Actual source code: pounders.c

petsc-master 2019-12-13
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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;

 37:   TaoComputeResidual(tao,x,F);
 38:   if (tao->res_weights_v) {
 39:     VecPointwiseMult(mfqP->workfvec,tao->res_weights_v,F);
 40:     VecDot(mfqP->workfvec,mfqP->workfvec,fsum);
 41:   } else if (tao->res_weights_w) {
 42:     *fsum=0;
 43:     for (i=0;i<tao->res_weights_n;i++) {
 44:       row=tao->res_weights_rows[i];
 45:       col=tao->res_weights_cols[i];
 46:       VecGetValues(F,1,&row,&fr);
 47:       VecGetValues(F,1,&col,&fc);
 48:       *fsum += tao->res_weights_w[i]*fc*fr;
 49:     }
 50:   } else {
 51:     VecDot(F,F,fsum);
 52:   }
 53:   PetscInfo1(tao,"Least-squares residual norm: %20.19e\n",(double)*fsum);
 54:   if (PetscIsInfOrNanReal(*fsum)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER, "User provided compute function generated Inf or NaN");
 55:   return(0);
 56: }

 58: static PetscErrorCode gqtwrap(Tao tao,PetscReal *gnorm, PetscReal *qmin)
 59: {
 61: #if defined(PETSC_USE_REAL_SINGLE)
 62:   PetscReal      atol=1.0e-5;
 63: #else
 64:   PetscReal      atol=1.0e-10;
 65: #endif
 66:   PetscInt       info,its;
 67:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;

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

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

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

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

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

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

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

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

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

129:     /* test bounds post-solution*/
130:     VecCopy(mfqP->subxl,mfqP->subpdel);
131:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subx);
132:     VecMax(mfqP->subpdel,NULL,&maxval);
133:     if (maxval > 1e-5) {
134:       PetscInfo(tao,"subproblem solution < lower bound\n");
135:       tao->reason = TAO_DIVERGED_TR_REDUCTION;
136:     }

138:     VecCopy(mfqP->subx,mfqP->subpdel);
139:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);
140:     VecMax(mfqP->subpdel,NULL,&maxval);
141:     if (maxval > 1e-5) {
142:       PetscInfo(tao,"subproblem solution > upper bound\n");
143:       tao->reason = TAO_DIVERGED_TR_REDUCTION;
144:     }
145:   } else {
146:     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);
147:   }
148:   *qmin *= -1;
149:   return(0);
150: }

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

161:   for (i=0;i<mfqP->n;i++) {
162:     mfqP->Gres[i]=0;
163:   }
164:   for (i=0;i<mfqP->n*mfqP->n;i++) {
165:     mfqP->Hres[i]=0;
166:   }

168:   /* Compute Gres= sum_ij[wij * (cjgi + cigj)] */
169:   if (tao->res_weights_v) {
170:     /* Vector(diagonal) weights: gres = sum_i(wii*ci*gi) */
171:     for (i=0;i<mfqP->m;i++) {
172:       VecGetValues(tao->res_weights_v,1,&i,&factor);
173:       factor=factor*mfqP->C[i];
174:       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn,&factor,&mfqP->Fdiff[blasn*i],&ione,mfqP->Gres,&ione));
175:     }

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

195:       factor = tao->res_weights_w[i]*mfqP->C[col]/2.0;
196:       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn,&factor,&mfqP->Fdiff[blasn*row],&ione,mfqP->Gres,&ione));
197:       factor = tao->res_weights_w[i]*mfqP->C[row]/2.0;
198:       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn,&factor,&mfqP->Fdiff[blasn*col],&ione,mfqP->Gres,&ione));
199:     }

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

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

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

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

234:     /* sum(F(xkin,i)*H(:,:,i)) */
235:     if (tao->niter>1) {
236:       for (i=0;i<mfqP->m;i++) {
237:         factor = mfqP->C[i];
238:         PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn2,&factor,&mfqP->H[i],&blasm,mfqP->Hres,&ione));
239:       }
240:     }
241:   }
242:   return(0);
243: }

