Actual source code: gpcg.c

petsc-3.7.7 2017-09-25
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  1: #include <petsc/private/kspimpl.h>
  2: #include <../src/tao/bound/impls/gpcg/gpcg.h>        /*I "gpcg.h" I*/


  5: static PetscErrorCode GPCGGradProjections(Tao tao);
  6: static PetscErrorCode GPCGObjectiveAndGradient(TaoLineSearch,Vec,PetscReal*,Vec,void*);

  8: /*------------------------------------------------------------*/
 11: static PetscErrorCode TaoDestroy_GPCG(Tao tao)
 12: {
 13:   TAO_GPCG       *gpcg = (TAO_GPCG *)tao->data;

 16:   /* Free allocated memory in GPCG structure */
 18:   VecDestroy(&gpcg->B);
 19:   VecDestroy(&gpcg->Work);
 20:   VecDestroy(&gpcg->X_New);
 21:   VecDestroy(&gpcg->G_New);
 22:   VecDestroy(&gpcg->DXFree);
 23:   VecDestroy(&gpcg->R);
 24:   VecDestroy(&gpcg->PG);
 25:   MatDestroy(&gpcg->Hsub);
 26:   MatDestroy(&gpcg->Hsub_pre);
 27:   ISDestroy(&gpcg->Free_Local);
 28:   PetscFree(tao->data);
 29:   tao->data = NULL;
 30:   return(0);
 31: }

 33: /*------------------------------------------------------------*/
 36: static PetscErrorCode TaoSetFromOptions_GPCG(PetscOptionItems *PetscOptionsObject,Tao tao)
 37: {
 38:   TAO_GPCG       *gpcg = (TAO_GPCG *)tao->data;
 40:   PetscBool      flg;

 43:   PetscOptionsHead(PetscOptionsObject,"Gradient Projection, Conjugate Gradient method for bound constrained optimization");
 44:   ierr=PetscOptionsInt("-tao_gpcg_maxpgits","maximum number of gradient projections per GPCG iterate",NULL,gpcg->maxgpits,&gpcg->maxgpits,&flg);
 45:   PetscOptionsTail();
 46:   KSPSetFromOptions(tao->ksp);
 47:   TaoLineSearchSetFromOptions(tao->linesearch);
 48:   return(0);
 49: }

 51: /*------------------------------------------------------------*/
 54: static PetscErrorCode TaoView_GPCG(Tao tao, PetscViewer viewer)
 55: {
 56:   TAO_GPCG       *gpcg = (TAO_GPCG *)tao->data;
 57:   PetscBool      isascii;

 61:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
 62:   if (isascii) {
 63:     PetscViewerASCIIPushTab(viewer);
 64:     PetscViewerASCIIPrintf(viewer,"Total PG its: %D,",gpcg->total_gp_its);
 65:     PetscViewerASCIIPrintf(viewer,"PG tolerance: %g \n",(double)gpcg->pg_ftol);
 66:     PetscViewerASCIIPopTab(viewer);
 67:   }
 68:   TaoLineSearchView(tao->linesearch,viewer);
 69:   return(0);
 70: }

 72: /* GPCGObjectiveAndGradient()
 73:    Compute f=0.5 * x'Hx + b'x + c
 74:            g=Hx + b
 75: */
 78: static PetscErrorCode GPCGObjectiveAndGradient(TaoLineSearch ls, Vec X, PetscReal *f, Vec G, void*tptr)
 79: {
 80:   Tao            tao = (Tao)tptr;
 81:   TAO_GPCG       *gpcg = (TAO_GPCG*)tao->data;
 83:   PetscReal      f1,f2;

 86:   MatMult(tao->hessian,X,G);
 87:   VecDot(G,X,&f1);
 88:   VecDot(gpcg->B,X,&f2);
 89:   VecAXPY(G,1.0,gpcg->B);
 90:   *f=f1/2.0 + f2 + gpcg->c;
 91:   return(0);
 92: }

 94: /* ---------------------------------------------------------- */
 97: static PetscErrorCode TaoSetup_GPCG(Tao tao)
 98: {
100:   TAO_GPCG       *gpcg = (TAO_GPCG *)tao->data;

