINITE_MAT:
448     case KSP_DIVERGED_INDEFINITE_PC:
449     case KSP_CONVERGED_CG_NEG_CURVE:
450       /* Matrix or preconditioner is indefinite; increase perturbation */
451       if (bnk->pert <= 0.0) {
452         /* Initialize the perturbation */
453         bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
454         if (bnk->is_gltr) {
455           ierr = KSPCGGLTRGetMinEig(tao->ksp, &e_min);CHKERRQ(ierr);
456           bnk->pert = PetscMax(bnk->pert, -e_min);
457         }
458       } else {
459         /* Increase the perturbation */
460         bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
461       }
462       break;
463 
464     default:
465       /* Newton step computation is good; decrease perturbation */
466       bnk->pert = PetscMin(bnk->psfac * bnk->pert, bnk->pmsfac * bnk->gnorm);
467       if (bnk->pert < bnk->pmin) {
468         bnk->pert = 0.0;
469       }
470       break;
471     }
472 
473     ++bnk->newt;
474     stepType = BNK_NEWTON;
475   }
476   PetscFunctionReturn(0);
477 }
478 
479 /* ---------------------------------------------------------- */
480 static PetscErrorCode TaoSetUp_BNK(Tao tao)
481 {
482   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
483   PetscErrorCode ierr;
484 
485   PetscFunctionBegin;
486   if (!tao->gradient) {ierr = VecDuplicate(tao->solution,&tao->gradient);CHKERRQ(ierr);}
487   if (!tao->stepdirection) {ierr = VecDuplicate(tao->solution,&tao->stepdirection);CHKERRQ(ierr);}
488   if (!bnk->W) {ierr = VecDuplicate(tao->solution,&bnk->W);CHKERRQ(ierr);}
489   if (!bnk->D) {ierr = VecDuplicate(tao->solution,&bnk->D);CHKERRQ(ierr);}
490   if (!bnk->Xold) {ierr = VecDuplicate(tao->solution,&bnk->Xold);CHKERRQ(ierr);}
491   if (!bnk->Gold) {ierr = VecDuplicate(tao->solution,&bnk->Gold);CHKERRQ(ierr);}
492   bnk->Diag = 0;
493   bnk->M = 0;
494   PetscFunctionReturn(0);
495 }
496 
497 /*------------------------------------------------------------*/
498 static PetscErrorCode TaoDestroy_BNK(Tao tao)
499 {
500   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
501   PetscErrorCode ierr;
502 
503   PetscFunctionBegin;
504   if (tao->setupcalled) {
505     ierr = VecDestroy(&bnk->D);CHKERRQ(ierr);
506     ierr = VecDestroy(&bnk->W);CHKERRQ(ierr);
507     ierr = VecDestroy(&bnk->Xold);CHKERRQ(ierr);
508     ierr = VecDestroy(&bnk->Gold);CHKERRQ(ierr);
509   }
510   ierr = VecDestroy(&bnk->Diag);CHKERRQ(ierr);
511   ierr = MatDestroy(&bnk->M);CHKERRQ(ierr);
512   ierr = PetscFree(tao->data);CHKERRQ(ierr);
513   PetscFunctionReturn(0);
514 }
515 
516 /*------------------------------------------------------------*/
517 static PetscErrorCode TaoSetFromOptions_BNK(PetscOptionItems *PetscOptionsObject,Tao tao)
518 {
519   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
520   PetscErrorCode ierr;
521 
522   PetscFunctionBegin;
