xref: /petsc/src/tao/unconstrained/impls/ntl/ntl.c (revision e4cb33bb7dbdbae9285fba102465ca0f1dcb3977)
1 #include <../src/tao/matrix/lmvmmat.h>
2 #include <../src/tao/unconstrained/impls/ntl/ntl.h>
3 
4 #include <petscksp.h>
5 #include <petscpc.h>
6 #include <petsc-private/kspimpl.h>
7 #include <petsc-private/pcimpl.h>
8 
9 #define NTL_KSP_NASH    0
10 #define NTL_KSP_STCG    1
11 #define NTL_KSP_GLTR    2
12 #define NTL_KSP_TYPES   3
13 
14 #define NTL_PC_NONE     0
15 #define NTL_PC_AHESS    1
16 #define NTL_PC_BFGS     2
17 #define NTL_PC_PETSC    3
18 #define NTL_PC_TYPES    4
19 
20 #define BFGS_SCALE_AHESS        0
21 #define BFGS_SCALE_BFGS         1
22 #define BFGS_SCALE_TYPES        2
23 
24 #define NTL_INIT_CONSTANT         0
25 #define NTL_INIT_DIRECTION        1
26 #define NTL_INIT_INTERPOLATION    2
27 #define NTL_INIT_TYPES            3
28 
29 #define NTL_UPDATE_REDUCTION      0
30 #define NTL_UPDATE_INTERPOLATION  1
31 #define NTL_UPDATE_TYPES          2
32 
33 static const char *NTL_KSP[64] = {"nash", "stcg", "gltr"};
34 
35 static const char *NTL_PC[64] = {"none", "ahess", "bfgs", "petsc"};
36 
37 static const char *BFGS_SCALE[64] = {"ahess", "bfgs"};
38 
39 static const char *NTL_INIT[64] = {"constant", "direction", "interpolation"};
40 
41 static const char *NTL_UPDATE[64] = {"reduction", "interpolation"};
42 
43 /* Routine for BFGS preconditioner */
44 
45 #undef __FUNCT__
46 #define __FUNCT__ "MatLMVMSolveShell"
47 static PetscErrorCode MatLMVMSolveShell(PC pc, Vec b, Vec x)
48 {
49   PetscErrorCode ierr;
50   Mat            M;
51 
52   PetscFunctionBegin;
53   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
54   PetscValidHeaderSpecific(b,VEC_CLASSID,2);
55   PetscValidHeaderSpecific(x,VEC_CLASSID,3);
56   ierr = PCShellGetContext(pc,(void**)&M);CHKERRQ(ierr);
57   ierr = MatLMVMSolve(M, b, x);CHKERRQ(ierr);
58   PetscFunctionReturn(0);
59 }
60 
61 /* Implements Newton's Method with a trust-region, line-search approach for
62    solving unconstrained minimization problems.  A More'-Thuente line search
63    is used to guarantee that the bfgs preconditioner remains positive
64    definite. */
65 
66 #define NTL_NEWTON              0
67 #define NTL_BFGS                1
68 #define NTL_SCALED_GRADIENT     2
69 #define NTL_GRADIENT            3
70 
71 #undef __FUNCT__
72 #define __FUNCT__ "TaoSolve_NTL"
73 static PetscErrorCode TaoSolve_NTL(Tao tao)
74 {
75   TAO_NTL                      *tl = (TAO_NTL *)tao->data;
76   PC                           pc;
77   KSPConvergedReason           ksp_reason;
78   TaoConvergedReason           reason;
79   TaoLineSearchConvergedReason ls_reason;
80 
81   PetscReal                    fmin, ftrial, prered, actred, kappa, sigma;
82   PetscReal                    tau, tau_1, tau_2, tau_max, tau_min, max_radius;
83   PetscReal                    f, fold, gdx, gnorm;
84   PetscReal                    step = 1.0;
85 
86   PetscReal                    delta;
87   PetscReal                    norm_d = 0.0;
88   MatStructure                 matflag;
89   PetscErrorCode               ierr;
90   PetscInt                     stepType;
91   PetscInt                     iter = 0,its;
92 
93   PetscInt                     bfgsUpdates = 0;
94   PetscInt                     needH;
95 
96   PetscInt                     i_max = 5;
97   PetscInt                     j_max = 1;
98   PetscInt                     i, j, n, N;
99 
100   PetscInt                     tr_reject;
101 
102   PetscFunctionBegin;
103   if (tao->XL || tao->XU || tao->ops->computebounds) {
104     ierr = PetscPrintf(((PetscObject)tao)->comm,"WARNING: Variable bounds have been set but will be ignored by ntl algorithm\n");CHKERRQ(ierr);
105   }
106 
107   /* Initialize trust-region radius */
108   tao->trust = tao->trust0;
109 
110   /* Modify the radius if it is too large or small */
111   tao->trust = PetscMax(tao->trust, tl->min_radius);
112   tao->trust = PetscMin(tao->trust, tl->max_radius);
113 
114   if (NTL_PC_BFGS == tl->pc_type && !tl->M) {
115     ierr = VecGetLocalSize(tao->solution,&n);CHKERRQ(ierr);
116     ierr = VecGetSize(tao->solution,&N);CHKERRQ(ierr);
117     ierr = MatCreateLMVM(((PetscObject)tao)->comm,n,N,&tl->M);CHKERRQ(ierr);
118     ierr = MatLMVMAllocateVectors(tl->M,tao->solution);CHKERRQ(ierr);
119   }
120 
121   /* Check convergence criteria */
122   ierr = TaoComputeObjectiveAndGradient(tao, tao->solution, &f, tao->gradient);CHKERRQ(ierr);
123   ierr = VecNorm(tao->gradient, NORM_2, &gnorm);CHKERRQ(ierr);
124   if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
125   needH = 1;
126 
127   ierr = TaoMonitor(tao, iter, f, gnorm, 0.0, 1.0, &reason);CHKERRQ(ierr);
128   if (reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);
129 
130   /* Create vectors for the limited memory preconditioner */
131   if ((NTL_PC_BFGS == tl->pc_type) && (BFGS_SCALE_BFGS != tl->bfgs_scale_type)) {
132     if (!tl->Diag) {
133       ierr = VecDuplicate(tao->solution, &tl->Diag);CHKERRQ(ierr);
134     }
135   }
136 
137   /* Modify the linear solver to a conjugate gradient method */
138   switch(tl->ksp_type) {
139   case NTL_KSP_NASH:
140     ierr = KSPSetType(tao->ksp, KSPNASH);CHKERRQ(ierr);
141     if (tao->ksp->ops->setfromoptions) {
142       (*tao->ksp->ops->setfromoptions)(tao->ksp);
143     }
144     break;
145 
146   case NTL_KSP_STCG:
147     ierr = KSPSetType(tao->ksp, KSPSTCG);CHKERRQ(ierr);
148     if (tao->ksp->ops->setfromoptions) {
149       (*tao->ksp->ops->setfromoptions)(tao->ksp);
150     }
151     break;
152 
153   default:
154     ierr = KSPSetType(tao->ksp, KSPGLTR);CHKERRQ(ierr);
155     if (tao->ksp->ops->setfromoptions) {
156       (*tao->ksp->ops->setfromoptions)(tao->ksp);
157     }
158     break;
159   }
160 
161   /* Modify the preconditioner to use the bfgs approximation */
162   ierr = KSPGetPC(tao->ksp, &pc);CHKERRQ(ierr);
163   switch(tl->pc_type) {
164   case NTL_PC_NONE:
165     ierr = PCSetType(pc, PCNONE);CHKERRQ(ierr);