103:   /* Allocate some arrays */
104:   if (!tao->gradient) {
105:       VecDuplicate(tao->solution, &tao->gradient);
106:   }
107:   if (!tao->stepdirection) {
108:       VecDuplicate(tao->solution, &tao->stepdirection);
109:   }
110:   if (!tao->XL) {
111:       VecDuplicate(tao->solution,&tao->XL);
112:       VecSet(tao->XL,PETSC_NINFINITY);
113:   }
114:   if (!tao->XU) {
115:       VecDuplicate(tao->solution,&tao->XU);
116:       VecSet(tao->XU,PETSC_INFINITY);
117:   }

119:   ierr=VecDuplicate(tao->solution,&gpcg->B);
120:   ierr=VecDuplicate(tao->solution,&gpcg->Work);
121:   ierr=VecDuplicate(tao->solution,&gpcg->X_New);
122:   ierr=VecDuplicate(tao->solution,&gpcg->G_New);
123:   ierr=VecDuplicate(tao->solution,&gpcg->DXFree);
124:   ierr=VecDuplicate(tao->solution,&gpcg->R);
125:   ierr=VecDuplicate(tao->solution,&gpcg->PG);
126:   /*
127:     if (gpcg->ksp_type == GPCG_KSP_NASH) {
128:         KSPSetType(tao->ksp,KSPNASH);
129:       } else if (gpcg->ksp_type == GPCG_KSP_STCG) {
130:         KSPSetType(tao->ksp,KSPSTCG);
131:       } else {
132:         KSPSetType(tao->ksp,KSPGLTR);
133:       }
134:       if (tao->ksp->ops->setfromoptions) {
135:         (*tao->ksp->ops->setfromoptions)(tao->ksp);
136:       }

138:     }
139:   */
140:   return(0);
141: }

145: static PetscErrorCode TaoSolve_GPCG(Tao tao)
146: {
147:   TAO_GPCG                     *gpcg = (TAO_GPCG *)tao->data;
148:   PetscErrorCode               ierr;
149:   PetscInt                     its;
150:   PetscReal                    actred,f,f_new,gnorm,gdx,stepsize,xtb;
151:   PetscReal                    xtHx;
152:   TaoConvergedReason           reason = TAO_CONTINUE_ITERATING;
153:   TaoLineSearchConvergedReason ls_status = TAOLINESEARCH_CONTINUE_ITERATING;


157:   TaoComputeVariableBounds(tao);
158:   VecMedian(tao->XL,tao->solution,tao->XU,tao->solution);
159:   TaoLineSearchSetVariableBounds(tao->linesearch,tao->XL,tao->XU);

161:   /* Using f = .5*x'Hx + x'b + c and g=Hx + b,  compute b,c */
162:   TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);
163:   TaoComputeObjectiveAndGradient(tao,tao->solution,&f,tao->gradient);
164:   VecCopy(tao->gradient, gpcg->B);
165:   MatMult(tao->hessian,tao->solution,gpcg->Work);
166:   VecDot(gpcg->Work, tao->solution, &xtHx);
167:   VecAXPY(gpcg->B,-1.0,gpcg->Work);
168:   VecDot(gpcg->B,tao->solution,&xtb);
169:   gpcg->c=f-xtHx/2.0-xtb;
170:   if (gpcg->Free_Local) {
171:       ISDestroy(&gpcg->Free_Local);
172:   }
173:   VecWhichBetween(tao->XL,tao->solution,tao->XU,&gpcg->Free_Local);

175:   /* Project the gradient and calculate the norm */
176:   VecCopy(tao->gradient,gpcg->G_New);
177:   VecBoundGradientProjection(tao->gradient,tao->solution,tao->XL,tao->XU,gpcg->PG);
178:   VecNorm(gpcg->PG,NORM_2,&gpcg->gnorm);
179:   tao->step=1.0;
180:   gpcg->f = f;

182:     /* Check Stopping Condition      */
183:   ierr=TaoMonitor(tao,tao->niter,f,gpcg->gnorm,0.0,tao->step,&reason);

185:   while (reason == TAO_CONTINUE_ITERATING){
186:     tao->ksp_its=0;

188:     GPCGGradProjections(tao);
189:     ISGetSize(gpcg->Free_Local,&gpcg->n_free);

191:     f=gpcg->f; gnorm=gpcg->gnorm;

193:     KSPReset(tao->ksp);

