Actual source code: pounders.c

petsc-3.12.5 2020-03-29
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  1:  #include <../src/tao/leastsquares/impls/pounders/pounders.h>

  3: static PetscErrorCode pounders_h(Tao subtao, Vec v, Mat H, Mat Hpre, void *ctx)
  4: {
  6:   return(0);
  7: }

  9: static PetscErrorCode  pounders_fg(Tao subtao, Vec x, PetscReal *f, Vec g, void *ctx)
 10: {
 11:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)ctx;
 12:   PetscReal      d1,d2;

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

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

 24:   /* now  g = g + b */
 25:   VecAXPY(g, 1.0, mfqP->subb);
 26:   return(0);
 27: }

 29: static PetscErrorCode pounders_feval(Tao tao, Vec x, Vec F, PetscReal *fsum)
 30: {
 32:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
 33:   PetscInt i,row,col;
 34:   PetscReal fr,fc;
 36:   TaoComputeResidual(tao,x,F);
 37:   if (tao->res_weights_v) {
 38:     VecPointwiseMult(mfqP->workfvec,tao->res_weights_v,F);
 39:     VecDot(mfqP->workfvec,mfqP->workfvec,fsum);
 40:   } else if (tao->res_weights_w) {
 41:     *fsum=0;
 42:     for (i=0;i<tao->res_weights_n;i++) {
 43:       row=tao->res_weights_rows[i];
 44:       col=tao->res_weights_cols[i];
 45:       VecGetValues(F,1,&row,&fr);
 46:       VecGetValues(F,1,&col,&fc);
 47:       *fsum += tao->res_weights_w[i]*fc*fr;
 48:     }
 49:   } else {
 50:     VecDot(F,F,fsum);
 51:   }
 52:   PetscInfo1(tao,"Least-squares residual norm: %20.19e\n",(double)*fsum);
 53:   if (PetscIsInfOrNanReal(*fsum)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
 54:   return(0);
 55: }

 57: PetscErrorCode gqtwrap(Tao tao,PetscReal *gnorm, PetscReal *qmin)
 58: {
 60: #if defined(PETSC_USE_REAL_SINGLE)
 61:   PetscReal      atol=1.0e-5;
 62: #else
 63:   PetscReal      atol=1.0e-10;
 64: #endif
 65:   PetscInt       info,its;
 66:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;

 69:   if (!mfqP->usegqt) {
 70:     PetscReal maxval;
 71:     PetscInt  i,j;

 73:     VecSetValues(mfqP->subb,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);
 74:     VecAssemblyBegin(mfqP->subb);
 75:     VecAssemblyEnd(mfqP->subb);

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

 79:     VecSet(mfqP->subndel,-1.0);
 80:     VecSet(mfqP->subpdel,+1.0);

 82:     /* Complete the lower triangle of the Hessian matrix */
 83:     for (i=0;i<mfqP->n;i++) {
 84:       for (j=i+1;j<mfqP->n;j++) {
 85:         mfqP->Hres[j+mfqP->n*i] = mfqP->Hres[mfqP->n*j+i];
 86:       }
 87:     }
 88:     MatSetValues(mfqP->subH,mfqP->n,mfqP->indices,mfqP->n,mfqP->indices,mfqP->Hres,INSERT_VALUES);
 89:     MatAssemblyBegin(mfqP->subH,MAT_FINAL_ASSEMBLY);
 90:     MatAssemblyEnd(mfqP->subH,MAT_FINAL_ASSEMBLY);

 92:     TaoResetStatistics(mfqP->subtao);
 93:     /* TaoSetTolerances(mfqP->subtao,*gnorm,*gnorm,PETSC_DEFAULT); */
 94:     /* enforce bound constraints -- experimental */
 95:     if (tao->XU && tao->XL) {
 96:       VecCopy(tao->XU,mfqP->subxu);
 97:       VecAXPY(mfqP->subxu,-1.0,tao->solution);
 98:       VecScale(mfqP->subxu,1.0/mfqP->delta);
 99:       VecCopy(tao->XL,mfqP->subxl);
100:       VecAXPY(mfqP->subxl,-1.0,tao->solution);
101:       VecScale(mfqP->subxl,1.0/mfqP->delta);

103:       VecPointwiseMin(mfqP->subxu,mfqP->subxu,mfqP->subpdel);
104:       VecPointwiseMax(mfqP->subxl,mfqP->subxl,mfqP->subndel);
105:     } else {
106:       VecCopy(mfqP->subpdel,mfqP->subxu);
107:       VecCopy(mfqP->subndel,mfqP->subxl);
108:     }
109:     /* Make sure xu > xl */
110:     VecCopy(mfqP->subxl,mfqP->subpdel);
111:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);
112:     VecMax(mfqP->subpdel,NULL,&maxval);
113:     if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"upper bound < lower bound in subproblem");
114:     /* Make sure xu > tao->solution > xl */
115:     VecCopy(mfqP->subxl,mfqP->subpdel);
116:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subx);
117:     VecMax(mfqP->subpdel,NULL,&maxval);
118:     if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"initial guess < lower bound in subproblem");

120:     VecCopy(mfqP->subx,mfqP->subpdel);
121:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);
122:     VecMax(mfqP->subpdel,NULL,&maxval);
123:     if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"initial guess > upper bound in subproblem");

125:     TaoSolve(mfqP->subtao);
126:     TaoGetSolutionStatus(mfqP->subtao,NULL,qmin,NULL,NULL,NULL,NULL);

128:     /* test bounds post-solution*/
129:     VecCopy(mfqP->subxl,mfqP->subpdel);
130:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subx);
131:     VecMax(mfqP->subpdel,NULL,&maxval);
132:     if (maxval > 1e-5) {
133:       PetscInfo(tao,"subproblem solution < lower bound\n");
134:       tao->reason = TAO_DIVERGED_TR_REDUCTION;
135:     }

137:     VecCopy(mfqP->subx,mfqP->subpdel);
138:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);
139:     VecMax(mfqP->subpdel,NULL,&maxval);
140:     if (maxval > 1e-5) {
141:       PetscInfo(tao,"subproblem solution > upper bound\n");
142:       tao->reason = TAO_DIVERGED_TR_REDUCTION;
143:     }
144:   } else {
145:     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);
146:   }
147:   *qmin *= -1;
148:   return(0);
149: }

151: static PetscErrorCode pounders_update_res(Tao tao)
152: {
153:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
154:   PetscInt i,row,col;
155:   PetscBLASInt blasn=mfqP->n,blasn2=blasn*blasn,blasm=mfqP->m,ione=1;
156:   PetscReal zero=0.0,one=1.0,wii,factor;

160:   for (i=0;i<mfqP->n;i++) {
161:     mfqP->Gres[i]=0;
162:   }
163:   for (i=0;i<mfqP->n*mfqP->n;i++) {
164:     mfqP->Hres[i]=0;
165:   }

167:   /* Compute Gres= sum_ij[wij * (cjgi + cigj)] */
168:   if (tao->res_weights_v) {
169:     /* Vector(diagonal) weights: gres = sum_i(wii*ci*gi) */
170:     for (i=0;i<mfqP->m;i++) {
171:       VecGetValues(tao->res_weights_v,1,&i,&factor);
172:       factor=factor*mfqP->C[i];
173:       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn,&factor,&mfqP->Fdiff[blasn*i],&ione,mfqP->Gres,&ione));
174:     }

176:     /* compute Hres = sum_ij [wij * (*ci*Hj + cj*Hi + gi gj' + gj gi') ] */
177:     /* vector(diagonal weights) Hres = sum_i(wii*(ci*Hi + gi * gi' )*/
178:     for (i=0;i<mfqP->m;i++) {
179:       VecGetValues(tao->res_weights_v,1,&i,&wii);
180:       if (tao->niter>1) {
181:         factor=wii*mfqP->C[i];
182:         /* add wii * ci * Hi */
183:         PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn2,&factor,&mfqP->H[i],&blasm,mfqP->Hres,&ione));
184:       }
185:       /* add wii * gi * gi' */
186:       PetscStackCallBLAS("BLASgemm",BLASgemm_("N","T",&blasn,&blasn,&ione,&wii,&mfqP->Fdiff[blasn*i],&blasn,&mfqP->Fdiff[blasn*i],&blasn,&one,mfqP->Hres,&blasn));
187:     }
188:   } else if (tao->res_weights_w) {
189:     /* General case: .5 * Gres= sum_ij[wij * (cjgi + cigj)] */
190:     for (i=0;i<tao->res_weights_n;i++) {
191:       row=tao->res_weights_rows[i];
192:       col=tao->res_weights_cols[i];