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

252:   j=0;
253:   for (i=0;i<n;i++) {
254:     phi[j] = 0.5 * x[i]*x[i];
255:     j++;
256:     for (k=i+1;k<n;k++) {
257:       phi[j]  = x[i]*x[k]/sqrt2;
258:       j++;
259:     }
260:   }
261:   return(0);
262: }

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

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

282:   for (i=0;i<mfqP->n*mfqP->m;i++) {
283:     mfqP->Gdel[i] = 0;
284:   }
285:   for (i=0;i<mfqP->n*mfqP->n*mfqP->m;i++) {
286:     mfqP->Hdel[i] = 0;
287:   }

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

293:   if (np == mfqP->n+1) {
294:     for (i=0;i<mfqP->npmax-mfqP->n-1;i++) {
295:       mfqP->omega[i]=0.0;
296:     }
297:     for (i=0;i<mfqP->n*(mfqP->n+1)/2;i++) {
298:       mfqP->beta[i]=0.0;
299:     }
300:   } else {
301:     /* Let Ltmp = (L'*L) */
302:     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));

304:     /* factor Ltmp */
305:     PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&blasint2,mfqP->L_tmp,&blasint,&info));
306:     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine potrf returned with value %d\n",info);
307:   }

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

316:       /* Beta = L*Omega */
317:       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasint,&blasint2,&one,&mfqP->L[(mfqP->n+1)*blasint],&blasint,mfqP->omega,&ione,&zero,mfqP->beta,&ione));
318:     }

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

325:     /* Gdel(:,k) = Alpha(2:n+1) */
326:     for (i=0;i<mfqP->n;i++) {
327:       mfqP->Gdel[i + mfqP->n*k] = mfqP->RES[mfqP->npmax*k + i+1];
328:     }

330:     /* Set Hdels */
331:     num=0;
332:     for (i=0;i<mfqP->n;i++) {
333:       /* H[i,i,k] = Beta(num) */
334:       mfqP->Hdel[(i*mfqP->n + i)*mfqP->m + k] = mfqP->beta[num];
335:       num++;
336:       for (j=i+1;j<mfqP->n;j++) {
337:         /* H[i,j,k] = H[j,i,k] = Beta(num)/sqrt(2) */
338:         mfqP->Hdel[(j*mfqP->n + i)*mfqP->m + k] = mfqP->beta[num]/sqrt2;
339:         mfqP->Hdel[(i*mfqP->n + j)*mfqP->m + k] = mfqP->beta[num]/sqrt2;
340:         num++;
341:       }
342:     }
343:   }
344:   return(0);
345: }

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

361:   /* Initialize M,N */
362:   for (i=0;i<mfqP->n+1;i++) {
363:     VecGetArrayRead(mfqP->Xhist[mfqP->model_indices[i]],&x);
364:     mfqP->M[(mfqP->n+1)*i] = 1.0;
365:     for (j=0;j<mfqP->n;j++) {
366:       mfqP->M[j+1+((mfqP->n+1)*i)] = (x[j]  - mfqP->xmin[j]) / mfqP->delta;
367:     }
368:     VecRestoreArrayRead(mfqP->Xhist[mfqP->model_indices[i]],&x);
369:     phi2eval(&mfqP->M[1+((mfqP->n+1)*i)],mfqP->n,&mfqP->N[mfqP->n*(mfqP->n+1)/2 * i]);
370:   }

372:   /* Now we add points until we have npmax starting with the most recent ones */
373:   point = mfqP->nHist-1;
374:   mfqP->nmodelpoints = mfqP->n+1;
375:   while (mfqP->nmodelpoints < mfqP->npmax && point>=0) {
376:     /* Reject any points already in the model */
377:     reject = 0;
378:     for (j=0;j<mfqP->n+1;j++) {
379:       if (point == mfqP->model_indices[j]) {
380:         reject = 1;
381:         break;
382:       }
383:     }

