Actual source code: ntl.c
petsc-3.7.7 2017-09-25
1: #include <../src/tao/matrix/lmvmmat.h>
2: #include <../src/tao/unconstrained/impls/ntl/ntl.h>
4: #include <petscksp.h>
5: #include <petscpc.h>
6: #include <petsc/private/kspimpl.h>
7: #include <petsc/private/pcimpl.h>
9: #define NTL_KSP_NASH 0
10: #define NTL_KSP_STCG 1
11: #define NTL_KSP_GLTR 2
12: #define NTL_KSP_TYPES 3
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
20: #define BFGS_SCALE_AHESS 0
21: #define BFGS_SCALE_BFGS 1
22: #define BFGS_SCALE_TYPES 2
24: #define NTL_INIT_CONSTANT 0
25: #define NTL_INIT_DIRECTION 1
26: #define NTL_INIT_INTERPOLATION 2
27: #define NTL_INIT_TYPES 3
29: #define NTL_UPDATE_REDUCTION 0
30: #define NTL_UPDATE_INTERPOLATION 1
31: #define NTL_UPDATE_TYPES 2
33: static const char *NTL_KSP[64] = {"nash", "stcg", "gltr"};
35: static const char *NTL_PC[64] = {"none", "ahess", "bfgs", "petsc"};
37: static const char *BFGS_SCALE[64] = {"ahess", "bfgs"};
39: static const char *NTL_INIT[64] = {"constant", "direction", "interpolation"};
41: static const char *NTL_UPDATE[64] = {"reduction", "interpolation"};
43: /* Routine for BFGS preconditioner */
47: static PetscErrorCode MatLMVMSolveShell(PC pc, Vec b, Vec x)
48: {
50: Mat M;
56: PCShellGetContext(pc,(void**)&M);
57: MatLMVMSolve(M, b, x);
58: return(0);
59: }
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. */
66: #define NTL_NEWTON 0
67: #define NTL_BFGS 1
68: #define NTL_SCALED_GRADIENT 2
69: #define NTL_GRADIENT 3
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;
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;
86: PetscReal delta;
87: PetscReal norm_d = 0.0;
88: PetscErrorCode ierr;
89: PetscInt stepType;
90: PetscInt its;
92: PetscInt bfgsUpdates = 0;
93: PetscInt needH;
95: PetscInt i_max = 5;
96: PetscInt j_max = 1;
97: PetscInt i, j, n, N;
99: PetscInt tr_reject;
102: if (tao->XL || tao->XU || tao->ops->computebounds) {
103: PetscPrintf(((PetscObject)tao)->comm,"WARNING: Variable bounds have been set but will be ignored by ntl algorithm\n");
104: }
106: /* Initialize trust-region radius */
107: tao->trust = tao->trust0;
109: /* Modify the radius if it is too large or small */
110: tao->trust = PetscMax(tao->trust, tl->min_radius);
111: tao->trust = PetscMin(tao->trust, tl->max_radius);
113: if (NTL_PC_BFGS == tl->pc_type && !tl->M) {
114: VecGetLocalSize(tao->solution,&n);
115: VecGetSize(tao->solution,&N);
116: MatCreateLMVM(((PetscObject)tao)->comm,n,N,&tl->M);
117: MatLMVMAllocateVectors(tl->M,tao->solution);
118: }
120: /* Check convergence criteria */
121: TaoComputeObjectiveAndGradient(tao, tao->solution, &f, tao->gradient);
122: VecNorm(tao->gradient, NORM_2, &gnorm);
123: if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
124: needH = 1;
126: TaoMonitor(tao, tao->niter, f, gnorm, 0.0, 1.0, &reason);
127: if (reason != TAO_CONTINUE_ITERATING) return(0);
129: /* Create vectors for the limited memory preconditioner */
130: if ((NTL_PC_BFGS == tl->pc_type) && (BFGS_SCALE_BFGS != tl->bfgs_scale_type)) {
131: if (!tl->Diag) {
132: VecDuplicate(tao->solution, &tl->Diag);
133: }
134: }
136: /* Modify the linear solver to a conjugate gradient method */
137: switch(tl->ksp_type) {
138: case NTL_KSP_NASH:
139: KSPSetType(tao->ksp, KSPNASH);
140: KSPSetFromOptions(tao->ksp);
141: break;
143: case NTL_KSP_STCG:
144: KSPSetType(tao->ksp, KSPSTCG);
145: KSPSetFromOptions(tao->ksp);
146: break;
148: default:
149: KSPSetType(tao->ksp, KSPGLTR);
150: KSPSetFromOptions(tao->ksp);
151: break;
152: }
154: /* Modify the preconditioner to use the bfgs approximation */
155: KSPGetPC(tao->ksp, &pc);
156: switch(tl->pc_type) {
157: case NTL_PC_NONE:
158: PCSetType(pc, PCNONE);
159: PCSetFromOptions(pc);
160: break;
162: case NTL_PC_AHESS:
163: PCSetType(pc, PCJACOBI);
164: PCSetFromOptions(pc);
165: PCJacobiSetUseAbs(pc,PETSC_TRUE);
166: break;
168: case NTL_PC_BFGS:
169: PCSetType(pc, PCSHELL);
170: PCSetFromOptions(pc);
171: PCShellSetName(pc, "bfgs");
172: PCShellSetContext(pc, tl->M);
173: PCShellSetApply(pc, MatLMVMSolveShell);
174: break;
176: default:
177: /* Use the pc method set by pc_type */
178: break;
179: }
181: /* Initialize trust-region radius. The initialization is only performed
182: when we are using Steihaug-Toint or the Generalized Lanczos method. */
183: switch(tl->init_type) {