195:     if (gpcg->n_free > 0){
196:       /* Create a reduced linear system */
197:       VecDestroy(&gpcg->R);
198:       VecDestroy(&gpcg->DXFree);
199:       TaoVecGetSubVec(tao->gradient,gpcg->Free_Local, tao->subset_type, 0.0, &gpcg->R);
200:       VecScale(gpcg->R, -1.0);
201:       TaoVecGetSubVec(tao->stepdirection,gpcg->Free_Local,tao->subset_type, 0.0, &gpcg->DXFree);
202:       VecSet(gpcg->DXFree,0.0);

204:       TaoMatGetSubMat(tao->hessian, gpcg->Free_Local, gpcg->Work, tao->subset_type, &gpcg->Hsub);

206:       if (tao->hessian_pre == tao->hessian) {
207:         MatDestroy(&gpcg->Hsub_pre);
208:         PetscObjectReference((PetscObject)gpcg->Hsub);
209:         gpcg->Hsub_pre = gpcg->Hsub;
210:       }  else {
211:         TaoMatGetSubMat(tao->hessian, gpcg->Free_Local, gpcg->Work, tao->subset_type, &gpcg->Hsub_pre);
212:       }

214:       KSPReset(tao->ksp);
215:       KSPSetOperators(tao->ksp,gpcg->Hsub,gpcg->Hsub_pre);

217:       KSPSolve(tao->ksp,gpcg->R,gpcg->DXFree);
218:       KSPGetIterationNumber(tao->ksp,&its);
219:       tao->ksp_its+=its;
220:       tao->ksp_tot_its+=its;
221:       VecSet(tao->stepdirection,0.0);
222:       VecISAXPY(tao->stepdirection,gpcg->Free_Local,1.0,gpcg->DXFree);

224:       VecDot(tao->stepdirection,tao->gradient,&gdx);
225:       TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);
226:       f_new=f;
227:       TaoLineSearchApply(tao->linesearch,tao->solution,&f_new,tao->gradient,tao->stepdirection,&stepsize,&ls_status);

229:       actred = f_new - f;

231:       /* Evaluate the function and gradient at the new point */
232:       VecBoundGradientProjection(tao->gradient,tao->solution,tao->XL,tao->XU, gpcg->PG);
233:       VecNorm(gpcg->PG, NORM_2, &gnorm);
234:       f=f_new;
235:       ISDestroy(&gpcg->Free_Local);
236:       VecWhichBetween(tao->XL,tao->solution,tao->XU,&gpcg->Free_Local);
237:     } else {
238:       actred = 0; gpcg->step=1.0;
239:       /* if there were no free variables, no cg method */
240:     }

242:     tao->niter++;
243:     TaoMonitor(tao,tao->niter,f,gnorm,0.0,gpcg->step,&reason);
244:     gpcg->f=f;gpcg->gnorm=gnorm; gpcg->actred=actred;
245:     if (reason!=TAO_CONTINUE_ITERATING) break;
246:   }  /* END MAIN LOOP  */

248:   return(0);
249: }

253: static PetscErrorCode GPCGGradProjections(Tao tao)
254: {
255:   PetscErrorCode                 ierr;
256:   TAO_GPCG                       *gpcg = (TAO_GPCG *)tao->data;
257:   PetscInt                       i;
258:   PetscReal                      actred=-1.0,actred_max=0.0, gAg,gtg=gpcg->gnorm,alpha;
259:   PetscReal                      f_new,gdx,stepsize;
260:   Vec                            DX=tao->stepdirection,XL=tao->XL,XU=tao->XU,Work=gpcg->Work;
261:   Vec                            X=tao->solution,G=tao->gradient;
262:   TaoLineSearchConvergedReason lsflag=TAOLINESEARCH_CONTINUE_ITERATING;

264:   /*
265:      The free, active, and binding variables should be already identified
266:   */
268:   for (i=0;i<gpcg->maxgpits;i++){
269:     if ( -actred <= (gpcg->pg_ftol)*actred_max) break;
270:     VecBoundGradientProjection(G,X,XL,XU,DX);
271:     VecScale(DX,-1.0);
272:     VecDot(DX,G,&gdx);

274:     MatMult(tao->hessian,DX,Work);
275:     VecDot(DX,Work,&gAg);

277:     gpcg->gp_iterates++;
278:     gpcg->total_gp_its++;

