Actual source code: pounders.c

petsc-3.6.1 2015-08-06
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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, void *ctx)
  6: {
  8:   return(0);
  9: }
 12: static PetscErrorCode  pounders_fg(Tao subtao, Vec x, PetscReal *f, Vec g, void *ctx)
 13: {
 14:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)ctx;
 15:   PetscReal      d1,d2;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

113:     VecCopy(mfqP->subx,mfqP->subpdel);
114:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);
115:     VecMax(mfqP->subpdel,NULL,&maxval);
116:     if (maxval > 1e-5) {
117:       PetscInfo(tao,"subproblem solution > upper bound\n");
118:       tao->reason = TAO_DIVERGED_TR_REDUCTION;
119:     }
120:   } else {
121:     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);
122:   }
123:   *qmin *= -1;
124:   return(0);
125: }

129: PetscErrorCode phi2eval(PetscReal *x, PetscInt n, PetscReal *phi)
130: {
131: /* 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] */
132:   PetscInt  i,j,k;
133:   PetscReal sqrt2 = PetscSqrtReal(2.0);

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

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

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

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

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

179:   if (np == mfqP->n+1) {
180:     for (i=0;i<mfqP->npmax-mfqP->n-1;i++) {
181:       mfqP->omega[i]=0.0;
182:     }
183:     for (i=0;i<mfqP->n*(mfqP->n+1)/2;i++) {
184:       mfqP->beta[i]=0.0;
185:     }
186:   } else {
187:     /* Let Ltmp = (L'*L) */
188:     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));

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

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

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

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

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

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

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

249:   /* Initialize M,N */
250:   for (i=0;i<mfqP->n+1;i++) {
251:     VecGetArrayRead(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:     VecRestoreArrayRead(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:     VecGetArrayRead(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:     VecRestoreArrayRead(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;

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:   const PetscReal *x;
482:   PetscErrorCode  ierr;

485:   for (i=mfqP->nHist-1;i>=0;i--) {
486:     VecGetArrayRead(mfqP->Xhist[i],&x);
487:     for (j=0;j<mfqP->n;j++) {
488:       mfqP->work[j] = (x[j] - xmin[j])/mfqP->delta;
489:     }
490:     VecRestoreArrayRead(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:   }

521:   return(0);
522: }

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

546:   /* n = # of parameters
547:      m = dimension (components) of function  */
549:   PetscCitationsRegister("@article{UNEDF0,\n"
550:                                 "title = {Nuclear energy density optimization},\n"
551:                                 "author = {Kortelainen, M.  and Lesinski, T.  and Mor\'e, J.  and Nazarewicz, W.\n"
552:                                 "          and Sarich, J.  and Schunck, N.  and Stoitsov, M. V. and Wild, S. },\n"
553:                                 "journal = {Phys. Rev. C},\n"
554:                                 "volume = {82},\n"
555:                                 "number = {2},\n"
556:                                 "pages = {024313},\n"
557:                                 "numpages = {18},\n"
558:                                 "year = {2010},\n"
559:                                 "month = {Aug},\n"
560:                                 "doi = {10.1103/PhysRevC.82.024313}\n}\n",&set);
561:   tao->niter=0;
562:   if (tao->XL && tao->XU) {
563:     /* Check x0 <= XU */
564:     PetscReal val;
565:     VecCopy(tao->solution,mfqP->Xhist[0]);
566:     VecAXPY(mfqP->Xhist[0],-1.0,tao->XU);
567:     VecMax(mfqP->Xhist[0],NULL,&val);
568:     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 > upper bound");

570:     /* Check x0 >= xl */
571:     VecCopy(tao->XL,mfqP->Xhist[0]);
572:     VecAXPY(mfqP->Xhist[0],-1.0,tao->solution);
573:     VecMax(mfqP->Xhist[0],NULL,&val);
574:     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 < lower bound");

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

578:     VecSet(mfqP->Xhist[0],mfqP->delta);
579:     VecAXPY(mfqP->Xhist[0],1.0,tao->solution);
580:     VecAXPY(mfqP->Xhist[0],-1.0,tao->XU);
581:     VecMax(mfqP->Xhist[0],NULL,&val);
582:     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 + delta > upper bound");
583:   }

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

589:   VecCopy(tao->solution,mfqP->Xhist[0]);
590:   CHKMEMQ;
591:   TaoComputeSeparableObjective(tao,tao->solution,mfqP->Fhist[0]);