184: case NTL_INIT_CONSTANT:
185: /* Use the initial radius specified */
186: break;
188: case NTL_INIT_INTERPOLATION:
189: /* Use the initial radius specified */
190: max_radius = 0.0;
192: for (j = 0; j < j_max; ++j) {
193: fmin = f;
194: sigma = 0.0;
196: if (needH) {
197: TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);
198: needH = 0;
199: }
201: for (i = 0; i < i_max; ++i) {
202: VecCopy(tao->solution, tl->W);
203: VecAXPY(tl->W, -tao->trust/gnorm, tao->gradient);
205: TaoComputeObjective(tao, tl->W, &ftrial);
206: if (PetscIsInfOrNanReal(ftrial)) {
207: tau = tl->gamma1_i;
208: } else {
209: if (ftrial < fmin) {
210: fmin = ftrial;
211: sigma = -tao->trust / gnorm;
212: }
214: MatMult(tao->hessian, tao->gradient, tao->stepdirection);
215: VecDot(tao->gradient, tao->stepdirection, &prered);
217: prered = tao->trust * (gnorm - 0.5 * tao->trust * prered / (gnorm * gnorm));
218: actred = f - ftrial;
219: if ((PetscAbsScalar(actred) <= tl->epsilon) && (PetscAbsScalar(prered) <= tl->epsilon)) {
220: kappa = 1.0;
221: } else {
222: kappa = actred / prered;
223: }
225: tau_1 = tl->theta_i * gnorm * tao->trust / (tl->theta_i * gnorm * tao->trust + (1.0 - tl->theta_i) * prered - actred);
226: tau_2 = tl->theta_i * gnorm * tao->trust / (tl->theta_i * gnorm * tao->trust - (1.0 + tl->theta_i) * prered + actred);
227: tau_min = PetscMin(tau_1, tau_2);
228: tau_max = PetscMax(tau_1, tau_2);
230: if (PetscAbsScalar(kappa - 1.0) <= tl->mu1_i) {
231: /* Great agreement */
232: max_radius = PetscMax(max_radius, tao->trust);
234: if (tau_max < 1.0) {
235: tau = tl->gamma3_i;
236: } else if (tau_max > tl->gamma4_i) {
237: tau = tl->gamma4_i;
238: } else if (tau_1 >= 1.0 && tau_1 <= tl->gamma4_i && tau_2 < 1.0) {
239: tau = tau_1;
240: } else if (tau_2 >= 1.0 && tau_2 <= tl->gamma4_i && tau_1 < 1.0) {
241: tau = tau_2;
242: } else {
243: tau = tau_max;
244: }
245: } else if (PetscAbsScalar(kappa - 1.0) <= tl->mu2_i) {
246: /* Good agreement */
247: max_radius = PetscMax(max_radius, tao->trust);
249: if (tau_max < tl->gamma2_i) {
250: tau = tl->gamma2_i;
251: } else if (tau_max > tl->gamma3_i) {
252: tau = tl->gamma3_i;
253: } else {
254: tau = tau_max;
255: }
256: } else {
257: /* Not good agreement */
258: if (tau_min > 1.0) {
259: tau = tl->gamma2_i;
260: } else if (tau_max < tl->gamma1_i) {
261: tau = tl->gamma1_i;
262: } else if ((tau_min < tl->gamma1_i) && (tau_max >= 1.0)) {
263: tau = tl->gamma1_i;
264: } else if ((tau_1 >= tl->gamma1_i) && (tau_1 < 1.0) && ((tau_2 < tl->gamma1_i) || (tau_2 >= 1.0))) {
265: tau = tau_1;
266: } else if ((tau_2 >= tl->gamma1_i) && (tau_2 < 1.0) && ((tau_1 < tl->gamma1_i) || (tau_2 >= 1.0))) {
267: tau = tau_2;
268: } else {
269: tau = tau_max;
270: }
271: }
272: }
273: tao->trust = tau * tao->trust;
274: }
276: if (fmin < f) {
277: f = fmin;
278: VecAXPY(tao->solution, sigma, tao->gradient);
279: TaoComputeGradient(tao, tao->solution, tao->gradient);
281: VecNorm(tao->gradient, NORM_2, &gnorm);
282: if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
283: needH = 1;
285: TaoMonitor(tao, tao->niter, f, gnorm, 0.0, 1.0, &reason);
286: if (reason != TAO_CONTINUE_ITERATING) return(0);
287: }
288: }
289: tao->trust = PetscMax(tao->trust, max_radius);
291: /* Modify the radius if it is too large or small */
292: tao->trust = PetscMax(tao->trust, tl->min_radius);
293: tao->trust = PetscMin(tao->trust, tl->max_radius);
294: break;
296: default:
297: /* Norm of the first direction will initialize radius */
298: tao->trust = 0.0;
299: break;
300: }
302: /* Set initial scaling for the BFGS preconditioner
303: This step is done after computing the initial trust-region radius
304: since the function value may have decreased */
305: if (NTL_PC_BFGS == tl->pc_type) {
306: if (f != 0.0) {
307: delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
308: } else {
309: delta = 2.0 / (gnorm*gnorm);
310: }
311: MatLMVMSetDelta(tl->M, delta);
312: }
314: /* Set counter for gradient/reset steps */
315: tl->ntrust = 0;
316: tl->newt = 0;
317: tl->bfgs = 0;
318: tl->sgrad = 0;
319: tl->grad = 0;
321: /* Have not converged; continue with Newton method */
322: while (reason == TAO_CONTINUE_ITERATING) {
323: ++tao->niter;
324: tao->ksp_its=0;
325: /* Compute the Hessian */
326: if (needH) {