523   ierr = PetscOptionsHead(PetscOptionsObject,"Newton line search method for unconstrained optimization");CHKERRQ(ierr);
524   ierr = PetscOptionsEList("-tao_BNK_pc_type", "pc type", "", BNK_PC, BNK_PC_TYPES, BNK_PC[bnk->pc_type], &bnk->pc_type, 0);CHKERRQ(ierr);
525   ierr = PetscOptionsEList("-tao_BNK_bfgs_scale_type", "bfgs scale type", "", BFGS_SCALE, BFGS_SCALE_TYPES, BFGS_SCALE[bnk->bfgs_scale_type], &bnk->bfgs_scale_type, 0);CHKERRQ(ierr);
526   ierr = PetscOptionsEList("-tao_BNK_init_type", "radius initialization type", "", BNK_INIT, BNK_INIT_TYPES, BNK_INIT[bnk->init_type], &bnk->init_type, 0);CHKERRQ(ierr);
527   ierr = PetscOptionsEList("-tao_BNK_update_type", "radius update type", "", BNK_UPDATE, BNK_UPDATE_TYPES, BNK_UPDATE[bnk->update_type], &bnk->update_type, 0);CHKERRQ(ierr);
528   ierr = PetscOptionsReal("-tao_BNK_sval", "perturbation starting value", "", bnk->sval, &bnk->sval,NULL);CHKERRQ(ierr);
529   ierr = PetscOptionsReal("-tao_BNK_imin", "minimum initial perturbation", "", bnk->imin, &bnk->imin,NULL);CHKERRQ(ierr);
530   ierr = PetscOptionsReal("-tao_BNK_imax", "maximum initial perturbation", "", bnk->imax, &bnk->imax,NULL);CHKERRQ(ierr);
531   ierr = PetscOptionsReal("-tao_BNK_imfac", "initial merit factor", "", bnk->imfac, &bnk->imfac,NULL);CHKERRQ(ierr);
532   ierr = PetscOptionsReal("-tao_BNK_pmin", "minimum perturbation", "", bnk->pmin, &bnk->pmin,NULL);CHKERRQ(ierr);
533   ierr = PetscOptionsReal("-tao_BNK_pmax", "maximum perturbation", "", bnk->pmax, &bnk->pmax,NULL);CHKERRQ(ierr);
534   ierr = PetscOptionsReal("-tao_BNK_pgfac", "growth factor", "", bnk->pgfac, &bnk->pgfac,NULL);CHKERRQ(ierr);
535   ierr = PetscOptionsReal("-tao_BNK_psfac", "shrink factor", "", bnk->psfac, &bnk->psfac,NULL);CHKERRQ(ierr);
536   ierr = PetscOptionsReal("-tao_BNK_pmgfac", "merit growth factor", "", bnk->pmgfac, &bnk->pmgfac,NULL);CHKERRQ(ierr);
537   ierr = PetscOptionsReal("-tao_BNK_pmsfac", "merit shrink factor", "", bnk->pmsfac, &bnk->pmsfac,NULL);CHKERRQ(ierr);
538   ierr = PetscOptionsReal("-tao_BNK_eta1", "poor steplength; reduce radius", "", bnk->eta1, &bnk->eta1,NULL);CHKERRQ(ierr);
539   ierr = PetscOptionsReal("-tao_BNK_eta2", "reasonable steplength; leave radius alone", "", bnk->eta2, &bnk->eta2,NULL);CHKERRQ(ierr);
540   ierr = PetscOptionsReal("-tao_BNK_eta3", "good steplength; increase radius", "", bnk->eta3, &bnk->eta3,NULL);CHKERRQ(ierr);
541   ierr = PetscOptionsReal("-tao_BNK_eta4", "excellent steplength; greatly increase radius", "", bnk->eta4, &bnk->eta4,NULL);CHKERRQ(ierr);
542   ierr = PetscOptionsReal("-tao_BNK_alpha1", "", "", bnk->alpha1, &bnk->alpha1,NULL);CHKERRQ(ierr);
543   ierr = PetscOptionsReal("-tao_BNK_alpha2", "", "", bnk->alpha2, &bnk->alpha2,NULL);CHKERRQ(ierr);
544   ierr = PetscOptionsReal("-tao_BNK_alpha3", "", "", bnk->alpha3, &bnk->alpha3,NULL);CHKERRQ(ierr);