593:   VecNorm(mfqP->Fhist[0],NORM_2,&mfqP->Fres[0]);
594:   if (PetscIsInfOrNanReal(mfqP->Fres[0])) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
595:   mfqP->Fres[0]*=mfqP->Fres[0];
596:   mfqP->minindex = 0;
597:   minnorm = mfqP->Fres[0];
598:   TaoMonitor(tao, tao->niter, minnorm, PETSC_INFINITY, 0.0, step, &reason);
599:   tao->niter++;

601:   VecGetOwnershipRange(mfqP->Xhist[0],&low,&high);
602:   for (i=1;i<mfqP->n+1;i++) {
603:     VecCopy(tao->solution,mfqP->Xhist[i]);
604:     if (i-1 >= low && i-1 < high) {
605:       VecGetArray(mfqP->Xhist[i],&x);
606:       x[i-1-low] += mfqP->delta;
607:       VecRestoreArray(mfqP->Xhist[i],&x);
608:     }
609:     CHKMEMQ;
610:     TaoComputeSeparableObjective(tao,mfqP->Xhist[i],mfqP->Fhist[i]);
611:     VecNorm(mfqP->Fhist[i],NORM_2,&mfqP->Fres[i]);
612:     if (PetscIsInfOrNanReal(mfqP->Fres[i])) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
613:     mfqP->Fres[i]*=mfqP->Fres[i];
614:     if (mfqP->Fres[i] < minnorm) {
615:       mfqP->minindex = i;
616:       minnorm = mfqP->Fres[i];
617:     }
618:   }
619:   VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);
620:   VecCopy(mfqP->Fhist[mfqP->minindex],tao->sep_objective);
621:   /* Gather mpi vecs to one big local vec */

623:   /* Begin serial code */

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

630:   if (mfqP->size == 1) {
631:     VecGetArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
632:     for (i=0;i<mfqP->n;i++) mfqP->xmin[i] = xmint[i];
633:     VecRestoreArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
634:     VecGetArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);
635:     for (i=0;i<mfqP->n+1;i++) {
636:       if (i == mfqP->minindex) continue;

638:       VecGetArray(mfqP->Xhist[i],&x);
639:       for (j=0;j<mfqP->n;j++) {
640:         mfqP->Disp[ii+mfqP->npmax*j] = (x[j] - mfqP->xmin[j])/mfqP->delta;
641:       }
642:       VecRestoreArray(mfqP->Xhist[i],&x);

644:       VecGetArray(mfqP->Fhist[i],&f);
645:       for (j=0;j<mfqP->m;j++) {
646:         mfqP->Fdiff[ii+mfqP->n*j] = f[j] - fmin[j];
647:       }
648:       VecRestoreArray(mfqP->Fhist[i],&f);
649:       mfqP->model_indices[ii++] = i;

651:     }
652:     for (j=0;j<mfqP->m;j++) {
653:       mfqP->C[j] = fmin[j];
654:     }
655:     VecRestoreArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);
656:   } else {
657:     VecScatterBegin(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);
658:     VecScatterEnd(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);
659:     VecGetArrayRead(mfqP->localxmin,&xmint);
660:     for (i=0;i<mfqP->n;i++) mfqP->xmin[i] = xmint[i];
661:     VecRestoreArrayRead(mfqP->localxmin,&xmint);

663:     VecScatterBegin(mfqP->scatterf,mfqP->Fhist[mfqP->minindex],mfqP->localfmin,INSERT_VALUES,SCATTER_FORWARD);
664:     VecScatterEnd(mfqP->scatterf,mfqP->Fhist[mfqP->minindex],mfqP->localfmin,INSERT_VALUES,SCATTER_FORWARD);
665:     VecGetArrayRead(mfqP->localfmin,&fmin);
666:     for (i=0;i<mfqP->n+1;i++) {
667:       if (i == mfqP->minindex) continue;

669:       mfqP->model_indices[ii++] = i;
670:       VecScatterBegin(mfqP->scatterx,mfqP->Xhist[ii],mfqP->localx,INSERT_VALUES, SCATTER_FORWARD);
671:       VecScatterEnd(mfqP->scatterx,mfqP->Xhist[ii],mfqP->localx,INSERT_VALUES, SCATTER_FORWARD);
672:       VecGetArray(mfqP->localx,&x);
673:       for (j=0;j<mfqP->n;j++) {
674:         mfqP->Disp[i+mfqP->npmax*j] = (x[j] - mfqP->xmin[j])/mfqP->delta;
675:       }
676:       VecRestoreArray(mfqP->localx,&x);

