Actual source code: pounders.c

petsc-3.9.4 2018-09-11
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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:   TaoComputeSeparableObjective(tao,x,F);
 37:   if (tao->sep_weights_v) {
 38:     VecPointwiseMult(mfqP->workfvec,tao->sep_weights_v,F);
 39:     VecDot(mfqP->workfvec,mfqP->workfvec,fsum);
 40:   } else if (tao->sep_weights_w) {
 41:     *fsum=0;
 42:     for (i=0;i<tao->sep_weights_n;i++) {
 43:       row=tao->sep_weights_rows[i];
 44:       col=tao->sep_weights_cols[i];
 45:       VecGetValues(F,1,&row,&fr);
 46:       VecGetValues(F,1,&col,&fc);
 47:       *fsum += tao->sep_weights_w[i]*fc*fr;
 48:     }
 49:   } else {
 50:     VecDot(F,F,fsum);
 51:   }
 52:   PetscInfo1(tao,"Separable objective 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->sep_weights_v) {
169:     /* Vector(diagonal) weights: gres = sum_i(wii*ci*gi) */
170:     for (i=0;i<mfqP->m;i++) {
171:       VecGetValues(tao->sep_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->sep_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],&blasn2,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->sep_weights_w) {
189:     /* General case: .5 * Gres= sum_ij[wij * (cjgi + cigj)] */
190:     for (i=0;i<tao->sep_weights_n;i++) {
191:       row=tao->sep_weights_rows[i];
192:       col=tao->sep_weights_cols[i];

194:       factor = tao->sep_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->sep_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->sep_weights_n;i++) {
203:       row=tao->sep_weights_rows[i];
204:       col=tao->sep_weights_cols[i];
205:       factor=tao->sep_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->sep_weights_n;i++) {
212:         row=tao->sep_weights_rows[i];
213:         col=tao->sep_weights_cols[i];

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

219:         /* add wij*ci*Hj */
220:         factor = tao->sep_weights_w[i]*mfqP->C[row]/2.0;
221:         PetscStackCallBLAS("BLASaxpy_",BLASaxpy_(&blasn2,&factor,&mfqP->H[col],&blasn2,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],&blasn2,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:     PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&blasint2,&blasnp,&blasnplus1,mfqP->Q_tmp,&blasnpmax,mfqP->tau_tmp,mfqP->L_tmp,&blasint2,mfqP->npmaxwork,&blasnmax,&info));
431:     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine ormqr returned with value %d\n",info);

433:     /* Copy L_tmp to L_save */
434:     for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
435:       mfqP->L_save[i] = mfqP->L_tmp[i];
436:     }

438:     /* Get svd for L_tmp(:,n+2:np+1) (L_tmp is modified in process) */
439:     blasint = mfqP->nmodelpoints - mfqP->n;
440:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
441:     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));
442:     PetscFPTrapPop();
443:     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine gesvd returned with value %d\n",info);

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

458:       /* Copy L_save to L */
459:       for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
460:         mfqP->L[i] = mfqP->L_save[i];
461:       }
462:     }
463:     point--;
464:   }

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

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

480:   /* Copy Q_tmp(:,n+2:np) to Z) */
481:   offset = mfqP->npmax * (mfqP->n+1);
482:   for (i=offset;i<mfqP->npmax*mfqP->npmax;i++) {
483:     mfqP->Z[i-offset] = mfqP->Q_tmp[i];
484:   }

486:   if (mfqP->nmodelpoints == mfqP->n + 1) {
487:     /* Set L to I_{n+1} */
488:     for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
489:       mfqP->L[i] = 0.0;
490:     }
491:     for (i=0;i<mfqP->n;i++) {
492:       mfqP->L[(mfqP->n*(mfqP->n+1)/2)*i + i] = 1.0;
493:     }
494:   }
495:   return(0);
496: }

498: /* Only call from modelimprove, addpoint() needs ->Q_tmp and ->work to be set */
499: PetscErrorCode addpoint(Tao tao, TAO_POUNDERS *mfqP, PetscInt index)
500: {

504:   /* Create new vector in history: X[newidx] = X[mfqP->index] + delta*X[index]*/
505:   VecDuplicate(mfqP->Xhist[0],&mfqP->Xhist[mfqP->nHist]);
506:   VecSetValues(mfqP->Xhist[mfqP->nHist],mfqP->n,mfqP->indices,&mfqP->Q_tmp[index*mfqP->npmax],INSERT_VALUES);
507:   VecAssemblyBegin(mfqP->Xhist[mfqP->nHist]);
508:   VecAssemblyEnd(mfqP->Xhist[mfqP->nHist]);
509:   VecAYPX(mfqP->Xhist[mfqP->nHist],mfqP->delta,mfqP->Xhist[mfqP->minindex]);

511:   /* Project into feasible region */
512:   if (tao->XU && tao->XL) {
513:     VecMedian(mfqP->Xhist[mfqP->nHist], tao->XL, tao->XU, mfqP->Xhist[mfqP->nHist]);
514:   }

516:   /* Compute value of new vector */
517:   VecDuplicate(mfqP->Fhist[0],&mfqP->Fhist[mfqP->nHist]);
518:   CHKMEMQ;
519:   pounders_feval(tao,mfqP->Xhist[mfqP->nHist],mfqP->Fhist[mfqP->nHist],&mfqP->Fres[mfqP->nHist]);

