Actual source code: pounders.c

petsc-dev 2014-02-02
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  1: #include <../src/tao/leastsquares/impls/pounders/pounders.h>

  5: static PetscErrorCode pounders_h(Tao subtao, Vec v, Mat *H, Mat *Hpre, MatStructure *flag, void *ctx)
  6: {
  8:   *flag = SAME_NONZERO_PATTERN;
  9:   return(0);
 10: }
 13: static PetscErrorCode  pounders_fg(Tao subtao, Vec x, PetscReal *f, Vec g, void *ctx)
 14: {
 15:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)ctx;
 16:   PetscReal      d1,d2;

 20:   /* g = A*x  (add b later)*/
 21:   MatMult(mfqP->subH,x,g);

 23:   /* f = 1/2 * x'*(Ax) + b'*x  */
 24:   VecDot(x,g,&d1);
 25:   VecDot(mfqP->subb,x,&d2);
 26:   *f = 0.5 *d1 + d2;

 28:   /* now  g = g + b */
 29:   VecAXPY(g, 1.0, mfqP->subb);
 30:   return(0);
 31: }

 35: PetscErrorCode gqtwrap(Tao tao,PetscReal *gnorm, PetscReal *qmin)
 36: {
 38: #if defined(PETSC_USE_REAL_SINGLE)
 39:   PetscReal      atol=1.0e-5;
 40: #else
 41:   PetscReal      atol=1.0e-10;
 42: #endif
 43:   PetscInt       info,its;
 44:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;

 47:   if (! mfqP->usegqt) {
 48:     PetscReal maxval;
 49:     PetscInt  i,j;

 51:     VecSetValues(mfqP->subb,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);
 52:     VecAssemblyBegin(mfqP->subb);
 53:     VecAssemblyEnd(mfqP->subb);

 55:     VecSet(mfqP->subx,0.0);

 57:     VecSet(mfqP->subndel,-mfqP->delta);
 58:     VecSet(mfqP->subpdel,mfqP->delta);

 60:     for (i=0;i<mfqP->n;i++) {
 61:       for (j=i;j<mfqP->n;j++) {
 62:         mfqP->Hres[j+mfqP->n*i] = mfqP->Hres[mfqP->n*j+i];
 63:       }
 64:     }
 65:     MatSetValues(mfqP->subH,mfqP->n,mfqP->indices,mfqP->n,mfqP->indices,mfqP->Hres,INSERT_VALUES);
 66:     MatAssemblyBegin(mfqP->subH,MAT_FINAL_ASSEMBLY);
 67:     MatAssemblyEnd(mfqP->subH,MAT_FINAL_ASSEMBLY);

 69:     TaoResetStatistics(mfqP->subtao);
 70:     TaoSetTolerances(mfqP->subtao,PETSC_DEFAULT,PETSC_DEFAULT,*gnorm,*gnorm,PETSC_DEFAULT);
 71:     /* enforce bound constraints -- experimental */
 72:     if (tao->XU && tao->XL) {
 73:       VecCopy(tao->XU,mfqP->subxu);
 74:       VecAXPY(mfqP->subxu,-1.0,tao->solution);
 75:       VecScale(mfqP->subxu,1.0/mfqP->delta);
 76:       VecCopy(tao->XL,mfqP->subxl);
 77:       VecAXPY(mfqP->subxl,-1.0,tao->solution);
 78:       VecScale(mfqP->subxl,1.0/mfqP->delta);

 80:       VecPointwiseMin(mfqP->subxu,mfqP->subxu,mfqP->subpdel);
 81:       VecPointwiseMax(mfqP->subxl,mfqP->subxl,mfqP->subndel);
 82:     } else {
 83:       VecCopy(mfqP->subpdel,mfqP->subxu);
 84:       VecCopy(mfqP->subndel,mfqP->subxl);
 85:     }
 86:     /* Make sure xu > xl */
 87:     VecCopy(mfqP->subxl,mfqP->subpdel);
 88:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);
 89:     VecMax(mfqP->subpdel,NULL,&maxval);
 90:     if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"upper bound < lower bound in subproblem");
 91:     /* Make sure xu > tao->solution > xl */
 92:     VecCopy(mfqP->subxl,mfqP->subpdel);
 93:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subx);
 94:     VecMax(mfqP->subpdel,NULL,&maxval);
 95:     if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"initial guess < lower bound in subproblem");

 97:     VecCopy(mfqP->subx,mfqP->subpdel);
 98:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);
 99:     VecMax(mfqP->subpdel,NULL,&maxval);
100:     if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"initial guess > upper bound in subproblem");

102:     TaoSolve(mfqP->subtao);
103:     TaoGetSolutionStatus(mfqP->subtao,NULL,qmin,NULL,NULL,NULL,NULL);

105:     /* test bounds post-solution*/
106:     VecCopy(mfqP->subxl,mfqP->subpdel);
107:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subx);
108:     VecMax(mfqP->subpdel,NULL,&maxval);
109:     if (maxval > 1e-5) {
110:       PetscInfo(tao,"subproblem solution < lower bound");
111:       tao->reason = TAO_DIVERGED_TR_REDUCTION;
112:     }

114:     VecCopy(mfqP->subx,mfqP->subpdel);
115:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);
116:     VecMax(mfqP->subpdel,NULL,&maxval);
117:     if (maxval > 1e-5) {
118:       PetscInfo(tao,"subproblem solution > upper bound");
119:       tao->reason = TAO_DIVERGED_TR_REDUCTION;
120:     }
121:   } else {
122:     gqt(mfqP->n,mfqP->Hres,mfqP->n,mfqP->Gres,1.0,mfqP->gqt_rtol,atol,mfqP->gqt_maxits,gnorm,qmin,mfqP->Xsubproblem,&info,&its,mfqP->work,mfqP->work2, mfqP->work3);
123:   }
124:   *qmin *= -1;
125:   return(0);
126: }

130: PetscErrorCode phi2eval(PetscReal *x, PetscInt n, PetscReal *phi)
131: {
132: /* Phi = .5*[x(1)^2  sqrt(2)*x(1)*x(2) ... sqrt(2)*x(1)*x(n) ... x(2)^2 sqrt(2)*x(2)*x(3) .. x(n)^2] */
133:   PetscInt  i,j,k;
134:   PetscReal sqrt2 = PetscSqrtReal(2.0);

137:   j=0;
138:   for (i=0;i<n;i++) {
139:     phi[j] = 0.5 * x[i]*x[i];
140:     j++;
141:     for (k=i+1;k<n;k++) {
142:       phi[j]  = x[i]*x[k]/sqrt2;
143:       j++;
144:     }
145:   }
146:   return(0);
147: }

151: PetscErrorCode getquadpounders(TAO_POUNDERS *mfqP)
152: {
153: /* Computes the parameters of the quadratic Q(x) = c + g'*x + 0.5*x*G*x'
154:    that satisfies the interpolation conditions Q(X[:,j]) = f(j)
155:    for j=1,...,m and with a Hessian matrix of least Frobenius norm */

157:     /* NB --we are ignoring c */
158:   PetscInt     i,j,k,num,np = mfqP->nmodelpoints;
159:   PetscReal    one = 1.0,zero=0.0,negone=-1.0;
160:   PetscBLASInt blasnpmax = mfqP->npmax;
161:   PetscBLASInt blasnplus1 = mfqP->n+1;
162:   PetscBLASInt blasnp = np;
163:   PetscBLASInt blasint = mfqP->n*(mfqP->n+1) / 2;
164:   PetscBLASInt blasint2 = np - mfqP->n-1;
165:   PetscBLASInt info,ione=1;
166:   PetscReal    sqrt2 = PetscSqrtReal(2.0);