678:       VecScatterBegin(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);
679:       VecScatterEnd(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);
680:       VecGetArray(mfqP->localf,&f);
681:       for (j=0;j<mfqP->m;j++) {
682:         mfqP->Fdiff[i*mfqP->n+j] = f[j] - fmin[j];
683:       }
684:       VecRestoreArray(mfqP->localf,&f);
685:     }
686:     for (j=0;j<mfqP->m;j++) {
687:       mfqP->C[j] = fmin[j];
688:     }
689:     VecRestoreArrayRead(mfqP->localfmin,&fmin);
690:   }

692:   /* Determine the initial quadratic models */
693:   /* G = D(ModelIn,:) \ (F(ModelIn,1:m)-repmat(F(xkin,1:m),n,1)); */
694:   /* D (nxn) Fdiff (nxm)  => G (nxm) */
695:   blasn2 = blasn;
696:   PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&blasn,&blasm,mfqP->Disp,&blasnpmax,mfqP->iwork,mfqP->Fdiff,&blasn2,&info));
697:   PetscInfo1(tao,"gesv returned %d\n",info);

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

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

706:   valid = PETSC_TRUE;

708:   VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);
709:   VecAssemblyBegin(tao->gradient);
710:   VecAssemblyEnd(tao->gradient);
711:   VecNorm(tao->gradient,NORM_2,&gnorm);
712:   gnorm *= mfqP->delta;
713:   VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);
714:   TaoMonitor(tao, tao->niter, minnorm, gnorm, 0.0, step, &reason);
715:   mfqP->nHist = mfqP->n+1;
716:   mfqP->nmodelpoints = mfqP->n+1;

718:   while (reason == TAO_CONTINUE_ITERATING) {
719:     PetscReal gnm = 1e-4;
720:     tao->niter++;
721:     /* Solve the subproblem min{Q(s): ||s|| <= delta} */
722:     gqtwrap(tao,&gnm,&mdec);
723:     /* Evaluate the function at the new point */

725:     for (i=0;i<mfqP->n;i++) {
726:         mfqP->work[i] = mfqP->Xsubproblem[i]*mfqP->delta + mfqP->xmin[i];
727:     }
728:     VecDuplicate(tao->solution,&mfqP->Xhist[mfqP->nHist]);
729:     VecDuplicate(tao->sep_objective,&mfqP->Fhist[mfqP->nHist]);
730:     VecSetValues(mfqP->Xhist[mfqP->nHist],mfqP->n,mfqP->indices,mfqP->work,INSERT_VALUES);
731:     VecAssemblyBegin(mfqP->Xhist[mfqP->nHist]);
732:     VecAssemblyEnd(mfqP->Xhist[mfqP->nHist]);

734:     TaoComputeSeparableObjective(tao,mfqP->Xhist[mfqP->nHist],mfqP->Fhist[mfqP->nHist]);
735:     VecNorm(mfqP->Fhist[mfqP->nHist],NORM_2,&mfqP->Fres[mfqP->nHist]);
736:     if (PetscIsInfOrNanReal(mfqP->Fres[mfqP->nHist])) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
737:     mfqP->Fres[mfqP->nHist]*=mfqP->Fres[mfqP->nHist];
738:     rho = (mfqP->Fres[mfqP->minindex] - mfqP->Fres[mfqP->nHist]) / mdec;
739:     mfqP->nHist++;

741:     /* Update the center */
742:     if ((rho >= mfqP->eta1) || (rho > mfqP->eta0 && valid==PETSC_TRUE)) {
743:       /* Update model to reflect new base point */
744:       for (i=0;i<mfqP->n;i++) {
745:         mfqP->work[i] = (mfqP->work[i] - mfqP->xmin[i])/mfqP->delta;
746:       }
747:       for (j=0;j<mfqP->m;j++) {
748:         /* C(j) = C(j) + work*G(:,j) + .5*work*H(:,:,j)*work';
749:          G(:,j) = G(:,j) + H(:,:,j)*work' */
750:         for (k=0;k<mfqP->n;k++) {
751:           mfqP->work2[k]=0.0;
752:           for (l=0;l<mfqP->n;l++) {
753:             mfqP->work2[k]+=mfqP->H[j + mfqP->m*(k + l*mfqP->n)]*mfqP->work[l];
754:           }
755:         }
756:         for (i=0;i<mfqP->n;i++) {
757:           mfqP->C[j]+=mfqP->work[i]*(mfqP->Fdiff[i + mfqP->n* j] + 0.5*mfqP->work2[i]);
758:           mfqP->Fdiff[i+mfqP->n*j] +=mfqP-> work2[i];
759:         }
760:       }
761:       /* Cres += work*Gres + .5*work*Hres*work';
762:        Gres += Hres*work'; */