194:       factor = tao->res_weights_w[i]*mfqP->C[col]/2.0;
195:       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn,&factor,&mfqP->Fdiff[blasn*row],&ione,mfqP->Gres,&ione));
196:       factor = tao->res_weights_w[i]*mfqP->C[row]/2.0;
197:       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn,&factor,&mfqP->Fdiff[blasn*col],&ione,mfqP->Gres,&ione));
198:     }

200:     /* compute Hres = sum_ij [wij * (*ci*Hj + cj*Hi + gi gj' + gj gi') ] */
201:     /* .5 * sum_ij [wij * (*ci*Hj + cj*Hi + gi gj' + gj gi') ] */
202:     for (i=0;i<tao->res_weights_n;i++) {
203:       row=tao->res_weights_rows[i];
204:       col=tao->res_weights_cols[i];
205:       factor=tao->res_weights_w[i]/2.0;
206:       /* add wij * gi gj' + wij * gj gi' */
207:       PetscStackCallBLAS("BLASgemm",BLASgemm_("N","T",&blasn,&blasn,&ione,&factor,&mfqP->Fdiff[blasn*row],&blasn,&mfqP->Fdiff[blasn*col],&blasn,&one,mfqP->Hres,&blasn));
208:       PetscStackCallBLAS("BLASgemm",BLASgemm_("N","T",&blasn,&blasn,&ione,&factor,&mfqP->Fdiff[blasn*col],&blasn,&mfqP->Fdiff[blasn*row],&blasn,&one,mfqP->Hres,&blasn));
209:     }
210:     if (tao->niter > 1) {
211:       for (i=0;i<tao->res_weights_n;i++) {
212:         row=tao->res_weights_rows[i];
213:         col=tao->res_weights_cols[i];

215:         /* add  wij*cj*Hi */
216:         factor = tao->res_weights_w[i]*mfqP->C[col]/2.0;
217:         PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn2,&factor,&mfqP->H[row],&blasm,mfqP->Hres,&ione));

219:         /* add wij*ci*Hj */
220:         factor = tao->res_weights_w[i]*mfqP->C[row]/2.0;
221:         PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn2,&factor,&mfqP->H[col],&blasm,mfqP->Hres,&ione));
222:       }
223:     }
224:   } else {
225:     /* Default: Gres= sum_i[cigi] = G*c' */
226:     PetscInfo(tao,"Identity weights\n");
227:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasm,&one,mfqP->Fdiff,&blasn,mfqP->C,&ione,&zero,mfqP->Gres,&ione));

229:     /* compute Hres = sum_ij [wij * (*ci*Hj + cj*Hi + gi gj' + gj gi') ] */
230:     /*  Hres = G*G' + 0.5 sum {F(xkin,i)*H(:,:,i)}  */
231:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","T",&blasn,&blasn,&blasm,&one,mfqP->Fdiff, &blasn,mfqP->Fdiff, &blasn,&zero,mfqP->Hres,&blasn));

233:     /* sum(F(xkin,i)*H(:,:,i)) */
234:     if (tao->niter>1) {
235:       for (i=0;i<mfqP->m;i++) {
236:         factor = mfqP->C[i];
237:         PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn2,&factor,&mfqP->H[i],&blasm,mfqP->Hres,&ione));
238:       }
239:     }
240:   }
241:   return(0);
242: }

244: PetscErrorCode phi2eval(PetscReal *x, PetscInt n, PetscReal *phi)
245: {
246: /* 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] */
247:   PetscInt  i,j,k;
248:   PetscReal sqrt2 = PetscSqrtReal(2.0);

251:   j=0;
252:   for (i=0;i<n;i++) {
253:     phi[j] = 0.5 * x[i]*x[i];
254:     j++;
255:     for (k=i+1;k<n;k++) {
256:       phi[j]  = x[i]*x[k]/sqrt2;
257:       j++;
258:     }
259:   }
260:   return(0);
261: }

263: PetscErrorCode getquadpounders(TAO_POUNDERS *mfqP)
264: {
265: /* Computes the parameters of the quadratic Q(x) = c + g'*x + 0.5*x*G*x'
266:    that satisfies the interpolation conditions Q(X[:,j]) = f(j)
267:    for j=1,...,m and with a Hessian matrix of least Frobenius norm */

269:     /* NB --we are ignoring c */
270:   PetscInt     i,j,k,num,np = mfqP->nmodelpoints;
271:   PetscReal    one = 1.0,zero=0.0,negone=-1.0;
272:   PetscBLASInt blasnpmax = mfqP->npmax;
273:   PetscBLASInt blasnplus1 = mfqP->n+1;
274:   PetscBLASInt blasnp = np;
275:   PetscBLASInt blasint = mfqP->n*(mfqP->n+1) / 2;
276:   PetscBLASInt blasint2 = np - mfqP->n-1;
277:   PetscBLASInt info,ione=1;
278:   PetscReal    sqrt2 = PetscSqrtReal(2.0);

281:   for (i=0;i<mfqP->n*mfqP->m;i++) {
282:     mfqP->Gdel[i] = 0;
283:   }
284:   for (i=0;i<mfqP->n*mfqP->n*mfqP->m;i++) {
285:     mfqP->Hdel[i] = 0;
286:   }

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

292:   if (np == mfqP->n+1) {
293:     for (i=0;i<mfqP->npmax-mfqP->n-1;i++) {
294:       mfqP->omega[i]=0.0;
295:     }
296:     for (i=0;i<mfqP->n*(mfqP->n+1)/2;i++) {
297:       mfqP->beta[i]=0.0;
298:     }
299:   } else {
300:     /* Let Ltmp = (L'*L) */
301:     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));

303:     /* factor Ltmp */
304:     PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&blasint2,mfqP->L_tmp,&blasint,&info));
305:     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine potrf returned with value %d\n",info);
306:   }

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

315:       /* Beta = L*Omega */
316:       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasint,&blasint2,&one,&mfqP->L[(mfqP->n+1)*blasint],&blasint,mfqP->omega,&ione,&zero,mfqP->beta,&ione));
317:     }

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

324:     /* Gdel(:,k) = Alpha(2:n+1) */
325:     for (i=0;i<mfqP->n;i++) {
326:       mfqP->Gdel[i + mfqP->n*k] = mfqP->RES[mfqP->npmax*k + i+1];
327:     }

329:     /* Set Hdels */
330:     num=0;
331:     for (i=0;i<mfqP->n;i++) {
332:       /* H[i,i,k] = Beta(num) */
333:       mfqP->Hdel[(i*mfqP->n + i)*mfqP->m + k] = mfqP->beta[num];
334:       num++;
335:       for (j=i+1;j<mfqP->n;j++) {
336:         /* H[i,j,k] = H[j,i,k] = Beta(num)/sqrt(2) */
337:         mfqP->Hdel[(j*mfqP->n + i)*mfqP->m + k] = mfqP->beta[num]/sqrt2;
338:         mfqP->Hdel[(i*mfqP->n + j)*mfqP->m + k] = mfqP->beta[num]/sqrt2;
339:         num++;
340:       }
341:     }
342:   }
343:   return(0);
344: }

346: PetscErrorCode morepoints(TAO_POUNDERS *mfqP)
347: {
348:   /* Assumes mfqP->model_indices[0]  is minimum index
349:    Finishes adding points to mfqP->model_indices (up to npmax)
350:    Computes L,Z,M,N
351:    np is actual number of points in model (should equal npmax?) */
352:   PetscInt        point,i,j,offset;
353:   PetscInt        reject;
354:   PetscBLASInt    blasn=mfqP->n,blasnpmax=mfqP->npmax,blasnplus1=mfqP->n+1,info,blasnmax=mfqP->nmax,blasint,blasint2,blasnp,blasmaxmn;
355:   const PetscReal *x;
356:   PetscReal       normd;
357:   PetscErrorCode  ierr;