169:   for (i=0;i<mfqP->n*mfqP->m;i++) {
170:     mfqP->Gdel[i] = 0;
171:   }
172:   for (i=0;i<mfqP->n*mfqP->n*mfqP->m;i++) {
173:     mfqP->Hdel[i] = 0;
174:   }

176:     /* factor M */
177:   PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&blasnplus1,&blasnpmax,mfqP->M,&blasnplus1,mfqP->npmaxiwork,&info));
178:   if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine getrf returned with value %d\n",info);

180:   if (np == mfqP->n+1) {
181:     for (i=0;i<mfqP->npmax-mfqP->n-1;i++) {
182:       mfqP->omega[i]=0.0;
183:     }
184:     for (i=0;i<mfqP->n*(mfqP->n+1)/2;i++) {
185:       mfqP->beta[i]=0.0;
186:     }
187:   } else {
188:     /* Let Ltmp = (L'*L) */
189:     PetscStackCallBLAS("BLASgemm",BLASgemm_("T","N",&blasint2,&blasint2,&blasint,&one,&mfqP->L[(mfqP->n+1)*blasint],&blasint,&mfqP->L[(mfqP->n+1)*blasint],&blasint,&zero,mfqP->L_tmp,&blasint));

191:     /* factor Ltmp */
192:     PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&blasint2,mfqP->L_tmp,&blasint,&info));
193:     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine potrf returned with value %d\n",info);
194:   }

196:   for (k=0;k<mfqP->m;k++) {
197:     if (np != mfqP->n+1) {
198:       /* Solve L'*L*Omega = Z' * RESk*/
199:       PetscStackCallBLAS("BLASgemv",BLASgemv_("T",&blasnp,&blasint2,&one,mfqP->Z,&blasnpmax,&mfqP->RES[mfqP->npmax*k],&ione,&zero,mfqP->omega,&ione));
200:       PetscStackCallBLAS("LAPACKpotrs",LAPACKpotrs_("L",&blasint2,&ione,mfqP->L_tmp,&blasint,mfqP->omega,&blasint2,&info));
201:       if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine potrs returned with value %d\n",info);

203:       /* Beta = L*Omega */
204:       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasint,&blasint2,&one,&mfqP->L[(mfqP->n+1)*blasint],&blasint,mfqP->omega,&ione,&zero,mfqP->beta,&ione));
205:     }

207:     /* solve M'*Alpha = RESk - N'*Beta */
208:     PetscStackCallBLAS("BLASgemv",BLASgemv_("T",&blasint,&blasnp,&negone,mfqP->N,&blasint,mfqP->beta,&ione,&one,&mfqP->RES[mfqP->npmax*k],&ione));
209:     PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("T",&blasnplus1,&ione,mfqP->M,&blasnplus1,mfqP->npmaxiwork,&mfqP->RES[mfqP->npmax*k],&blasnplus1,&info));
210:     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine getrs returned with value %d\n",info);

212:     /* Gdel(:,k) = Alpha(2:n+1) */
213:     for (i=0;i<mfqP->n;i++) {
214:       mfqP->Gdel[i + mfqP->n*k] = mfqP->RES[mfqP->npmax*k + i+1];
215:     }

217:     /* Set Hdels */
218:     num=0;
219:     for (i=0;i<mfqP->n;i++) {
220:       /* H[i,i,k] = Beta(num) */
221:       mfqP->Hdel[(i*mfqP->n + i)*mfqP->m + k] = mfqP->beta[num];
222:       num++;
223:       for (j=i+1;j<mfqP->n;j++) {
224:         /* H[i,j,k] = H[j,i,k] = Beta(num)/sqrt(2) */
225:         mfqP->Hdel[(j*mfqP->n + i)*mfqP->m + k] = mfqP->beta[num]/sqrt2;
226:         mfqP->Hdel[(i*mfqP->n + j)*mfqP->m + k] = mfqP->beta[num]/sqrt2;
227:         num++;
228:       }
229:     }
230:   }
231:   return(0);
232: }

236: PetscErrorCode morepoints(TAO_POUNDERS *mfqP)
237: {
238:   /* Assumes mfqP->model_indices[0]  is minimum index
239:    Finishes adding points to mfqP->model_indices (up to npmax)
240:    Computes L,Z,M,N
241:    np is actual number of points in model (should equal npmax?) */
242:   PetscInt       point,i,j,offset;
243:   PetscInt       reject;
244:   PetscBLASInt   blasn=mfqP->n,blasnpmax=mfqP->npmax,blasnplus1=mfqP->n+1,info,blasnmax=mfqP->nmax,blasint,blasint2,blasnp,blasmaxmn;
245:   PetscReal      *x,normd;

249:   /* Initialize M,N */
250:   for (i=0;i<mfqP->n+1;i++) {
251:     VecGetArray(mfqP->Xhist[mfqP->model_indices[i]],&x);
252:     mfqP->M[(mfqP->n+1)*i] = 1.0;
253:     for (j=0;j<mfqP->n;j++) {
254:       mfqP->M[j+1+((mfqP->n+1)*i)] = (x[j]  - mfqP->xmin[j]) / mfqP->delta;
255:     }
256:     VecRestoreArray(mfqP->Xhist[mfqP->model_indices[i]],&x);
257:     phi2eval(&mfqP->M[1+((mfqP->n+1)*i)],mfqP->n,&mfqP->N[mfqP->n*(mfqP->n+1)/2 * i]);
258:   }

260:   /* Now we add points until we have npmax starting with the most recent ones */
261:   point = mfqP->nHist-1;
262:   mfqP->nmodelpoints = mfqP->n+1;
263:   while (mfqP->nmodelpoints < mfqP->npmax && point>=0) {
264:     /* Reject any points already in the model */
265:     reject = 0;
266:     for (j=0;j<mfqP->n+1;j++) {
267:       if (point == mfqP->model_indices[j]) {
268:         reject = 1;
269:         break;
270:       }
271:     }

273:     /* Reject if norm(d) >c2 */
274:     if (!reject) {
275:       VecCopy(mfqP->Xhist[point],mfqP->workxvec);
276:       VecAXPY(mfqP->workxvec,-1.0,mfqP->Xhist[mfqP->minindex]);
277:       VecNorm(mfqP->workxvec,NORM_2,&normd);
278:       normd /= mfqP->delta;
279:       if (normd > mfqP->c2) {
280:         reject =1;
281:       }
282:     }
283:     if (reject){
284:       point--;
285:       continue;
286:     }

288:     VecGetArray(mfqP->Xhist[point],&x);
289:     mfqP->M[(mfqP->n+1)*mfqP->nmodelpoints] = 1.0;
290:     for (j=0;j<mfqP->n;j++) {
291:       mfqP->M[j+1+((mfqP->n+1)*mfqP->nmodelpoints)] = (x[j]  - mfqP->xmin[j]) / mfqP->delta;
292:     }
293:     VecRestoreArray(mfqP->Xhist[point],&x);
294:     phi2eval(&mfqP->M[1+(mfqP->n+1)*mfqP->nmodelpoints],mfqP->n,&mfqP->N[mfqP->n*(mfqP->n+1)/2 * (mfqP->nmodelpoints)]);

