Date: 2021-03-03T22:28:08+00:00

Actual source code: neldermead.c
petsc-3.14.5 2021-03-03
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      1: #include <../src/tao/unconstrained/impls/neldermead/neldermead.h>
      2: #include <petscvec.h>

      5: /*------------------------------------------------------------*/
      6: static PetscErrorCode NelderMeadSort(TAO_NelderMead *nm)
      7: {
      8:   PetscReal *values = nm->f_values;
      9:   PetscInt  *indices = nm->indices;
     10:   PetscInt  dim = nm->N+1;
     11:   PetscInt  i,j,index;
     12:   PetscReal val;

     15:   for (i=1;i<dim;i++) {
     16:     index = indices[i];
     17:     val = values[index];
     18:     for (j=i-1; j>=0 && values[indices[j]] > val; j--) {
     19:       indices[j+1] = indices[j];
     20:     }
     21:     indices[j+1] = index;
     22:   }
     23:   return(0);
     24: }

     27: /*------------------------------------------------------------*/
     28: static PetscErrorCode NelderMeadReplace(TAO_NelderMead *nm, PetscInt index, Vec Xmu, PetscReal f)
     29: {

     33:   /*  Add new vector's fraction of average */
     34:   VecAXPY(nm->Xbar,nm->oneOverN,Xmu);
     35:   VecCopy(Xmu,nm->simplex[index]);
     36:   nm->f_values[index] = f;

     38:   NelderMeadSort(nm);

     40:   /*  Subtract last vector from average */
     41:   VecAXPY(nm->Xbar,-nm->oneOverN,nm->simplex[nm->indices[nm->N]]);
     42:   return(0);
     43: }

     45: /* ---------------------------------------------------------- */
     46: static PetscErrorCode TaoSetUp_NM(Tao tao)
     47: {
     49:   TAO_NelderMead *nm = (TAO_NelderMead *)tao->data;
     50:   PetscInt       n;

     53:   VecGetSize(tao->solution,&n);
     54:   nm->N = n;
     55:   nm->oneOverN = 1.0/n;
     56:   VecDuplicateVecs(tao->solution,nm->N+1,&nm->simplex);
     57:   PetscMalloc1(nm->N+1,&nm->f_values);
     58:   PetscMalloc1(nm->N+1,&nm->indices);
     59:   VecDuplicate(tao->solution,&nm->Xbar);
     60:   VecDuplicate(tao->solution,&nm->Xmur);
     61:   VecDuplicate(tao->solution,&nm->Xmue);
     62:   VecDuplicate(tao->solution,&nm->Xmuc);

     64:   tao->gradient=NULL;
     65:   tao->step=0;
     66:   return(0);
     67: }

     69: /* ---------------------------------------------------------- */
     70: static PetscErrorCode TaoDestroy_NM(Tao tao)
     71: {
     72:   TAO_NelderMead *nm = (TAO_NelderMead*)tao->data;

     76:   if (tao->setupcalled) {
     77:     VecDestroyVecs(nm->N+1,&nm->simplex);
     78:     VecDestroy(&nm->Xmuc);
     79:     VecDestroy(&nm->Xmue);
     80:     VecDestroy(&nm->Xmur);
     81:     VecDestroy(&nm->Xbar);
     82:   }
     83:   PetscFree(nm->indices);
     84:   PetscFree(nm->f_values);
     85:   PetscFree(tao->data);
     86:   return(0);
     87: }

     89: /*------------------------------------------------------------*/
     90: static PetscErrorCode TaoSetFromOptions_NM(PetscOptionItems *PetscOptionsObject,Tao tao)
     91: {
     92:   TAO_NelderMead *nm = (TAO_NelderMead*)tao->data;

     96:   PetscOptionsHead(PetscOptionsObject,"Nelder-Mead options");
     97:   PetscOptionsReal("-tao_nm_lamda","initial step length","",nm->lamda,&nm->lamda,NULL);
     98:   PetscOptionsReal("-tao_nm_mu","mu","",nm->mu_oc,&nm->mu_oc,NULL);
     99:   nm->mu_ic = -nm->mu_oc;
    100:   nm->mu_r = nm->mu_oc*2.0;
    101:   nm->mu_e = nm->mu_oc*4.0;
    102:   PetscOptionsTail();
    103:   return(0);
    104: }