385:     /* Reject if norm(d) >c2 */
386:     if (!reject) {
387:       VecCopy(mfqP->Xhist[point],mfqP->workxvec);
388:       VecAXPY(mfqP->workxvec,-1.0,mfqP->Xhist[mfqP->minindex]);
389:       VecNorm(mfqP->workxvec,NORM_2,&normd);
390:       normd /= mfqP->delta;
391:       if (normd > mfqP->c2) {
392:         reject =1;
393:       }
394:     }
395:     if (reject){
396:       point--;
397:       continue;
398:     }

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

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

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

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

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

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

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

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

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

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

481:   /* Copy Q_tmp(:,n+2:np) to Z) */
482:   offset = mfqP->npmax * (mfqP->n+1);
483:   for (i=offset;i<mfqP->npmax*mfqP->npmax;i++) {
484:     mfqP->Z[i-offset] = mfqP->Q_tmp[i];
485:   }

487:   if (mfqP->nmodelpoints == mfqP->n + 1) {
488:     /* Set L to I_{n+1} */
489:     for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
490:       mfqP->L[i] = 0.0;
491:     }
492:     for (i=0;i<mfqP->n;i++) {
493:       mfqP->L[(mfqP->n*(mfqP->n+1)/2)*i + i] = 1.0;
494:     }
495:   }
496:   return(0);
497: }

499: /* Only call from modelimprove, addpoint() needs ->Q_tmp and ->work to be set */
500: static PetscErrorCode addpoint(Tao tao, TAO_POUNDERS *mfqP, PetscInt index)
501: {

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

512:   /* Project into feasible region */
513:   if (tao->XU && tao->XL) {
514:     VecMedian(mfqP->Xhist[mfqP->nHist], tao->XL, tao->XU, mfqP->Xhist[mfqP->nHist]);
515:   }

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

522:   /* Add new vector to model */
523:   mfqP->model_indices[mfqP->nmodelpoints] = mfqP->nHist;
524:   mfqP->nmodelpoints++;
525:   mfqP->nHist++;
526:   return(0);
527: }

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

538:   blask = mfqP->nmodelpoints;
539:   /* Qtmp = I(n x n) */
540:   for (i=0;i<mfqP->n;i++) {
541:     for (j=0;j<mfqP->n;j++) {
542:       mfqP->Q_tmp[i + mfqP->npmax*j] = 0.0;
543:     }
544:   }
545:   for (j=0;j<mfqP->n;j++) {
546:     mfqP->Q_tmp[j + mfqP->npmax*j] = 1.0;
547:   }

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

552:   for (i=mfqP->nmodelpoints;i<mfqP->n;i++) {
553:     dp = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->Gres,&blas1);
554:     if (dp>0.0) { /* Model says use the other direction! */
555:       for (j=0;j<mfqP->n;j++) {
556:         mfqP->Q_tmp[i*mfqP->npmax+j] *= -1;
557:       }
558:     }
559:     /* mfqP->work[i] = Cres+Modeld(i,:)*(Gres+.5*Hres*Modeld(i,:)') */
560:     for (j=0;j<mfqP->n;j++) {
561:       mfqP->work2[j] = mfqP->Gres[j];
562:     }
563:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&half,mfqP->Hres,&blasn,&mfqP->Q_tmp[i*mfqP->npmax], &blas1, &one, mfqP->work2,&blas1));
564:     mfqP->work[i] = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->work2,&blas1);
565:     if (i==mfqP->nmodelpoints || mfqP->work[i] < minvalue) {
566:       minindex=i;
567:       minvalue = mfqP->work[i];
568:     }
569:     if (addallpoints != 0) {
570:       addpoint(tao,mfqP,i);
571:     }
572:   }
573:   if (!addallpoints) {
574:     addpoint(tao,mfqP,minindex);
575:   }
576:   return(0);
577: }