296:     /* Update QR factorization */
297:     /* Copy M' to Q_tmp */
298:     for (i=0;i<mfqP->n+1;i++) {
299:       for (j=0;j<mfqP->npmax;j++) {
300:         mfqP->Q_tmp[j+mfqP->npmax*i] = mfqP->M[i+(mfqP->n+1)*j];
301:       }
302:     }
303:     blasnp = mfqP->nmodelpoints+1;
304:     /* Q_tmp,R = qr(M') */
305:     blasmaxmn=PetscMax(mfqP->m,mfqP->n+1);
306:     PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&blasnp,&blasnplus1,mfqP->Q_tmp,&blasnpmax,mfqP->tau_tmp,mfqP->mwork,&blasmaxmn,&info));
307:     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine geqrf returned with value %d\n",info);

309:     /* Reject if min(svd(N*Q(:,n+2:np+1)) <= theta2 */
310:     /* L = N*Qtmp */
311:     blasint2 = mfqP->n * (mfqP->n+1) / 2;
312:     /* Copy N to L_tmp */
313:     for (i=0;i<mfqP->n*(mfqP->n+1)/2 * mfqP->npmax;i++) {
314:       mfqP->L_tmp[i]= mfqP->N[i];
315:     }
316:     /* Copy L_save to L_tmp */

318:     /* L_tmp = N*Qtmp' */
319:     PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&blasint2,&blasnp,&blasnplus1,mfqP->Q_tmp,&blasnpmax,mfqP->tau_tmp,mfqP->L_tmp,&blasint2,mfqP->npmaxwork,&blasnmax,&info));
320:     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine ormqr returned with value %d\n",info);

322:     /* Copy L_tmp to L_save */
323:     for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
324:       mfqP->L_save[i] = mfqP->L_tmp[i];
325:     }

327:     /* Get svd for L_tmp(:,n+2:np+1) (L_tmp is modified in process) */
328:     blasint = mfqP->nmodelpoints - mfqP->n;
329:     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","N",&blasint2,&blasint,&mfqP->L_tmp[(mfqP->n+1)*blasint2],&blasint2,mfqP->beta,mfqP->work,&blasn,mfqP->work,&blasn,mfqP->npmaxwork,&blasnmax,&info));
330:     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine gesvd returned with value %d\n",info);

332:     if (mfqP->beta[PetscMin(blasint,blasint2)-1] > mfqP->theta2) {
333:       /* accept point */
334:       mfqP->model_indices[mfqP->nmodelpoints] = point;
335:       /* Copy Q_tmp to Q */
336:       for (i=0;i<mfqP->npmax* mfqP->npmax;i++) {
337:         mfqP->Q[i] = mfqP->Q_tmp[i];
338:       }
339:       for (i=0;i<mfqP->npmax;i++){
340:         mfqP->tau[i] = mfqP->tau_tmp[i];
341:       }
342:       mfqP->nmodelpoints++;
343:       blasnp = mfqP->nmodelpoints+1;

345:       /* Copy L_save to L */
346:       for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
347:         mfqP->L[i] = mfqP->L_save[i];
348:       }
349:     }
350:     point--;
351:   }

353:   blasnp = mfqP->nmodelpoints;
354:   /* Copy Q(:,n+2:np) to Z */
355:   /* First set Q_tmp to I */
356:   for (i=0;i<mfqP->npmax*mfqP->npmax;i++) {
357:     mfqP->Q_tmp[i] = 0.0;
358:   }
359:   for (i=0;i<mfqP->npmax;i++) {
360:     mfqP->Q_tmp[i + mfqP->npmax*i] = 1.0;
361:   }

363:   /* Q_tmp = I * Q */
364:   PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&blasnp,&blasnp,&blasnplus1,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->Q_tmp,&blasnpmax,mfqP->npmaxwork,&blasnmax,&info));
365:   if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine ormqr returned with value %d\n",info);

367:   /* Copy Q_tmp(:,n+2:np) to Z) */
368:   offset = mfqP->npmax * (mfqP->n+1);
369:   for (i=offset;i<mfqP->npmax*mfqP->npmax;i++) {
370:     mfqP->Z[i-offset] = mfqP->Q_tmp[i];
371:   }

373:   if (mfqP->nmodelpoints == mfqP->n + 1) {
374:     /* Set L to I_{n+1} */
375:     for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
376:       mfqP->L[i] = 0.0;
377:     }
378:     for (i=0;i<mfqP->n;i++) {
379:       mfqP->L[(mfqP->n*(mfqP->n+1)/2)*i + i] = 1.0;
380:     }
381:   }
382:   return(0);
383: }

387: /* Only call from modelimprove, addpoint() needs ->Q_tmp and ->work to be set */
388: PetscErrorCode addpoint(Tao tao, TAO_POUNDERS *mfqP, PetscInt index)
389: {

393:   /* Create new vector in history: X[newidx] = X[mfqP->index] + delta*X[index]*/
394:   VecDuplicate(mfqP->Xhist[0],&mfqP->Xhist[mfqP->nHist]);
395:   VecSetValues(mfqP->Xhist[mfqP->nHist],mfqP->n,mfqP->indices,&mfqP->Q_tmp[index*mfqP->npmax],INSERT_VALUES);
396:   VecAssemblyBegin(mfqP->Xhist[mfqP->nHist]);
397:   VecAssemblyEnd(mfqP->Xhist[mfqP->nHist]);
398:   VecAYPX(mfqP->Xhist[mfqP->nHist],mfqP->delta,mfqP->Xhist[mfqP->minindex]);

400:   /* Project into feasible region */
401:   if (tao->XU && tao->XL) {
402:     VecMedian(mfqP->Xhist[mfqP->nHist], tao->XL, tao->XU, mfqP->Xhist[mfqP->nHist]);
403:   }

405:   /* Compute value of new vector */
406:   VecDuplicate(mfqP->Fhist[0],&mfqP->Fhist[mfqP->nHist]);
407:   CHKMEMQ;
408:   TaoComputeSeparableObjective(tao,mfqP->Xhist[mfqP->nHist],mfqP->Fhist[mfqP->nHist]);
409:   VecNorm(mfqP->Fhist[mfqP->nHist],NORM_2,&mfqP->Fres[mfqP->nHist]);
410:   if (PetscIsInfOrNanReal(mfqP->Fres[mfqP->nHist])) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
411:   mfqP->Fres[mfqP->nHist]*=mfqP->Fres[mfqP->nHist];

413:   /* Add new vector to model */
414:   mfqP->model_indices[mfqP->nmodelpoints] = mfqP->nHist;
415:   mfqP->nmodelpoints++;
416:   mfqP->nHist++;
417:   return(0);
418: }

422: PetscErrorCode modelimprove(Tao tao, TAO_POUNDERS *mfqP, PetscInt addallpoints)
423: {
424:   /* modeld = Q(:,np+1:n)' */
426:   PetscInt       i,j,minindex=0;
427:   PetscReal      dp,half=0.5,one=1.0,minvalue=PETSC_INFINITY;
428:   PetscBLASInt   blasn=mfqP->n,  blasnpmax = mfqP->npmax, blask,info;
429:   PetscBLASInt   blas1=1,blasnmax = mfqP->nmax;