    106: /*------------------------------------------------------------*/
    107: static PetscErrorCode TaoView_NM(Tao tao,PetscViewer viewer)
    108: {
    109:   TAO_NelderMead *nm = (TAO_NelderMead*)tao->data;
    110:   PetscBool      isascii;

    114:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    115:   if (isascii) {
    116:     PetscViewerASCIIPushTab(viewer);
    117:     PetscViewerASCIIPrintf(viewer,"expansions: %D\n",nm->nexpand);
    118:     PetscViewerASCIIPrintf(viewer,"reflections: %D\n",nm->nreflect);
    119:     PetscViewerASCIIPrintf(viewer,"inside contractions: %D\n",nm->nincontract);
    120:     PetscViewerASCIIPrintf(viewer,"outside contractionss: %D\n",nm->noutcontract);
    121:     PetscViewerASCIIPrintf(viewer,"Shrink steps: %D\n",nm->nshrink);
    122:     PetscViewerASCIIPopTab(viewer);
    123:   }
    124:   return(0);
    125: }

    127: /*------------------------------------------------------------*/
    128: static PetscErrorCode TaoSolve_NM(Tao tao)
    129: {
    130:   PetscErrorCode     ierr;
    131:   TAO_NelderMead     *nm = (TAO_NelderMead*)tao->data;
    132:   PetscReal          *x;
    133:   PetscInt           i;
    134:   Vec                Xmur=nm->Xmur, Xmue=nm->Xmue, Xmuc=nm->Xmuc, Xbar=nm->Xbar;
    135:   PetscReal          fr,fe,fc;
    136:   PetscInt           shrink;
    137:   PetscInt           low,high;

    140:   nm->nshrink =      0;
    141:   nm->nreflect =     0;
    142:   nm->nincontract =  0;
    143:   nm->noutcontract = 0;
    144:   nm->nexpand =      0;

    146:   if (tao->XL || tao->XU || tao->ops->computebounds) {
    147:     PetscInfo(tao,"WARNING: Variable bounds have been set but will be ignored by NelderMead algorithm\n");
    148:   }

    150:   VecCopy(tao->solution,nm->simplex[0]);
    151:   TaoComputeObjective(tao,nm->simplex[0],&nm->f_values[0]);
    152:   nm->indices[0]=0;
    153:   for (i=1;i<nm->N+1;i++){
    154:     VecCopy(tao->solution,nm->simplex[i]);
    155:     VecGetOwnershipRange(nm->simplex[i],&low,&high);
    156:     if (i-1 >= low && i-1 < high) {
    157:       VecGetArray(nm->simplex[i],&x);
    158:       x[i-1-low] += nm->lamda;
    159:       VecRestoreArray(nm->simplex[i],&x);
    160:     }

    162:     TaoComputeObjective(tao,nm->simplex[i],&nm->f_values[i]);
    163:     nm->indices[i] = i;
    164:   }

    166:   /*  Xbar  = (Sum of all simplex vectors - worst vector)/N */
    167:   NelderMeadSort(nm);
    168:   VecSet(Xbar,0.0);
    169:   for (i=0;i<nm->N;i++) {
    170:     VecAXPY(Xbar,1.0,nm->simplex[nm->indices[i]]);
    171:   }
    172:   VecScale(Xbar,nm->oneOverN);
    173:   tao->reason = TAO_CONTINUE_ITERATING;
    174:   while (1) {
    175:     /* Call general purpose update function */
    176:     if (tao->ops->update) {
    177:       (*tao->ops->update)(tao, tao->niter, tao->user_update);
    178:     }
    179:     ++tao->niter;
    180:     shrink = 0;
    181:     VecCopy(nm->simplex[nm->indices[0]],tao->solution);
    182:     TaoLogConvergenceHistory(tao, nm->f_values[nm->indices[0]], nm->f_values[nm->indices[nm->N]]-nm->f_values[nm->indices[0]], 0.0, tao->ksp_its);
    183:     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);
    184:     (*tao->ops->convergencetest)(tao,tao->cnvP);
    185:     if (tao->reason != TAO_CONTINUE_ITERATING) break;