166     if (pc->ops->setfromoptions) {
167       (*pc->ops->setfromoptions)(pc);
168     }
169     break;
170 
171   case NTL_PC_AHESS:
172     ierr = PCSetType(pc, PCJACOBI);CHKERRQ(ierr);
173     if (pc->ops->setfromoptions) {
174       (*pc->ops->setfromoptions)(pc);
175     }
176     ierr = PCJacobiSetUseAbs(pc);CHKERRQ(ierr);
177     break;
178 
179   case NTL_PC_BFGS:
180     ierr = PCSetType(pc, PCSHELL);CHKERRQ(ierr);
181     if (pc->ops->setfromoptions) {
182       (*pc->ops->setfromoptions)(pc);
183     }
184     ierr = PCShellSetName(pc, "bfgs");CHKERRQ(ierr);
185     ierr = PCShellSetContext(pc, tl->M);CHKERRQ(ierr);
186     ierr = PCShellSetApply(pc, MatLMVMSolveShell);CHKERRQ(ierr);
187     break;
188 
189   default:
190     /* Use the pc method set by pc_type */
191     break;
192   }
193 
194   /* Initialize trust-region radius.  The initialization is only performed
195      when we are using Steihaug-Toint or the Generalized Lanczos method. */
196   switch(tl->init_type) {
197   case NTL_INIT_CONSTANT:
198     /* Use the initial radius specified */
199     break;
200 
201   case NTL_INIT_INTERPOLATION:
202     /* Use the initial radius specified */
203     max_radius = 0.0;
204 
205     for (j = 0; j < j_max; ++j) {
206       fmin = f;
207       sigma = 0.0;
208 
209       if (needH) {
210         ierr = TaoComputeHessian(tao, tao->solution, &tao->hessian, &tao->hessian_pre, &matflag);CHKERRQ(ierr);
211         needH = 0;
212       }
213 
214       for (i = 0; i < i_max; ++i) {
215         ierr = VecCopy(tao->solution, tl->W);CHKERRQ(ierr);
216         ierr = VecAXPY(tl->W, -tao->trust/gnorm, tao->gradient);CHKERRQ(ierr);
217 
218         ierr = TaoComputeObjective(tao, tl->W, &ftrial);CHKERRQ(ierr);
219         if (PetscIsInfOrNanReal(ftrial)) {
220           tau = tl->gamma1_i;
221         } else {
222           if (ftrial < fmin) {
223             fmin = ftrial;
224             sigma = -tao->trust / gnorm;
225           }
226 
227           ierr = MatMult(tao->hessian, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
228           ierr = VecDot(tao->gradient, tao->stepdirection, &prered);CHKERRQ(ierr);
229 
230           prered = tao->trust * (gnorm - 0.5 * tao->trust * prered / (gnorm * gnorm));
231           actred = f - ftrial;
232           if ((PetscAbsScalar(actred) <= tl->epsilon) && (PetscAbsScalar(prered) <= tl->epsilon)) {
233             kappa = 1.0;
234           } else {
235             kappa = actred / prered;
236           }
237 
238           tau_1 = tl->theta_i * gnorm * tao->trust / (tl->theta_i * gnorm * tao->trust + (1.0 - tl->theta_i) * prered - actred);
239           tau_2 = tl->theta_i * gnorm * tao->trust / (tl->theta_i * gnorm * tao->trust - (1.0 + tl->theta_i) * prered + actred);
240           tau_min = PetscMin(tau_1, tau_2);
241           tau_max = PetscMax(tau_1, tau_2);
242 
243           if (PetscAbsScalar(kappa - 1.0) <= tl->mu1_i) {
244             /* Great agreement */
245             max_radius = PetscMax(max_radius, tao->trust);
246 
247             if (tau_max < 1.0) {
248               tau = tl->gamma3_i;
249             } else if (tau_max > tl->gamma4_i) {
250               tau = tl->gamma4_i;
251             } else if (tau_1 >= 1.0 && tau_1 <= tl->gamma4_i && tau_2 < 1.0) {
252               tau = tau_1;
253             } else if (tau_2 >= 1.0 && tau_2 <= tl->gamma4_i && tau_1 < 1.0) {
254               tau = tau_2;
255             } else {
256               tau = tau_max;
257             }
258           } else if (PetscAbsScalar(kappa - 1.0) <= tl->mu2_i) {
259             /* Good agreement */
260             max_radius = PetscMax(max_radius, tao->trust);
261 
262             if (tau_max < tl->gamma2_i) {
263               tau = tl->gamma2_i;
264             } else if (tau_max > tl->gamma3_i) {
265               tau = tl->gamma3_i;
266             } else {
267               tau = tau_max;
268             }
269           } else {
270             /* Not good agreement */
271             if (tau_min > 1.0) {
272               tau = tl->gamma2_i;
273             } else if (tau_max < tl->gamma1_i) {
274               tau = tl->gamma1_i;
275             } else if ((tau_min < tl->gamma1_i) && (tau_max >= 1.0)) {
276               tau = tl->gamma1_i;
277             } else if ((tau_1 >= tl->gamma1_i) && (tau_1 < 1.0) &&  ((tau_2 < tl->gamma1_i) || (tau_2 >= 1.0))) {
278               tau = tau_1;
279             } else if ((tau_2 >= tl->gamma1_i) && (tau_2 < 1.0) &&  ((tau_1 < tl->gamma1_i) || (tau_2 >= 1.0))) {
280               tau = tau_2;
281             } else {
282               tau = tau_max;
283             }
284           }
285         }
286         tao->trust = tau * tao->trust;
287       }
288 
289       if (fmin < f) {
290         f = fmin;
291         ierr = VecAXPY(tao->solution, sigma, tao->gradient);CHKERRQ(ierr);
292         ierr = TaoComputeGradient(tao, tao->solution, tao->gradient);CHKERRQ(ierr);
293 
294         ierr = VecNorm(tao->gradient, NORM_2, &gnorm);CHKERRQ(ierr);
295         if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
296         needH = 1;
297 
298         ierr = TaoMonitor(tao, iter, f, gnorm, 0.0, 1.0, &reason);CHKERRQ(ierr);
299         if (reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);
300       }
301     }
302     tao->trust = PetscMax(tao->trust, max_radius);
303 
304     /* Modify the radius if it is too large or small */
305     tao->trust = PetscMax(tao->trust, tl->min_radius);
306     tao->trust = PetscMin(tao->trust, tl->max_radius);
307     break;
308 
309   default:
310     /* Norm of the first direction will initialize radius */
311     tao->trust = 0.0;
312     break;
313   }
314 
315   /* Set initial scaling for the BFGS preconditioner
316      This step is done after computing the initial trust-region radius
317      since the function value may have decreased */
318   if (NTL_PC_BFGS == tl->pc_type) {
319     if (f != 0.0) {