431:   blask = mfqP->nmodelpoints;
432:   /* Qtmp = I(n x n) */
433:   for (i=0;i<mfqP->n;i++) {
434:     for (j=0;j<mfqP->n;j++) {
435:       mfqP->Q_tmp[i + mfqP->npmax*j] = 0.0;
436:     }
437:   }
438:   for (j=0;j<mfqP->n;j++) {
439:     mfqP->Q_tmp[j + mfqP->npmax*j] = 1.0;
440:   }

442:   /* Qtmp = Q * I */
443:   PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&blasn,&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau, mfqP->Q_tmp, &blasnpmax, mfqP->npmaxwork,&blasnmax, &info));

445:   for (i=mfqP->nmodelpoints;i<mfqP->n;i++) {
446:     dp = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->Gres,&blas1);
447:     if (dp>0.0) { /* Model says use the other direction! */
448:       for (j=0;j<mfqP->n;j++) {
449:         mfqP->Q_tmp[i*mfqP->npmax+j] *= -1;
450:       }
451:     }
452:     /* mfqP->work[i] = Cres+Modeld(i,:)*(Gres+.5*Hres*Modeld(i,:)') */
453:     for (j=0;j<mfqP->n;j++) {
454:       mfqP->work2[j] = mfqP->Gres[j];
455:     }
456:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&half,mfqP->Hres,&blasn,&mfqP->Q_tmp[i*mfqP->npmax], &blas1, &one, mfqP->work2,&blas1));
457:     mfqP->work[i] = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->work2,&blas1);
458:     if (i==mfqP->nmodelpoints || mfqP->work[i] < minvalue) {
459:       minindex=i;
460:       minvalue = mfqP->work[i];
461:     }
462:     if (addallpoints != 0) {
463:       addpoint(tao,mfqP,i);
464:     }
465:   }
466:   if (!addallpoints) {
467:     addpoint(tao,mfqP,minindex);
468:   }
469:   return(0);
470: }


475: PetscErrorCode affpoints(TAO_POUNDERS *mfqP, PetscReal *xmin,PetscReal c)
476: {
477:   PetscInt       i,j;
478:   PetscBLASInt   blasm=mfqP->m,blasj,blask,blasn=mfqP->n,ione=1,info;
479:   PetscBLASInt   blasnpmax = mfqP->npmax,blasmaxmn;
480:   PetscReal      proj,normd;
481:   PetscReal      *x;

485:   for (i=mfqP->nHist-1;i>=0;i--) {
486:     VecGetArray(mfqP->Xhist[i],&x);
487:     for (j=0;j<mfqP->n;j++) {
488:       mfqP->work[j] = (x[j] - xmin[j])/mfqP->delta;
489:     }
490:     VecRestoreArray(mfqP->Xhist[i],&x);
491:     PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,mfqP->work,&ione,mfqP->work2,&ione));
492:     normd = BLASnrm2_(&blasn,mfqP->work,&ione);
493:     if (normd <= c*c) {
494:       blasj=PetscMax((mfqP->n - mfqP->nmodelpoints),0);
495:       if (!mfqP->q_is_I) {
496:         /* project D onto null */
497:         blask=(mfqP->nmodelpoints);
498:         PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&ione,&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->work2,&ione,mfqP->mwork,&blasm,&info));
499:         if (info < 0) SETERRQ1(PETSC_COMM_SELF,1,"ormqr returned value %d\n",info);
500:       }
501:       proj = BLASnrm2_(&blasj,&mfqP->work2[mfqP->nmodelpoints],&ione);

503:       if (proj >= mfqP->theta1) { /* add this index to model */
504:         mfqP->model_indices[mfqP->nmodelpoints]=i;
505:         mfqP->nmodelpoints++;
506:         PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,mfqP->work,&ione,&mfqP->Q_tmp[mfqP->npmax*(mfqP->nmodelpoints-1)],&ione));
507:         blask=mfqP->npmax*(mfqP->nmodelpoints);
508:         PetscStackCallBLAS("BLAScopy",BLAScopy_(&blask,mfqP->Q_tmp,&ione,mfqP->Q,&ione));
509:         blask = mfqP->nmodelpoints;
510:         blasmaxmn = PetscMax(mfqP->m,mfqP->n);
511:         PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->mwork,&blasmaxmn,&info));
512:         if (info < 0) SETERRQ1(PETSC_COMM_SELF,1,"geqrf returned value %d\n",info);
513:         mfqP->q_is_I = 0;
514:       }
515:       if (mfqP->nmodelpoints == mfqP->n)  {
516:         break;
517:       }
518:     }
519:   }
520:   return(0);
521: }

525: static PetscErrorCode TaoSolve_POUNDERS(Tao tao)
526: {
527:   TAO_POUNDERS               *mfqP = (TAO_POUNDERS *)tao->data;
528:   PetscInt                   i,ii,j,k,l,iter=0;
529:   PetscReal                  step=1.0;
530:   TaoTerminationReason reason = TAO_CONTINUE_ITERATING;
531:   PetscInt                   low,high;
532:   PetscReal                  minnorm;
533:   PetscReal                  *x,*f,*fmin,*xmint;
534:   PetscReal                  cres,deltaold;
535:   PetscReal                  gnorm;
536:   PetscBLASInt               info,ione=1,iblas;
537:   PetscBool                  valid;
538:   PetscReal                  mdec, rho, normxsp;
539:   PetscReal                  one=1.0,zero=0.0,ratio;
540:   PetscBLASInt               blasm,blasn,blasnpmax,blasn2;
541:   PetscErrorCode             ierr;

543:   /* n = # of parameters
544:      m = dimension (components) of function  */
546:   if (tao->XL && tao->XU) {
547:     /* Check x0 <= XU */
548:     PetscReal val;
549:     VecCopy(tao->solution,mfqP->Xhist[0]);
550:     VecAXPY(mfqP->Xhist[0],-1.0,tao->XU);
551:     VecMax(mfqP->Xhist[0],NULL,&val);
552:     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 > upper bound");

554:     /* Check x0 >= xl */
555:     VecCopy(tao->XL,mfqP->Xhist[0]);
556:     VecAXPY(mfqP->Xhist[0],-1.0,tao->solution);
557:     VecMax(mfqP->Xhist[0],NULL,&val);
558:     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 < lower bound");

560:     /* Check x0 + delta < XU  -- should be able to get around this eventually */

562:     VecSet(mfqP->Xhist[0],mfqP->delta);
563:     VecAXPY(mfqP->Xhist[0],1.0,tao->solution);
564:     VecAXPY(mfqP->Xhist[0],-1.0,tao->XU);
565:     VecMax(mfqP->Xhist[0],NULL,&val);
566:     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 + delta > upper bound");
567:   }

569:   CHKMEMQ;
570:   blasm = mfqP->m; blasn=mfqP->n; blasnpmax = mfqP->npmax;
571:   for (i=0;i<mfqP->n*mfqP->n*mfqP->m;i++) mfqP->H[i]=0;

573:   VecCopy(tao->solution,mfqP->Xhist[0]);
574:   CHKMEMQ;
575:   TaoComputeSeparableObjective(tao,tao->solution,mfqP->Fhist[0]);