360:   /* Initialize M,N */
361:   for (i=0;i<mfqP->n+1;i++) {
362:     VecGetArrayRead(mfqP->Xhist[mfqP->model_indices[i]],&x);
363:     mfqP->M[(mfqP->n+1)*i] = 1.0;
364:     for (j=0;j<mfqP->n;j++) {
365:       mfqP->M[j+1+((mfqP->n+1)*i)] = (x[j]  - mfqP->xmin[j]) / mfqP->delta;
366:     }
367:     VecRestoreArrayRead(mfqP->Xhist[mfqP->model_indices[i]],&x);
368:     phi2eval(&mfqP->M[1+((mfqP->n+1)*i)],mfqP->n,&mfqP->N[mfqP->n*(mfqP->n+1)/2 * i]);
369:   }

371:   /* Now we add points until we have npmax starting with the most recent ones */
372:   point = mfqP->nHist-1;
373:   mfqP->nmodelpoints = mfqP->n+1;
374:   while (mfqP->nmodelpoints < mfqP->npmax && point>=0) {
375:     /* Reject any points already in the model */
376:     reject = 0;
377:     for (j=0;j<mfqP->n+1;j++) {
378:       if (point == mfqP->model_indices[j]) {
379:         reject = 1;
380:         break;
381:       }
382:     }

384:     /* Reject if norm(d) >c2 */
385:     if (!reject) {
386:       VecCopy(mfqP->Xhist[point],mfqP->workxvec);
387:       VecAXPY(mfqP->workxvec,-1.0,mfqP->Xhist[mfqP->minindex]);
388:       VecNorm(mfqP->workxvec,NORM_2,&normd);
389:       normd /= mfqP->delta;
390:       if (normd > mfqP->c2) {
391:         reject =1;
392:       }
393:     }
394:     if (reject){
395:       point--;
396:       continue;
397:     }

399:     VecGetArrayRead(mfqP->Xhist[point],&x);
400:     mfqP->M[(mfqP->n+1)*mfqP->nmodelpoints] = 1.0;
401:     for (j=0;j<mfqP->n;j++) {
402:       mfqP->M[j+1+((mfqP->n+1)*mfqP->nmodelpoints)] = (x[j]  - mfqP->xmin[j]) / mfqP->delta;
403:     }
404:     VecRestoreArrayRead(mfqP->Xhist[point],&x);
405:     phi2eval(&mfqP->M[1+(mfqP->n+1)*mfqP->nmodelpoints],mfqP->n,&mfqP->N[mfqP->n*(mfqP->n+1)/2 * (mfqP->nmodelpoints)]);

407:     /* Update QR factorization */
408:     /* Copy M' to Q_tmp */
409:     for (i=0;i<mfqP->n+1;i++) {
410:       for (j=0;j<mfqP->npmax;j++) {
411:         mfqP->Q_tmp[j+mfqP->npmax*i] = mfqP->M[i+(mfqP->n+1)*j];
412:       }
413:     }
414:     blasnp = mfqP->nmodelpoints+1;
415:     /* Q_tmp,R = qr(M') */
416:     blasmaxmn=PetscMax(mfqP->m,mfqP->n+1);
417:     PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&blasnp,&blasnplus1,mfqP->Q_tmp,&blasnpmax,mfqP->tau_tmp,mfqP->mwork,&blasmaxmn,&info));
418:     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine geqrf returned with value %d\n",info);

420:     /* Reject if min(svd(N*Q(:,n+2:np+1)) <= theta2 */
421:     /* L = N*Qtmp */
422:     blasint2 = mfqP->n * (mfqP->n+1) / 2;
423:     /* Copy N to L_tmp */
424:     for (i=0;i<mfqP->n*(mfqP->n+1)/2 * mfqP->npmax;i++) {
425:       mfqP->L_tmp[i]= mfqP->N[i];
426:     }
427:     /* Copy L_save to L_tmp */

429:     /* L_tmp = N*Qtmp' */
430: #if defined(PETSC_MISSING_LAPACK_ORMQR)
431:     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"ORMQR - Lapack routine is unavailable.");
432: #else
433:     PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&blasint2,&blasnp,&blasnplus1,mfqP->Q_tmp,&blasnpmax,mfqP->tau_tmp,mfqP->L_tmp,&blasint2,mfqP->npmaxwork,&blasnmax,&info));
434:     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine ormqr returned with value %d\n",info);
435: #endif

437:     /* Copy L_tmp to L_save */
438:     for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
439:       mfqP->L_save[i] = mfqP->L_tmp[i];
440:     }

442:     /* Get svd for L_tmp(:,n+2:np+1) (L_tmp is modified in process) */
443:     blasint = mfqP->nmodelpoints - mfqP->n;
444:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
445:     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));
446:     PetscFPTrapPop();
447:     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine gesvd returned with value %d\n",info);

449:     if (mfqP->beta[PetscMin(blasint,blasint2)-1] > mfqP->theta2) {
450:       /* accept point */
451:       mfqP->model_indices[mfqP->nmodelpoints] = point;
452:       /* Copy Q_tmp to Q */
453:       for (i=0;i<mfqP->npmax* mfqP->npmax;i++) {
454:         mfqP->Q[i] = mfqP->Q_tmp[i];
455:       }
456:       for (i=0;i<mfqP->npmax;i++){
457:         mfqP->tau[i] = mfqP->tau_tmp[i];
458:       }
459:       mfqP->nmodelpoints++;
460:       blasnp = mfqP->nmodelpoints;

462:       /* Copy L_save to L */
463:       for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
464:         mfqP->L[i] = mfqP->L_save[i];
465:       }
466:     }
467:     point--;
468:   }

470:   blasnp = mfqP->nmodelpoints;
471:   /* Copy Q(:,n+2:np) to Z */
472:   /* First set Q_tmp to I */
473:   for (i=0;i<mfqP->npmax*mfqP->npmax;i++) {
474:     mfqP->Q_tmp[i] = 0.0;
475:   }
476:   for (i=0;i<mfqP->npmax;i++) {
477:     mfqP->Q_tmp[i + mfqP->npmax*i] = 1.0;
478:   }

480:   /* Q_tmp = I * Q */
481: #if defined(PETSC_MISSING_LAPACK_ORMQR)
482:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"ORMQR - Lapack routine is unavailable.");
483: #else
484:   PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&blasnp,&blasnp,&blasnplus1,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->Q_tmp,&blasnpmax,mfqP->npmaxwork,&blasnmax,&info));
485:   if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine ormqr returned with value %d\n",info);
486: #endif

488:   /* Copy Q_tmp(:,n+2:np) to Z) */
489:   offset = mfqP->npmax * (mfqP->n+1);
490:   for (i=offset;i<mfqP->npmax*mfqP->npmax;i++) {
491:     mfqP->Z[i-offset] = mfqP->Q_tmp[i];
492:   }

494:   if (mfqP->nmodelpoints == mfqP->n + 1) {
495:     /* Set L to I_{n+1} */
496:     for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
497:       mfqP->L[i] = 0.0;
498:     }
499:     for (i=0;i<mfqP->n;i++) {
500:       mfqP->L[(mfqP->n*(mfqP->n+1)/2)*i + i] = 1.0;
501:     }
502:   }
503:   return(0);
504: }

506: /* Only call from modelimprove, addpoint() needs ->Q_tmp and ->work to be set */
507: PetscErrorCode addpoint(Tao tao, TAO_POUNDERS *mfqP, PetscInt index)
508: {

512:   /* Create new vector in history: X[newidx] = X[mfqP->index] + delta*X[index]*/
513:   VecDuplicate(mfqP->Xhist[0],&mfqP->Xhist[mfqP->nHist]);
514:   VecSetValues(mfqP->Xhist[mfqP->nHist],mfqP->n,mfqP->indices,&mfqP->Q_tmp[index*mfqP->npmax],INSERT_VALUES);
515:   VecAssemblyBegin(mfqP->Xhist[mfqP->nHist]);
516:   VecAssemblyEnd(mfqP->Xhist[mfqP->nHist]);
517:   VecAYPX(mfqP->Xhist[mfqP->nHist],mfqP->delta,mfqP->Xhist[mfqP->minindex]);