327: TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);
328: }
330: if (NTL_PC_BFGS == tl->pc_type) {
331: if (BFGS_SCALE_AHESS == tl->bfgs_scale_type) {
332: /* Obtain diagonal for the bfgs preconditioner */
333: MatGetDiagonal(tao->hessian, tl->Diag);
334: VecAbs(tl->Diag);
335: VecReciprocal(tl->Diag);
336: MatLMVMSetScale(tl->M, tl->Diag);
337: }
339: /* Update the limited memory preconditioner */
340: MatLMVMUpdate(tl->M,tao->solution, tao->gradient);
341: ++bfgsUpdates;
342: }
343: KSPSetOperators(tao->ksp, tao->hessian, tao->hessian_pre);
344: /* Solve the Newton system of equations */
345: if (NTL_KSP_NASH == tl->ksp_type) {
346: KSPNASHSetRadius(tao->ksp,tl->max_radius);
347: KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);
348: KSPGetIterationNumber(tao->ksp,&its);
349: tao->ksp_its+=its;
350: tao->ksp_tot_its+=its;
351: KSPNASHGetNormD(tao->ksp, &norm_d);
352: } else if (NTL_KSP_STCG == tl->ksp_type) {
353: KSPSTCGSetRadius(tao->ksp,tl->max_radius);
354: KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);
355: KSPGetIterationNumber(tao->ksp,&its);
356: tao->ksp_its+=its;
357: tao->ksp_tot_its+=its;
358: KSPSTCGGetNormD(tao->ksp, &norm_d);
359: } else { /* NTL_KSP_GLTR */
360: KSPGLTRSetRadius(tao->ksp,tl->max_radius);
361: KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);
362: KSPGetIterationNumber(tao->ksp,&its);
363: tao->ksp_its+=its;
364: tao->ksp_tot_its+=its;
365: KSPGLTRGetNormD(tao->ksp, &norm_d);
366: }
368: if (0.0 == tao->trust) {
369: /* Radius was uninitialized; use the norm of the direction */
370: if (norm_d > 0.0) {
371: tao->trust = norm_d;
373: /* Modify the radius if it is too large or small */
374: tao->trust = PetscMax(tao->trust, tl->min_radius);
375: tao->trust = PetscMin(tao->trust, tl->max_radius);
376: } else {
377: /* The direction was bad; set radius to default value and re-solve
378: the trust-region subproblem to get a direction */
379: tao->trust = tao->trust0;
381: /* Modify the radius if it is too large or small */
382: tao->trust = PetscMax(tao->trust, tl->min_radius);
383: tao->trust = PetscMin(tao->trust, tl->max_radius);
385: if (NTL_KSP_NASH == tl->ksp_type) {
386: KSPNASHSetRadius(tao->ksp,tl->max_radius);
387: KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);
388: KSPGetIterationNumber(tao->ksp,&its);
389: tao->ksp_its+=its;
390: tao->ksp_tot_its+=its;
391: KSPNASHGetNormD(tao->ksp, &norm_d);
392: } else if (NTL_KSP_STCG == tl->ksp_type) {
393: KSPSTCGSetRadius(tao->ksp,tl->max_radius);
394: KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);
395: KSPGetIterationNumber(tao->ksp,&its);
396: tao->ksp_its+=its;
397: tao->ksp_tot_its+=its;
398: KSPSTCGGetNormD(tao->ksp, &norm_d);
399: } else { /* NTL_KSP_GLTR */
400: KSPGLTRSetRadius(tao->ksp,tl->max_radius);
401: KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);
402: KSPGetIterationNumber(tao->ksp,&its);
403: tao->ksp_its+=its;
404: tao->ksp_tot_its+=its;
405: KSPGLTRGetNormD(tao->ksp, &norm_d);
406: }
409: if (norm_d == 0.0) SETERRQ(PETSC_COMM_SELF,1, "Initial direction zero");
410: }
411: }
413: VecScale(tao->stepdirection, -1.0);
414: KSPGetConvergedReason(tao->ksp, &ksp_reason);
415: if ((KSP_DIVERGED_INDEFINITE_PC == ksp_reason) && (NTL_PC_BFGS == tl->pc_type) && (bfgsUpdates > 1)) {
416: /* Preconditioner is numerically indefinite; reset the
417: approximate if using BFGS preconditioning. */
419: if (f != 0.0) {
420: delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
421: } else {
422: delta = 2.0 / (gnorm*gnorm);
423: }
424: MatLMVMSetDelta(tl->M, delta);
425: MatLMVMReset(tl->M);
426: MatLMVMUpdate(tl->M, tao->solution, tao->gradient);
427: bfgsUpdates = 1;
428: }
430: /* Check trust-region reduction conditions */
431: tr_reject = 0;
432: if (NTL_UPDATE_REDUCTION == tl->update_type) {
433: /* Get predicted reduction */
434: if (NTL_KSP_NASH == tl->ksp_type) {
435: KSPNASHGetObjFcn(tao->ksp,&prered);
436: } else if (NTL_KSP_STCG == tl->ksp_type) {
437: KSPSTCGGetObjFcn(tao->ksp,&prered);
438: } else { /* gltr */
439: KSPGLTRGetObjFcn(tao->ksp,&prered);
440: }
442: if (prered >= 0.0) {
443: /* The predicted reduction has the wrong sign. This cannot
444: happen in infinite precision arithmetic. Step should
445: be rejected! */
446: tao->trust = tl->alpha1 * PetscMin(tao->trust, norm_d);
447: tr_reject = 1;
448: } else {