579: static 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(PetscObjectComm((PetscObject)tao),PETSC_ERR_ARG_OUTOFRANGE,"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(PetscObjectComm((PetscObject)tao),PETSC_ERR_ARG_OUTOFRANGE,"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(PetscObjectComm((PetscObject)tao),PETSC_ERR_ARG_OUTOFRANGE,"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->ls_res);
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);

750:       mfqP->model_indices[ii++] = i;
751:     }
752:     for (j=0;j<mfqP->m;j++) {
753:       mfqP->C[j] = fmin[j];
754:     }
755:     VecRestoreArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);
756:   } else {
757:     VecSet(mfqP->localxmin,0);
758:     VecScatterBegin(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);
759:     VecScatterEnd(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);

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

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

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[ii+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[ii+mfqP->n*j] = f[j] - fmin[j];
784:       }
785:       VecRestoreArray(mfqP->localf,&f);

787:       mfqP->model_indices[ii++] = i;
788:     }
789:     for (j=0;j<mfqP->m;j++) {
790:       mfqP->C[j] = fmin[j];
791:     }
792:     VecRestoreArrayRead(mfqP->localfmin,&fmin);
793:   }

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

802:   cres = minnorm;
803:   pounders_update_res(tao);

805:   valid = PETSC_TRUE;

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

823:   while (tao->reason == TAO_CONTINUE_ITERATING) {
824:     PetscReal gnm = 1e-4;
825:     /* Call general purpose update function */
826:     if (tao->ops->update) {
827:       (*tao->ops->update)(tao, tao->niter, tao->user_update);
828:     }
829:     tao->niter++;
830:     /* Solve the subproblem min{Q(s): ||s|| <= 1.0} */
831:     gqtwrap(tao,&gnm,&mdec);
832:     /* Evaluate the function at the new point */

834:     for (i=0;i<mfqP->n;i++) {
835:         mfqP->work[i] = mfqP->Xsubproblem[i]*mfqP->delta + mfqP->xmin[i];
836:     }
837:     VecDuplicate(tao->solution,&mfqP->Xhist[mfqP->nHist]);
838:     VecDuplicate(tao->ls_res,&mfqP->Fhist[mfqP->nHist]);
839:     VecSetValues(mfqP->Xhist[mfqP->nHist],mfqP->n,mfqP->indices,mfqP->work,INSERT_VALUES);
840:     VecAssemblyBegin(mfqP->Xhist[mfqP->nHist]);
841:     VecAssemblyEnd(mfqP->Xhist[mfqP->nHist]);

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

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

848:     /* Update the center */
849:     if ((rho >= mfqP->eta1) || (rho > mfqP->eta0 && valid==PETSC_TRUE)) {
850:       /* Update model to reflect new base point */
851:       for (i=0;i<mfqP->n;i++) {
852:         mfqP->work[i] = (mfqP->work[i] - mfqP->xmin[i])/mfqP->delta;
853:       }
854:       for (j=0;j<mfqP->m;j++) {
855:         /* C(j) = C(j) + work*G(:,j) + .5*work*H(:,:,j)*work';
856:          G(:,j) = G(:,j) + H(:,:,j)*work' */
857:         for (k=0;k<mfqP->n;k++) {
858:           mfqP->work2[k]=0.0;
859:           for (l=0;l<mfqP->n;l++) {
860:             mfqP->work2[k]+=mfqP->H[j + mfqP->m*(k + l*mfqP->n)]*mfqP->work[l];
861:           }
862:         }
863:         for (i=0;i<mfqP->n;i++) {
864:           mfqP->C[j]+=mfqP->work[i]*(mfqP->Fdiff[i + mfqP->n* j] + 0.5*mfqP->work2[i]);
865:           mfqP->Fdiff[i+mfqP->n*j] +=mfqP-> work2[i];
866:         }
867:       }
868:       /* Cres += work*Gres + .5*work*Hres*work';
869:        Gres += Hres*work'; */

