Actual source code: neldermead.c

petsc-3.6.1 2015-08-06
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  1: #include <../src/tao/unconstrained/impls/neldermead/neldermead.h>
  2: #include <petscvec.h>

  4: static PetscErrorCode NelderMeadSort(TAO_NelderMead *nm);
  5: static PetscErrorCode NelderMeadReplace(TAO_NelderMead *nm, PetscInt index, Vec Xmu, PetscReal f);
  6: /* ---------------------------------------------------------- */
  9: static PetscErrorCode TaoSetUp_NM(Tao tao)
 10: {
 12:   TAO_NelderMead *nm = (TAO_NelderMead *)tao->data;
 13:   PetscInt       n;

 16:   VecGetSize(tao->solution,&n);
 17:   nm->N = n;
 18:   nm->oneOverN = 1.0/n;
 19:   VecDuplicateVecs(tao->solution,nm->N+1,&nm->simplex);
 20:   PetscMalloc1(nm->N+1,&nm->f_values);
 21:   PetscMalloc1(nm->N+1,&nm->indices);
 22:   VecDuplicate(tao->solution,&nm->Xbar);
 23:   VecDuplicate(tao->solution,&nm->Xmur);
 24:   VecDuplicate(tao->solution,&nm->Xmue);
 25:   VecDuplicate(tao->solution,&nm->Xmuc);

 27:   tao->gradient=0;
 28:   tao->step=0;
 29:   return(0);
 30: }

 32: /* ---------------------------------------------------------- */
 35: PetscErrorCode TaoDestroy_NM(Tao tao)
 36: {
 37:   TAO_NelderMead *nm = (TAO_NelderMead*)tao->data;

 41:   if (tao->setupcalled) {
 42:     VecDestroyVecs(nm->N+1,&nm->simplex);
 43:     VecDestroy(&nm->Xmuc);
 44:     VecDestroy(&nm->Xmue);
 45:     VecDestroy(&nm->Xmur);
 46:     VecDestroy(&nm->Xbar);
 47:   }
 48:   PetscFree(nm->indices);
 49:   PetscFree(nm->f_values);
 50:   PetscFree(tao->data);
 51:   tao->data = 0;
 52:   return(0);
 53: }

 55: /*------------------------------------------------------------*/
 58: PetscErrorCode TaoSetFromOptions_NM(PetscOptions *PetscOptionsObject,Tao tao)
 59: {
 60:   TAO_NelderMead *nm = (TAO_NelderMead*)tao->data;

 64:   PetscOptionsHead(PetscOptionsObject,"Nelder-Mead options");
 65:   PetscOptionsReal("-tao_nm_lamda","initial step length","",nm->lamda,&nm->lamda,NULL);
 66:   PetscOptionsReal("-tao_nm_mu","mu","",nm->mu_oc,&nm->mu_oc,NULL);
 67:   nm->mu_ic = -nm->mu_oc;
 68:   nm->mu_r = nm->mu_oc*2.0;
 69:   nm->mu_e = nm->mu_oc*4.0;
 70:   PetscOptionsTail();
 71:   return(0);
 72: }

 74: /*------------------------------------------------------------*/
 77: PetscErrorCode TaoView_NM(Tao tao,PetscViewer viewer)
 78: {
 79:   TAO_NelderMead *nm = (TAO_NelderMead*)tao->data;
 80:   PetscBool      isascii;

 84:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
 85:   if (isascii) {
 86:     PetscViewerASCIIPushTab(viewer);
 87:     PetscViewerASCIIPrintf(viewer,"expansions: %D\n",nm->nexpand);
 88:     PetscViewerASCIIPrintf(viewer,"reflections: %D\n",nm->nreflect);
 89:     PetscViewerASCIIPrintf(viewer,"inside contractions: %D\n",nm->nincontract);
 90:     PetscViewerASCIIPrintf(viewer,"outside contractionss: %D\n",nm->noutcontract);
 91:     PetscViewerASCIIPrintf(viewer,"Shrink steps: %D\n",nm->nshrink);
 92:     PetscViewerASCIIPopTab(viewer);
 93:   }
 94:   return(0);
 95: }

 97: /*------------------------------------------------------------*/
100: PetscErrorCode TaoSolve_NM(Tao tao)
101: {
102:   PetscErrorCode     ierr;
103:   TAO_NelderMead     *nm = (TAO_NelderMead*)tao->data;
104:   TaoConvergedReason reason;
105:   PetscReal          *x;
106:   PetscInt           i;
107:   Vec                Xmur=nm->Xmur, Xmue=nm->Xmue, Xmuc=nm->Xmuc, Xbar=nm->Xbar;
108:   PetscReal          fr,fe,fc;
109:   PetscInt           shrink;
110:   PetscInt           low,high;