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

    191:     if (nm->f_values[nm->indices[0]] <= fr && fr < nm->f_values[nm->indices[nm->N-1]]) {
    192:       /*  reflect */
    193:       nm->nreflect++;
    194:       PetscInfo(0,"Reflect\n");
    195:       NelderMeadReplace(nm,nm->indices[nm->N],Xmur,fr);
    196:     } else if (fr < nm->f_values[nm->indices[0]]) {
    197:       /*  expand */
    198:       nm->nexpand++;
    199:       PetscInfo(0,"Expand\n");
    200:       VecAXPBYPCZ(Xmue,1+nm->mu_e,-nm->mu_e,0,Xbar,nm->simplex[nm->indices[nm->N]]);
    201:       TaoComputeObjective(tao,Xmue,&fe);
    202:       if (fe < fr) {
    203:         NelderMeadReplace(nm,nm->indices[nm->N],Xmue,fe);
    204:       } else {
    205:         NelderMeadReplace(nm,nm->indices[nm->N],Xmur,fr);
    206:       }
    207:     } else if (nm->f_values[nm->indices[nm->N-1]] <= fr && fr < nm->f_values[nm->indices[nm->N]]) {
    208:       /* outside contraction */
    209:       nm->noutcontract++;
    210:       PetscInfo(0,"Outside Contraction\n");
    211:       VecAXPBYPCZ(Xmuc,1+nm->mu_oc,-nm->mu_oc,0,Xbar,nm->simplex[nm->indices[nm->N]]);

    213:       TaoComputeObjective(tao,Xmuc,&fc);
    214:       if (fc <= fr) {
    215:         NelderMeadReplace(nm,nm->indices[nm->N],Xmuc,fc);
    216:       } else shrink=1;
    217:     } else {
    218:       /* inside contraction */
    219:       nm->nincontract++;
    220:       PetscInfo(0,"Inside Contraction\n");
    221:       VecAXPBYPCZ(Xmuc,1+nm->mu_ic,-nm->mu_ic,0,Xbar,nm->simplex[nm->indices[nm->N]]);
    222:       TaoComputeObjective(tao,Xmuc,&fc);
    223:       if (fc < nm->f_values[nm->indices[nm->N]]) {
    224:         NelderMeadReplace(nm,nm->indices[nm->N],Xmuc,fc);
    225:       } else shrink = 1;
    226:     }

    228:     if (shrink) {
    229:       nm->nshrink++;
    230:       PetscInfo(0,"Shrink\n");

    232:       for (i=1;i<nm->N+1;i++) {
    233:         VecAXPBY(nm->simplex[nm->indices[i]],1.5,-0.5,nm->simplex[nm->indices[0]]);
    234:         TaoComputeObjective(tao,nm->simplex[nm->indices[i]], &nm->f_values[nm->indices[i]]);
    235:       }
    236:       VecAXPBY(Xbar,1.5*nm->oneOverN,-0.5,nm->simplex[nm->indices[0]]);

    238:       /*  Add last vector's fraction of average */
    239:       VecAXPY(Xbar,nm->oneOverN,nm->simplex[nm->indices[nm->N]]);
    240:       NelderMeadSort(nm);
    241:       /*  Subtract new last vector from average */
    242:       VecAXPY(Xbar,-nm->oneOverN,nm->simplex[nm->indices[nm->N]]);
    243:     }
    244:   }
    245:   return(0);
    246: }

    248: /* ---------------------------------------------------------- */
    249: /*MC
    250:  TAONM - Nelder-Mead solver for derivative free, unconstrained minimization

    252:  Options Database Keys:
    253: + -tao_nm_lamda - initial step length
    254: - -tao_nm_mu - expansion/contraction factor

    256:  Level: beginner
    257: M*/

    259: PETSC_EXTERN PetscErrorCode TaoCreate_NM(Tao tao)
    260: {
    261:   TAO_NelderMead *nm;

    265:   PetscNewLog(tao,&nm);
    266:   tao->data = (void*)nm;

    268:   tao->ops->setup = TaoSetUp_NM;
    269:   tao->ops->solve = TaoSolve_NM;
    270:   tao->ops->view = TaoView_NM;
    271:   tao->ops->setfromoptions = TaoSetFromOptions_NM;
    272:   tao->ops->destroy = TaoDestroy_NM;

    274:   /* Override default settings (unless already changed) */
    275:   if (!tao->max_it_changed) tao->max_it = 2000;
    276:   if (!tao->max_funcs_changed) tao->max_funcs = 4000;

    278:   nm->simplex = NULL;
    279:   nm->lamda = 1;

    281:   nm->mu_ic = -0.5;
    282:   nm->mu_oc = 0.5;
    283:   nm->mu_r = 1.0;
    284:   nm->mu_e = 2.0;

    286:   return(0);
    287: }