871:       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&one,mfqP->Hres,&blasn,mfqP->work,&ione,&zero,mfqP->work2,&ione));
872:       for (i=0;i<mfqP->n;i++) {
873:         cres += mfqP->work[i]*(mfqP->Gres[i]  + 0.5*mfqP->work2[i]);
874:         mfqP->Gres[i] += mfqP->work2[i];
875:       }
876:       mfqP->minindex = mfqP->nHist-1;
877:       minnorm = mfqP->Fres[mfqP->minindex];
878:       VecCopy(mfqP->Fhist[mfqP->minindex],tao->ls_res);
879:       /* Change current center */
880:       VecGetArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
881:       for (i=0;i<mfqP->n;i++) {
882:         mfqP->xmin[i] = xmint[i];
883:       }
884:       VecRestoreArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
885:     }

887:     /* Evaluate at a model-improving point if necessary */
888:     if (valid == PETSC_FALSE) {
889:       mfqP->q_is_I = 1;
890:       mfqP->nmodelpoints = 0;
891:       affpoints(mfqP,mfqP->xmin,mfqP->c1);
892:       if (mfqP->nmodelpoints < mfqP->n) {
893:         PetscInfo(tao,"Model not valid -- model-improving\n");
894:         modelimprove(tao,mfqP,1);
895:       }
896:     }

898:     /* Update the trust region radius */
899:     deltaold = mfqP->delta;
900:     normxsp = 0;
901:     for (i=0;i<mfqP->n;i++) {
902:       normxsp += mfqP->Xsubproblem[i]*mfqP->Xsubproblem[i];
903:     }
904:     normxsp = PetscSqrtReal(normxsp);
905:     if (rho >= mfqP->eta1 && normxsp > 0.5*mfqP->delta) {
906:       mfqP->delta = PetscMin(mfqP->delta*mfqP->gamma1,mfqP->deltamax);
907:     } else if (valid == PETSC_TRUE) {
908:       mfqP->delta = PetscMax(mfqP->delta*mfqP->gamma0,mfqP->deltamin);
909:     }

911:     /* Compute the next interpolation set */
912:     mfqP->q_is_I = 1;
913:     mfqP->nmodelpoints=0;
914:     PetscInfo2(tao,"Affine Points: xmin = %20.19e, c1 = %20.19e\n",(double)*mfqP->xmin,(double)mfqP->c1);
915:     affpoints(mfqP,mfqP->xmin,mfqP->c1);
916:     if (mfqP->nmodelpoints == mfqP->n) {
917:       valid = PETSC_TRUE;
918:     } else {
919:       valid = PETSC_FALSE;
920:       PetscInfo2(tao,"Affine Points: xmin = %20.19e, c2 = %20.19e\n",(double)*mfqP->xmin,(double)mfqP->c2);
921:       affpoints(mfqP,mfqP->xmin,mfqP->c2);
922:       if (mfqP->n > mfqP->nmodelpoints) {
923:         PetscInfo(tao,"Model not valid -- adding geometry points\n");
924:         modelimprove(tao,mfqP,mfqP->n - mfqP->nmodelpoints);
925:       }
926:     }
927:     for (i=mfqP->nmodelpoints;i>0;i--) {
928:       mfqP->model_indices[i] = mfqP->model_indices[i-1];
929:     }
930:     mfqP->nmodelpoints++;
931:     mfqP->model_indices[0] = mfqP->minindex;
932:     morepoints(mfqP);
933:     for (i=0;i<mfqP->nmodelpoints;i++) {
934:       VecGetArray(mfqP->Xhist[mfqP->model_indices[i]],&x);
935:       for (j=0;j<mfqP->n;j++) {
936:         mfqP->Disp[i + mfqP->npmax*j] = (x[j]  - mfqP->xmin[j]) / deltaold;
937:       }
938:       VecRestoreArray(mfqP->Xhist[mfqP->model_indices[i]],&x);
939:       VecGetArray(mfqP->Fhist[mfqP->model_indices[i]],&f);
940:       for (j=0;j<mfqP->m;j++) {
941:         for (k=0;k<mfqP->n;k++)  {
942:           mfqP->work[k]=0.0;
943:           for (l=0;l<mfqP->n;l++) {
944:             mfqP->work[k] += mfqP->H[j + mfqP->m*(k + mfqP->n*l)] * mfqP->Disp[i + mfqP->npmax*l];
945:           }
946:         }
947:         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];
948:       }
949:       VecRestoreArray(mfqP->Fhist[mfqP->model_indices[i]],&f);
950:     }