764:       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&one,mfqP->Hres,&blasn,mfqP->work,&ione,&zero,mfqP->work2,&ione));
765:       for (i=0;i<mfqP->n;i++) {
766:         cres += mfqP->work[i]*(mfqP->Gres[i]  + 0.5*mfqP->work2[i]);
767:         mfqP->Gres[i] += mfqP->work2[i];
768:       }
769:       mfqP->minindex = mfqP->nHist-1;
770:       minnorm = mfqP->Fres[mfqP->minindex];
771:       VecCopy(mfqP->Fhist[mfqP->minindex],tao->sep_objective);
772:       /* Change current center */
773:       VecGetArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
774:       for (i=0;i<mfqP->n;i++) {
775:         mfqP->xmin[i] = xmint[i];
776:       }
777:       VecRestoreArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
778:     }

780:     /* Evaluate at a model-improving point if necessary */
781:     if (valid == PETSC_FALSE) {
782:       mfqP->q_is_I = 1;
783:       mfqP->nmodelpoints = 0;
784:       affpoints(mfqP,mfqP->xmin,mfqP->c1);
785:       if (mfqP->nmodelpoints < mfqP->n) {
786:         PetscInfo(tao,"Model not valid -- model-improving\n");
787:         modelimprove(tao,mfqP,1);
788:       }
789:     }

791:     /* Update the trust region radius */
792:     deltaold = mfqP->delta;
793:     normxsp = 0;
794:     for (i=0;i<mfqP->n;i++) {
795:       normxsp += mfqP->Xsubproblem[i]*mfqP->Xsubproblem[i];
796:     }
797:     normxsp = PetscSqrtReal(normxsp);
798:     if (rho >= mfqP->eta1 && normxsp > 0.5*mfqP->delta) {
799:       mfqP->delta = PetscMin(mfqP->delta*mfqP->gamma1,mfqP->deltamax);
800:     } else if (valid == PETSC_TRUE) {
801:       mfqP->delta = PetscMax(mfqP->delta*mfqP->gamma0,mfqP->deltamin);
802:     }

804:     /* Compute the next interpolation set */
805:     mfqP->q_is_I = 1;
806:     mfqP->nmodelpoints=0;
807:     affpoints(mfqP,mfqP->xmin,mfqP->c1);
808:     if (mfqP->nmodelpoints == mfqP->n) {
809:       valid = PETSC_TRUE;
810:     } else {
811:       valid = PETSC_FALSE;
812:       affpoints(mfqP,mfqP->xmin,mfqP->c2);
813:       if (mfqP->n > mfqP->nmodelpoints) {
814:         PetscInfo(tao,"Model not valid -- adding geometry points\n");
815:         modelimprove(tao,mfqP,mfqP->n - mfqP->nmodelpoints);
816:       }
817:     }
818:     for (i=mfqP->nmodelpoints;i>0;i--) {
819:       mfqP->model_indices[i] = mfqP->model_indices[i-1];
820:     }
821:     mfqP->nmodelpoints++;
822:     mfqP->model_indices[0] = mfqP->minindex;
823:     morepoints(mfqP);
824:     for (i=0;i<mfqP->nmodelpoints;i++) {
825:       VecGetArray(mfqP->Xhist[mfqP->model_indices[i]],&x);
826:       for (j=0;j<mfqP->n;j++) {
827:         mfqP->Disp[i + mfqP->npmax*j] = (x[j]  - mfqP->xmin[j]) / deltaold;
828:       }
829:       VecRestoreArray(mfqP->Xhist[mfqP->model_indices[i]],&x);
830:       VecGetArray(mfqP->Fhist[mfqP->model_indices[i]],&f);
831:       for (j=0;j<mfqP->m;j++) {
832:         for (k=0;k<mfqP->n;k++)  {
833:           mfqP->work[k]=0.0;
834:           for (l=0;l<mfqP->n;l++) {
835:             mfqP->work[k] += mfqP->H[j + mfqP->m*(k + mfqP->n*l)] * mfqP->Disp[i + mfqP->npmax*l];
836:           }
837:         }
838:         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];
839:       }
840:       VecRestoreArray(mfqP->Fhist[mfqP->model_indices[i]],&f);
841:     }