545   ierr = PetscOptionsReal("-tao_BNK_alpha4", "", "", bnk->alpha4, &bnk->alpha4,NULL);CHKERRQ(ierr);
546   ierr = PetscOptionsReal("-tao_BNK_alpha5", "", "", bnk->alpha5, &bnk->alpha5,NULL);CHKERRQ(ierr);
547   ierr = PetscOptionsReal("-tao_BNK_nu1", "poor steplength; reduce radius", "", bnk->nu1, &bnk->nu1,NULL);CHKERRQ(ierr);
548   ierr = PetscOptionsReal("-tao_BNK_nu2", "reasonable steplength; leave radius alone", "", bnk->nu2, &bnk->nu2,NULL);CHKERRQ(ierr);
549   ierr = PetscOptionsReal("-tao_BNK_nu3", "good steplength; increase radius", "", bnk->nu3, &bnk->nu3,NULL);CHKERRQ(ierr);
550   ierr = PetscOptionsReal("-tao_BNK_nu4", "excellent steplength; greatly increase radius", "", bnk->nu4, &bnk->nu4,NULL);CHKERRQ(ierr);
551   ierr = PetscOptionsReal("-tao_BNK_omega1", "", "", bnk->omega1, &bnk->omega1,NULL);CHKERRQ(ierr);
552   ierr = PetscOptionsReal("-tao_BNK_omega2", "", "", bnk->omega2, &bnk->omega2,NULL);CHKERRQ(ierr);
553   ierr = PetscOptionsReal("-tao_BNK_omega3", "", "", bnk->omega3, &bnk->omega3,NULL);CHKERRQ(ierr);
554   ierr = PetscOptionsReal("-tao_BNK_omega4", "", "", bnk->omega4, &bnk->omega4,NULL);CHKERRQ(ierr);
555   ierr = PetscOptionsReal("-tao_BNK_omega5", "", "", bnk->omega5, &bnk->omega5,NULL);CHKERRQ(ierr);
556   ierr = PetscOptionsReal("-tao_BNK_mu1_i", "", "", bnk->mu1_i, &bnk->mu1_i,NULL);CHKERRQ(ierr);
557   ierr = PetscOptionsReal("-tao_BNK_mu2_i", "", "", bnk->mu2_i, &bnk->mu2_i,NULL);CHKERRQ(ierr);
558   ierr = PetscOptionsReal("-tao_BNK_gamma1_i", "", "", bnk->gamma1_i, &bnk->gamma1_i,NULL);CHKERRQ(ierr);
559   ierr = PetscOptionsReal("-tao_BNK_gamma2_i", "", "", bnk->gamma2_i, &bnk->gamma2_i,NULL);CHKERRQ(ierr);
560   ierr = PetscOptionsReal("-tao_BNK_gamma3_i", "", "", bnk->gamma3_i, &bnk->gamma3_i,NULL);CHKERRQ(ierr);
561   ierr = PetscOptionsReal("-tao_BNK_gamma4_i", "", "", bnk->gamma4_i, &bnk->gamma4_i,NULL);CHKERRQ(ierr);
562   ierr = PetscOptionsReal("-tao_BNK_theta_i", "", "", bnk->theta_i, &bnk->theta_i,NULL);CHKERRQ(ierr);
563   ierr = PetscOptionsReal("-tao_BNK_mu1", "", "", bnk->mu1, &bnk->mu1,NULL);CHKERRQ(ierr);
564   ierr = PetscOptionsReal("-tao_BNK_mu2", "", "", bnk->mu2, &bnk->mu2,NULL);CHKERRQ(ierr);
565   ierr = PetscOptionsReal("-tao_BNK_gamma1", "", "", bnk->gamma1, &bnk->gamma1,NULL);CHKERRQ(ierr);
566   ierr = PetscOptionsReal("-tao_BNK_gamma2", "", "", bnk->gamma2, &bnk->gamma2,NULL);CHKERRQ(ierr);
567   ierr = PetscOptionsReal("-tao_BNK_gamma3", "", "", bnk->gamma3, &bnk->gamma3,NULL);CHKERRQ(ierr);
568   ierr = PetscOptionsReal("-tao_BNK_gamma4", "", "", bnk->gamma4, &bnk->gamma4,NULL);CHKERRQ(ierr);
569   ierr = PetscOptionsReal("-tao_BNK_theta", "", "", bnk->theta, &bnk->theta,NULL);CHKERRQ(ierr);
570   ierr = PetscOptionsReal("-tao_BNK_min_radius", "lower bound on initial radius", "", bnk->min_radius, &bnk->min_radius,NULL);CHKERRQ(ierr);