521:   /* Add new vector to model */
522:   mfqP->model_indices[mfqP->nmodelpoints] = mfqP->nHist;
523:   mfqP->nmodelpoints++;
524:   mfqP->nHist++;
525:   return(0);
526: }

528: PetscErrorCode modelimprove(Tao tao, TAO_POUNDERS *mfqP, PetscInt addallpoints)
529: {
530:   /* modeld = Q(:,np+1:n)' */
532:   PetscInt       i,j,minindex=0;
533:   PetscReal      dp,half=0.5,one=1.0,minvalue=PETSC_INFINITY;
534:   PetscBLASInt   blasn=mfqP->n,  blasnpmax = mfqP->npmax, blask,info;
535:   PetscBLASInt   blas1=1,blasnmax = mfqP->nmax;

537:   blask = mfqP->nmodelpoints;
538:   /* Qtmp = I(n x n) */
539:   for (i=0;i<mfqP->n;i++) {
540:     for (j=0;j<mfqP->n;j++) {
541:       mfqP->Q_tmp[i + mfqP->npmax*j] = 0.0;
542:     }
543:   }
544:   for (j=0;j<mfqP->n;j++) {
545:     mfqP->Q_tmp[j + mfqP->npmax*j] = 1.0;
546:   }

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

551:   for (i=mfqP->nmodelpoints;i<mfqP->n;i++) {
552:     dp = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->Gres,&blas1);
553:     if (dp>0.0) { /* Model says use the other direction! */
554:       for (j=0;j<mfqP->n;j++) {
555:         mfqP->Q_tmp[i*mfqP->npmax+j] *= -1;
556:       }
557:     }
558:     /* mfqP->work[i] = Cres+Modeld(i,:)*(Gres+.5*Hres*Modeld(i,:)') */
559:     for (j=0;j<mfqP->n;j++) {
560:       mfqP->work2[j] = mfqP->Gres[j];
561:     }
562:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&half,mfqP->Hres,&blasn,&mfqP->Q_tmp[i*mfqP->npmax], &blas1, &one, mfqP->work2,&blas1));
563:     mfqP->work[i] = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->work2,&blas1);
564:     if (i==mfqP->nmodelpoints || mfqP->work[i] < minvalue) {
565:       minindex=i;
566:       minvalue = mfqP->work[i];
567:     }
568:     if (addallpoints != 0) {
569:       addpoint(tao,mfqP,i);
570:     }
571:   }
572:   if (!addallpoints) {
573:     addpoint(tao,mfqP,minindex);
574:   }
575:   return(0);
576: }


579: PetscErrorCode affpoints(TAO_POUNDERS *mfqP, PetscReal *xmin,PetscReal c)
580: {
581:   PetscInt        i,j;
582:   PetscBLASInt    blasm=mfqP->m,blasj,blask,blasn=mfqP->n,ione=1,info;
583:   PetscBLASInt    blasnpmax = mfqP->npmax,blasmaxmn;
584:   PetscReal       proj,normd;
585:   const PetscReal *x;
586:   PetscErrorCode  ierr;

589:   for (i=mfqP->nHist-1;i>=0;i--) {
590:     VecGetArrayRead(mfqP->Xhist[i],&x);
591:     for (j=0;j<mfqP->n;j++) {
592:       mfqP->work[j] = (x[j] - xmin[j])/mfqP->delta;
593:     }
594:     VecRestoreArrayRead(mfqP->Xhist[i],&x);
595:     PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,mfqP->work,&ione,mfqP->work2,&ione));
596:     normd = BLASnrm2_(&blasn,mfqP->work,&ione);
597:     if (normd <= c) {
598:       blasj=PetscMax((mfqP->n - mfqP->nmodelpoints),0);
599:       if (!mfqP->q_is_I) {
600:         /* project D onto null */
601:         blask=(mfqP->nmodelpoints);
602:         PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&ione,&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->work2,&ione,mfqP->mwork,&blasm,&info));
603:         if (info < 0) SETERRQ1(PETSC_COMM_SELF,1,"ormqr returned value %d\n",info);
604:       }
605:       proj = BLASnrm2_(&blasj,&mfqP->work2[mfqP->nmodelpoints],&ione);

607:       if (proj >= mfqP->theta1) { /* add this index to model */
608:         mfqP->model_indices[mfqP->nmodelpoints]=i;
609:         mfqP->nmodelpoints++;
610:         PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,mfqP->work,&ione,&mfqP->Q_tmp[mfqP->npmax*(mfqP->nmodelpoints-1)],&ione));
611:         blask=mfqP->npmax*(mfqP->nmodelpoints);
612:         PetscStackCallBLAS("BLAScopy",BLAScopy_(&blask,mfqP->Q_tmp,&ione,mfqP->Q,&ione));
613:         blask = mfqP->nmodelpoints;
614:         blasmaxmn = PetscMax(mfqP->m,mfqP->n);
615:         PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->mwork,&blasmaxmn,&info));
616:         if (info < 0) SETERRQ1(PETSC_COMM_SELF,1,"geqrf returned value %d\n",info);
617:         mfqP->q_is_I = 0;
618:       }
619:       if (mfqP->nmodelpoints == mfqP->n)  {
620:         break;
621:       }
622:     }
623:   }