843:     /* Update the quadratic model */
844:     getquadpounders(mfqP);
845:     VecGetArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);
846:     PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasm,fmin,&ione,mfqP->C,&ione));
847:     /* G = G*(delta/deltaold) + Gdel */
848:     ratio = mfqP->delta/deltaold;
849:     iblas = blasm*blasn;
850:     PetscStackCallBLAS("BLASscal",BLASscal_(&iblas,&ratio,mfqP->Fdiff,&ione));
851:     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&one,mfqP->Gdel,&ione,mfqP->Fdiff,&ione));
852:     /* H = H*(delta/deltaold) + Hdel */
853:     iblas = blasm*blasn*blasn;
854:     ratio *= ratio;
855:     PetscStackCallBLAS("BLASscal",BLASscal_(&iblas,&ratio,mfqP->H,&ione));
856:     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&one,mfqP->Hdel,&ione,mfqP->H,&ione));

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

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

867:     for (j=0;j<mfqP->m;j++) {
868:       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&fmin[j],&mfqP->H[j],&blasm,mfqP->Hres,&ione));
869:     }

871:     /* Export solution and gradient residual to TAO */
872:     VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);
873:     VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);
874:     VecAssemblyBegin(tao->gradient);
875:     VecAssemblyEnd(tao->gradient);
876:     VecNorm(tao->gradient,NORM_2,&gnorm);
877:     gnorm *= mfqP->delta;
878:     /*  final criticality test */
879:     TaoMonitor(tao, tao->niter, minnorm, gnorm, 0.0, step, &reason);
880:     /* test for repeated model */
881:     if (mfqP->nmodelpoints==mfqP->last_nmodelpoints) {
882:       same = PETSC_TRUE;
883:     } else {
884:       same = PETSC_FALSE;
885:     }
886:     for (i=0;i<mfqP->nmodelpoints;i++) {
887:       if (same) {
888:         if (mfqP->model_indices[i] == mfqP->last_model_indices[i]) {
889:           same = PETSC_TRUE;
890:         } else {
891:           same = PETSC_FALSE;
892:         }
893:       }
894:       mfqP->last_model_indices[i] = mfqP->model_indices[i];
895:     }
896:     mfqP->last_nmodelpoints = mfqP->nmodelpoints;
897:     if (same && mfqP->delta == deltaold) {
898:       PetscInfo(tao,"Identical model used in successive iterations\n");
899:       reason = TAO_CONVERGED_STEPTOL;
900:       tao->reason = TAO_CONVERGED_STEPTOL;
901:     }
902:   }
903:   return(0);
904: }

908: static PetscErrorCode TaoSetUp_POUNDERS(Tao tao)
909: {
910:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
911:   PetscInt       i;
912:   IS             isfloc,isfglob,isxloc,isxglob;

916:   if (!tao->gradient) {VecDuplicate(tao->solution,&tao->gradient);  }
917:   if (!tao->stepdirection) {VecDuplicate(tao->solution,&tao->stepdirection);  }
918:   VecGetSize(tao->solution,&mfqP->n);
919:   VecGetSize(tao->sep_objective,&mfqP->m);
920:   mfqP->c1 = PetscSqrtReal((PetscReal)mfqP->n);
921:   if (mfqP->npmax == PETSC_DEFAULT) {
922:     mfqP->npmax = 2*mfqP->n + 1;
923:   }
924:   mfqP->npmax = PetscMin((mfqP->n+1)*(mfqP->n+2)/2,mfqP->npmax);
925:   mfqP->npmax = PetscMax(mfqP->npmax, mfqP->n+2);

927:   PetscMalloc1(tao->max_funcs+10,&mfqP->Xhist);
928:   PetscMalloc1(tao->max_funcs+10,&mfqP->Fhist);
929:   for (i=0;i<mfqP->n +1;i++) {
930:     VecDuplicate(tao->solution,&mfqP->Xhist[i]);
931:     VecDuplicate(tao->sep_objective,&mfqP->Fhist[i]);
932:   }
933:   VecDuplicate(tao->solution,&mfqP->workxvec);
934:   mfqP->nHist = 0;