320       delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
321     } else {
322       delta = 2.0 / (gnorm*gnorm);
323     }
324     ierr = MatLMVMSetDelta(tl->M, delta);CHKERRQ(ierr);
325   }
326 
327   /* Set counter for gradient/reset steps */
328   tl->ntrust = 0;
329   tl->newt = 0;
330   tl->bfgs = 0;
331   tl->sgrad = 0;
332   tl->grad = 0;
333 
334   /* Have not converged; continue with Newton method */
335   while (reason == TAO_CONTINUE_ITERATING) {
336     ++iter;
337 
338     /* Compute the Hessian */
339     if (needH) {
340       ierr = TaoComputeHessian(tao, tao->solution, &tao->hessian, &tao->hessian_pre, &matflag);CHKERRQ(ierr);
341       needH = 0;
342     }
343 
344     if (NTL_PC_BFGS == tl->pc_type) {
345       if (BFGS_SCALE_AHESS == tl->bfgs_scale_type) {
346         /* Obtain diagonal for the bfgs preconditioner */
347         ierr = MatGetDiagonal(tao->hessian, tl->Diag);CHKERRQ(ierr);
348         ierr = VecAbs(tl->Diag);CHKERRQ(ierr);
349         ierr = VecReciprocal(tl->Diag);CHKERRQ(ierr);
350         ierr = MatLMVMSetScale(tl->M, tl->Diag);CHKERRQ(ierr);
351       }
352 
353       /* Update the limited memory preconditioner */
354       ierr = MatLMVMUpdate(tl->M,tao->solution, tao->gradient);CHKERRQ(ierr);
355       ++bfgsUpdates;
356     }
357     ierr = KSPSetOperators(tao->ksp, tao->hessian, tao->hessian_pre, matflag);CHKERRQ(ierr);
358     /* Solve the Newton system of equations */
359     if (NTL_KSP_NASH == tl->ksp_type) {
360       ierr = KSPNASHSetRadius(tao->ksp,tl->max_radius);CHKERRQ(ierr);
361       ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
362       ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr);
363       tao->ksp_its+=its;
364       ierr = KSPNASHGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr);
365     } else if (NTL_KSP_STCG == tl->ksp_type) {
366       ierr = KSPSTCGSetRadius(tao->ksp,tl->max_radius);CHKERRQ(ierr);
367       ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
368       ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr);
369       tao->ksp_its+=its;
370       ierr = KSPSTCGGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr);
371     } else { /* NTL_KSP_GLTR */
372       ierr = KSPGLTRSetRadius(tao->ksp,tl->max_radius);CHKERRQ(ierr);
373       ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
374       ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr);
375       tao->ksp_its+=its;
376       ierr = KSPGLTRGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr);
377     }
378 
379     if (0.0 == tao->trust) {
380       /* Radius was uninitialized; use the norm of the direction */
381       if (norm_d > 0.0) {
382         tao->trust = norm_d;
383 
384         /* Modify the radius if it is too large or small */
385         tao->trust = PetscMax(tao->trust, tl->min_radius);
386         tao->trust = PetscMin(tao->trust, tl->max_radius);
387       } else {
388         /* The direction was bad; set radius to default value and re-solve
389            the trust-region subproblem to get a direction */
390         tao->trust = tao->trust0;
391 
392         /* Modify the radius if it is too large or small */
393         tao->trust = PetscMax(tao->trust, tl->min_radius);
394         tao->trust = PetscMin(tao->trust, tl->max_radius);
395 
396         if (NTL_KSP_NASH == tl->ksp_type) {
397           ierr = KSPNASHSetRadius(tao->ksp,tl->max_radius);CHKERRQ(ierr);
398           ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
399           ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr);
400           tao->ksp_its+=its;
401           ierr = KSPNASHGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr);
402         } else if (NTL_KSP_STCG == tl->ksp_type) {
403           ierr = KSPSTCGSetRadius(tao->ksp,tl->max_radius);CHKERRQ(ierr);
404           ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
405           ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr);
406           tao->ksp_its+=its;
407           ierr = KSPSTCGGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr);
408         } else { /* NTL_KSP_GLTR */
409           ierr = KSPGLTRSetRadius(tao->ksp,tl->max_radius);CHKERRQ(ierr);
410           ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
411           ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr);
412           tao->ksp_its+=its;
413           ierr = KSPGLTRGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr);
414         }
415 
416 
417         if (norm_d == 0.0) SETERRQ(PETSC_COMM_SELF,1, "Initial direction zero");
418       }
419     }
420 
421     ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
422     ierr = KSPGetConvergedReason(tao->ksp, &ksp_reason);CHKERRQ(ierr);
423     if ((KSP_DIVERGED_INDEFINITE_PC == ksp_reason) && (NTL_PC_BFGS == tl->pc_type) && (bfgsUpdates > 1)) {
424       /* Preconditioner is numerically indefinite; reset the
425          approximate if using BFGS preconditioning. */
426 
427       if (f != 0.0) {
428         delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
429       } else {
430         delta = 2.0 / (gnorm*gnorm);
431       }
432       ierr = MatLMVMSetDelta(tl->M, delta);CHKERRQ(ierr);
433       ierr = MatLMVMReset(tl->M);CHKERRQ(ierr);
434       ierr = MatLMVMUpdate(tl->M, tao->solution, tao->gradient);CHKERRQ(ierr);
435       bfgsUpdates = 1;
436     }
437 
438     /* Check trust-region reduction conditions */
439     tr_reject = 0;
440     if (NTL_UPDATE_REDUCTION == tl->update_type) {
441       /* Get predicted reduction */
442       if (NTL_KSP_NASH == tl->ksp_type) {
443         ierr = KSPNASHGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr);
444       } else if (NTL_KSP_STCG == tl->ksp_type) {
445         ierr = KSPSTCGGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr);
446       } else { /* gltr */
447         ierr = KSPGLTRGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr);
448       }
449 
450       if (prered >= 0.0) {