625:   return(0);
626: }

628: static PetscErrorCode TaoSolve_POUNDERS(Tao tao)
629: {
630:   TAO_POUNDERS       *mfqP = (TAO_POUNDERS *)tao->data;
631:   PetscInt           i,ii,j,k,l;
632:   PetscReal          step=1.0;
633:   PetscInt           low,high;
634:   PetscReal          minnorm;
635:   PetscReal          *x,*f;
636:   const PetscReal    *xmint,*fmin;
637:   PetscReal          cres,deltaold;
638:   PetscReal          gnorm;
639:   PetscBLASInt       info,ione=1,iblas;
640:   PetscBool          valid,same;
641:   PetscReal          mdec, rho, normxsp;
642:   PetscReal          one=1.0,zero=0.0,ratio;
643:   PetscBLASInt       blasm,blasn,blasncopy,blasnpmax;
644:   PetscErrorCode     ierr;
645:   static PetscBool   set = PETSC_FALSE;

647:   /* n = # of parameters
648:      m = dimension (components) of function  */
650:   PetscCitationsRegister("@article{UNEDF0,\n"
651:                                 "title = {Nuclear energy density optimization},\n"
652:                                 "author = {Kortelainen, M.  and Lesinski, T.  and Mor\'e, J.  and Nazarewicz, W.\n"
653:                                 "          and Sarich, J.  and Schunck, N.  and Stoitsov, M. V. and Wild, S. },\n"
654:                                 "journal = {Phys. Rev. C},\n"
655:                                 "volume = {82},\n"
656:                                 "number = {2},\n"
657:                                 "pages = {024313},\n"
658:                                 "numpages = {18},\n"
659:                                 "year = {2010},\n"
660:                                 "month = {Aug},\n"
661:                                 "doi = {10.1103/PhysRevC.82.024313}\n}\n",&set);
662:   tao->niter=0;
663:   if (tao->XL && tao->XU) {
664:     /* Check x0 <= XU */
665:     PetscReal val;

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

672:     /* Check x0 >= xl */
673:     VecCopy(tao->XL,mfqP->Xhist[0]);
674:     VecAXPY(mfqP->Xhist[0],-1.0,tao->solution);
675:     VecMax(mfqP->Xhist[0],NULL,&val);
676:     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 < lower bound");

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

680:     VecSet(mfqP->Xhist[0],mfqP->delta);
681:     VecAXPY(mfqP->Xhist[0],1.0,tao->solution);
682:     VecAXPY(mfqP->Xhist[0],-1.0,tao->XU);
683:     VecMax(mfqP->Xhist[0],NULL,&val);
684:     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 + delta > upper bound");
685:   }

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

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

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

695:   PetscInfo1(tao,"Initialize simplex; delta = %10.9e\n",(double)mfqP->delta);
696:   pounders_feval(tao,mfqP->Xhist[0],mfqP->Fhist[0],&mfqP->Fres[0]);
697:   mfqP->minindex = 0;
698:   minnorm = mfqP->Fres[0];

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

704:     if (i-1 >= low && i-1 < high) {
705:       VecGetArray(mfqP->Xhist[i],&x);
706:       x[i-1-low] += mfqP->delta;
707:       VecRestoreArray(mfqP->Xhist[i],&x);
708:     }
709:     CHKMEMQ;
710:     pounders_feval(tao,mfqP->Xhist[i],mfqP->Fhist[i],&mfqP->Fres[i]);
711:     if (mfqP->Fres[i] < minnorm) {
712:       mfqP->minindex = i;
713:       minnorm = mfqP->Fres[i];
714:     }
715:   }
716:   VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);
717:   VecCopy(mfqP->Fhist[mfqP->minindex],tao->sep_objective);
718:   PetscInfo1(tao,"Finalize simplex; minnorm = %10.9e\n",(double)minnorm);

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

722:   /* Begin serial code */

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

729:   PetscInfo1(tao,"Build matrix: %D\n",(PetscInt)mfqP->size);
730:   if (1 == mfqP->size) {
731:     VecGetArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
732:     for (i=0;i<mfqP->n;i++) mfqP->xmin[i] = xmint[i];
733:     VecRestoreArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
734:     VecGetArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);
735:     for (i=0;i<mfqP->n+1;i++) {
736:       if (i == mfqP->minindex) continue;

738:       VecGetArray(mfqP->Xhist[i],&x);
739:       for (j=0;j<mfqP->n;j++) {
740:         mfqP->Disp[ii+mfqP->npmax*j] = (x[j] - mfqP->xmin[j])/mfqP->delta;
741:       }
742:       VecRestoreArray(mfqP->Xhist[i],&x);

744:       VecGetArray(mfqP->Fhist[i],&f);
745:       for (j=0;j<mfqP->m;j++) {
746:         mfqP->Fdiff[ii+mfqP->n*j] = f[j] - fmin[j];
747:       }
748:       VecRestoreArray(mfqP->Fhist[i],&f);
749:       mfqP->model_indices[ii++] = i;
750:     }
751:     for (j=0;j<mfqP->m;j++) {
752:       mfqP->C[j] = fmin[j];
753:     }
754:     VecRestoreArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);
755:   } else {
756:     VecSet(mfqP->localxmin,0);
757:     VecScatterBegin(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);
758:     VecScatterEnd(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);

760:     VecGetArrayRead(mfqP->localxmin,&xmint);
761:     for (i=0;i<mfqP->n;i++) mfqP->xmin[i] = xmint[i];
762:     VecRestoreArrayRead(mfqP->localxmin,&xmint);