936:   PetscMalloc1(tao->max_funcs+10,&mfqP->Fres);
937:   PetscMalloc1(mfqP->npmax*mfqP->m,&mfqP->RES);
938:   PetscMalloc1(mfqP->n,&mfqP->work);
939:   PetscMalloc1(mfqP->n,&mfqP->work2);
940:   PetscMalloc1(mfqP->n,&mfqP->work3);
941:   PetscMalloc1(PetscMax(mfqP->m,mfqP->n+1),&mfqP->mwork);
942:   PetscMalloc1(mfqP->npmax - mfqP->n - 1,&mfqP->omega);
943:   PetscMalloc1(mfqP->n * (mfqP->n+1) / 2,&mfqP->beta);
944:   PetscMalloc1(mfqP->n + 1 ,&mfqP->alpha);

946:   PetscMalloc1(mfqP->n*mfqP->n*mfqP->m,&mfqP->H);
947:   PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q);
948:   PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q_tmp);
949:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L);
950:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_tmp);
951:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_save);
952:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->N);
953:   PetscMalloc1(mfqP->npmax * (mfqP->n+1) ,&mfqP->M);
954:   PetscMalloc1(mfqP->npmax * (mfqP->npmax - mfqP->n - 1) , &mfqP->Z);
955:   PetscMalloc1(mfqP->npmax,&mfqP->tau);
956:   PetscMalloc1(mfqP->npmax,&mfqP->tau_tmp);
957:   mfqP->nmax = PetscMax(5*mfqP->npmax,mfqP->n*(mfqP->n+1)/2);
958:   PetscMalloc1(mfqP->nmax,&mfqP->npmaxwork);
959:   PetscMalloc1(mfqP->nmax,&mfqP->npmaxiwork);
960:   PetscMalloc1(mfqP->n,&mfqP->xmin);
961:   PetscMalloc1(mfqP->m,&mfqP->C);
962:   PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Fdiff);
963:   PetscMalloc1(mfqP->npmax*mfqP->n,&mfqP->Disp);
964:   PetscMalloc1(mfqP->n,&mfqP->Gres);
965:   PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Hres);
966:   PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Gpoints);
967:   PetscMalloc1(mfqP->npmax,&mfqP->model_indices);
968:   PetscMalloc1(mfqP->npmax,&mfqP->last_model_indices);
969:   PetscMalloc1(mfqP->n,&mfqP->Xsubproblem);
970:   PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Gdel);
971:   PetscMalloc1(mfqP->n*mfqP->n*mfqP->m, &mfqP->Hdel);
972:   PetscMalloc1(PetscMax(mfqP->m,mfqP->n),&mfqP->indices);
973:   PetscMalloc1(mfqP->n,&mfqP->iwork);
974:   for (i=0;i<PetscMax(mfqP->m,mfqP->n);i++) {
975:     mfqP->indices[i] = i;
976:   }
977:   MPI_Comm_size(((PetscObject)tao)->comm,&mfqP->size);
978:   if (mfqP->size > 1) {
979:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localx);
980:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localxmin);
981:     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localf);
982:     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localfmin);
983:     ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxloc);
984:     ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxglob);
985:     ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfloc);
986:     ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfglob);


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

992:     ISDestroy(&isxloc);
993:     ISDestroy(&isxglob);
994:     ISDestroy(&isfloc);
995:     ISDestroy(&isfglob);
996:   }

998:   if (!mfqP->usegqt) {
999:     KSP       ksp;
1000:     PC        pc;
1001:     VecCreateSeqWithArray(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Xsubproblem,&mfqP->subx);
1002:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->subxl);
1003:     VecDuplicate(mfqP->subxl,&mfqP->subb);
1004:     VecDuplicate(mfqP->subxl,&mfqP->subxu);
1005:     VecDuplicate(mfqP->subxl,&mfqP->subpdel);
1006:     VecDuplicate(mfqP->subxl,&mfqP->subndel);
1007:     TaoCreate(PETSC_COMM_SELF,&mfqP->subtao);
1008:     TaoSetType(mfqP->subtao,TAOTRON);
1009:     TaoSetOptionsPrefix(mfqP->subtao,"pounders_subsolver_");
1010:     TaoSetInitialVector(mfqP->subtao,mfqP->subx);
1011:     TaoSetObjectiveAndGradientRoutine(mfqP->subtao,pounders_fg,(void*)mfqP);
1012:     TaoSetMaximumIterations(mfqP->subtao,mfqP->gqt_maxits);
1013:     TaoSetFromOptions(mfqP->subtao);
1014:     TaoGetKSP(mfqP->subtao,&ksp);
1015:     if (ksp) {
1016:       KSPGetPC(ksp,&pc);
1017:       PCSetType(pc,PCNONE);
1018:     }
1019:     TaoSetVariableBounds(mfqP->subtao,mfqP->subxl,mfqP->subxu);
1020:     MatCreateSeqDense(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Hres,&mfqP->subH);
1021:     TaoSetHessianRoutine(mfqP->subtao,mfqP->subH,mfqP->subH,pounders_h,(void*)mfqP);
1022:   }
1023:   return(0);
1024: }