519:   /* Project into feasible region */
520:   if (tao->XU && tao->XL) {
521:     VecMedian(mfqP->Xhist[mfqP->nHist], tao->XL, tao->XU, mfqP->Xhist[mfqP->nHist]);
522:   }

524:   /* Compute value of new vector */
525:   VecDuplicate(mfqP->Fhist[0],&mfqP->Fhist[mfqP->nHist]);
526:   CHKMEMQ;
527:   pounders_feval(tao,mfqP->Xhist[mfqP->nHist],mfqP->Fhist[mfqP->nHist],&mfqP->Fres[mfqP->nHist]);

529:   /* Add new vector to model */
530:   mfqP->model_indices[mfqP->nmodelpoints] = mfqP->nHist;
531:   mfqP->nmodelpoints++;
532:   mfqP->nHist++;
533:   return(0);
534: }

536: PetscErrorCode modelimprove(Tao tao, TAO_POUNDERS *mfqP, PetscInt addallpoints)
537: {
538:   /* modeld = Q(:,np+1:n)' */
540:   PetscInt       i,j,minindex=0;
541:   PetscReal      dp,half=0.5,one=1.0,minvalue=PETSC_INFINITY;
542:   PetscBLASInt   blasn=mfqP->n,  blasnpmax = mfqP->npmax, blask,info;
543:   PetscBLASInt   blas1=1,blasnmax = mfqP->nmax;

545:   blask = mfqP->nmodelpoints;
546:   /* Qtmp = I(n x n) */
547:   for (i=0;i<mfqP->n;i++) {
548:     for (j=0;j<mfqP->n;j++) {
549:       mfqP->Q_tmp[i + mfqP->npmax*j] = 0.0;
550:     }
551:   }
552:   for (j=0;j<mfqP->n;j++) {
553:     mfqP->Q_tmp[j + mfqP->npmax*j] = 1.0;
554:   }

556:   /* Qtmp = Q * I */
557: #if defined(PETSC_MISSING_LAPACK_ORMQR)
558:   SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_SUP,"ORMQR - Lapack routine is unavailable.");
559: #else
560:   PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&blasn,&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau, mfqP->Q_tmp, &blasnpmax, mfqP->npmaxwork,&blasnmax, &info));
561: #endif

563:   for (i=mfqP->nmodelpoints;i<mfqP->n;i++) {
564:     dp = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->Gres,&blas1);
565:     if (dp>0.0) { /* Model says use the other direction! */
566:       for (j=0;j<mfqP->n;j++) {
567:         mfqP->Q_tmp[i*mfqP->npmax+j] *= -1;
568:       }
569:     }
570:     /* mfqP->work[i] = Cres+Modeld(i,:)*(Gres+.5*Hres*Modeld(i,:)') */
571:     for (j=0;j<mfqP->n;j++) {
572:       mfqP->work2[j] = mfqP->Gres[j];
573:     }
574:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&half,mfqP->Hres,&blasn,&mfqP->Q_tmp[i*mfqP->npmax], &blas1, &one, mfqP->work2,&blas1));
575:     mfqP->work[i] = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->work2,&blas1);
576:     if (i==mfqP->nmodelpoints || mfqP->work[i] < minvalue) {
577:       minindex=i;
578:       minvalue = mfqP->work[i];
579:     }
580:     if (addallpoints != 0) {
581:       addpoint(tao,mfqP,i);
582:     }
583:   }
584:   if (!addallpoints) {
585:     addpoint(tao,mfqP,minindex);
586:   }
587:   return(0);
588: }


591: PetscErrorCode affpoints(TAO_POUNDERS *mfqP, PetscReal *xmin,PetscReal c)
592: {
593:   PetscInt        i,j;
594:   PetscBLASInt    blasm=mfqP->m,blasj,blask,blasn=mfqP->n,ione=1,info;
595:   PetscBLASInt    blasnpmax = mfqP->npmax,blasmaxmn;
596:   PetscReal       proj,normd;
597:   const PetscReal *x;
598:   PetscErrorCode  ierr;

601:   for (i=mfqP->nHist-1;i>=0;i--) {
602:     VecGetArrayRead(mfqP->Xhist[i],&x);
603:     for (j=0;j<mfqP->n;j++) {
604:       mfqP->work[j] = (x[j] - xmin[j])/mfqP->delta;
605:     }
606:     VecRestoreArrayRead(mfqP->Xhist[i],&x);
607:     PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,mfqP->work,&ione,mfqP->work2,&ione));
608:     normd = BLASnrm2_(&blasn,mfqP->work,&ione);
609:     if (normd <= c) {
610:       blasj=PetscMax((mfqP->n - mfqP->nmodelpoints),0);
611:       if (!mfqP->q_is_I) {
612:         /* project D onto null */
613:         blask=(mfqP->nmodelpoints);
614: #if defined(PETSC_MISSING_LAPACK_ORMQR)
615:         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"ORMQR - Lapack routine is unavailable.");
616: #else
617:         PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&ione,&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->work2,&ione,mfqP->mwork,&blasm,&info));
618:         if (info < 0) SETERRQ1(PETSC_COMM_SELF,1,"ormqr returned value %d\n",info);
619: #endif
620:       }
621:       proj = BLASnrm2_(&blasj,&mfqP->work2[mfqP->nmodelpoints],&ione);

623:       if (proj >= mfqP->theta1) { /* add this index to model */
624:         mfqP->model_indices[mfqP->nmodelpoints]=i;
625:         mfqP->nmodelpoints++;
626:         PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,mfqP->work,&ione,&mfqP->Q_tmp[mfqP->npmax*(mfqP->nmodelpoints-1)],&ione));
627:         blask=mfqP->npmax*(mfqP->nmodelpoints);
628:         PetscStackCallBLAS("BLAScopy",BLAScopy_(&blask,mfqP->Q_tmp,&ione,mfqP->Q,&ione));
629:         blask = mfqP->nmodelpoints;
630:         blasmaxmn = PetscMax(mfqP->m,mfqP->n);
631:         PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->mwork,&blasmaxmn,&info));
632:         if (info < 0) SETERRQ1(PETSC_COMM_SELF,1,"geqrf returned value %d\n",info);
633:         mfqP->q_is_I = 0;
634:       }
635:       if (mfqP->nmodelpoints == mfqP->n)  {
636:         break;
637:       }
638:     }
639:   }

641:   return(0);
642: }

644: static PetscErrorCode TaoSolve_POUNDERS(Tao tao)
645: {
646:   TAO_POUNDERS       *mfqP = (TAO_POUNDERS *)tao->data;
647:   PetscInt           i,ii,j,k,l;
648:   PetscReal          step=1.0;
649:   PetscInt           low,high;
650:   PetscReal          minnorm;
651:   PetscReal          *x,*f;
652:   const PetscReal    *xmint,*fmin;
653:   PetscReal          cres,deltaold;
654:   PetscReal          gnorm;
655:   PetscBLASInt       info,ione=1,iblas;
656:   PetscBool          valid,same;
657:   PetscReal          mdec, rho, normxsp;
658:   PetscReal          one=1.0,zero=0.0,ratio;
659:   PetscBLASInt       blasm,blasn,blasncopy,blasnpmax;
660:   PetscErrorCode     ierr;
661:   static PetscBool   set = PETSC_FALSE;

663:   /* n = # of parameters
664:      m = dimension (components) of function  */
666:   PetscCitationsRegister("@article{UNEDF0,\n"
667:                                 "title = {Nuclear energy density optimization},\n"
668:                                 "author = {Kortelainen, M.  and Lesinski, T.  and Mor\'e, J.  and Nazarewicz, W.\n"
669:                                 "          and Sarich, J.  and Schunck, N.  and Stoitsov, M. V. and Wild, S. },\n"
670:                                 "journal = {Phys. Rev. C},\n"
671:                                 "volume = {82},\n"
672:                                 "number = {2},\n"
673:                                 "pages = {024313},\n"
674:                                 "numpages = {18},\n"
675:                                 "year = {2010},\n"
676:                                 "month = {Aug},\n"
677:                                 "doi = {10.1103/PhysRevC.82.024313}\n}\n",&set);
678:   tao->niter=0;
679:   if (tao->XL && tao->XU) {
680:     /* Check x0 <= XU */
681:     PetscReal val;