764:     VecScatterBegin(mfqP->scatterf,mfqP->Fhist[mfqP->minindex],mfqP->localfmin,INSERT_VALUES,SCATTER_FORWARD);
765:     VecScatterEnd(mfqP->scatterf,mfqP->Fhist[mfqP->minindex],mfqP->localfmin,INSERT_VALUES,SCATTER_FORWARD);
766:     VecGetArrayRead(mfqP->localfmin,&fmin);
767:     for (i=0;i<mfqP->n+1;i++) {
768:       if (i == mfqP->minindex) continue;

770:       mfqP->model_indices[ii++] = i;
771:       VecScatterBegin(mfqP->scatterx,mfqP->Xhist[ii],mfqP->localx,INSERT_VALUES, SCATTER_FORWARD);
772:       VecScatterEnd(mfqP->scatterx,mfqP->Xhist[ii],mfqP->localx,INSERT_VALUES, SCATTER_FORWARD);
773:       VecGetArray(mfqP->localx,&x);
774:       for (j=0;j<mfqP->n;j++) {
775:         mfqP->Disp[i+mfqP->npmax*j] = (x[j] - mfqP->xmin[j])/mfqP->delta;
776:       }
777:       VecRestoreArray(mfqP->localx,&x);

779:       VecScatterBegin(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);
780:       VecScatterEnd(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);
781:       VecGetArray(mfqP->localf,&f);
782:       for (j=0;j<mfqP->m;j++) {
783:         mfqP->Fdiff[i*mfqP->n+j] = f[j] - fmin[j];
784:       }
785:       VecRestoreArray(mfqP->localf,&f);
786:     }
787:     for (j=0;j<mfqP->m;j++) {
788:       mfqP->C[j] = fmin[j];
789:     }
790:     VecRestoreArrayRead(mfqP->localfmin,&fmin);
791:   }

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

800:   cres = minnorm;
801:   pounders_update_res(tao);

803:   valid = PETSC_TRUE;

805:   VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);
806:   VecAssemblyBegin(tao->gradient);
807:   VecAssemblyEnd(tao->gradient);
808:   VecNorm(tao->gradient,NORM_2,&gnorm);
809:   gnorm *= mfqP->delta;
810:   VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);
811: 
812:   tao->reason = TAO_CONTINUE_ITERATING;
813:   TaoLogConvergenceHistory(tao,minnorm,gnorm,0.0,tao->ksp_its);
814:   TaoMonitor(tao,tao->niter,minnorm,gnorm,0.0,step);
815:   (*tao->ops->convergencetest)(tao,tao->cnvP);
816: 
817:   mfqP->nHist = mfqP->n+1;
818:   mfqP->nmodelpoints = mfqP->n+1;
819:   PetscInfo1(tao,"Initial gradient: %20.19e\n",(double)gnorm);

821:   while (tao->reason == TAO_CONTINUE_ITERATING) {
822:     PetscReal gnm = 1e-4;
823:     tao->niter++;
824:     /* Solve the subproblem min{Q(s): ||s|| <= 1.0} */
825:     gqtwrap(tao,&gnm,&mdec);
826:     /* Evaluate the function at the new point */

828:     for (i=0;i<mfqP->n;i++) {
829:         mfqP->work[i] = mfqP->Xsubproblem[i]*mfqP->delta + mfqP->xmin[i];
830:     }
831:     VecDuplicate(tao->solution,&mfqP->Xhist[mfqP->nHist]);
832:     VecDuplicate(tao->sep_objective,&mfqP->Fhist[mfqP->nHist]);
833:     VecSetValues(mfqP->Xhist[mfqP->nHist],mfqP->n,mfqP->indices,mfqP->work,INSERT_VALUES);
834:     VecAssemblyBegin(mfqP->Xhist[mfqP->nHist]);
835:     VecAssemblyEnd(mfqP->Xhist[mfqP->nHist]);

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

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

842:     /* Update the center */
843:     if ((rho >= mfqP->eta1) || (rho > mfqP->eta0 && valid==PETSC_TRUE)) {
844:       /* Update model to reflect new base point */
845:       for (i=0;i<mfqP->n;i++) {
846:         mfqP->work[i] = (mfqP->work[i] - mfqP->xmin[i])/mfqP->delta;
847:       }
848:       for (j=0;j<mfqP->m;j++) {
849:         /* C(j) = C(j) + work*G(:,j) + .5*work*H(:,:,j)*work';
850:          G(:,j) = G(:,j) + H(:,:,j)*work' */
851:         for (k=0;k<mfqP->n;k++) {
852:           mfqP->work2[k]=0.0;
853:           for (l=0;l<mfqP->n;l++) {
854:             mfqP->work2[k]+=mfqP->H[j + mfqP->m*(k + l*mfqP->n)]*mfqP->work[l];
855:           }
856:         }
857:         for (i=0;i<mfqP->n;i++) {
858:           mfqP->C[j]+=mfqP->work[i]*(mfqP->Fdiff[i + mfqP->n* j] + 0.5*mfqP->work2[i]);
859:           mfqP->Fdiff[i+mfqP->n*j] +=mfqP-> work2[i];
860:         }
861:       }
862:       /* Cres += work*Gres + .5*work*Hres*work';
863:        Gres += Hres*work'; */