1028: static PetscErrorCode TaoDestroy_POUNDERS(Tao tao)
1029: {
1030:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
1031:   PetscInt       i;

1035:   if (!mfqP->usegqt) {
1036:     TaoDestroy(&mfqP->subtao);
1037:     VecDestroy(&mfqP->subx);
1038:     VecDestroy(&mfqP->subxl);
1039:     VecDestroy(&mfqP->subxu);
1040:     VecDestroy(&mfqP->subb);
1041:     VecDestroy(&mfqP->subpdel);
1042:     VecDestroy(&mfqP->subndel);
1043:     MatDestroy(&mfqP->subH);
1044:   }
1045:   PetscFree(mfqP->Fres);
1046:   PetscFree(mfqP->RES);
1047:   PetscFree(mfqP->work);
1048:   PetscFree(mfqP->work2);
1049:   PetscFree(mfqP->work3);
1050:   PetscFree(mfqP->mwork);
1051:   PetscFree(mfqP->omega);
1052:   PetscFree(mfqP->beta);
1053:   PetscFree(mfqP->alpha);
1054:   PetscFree(mfqP->H);
1055:   PetscFree(mfqP->Q);
1056:   PetscFree(mfqP->Q_tmp);
1057:   PetscFree(mfqP->L);
1058:   PetscFree(mfqP->L_tmp);
1059:   PetscFree(mfqP->L_save);
1060:   PetscFree(mfqP->N);
1061:   PetscFree(mfqP->M);
1062:   PetscFree(mfqP->Z);
1063:   PetscFree(mfqP->tau);
1064:   PetscFree(mfqP->tau_tmp);
1065:   PetscFree(mfqP->npmaxwork);
1066:   PetscFree(mfqP->npmaxiwork);
1067:   PetscFree(mfqP->xmin);
1068:   PetscFree(mfqP->C);
1069:   PetscFree(mfqP->Fdiff);
1070:   PetscFree(mfqP->Disp);
1071:   PetscFree(mfqP->Gres);
1072:   PetscFree(mfqP->Hres);
1073:   PetscFree(mfqP->Gpoints);
1074:   PetscFree(mfqP->model_indices);
1075:   PetscFree(mfqP->last_model_indices);
1076:   PetscFree(mfqP->Xsubproblem);
1077:   PetscFree(mfqP->Gdel);
1078:   PetscFree(mfqP->Hdel);
1079:   PetscFree(mfqP->indices);
1080:   PetscFree(mfqP->iwork);

1082:   for (i=0;i<mfqP->nHist;i++) {
1083:     VecDestroy(&mfqP->Xhist[i]);
1084:     VecDestroy(&mfqP->Fhist[i]);
1085:   }
1086:   if (mfqP->workxvec) {
1087:     VecDestroy(&mfqP->workxvec);
1088:   }
1089:   PetscFree(mfqP->Xhist);
1090:   PetscFree(mfqP->Fhist);

1092:   if (mfqP->size > 1) {
1093:     VecDestroy(&mfqP->localx);
1094:     VecDestroy(&mfqP->localxmin);
1095:     VecDestroy(&mfqP->localf);
1096:     VecDestroy(&mfqP->localfmin);
1097:   }
1098:   PetscFree(tao->data);
1099:   return(0);
1100: }

1104: static PetscErrorCode TaoSetFromOptions_POUNDERS(PetscOptions *PetscOptionsObject,Tao tao)
1105: {
1106:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;