449: /* Compute trial step and function value */
450: VecCopy(tao->solution, tl->W);
451: VecAXPY(tl->W, 1.0, tao->stepdirection);
452: TaoComputeObjective(tao, tl->W, &ftrial);
454: if (PetscIsInfOrNanReal(ftrial)) {
455: tao->trust = tl->alpha1 * PetscMin(tao->trust, norm_d);
456: tr_reject = 1;
457: } else {
458: /* Compute and actual reduction */
459: actred = f - ftrial;
460: prered = -prered;
461: if ((PetscAbsScalar(actred) <= tl->epsilon) &&
462: (PetscAbsScalar(prered) <= tl->epsilon)) {
463: kappa = 1.0;
464: } else {
465: kappa = actred / prered;
466: }
468: /* Accept of reject the step and update radius */
469: if (kappa < tl->eta1) {
470: /* Reject the step */
471: tao->trust = tl->alpha1 * PetscMin(tao->trust, norm_d);
472: tr_reject = 1;
473: } else {
474: /* Accept the step */
475: if (kappa < tl->eta2) {
476: /* Marginal bad step */
477: tao->trust = tl->alpha2 * PetscMin(tao->trust, norm_d);
478: } else if (kappa < tl->eta3) {
479: /* Reasonable step */
480: tao->trust = tl->alpha3 * tao->trust;
481: } else if (kappa < tl->eta4) {
482: /* Good step */
483: tao->trust = PetscMax(tl->alpha4 * norm_d, tao->trust);
484: } else {
485: /* Very good step */
486: tao->trust = PetscMax(tl->alpha5 * norm_d, tao->trust);
487: }
488: }
489: }
490: }
491: } else {
492: /* Get predicted reduction */
493: if (NTL_KSP_NASH == tl->ksp_type) {
494: KSPNASHGetObjFcn(tao->ksp,&prered);
495: } else if (NTL_KSP_STCG == tl->ksp_type) {
496: KSPSTCGGetObjFcn(tao->ksp,&prered);
497: } else { /* gltr */
498: KSPGLTRGetObjFcn(tao->ksp,&prered);
499: }
501: if (prered >= 0.0) {
502: /* The predicted reduction has the wrong sign. This cannot
503: happen in infinite precision arithmetic. Step should
504: be rejected! */
505: tao->trust = tl->gamma1 * PetscMin(tao->trust, norm_d);
506: tr_reject = 1;
507: } else {
508: VecCopy(tao->solution, tl->W);
509: VecAXPY(tl->W, 1.0, tao->stepdirection);
510: TaoComputeObjective(tao, tl->W, &ftrial);
511: if (PetscIsInfOrNanReal(ftrial)) {
512: tao->trust = tl->gamma1 * PetscMin(tao->trust, norm_d);
513: tr_reject = 1;
514: } else {
515: VecDot(tao->gradient, tao->stepdirection, &gdx);
517: actred = f - ftrial;
518: prered = -prered;
519: if ((PetscAbsScalar(actred) <= tl->epsilon) &&
520: (PetscAbsScalar(prered) <= tl->epsilon)) {
521: kappa = 1.0;
522: } else {
523: kappa = actred / prered;
524: }
526: tau_1 = tl->theta * gdx / (tl->theta * gdx - (1.0 - tl->theta) * prered + actred);
527: tau_2 = tl->theta * gdx / (tl->theta * gdx + (1.0 + tl->theta) * prered - actred);
528: tau_min = PetscMin(tau_1, tau_2);
529: tau_max = PetscMax(tau_1, tau_2);
531: if (kappa >= 1.0 - tl->mu1) {
532: /* Great agreement; accept step and update radius */
533: if (tau_max < 1.0) {
534: tao->trust = PetscMax(tao->trust, tl->gamma3 * norm_d);
535: } else if (tau_max > tl->gamma4) {
536: tao->trust = PetscMax(tao->trust, tl->gamma4 * norm_d);
537: } else {
538: tao->trust = PetscMax(tao->trust, tau_max * norm_d);
539: }
540: } else if (kappa >= 1.0 - tl->mu2) {
541: /* Good agreement */
543: if (tau_max < tl->gamma2) {
544: tao->trust = tl->gamma2 * PetscMin(tao->trust, norm_d);
545: } else if (tau_max > tl->gamma3) {
546: tao->trust = PetscMax(tao->trust, tl->gamma3 * norm_d);
547: } else if (tau_max < 1.0) {
548: tao->trust = tau_max * PetscMin(tao->trust, norm_d);
549: } else {
550: tao->trust = PetscMax(tao->trust, tau_max * norm_d);
551: }
552: } else {
553: /* Not good agreement */
554: if (tau_min > 1.0) {
555: tao->trust = tl->gamma2 * PetscMin(tao->trust, norm_d);
556: } else if (tau_max < tl->gamma1) {
557: tao->trust = tl->gamma1 * PetscMin(tao->trust, norm_d);
558: } else if ((tau_min < tl->gamma1) && (tau_max >= 1.0)) {
559: tao->trust = tl->gamma1 * PetscMin(tao->trust, norm_d);
560: } else if ((tau_1 >= tl->gamma1) && (tau_1 < 1.0) && ((tau_2 < tl->gamma1) || (tau_2 >= 1.0))) {
561: tao->trust = tau_1 * PetscMin(tao->trust, norm_d);
562: } else if ((tau_2 >= tl->gamma1) && (tau_2 < 1.0) && ((tau_1 < tl->gamma1) || (tau_2 >= 1.0))) {
563: tao->trust = tau_2 * PetscMin(tao->trust, norm_d);
564: } else {
565: tao->trust = tau_max * PetscMin(tao->trust, norm_d);
566: }
567: tr_reject = 1;
568: }
569: }
570: }
571: }
573: if (tr_reject) {
574: /* The trust-region constraints rejected the step. Apply a linesearch.