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

968:     /* Get residuals */
969:     cres = mfqP->Fres[mfqP->minindex];
970:     pounders_update_res(tao);

972:     /* Export solution and gradient residual to TAO */
973:     VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);
974:     VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);
975:     VecAssemblyBegin(tao->gradient);
976:     VecAssemblyEnd(tao->gradient);
977:     VecNorm(tao->gradient,NORM_2,&gnorm);
978:     gnorm *= mfqP->delta;
979:     /*  final criticality test */
980:     TaoLogConvergenceHistory(tao,minnorm,gnorm,0.0,tao->ksp_its);
981:     TaoMonitor(tao,tao->niter,minnorm,gnorm,0.0,step);
982:     (*tao->ops->convergencetest)(tao,tao->cnvP);
983:     /* test for repeated model */
984:     if (mfqP->nmodelpoints==mfqP->last_nmodelpoints) {
985:       same = PETSC_TRUE;
986:     } else {
987:       same = PETSC_FALSE;
988:     }
989:     for (i=0;i<mfqP->nmodelpoints;i++) {
990:       if (same) {
991:         if (mfqP->model_indices[i] == mfqP->last_model_indices[i]) {
992:           same = PETSC_TRUE;
993:         } else {
994:           same = PETSC_FALSE;
995:         }
996:       }
997:       mfqP->last_model_indices[i] = mfqP->model_indices[i];
998:     }
999:     mfqP->last_nmodelpoints = mfqP->nmodelpoints;
1000:     if (same && mfqP->delta == deltaold) {
1001:       PetscInfo(tao,"Identical model used in successive iterations\n");
1002:       tao->reason = TAO_CONVERGED_STEPTOL;
1003:     }
1004:   }
1005:   return(0);
1006: }

1008: static PetscErrorCode TaoSetUp_POUNDERS(Tao tao)
1009: {
1010:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
1011:   PetscInt       i,j;
1012:   IS             isfloc,isfglob,isxloc,isxglob;

1016:   if (!tao->gradient) {VecDuplicate(tao->solution,&tao->gradient);  }
1017:   if (!tao->stepdirection) {VecDuplicate(tao->solution,&tao->stepdirection);  }
1018:   VecGetSize(tao->solution,&mfqP->n);
1019:   VecGetSize(tao->ls_res,&mfqP->m);
1020:   mfqP->c1 = PetscSqrtReal((PetscReal)mfqP->n);
1021:   if (mfqP->npmax == PETSC_DEFAULT) {
1022:     mfqP->npmax = 2*mfqP->n + 1;
1023:   }
1024:   mfqP->npmax = PetscMin((mfqP->n+1)*(mfqP->n+2)/2,mfqP->npmax);
1025:   mfqP->npmax = PetscMax(mfqP->npmax, mfqP->n+2);

1027:   PetscMalloc1(tao->max_funcs+100,&mfqP->Xhist);
1028:   PetscMalloc1(tao->max_funcs+100,&mfqP->Fhist);
1029:   for (i=0;i<mfqP->n+1;i++) {
1030:     VecDuplicate(tao->solution,&mfqP->Xhist[i]);
1031:     VecDuplicate(tao->ls_res,&mfqP->Fhist[i]);
1032:   }
1033:   VecDuplicate(tao->solution,&mfqP->workxvec);
1034:   VecDuplicate(tao->ls_res,&mfqP->workfvec);
1035:   mfqP->nHist = 0;