865:       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&one,mfqP->Hres,&blasn,mfqP->work,&ione,&zero,mfqP->work2,&ione));
866:       for (i=0;i<mfqP->n;i++) {
867:         cres += mfqP->work[i]*(mfqP->Gres[i]  + 0.5*mfqP->work2[i]);
868:         mfqP->Gres[i] += mfqP->work2[i];
869:       }
870:       mfqP->minindex = mfqP->nHist-1;
871:       minnorm = mfqP->Fres[mfqP->minindex];
872:       VecCopy(mfqP->Fhist[mfqP->minindex],tao->sep_objective);
873:       /* Change current center */
874:       VecGetArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
875:       for (i=0;i<mfqP->n;i++) {
876:         mfqP->xmin[i] = xmint[i];
877:       }
878:       VecRestoreArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
879:     }

881:     /* Evaluate at a model-improving point if necessary */
882:     if (valid == PETSC_FALSE) {
883:       mfqP->q_is_I = 1;
884:       mfqP->nmodelpoints = 0;
885:       affpoints(mfqP,mfqP->xmin,mfqP->c1);
886:       if (mfqP->nmodelpoints < mfqP->n) {
887:         PetscInfo(tao,"Model not valid -- model-improving\n");
888:         modelimprove(tao,mfqP,1);
889:       }
890:     }

892:     /* Update the trust region radius */
893:     deltaold = mfqP->delta;
894:     normxsp = 0;
895:     for (i=0;i<mfqP->n;i++) {
896:       normxsp += mfqP->Xsubproblem[i]*mfqP->Xsubproblem[i];
897:     }
898:     normxsp = PetscSqrtReal(normxsp);
899:     if (rho >= mfqP->eta1 && normxsp > 0.5*mfqP->delta) {
900:       mfqP->delta = PetscMin(mfqP->delta*mfqP->gamma1,mfqP->deltamax);
901:     } else if (valid == PETSC_TRUE) {
902:       mfqP->delta = PetscMax(mfqP->delta*mfqP->gamma0,mfqP->deltamin);
903:     }

905:     /* Compute the next interpolation set */
906:     mfqP->q_is_I = 1;
907:     mfqP->nmodelpoints=0;
908:     PetscInfo2(tao,"Affine Points: xmin = %20.19e, c1 = %20.19e\n",(double)*mfqP->xmin,(double)mfqP->c1);
909:     affpoints(mfqP,mfqP->xmin,mfqP->c1);
910:     if (mfqP->nmodelpoints == mfqP->n) {
911:       valid = PETSC_TRUE;
912:     } else {
913:       valid = PETSC_FALSE;
914:       PetscInfo2(tao,"Affine Points: xmin = %20.19e, c2 = %20.19e\n",(double)*mfqP->xmin,(double)mfqP->c2);
915:       affpoints(mfqP,mfqP->xmin,mfqP->c2);
916:       if (mfqP->n > mfqP->nmodelpoints) {
917:         PetscInfo(tao,"Model not valid -- adding geometry points\n");
918:         modelimprove(tao,mfqP,mfqP->n - mfqP->nmodelpoints);
919:       }
920:     }
921:     for (i=mfqP->nmodelpoints;i>0;i--) {
922:       mfqP->model_indices[i] = mfqP->model_indices[i-1];
923:     }
924:     mfqP->nmodelpoints++;
925:     mfqP->model_indices[0] = mfqP->minindex;
926:     morepoints(mfqP);
927:     for (i=0;i<mfqP->nmodelpoints;i++) {
928:       VecGetArray(mfqP->Xhist[mfqP->model_indices[i]],&x);
929:       for (j=0;j<mfqP->n;j++) {
930:         mfqP->Disp[i + mfqP->npmax*j] = (x[j]  - mfqP->xmin[j]) / deltaold;
931:       }
932:       VecRestoreArray(mfqP->Xhist[mfqP->model_indices[i]],&x);
933:       VecGetArray(mfqP->Fhist[mfqP->model_indices[i]],&f);
934:       for (j=0;j<mfqP->m;j++) {
935:         for (k=0;k<mfqP->n;k++)  {
936:           mfqP->work[k]=0.0;
937:           for (l=0;l<mfqP->n;l++) {
938:             mfqP->work[k] += mfqP->H[j + mfqP->m*(k + mfqP->n*l)] * mfqP->Disp[i + mfqP->npmax*l];
939:           }
940:         }
941:         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];
942:       }
943:       VecRestoreArray(mfqP->Fhist[mfqP->model_indices[i]],&f);
944:     }

946:     /* Update the quadratic model */
947:     PetscInfo2(tao,"Get Quad, size: %D, points: %D\n",mfqP->n,mfqP->nmodelpoints);
948:     getquadpounders(mfqP);
949:     VecGetArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);
950:     PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasm,fmin,&ione,mfqP->C,&ione));
951:     /* G = G*(delta/deltaold) + Gdel */
952:     ratio = mfqP->delta/deltaold;
953:     iblas = blasm*blasn;
954:     PetscStackCallBLAS("BLASscal",BLASscal_(&iblas,&ratio,mfqP->Fdiff,&ione));
955:     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&one,mfqP->Gdel,&ione,mfqP->Fdiff,&ione));
956:     /* H = H*(delta/deltaold)^2 + Hdel */
957:     iblas = blasm*blasn*blasn;
958:     ratio *= ratio;
959:     PetscStackCallBLAS("BLASscal",BLASscal_(&iblas,&ratio,mfqP->H,&ione));
960:     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&one,mfqP->Hdel,&ione,mfqP->H,&ione));

962:     /* Get residuals */
963:     cres = mfqP->Fres[mfqP->minindex];
964:     pounders_update_res(tao);