575: Check for descent direction. */
576: VecDot(tao->stepdirection, tao->gradient, &gdx);
577: if ((gdx >= 0.0) || PetscIsInfOrNanReal(gdx)) {
578: /* Newton step is not descent or direction produced Inf or NaN */
580: if (NTL_PC_BFGS != tl->pc_type) {
581: /* We don't have the bfgs matrix around and updated
582: Must use gradient direction in this case */
583: VecCopy(tao->gradient, tao->stepdirection);
584: VecScale(tao->stepdirection, -1.0);
585: ++tl->grad;
586: stepType = NTL_GRADIENT;
587: } else {
588: /* Attempt to use the BFGS direction */
589: MatLMVMSolve(tl->M, tao->gradient, tao->stepdirection);
590: VecScale(tao->stepdirection, -1.0);
592: /* Check for success (descent direction) */
593: VecDot(tao->stepdirection, tao->gradient, &gdx);
594: if ((gdx >= 0) || PetscIsInfOrNanReal(gdx)) {
595: /* BFGS direction is not descent or direction produced not a number
596: We can assert bfgsUpdates > 1 in this case because
597: the first solve produces the scaled gradient direction,
598: which is guaranteed to be descent */
600: /* Use steepest descent direction (scaled) */
601: if (f != 0.0) {
602: delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
603: } else {
604: delta = 2.0 / (gnorm*gnorm);
605: }
606: MatLMVMSetDelta(tl->M, delta);
607: MatLMVMReset(tl->M);
608: MatLMVMUpdate(tl->M, tao->solution, tao->gradient);
609: MatLMVMSolve(tl->M, tao->gradient, tao->stepdirection);
610: VecScale(tao->stepdirection, -1.0);
612: bfgsUpdates = 1;
613: ++tl->sgrad;
614: stepType = NTL_SCALED_GRADIENT;
615: } else {
616: if (1 == bfgsUpdates) {
617: /* The first BFGS direction is always the scaled gradient */
618: ++tl->sgrad;
619: stepType = NTL_SCALED_GRADIENT;
620: } else {
621: ++tl->bfgs;
622: stepType = NTL_BFGS;
623: }
624: }
625: }
626: } else {
627: /* Computed Newton step is descent */
628: ++tl->newt;
629: stepType = NTL_NEWTON;
630: }
632: /* Perform the linesearch */
633: fold = f;
634: VecCopy(tao->solution, tl->Xold);
635: VecCopy(tao->gradient, tl->Gold);
637: step = 1.0;
638: TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, tao->stepdirection, &step, &ls_reason);
639: TaoAddLineSearchCounts(tao);
641: while (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER && stepType != NTL_GRADIENT) { /* Linesearch failed */
642: /* Linesearch failed */
643: f = fold;
644: VecCopy(tl->Xold, tao->solution);
645: VecCopy(tl->Gold, tao->gradient);
647: switch(stepType) {
648: case NTL_NEWTON:
649: /* Failed to obtain acceptable iterate with Newton step */
651: if (NTL_PC_BFGS != tl->pc_type) {
652: /* We don't have the bfgs matrix around and being updated
653: Must use gradient direction in this case */
654: VecCopy(tao->gradient, tao->stepdirection);
655: ++tl->grad;
656: stepType = NTL_GRADIENT;
657: } else {
658: /* Attempt to use the BFGS direction */
659: MatLMVMSolve(tl->M, tao->gradient, tao->stepdirection);
662: /* Check for success (descent direction) */
663: VecDot(tao->stepdirection, tao->gradient, &gdx);
664: if ((gdx <= 0) || PetscIsInfOrNanReal(gdx)) {
665: /* BFGS direction is not descent or direction produced
666: not a number. We can assert bfgsUpdates > 1 in this case
667: Use steepest descent direction (scaled) */
669: if (f != 0.0) {
670: delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
671: } else {
672: delta = 2.0 / (gnorm*gnorm);
673: }
674: MatLMVMSetDelta(tl->M, delta);
675: MatLMVMReset(tl->M);
676: MatLMVMUpdate(tl->M, tao->solution, tao->gradient);
677: MatLMVMSolve(tl->M, tao->gradient, tao->stepdirection);
679: bfgsUpdates = 1;
680: ++tl->sgrad;
681: stepType = NTL_SCALED_GRADIENT;
682: } else {
683: if (1 == bfgsUpdates) {
684: /* The first BFGS direction is always the scaled gradient */
685: ++tl->sgrad;
686: stepType = NTL_SCALED_GRADIENT;
687: } else {
688: ++tl->bfgs;
689: stepType = NTL_BFGS;
690: }
691: }
692: }
693: break;
695: case NTL_BFGS:
696: /* Can only enter if pc_type == NTL_PC_BFGS
697: Failed to obtain acceptable iterate with BFGS step
698: Attempt to use the scaled gradient direction */
700: if (f != 0.0) {
701: delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
702: } else {
703: delta = 2.0 / (gnorm*gnorm);
704: }
705: MatLMVMSetDelta(tl->M, delta);
706: MatLMVMReset(tl->M);
707: MatLMVMUpdate(tl->M, tao->solution, tao->gradient);
708: MatLMVMSolve(tl->M, tao->gradient, tao->stepdirection);
710: bfgsUpdates = 1;
711: ++tl->sgrad;
712: stepType = NTL_SCALED_GRADIENT;
713: break;
715: case NTL_SCALED_GRADIENT:
716: /* Can only enter if pc_type == NTL_PC_BFGS
717: The scaled gradient step did not produce a new iterate;
718: attemp to use the gradient direction.