451         /* The predicted reduction has the wrong sign.  This cannot
452            happen in infinite precision arithmetic.  Step should
453            be rejected! */
454         tao->trust = tl->alpha1 * PetscMin(tao->trust, norm_d);
455         tr_reject = 1;
456       } else {
457         /* Compute trial step and function value */
458         ierr = VecCopy(tao->solution, tl->W);CHKERRQ(ierr);
459         ierr = VecAXPY(tl->W, 1.0, tao->stepdirection);CHKERRQ(ierr);
460         ierr = TaoComputeObjective(tao, tl->W, &ftrial);CHKERRQ(ierr);
461 
462         if (PetscIsInfOrNanReal(ftrial)) {
463           tao->trust = tl->alpha1 * PetscMin(tao->trust, norm_d);
464           tr_reject = 1;
465         } else {
466           /* Compute and actual reduction */
467           actred = f - ftrial;
468           prered = -prered;
469           if ((PetscAbsScalar(actred) <= tl->epsilon) &&
470               (PetscAbsScalar(prered) <= tl->epsilon)) {
471             kappa = 1.0;
472           } else {
473             kappa = actred / prered;
474           }
475 
476           /* Accept of reject the step and update radius */
477           if (kappa < tl->eta1) {
478             /* Reject the step */
479             tao->trust = tl->alpha1 * PetscMin(tao->trust, norm_d);
480             tr_reject = 1;
481           } else {
482             /* Accept the step */
483             if (kappa < tl->eta2) {
484               /* Marginal bad step */
485               tao->trust = tl->alpha2 * PetscMin(tao->trust, norm_d);
486             } else if (kappa < tl->eta3) {
487               /* Reasonable step */
488               tao->trust = tl->alpha3 * tao->trust;
489             } else if (kappa < tl->eta4) {
490               /* Good step */
491               tao->trust = PetscMax(tl->alpha4 * norm_d, tao->trust);
492             } else {
493               /* Very good step */
494               tao->trust = PetscMax(tl->alpha5 * norm_d, tao->trust);
495             }
496           }
497         }
498       }
499     } else {
500       /* Get predicted reduction */
501       if (NTL_KSP_NASH == tl->ksp_type) {
502         ierr = KSPNASHGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr);
503       } else if (NTL_KSP_STCG == tl->ksp_type) {
504         ierr = KSPSTCGGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr);
505       } else { /* gltr */
506         ierr = KSPGLTRGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr);
507       }
508 
509       if (prered >= 0.0) {
510         /* The predicted reduction has the wrong sign.  This cannot
511            happen in infinite precision arithmetic.  Step should
512            be rejected! */
513         tao->trust = tl->gamma1 * PetscMin(tao->trust, norm_d);
514         tr_reject = 1;
515       } else {
516         ierr = VecCopy(tao->solution, tl->W);CHKERRQ(ierr);
517         ierr = VecAXPY(tl->W, 1.0, tao->stepdirection);CHKERRQ(ierr);
518         ierr = TaoComputeObjective(tao, tl->W, &ftrial);CHKERRQ(ierr);
519         if (PetscIsInfOrNanReal(ftrial)) {
520           tao->trust = tl->gamma1 * PetscMin(tao->trust, norm_d);
521           tr_reject = 1;
522         } else {
523           ierr = VecDot(tao->gradient, tao->stepdirection, &gdx);CHKERRQ(ierr);
524 
525           actred = f - ftrial;
526           prered = -prered;
527           if ((PetscAbsScalar(actred) <= tl->epsilon) &&
528               (PetscAbsScalar(prered) <= tl->epsilon)) {
529             kappa = 1.0;
530           } else {
531             kappa = actred / prered;
532           }
533 
534           tau_1 = tl->theta * gdx / (tl->theta * gdx - (1.0 - tl->theta) * prered + actred);
535           tau_2 = tl->theta * gdx / (tl->theta * gdx + (1.0 + tl->theta) * prered - actred);
536           tau_min = PetscMin(tau_1, tau_2);
537           tau_max = PetscMax(tau_1, tau_2);
538 
539           if (kappa >= 1.0 - tl->mu1) {
540             /* Great agreement; accept step and update radius */
541             if (tau_max < 1.0) {
542               tao->trust = PetscMax(tao->trust, tl->gamma3 * norm_d);
543             } else if (tau_max > tl->gamma4) {
544               tao->trust = PetscMax(tao->trust, tl->gamma4 * norm_d);
545             } else {
546               tao->trust = PetscMax(tao->trust, tau_max * norm_d);
547             }
548           } else if (kappa >= 1.0 - tl->mu2) {
549             /* Good agreement */
550 
551             if (tau_max < tl->gamma2) {
552               tao->trust = tl->gamma2 * PetscMin(tao->trust, norm_d);
553             } else if (tau_max > tl->gamma3) {
554               tao->trust = PetscMax(tao->trust, tl->gamma3 * norm_d);
555             } else if (tau_max < 1.0) {
556               tao->trust = tau_max * PetscMin(tao->trust, norm_d);
557             } else {
558               tao->trust = PetscMax(tao->trust, tau_max * norm_d);
559             }
560           } else {
561             /* Not good agreement */
562             if (tau_min > 1.0) {
563               tao->trust = tl->gamma2 * PetscMin(tao->trust, norm_d);
564             } else if (tau_max < tl->gamma1) {
565               tao->trust = tl->gamma1 * PetscMin(tao->trust, norm_d);
566             } else if ((tau_min < tl->gamma1) && (tau_max >= 1.0)) {
567               tao->trust = tl->gamma1 * PetscMin(tao->trust, norm_d);
568             } else if ((tau_1 >= tl->gamma1) && (tau_1 < 1.0) && ((tau_2 < tl->gamma1) || (tau_2 >= 1.0))) {
569               tao->trust = tau_1 * PetscMin(tao->trust, norm_d);
570             } else if ((tau_2 >= tl->gamma1) && (tau_2 < 1.0) && ((tau_1 < tl->gamma1) || (tau_2 >= 1.0))) {
571               tao->trust = tau_2 * PetscMin(tao->trust, norm_d);
572             } else {
573               tao->trust = tau_max * PetscMin(tao->trust, norm_d);
574             }
575             tr_reject = 1;
576           }
577         }
578       }
579     }
580 
581     if (tr_reject) {
582       /* The trust-region constraints rejected the step.  Apply a linesearch.