1110:   PetscOptionsHead(PetscOptionsObject,"POUNDERS method for least-squares optimization");
1111:   PetscOptionsReal("-tao_pounders_delta","initial delta","",mfqP->delta,&mfqP->delta0,NULL);
1112:   mfqP->delta = mfqP->delta0;
1113:   mfqP->npmax = PETSC_DEFAULT;
1114:   PetscOptionsInt("-tao_pounders_npmax","max number of points in model","",mfqP->npmax,&mfqP->npmax,NULL);
1115:   mfqP->usegqt = PETSC_FALSE;
1116:   PetscOptionsBool("-tao_pounders_gqt","use gqt algorithm for subproblem","",mfqP->usegqt,&mfqP->usegqt,NULL);
1117:   PetscOptionsTail();
1118:   return(0);
1119: }

1123: static PetscErrorCode TaoView_POUNDERS(Tao tao, PetscViewer viewer)
1124: {
1125:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS *)tao->data;
1126:   PetscBool      isascii;
1127:   PetscInt       nits;

1131:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
1132:   if (isascii) {
1133:     PetscViewerASCIIPushTab(viewer);
1134:     PetscViewerASCIIPrintf(viewer, "initial delta: %g\n",(double)mfqP->delta0);
1135:     PetscViewerASCIIPrintf(viewer, "final delta: %g\n",(double)mfqP->delta);
1136:     PetscViewerASCIIPrintf(viewer, "model points: %D\n",mfqP->nmodelpoints);
1137:     if (mfqP->usegqt) {
1138:       PetscViewerASCIIPrintf(viewer, "subproblem solver: gqt\n");
1139:     } else {
1140:       PetscViewerASCIIPrintf(viewer, "subproblem solver: %s\n",((PetscObject)mfqP->subtao)->type_name);
1141:       TaoGetTotalIterationNumber(mfqP->subtao,&nits);
1142:       PetscViewerASCIIPrintf(viewer, "total subproblem iterations: %D\n",nits);
1143:     }
1144:     PetscViewerASCIIPopTab(viewer);
1145:   }
1146:   return(0);
1147: }
1148: /*MC
1149:   TAOPOUNDERS - POUNDERS derivate-free model-based algorithm for nonlinear least squares

1151:   Options Database Keys:
1152: + -tao_pounders_delta - initial step length
1153: . -tao_pounders_npmax - maximum number of points in model
1154: - -tao_pounders_gqt - use gqt algorithm for subproblem instead of TRON

1156:   Level: beginner
1157:  
1158: M*/

1162: PETSC_EXTERN PetscErrorCode TaoCreate_POUNDERS(Tao tao)
1163: {
1164:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;

1168:   tao->ops->setup = TaoSetUp_POUNDERS;
1169:   tao->ops->solve = TaoSolve_POUNDERS;
1170:   tao->ops->view = TaoView_POUNDERS;
1171:   tao->ops->setfromoptions = TaoSetFromOptions_POUNDERS;
1172:   tao->ops->destroy = TaoDestroy_POUNDERS;

1174:   PetscNewLog(tao,&mfqP);
1175:   tao->data = (void*)mfqP;
1176:   /* Override default settings (unless already changed) */
1177:   if (!tao->max_it_changed) tao->max_it = 2000;
1178:   if (!tao->max_funcs_changed) tao->max_funcs = 4000;
1179: #if defined(PETSC_USE_REAL_SINGLE)
1180:   if (!tao->fatol_changed) tao->fatol = 1.0e-4;
1181:   if (!tao->frtol_changed) tao->frtol = 1.0e-4;
1182:   mfqP->deltamin=1e-3;
1183: #else
1184:   if (!tao->fatol_changed) tao->fatol = 1.0e-8;
1185:   if (!tao->frtol_changed) tao->frtol = 1.0e-8;
1186:   mfqP->deltamin=1e-6;
1187: #endif
1188:   mfqP->delta0 = 0.1;
1189:   mfqP->delta = 0.1;
1190:   mfqP->deltamax=1e3;
1191:   mfqP->c2 = 100.0;
1192:   mfqP->theta1=1e-5;
1193:   mfqP->theta2=1e-4;
1194:   mfqP->gamma0=0.5;
1195:   mfqP->gamma1=2.0;
1196:   mfqP->eta0 = 0.0;
1197:   mfqP->eta1 = 0.1;
1198:   mfqP->gqt_rtol = 0.001;
1199:   mfqP->gqt_maxits = 50;
1200:   mfqP->workxvec = 0;
1201:   return(0);
1202: }