719: Need to make sure we are not using a different diagonal scaling */
720: MatLMVMSetScale(tl->M, tl->Diag);
721: MatLMVMSetDelta(tl->M, 1.0);
722: MatLMVMReset(tl->M);
723: MatLMVMUpdate(tl->M, tao->solution, tao->gradient);
724: MatLMVMSolve(tl->M, tao->gradient, tao->stepdirection);
726: bfgsUpdates = 1;
727: ++tl->grad;
728: stepType = NTL_GRADIENT;
729: break;
730: }
731: VecScale(tao->stepdirection, -1.0);
733: /* This may be incorrect; linesearch has values for stepmax and stepmin
734: that should be reset. */
735: step = 1.0;
736: TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, tao->stepdirection, &step, &ls_reason);
737: TaoAddLineSearchCounts(tao);
738: }
740: if (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER) {
741: /* Failed to find an improving point */
742: f = fold;
743: VecCopy(tl->Xold, tao->solution);
744: VecCopy(tl->Gold, tao->gradient);
745: tao->trust = 0.0;
746: step = 0.0;
747: reason = TAO_DIVERGED_LS_FAILURE;
748: tao->reason = TAO_DIVERGED_LS_FAILURE;
749: break;
750: } else if (stepType == NTL_NEWTON) {
751: if (step < tl->nu1) {
752: /* Very bad step taken; reduce radius */
753: tao->trust = tl->omega1 * PetscMin(norm_d, tao->trust);
754: } else if (step < tl->nu2) {
755: /* Reasonably bad step taken; reduce radius */
756: tao->trust = tl->omega2 * PetscMin(norm_d, tao->trust);
757: } else if (step < tl->nu3) {
758: /* Reasonable step was taken; leave radius alone */
759: if (tl->omega3 < 1.0) {
760: tao->trust = tl->omega3 * PetscMin(norm_d, tao->trust);
761: } else if (tl->omega3 > 1.0) {
762: tao->trust = PetscMax(tl->omega3 * norm_d, tao->trust);
763: }
764: } else if (step < tl->nu4) {
765: /* Full step taken; increase the radius */
766: tao->trust = PetscMax(tl->omega4 * norm_d, tao->trust);
767: } else {
768: /* More than full step taken; increase the radius */
769: tao->trust = PetscMax(tl->omega5 * norm_d, tao->trust);
770: }
771: } else {
772: /* Newton step was not good; reduce the radius */
773: tao->trust = tl->omega1 * PetscMin(norm_d, tao->trust);
774: }
775: } else {
776: /* Trust-region step is accepted */
777: VecCopy(tl->W, tao->solution);
778: f = ftrial;
779: TaoComputeGradient(tao, tao->solution, tao->gradient);
780: ++tl->ntrust;
781: }
783: /* The radius may have been increased; modify if it is too large */
784: tao->trust = PetscMin(tao->trust, tl->max_radius);
786: /* Check for converged */
787: VecNorm(tao->gradient, NORM_2, &gnorm);
788: if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1,"User provided compute function generated Not-a-Number");
789: needH = 1;
791: TaoMonitor(tao, tao->niter, f, gnorm, 0.0, tao->trust, &reason);
792: }
793: return(0);
794: }
796: /* ---------------------------------------------------------- */
799: static PetscErrorCode TaoSetUp_NTL(Tao tao)
800: {
801: TAO_NTL *tl = (TAO_NTL *)tao->data;
805: if (!tao->gradient) {VecDuplicate(tao->solution, &tao->gradient); }
806: if (!tao->stepdirection) {VecDuplicate(tao->solution, &tao->stepdirection);}
807: if (!tl->W) { VecDuplicate(tao->solution, &tl->W);}
808: if (!tl->Xold) { VecDuplicate(tao->solution, &tl->Xold);}
809: if (!tl->Gold) { VecDuplicate(tao->solution, &tl->Gold);}
810: tl->Diag = 0;
811: tl->M = 0;
812: return(0);
813: }
815: /*------------------------------------------------------------*/
818: static PetscErrorCode TaoDestroy_NTL(Tao tao)
819: {
820: TAO_NTL *tl = (TAO_NTL *)tao->data;
824: if (tao->setupcalled) {
825: VecDestroy(&tl->W);
826: VecDestroy(&tl->Xold);
827: VecDestroy(&tl->Gold);
828: }
829: VecDestroy(&tl->Diag);
830: MatDestroy(&tl->M);
831: PetscFree(tao->data);
832: return(0);
833: }
835: /*------------------------------------------------------------*/
838: static PetscErrorCode TaoSetFromOptions_NTL(PetscOptionItems *PetscOptionsObject,Tao tao)
839: {
840: TAO_NTL *tl = (TAO_NTL *)tao->data;
844: PetscOptionsHead(PetscOptionsObject,"Newton trust region with line search method for unconstrained optimization");
845: PetscOptionsEList("-tao_ntl_ksp_type", "ksp type", "", NTL_KSP, NTL_KSP_TYPES, NTL_KSP[tl->ksp_type], &tl->ksp_type,NULL);
846: PetscOptionsEList("-tao_ntl_pc_type", "pc type", "", NTL_PC, NTL_PC_TYPES, NTL_PC[tl->pc_type], &tl->pc_type,NULL);
847: PetscOptionsEList("-tao_ntl_bfgs_scale_type", "bfgs scale type", "", BFGS_SCALE, BFGS_SCALE_TYPES, BFGS_SCALE[tl->bfgs_scale_type], &tl->bfgs_scale_type,NULL);
848: PetscOptionsEList("-tao_ntl_init_type", "radius initialization type", "", NTL_INIT, NTL_INIT_TYPES, NTL_INIT[tl->init_type], &tl->init_type,NULL);