577:   VecNorm(mfqP->Fhist[0],NORM_2,&mfqP->Fres[0]);
578:   if (PetscIsInfOrNanReal(mfqP->Fres[0])) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
579:   mfqP->Fres[0]*=mfqP->Fres[0];
580:   mfqP->minindex = 0;
581:   minnorm = mfqP->Fres[0];
582:   VecGetOwnershipRange(mfqP->Xhist[0],&low,&high);
583:   for (i=1;i<mfqP->n+1;i++) {
584:     VecCopy(tao->solution,mfqP->Xhist[i]);
585:     if (i-1 >= low && i-1 < high) {
586:       VecGetArray(mfqP->Xhist[i],&x);
587:       x[i-1-low] += mfqP->delta;
588:       VecRestoreArray(mfqP->Xhist[i],&x);
589:     }
590:     CHKMEMQ;
591:     TaoComputeSeparableObjective(tao,mfqP->Xhist[i],mfqP->Fhist[i]);
592:     VecNorm(mfqP->Fhist[i],NORM_2,&mfqP->Fres[i]);
593:     if (PetscIsInfOrNanReal(mfqP->Fres[i])) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
594:     mfqP->Fres[i]*=mfqP->Fres[i];
595:     if (mfqP->Fres[i] < minnorm) {
596:       mfqP->minindex = i;
597:       minnorm = mfqP->Fres[i];
598:     }
599:   }

601:   VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);
602:   VecCopy(mfqP->Fhist[mfqP->minindex],tao->sep_objective);
603:   /* Gather mpi vecs to one big local vec */

605:   /* Begin serial code */

607:   /* Disp[i] = Xi-xmin, i=1,..,mfqP->minindex-1,mfqP->minindex+1,..,n */
608:   /* Fdiff[i] = (Fi-Fmin)', i=1,..,mfqP->minindex-1,mfqP->minindex+1,..,n */
609:   /* (Column oriented for blas calls) */
610:   ii=0;

612:   if (mfqP->size == 1) {
613:     VecGetArray(mfqP->Xhist[mfqP->minindex],&xmint);
614:     for (i=0;i<mfqP->n;i++) mfqP->xmin[i] = xmint[i];
615:     VecRestoreArray(mfqP->Xhist[mfqP->minindex],&xmint);
616:     VecGetArray(mfqP->Fhist[mfqP->minindex],&fmin);
617:     for (i=0;i<mfqP->n+1;i++) {
618:       if (i == mfqP->minindex) continue;

620:       VecGetArray(mfqP->Xhist[i],&x);
621:       for (j=0;j<mfqP->n;j++) {
622:         mfqP->Disp[ii+mfqP->npmax*j] = (x[j] - mfqP->xmin[j])/mfqP->delta;
623:       }
624:       VecRestoreArray(mfqP->Xhist[i],&x);

626:       VecGetArray(mfqP->Fhist[i],&f);
627:       for (j=0;j<mfqP->m;j++) {
628:         mfqP->Fdiff[ii+mfqP->n*j] = f[j] - fmin[j];
629:       }
630:       VecRestoreArray(mfqP->Fhist[i],&f);
631:       mfqP->model_indices[ii++] = i;

633:     }
634:     for (j=0;j<mfqP->m;j++) {
635:       mfqP->C[j] = fmin[j];
636:     }
637:     VecRestoreArray(mfqP->Fhist[mfqP->minindex],&fmin);
638:   } else {
639:     VecScatterBegin(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);
640:     VecScatterEnd(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);
641:     VecGetArray(mfqP->localxmin,&xmint);
642:     for (i=0;i<mfqP->n;i++) mfqP->xmin[i] = xmint[i];
643:     VecRestoreArray(mfqP->localxmin,&mfqP->xmin);

645:     VecScatterBegin(mfqP->scatterf,mfqP->Fhist[mfqP->minindex],mfqP->localfmin,INSERT_VALUES,SCATTER_FORWARD);
646:     VecScatterEnd(mfqP->scatterf,mfqP->Fhist[mfqP->minindex],mfqP->localfmin,INSERT_VALUES,SCATTER_FORWARD);
647:     VecGetArray(mfqP->localfmin,&fmin);
648:     for (i=0;i<mfqP->n+1;i++) {
649:       if (i == mfqP->minindex) continue;

651:       mfqP->model_indices[ii++] = i;
652:       VecScatterBegin(mfqP->scatterx,mfqP->Xhist[ii],mfqP->localx,INSERT_VALUES, SCATTER_FORWARD);
653:       VecScatterEnd(mfqP->scatterx,mfqP->Xhist[ii],mfqP->localx,INSERT_VALUES, SCATTER_FORWARD);
654:       VecGetArray(mfqP->localx,&x);
655:       for (j=0;j<mfqP->n;j++) {
656:         mfqP->Disp[i+mfqP->npmax*j] = (x[j] - mfqP->xmin[j])/mfqP->delta;
657:       }
658:       VecRestoreArray(mfqP->localx,&x);

660:       VecScatterBegin(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);
661:       VecScatterEnd(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);
662:       VecGetArray(mfqP->localf,&f);
663:       for (j=0;j<mfqP->m;j++) {
664:         mfqP->Fdiff[i*mfqP->n+j] = f[j] - fmin[j];
665:       }
666:       VecRestoreArray(mfqP->localf,&f);
667:     }
668:     for (j=0;j<mfqP->m;j++) {
669:       mfqP->C[j] = fmin[j];
670:     }
671:     VecRestoreArray(mfqP->localfmin,&fmin);
672:   }

674:   /* Determine the initial quadratic models */
675:   /* G = D(ModelIn,:) \ (F(ModelIn,1:m)-repmat(F(xkin,1:m),n,1)); */
676:   /* D (nxn) Fdiff (nxm)  => G (nxm) */
677:   blasn2 = blasn;
678:   PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&blasn,&blasm,mfqP->Disp,&blasnpmax,mfqP->iwork,mfqP->Fdiff,&blasn2,&info));
679:   PetscInfo1(tao,"gesv returned %d\n",info);

681:   cres = minnorm;
682:   /* Gres = G*F(xkin,1:m)'  G (nxm)   Fk (m)   */
683:   PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasm,&one,mfqP->Fdiff,&blasn,mfqP->C,&ione,&zero,mfqP->Gres,&ione));

685:   /*  Hres = G*G'  */
686:   PetscStackCallBLAS("BLASgemm",BLASgemm_("N","T",&blasn,&blasn,&blasm,&one,mfqP->Fdiff, &blasn,mfqP->Fdiff,&blasn,&zero,mfqP->Hres,&blasn));

688:   valid = PETSC_TRUE;

690:   VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);
691:   VecAssemblyBegin(tao->gradient);
692:   VecAssemblyEnd(tao->gradient);
693:   VecNorm(tao->gradient,NORM_2,&gnorm);
694:   gnorm *= mfqP->delta;
695:   VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);
696:   TaoMonitor(tao, iter, minnorm, gnorm, 0.0, step, &reason);
697:   mfqP->nHist = mfqP->n+1;
698:   mfqP->nmodelpoints = mfqP->n+1;

700:   while (reason == TAO_CONTINUE_ITERATING) {
701:     PetscReal gnm = 1e-4;
702:     iter++;
703:     /* Solve the subproblem min{Q(s): ||s|| <= delta} */
704:     gqtwrap(tao,&gnm,&mdec);
705:     /* Evaluate the function at the new point */

707:     for (i=0;i<mfqP->n;i++) {
708:         mfqP->work[i] = mfqP->Xsubproblem[i]*mfqP->delta + mfqP->xmin[i];
709:     }
710:     VecDuplicate(tao->solution,&mfqP->Xhist[mfqP->nHist]);
711:     VecDuplicate(tao->sep_objective,&mfqP->Fhist[mfqP->nHist]);
712:     VecSetValues(mfqP->Xhist[mfqP->nHist],mfqP->n,mfqP->indices,mfqP->work,INSERT_VALUES);
713:     VecAssemblyBegin(mfqP->Xhist[mfqP->nHist]);
714:     VecAssemblyEnd(mfqP->Xhist[mfqP->nHist]);