113:   nm->nshrink =      0;
114:   nm->nreflect =     0;
115:   nm->nincontract =  0;
116:   nm->noutcontract = 0;
117:   nm->nexpand =      0;

119:   if (tao->XL || tao->XU || tao->ops->computebounds) {
120:     PetscPrintf(((PetscObject)tao)->comm,"WARNING: Variable bounds have been set but will be ignored by NelderMead algorithm\n");
121:   }

123:   VecCopy(tao->solution,nm->simplex[0]);
124:   TaoComputeObjective(tao,nm->simplex[0],&nm->f_values[0]);
125:   nm->indices[0]=0;
126:   for (i=1;i<nm->N+1;i++){
127:     VecCopy(tao->solution,nm->simplex[i]);
128:     VecGetOwnershipRange(nm->simplex[i],&low,&high);
129:     if (i-1 >= low && i-1 < high) {
130:       VecGetArray(nm->simplex[i],&x);
131:       x[i-1-low] += nm->lamda;
132:       VecRestoreArray(nm->simplex[i],&x);
133:     }

135:     TaoComputeObjective(tao,nm->simplex[i],&nm->f_values[i]);
136:     nm->indices[i] = i;
137:   }

139:   /*  Xbar  = (Sum of all simplex vectors - worst vector)/N */
140:   NelderMeadSort(nm);
141:   VecSet(Xbar,0.0);
142:   for (i=0;i<nm->N;i++) {
143:     VecAXPY(Xbar,1.0,nm->simplex[nm->indices[i]]);
144:   }
145:   VecScale(Xbar,nm->oneOverN);
146:   reason = TAO_CONTINUE_ITERATING;
147:   while (1) {
148:     shrink = 0;
149:     VecCopy(nm->simplex[nm->indices[0]],tao->solution);
150:     TaoMonitor(tao,tao->niter++,nm->f_values[nm->indices[0]],nm->f_values[nm->indices[nm->N]]-nm->f_values[nm->indices[0]],0.0,1.0,&reason);
151:     if (reason != TAO_CONTINUE_ITERATING) break;

153:     /* x(mu) = (1 + mu)Xbar - mu*X_N+1 */
154:     VecAXPBYPCZ(Xmur,1+nm->mu_r,-nm->mu_r,0,Xbar,nm->simplex[nm->indices[nm->N]]);
155:     TaoComputeObjective(tao,Xmur,&fr);

157:     if (nm->f_values[nm->indices[0]] <= fr && fr < nm->f_values[nm->indices[nm->N-1]]) {
158:       /*  reflect */
159:       nm->nreflect++;
160:       PetscInfo(0,"Reflect\n");
161:       NelderMeadReplace(nm,nm->indices[nm->N],Xmur,fr);
162:     } else if (fr < nm->f_values[nm->indices[0]]) {
163:       /*  expand */
164:       nm->nexpand++;
165:       PetscInfo(0,"Expand\n");
166:       VecAXPBYPCZ(Xmue,1+nm->mu_e,-nm->mu_e,0,Xbar,nm->simplex[nm->indices[nm->N]]);
167:       TaoComputeObjective(tao,Xmue,&fe);
168:       if (fe < fr) {
169:         NelderMeadReplace(nm,nm->indices[nm->N],Xmue,fe);
170:       } else {
171:         NelderMeadReplace(nm,nm->indices[nm->N],Xmur,fr);
172:       }
173:     } else if (nm->f_values[nm->indices[nm->N-1]] <= fr && fr < nm->f_values[nm->indices[nm->N]]) {
174:       /* outside contraction */
175:       nm->noutcontract++;
176:       PetscInfo(0,"Outside Contraction\n");
177:       VecAXPBYPCZ(Xmuc,1+nm->mu_oc,-nm->mu_oc,0,Xbar,nm->simplex[nm->indices[nm->N]]);