849: PetscOptionsEList("-tao_ntl_update_type", "radius update type", "", NTL_UPDATE, NTL_UPDATE_TYPES, NTL_UPDATE[tl->update_type], &tl->update_type,NULL);
850: PetscOptionsReal("-tao_ntl_eta1", "poor steplength; reduce radius", "", tl->eta1, &tl->eta1,NULL);
851: PetscOptionsReal("-tao_ntl_eta2", "reasonable steplength; leave radius alone", "", tl->eta2, &tl->eta2,NULL);
852: PetscOptionsReal("-tao_ntl_eta3", "good steplength; increase radius", "", tl->eta3, &tl->eta3,NULL);
853: PetscOptionsReal("-tao_ntl_eta4", "excellent steplength; greatly increase radius", "", tl->eta4, &tl->eta4,NULL);
854: PetscOptionsReal("-tao_ntl_alpha1", "", "", tl->alpha1, &tl->alpha1,NULL);
855: PetscOptionsReal("-tao_ntl_alpha2", "", "", tl->alpha2, &tl->alpha2,NULL);
856: PetscOptionsReal("-tao_ntl_alpha3", "", "", tl->alpha3, &tl->alpha3,NULL);
857: PetscOptionsReal("-tao_ntl_alpha4", "", "", tl->alpha4, &tl->alpha4,NULL);
858: PetscOptionsReal("-tao_ntl_alpha5", "", "", tl->alpha5, &tl->alpha5,NULL);
859: PetscOptionsReal("-tao_ntl_nu1", "poor steplength; reduce radius", "", tl->nu1, &tl->nu1,NULL);
860: PetscOptionsReal("-tao_ntl_nu2", "reasonable steplength; leave radius alone", "", tl->nu2, &tl->nu2,NULL);
861: PetscOptionsReal("-tao_ntl_nu3", "good steplength; increase radius", "", tl->nu3, &tl->nu3,NULL);
862: PetscOptionsReal("-tao_ntl_nu4", "excellent steplength; greatly increase radius", "", tl->nu4, &tl->nu4,NULL);
863: PetscOptionsReal("-tao_ntl_omega1", "", "", tl->omega1, &tl->omega1,NULL);
864: PetscOptionsReal("-tao_ntl_omega2", "", "", tl->omega2, &tl->omega2,NULL);
865: PetscOptionsReal("-tao_ntl_omega3", "", "", tl->omega3, &tl->omega3,NULL);
866: PetscOptionsReal("-tao_ntl_omega4", "", "", tl->omega4, &tl->omega4,NULL);
867: PetscOptionsReal("-tao_ntl_omega5", "", "", tl->omega5, &tl->omega5,NULL);
868: PetscOptionsReal("-tao_ntl_mu1_i", "", "", tl->mu1_i, &tl->mu1_i,NULL);
869: PetscOptionsReal("-tao_ntl_mu2_i", "", "", tl->mu2_i, &tl->mu2_i,NULL);
870: PetscOptionsReal("-tao_ntl_gamma1_i", "", "", tl->gamma1_i, &tl->gamma1_i,NULL);
871: PetscOptionsReal("-tao_ntl_gamma2_i", "", "", tl->gamma2_i, &tl->gamma2_i,NULL);
872: PetscOptionsReal("-tao_ntl_gamma3_i", "", "", tl->gamma3_i, &tl->gamma3_i,NULL);
873: PetscOptionsReal("-tao_ntl_gamma4_i", "", "", tl->gamma4_i, &tl->gamma4_i,NULL);
874: PetscOptionsReal("-tao_ntl_theta_i", "", "", tl->theta_i, &tl->theta_i,NULL);
875: PetscOptionsReal("-tao_ntl_mu1", "", "", tl->mu1, &tl->mu1,NULL);
876: PetscOptionsReal("-tao_ntl_mu2", "", "", tl->mu2, &tl->mu2,NULL);
877: PetscOptionsReal("-tao_ntl_gamma1", "", "", tl->gamma1, &tl->gamma1,NULL);
878: PetscOptionsReal("-tao_ntl_gamma2", "", "", tl->gamma2, &tl->gamma2,NULL);
879: PetscOptionsReal("-tao_ntl_gamma3", "", "", tl->gamma3, &tl->gamma3,NULL);
880: PetscOptionsReal("-tao_ntl_gamma4", "", "", tl->gamma4, &tl->gamma4,NULL);
881: PetscOptionsReal("-tao_ntl_theta", "", "", tl->theta, &tl->theta,NULL);
882: PetscOptionsReal("-tao_ntl_min_radius", "lower bound on initial radius", "", tl->min_radius, &tl->min_radius,NULL);
883: PetscOptionsReal("-tao_ntl_max_radius", "upper bound on radius", "", tl->max_radius, &tl->max_radius,NULL);
884: PetscOptionsReal("-tao_ntl_epsilon", "tolerance used when computing actual and predicted reduction", "", tl->epsilon, &tl->epsilon,NULL);
885: PetscOptionsTail();
886: TaoLineSearchSetFromOptions(tao->linesearch);
887: KSPSetFromOptions(tao->ksp);
888: return(0);
889: }
891: /*------------------------------------------------------------*/
894: static PetscErrorCode TaoView_NTL(Tao tao, PetscViewer viewer)
895: {
896: TAO_NTL *tl = (TAO_NTL *)tao->data;
897: PetscInt nrejects;
898: PetscBool isascii;
902: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
903: if (isascii) {
904: PetscViewerASCIIPushTab(viewer);
905: if (NTL_PC_BFGS == tl->pc_type && tl->M) {
906: MatLMVMGetRejects(tl->M, &nrejects);
907: PetscViewerASCIIPrintf(viewer, "Rejected matrix updates: %D\n", nrejects);
908: }
909: PetscViewerASCIIPrintf(viewer, "Trust-region steps: %D\n", tl->ntrust);
910: PetscViewerASCIIPrintf(viewer, "Newton search steps: %D\n", tl->newt);
911: PetscViewerASCIIPrintf(viewer, "BFGS search steps: %D\n", tl->bfgs);
912: PetscViewerASCIIPrintf(viewer, "Scaled gradient search steps: %D\n", tl->sgrad);
913: PetscViewerASCIIPrintf(viewer, "Gradient search steps: %D\n", tl->grad);
914: PetscViewerASCIIPopTab(viewer);
915: }
916: return(0);
917: }
919: /* ---------------------------------------------------------- */
920: /*MC
921: TAONTR - Newton's method with trust region and linesearch
922: for unconstrained minimization.