966:     /* Export solution and gradient residual to TAO */
967:     VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);
968:     VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);
969:     VecAssemblyBegin(tao->gradient);
970:     VecAssemblyEnd(tao->gradient);
971:     VecNorm(tao->gradient,NORM_2,&gnorm);
972:     gnorm *= mfqP->delta;
973:     /*  final criticality test */
974:     TaoLogConvergenceHistory(tao,minnorm,gnorm,0.0,tao->ksp_its);
975:     TaoMonitor(tao,tao->niter,minnorm,gnorm,0.0,step);
976:     (*tao->ops->convergencetest)(tao,tao->cnvP);
977:     /* test for repeated model */
978:     if (mfqP->nmodelpoints==mfqP->last_nmodelpoints) {
979:       same = PETSC_TRUE;
980:     } else {
981:       same = PETSC_FALSE;
982:     }
983:     for (i=0;i<mfqP->nmodelpoints;i++) {
984:       if (same) {
985:         if (mfqP->model_indices[i] == mfqP->last_model_indices[i]) {
986:           same = PETSC_TRUE;
987:         } else {
988:           same = PETSC_FALSE;
989:         }
990:       }
991:       mfqP->last_model_indices[i] = mfqP->model_indices[i];
992:     }
993:     mfqP->last_nmodelpoints = mfqP->nmodelpoints;
994:     if (same && mfqP->delta == deltaold) {
995:       PetscInfo(tao,"Identical model used in successive iterations\n");
996:       tao->reason = TAO_CONVERGED_STEPTOL;
997:     }
998:   }
999:   return(0);
1000: }

1002: static PetscErrorCode TaoSetUp_POUNDERS(Tao tao)
1003: {
1004:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
1005:   PetscInt       i,j;
1006:   IS             isfloc,isfglob,isxloc,isxglob;

1010:   if (!tao->gradient) {VecDuplicate(tao->solution,&tao->gradient);  }
1011:   if (!tao->stepdirection) {VecDuplicate(tao->solution,&tao->stepdirection);  }
1012:   VecGetSize(tao->solution,&mfqP->n);
1013:   VecGetSize(tao->sep_objective,&mfqP->m);
1014:   mfqP->c1 = PetscSqrtReal((PetscReal)mfqP->n);
1015:   if (mfqP->npmax == PETSC_DEFAULT) {
1016:     mfqP->npmax = 2*mfqP->n + 1;
1017:   }
1018:   mfqP->npmax = PetscMin((mfqP->n+1)*(mfqP->n+2)/2,mfqP->npmax);
1019:   mfqP->npmax = PetscMax(mfqP->npmax, mfqP->n+2);

1021:   PetscMalloc1(tao->max_funcs+10,&mfqP->Xhist);
1022:   PetscMalloc1(tao->max_funcs+10,&mfqP->Fhist);
1023:   for (i=0;i<mfqP->n+1;i++) {
1024:     VecDuplicate(tao->solution,&mfqP->Xhist[i]);
1025:     VecDuplicate(tao->sep_objective,&mfqP->Fhist[i]);
1026:   }
1027:   VecDuplicate(tao->solution,&mfqP->workxvec);
1028:   VecDuplicate(tao->sep_objective,&mfqP->workfvec);
1029:   mfqP->nHist = 0;

1031:   PetscMalloc1(tao->max_funcs+10,&mfqP->Fres);
1032:   PetscMalloc1(mfqP->npmax*mfqP->m,&mfqP->RES);
1033:   PetscMalloc1(mfqP->n,&mfqP->work);
1034:   PetscMalloc1(mfqP->n,&mfqP->work2);
1035:   PetscMalloc1(mfqP->n,&mfqP->work3);
1036:   PetscMalloc1(PetscMax(mfqP->m,mfqP->n+1),&mfqP->mwork);
1037:   PetscMalloc1(mfqP->npmax - mfqP->n - 1,&mfqP->omega);
1038:   PetscMalloc1(mfqP->n * (mfqP->n+1) / 2,&mfqP->beta);
1039:   PetscMalloc1(mfqP->n + 1 ,&mfqP->alpha);