179:       TaoComputeObjective(tao,Xmuc,&fc);
180:       if (fc <= fr) {
181:         NelderMeadReplace(nm,nm->indices[nm->N],Xmuc,fc);
182:       } else shrink=1;
183:     } else {
184:       /* inside contraction */
185:       nm->nincontract++;
186:       PetscInfo(0,"Inside Contraction\n");
187:       VecAXPBYPCZ(Xmuc,1+nm->mu_ic,-nm->mu_ic,0,Xbar,nm->simplex[nm->indices[nm->N]]);
188:       TaoComputeObjective(tao,Xmuc,&fc);
189:       if (fc < nm->f_values[nm->indices[nm->N]]) {
190:         NelderMeadReplace(nm,nm->indices[nm->N],Xmuc,fc);
191:       } else shrink = 1;
192:     }

194:     if (shrink) {
195:       nm->nshrink++;
196:       PetscInfo(0,"Shrink\n");

198:       for (i=1;i<nm->N+1;i++) {
199:         VecAXPBY(nm->simplex[nm->indices[i]],1.5,-0.5,nm->simplex[nm->indices[0]]);
200:         TaoComputeObjective(tao,nm->simplex[nm->indices[i]], &nm->f_values[nm->indices[i]]);
201:       }
202:       VecAXPBY(Xbar,1.5*nm->oneOverN,-0.5,nm->simplex[nm->indices[0]]);

204:       /*  Add last vector's fraction of average */
205:       VecAXPY(Xbar,nm->oneOverN,nm->simplex[nm->indices[nm->N]]);
206:       NelderMeadSort(nm);
207:       /*  Subtract new last vector from average */
208:       VecAXPY(Xbar,-nm->oneOverN,nm->simplex[nm->indices[nm->N]]);
209:     }
210:   }
211:   return(0);
212: }

214: /* ---------------------------------------------------------- */
215: /*MC
216:  TAONM - Nelder-Mead solver for derivative free, unconstrained minimization

218:  Options Database Keys:
219: + -tao_nm_lamda - initial step length
220: . -tao_nm_mu - expansion/contraction factor

222:  Level: beginner
223: M*/

227: PETSC_EXTERN PetscErrorCode TaoCreate_NM(Tao tao)
228: {
229:   TAO_NelderMead *nm;

233:   PetscNewLog(tao,&nm);
234:   tao->data = (void*)nm;

236:   tao->ops->setup = TaoSetUp_NM;
237:   tao->ops->solve = TaoSolve_NM;
238:   tao->ops->view = TaoView_NM;
239:   tao->ops->setfromoptions = TaoSetFromOptions_NM;
240:   tao->ops->destroy = TaoDestroy_NM;

242:   /* Override default settings (unless already changed) */
243:   if (!tao->max_it_changed) tao->max_it = 2000;
244:   if (!tao->max_funcs_changed) tao->max_funcs = 4000;
245: #if defined(PETSC_USE_REAL_SINGLE)
246:   if (!tao->fatol_changed) tao->fatol = 1.0e-5;
247:   if (!tao->frtol_changed) tao->frtol = 1.0e-5;
248: #else
249:   if (!tao->fatol_changed) tao->fatol = 1.0e-8;
250:   if (!tao->frtol_changed) tao->frtol = 1.0e-8;
251: #endif

253:   nm->simplex = 0;
254:   nm->lamda = 1;

256:   nm->mu_ic = -0.5;
257:   nm->mu_oc = 0.5;
258:   nm->mu_r = 1.0;
259:   nm->mu_e = 2.0;

261:   return(0);
262: }


265: /*------------------------------------------------------------*/
268: PetscErrorCode NelderMeadSort(TAO_NelderMead *nm)
269: {
270:   PetscReal *values = nm->f_values;
271:   PetscInt  *indices = nm->indices;
272:   PetscInt  dim = nm->N+1;
273:   PetscInt  i,j,index;
274:   PetscReal val;

277:   for (i=1;i<dim;i++) {
278:     index = indices[i];
279:     val = values[index];
280:     for (j=i-1; j>=0 && values[indices[j]] > val; j--) {
281:       indices[j+1] = indices[j];
282:     }
283:     indices[j+1] = index;
284:   }
285:   return(0);
286: }


289: /*------------------------------------------------------------*/
292: PetscErrorCode NelderMeadReplace(TAO_NelderMead *nm, PetscInt index, Vec Xmu, PetscReal f)
293: {

297:   /*  Add new vector's fraction of average */
298:   VecAXPY(nm->Xbar,nm->oneOverN,Xmu);
299:   VecCopy(Xmu,nm->simplex[index]);
300:   nm->f_values[index] = f;

302:   NelderMeadSort(nm);

304:   /*  Subtract last vector from average */
305:   VecAXPY(nm->Xbar,-nm->oneOverN,nm->simplex[nm->indices[nm->N]]);
306:   return(0);
307: }