683:     VecCopy(tao->solution,mfqP->Xhist[0]);
684:     VecAXPY(mfqP->Xhist[0],-1.0,tao->XU);
685:     VecMax(mfqP->Xhist[0],NULL,&val);
686:     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 > upper bound");

688:     /* Check x0 >= xl */
689:     VecCopy(tao->XL,mfqP->Xhist[0]);
690:     VecAXPY(mfqP->Xhist[0],-1.0,tao->solution);
691:     VecMax(mfqP->Xhist[0],NULL,&val);
692:     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 < lower bound");

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

696:     VecSet(mfqP->Xhist[0],mfqP->delta);
697:     VecAXPY(mfqP->Xhist[0],1.0,tao->solution);
698:     VecAXPY(mfqP->Xhist[0],-1.0,tao->XU);
699:     VecMax(mfqP->Xhist[0],NULL,&val);
700:     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 + delta > upper bound");
701:   }

703:   blasm = mfqP->m; blasn=mfqP->n; blasnpmax = mfqP->npmax;
704:   for (i=0;i<mfqP->n*mfqP->n*mfqP->m;++i) mfqP->H[i]=0;

706:   VecCopy(tao->solution,mfqP->Xhist[0]);

708:   /* This provides enough information to approximate the gradient of the objective */
709:   /* using a forward difference scheme. */

711:   PetscInfo1(tao,"Initialize simplex; delta = %10.9e\n",(double)mfqP->delta);
712:   pounders_feval(tao,mfqP->Xhist[0],mfqP->Fhist[0],&mfqP->Fres[0]);
713:   mfqP->minindex = 0;
714:   minnorm = mfqP->Fres[0];

716:   VecGetOwnershipRange(mfqP->Xhist[0],&low,&high);
717:   for (i=1;i<mfqP->n+1;++i) {
718:     VecCopy(mfqP->Xhist[0],mfqP->Xhist[i]);

720:     if (i-1 >= low && i-1 < high) {
721:       VecGetArray(mfqP->Xhist[i],&x);
722:       x[i-1-low] += mfqP->delta;
723:       VecRestoreArray(mfqP->Xhist[i],&x);
724:     }
725:     CHKMEMQ;
726:     pounders_feval(tao,mfqP->Xhist[i],mfqP->Fhist[i],&mfqP->Fres[i]);
727:     if (mfqP->Fres[i] < minnorm) {
728:       mfqP->minindex = i;
729:       minnorm = mfqP->Fres[i];
730:     }
731:   }
732:   VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);
733:   VecCopy(mfqP->Fhist[mfqP->minindex],tao->ls_res);
734:   PetscInfo1(tao,"Finalize simplex; minnorm = %10.9e\n",(double)minnorm);

736:   /* Gather mpi vecs to one big local vec */

738:   /* Begin serial code */

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

745:   PetscInfo1(tao,"Build matrix: %D\n",(PetscInt)mfqP->size);
746:   if (1 == mfqP->size) {
747:     VecGetArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
748:     for (i=0;i<mfqP->n;i++) mfqP->xmin[i] = xmint[i];
749:     VecRestoreArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
750:     VecGetArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);
751:     for (i=0;i<mfqP->n+1;i++) {
752:       if (i == mfqP->minindex) continue;

754:       VecGetArray(mfqP->Xhist[i],&x);
755:       for (j=0;j<mfqP->n;j++) {
756:         mfqP->Disp[ii+mfqP->npmax*j] = (x[j] - mfqP->xmin[j])/mfqP->delta;
757:       }
758:       VecRestoreArray(mfqP->Xhist[i],&x);

760:       VecGetArray(mfqP->Fhist[i],&f);
761:       for (j=0;j<mfqP->m;j++) {
762:         mfqP->Fdiff[ii+mfqP->n*j] = f[j] - fmin[j];
763:       }
764:       VecRestoreArray(mfqP->Fhist[i],&f);

766:       mfqP->model_indices[ii++] = i;
767:     }
768:     for (j=0;j<mfqP->m;j++) {
769:       mfqP->C[j] = fmin[j];
770:     }
771:     VecRestoreArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);
772:   } else {
773:     VecSet(mfqP->localxmin,0);
774:     VecScatterBegin(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);
775:     VecScatterEnd(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);

777:     VecGetArrayRead(mfqP->localxmin,&xmint);
778:     for (i=0;i<mfqP->n;i++) mfqP->xmin[i] = xmint[i];
779:     VecRestoreArrayRead(mfqP->localxmin,&xmint);

781:     VecScatterBegin(mfqP->scatterf,mfqP->Fhist[mfqP->minindex],mfqP->localfmin,INSERT_VALUES,SCATTER_FORWARD);
782:     VecScatterEnd(mfqP->scatterf,mfqP->Fhist[mfqP->minindex],mfqP->localfmin,INSERT_VALUES,SCATTER_FORWARD);
783:     VecGetArrayRead(mfqP->localfmin,&fmin);
784:     for (i=0;i<mfqP->n+1;i++) {
785:       if (i == mfqP->minindex) continue;

787:       VecScatterBegin(mfqP->scatterx,mfqP->Xhist[ii],mfqP->localx,INSERT_VALUES, SCATTER_FORWARD);
788:       VecScatterEnd(mfqP->scatterx,mfqP->Xhist[ii],mfqP->localx,INSERT_VALUES, SCATTER_FORWARD);
789:       VecGetArray(mfqP->localx,&x);
790:       for (j=0;j<mfqP->n;j++) {
791:         mfqP->Disp[ii+mfqP->npmax*j] = (x[j] - mfqP->xmin[j])/mfqP->delta;
792:       }
793:       VecRestoreArray(mfqP->localx,&x);

795:       VecScatterBegin(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);
796:       VecScatterEnd(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);
797:       VecGetArray(mfqP->localf,&f);
798:       for (j=0;j<mfqP->m;j++) {
799:         mfqP->Fdiff[ii+mfqP->n*j] = f[j] - fmin[j];
800:       }
801:       VecRestoreArray(mfqP->localf,&f);

803:       mfqP->model_indices[ii++] = i;
804:     }
805:     for (j=0;j<mfqP->m;j++) {
806:       mfqP->C[j] = fmin[j];
807:     }
808:     VecRestoreArrayRead(mfqP->localfmin,&fmin);
809:   }

811:   /* Determine the initial quadratic models */
812:   /* G = D(ModelIn,:) \ (F(ModelIn,1:m)-repmat(F(xkin,1:m),n,1)); */
813:   /* D (nxn) Fdiff (nxm)  => G (nxm) */
814:   blasncopy = blasn;
815:   PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&blasn,&blasm,mfqP->Disp,&blasnpmax,mfqP->iwork,mfqP->Fdiff,&blasncopy,&info));
816:   PetscInfo1(tao,"Linear solve return: %D\n",(PetscInt)info);

818:   cres = minnorm;
819:   pounders_update_res(tao);

821:   valid = PETSC_TRUE;

823:   VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);
824:   VecAssemblyBegin(tao->gradient);
825:   VecAssemblyEnd(tao->gradient);
826:   VecNorm(tao->gradient,NORM_2,&gnorm);
827:   gnorm *= mfqP->delta;
828:   VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);
829: 
830:   tao->reason = TAO_CONTINUE_ITERATING;
831:   TaoLogConvergenceHistory(tao,minnorm,gnorm,0.0,tao->ksp_its);
832:   TaoMonitor(tao,tao->niter,minnorm,gnorm,0.0,step);
833:   (*tao->ops->convergencetest)(tao,tao->cnvP);
834: 
835:   mfqP->nHist = mfqP->n+1;
836:   mfqP->nmodelpoints = mfqP->n+1;
837:   PetscInfo1(tao,"Initial gradient: %20.19e\n",(double)gnorm);

839:   while (tao->reason == TAO_CONTINUE_ITERATING) {
840:     PetscReal gnm = 1e-4;
841:     /* Call general purpose update function */
842:     if (tao->ops->update) {
843:       (*tao->ops->update)(tao, tao->niter, tao->user_update);
844:     }
845:     tao->niter++;
846:     /* Solve the subproblem min{Q(s): ||s|| <= 1.0} */
847:     gqtwrap(tao,&gnm,&mdec);
848:     /* Evaluate the function at the new point */