716:     TaoComputeSeparableObjective(tao,mfqP->Xhist[mfqP->nHist],mfqP->Fhist[mfqP->nHist]);
717:     VecNorm(mfqP->Fhist[mfqP->nHist],NORM_2,&mfqP->Fres[mfqP->nHist]);
718:     if (PetscIsInfOrNanReal(mfqP->Fres[mfqP->nHist])) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
719:     mfqP->Fres[mfqP->nHist]*=mfqP->Fres[mfqP->nHist];
720:     rho = (mfqP->Fres[mfqP->minindex] - mfqP->Fres[mfqP->nHist]) / mdec;
721:     mfqP->nHist++;

723:     /* Update the center */
724:     if ((rho >= mfqP->eta1) || (rho > mfqP->eta0 && valid==PETSC_TRUE)) {
725:       /* Update model to reflect new base point */
726:       for (i=0;i<mfqP->n;i++) {
727:         mfqP->work[i] = (mfqP->work[i] - mfqP->xmin[i])/mfqP->delta;
728:       }
729:       for (j=0;j<mfqP->m;j++) {
730:         /* C(j) = C(j) + work*G(:,j) + .5*work*H(:,:,j)*work';
731:          G(:,j) = G(:,j) + H(:,:,j)*work' */
732:         for (k=0;k<mfqP->n;k++) {
733:           mfqP->work2[k]=0.0;
734:           for (l=0;l<mfqP->n;l++) {
735:             mfqP->work2[k]+=mfqP->H[j + mfqP->m*(k + l*mfqP->n)]*mfqP->work[l];
736:           }
737:         }
738:         for (i=0;i<mfqP->n;i++) {
739:           mfqP->C[j]+=mfqP->work[i]*(mfqP->Fdiff[i + mfqP->n* j] + 0.5*mfqP->work2[i]);
740:           mfqP->Fdiff[i+mfqP->n*j] +=mfqP-> work2[i];
741:         }
742:       }
743:       /* Cres += work*Gres + .5*work*Hres*work';
744:        Gres += Hres*work'; */

746:       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&one,mfqP->Hres,&blasn,mfqP->work,&ione,&zero,mfqP->work2,&ione));
747:       for (i=0;j<mfqP->n;j++) {
748:         cres += mfqP->work[i]*(mfqP->Gres[i]  + 0.5*mfqP->work2[i]);
749:         mfqP->Gres[i] += mfqP->work2[i];
750:       }
751:       mfqP->minindex = mfqP->nHist-1;
752:       minnorm = mfqP->Fres[mfqP->minindex];
753:       /* Change current center */
754:       VecGetArray(mfqP->Xhist[mfqP->minindex],&xmint);
755:       for (i=0;i<mfqP->n;i++) {
756:         mfqP->xmin[i] = xmint[i];
757:       }
758:       VecRestoreArray(mfqP->Xhist[mfqP->minindex],&xmint);
759:     }

761:     /* Evaluate at a model-improving point if necessary */
762:     if (valid == PETSC_FALSE) {
763:       mfqP->q_is_I = 1;
764:       mfqP->nmodelpoints = 0;
765:       affpoints(mfqP,mfqP->xmin,mfqP->c1);
766:       if (mfqP->nmodelpoints < mfqP->n) {
767:         PetscInfo(tao,"Model not valid -- model-improving");
768:         modelimprove(tao,mfqP,1);
769:       }
770:     }

772:     /* Update the trust region radius */
773:     deltaold = mfqP->delta;
774:     normxsp = 0;
775:     for (i=0;i<mfqP->n;i++) {
776:       normxsp += mfqP->Xsubproblem[i]*mfqP->Xsubproblem[i];
777:     }
778:     normxsp = PetscSqrtReal(normxsp);
779:     if (rho >= mfqP->eta1 && normxsp > 0.5*mfqP->delta) {
780:       mfqP->delta = PetscMin(mfqP->delta*mfqP->gamma1,mfqP->deltamax);
781:     } else if (valid == PETSC_TRUE) {
782:       mfqP->delta = PetscMax(mfqP->delta*mfqP->gamma0,mfqP->deltamin);
783:     }

785:     /* Compute the next interpolation set */
786:     mfqP->q_is_I = 1;
787:     mfqP->nmodelpoints=0;
788:     affpoints(mfqP,mfqP->xmin,mfqP->c1);
789:     if (mfqP->nmodelpoints == mfqP->n) {
790:       valid = PETSC_TRUE;
791:     } else {
792:       valid = PETSC_FALSE;
793:       affpoints(mfqP,mfqP->xmin,mfqP->c2);
794:       if (mfqP->n > mfqP->nmodelpoints) {
795:         PetscInfo(tao,"Model not valid -- adding geometry points");
796:         modelimprove(tao,mfqP,mfqP->n - mfqP->nmodelpoints);
797:       }
798:     }
799:     for (i=mfqP->nmodelpoints;i>0;i--) {
800:       mfqP->model_indices[i] = mfqP->model_indices[i-1];
801:     }
802:     mfqP->nmodelpoints++;
803:     mfqP->model_indices[0] = mfqP->minindex;
804:     morepoints(mfqP);
805:     for (i=0;i<mfqP->nmodelpoints;i++) {
806:       VecGetArray(mfqP->Xhist[mfqP->model_indices[i]],&x);
807:       for (j=0;j<mfqP->n;j++) {
808:         mfqP->Disp[i + mfqP->npmax*j] = (x[j]  - mfqP->xmin[j]) / deltaold;
809:       }
810:       VecRestoreArray(mfqP->Xhist[mfqP->model_indices[i]],&x);
811:       VecGetArray(mfqP->Fhist[mfqP->model_indices[i]],&f);
812:       for (j=0;j<mfqP->m;j++) {
813:         for (k=0;k<mfqP->n;k++)  {
814:           mfqP->work[k]=0.0;
815:           for (l=0;l<mfqP->n;l++) {
816:             mfqP->work[k] += mfqP->H[j + mfqP->m*(k + mfqP->n*l)] * mfqP->Disp[i + mfqP->npmax*l];
817:           }
818:         }
819:         mfqP->RES[j*mfqP->npmax + i] = -mfqP->C[j] - BLASdot_(&blasn,&mfqP->Fdiff[j*mfqP->n],&ione,&mfqP->Disp[i],&blasnpmax) - 0.5*BLASdot_(&blasn,mfqP->work,&ione,&mfqP->Disp[i],&blasnpmax) + f[j];
820:       }
821:       VecRestoreArray(mfqP->Fhist[mfqP->model_indices[i]],&f);
822:     }

824:     /* Update the quadratic model */
825:     getquadpounders(mfqP);
826:     VecGetArray(mfqP->Fhist[mfqP->minindex],&fmin);
827:     PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasm,fmin,&ione,mfqP->C,&ione));
828:     /* G = G*(delta/deltaold) + Gdel */
829:     ratio = mfqP->delta/deltaold;
830:     iblas = blasm*blasn;
831:     PetscStackCallBLAS("BLASscal",BLASscal_(&iblas,&ratio,mfqP->Fdiff,&ione));
832:     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&one,mfqP->Gdel,&ione,mfqP->Fdiff,&ione));
833:     /* H = H*(delta/deltaold) + Hdel */
834:     iblas = blasm*blasn*blasn;
835:     ratio *= ratio;
836:     PetscStackCallBLAS("BLASscal",BLASscal_(&iblas,&ratio,mfqP->H,&ione));
837:     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&one,mfqP->Hdel,&ione,mfqP->H,&ione));