923: At each iteration, the Newton trust region method solves the system for d
924: and performs a line search in the d direction:
926: min_d .5 dT Hk d + gkT d, s.t. ||d|| < Delta_k
928: Options Database Keys:
929: + -tao_ntl_ksp_type - "nash","stcg","gltr"
930: . -tao_ntl_pc_type - "none","ahess","bfgs","petsc"
931: . -tao_ntl_bfgs_scale_type - type of scaling with bfgs pc, "ahess" or "bfgs"
932: . -tao_ntl_init_type - "constant","direction","interpolation"
933: . -tao_ntl_update_type - "reduction","interpolation"
934: . -tao_ntl_min_radius - lower bound on trust region radius
935: . -tao_ntl_max_radius - upper bound on trust region radius
936: . -tao_ntl_epsilon - tolerance for accepting actual / predicted reduction
937: . -tao_ntl_mu1_i - mu1 interpolation init factor
938: . -tao_ntl_mu2_i - mu2 interpolation init factor
939: . -tao_ntl_gamma1_i - gamma1 interpolation init factor
940: . -tao_ntl_gamma2_i - gamma2 interpolation init factor
941: . -tao_ntl_gamma3_i - gamma3 interpolation init factor
942: . -tao_ntl_gamma4_i - gamma4 interpolation init factor
943: . -tao_ntl_theta_i - thetha1 interpolation init factor
944: . -tao_ntl_eta1 - eta1 reduction update factor
945: . -tao_ntl_eta2 - eta2 reduction update factor
946: . -tao_ntl_eta3 - eta3 reduction update factor
947: . -tao_ntl_eta4 - eta4 reduction update factor
948: . -tao_ntl_alpha1 - alpha1 reduction update factor
949: . -tao_ntl_alpha2 - alpha2 reduction update factor
950: . -tao_ntl_alpha3 - alpha3 reduction update factor
951: . -tao_ntl_alpha4 - alpha4 reduction update factor
952: . -tao_ntl_alpha4 - alpha4 reduction update factor
953: . -tao_ntl_mu1 - mu1 interpolation update
954: . -tao_ntl_mu2 - mu2 interpolation update
955: . -tao_ntl_gamma1 - gamma1 interpolcation update
956: . -tao_ntl_gamma2 - gamma2 interpolcation update
957: . -tao_ntl_gamma3 - gamma3 interpolcation update
958: . -tao_ntl_gamma4 - gamma4 interpolation update
959: - -tao_ntl_theta - theta1 interpolation update
961: Level: beginner
962: M*/
966: PETSC_EXTERN PetscErrorCode TaoCreate_NTL(Tao tao)
967: {
968: TAO_NTL *tl;
970: const char *morethuente_type = TAOLINESEARCHMT;
973: PetscNewLog(tao,&tl);
974: tao->ops->setup = TaoSetUp_NTL;
975: tao->ops->solve = TaoSolve_NTL;
976: tao->ops->view = TaoView_NTL;
977: tao->ops->setfromoptions = TaoSetFromOptions_NTL;
978: tao->ops->destroy = TaoDestroy_NTL;
980: /* Override default settings (unless already changed) */
981: if (!tao->max_it_changed) tao->max_it = 50;
982: if (!tao->trust0_changed) tao->trust0 = 100.0;
984: tao->data = (void*)tl;
986: /* Default values for trust-region radius update based on steplength */
987: tl->nu1 = 0.25;
988: tl->nu2 = 0.50;
989: tl->nu3 = 1.00;
990: tl->nu4 = 1.25;
992: tl->omega1 = 0.25;
993: tl->omega2 = 0.50;
994: tl->omega3 = 1.00;
995: tl->omega4 = 2.00;
996: tl->omega5 = 4.00;
998: /* Default values for trust-region radius update based on reduction */
999: tl->eta1 = 1.0e-4;
1000: tl->eta2 = 0.25;
1001: tl->eta3 = 0.50;
1002: tl->eta4 = 0.90;
1004: tl->alpha1 = 0.25;
1005: tl->alpha2 = 0.50;
1006: tl->alpha3 = 1.00;
1007: tl->alpha4 = 2.00;
1008: tl->alpha5 = 4.00;
1010: /* Default values for trust-region radius update based on interpolation */
1011: tl->mu1 = 0.10;
1012: tl->mu2 = 0.50;
1014: tl->gamma1 = 0.25;
1015: tl->gamma2 = 0.50;
1016: tl->gamma3 = 2.00;
1017: tl->gamma4 = 4.00;
1019: tl->theta = 0.05;
1021: /* Default values for trust region initialization based on interpolation */
1022: tl->mu1_i = 0.35;
1023: tl->mu2_i = 0.50;
1025: tl->gamma1_i = 0.0625;
1026: tl->gamma2_i = 0.5;
1027: tl->gamma3_i = 2.0;
1028: tl->gamma4_i = 5.0;
1030: tl->theta_i = 0.25;
1032: /* Remaining parameters */
1033: tl->min_radius = 1.0e-10;
1034: tl->max_radius = 1.0e10;
1035: tl->epsilon = 1.0e-6;
1037: tl->ksp_type = NTL_KSP_STCG;
1038: tl->pc_type = NTL_PC_BFGS;
1039: tl->bfgs_scale_type = BFGS_SCALE_AHESS;
1040: tl->init_type = NTL_INIT_INTERPOLATION;
1041: tl->update_type = NTL_UPDATE_REDUCTION;
1043: TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch);
1044: TaoLineSearchSetType(tao->linesearch, morethuente_type);
1045: TaoLineSearchUseTaoRoutines(tao->linesearch, tao);
1046: TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);
1047: KSPCreate(((PetscObject)tao)->comm, &tao->ksp);
1048: KSPSetOptionsPrefix(tao->ksp, tao->hdr.prefix);
1049: return(0);
1050: }