583          Check for descent direction. */
584       ierr = VecDot(tao->stepdirection, tao->gradient, &gdx);CHKERRQ(ierr);
585       if ((gdx >= 0.0) || PetscIsInfOrNanReal(gdx)) {
586         /* Newton step is not descent or direction produced Inf or NaN */
587 
588         if (NTL_PC_BFGS != tl->pc_type) {
589           /* We don't have the bfgs matrix around and updated
590              Must use gradient direction in this case */
591           ierr = VecCopy(tao->gradient, tao->stepdirection);CHKERRQ(ierr);
592           ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
593           ++tl->grad;
594           stepType = NTL_GRADIENT;
595         } else {
596           /* Attempt to use the BFGS direction */
597           ierr = MatLMVMSolve(tl->M, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
598           ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
599 
600           /* Check for success (descent direction) */
601           ierr = VecDot(tao->stepdirection, tao->gradient, &gdx);CHKERRQ(ierr);
602           if ((gdx >= 0) || PetscIsInfOrNanReal(gdx)) {
603             /* BFGS direction is not descent or direction produced not a number
604                We can assert bfgsUpdates > 1 in this case because
605                the first solve produces the scaled gradient direction,
606                which is guaranteed to be descent */
607 
608             /* Use steepest descent direction (scaled) */
609             if (f != 0.0) {
610               delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
611             } else {
612               delta = 2.0 / (gnorm*gnorm);
613             }
614             ierr = MatLMVMSetDelta(tl->M, delta);CHKERRQ(ierr);
615             ierr = MatLMVMReset(tl->M);CHKERRQ(ierr);
616             ierr = MatLMVMUpdate(tl->M, tao->solution, tao->gradient);CHKERRQ(ierr);
617             ierr = MatLMVMSolve(tl->M, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
618             ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
619 
620             bfgsUpdates = 1;
621             ++tl->sgrad;
622             stepType = NTL_SCALED_GRADIENT;
623           } else {
624             if (1 == bfgsUpdates) {
625               /* The first BFGS direction is always the scaled gradient */
626               ++tl->sgrad;
627               stepType = NTL_SCALED_GRADIENT;
628             } else {
629               ++tl->bfgs;
630               stepType = NTL_BFGS;
631             }
632           }
633         }
634       } else {
635         /* Computed Newton step is descent */
636         ++tl->newt;
637         stepType = NTL_NEWTON;
638       }
639 
640       /* Perform the linesearch */
641       fold = f;
642       ierr = VecCopy(tao->solution, tl->Xold);CHKERRQ(ierr);
643       ierr = VecCopy(tao->gradient, tl->Gold);CHKERRQ(ierr);
644 
645       step = 1.0;
646       ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, tao->stepdirection, &step, &ls_reason);CHKERRQ(ierr);
647       ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);
648 
649       while (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER && stepType != NTL_GRADIENT) {      /* Linesearch failed */
650         /* Linesearch failed */
651         f = fold;
652         ierr = VecCopy(tl->Xold, tao->solution);CHKERRQ(ierr);
653         ierr = VecCopy(tl->Gold, tao->gradient);CHKERRQ(ierr);
654 
655         switch(stepType) {
656         case NTL_NEWTON:
657           /* Failed to obtain acceptable iterate with Newton step */
658 
659           if (NTL_PC_BFGS != tl->pc_type) {
660             /* We don't have the bfgs matrix around and being updated
661                Must use gradient direction in this case */
662             ierr = VecCopy(tao->gradient, tao->stepdirection);CHKERRQ(ierr);
663             ++tl->grad;
664             stepType = NTL_GRADIENT;
665           } else {
666             /* Attempt to use the BFGS direction */
667             ierr = MatLMVMSolve(tl->M, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
668 
669 
670             /* Check for success (descent direction) */
671             ierr = VecDot(tao->stepdirection, tao->gradient, &gdx);CHKERRQ(ierr);
672             if ((gdx <= 0) || PetscIsInfOrNanReal(gdx)) {
673               /* BFGS direction is not descent or direction produced
674                  not a number.  We can assert bfgsUpdates > 1 in this case
675                  Use steepest descent direction (scaled) */
676 
677               if (f != 0.0) {
678                 delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
679               } else {
680                 delta = 2.0 / (gnorm*gnorm);
681               }
682               ierr = MatLMVMSetDelta(tl->M, delta);CHKERRQ(ierr);
683               ierr = MatLMVMReset(tl->M);CHKERRQ(ierr);
684               ierr = MatLMVMUpdate(tl->M, tao->solution, tao->gradient);CHKERRQ(ierr);
685               ierr = MatLMVMSolve(tl->M, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
686 
687               bfgsUpdates = 1;
688               ++tl->sgrad;
689               stepType = NTL_SCALED_GRADIENT;
690             } else {
691               if (1 == bfgsUpdates) {
692                 /* The first BFGS direction is always the scaled gradient */
693                 ++tl->sgrad;
694                 stepType = NTL_SCALED_GRADIENT;
695               } else {
696                 ++tl->bfgs;
697                 stepType = NTL_BFGS;
698               }
699             }
700           }
701           break;
702 
703         case NTL_BFGS:
704           /* Can only enter if pc_type == NTL_PC_BFGS
705              Failed to obtain acceptable iterate with BFGS step
706              Attempt to use the scaled gradient direction */
707 
708           if (f != 0.0) {
709             delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
710           } else {
711             delta = 2.0 / (gnorm*gnorm);
712           }
713           ierr = MatLMVMSetDelta(tl->M, delta);CHKERRQ(ierr);
714           ierr = MatLMVMReset(tl->M);CHKERRQ(ierr);
715           ierr = MatLMVMUpdate(tl->M, tao->solution, tao->gradient);CHKERRQ(ierr);
716           ierr = MatLMVMSolve(tl->M, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
717 
718           bfgsUpdates = 1;
719           ++tl->sgrad;
720           stepType = NTL_SCALED_GRADIENT;
721           break;
722 
723         case NTL_SCALED_GRADIENT:
724           /* Can only enter if pc_type == NTL_PC_BFGS
725              The scaled gradient step did not produce a new iterate;
726              attemp to use the gradient direction.