839:     /* Get residuals */
840:     cres = mfqP->Fres[mfqP->minindex];
841:     /* Gres = G*F(xkin,1:m)' */
842:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasm,&one,mfqP->Fdiff,&blasn,mfqP->C,&ione,&zero,mfqP->Gres,&ione));
843:     /* Hres = sum i=1..m {F(xkin,i)*H(:,:,i)}   + G*G' */
844:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","T",&blasn,&blasn,&blasm,&one,mfqP->Fdiff,&blasn,mfqP->Fdiff,&blasn,&zero,mfqP->Hres,&blasn));

846:     iblas = mfqP->n*mfqP->n;

848:     for (j=0;j<mfqP->m;j++) {
849:       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&fmin[j],&mfqP->H[j],&blasm,mfqP->Hres,&ione));
850:     }

852:     /* Export solution and gradient residual to TAO */
853:     VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);
854:     VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);
855:     VecAssemblyBegin(tao->gradient);
856:     VecAssemblyEnd(tao->gradient);
857:     VecNorm(tao->gradient,NORM_2,&gnorm);
858:     gnorm *= mfqP->delta;
859:     /*  final criticality test */
860:     TaoMonitor(tao, iter, minnorm, gnorm, 0.0, step, &reason);
861:   }
862:   return(0);
863: }

867: static PetscErrorCode TaoSetUp_POUNDERS(Tao tao)
868: {
869:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
870:   PetscInt       i;
871:   IS             isfloc,isfglob,isxloc,isxglob;

875:   if (!tao->gradient) {VecDuplicate(tao->solution,&tao->gradient);  }
876:   if (!tao->stepdirection) {VecDuplicate(tao->solution,&tao->stepdirection);  }
877:   VecGetSize(tao->solution,&mfqP->n);
878:   VecGetSize(tao->sep_objective,&mfqP->m);
879:   mfqP->c1 = PetscSqrtReal((PetscReal)mfqP->n);
880:   if (mfqP->npmax == PETSC_DEFAULT) {
881:     mfqP->npmax = 2*mfqP->n + 1;
882:   }
883:   mfqP->npmax = PetscMin((mfqP->n+1)*(mfqP->n+2)/2,mfqP->npmax);
884:   mfqP->npmax = PetscMax(mfqP->npmax, mfqP->n+2);

886:   PetscMalloc1((tao->max_funcs+10),&mfqP->Xhist);
887:   PetscMalloc1((tao->max_funcs+10),&mfqP->Fhist);
888:   for (i=0;i<mfqP->n +1;i++) {
889:     VecDuplicate(tao->solution,&mfqP->Xhist[i]);
890:     VecDuplicate(tao->sep_objective,&mfqP->Fhist[i]);
891:   }
892:   VecDuplicate(tao->solution,&mfqP->workxvec);
893:   mfqP->nHist = 0;

895:   PetscMalloc1((tao->max_funcs+10),&mfqP->Fres);
896:   PetscMalloc1(mfqP->npmax*mfqP->m,&mfqP->RES);
897:   PetscMalloc1(mfqP->n,&mfqP->work);
898:   PetscMalloc1(mfqP->n,&mfqP->work2);
899:   PetscMalloc1(mfqP->n,&mfqP->work3);
900:   PetscMalloc1(PetscMax(mfqP->m,mfqP->n+1),&mfqP->mwork);
901:   PetscMalloc1((mfqP->npmax - mfqP->n - 1),&mfqP->omega);
902:   PetscMalloc1((mfqP->n * (mfqP->n+1) / 2),&mfqP->beta);
903:   PetscMalloc1((mfqP->n + 1) ,&mfqP->alpha);

905:   PetscMalloc1(mfqP->n*mfqP->n*mfqP->m,&mfqP->H);
906:   PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q);
907:   PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q_tmp);
908:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L);
909:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_tmp);
910:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_save);
911:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->N);
912:   PetscMalloc1(mfqP->npmax * (mfqP->n+1) ,&mfqP->M);
913:   PetscMalloc1(mfqP->npmax * (mfqP->npmax - mfqP->n - 1) , &mfqP->Z);
914:   PetscMalloc1(mfqP->npmax,&mfqP->tau);
915:   PetscMalloc1(mfqP->npmax,&mfqP->tau_tmp);
916:   mfqP->nmax = PetscMax(5*mfqP->npmax,mfqP->n*(mfqP->n+1)/2);
917:   PetscMalloc1(mfqP->nmax,&mfqP->npmaxwork);
918:   PetscMalloc1(mfqP->nmax,&mfqP->npmaxiwork);
919:   PetscMalloc1(mfqP->n,&mfqP->xmin);
920:   PetscMalloc1(mfqP->m,&mfqP->C);
921:   PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Fdiff);
922:   PetscMalloc1(mfqP->npmax*mfqP->n,&mfqP->Disp);
923:   PetscMalloc1(mfqP->n,&mfqP->Gres);
924:   PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Hres);
925:   PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Gpoints);
926:   PetscMalloc1(mfqP->npmax,&mfqP->model_indices);
927:   PetscMalloc1(mfqP->n,&mfqP->Xsubproblem);
928:   PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Gdel);
929:   PetscMalloc1(mfqP->n*mfqP->n*mfqP->m, &mfqP->Hdel);
930:   PetscMalloc1(PetscMax(mfqP->m,mfqP->n),&mfqP->indices);
931:   PetscMalloc1(mfqP->n,&mfqP->iwork);
932:   for (i=0;i<PetscMax(mfqP->m,mfqP->n);i++) {
933:     mfqP->indices[i] = i;
934:   }
935:   MPI_Comm_size(((PetscObject)tao)->comm,&mfqP->size);
936:   if (mfqP->size > 1) {
937:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localx);
938:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localxmin);
939:     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localf);
940:     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localfmin);
941:     ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxloc);
942:     ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxglob);
943:     ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfloc);
944:     ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfglob);


947:     VecScatterCreate(tao->solution,isxglob,mfqP->localx,isxloc,&mfqP->scatterx);
948:     VecScatterCreate(tao->sep_objective,isfglob,mfqP->localf,isfloc,&mfqP->scatterf);

950:     ISDestroy(&isxloc);
951:     ISDestroy(&isxglob);
952:     ISDestroy(&isfloc);
953:     ISDestroy(&isfglob);
954:   }