571   ierr = PetscOptionsReal("-tao_BNK_max_radius", "upper bound on radius", "", bnk->max_radius, &bnk->max_radius,NULL);CHKERRQ(ierr);
572   ierr = PetscOptionsReal("-tao_BNK_epsilon", "tolerance used when computing actual and predicted reduction", "", bnk->epsilon, &bnk->epsilon,NULL);CHKERRQ(ierr);
573   ierr = PetscOptionsTail();CHKERRQ(ierr);
574   ierr = TaoLineSearchSetFromOptions(tao->linesearch);CHKERRQ(ierr);
575   ierr = KSPSetFromOptions(tao->ksp);CHKERRQ(ierr);
576   PetscFunctionReturn(0);
577 }
578 
579 
580 /*------------------------------------------------------------*/
581 static PetscErrorCode TaoView_BNK(Tao tao, PetscViewer viewer)
582 {
583   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
584   PetscInt       nrejects;
585   PetscBool      isascii;
586   PetscErrorCode ierr;
587 
588   PetscFunctionBegin;
589   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);
590   if (isascii) {
591     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
592     if (BNK_PC_BFGS == bnk->pc_type && bnk->M) {
593       ierr = MatLMVMGetRejects(bnk->M,&nrejects);CHKERRQ(ierr);
594       ierr = PetscViewerASCIIPrintf(viewer, "Rejected matrix updates: %D\n",nrejects);CHKERRQ(ierr);
595     }
596     ierr = PetscViewerASCIIPrintf(viewer, "Newton steps: %D\n", bnk->newt);CHKERRQ(ierr);
597     ierr = PetscViewerASCIIPrintf(viewer, "BFGS steps: %D\n", bnk->bfgs);CHKERRQ(ierr);
598     ierr = PetscViewerASCIIPrintf(viewer, "Scaled gradient steps: %D\n", bnk->sgrad);CHKERRQ(ierr);
599     ierr = PetscViewerASCIIPrintf(viewer, "Gradient steps: %D\n", bnk->grad);CHKERRQ(ierr);
600     ierr = PetscViewerASCIIPrintf(viewer, "KSP termination reasons:\n");CHKERRQ(ierr);
601     ierr = PetscViewerASCIIPrintf(viewer, "  atol: %D\n", bnk->ksp_atol);CHKERRQ(ierr);
602     ierr = PetscViewerASCIIPrintf(viewer, "  rtol: %D\n", bnk->ksp_rtol);CHKERRQ(ierr);
603     ierr = PetscViewerASCIIPrintf(viewer, "  ctol: %D\n", bnk->ksp_ctol);CHKERRQ(ierr);
604     ierr = PetscViewerASCIIPrintf(viewer, "  negc: %D\n", bnk->ksp_negc);CHKERRQ(ierr);
605     ierr = PetscViewerASCIIPrintf(viewer, "  dtol: %D\n", bnk->ksp_dtol);CHKERRQ(ierr);
606     ierr = PetscViewerASCIIPrintf(viewer, "  iter: %D\n", bnk->ksp_iter);CHKERRQ(ierr);
607     ierr = PetscViewerASCIIPrintf(viewer, "  othr: %D\n", bnk->ksp_othr);CHKERRQ(ierr);
608     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
609   }
610   PetscFunctionReturn(0);
611 }
612 
613 /* ---------------------------------------------------------- */
614 /*MC
615   TAOBNK - Shared base-type for Bounded Newton-Krylov type algorithms.
616   At each iteration, the BNK method solves the symmetric
617   system of equations to obtain the step diretion dk:
618               Hk dk = -gk
619   at which point the step can be globalized either through trust-region
620   methods, or a line search, or a heuristic mixture of both.