727              Need to make sure we are not using a different diagonal scaling */
728           ierr = MatLMVMSetScale(tl->M, tl->Diag);CHKERRQ(ierr);
729           ierr = MatLMVMSetDelta(tl->M, 1.0);CHKERRQ(ierr);
730           ierr = MatLMVMReset(tl->M);CHKERRQ(ierr);
731           ierr = MatLMVMUpdate(tl->M, tao->solution, tao->gradient);CHKERRQ(ierr);
732           ierr = MatLMVMSolve(tl->M, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
733 
734           bfgsUpdates = 1;
735           ++tl->grad;
736           stepType = NTL_GRADIENT;
737           break;
738         }
739         ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
740 
741         /* This may be incorrect; linesearch has values for stepmax and stepmin
742            that should be reset. */
743         step = 1.0;
744         ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, tao->stepdirection, &step, &ls_reason);CHKERRQ(ierr);
745         ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);
746       }
747 
748       if (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER) {
749         /* Failed to find an improving point */
750         f = fold;
751         ierr = VecCopy(tl->Xold, tao->solution);CHKERRQ(ierr);
752         ierr = VecCopy(tl->Gold, tao->gradient);CHKERRQ(ierr);
753         tao->trust = 0.0;
754         step = 0.0;
755         reason = TAO_DIVERGED_LS_FAILURE;
756         tao->reason = TAO_DIVERGED_LS_FAILURE;
757         break;
758       } else if (stepType == NTL_NEWTON) {
759         if (step < tl->nu1) {
760           /* Very bad step taken; reduce radius */
761           tao->trust = tl->omega1 * PetscMin(norm_d, tao->trust);
762         } else if (step < tl->nu2) {
763           /* Reasonably bad step taken; reduce radius */
764           tao->trust = tl->omega2 * PetscMin(norm_d, tao->trust);
765         } else if (step < tl->nu3) {
766           /* Reasonable step was taken; leave radius alone */
767           if (tl->omega3 < 1.0) {
768             tao->trust = tl->omega3 * PetscMin(norm_d, tao->trust);
769           } else if (tl->omega3 > 1.0) {
770             tao->trust = PetscMax(tl->omega3 * norm_d, tao->trust);
771           }
772         } else if (step < tl->nu4) {
773           /* Full step taken; increase the radius */
774           tao->trust = PetscMax(tl->omega4 * norm_d, tao->trust);
775         } else {
776           /* More than full step taken; increase the radius */
777           tao->trust = PetscMax(tl->omega5 * norm_d, tao->trust);
778         }
779       } else {
780         /* Newton step was not good; reduce the radius */
781         tao->trust = tl->omega1 * PetscMin(norm_d, tao->trust);
782       }
783     } else {
784       /* Trust-region step is accepted */
785       ierr = VecCopy(tl->W, tao->solution);CHKERRQ(ierr);
786       f = ftrial;
787       ierr = TaoComputeGradient(tao, tao->solution, tao->gradient);CHKERRQ(ierr);
788       ++tl->ntrust;
789     }
790 
791     /* The radius may have been increased; modify if it is too large */
792     tao->trust = PetscMin(tao->trust, tl->max_radius);
793 
794     /* Check for converged */
795     ierr = VecNorm(tao->gradient, NORM_2, &gnorm);CHKERRQ(ierr);
796     if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1,"User provided compute function generated Not-a-Number");
797     needH = 1;
798 
799     ierr = TaoMonitor(tao, iter, f, gnorm, 0.0, tao->trust, &reason);CHKERRQ(ierr);
800   }
801   PetscFunctionReturn(0);
802 }
803 
804 /* ---------------------------------------------------------- */
805 #undef __FUNCT__
806 #define __FUNCT__ "TaoSetUp_NTL"
807 static PetscErrorCode TaoSetUp_NTL(Tao tao)
808 {
809   TAO_NTL        *tl = (TAO_NTL *)tao->data;
810   PetscErrorCode ierr;
811 
812   PetscFunctionBegin;
813   if (!tao->gradient) {ierr = VecDuplicate(tao->solution, &tao->gradient);CHKERRQ(ierr); }
814   if (!tao->stepdirection) {ierr = VecDuplicate(tao->solution, &tao->stepdirection);CHKERRQ(ierr);}
815   if (!tl->W) { ierr = VecDuplicate(tao->solution, &tl->W);CHKERRQ(ierr);}
816   if (!tl->Xold) { ierr = VecDuplicate(tao->solution, &tl->Xold);CHKERRQ(ierr);}
817   if (!tl->Gold) { ierr = VecDuplicate(tao->solution, &tl->Gold);CHKERRQ(ierr);}
818   tl->Diag = 0;
819   tl->M = 0;
820   PetscFunctionReturn(0);
821 }
822 
823 /*------------------------------------------------------------*/
824 #undef __FUNCT__
825 #define __FUNCT__ "TaoDestroy_NTL"
826 static PetscErrorCode TaoDestroy_NTL(Tao tao)
827 {
828   TAO_NTL        *tl = (TAO_NTL *)tao->data;
829   PetscErrorCode ierr;
830 
831   PetscFunctionBegin;
832   if (tao->setupcalled) {
833     ierr = VecDestroy(&tl->W);CHKERRQ(ierr);
834     ierr = VecDestroy(&tl->Xold);CHKERRQ(ierr);
835     ierr = VecDestroy(&tl->Gold);CHKERRQ(ierr);
836   }
837   ierr = VecDestroy(&tl->Diag);CHKERRQ(ierr);