280:     gtg=-gdx;
281:     if (PetscAbsReal(gAg) == 0.0) {
282:       alpha = 1.0;
283:     } else {
284:       alpha = PetscAbsReal(gtg/gAg);
285:     }
286:     TaoLineSearchSetInitialStepLength(tao->linesearch,alpha);
287:     f_new=gpcg->f;
288:     TaoLineSearchApply(tao->linesearch,X,&f_new,G,DX,&stepsize,&lsflag);

290:     /* Update the iterate */
291:     actred = f_new - gpcg->f;
292:     actred_max = PetscMax(actred_max,-(f_new - gpcg->f));
293:     gpcg->f = f_new;
294:     ISDestroy(&gpcg->Free_Local);
295:     VecWhichBetween(XL,X,XU,&gpcg->Free_Local);
296:   }

298:   gpcg->gnorm=gtg;
299:   return(0);
300: } /* End gradient projections */

304: static PetscErrorCode TaoComputeDual_GPCG(Tao tao, Vec DXL, Vec DXU)
305: {
306:   TAO_GPCG       *gpcg = (TAO_GPCG *)tao->data;

310:   VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, gpcg->Work);
311:   VecCopy(gpcg->Work, DXL);
312:   VecAXPY(DXL,-1.0,tao->gradient);
313:   VecSet(DXU,0.0);
314:   VecPointwiseMax(DXL,DXL,DXU);

316:   VecCopy(tao->gradient,DXU);
317:   VecAXPY(DXU,-1.0,gpcg->Work);
318:   VecSet(gpcg->Work,0.0);
319:   VecPointwiseMin(DXU,gpcg->Work,DXU);
320:   return(0);
321: }

323: /*------------------------------------------------------------*/
324: /*MC
325:   TAOGPCG - gradient projected conjugate gradient algorithm is an active-set
326:         conjugate-gradient based method for bound-constrained minimization

328:   Options Database Keys:
329: + -tao_gpcg_maxpgits - maximum number of gradient projections for GPCG iterate
330: - -tao_subset_type - "subvec","mask","matrix-free", strategies for handling active-sets

332:   Level: beginner
333: M*/
336: PETSC_EXTERN PetscErrorCode TaoCreate_GPCG(Tao tao)
337: {
338:   TAO_GPCG       *gpcg;

342:   tao->ops->setup = TaoSetup_GPCG;
343:   tao->ops->solve = TaoSolve_GPCG;
344:   tao->ops->view  = TaoView_GPCG;
345:   tao->ops->setfromoptions = TaoSetFromOptions_GPCG;
346:   tao->ops->destroy = TaoDestroy_GPCG;
347:   tao->ops->computedual = TaoComputeDual_GPCG;

349:   PetscNewLog(tao,&gpcg);
350:   tao->data = (void*)gpcg;

352:   /* Override default settings (unless already changed) */
353:   if (!tao->max_it_changed) tao->max_it=500;
354:   if (!tao->max_funcs_changed) tao->max_funcs = 100000;
355: #if defined(PETSC_USE_REAL_SINGLE)
356:   if (!tao->gatol_changed) tao->gatol=1e-6;
357:   if (!tao->grtol_changed) tao->grtol=1e-6;
358: #else
359:   if (!tao->gatol_changed) tao->gatol=1e-12;
360:   if (!tao->grtol_changed) tao->grtol=1e-12;
361: #endif

363:   /* Initialize pointers and variables */
364:   gpcg->n=0;
365:   gpcg->maxgpits = 8;
366:   gpcg->pg_ftol = 0.1;

368:   gpcg->gp_iterates=0; /* Cumulative number */
369:   gpcg->total_gp_its = 0;

371:   /* Initialize pointers and variables */
372:   gpcg->n_bind=0;
373:   gpcg->n_free = 0;
374:   gpcg->n_upper=0;
375:   gpcg->n_lower=0;
376:   gpcg->subset_type = TAO_SUBSET_MASK;
377:   gpcg->Hsub=NULL;
378:   gpcg->Hsub_pre=NULL;

380:   KSPCreate(((PetscObject)tao)->comm, &tao->ksp);
381:   KSPSetOptionsPrefix(tao->ksp, tao->hdr.prefix);
382:   KSPSetType(tao->ksp,KSPNASH);

384:   TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch);
385:   TaoLineSearchSetType(tao->linesearch, TAOLINESEARCHGPCG);
386:   TaoLineSearchSetObjectiveAndGradientRoutine(tao->linesearch, GPCGObjectiveAndGradient, tao);
387:   TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);
388:   return(0);
389: }