850:     for (i=0;i<mfqP->n;i++) {
851:         mfqP->work[i] = mfqP->Xsubproblem[i]*mfqP->delta + mfqP->xmin[i];
852:     }
853:     VecDuplicate(tao->solution,&mfqP->Xhist[mfqP->nHist]);
854:     VecDuplicate(tao->ls_res,&mfqP->Fhist[mfqP->nHist]);
855:     VecSetValues(mfqP->Xhist[mfqP->nHist],mfqP->n,mfqP->indices,mfqP->work,INSERT_VALUES);
856:     VecAssemblyBegin(mfqP->Xhist[mfqP->nHist]);
857:     VecAssemblyEnd(mfqP->Xhist[mfqP->nHist]);

859:     pounders_feval(tao,mfqP->Xhist[mfqP->nHist],mfqP->Fhist[mfqP->nHist],&mfqP->Fres[mfqP->nHist]);

861:     rho = (mfqP->Fres[mfqP->minindex] - mfqP->Fres[mfqP->nHist]) / mdec;
862:     mfqP->nHist++;

864:     /* Update the center */
865:     if ((rho >= mfqP->eta1) || (rho > mfqP->eta0 && valid==PETSC_TRUE)) {
866:       /* Update model to reflect new base point */
867:       for (i=0;i<mfqP->n;i++) {
868:         mfqP->work[i] = (mfqP->work[i] - mfqP->xmin[i])/mfqP->delta;
869:       }
870:       for (j=0;j<mfqP->m;j++) {
871:         /* C(j) = C(j) + work*G(:,j) + .5*work*H(:,:,j)*work';
872:          G(:,j) = G(:,j) + H(:,:,j)*work' */
873:         for (k=0;k<mfqP->n;k++) {
874:           mfqP->work2[k]=0.0;
875:           for (l=0;l<mfqP->n;l++) {
876:             mfqP->work2[k]+=mfqP->H[j + mfqP->m*(k + l*mfqP->n)]*mfqP->work[l];
877:           }
878:         }
879:         for (i=0;i<mfqP->n;i++) {
880:           mfqP->C[j]+=mfqP->work[i]*(mfqP->Fdiff[i + mfqP->n* j] + 0.5*mfqP->work2[i]);
881:           mfqP->Fdiff[i+mfqP->n*j] +=mfqP-> work2[i];
882:         }
883:       }
884:       /* Cres += work*Gres + .5*work*Hres*work';
885:        Gres += Hres*work'; */

887:       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&one,mfqP->Hres,&blasn,mfqP->work,&ione,&zero,mfqP->work2,&ione));
888:       for (i=0;i<mfqP->n;i++) {
889:         cres += mfqP->work[i]*(mfqP->Gres[i]  + 0.5*mfqP->work2[i]);
890:         mfqP->Gres[i] += mfqP->work2[i];
891:       }
892:       mfqP->minindex = mfqP->nHist-1;
893:       minnorm = mfqP->Fres[mfqP->minindex];
894:       VecCopy(mfqP->Fhist[mfqP->minindex],tao->ls_res);
895:       /* Change current center */
896:       VecGetArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
897:       for (i=0;i<mfqP->n;i++) {
898:         mfqP->xmin[i] = xmint[i];
899:       }
900:       VecRestoreArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
901:     }

903:     /* Evaluate at a model-improving point if necessary */
904:     if (valid == PETSC_FALSE) {
905:       mfqP->q_is_I = 1;
906:       mfqP->nmodelpoints = 0;
907:       affpoints(mfqP,mfqP->xmin,mfqP->c1);
908:       if (mfqP->nmodelpoints < mfqP->n) {
909:         PetscInfo(tao,"Model not valid -- model-improving\n");
910:         modelimprove(tao,mfqP,1);
911:       }
912:     }

914:     /* Update the trust region radius */
915:     deltaold = mfqP->delta;
916:     normxsp = 0;
917:     for (i=0;i<mfqP->n;i++) {
918:       normxsp += mfqP->Xsubproblem[i]*mfqP->Xsubproblem[i];
919:     }
920:     normxsp = PetscSqrtReal(normxsp);
921:     if (rho >= mfqP->eta1 && normxsp > 0.5*mfqP->delta) {
922:       mfqP->delta = PetscMin(mfqP->delta*mfqP->gamma1,mfqP->deltamax);
923:     } else if (valid == PETSC_TRUE) {
924:       mfqP->delta = PetscMax(mfqP->delta*mfqP->gamma0,mfqP->deltamin);
925:     }

927:     /* Compute the next interpolation set */
928:     mfqP->q_is_I = 1;
929:     mfqP->nmodelpoints=0;
930:     PetscInfo2(tao,"Affine Points: xmin = %20.19e, c1 = %20.19e\n",(double)*mfqP->xmin,(double)mfqP->c1);
931:     affpoints(mfqP,mfqP->xmin,mfqP->c1);
932:     if (mfqP->nmodelpoints == mfqP->n) {
933:       valid = PETSC_TRUE;
934:     } else {
935:       valid = PETSC_FALSE;
936:       PetscInfo2(tao,"Affine Points: xmin = %20.19e, c2 = %20.19e\n",(double)*mfqP->xmin,(double)mfqP->c2);
937:       affpoints(mfqP,mfqP->xmin,mfqP->c2);
938:       if (mfqP->n > mfqP->nmodelpoints) {
939:         PetscInfo(tao,"Model not valid -- adding geometry points\n");
940:         modelimprove(tao,mfqP,mfqP->n - mfqP->nmodelpoints);
941:       }
942:     }
943:     for (i=mfqP->nmodelpoints;i>0;i--) {
944:       mfqP->model_indices[i] = mfqP->model_indices[i-1];
945:     }
946:     mfqP->nmodelpoints++;
947:     mfqP->model_indices[0] = mfqP->minindex;
948:     morepoints(mfqP);
949:     for (i=0;i<mfqP->nmodelpoints;i++) {
950:       VecGetArray(mfqP->Xhist[mfqP->model_indices[i]],&x);
951:       for (j=0;j<mfqP->n;j++) {
952:         mfqP->Disp[i + mfqP->npmax*j] = (x[j]  - mfqP->xmin[j]) / deltaold;
953:       }
954:       VecRestoreArray(mfqP->Xhist[mfqP->model_indices[i]],&x);
955:       VecGetArray(mfqP->Fhist[mfqP->model_indices[i]],&f);
956:       for (j=0;j<mfqP->m;j++) {
957:         for (k=0;k<mfqP->n;k++)  {
958:           mfqP->work[k]=0.0;
959:           for (l=0;l<mfqP->n;l++) {
960:             mfqP->work[k] += mfqP->H[j + mfqP->m*(k + mfqP->n*l)] * mfqP->Disp[i + mfqP->npmax*l];
961:           }
962:         }
963:         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];
964:       }
965:       VecRestoreArray(mfqP->Fhist[mfqP->model_indices[i]],&f);
966:     }

968:     /* Update the quadratic model */
969:     PetscInfo2(tao,"Get Quad, size: %D, points: %D\n",mfqP->n,mfqP->nmodelpoints);
970:     getquadpounders(mfqP);
971:     VecGetArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);
972:     PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasm,fmin,&ione,mfqP->C,&ione));
973:     /* G = G*(delta/deltaold) + Gdel */
974:     ratio = mfqP->delta/deltaold;
975:     iblas = blasm*blasn;
976:     PetscStackCallBLAS("BLASscal",BLASscal_(&iblas,&ratio,mfqP->Fdiff,&ione));
977:     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&one,mfqP->Gdel,&ione,mfqP->Fdiff,&ione));
978:     /* H = H*(delta/deltaold)^2 + Hdel */
979:     iblas = blasm*blasn*blasn;
980:     ratio *= ratio;
981:     PetscStackCallBLAS("BLASscal",BLASscal_(&iblas,&ratio,mfqP->H,&ione));
982:     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&one,mfqP->Hdel,&ione,mfqP->H,&ione));