838   ierr = MatDestroy(&tl->M);CHKERRQ(ierr);
839   ierr = PetscFree(tao->data);CHKERRQ(ierr);
840   PetscFunctionReturn(0);
841 }
842 
843 /*------------------------------------------------------------*/
844 #undef __FUNCT__
845 #define __FUNCT__ "TaoSetFromOptions_NTL"
846 static PetscErrorCode TaoSetFromOptions_NTL(Tao tao)
847 {
848   TAO_NTL        *tl = (TAO_NTL *)tao->data;
849   PetscErrorCode ierr;
850 
851   PetscFunctionBegin;
852   ierr = PetscOptionsHead("Newton line search method for unconstrained optimization");CHKERRQ(ierr);
853   ierr = PetscOptionsEList("-tao_ntl_ksp_type", "ksp type", "", NTL_KSP, NTL_KSP_TYPES, NTL_KSP[tl->ksp_type], &tl->ksp_type, 0);CHKERRQ(ierr);
854   ierr = PetscOptionsEList("-tao_ntl_pc_type", "pc type", "", NTL_PC, NTL_PC_TYPES, NTL_PC[tl->pc_type], &tl->pc_type, 0);CHKERRQ(ierr);
855   ierr = PetscOptionsEList("-tao_ntl_bfgs_scale_type", "bfgs scale type", "", BFGS_SCALE, BFGS_SCALE_TYPES, BFGS_SCALE[tl->bfgs_scale_type], &tl->bfgs_scale_type, 0);CHKERRQ(ierr);
856   ierr = PetscOptionsEList("-tao_ntl_init_type", "radius initialization type", "", NTL_INIT, NTL_INIT_TYPES, NTL_INIT[tl->init_type], &tl->init_type, 0);CHKERRQ(ierr);
857   ierr = PetscOptionsEList("-tao_ntl_update_type", "radius update type", "", NTL_UPDATE, NTL_UPDATE_TYPES, NTL_UPDATE[tl->update_type], &tl->update_type, 0);CHKERRQ(ierr);
858   ierr = PetscOptionsReal("-tao_ntl_eta1", "poor steplength; reduce radius", "", tl->eta1, &tl->eta1, 0);CHKERRQ(ierr);
859   ierr = PetscOptionsReal("-tao_ntl_eta2", "reasonable steplength; leave radius alone", "", tl->eta2, &tl->eta2, 0);CHKERRQ(ierr);
860   ierr = PetscOptionsReal("-tao_ntl_eta3", "good steplength; increase radius", "", tl->eta3, &tl->eta3, 0);CHKERRQ(ierr);
861   ierr = PetscOptionsReal("-tao_ntl_eta4", "excellent steplength; greatly increase radius", "", tl->eta4, &tl->eta4, 0);CHKERRQ(ierr);
862   ierr = PetscOptionsReal("-tao_ntl_alpha1", "", "", tl->alpha1, &tl->alpha1, 0);CHKERRQ(ierr);
863   ierr = PetscOptionsReal("-tao_ntl_alpha2", "", "", tl->alpha2, &tl->alpha2, 0);CHKERRQ(ierr);
864   ierr = PetscOptionsReal("-tao_ntl_alpha3", "", "", tl->alpha3, &tl->alpha3, 0);CHKERRQ(ierr);
865   ierr = PetscOptionsReal("-tao_ntl_alpha4", "", "", tl->alpha4, &tl->alpha4, 0);CHKERRQ(ierr);
866   ierr = PetscOptionsReal("-tao_ntl_alpha5", "", "", tl->alpha5, &tl->alpha5, 0);CHKERRQ(ierr);
867   ierr = PetscOptionsReal("-tao_ntl_nu1", "poor steplength; reduce radius", "", tl->nu1, &tl->nu1, 0);CHKERRQ(ierr);
868   ierr = PetscOptionsReal("-tao_ntl_nu2", "reasonable steplength; leave radius alone", "", tl->nu2, &tl->nu2, 0);CHKERRQ(ierr);
869   ierr = PetscOptionsReal("-tao_ntl_nu3", "good steplength; increase radius", "", tl->nu3, &tl->nu3, 0);CHKERRQ(ierr);
870   ierr = PetscOptionsReal("-tao_ntl_nu4", "excellent steplength; greatly increase radius", "", tl->nu4, &tl->nu4, 0);CHKERRQ(ierr);
871   ierr = PetscOptionsReal("-tao_ntl_omega1", "", "", tl->omega1, &tl->omega1, 0);CHKERRQ(ierr);
872   ierr = PetscOptionsReal("-tao_ntl_omega2", "", "", tl->omega2, &tl->omega2, 0);CHKERRQ(ierr);
873   ierr = PetscOptionsReal("-tao_ntl_omega3", "", "", tl->omega3, &tl->omega3, 0);CHKERRQ(ierr);
874   ierr = PetscOptionsReal("-tao_ntl_omega4", "", "", tl->omega4, &tl->omega4, 0);CHKERRQ(ierr);
875   ierr = PetscOptionsReal("-tao_ntl_omega5", "", "", tl->omega5, &tl->omega5, 0);CHKERRQ(ierr);
876   ierr = PetscOptionsReal("-tao_ntl_mu1_i", "", "", tl->mu1_i, &tl->mu1_i, 0);CHKERRQ(ierr);
877   ierr = PetscOptionsReal("-tao_ntl_mu2_i", "", "", tl->mu2_i, &tl->mu2_i, 0);CHKERRQ(ierr);
878   ierr = PetscOptionsReal("-tao_ntl_gamma1_i", "", "", tl->gamma1_i, &tl->gamma1_i, 0);CHKERRQ(ierr);
879   ierr = PetscOptionsReal("-tao_ntl_gamma2_i", "", "", tl->gamma2_i, &tl->gamma2_i, 0);CHKERRQ(ierr);
880   ierr = PetscOptionsReal("-tao_ntl_gamma3_i", "", "", tl->gamma3_i, &tl->gamma3_i, 0);CHKERRQ(ierr);
881   ierr = PetscOptionsReal("-tao_ntl_gamma4_i", "", "", tl->gamma4_i, &tl->gamma4_i, 0);CHKERRQ(ierr);
882   ierr = PetscOptionsReal("-tao_ntl_theta_i", "", "", tl->theta_i, &tl->theta_i, 0);CHKERRQ(ierr);
883   ierr = PetscOptionsReal("-tao_ntl_mu1", "", "", tl->mu1, &tl->mu1, 0);CHKERRQ(ierr);
884   ierr = PetscOptionsReal("-tao_ntl_mu2", "", "", tl->mu2, &tl->mu2, 0);CHKERRQ(ierr);
885   ierr = PetscOptionsReal("-tao_ntl_gamma1", "", "", tl->gamma1, &tl->gamma1, 0);CHKERRQ(ierr);
886   ierr = PetscOptionsReal("-tao_ntl_gamma2", "", "", tl->gamma2, &tl->gamma2, 0);CHKERRQ(ierr);
887   ierr = PetscOptionsReal("-tao_ntl_gamma3", "", "", tl->gamma3, &tl->gamma3, 0);CHKERRQ(ierr);
888   ierr = PetscOptionsReal("-tao_ntl_gamma4", "", "", tl->gamma4, &tl->gamma4, 0);CHKERRQ(ierr);
889   ierr = PetscOptionsReal("-tao_ntl_theta", "", "", tl->theta, &tl->theta, 0);CHKERRQ(ierr);