621 
622     Options Database Keys:
623 + -tao_BNK_pc_type - "none","ahess","bfgs","petsc"
624 . -tao_BNK_bfgs_scale_type - "ahess","phess","bfgs"
625 . -tao_BNK_init_type - "constant","direction","interpolation"
626 . -tao_BNK_update_type - "step","direction","interpolation"
627 . -tao_BNK_sval - perturbation starting value
628 . -tao_BNK_imin - minimum initial perturbation
629 . -tao_BNK_imax - maximum initial perturbation
630 . -tao_BNK_pmin - minimum perturbation
631 . -tao_BNK_pmax - maximum perturbation
632 . -tao_BNK_pgfac - growth factor
633 . -tao_BNK_psfac - shrink factor
634 . -tao_BNK_imfac - initial merit factor
635 . -tao_BNK_pmgfac - merit growth factor
636 . -tao_BNK_pmsfac - merit shrink factor
637 . -tao_BNK_eta1 - poor steplength; reduce radius
638 . -tao_BNK_eta2 - reasonable steplength; leave radius
639 . -tao_BNK_eta3 - good steplength; increase readius
640 . -tao_BNK_eta4 - excellent steplength; greatly increase radius
641 . -tao_BNK_alpha1 - alpha1 reduction
642 . -tao_BNK_alpha2 - alpha2 reduction
643 . -tao_BNK_alpha3 - alpha3 reduction
644 . -tao_BNK_alpha4 - alpha4 reduction
645 . -tao_BNK_alpha - alpha5 reduction
646 . -tao_BNK_mu1 - mu1 interpolation update
647 . -tao_BNK_mu2 - mu2 interpolation update
648 . -tao_BNK_gamma1 - gamma1 interpolation update
649 . -tao_BNK_gamma2 - gamma2 interpolation update
650 . -tao_BNK_gamma3 - gamma3 interpolation update
651 . -tao_BNK_gamma4 - gamma4 interpolation update
652 . -tao_BNK_theta - theta interpolation update
653 . -tao_BNK_omega1 - omega1 step update
654 . -tao_BNK_omega2 - omega2 step update
655 . -tao_BNK_omega3 - omega3 step update
656 . -tao_BNK_omega4 - omega4 step update
657 . -tao_BNK_omega5 - omega5 step update
658 . -tao_BNK_mu1_i -  mu1 interpolation init factor
659 . -tao_BNK_mu2_i -  mu2 interpolation init factor
660 . -tao_BNK_gamma1_i -  gamma1 interpolation init factor
661 . -tao_BNK_gamma2_i -  gamma2 interpolation init factor
662 . -tao_BNK_gamma3_i -  gamma3 interpolation init factor
663 . -tao_BNK_gamma4_i -  gamma4 interpolation init factor
664 - -tao_BNK_theta_i -  theta interpolation init factor
665 
666   Level: beginner
667 M*/
668 
669 PetscErrorCode TaoCreate_BNK(Tao tao)
670 {
671   TAO_BNK        *bnk;
672   const char     *morethuente_type = TAOLINESEARCHMT;
673   PetscErrorCode ierr;
674 
675   PetscFunctionBegin;
676   ierr = PetscNewLog(tao,&bnk);CHKERRQ(ierr);
677 
678   tao->ops->setup = TaoSetUp_BNK;
679   tao->ops->view = TaoView_BNK;
680   tao->ops->setfromoptions = TaoSetFromOptions_BNK;
681   tao->ops->destroy = TaoDestroy_BNK;
682 
683   /* Override default settings (unless already changed) */
684   if (!tao->max_it_changed) tao->max_it = 50;