1041:   PetscMalloc1(mfqP->n*mfqP->n*mfqP->m,&mfqP->H);
1042:   PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q);
1043:   PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q_tmp);
1044:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L);
1045:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_tmp);
1046:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_save);
1047:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->N);
1048:   PetscMalloc1(mfqP->npmax * (mfqP->n+1) ,&mfqP->M);
1049:   PetscMalloc1(mfqP->npmax * (mfqP->npmax - mfqP->n - 1) , &mfqP->Z);
1050:   PetscMalloc1(mfqP->npmax,&mfqP->tau);
1051:   PetscMalloc1(mfqP->npmax,&mfqP->tau_tmp);
1052:   mfqP->nmax = PetscMax(5*mfqP->npmax,mfqP->n*(mfqP->n+1)/2);
1053:   PetscMalloc1(mfqP->nmax,&mfqP->npmaxwork);
1054:   PetscMalloc1(mfqP->nmax,&mfqP->npmaxiwork);
1055:   PetscMalloc1(mfqP->n,&mfqP->xmin);
1056:   PetscMalloc1(mfqP->m,&mfqP->C);
1057:   PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Fdiff);
1058:   PetscMalloc1(mfqP->npmax*mfqP->n,&mfqP->Disp);
1059:   PetscMalloc1(mfqP->n,&mfqP->Gres);
1060:   PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Hres);
1061:   PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Gpoints);
1062:   PetscMalloc1(mfqP->npmax,&mfqP->model_indices);
1063:   PetscMalloc1(mfqP->npmax,&mfqP->last_model_indices);
1064:   PetscMalloc1(mfqP->n,&mfqP->Xsubproblem);
1065:   PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Gdel);
1066:   PetscMalloc1(mfqP->n*mfqP->n*mfqP->m, &mfqP->Hdel);
1067:   PetscMalloc1(PetscMax(mfqP->m,mfqP->n),&mfqP->indices);
1068:   PetscMalloc1(mfqP->n,&mfqP->iwork);
1069:   PetscMalloc1(mfqP->m*mfqP->m,&mfqP->w);
1070:   for (i=0;i<mfqP->m;i++) {
1071:     for (j=0;j<mfqP->m;j++) {
1072:       if (i==j) {
1073:         mfqP->w[i+mfqP->m*j]=1.0;
1074:       } else {
1075:         mfqP->w[i+mfqP->m*j]=0.0;
1076:       }
1077:     }
1078:   }
1079:   for (i=0;i<PetscMax(mfqP->m,mfqP->n);i++) {
1080:     mfqP->indices[i] = i;
1081:   }
1082:   MPI_Comm_size(((PetscObject)tao)->comm,&mfqP->size);
1083:   if (mfqP->size > 1) {
1084:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localx);
1085:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localxmin);
1086:     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localf);
1087:     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localfmin);
1088:     ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxloc);
1089:     ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxglob);
1090:     ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfloc);
1091:     ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfglob);


1094:     VecScatterCreate(tao->solution,isxglob,mfqP->localx,isxloc,&mfqP->scatterx);
1095:     VecScatterCreate(tao->sep_objective,isfglob,mfqP->localf,isfloc,&mfqP->scatterf);

1097:     ISDestroy(&isxloc);
1098:     ISDestroy(&isxglob);
1099:     ISDestroy(&isfloc);
1100:     ISDestroy(&isfglob);
1101:   }

1103:   if (!mfqP->usegqt) {
1104:     KSP       ksp;
1105:     PC        pc;
1106:     VecCreateSeqWithArray(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Xsubproblem,&mfqP->subx);
1107:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->subxl);
1108:     VecDuplicate(mfqP->subxl,&mfqP->subb);
1109:     VecDuplicate(mfqP->subxl,&mfqP->subxu);
1110:     VecDuplicate(mfqP->subxl,&mfqP->subpdel);
1111:     VecDuplicate(mfqP->subxl,&mfqP->subndel);
1112:     TaoCreate(PETSC_COMM_SELF,&mfqP->subtao);
1113:     PetscObjectIncrementTabLevel((PetscObject)mfqP->subtao, (PetscObject)mfqP, 1);
1114:     TaoSetType(mfqP->subtao,TAOTRON);
1115:     TaoSetOptionsPrefix(mfqP->subtao,"pounders_subsolver_");
1116:     TaoSetInitialVector(mfqP->subtao,mfqP->subx);
1117:     TaoSetObjectiveAndGradientRoutine(mfqP->subtao,pounders_fg,(void*)mfqP);
1118:     TaoSetMaximumIterations(mfqP->subtao,mfqP->gqt_maxits);
1119:     TaoSetFromOptions(mfqP->subtao);
1120:     TaoGetKSP(mfqP->subtao,&ksp);
1121:     if (ksp) {
1122:       KSPGetPC(ksp,&pc);
1123:       PCSetType(pc,PCNONE);
1124:     }
1125:     TaoSetVariableBounds(mfqP->subtao,mfqP->subxl,mfqP->subxu);
1126:     MatCreateSeqDense(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Hres,&mfqP->subH);
1127:     TaoSetHessianRoutine(mfqP->subtao,mfqP->subH,mfqP->subH,pounders_h,(void*)mfqP);
1128:   }
1129:   return(0);
1130: }

1132: static PetscErrorCode TaoDestroy_POUNDERS(Tao tao)
1133: {
1134:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
1135:   PetscInt       i;

1139:   if (!mfqP->usegqt) {
1140:     TaoDestroy(&mfqP->subtao);
1141:     VecDestroy(&mfqP->subx);
1142:     VecDestroy(&mfqP->subxl);
1143:     VecDestroy(&mfqP->subxu);
1144:     VecDestroy(&mfqP->subb);
1145:     VecDestroy(&mfqP->subpdel);
1146:     VecDestroy(&mfqP->subndel);
1147:     MatDestroy(&mfqP->subH);
1148:   }
1149:   PetscFree(mfqP->Fres);
1150:   PetscFree(mfqP->RES);
1151:   PetscFree(mfqP->work);
1152:   PetscFree(mfqP->work2);
1153:   PetscFree(mfqP->work3);
1154:   PetscFree(mfqP->mwork);
1155:   PetscFree(mfqP->omega);
1156:   PetscFree(mfqP->beta);
1157:   PetscFree(mfqP->alpha);
1158:   PetscFree(mfqP->H);
1159:   PetscFree(mfqP->Q);
1160:   PetscFree(mfqP->Q_tmp);
1161:   PetscFree(mfqP->L);
1162:   PetscFree(mfqP->L_tmp);
1163:   PetscFree(mfqP->L_save);
1164:   PetscFree(mfqP->N);
1165:   PetscFree(mfqP->M);
1166:   PetscFree(mfqP->Z);
1167:   PetscFree(mfqP->tau);
1168:   PetscFree(mfqP->tau_tmp);
1169:   PetscFree(mfqP->npmaxwork);
1170:   PetscFree(mfqP->npmaxiwork);
1171:   PetscFree(mfqP->xmin);
1172:   PetscFree(mfqP->C);
1173:   PetscFree(mfqP->Fdiff);
1174:   PetscFree(mfqP->Disp);
1175:   PetscFree(mfqP->Gres);
1176:   PetscFree(mfqP->Hres);
1177:   PetscFree(mfqP->Gpoints);
1178:   PetscFree(mfqP->model_indices);
1179:   PetscFree(mfqP->last_model_indices);
1180:   PetscFree(mfqP->Xsubproblem);
1181:   PetscFree(mfqP->Gdel);
1182:   PetscFree(mfqP->Hdel);
1183:   PetscFree(mfqP->indices);
1184:   PetscFree(mfqP->iwork);
1185:   PetscFree(mfqP->w);
1186:   for (i=0;i<mfqP->nHist;i++) {
1187:     VecDestroy(&mfqP->Xhist[i]);
1188:     VecDestroy(&mfqP->Fhist[i]);
1189:   }
1190:   VecDestroy(&mfqP->workxvec);
1191:   VecDestroy(&mfqP->workfvec);
1192:   PetscFree(mfqP->Xhist);
1193:   PetscFree(mfqP->Fhist);