890   ierr = PetscOptionsReal("-tao_ntl_min_radius", "lower bound on initial radius", "", tl->min_radius, &tl->min_radius, 0);CHKERRQ(ierr);
891   ierr = PetscOptionsReal("-tao_ntl_max_radius", "upper bound on radius", "", tl->max_radius, &tl->max_radius, 0);CHKERRQ(ierr);
892   ierr = PetscOptionsReal("-tao_ntl_epsilon", "tolerance used when computing actual and predicted reduction", "", tl->epsilon, &tl->epsilon, 0);CHKERRQ(ierr);
893   ierr = PetscOptionsTail();CHKERRQ(ierr);
894   ierr = TaoLineSearchSetFromOptions(tao->linesearch);CHKERRQ(ierr);
895   ierr = KSPSetFromOptions(tao->ksp);CHKERRQ(ierr);
896   PetscFunctionReturn(0);
897 }
898 
899 /*------------------------------------------------------------*/
900 #undef __FUNCT__
901 #define __FUNCT__ "TaoView_NTL"
902 static PetscErrorCode TaoView_NTL(Tao tao, PetscViewer viewer)
903 {
904   TAO_NTL        *tl = (TAO_NTL *)tao->data;
905   PetscInt       nrejects;
906   PetscBool      isascii;
907   PetscErrorCode ierr;
908 
909   PetscFunctionBegin;
910   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);
911   if (isascii) {
912     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
913     if (NTL_PC_BFGS == tl->pc_type && tl->M) {
914       ierr = MatLMVMGetRejects(tl->M, &nrejects);CHKERRQ(ierr);
915       ierr = PetscViewerASCIIPrintf(viewer, "Rejected matrix updates: %D\n", nrejects);CHKERRQ(ierr);
916     }
917     ierr = PetscViewerASCIIPrintf(viewer, "Trust-region steps: %D\n", tl->ntrust);CHKERRQ(ierr);
918     ierr = PetscViewerASCIIPrintf(viewer, "Newton search steps: %D\n", tl->newt);CHKERRQ(ierr);
919     ierr = PetscViewerASCIIPrintf(viewer, "BFGS search steps: %D\n", tl->bfgs);CHKERRQ(ierr);
920     ierr = PetscViewerASCIIPrintf(viewer, "Scaled gradient search steps: %D\n", tl->sgrad);CHKERRQ(ierr);
921     ierr = PetscViewerASCIIPrintf(viewer, "Gradient search steps: %D\n", tl->grad);CHKERRQ(ierr);
922     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
923   }
924   PetscFunctionReturn(0);
925 }
926 
927 /* ---------------------------------------------------------- */
928 EXTERN_C_BEGIN
929 #undef __FUNCT__
930 #define __FUNCT__ "TaoCreate_NTL"
931 PetscErrorCode TaoCreate_NTL(Tao tao)
932 {
933   TAO_NTL        *tl;
934   PetscErrorCode ierr;
935   const char     *morethuente_type = TAOLINESEARCH_MT;
936 
937   PetscFunctionBegin;
938   ierr = PetscNewLog(tao,&tl);CHKERRQ(ierr);
939   tao->ops->setup = TaoSetUp_NTL;
940   tao->ops->solve = TaoSolve_NTL;
941   tao->ops->view = TaoView_NTL;
942   tao->ops->setfromoptions = TaoSetFromOptions_NTL;
943   tao->ops->destroy = TaoDestroy_NTL;
944 
945   tao->max_it = 50;
946 #if defined(PETSC_USE_REAL_SINGLE)
947   tao->fatol = 1e-5;
948   tao->frtol = 1e-5;
949 #else
950   tao->fatol = 1e-10;
951   tao->frtol = 1e-10;
952 #endif
953   tao->data = (void*)tl;
954 
955   tao->trust0 = 100.0;
956 
957 
958   /* Default values for trust-region radius update based on steplength */
959   tl->nu1 = 0.25;
960   tl->nu2 = 0.50;
961   tl->nu3 = 1.00;
962   tl->nu4 = 1.25;
963 
964   tl->omega1 = 0.25;
965   tl->omega2 = 0.50;
966   tl->omega3 = 1.00;
967   tl->omega4 = 2.00;
968   tl->omega5 = 4.00;
969 
970   /* Default values for trust-region radius update based on reduction */
971   tl->eta1 = 1.0e-4;
972   tl->eta2 = 0.25;
973   tl->eta3 = 0.50;
974   tl->eta4 = 0.90;
975 
976   tl->alpha1 = 0.25;
977   tl->alpha2 = 0.50;
978   tl->alpha3 = 1.00;
979   tl->alpha4 = 2.00;
980   tl->alpha5 = 4.00;
981 
982   /* Default values for trust-region radius update based on interpolation */
983   tl->mu1 = 0.10;
984   tl->mu2 = 0.50;
985 
986   tl->gamma1 = 0.25;
987   tl->gamma2 = 0.50;
988   tl->gamma3 = 2.00;
989   tl->gamma4 = 4.00;
990 
991   tl->theta = 0.05;
992 
993   /* Default values for trust region initialization based on interpolation */
994   tl->mu1_i = 0.35;
995   tl->mu2_i = 0.50;
996 
997   tl->gamma1_i = 0.0625;
998   tl->gamma2_i = 0.5;
999   tl->gamma3_i = 2.0;
1000   tl->gamma4_i = 5.0;
1001 
1002   tl->theta_i = 0.25;
1003 
1004   /* Remaining parameters */
1005   tl->min_radius = 1.0e-10;
1006   tl->max_radius = 1.0e10;
1007   tl->epsilon = 1.0e-6;
1008 
1009   tl->ksp_type        = NTL_KSP_STCG;
1010   tl->pc_type         = NTL_PC_BFGS;
1011   tl->bfgs_scale_type = BFGS_SCALE_AHESS;
1012   tl->init_type       = NTL_INIT_INTERPOLATION;
1013   tl->update_type     = NTL_UPDATE_REDUCTION;
1014 
1015   ierr = TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch);CHKERRQ(ierr);
1016   ierr = TaoLineSearchSetType(tao->linesearch, morethuente_type);CHKERRQ(ierr);
1017   ierr = TaoLineSearchUseTaoRoutines(tao->linesearch, tao);CHKERRQ(ierr);
1018   ierr = KSPCreate(((PetscObject)tao)->comm, &tao->ksp);CHKERRQ(ierr);
1019   PetscFunctionReturn(0);
1020 }
1021 EXTERN_C_END
1022 
1023 
1024 
1025