Actual source code: neldermead.c
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: }