1195:   if (mfqP->size > 1) {
1196:     VecDestroy(&mfqP->localx);
1197:     VecDestroy(&mfqP->localxmin);
1198:     VecDestroy(&mfqP->localf);
1199:     VecDestroy(&mfqP->localfmin);
1200:   }
1201:   PetscFree(tao->data);
1202:   return(0);
1203: }

1205: static PetscErrorCode TaoSetFromOptions_POUNDERS(PetscOptionItems *PetscOptionsObject,Tao tao)
1206: {
1207:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;

1211:   PetscOptionsHead(PetscOptionsObject,"POUNDERS method for least-squares optimization");
1212:   PetscOptionsReal("-tao_pounders_delta","initial delta","",mfqP->delta,&mfqP->delta0,NULL);
1213:   mfqP->delta = mfqP->delta0;
1214:   mfqP->npmax = PETSC_DEFAULT;
1215:   PetscOptionsInt("-tao_pounders_npmax","max number of points in model","",mfqP->npmax,&mfqP->npmax,NULL);
1216:   mfqP->usegqt = PETSC_FALSE;
1217:   PetscOptionsBool("-tao_pounders_gqt","use gqt algorithm for subproblem","",mfqP->usegqt,&mfqP->usegqt,NULL);
1218:   PetscOptionsTail();
1219:   return(0);
1220: }

1222: static PetscErrorCode TaoView_POUNDERS(Tao tao, PetscViewer viewer)
1223: {
1224:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS *)tao->data;
1225:   PetscBool      isascii;

1229:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
1230:   if (isascii) {
1231:     PetscViewerASCIIPrintf(viewer, "initial delta: %g\n",(double)mfqP->delta0);
1232:     PetscViewerASCIIPrintf(viewer, "final delta: %g\n",(double)mfqP->delta);
1233:     PetscViewerASCIIPrintf(viewer, "model points: %D\n",mfqP->nmodelpoints);
1234:     if (mfqP->usegqt) {
1235:       PetscViewerASCIIPrintf(viewer, "subproblem solver: gqt\n");
1236:     } else {
1237:       TaoView(mfqP->subtao, viewer);
1238:     }
1239:   }
1240:   return(0);
1241: }
1242: /*MC
1243:   TAOPOUNDERS - POUNDERS derivate-free model-based algorithm for nonlinear least squares

1245:   Options Database Keys:
1246: + -tao_pounders_delta - initial step length
1247: . -tao_pounders_npmax - maximum number of points in model
1248: - -tao_pounders_gqt - use gqt algorithm for subproblem instead of TRON

1250:   Level: beginner

1252: M*/

1254: PETSC_EXTERN PetscErrorCode TaoCreate_POUNDERS(Tao tao)
1255: {
1256:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;

1260:   tao->ops->setup = TaoSetUp_POUNDERS;
1261:   tao->ops->solve = TaoSolve_POUNDERS;
1262:   tao->ops->view = TaoView_POUNDERS;
1263:   tao->ops->setfromoptions = TaoSetFromOptions_POUNDERS;
1264:   tao->ops->destroy = TaoDestroy_POUNDERS;

1266:   PetscNewLog(tao,&mfqP);
1267:   tao->data = (void*)mfqP;
1268:   /* Override default settings (unless already changed) */
1269:   if (!tao->max_it_changed) tao->max_it = 2000;
1270:   if (!tao->max_funcs_changed) tao->max_funcs = 4000;
1271:   mfqP->delta0 = 0.1;
1272:   mfqP->delta = 0.1;
1273:   mfqP->deltamax=1e3;
1274:   mfqP->deltamin=1e-6;
1275:   mfqP->c2 = 10.0;
1276:   mfqP->theta1=1e-5;
1277:   mfqP->theta2=1e-4;
1278:   mfqP->gamma0=0.5;
1279:   mfqP->gamma1=2.0;
1280:   mfqP->eta0 = 0.0;
1281:   mfqP->eta1 = 0.1;
1282:   mfqP->gqt_rtol = 0.001;
1283:   mfqP->gqt_maxits = 50;
1284:   mfqP->workxvec = 0;
1285:   return(0);
1286: }