956:   if (!mfqP->usegqt) {
957:     KSP       ksp;
958:     PC        pc;
959:     VecCreateSeqWithArray(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Xsubproblem,&mfqP->subx);
960:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->subxl);
961:     VecDuplicate(mfqP->subxl,&mfqP->subb);
962:     VecDuplicate(mfqP->subxl,&mfqP->subxu);
963:     VecDuplicate(mfqP->subxl,&mfqP->subpdel);
964:     VecDuplicate(mfqP->subxl,&mfqP->subndel);
965:     TaoCreate(PETSC_COMM_SELF,&mfqP->subtao);
966:     /* TaoSetType(mfqP->subtao,"tao_bqpip"); */
967:     TaoSetType(mfqP->subtao,"tao_tron");
968:     TaoSetOptionsPrefix(mfqP->subtao,"pounders_subsolver_");
969:     TaoSetInitialVector(mfqP->subtao,mfqP->subx);
970:     TaoSetObjectiveAndGradientRoutine(mfqP->subtao,pounders_fg,(void*)mfqP);
971:     TaoSetMaximumIterations(mfqP->subtao,mfqP->gqt_maxits);
972:     TaoGetKSP(mfqP->subtao,&ksp);
973:     if (ksp) {
974:       KSPGetPC(ksp,&pc);
975:       PCSetType(pc,PCNONE);
976:     }
977:     TaoSetVariableBounds(mfqP->subtao,mfqP->subxl,mfqP->subxu);
978:     TaoSetFromOptions(mfqP->subtao);
979:     MatCreateSeqDense(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Hres,&mfqP->subH);
980:     TaoSetHessianRoutine(mfqP->subtao,mfqP->subH,mfqP->subH,pounders_h,(void*)mfqP);
981:   }
982:   return(0);
983: }

987: static PetscErrorCode TaoDestroy_POUNDERS(Tao tao)
988: {
989:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
990:   PetscInt       i;

994:   if (!mfqP->usegqt) {
995:     TaoDestroy(&mfqP->subtao);
996:     VecDestroy(&mfqP->subx);
997:     VecDestroy(&mfqP->subxl);
998:     VecDestroy(&mfqP->subxu);
999:     VecDestroy(&mfqP->subb);
1000:     VecDestroy(&mfqP->subpdel);
1001:     VecDestroy(&mfqP->subndel);
1002:     MatDestroy(&mfqP->subH);
1003:   }
1004:   PetscFree(mfqP->Fres);
1005:   PetscFree(mfqP->RES);
1006:   PetscFree(mfqP->work);
1007:   PetscFree(mfqP->work2);
1008:   PetscFree(mfqP->work3);
1009:   PetscFree(mfqP->mwork);
1010:   PetscFree(mfqP->omega);
1011:   PetscFree(mfqP->beta);
1012:   PetscFree(mfqP->alpha);
1013:   PetscFree(mfqP->H);
1014:   PetscFree(mfqP->Q);
1015:   PetscFree(mfqP->Q_tmp);
1016:   PetscFree(mfqP->L);
1017:   PetscFree(mfqP->L_tmp);
1018:   PetscFree(mfqP->L_save);
1019:   PetscFree(mfqP->N);
1020:   PetscFree(mfqP->M);
1021:   PetscFree(mfqP->Z);
1022:   PetscFree(mfqP->tau);
1023:   PetscFree(mfqP->tau_tmp);
1024:   PetscFree(mfqP->npmaxwork);
1025:   PetscFree(mfqP->npmaxiwork);
1026:   PetscFree(mfqP->xmin);
1027:   PetscFree(mfqP->C);
1028:   PetscFree(mfqP->Fdiff);
1029:   PetscFree(mfqP->Disp);
1030:   PetscFree(mfqP->Gres);
1031:   PetscFree(mfqP->Hres);
1032:   PetscFree(mfqP->Gpoints);
1033:   PetscFree(mfqP->model_indices);
1034:   PetscFree(mfqP->Xsubproblem);
1035:   PetscFree(mfqP->Gdel);
1036:   PetscFree(mfqP->Hdel);
1037:   PetscFree(mfqP->indices);
1038:   PetscFree(mfqP->iwork);

1040:   for (i=0;i<mfqP->nHist;i++) {
1041:     VecDestroy(&mfqP->Xhist[i]);
1042:     VecDestroy(&mfqP->Fhist[i]);
1043:   }
1044:   if (mfqP->workxvec) {
1045:     VecDestroy(&mfqP->workxvec);
1046:   }
1047:   PetscFree(mfqP->Xhist);
1048:   PetscFree(mfqP->Fhist);

1050:   if (mfqP->size > 1) {
1051:     VecDestroy(&mfqP->localx);
1052:     VecDestroy(&mfqP->localxmin);
1053:     VecDestroy(&mfqP->localf);
1054:     VecDestroy(&mfqP->localfmin);
1055:   }
1056:   PetscFree(tao->data);
1057:   return(0);
1058: }

1062: static PetscErrorCode TaoSetFromOptions_POUNDERS(Tao tao)
1063: {
1064:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;

1068:   PetscOptionsHead("POUNDERS method for least-squares optimization");
1069:   PetscOptionsReal("-tao_pounders_delta","initial delta","",mfqP->delta,&mfqP->delta,0);
1070:   mfqP->npmax = PETSC_DEFAULT;
1071:   PetscOptionsInt("-tao_pounders_npmax","max number of points in model","",mfqP->npmax,&mfqP->npmax,0);
1072:   mfqP->usegqt = PETSC_FALSE;
1073:   PetscOptionsBool("-tao_pounders_gqt","use gqt algorithm for subproblem","",mfqP->usegqt,&mfqP->usegqt,0);
1074:   PetscOptionsTail();
1075:   return(0);
1076: }

1080: static PetscErrorCode TaoView_POUNDERS(Tao tao, PetscViewer viewer)
1081: {
1082:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS *)tao->data;
1083:   PetscBool      isascii;

1087:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
1088:   if (isascii) {
1089:     PetscViewerASCIIPushTab(viewer);
1090:     if (mfqP->usegqt) {
1091:       PetscViewerASCIIPrintf(viewer, "Subproblem solver: gqt\n");
1092:     } else {
1093:       PetscViewerASCIIPrintf(viewer, "Subproblem solver: tron\n");
1094:     }
1095:     PetscViewerASCIIPopTab(viewer);
1096:   }
1097:   return(0);
1098: }

1100: EXTERN_C_BEGIN
1103: PetscErrorCode TaoCreate_POUNDERS(Tao tao)
1104: {
1105:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;

1109:   tao->ops->setup = TaoSetUp_POUNDERS;
1110:   tao->ops->solve = TaoSolve_POUNDERS;
1111:   tao->ops->view = TaoView_POUNDERS;
1112:   tao->ops->setfromoptions = TaoSetFromOptions_POUNDERS;
1113:   tao->ops->destroy = TaoDestroy_POUNDERS;

1115:   PetscNewLog(tao,&mfqP);
1116:   tao->data = (void*)mfqP;
1117:   tao->max_it = 2000;
1118:   tao->max_funcs = 4000;
1119: #if defined(PETSC_USE_REAL_SINGLE)
1120:   tao->fatol = 1e-4;
1121:   tao->frtol = 1e-4;
1122:   mfqP->deltamin=1e-3;
1123: #else
1124:   tao->fatol = 1e-8;
1125:   tao->frtol = 1e-8;
1126:   mfqP->deltamin=1e-6;
1127: #endif
1128:   mfqP->delta = 0.1;
1129:   mfqP->deltamax=1e3;
1130:   mfqP->c2 = 100.0;
1131:   mfqP->theta1=1e-5;
1132:   mfqP->theta2=1e-4;
1133:   mfqP->gamma0=0.5;
1134:   mfqP->gamma1=2.0;
1135:   mfqP->eta0 = 0.0;
1136:   mfqP->eta1 = 0.1;
1137:   mfqP->gqt_rtol = 0.001;
1138:   mfqP->gqt_maxits = 50;
1139:   mfqP->workxvec = 0;
1140:   return(0);
1141: }
1142: EXTERN_C_END