984:     /* Get residuals */
985:     cres = mfqP->Fres[mfqP->minindex];
986:     pounders_update_res(tao);

988:     /* Export solution and gradient residual to TAO */
989:     VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);
990:     VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);
991:     VecAssemblyBegin(tao->gradient);
992:     VecAssemblyEnd(tao->gradient);
993:     VecNorm(tao->gradient,NORM_2,&gnorm);
994:     gnorm *= mfqP->delta;
995:     /*  final criticality test */
996:     TaoLogConvergenceHistory(tao,minnorm,gnorm,0.0,tao->ksp_its);
997:     TaoMonitor(tao,tao->niter,minnorm,gnorm,0.0,step);
998:     (*tao->ops->convergencetest)(tao,tao->cnvP);
999:     /* test for repeated model */
1000:     if (mfqP->nmodelpoints==mfqP->last_nmodelpoints) {
1001:       same = PETSC_TRUE;
1002:     } else {
1003:       same = PETSC_FALSE;
1004:     }
1005:     for (i=0;i<mfqP->nmodelpoints;i++) {
1006:       if (same) {
1007:         if (mfqP->model_indices[i] == mfqP->last_model_indices[i]) {
1008:           same = PETSC_TRUE;
1009:         } else {
1010:           same = PETSC_FALSE;
1011:         }
1012:       }
1013:       mfqP->last_model_indices[i] = mfqP->model_indices[i];
1014:     }
1015:     mfqP->last_nmodelpoints = mfqP->nmodelpoints;
1016:     if (same && mfqP->delta == deltaold) {
1017:       PetscInfo(tao,"Identical model used in successive iterations\n");
1018:       tao->reason = TAO_CONVERGED_STEPTOL;
1019:     }
1020:   }
1021:   return(0);
1022: }

1024: static PetscErrorCode TaoSetUp_POUNDERS(Tao tao)
1025: {
1026:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
1027:   PetscInt       i,j;
1028:   IS             isfloc,isfglob,isxloc,isxglob;

1032:   if (!tao->gradient) {VecDuplicate(tao->solution,&tao->gradient);  }
1033:   if (!tao->stepdirection) {VecDuplicate(tao->solution,&tao->stepdirection);  }
1034:   VecGetSize(tao->solution,&mfqP->n);
1035:   VecGetSize(tao->ls_res,&mfqP->m);
1036:   mfqP->c1 = PetscSqrtReal((PetscReal)mfqP->n);
1037:   if (mfqP->npmax == PETSC_DEFAULT) {
1038:     mfqP->npmax = 2*mfqP->n + 1;
1039:   }
1040:   mfqP->npmax = PetscMin((mfqP->n+1)*(mfqP->n+2)/2,mfqP->npmax);
1041:   mfqP->npmax = PetscMax(mfqP->npmax, mfqP->n+2);

1043:   PetscMalloc1(tao->max_funcs+100,&mfqP->Xhist);
1044:   PetscMalloc1(tao->max_funcs+100,&mfqP->Fhist);
1045:   for (i=0;i<mfqP->n+1;i++) {
1046:     VecDuplicate(tao->solution,&mfqP->Xhist[i]);
1047:     VecDuplicate(tao->ls_res,&mfqP->Fhist[i]);
1048:   }
1049:   VecDuplicate(tao->solution,&mfqP->workxvec);
1050:   VecDuplicate(tao->ls_res,&mfqP->workfvec);
1051:   mfqP->nHist = 0;

1053:   PetscMalloc1(tao->max_funcs+100,&mfqP->Fres);
1054:   PetscMalloc1(mfqP->npmax*mfqP->m,&mfqP->RES);
1055:   PetscMalloc1(mfqP->n,&mfqP->work);
1056:   PetscMalloc1(mfqP->n,&mfqP->work2);
1057:   PetscMalloc1(mfqP->n,&mfqP->work3);
1058:   PetscMalloc1(PetscMax(mfqP->m,mfqP->n+1),&mfqP->mwork);
1059:   PetscMalloc1(mfqP->npmax - mfqP->n - 1,&mfqP->omega);
1060:   PetscMalloc1(mfqP->n * (mfqP->n+1) / 2,&mfqP->beta);
1061:   PetscMalloc1(mfqP->n + 1 ,&mfqP->alpha);

1063:   PetscMalloc1(mfqP->n*mfqP->n*mfqP->m,&mfqP->H);
1064:   PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q);
1065:   PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q_tmp);
1066:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L);
1067:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_tmp);
1068:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_save);
1069:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->N);
1070:   PetscMalloc1(mfqP->npmax * (mfqP->n+1) ,&mfqP->M);
1071:   PetscMalloc1(mfqP->npmax * (mfqP->npmax - mfqP->n - 1) , &mfqP->Z);
1072:   PetscMalloc1(mfqP->npmax,&mfqP->tau);
1073:   PetscMalloc1(mfqP->npmax,&mfqP->tau_tmp);
1074:   mfqP->nmax = PetscMax(5*mfqP->npmax,mfqP->n*(mfqP->n+1)/2);
1075:   PetscMalloc1(mfqP->nmax,&mfqP->npmaxwork);
1076:   PetscMalloc1(mfqP->nmax,&mfqP->npmaxiwork);
1077:   PetscMalloc1(mfqP->n,&mfqP->xmin);
1078:   PetscMalloc1(mfqP->m,&mfqP->C);
1079:   PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Fdiff);
1080:   PetscMalloc1(mfqP->npmax*mfqP->n,&mfqP->Disp);
1081:   PetscMalloc1(mfqP->n,&mfqP->Gres);
1082:   PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Hres);
1083:   PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Gpoints);
1084:   PetscMalloc1(mfqP->npmax,&mfqP->model_indices);
1085:   PetscMalloc1(mfqP->npmax,&mfqP->last_model_indices);
1086:   PetscMalloc1(mfqP->n,&mfqP->Xsubproblem);
1087:   PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Gdel);
1088:   PetscMalloc1(mfqP->n*mfqP->n*mfqP->m, &mfqP->Hdel);
1089:   PetscMalloc1(PetscMax(mfqP->m,mfqP->n),&mfqP->indices);
1090:   PetscMalloc1(mfqP->n,&mfqP->iwork);
1091:   PetscMalloc1(mfqP->m*mfqP->m,&mfqP->w);
1092:   for (i=0;i<mfqP->m;i++) {
1093:     for (j=0;j<mfqP->m;j++) {
1094:       if (i==j) {
1095:         mfqP->w[i+mfqP->m*j]=1.0;
1096:       } else {
1097:         mfqP->w[i+mfqP->m*j]=0.0;
1098:       }
1099:     }
1100:   }
1101:   for (i=0;i<PetscMax(mfqP->m,mfqP->n);i++) {
1102:     mfqP->indices[i] = i;
1103:   }
1104:   MPI_Comm_size(((PetscObject)tao)->comm,&mfqP->size);
1105:   if (mfqP->size > 1) {
1106:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localx);
1107:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localxmin);
1108:     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localf);
1109:     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localfmin);
1110:     ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxloc);
1111:     ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxglob);
1112:     ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfloc);
1113:     ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfglob);


1116:     VecScatterCreate(tao->solution,isxglob,mfqP->localx,isxloc,&mfqP->scatterx);
1117:     VecScatterCreate(tao->ls_res,isfglob,mfqP->localf,isfloc,&mfqP->scatterf);

1119:     ISDestroy(&isxloc);
1120:     ISDestroy(&isxglob);
1121:     ISDestroy(&isfloc);
1122:     ISDestroy(&isfglob);
1123:   }