685   if (!tao->trust0_changed) tao->trust0 = 100.0;
686 
687   tao->data = (void*)bnk;
688 
689   bnk->sval   = 0.0;
690   bnk->imin   = 1.0e-4;
691   bnk->imax   = 1.0e+2;
692   bnk->imfac  = 1.0e-1;
693 
694   bnk->pmin   = 1.0e-12;
695   bnk->pmax   = 1.0e+2;
696   bnk->pgfac  = 1.0e+1;
697   bnk->psfac  = 4.0e-1;
698   bnk->pmgfac = 1.0e-1;
699   bnk->pmsfac = 1.0e-1;
700 
701   /*  Default values for trust-region radius update based on steplength */
702   bnk->nu1 = 0.25;
703   bnk->nu2 = 0.50;
704   bnk->nu3 = 1.00;
705   bnk->nu4 = 1.25;
706 
707   bnk->omega1 = 0.25;
708   bnk->omega2 = 0.50;
709   bnk->omega3 = 1.00;
710   bnk->omega4 = 2.00;
711   bnk->omega5 = 4.00;
712 
713   /*  Default values for trust-region radius update based on reduction */
714   bnk->eta1 = 1.0e-4;
715   bnk->eta2 = 0.25;
716   bnk->eta3 = 0.50;
717   bnk->eta4 = 0.90;
718 
719   bnk->alpha1 = 0.25;
720   bnk->alpha2 = 0.50;
721   bnk->alpha3 = 1.00;
722   bnk->alpha4 = 2.00;
723   bnk->alpha5 = 4.00;
724 
725   /*  Default values for trust-region radius update based on interpolation */
726   bnk->mu1 = 0.10;
727   bnk->mu2 = 0.50;
728 
729   bnk->gamma1 = 0.25;
730   bnk->gamma2 = 0.50;
731   bnk->gamma3 = 2.00;
732   bnk->gamma4 = 4.00;
733 
734   bnk->theta = 0.05;
735 
736   /*  Default values for trust region initialization based on interpolation */
737   bnk->mu1_i = 0.35;
738   bnk->mu2_i = 0.50;
739 
740   bnk->gamma1_i = 0.0625;
741   bnk->gamma2_i = 0.5;
742   bnk->gamma3_i = 2.0;
743   bnk->gamma4_i = 5.0;
744 
745   bnk->theta_i = 0.25;
746 
747   /*  Remaining parameters */
748   bnk->min_radius = 1.0e-10;
749   bnk->max_radius = 1.0e10;
750   bnk->epsilon = 1.0e-6;
751 
752   bnk->pc_type         = BNK_PC_BFGS;
753   bnk->bfgs_scale_type = BFGS_SCALE_PHESS;
754   bnk->init_type       = BNK_INIT_INTERPOLATION;
755   bnk->update_type     = BNK_UPDATE_STEP;
756 
757   ierr = TaoLineSearchCreate(((PetscObject)tao)->comm,&tao->linesearch);CHKERRQ(ierr);
758   ierr = PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1);CHKERRQ(ierr);
759   ierr = TaoLineSearchSetType(tao->linesearch,morethuente_type);CHKERRQ(ierr);
760   ierr = TaoLineSearchUseTaoRoutines(tao->linesearch,tao);CHKERRQ(ierr);
761   ierr = TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);CHKERRQ(ierr);
762 
763   /*  Set linear solver to default for symmetric matrices */
764   ierr = KSPCreate(((PetscObject)tao)->comm,&tao->ksp);CHKERRQ(ierr);
765   ierr = PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1);CHKERRQ(ierr);
766   ierr = KSPSetOptionsPrefix(tao->ksp,tao->hdr.prefix);CHKERRQ(ierr);
767   ierr = KSPSetType(tao->ksp,KSPCGSTCG);CHKERRQ(ierr);
768   PetscFunctionReturn(0);
769 }
770