1125:   if (!mfqP->usegqt) {
1126:     KSP       ksp;
1127:     PC        pc;
1128:     VecCreateSeqWithArray(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Xsubproblem,&mfqP->subx);
1129:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->subxl);
1130:     VecDuplicate(mfqP->subxl,&mfqP->subb);
1131:     VecDuplicate(mfqP->subxl,&mfqP->subxu);
1132:     VecDuplicate(mfqP->subxl,&mfqP->subpdel);
1133:     VecDuplicate(mfqP->subxl,&mfqP->subndel);
1134:     TaoCreate(PETSC_COMM_SELF,&mfqP->subtao);
1135:     PetscObjectIncrementTabLevel((PetscObject)mfqP->subtao, (PetscObject)tao, 1);
1136:     TaoSetType(mfqP->subtao,TAOBNTR);
1137:     TaoSetOptionsPrefix(mfqP->subtao,"pounders_subsolver_");
1138:     TaoSetInitialVector(mfqP->subtao,mfqP->subx);
1139:     TaoSetObjectiveAndGradientRoutine(mfqP->subtao,pounders_fg,(void*)mfqP);
1140:     TaoSetMaximumIterations(mfqP->subtao,mfqP->gqt_maxits);
1141:     TaoSetFromOptions(mfqP->subtao);
1142:     TaoGetKSP(mfqP->subtao,&ksp);
1143:     if (ksp) {
1144:       KSPGetPC(ksp,&pc);
1145:       PCSetType(pc,PCNONE);
1146:     }
1147:     TaoSetVariableBounds(mfqP->subtao,mfqP->subxl,mfqP->subxu);
1148:     MatCreateSeqDense(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Hres,&mfqP->subH);
1149:     TaoSetHessianRoutine(mfqP->subtao,mfqP->subH,mfqP->subH,pounders_h,(void*)mfqP);
1150:   }
1151:   return(0);
1152: }

1154: static PetscErrorCode TaoDestroy_POUNDERS(Tao tao)
1155: {
1156:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
1157:   PetscInt       i;

1161:   if (!mfqP->usegqt) {
1162:     TaoDestroy(&mfqP->subtao);
1163:     VecDestroy(&mfqP->subx);
1164:     VecDestroy(&mfqP->subxl);
1165:     VecDestroy(&mfqP->subxu);
1166:     VecDestroy(&mfqP->subb);
1167:     VecDestroy(&mfqP->subpdel);
1168:     VecDestroy(&mfqP->subndel);
1169:     MatDestroy(&mfqP->subH);
1170:   }
1171:   PetscFree(mfqP->Fres);
1172:   PetscFree(mfqP->RES);
1173:   PetscFree(mfqP->work);
1174:   PetscFree(mfqP->work2);
1175:   PetscFree(mfqP->work3);
1176:   PetscFree(mfqP->mwork);
1177:   PetscFree(mfqP->omega);
1178:   PetscFree(mfqP->beta);
1179:   PetscFree(mfqP->alpha);
1180:   PetscFree(mfqP->H);
1181:   PetscFree(mfqP->Q);
1182:   PetscFree(mfqP->Q_tmp);
1183:   PetscFree(mfqP->L);
1184:   PetscFree(mfqP->L_tmp);
1185:   PetscFree(mfqP->L_save);
1186:   PetscFree(mfqP->N);
1187:   PetscFree(mfqP->M);
1188:   PetscFree(mfqP->Z);
1189:   PetscFree(mfqP->tau);
1190:   PetscFree(mfqP->tau_tmp);
1191:   PetscFree(mfqP->npmaxwork);
1192:   PetscFree(mfqP->npmaxiwork);
1193:   PetscFree(mfqP->xmin);
1194:   PetscFree(mfqP->C);
1195:   PetscFree(mfqP->Fdiff);
1196:   PetscFree(mfqP->Disp);
1197:   PetscFree(mfqP->Gres);
1198:   PetscFree(mfqP->Hres);
1199:   PetscFree(mfqP->Gpoints);
1200:   PetscFree(mfqP->model_indices);
1201:   PetscFree(mfqP->last_model_indices);
1202:   PetscFree(mfqP->Xsubproblem);
1203:   PetscFree(mfqP->Gdel);
1204:   PetscFree(mfqP->Hdel);
1205:   PetscFree(mfqP->indices);
1206:   PetscFree(mfqP->iwork);
1207:   PetscFree(mfqP->w);
1208:   for (i=0;i<mfqP->nHist;i++) {
1209:     VecDestroy(&mfqP->Xhist[i]);
1210:     VecDestroy(&mfqP->Fhist[i]);
1211:   }
1212:   VecDestroy(&mfqP->workxvec);
1213:   VecDestroy(&mfqP->workfvec);
1214:   PetscFree(mfqP->Xhist);
1215:   PetscFree(mfqP->Fhist);

1217:   if (mfqP->size > 1) {
1218:     VecDestroy(&mfqP->localx);
1219:     VecDestroy(&mfqP->localxmin);
1220:     VecDestroy(&mfqP->localf);
1221:     VecDestroy(&mfqP->localfmin);
1222:   }
1223:   PetscFree(tao->data);
1224:   return(0);
1225: }

1227: static PetscErrorCode TaoSetFromOptions_POUNDERS(PetscOptionItems *PetscOptionsObject,Tao tao)
1228: {
1229:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;

1233:   PetscOptionsHead(PetscOptionsObject,"POUNDERS method for least-squares optimization");
1234:   PetscOptionsReal("-tao_pounders_delta","initial delta","",mfqP->delta,&mfqP->delta0,NULL);
1235:   mfqP->delta = mfqP->delta0;
1236:   PetscOptionsInt("-tao_pounders_npmax","max number of points in model","",mfqP->npmax,&mfqP->npmax,NULL);
1237:   PetscOptionsBool("-tao_pounders_gqt","use gqt algorithm for subproblem","",mfqP->usegqt,&mfqP->usegqt,NULL);
1238:   PetscOptionsTail();
1239:   return(0);
1240: }

1242: static PetscErrorCode TaoView_POUNDERS(Tao tao, PetscViewer viewer)
1243: {
1244:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS *)tao->data;
1245:   PetscBool      isascii;

1249:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
1250:   if (isascii) {
1251:     PetscViewerASCIIPrintf(viewer, "initial delta: %g\n",(double)mfqP->delta0);
1252:     PetscViewerASCIIPrintf(viewer, "final delta: %g\n",(double)mfqP->delta);
1253:     PetscViewerASCIIPrintf(viewer, "model points: %D\n",mfqP->nmodelpoints);
1254:     if (mfqP->usegqt) {
1255:       PetscViewerASCIIPrintf(viewer, "subproblem solver: gqt\n");
1256:     } else {
1257:       TaoView(mfqP->subtao, viewer);
1258:     }
1259:   }
1260:   return(0);
1261: }
1262: /*MC
1263:   TAOPOUNDERS - POUNDERS derivate-free model-based algorithm for nonlinear least squares

1265:   Options Database Keys:
1266: + -tao_pounders_delta - initial step length
1267: . -tao_pounders_npmax - maximum number of points in model
1268: - -tao_pounders_gqt - use gqt algorithm for subproblem instead of TRON

1270:   Level: beginner

1272: M*/

1274: PETSC_EXTERN PetscErrorCode TaoCreate_POUNDERS(Tao tao)
1275: {
1276:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;

1280:   tao->ops->setup = TaoSetUp_POUNDERS;
1281:   tao->ops->solve = TaoSolve_POUNDERS;
1282:   tao->ops->view = TaoView_POUNDERS;
1283:   tao->ops->setfromoptions = TaoSetFromOptions_POUNDERS;
1284:   tao->ops->destroy = TaoDestroy_POUNDERS;

1286:   PetscNewLog(tao,&mfqP);
1287:   tao->data = (void*)mfqP;
1288:   /* Override default settings (unless already changed) */
1289:   if (!tao->max_it_changed) tao->max_it = 2000;
1290:   if (!tao->max_funcs_changed) tao->max_funcs = 4000;
1291:   mfqP->npmax = PETSC_DEFAULT;
1292:   mfqP->delta0 = 0.1;
1293:   mfqP->delta = 0.1;
1294:   mfqP->deltamax=1e3;
1295:   mfqP->deltamin=1e-6;
1296:   mfqP->c2 = 10.0;
1297:   mfqP->theta1=1e-5;
1298:   mfqP->theta2=1e-4;
1299:   mfqP->gamma0=0.5;
1300:   mfqP->gamma1=2.0;
1301:   mfqP->eta0 = 0.0;
1302:   mfqP->eta1 = 0.1;
1303:   mfqP->usegqt = PETSC_FALSE;
1304:   mfqP->gqt_rtol = 0.001;
1305:   mfqP->gqt_maxits = 50;
1306:   mfqP->workxvec = 0;
1307:   return(0);
1308: }