1037:   PetscMalloc1(tao->max_funcs+100,&mfqP->Fres);
1038:   PetscMalloc1(mfqP->npmax*mfqP->m,&mfqP->RES);
1039:   PetscMalloc1(mfqP->n,&mfqP->work);
1040:   PetscMalloc1(mfqP->n,&mfqP->work2);
1041:   PetscMalloc1(mfqP->n,&mfqP->work3);
1042:   PetscMalloc1(PetscMax(mfqP->m,mfqP->n+1),&mfqP->mwork);
1043:   PetscMalloc1(mfqP->npmax - mfqP->n - 1,&mfqP->omega);
1044:   PetscMalloc1(mfqP->n * (mfqP->n+1) / 2,&mfqP->beta);
1045:   PetscMalloc1(mfqP->n + 1 ,&mfqP->alpha);

1047:   PetscMalloc1(mfqP->n*mfqP->n*mfqP->m,&mfqP->H);
1048:   PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q);
1049:   PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q_tmp);
1050:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L);
1051:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_tmp);
1052:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_save);
1053:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->N);
1054:   PetscMalloc1(mfqP->npmax * (mfqP->n+1) ,&mfqP->M);
1055:   PetscMalloc1(mfqP->npmax * (mfqP->npmax - mfqP->n - 1) , &mfqP->Z);
1056:   PetscMalloc1(mfqP->npmax,&mfqP->tau);
1057:   PetscMalloc1(mfqP->npmax,&mfqP->tau_tmp);
1058:   mfqP->nmax = PetscMax(5*mfqP->npmax,mfqP->n*(mfqP->n+1)/2);
1059:   PetscMalloc1(mfqP->nmax,&mfqP->npmaxwork);
1060:   PetscMalloc1(mfqP->nmax,&mfqP->npmaxiwork);
1061:   PetscMalloc1(mfqP->n,&mfqP->xmin);
1062:   PetscMalloc1(mfqP->m,&mfqP->C);
1063:   PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Fdiff);
1064:   PetscMalloc1(mfqP->npmax*mfqP->n,&mfqP->Disp);
1065:   PetscMalloc1(mfqP->n,&mfqP->Gres);
1066:   PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Hres);
1067:   PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Gpoints);
1068:   PetscMalloc1(mfqP->npmax,&mfqP->model_indices);
1069:   PetscMalloc1(mfqP->npmax,&mfqP->last_model_indices);
1070:   PetscMalloc1(mfqP->n,&mfqP->Xsubproblem);
1071:   PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Gdel);
1072:   PetscMalloc1(mfqP->n*mfqP->n*mfqP->m, &mfqP->Hdel);
1073:   PetscMalloc1(PetscMax(mfqP->m,mfqP->n),&mfqP->indices);
1074:   PetscMalloc1(mfqP->n,&mfqP->iwork);
1075:   PetscMalloc1(mfqP->m*mfqP->m,&mfqP->w);
1076:   for (i=0;i<mfqP->m;i++) {
1077:     for (j=0;j<mfqP->m;j++) {
1078:       if (i==j) {
1079:         mfqP->w[i+mfqP->m*j]=1.0;
1080:       } else {
1081:         mfqP->w[i+mfqP->m*j]=0.0;
1082:       }
1083:     }
1084:   }
1085:   for (i=0;i<PetscMax(mfqP->m,mfqP->n);i++) {
1086:     mfqP->indices[i] = i;
1087:   }
1088:   MPI_Comm_size(((PetscObject)tao)->comm,&mfqP->size);
1089:   if (mfqP->size > 1) {
1090:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localx);
1091:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localxmin);
1092:     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localf);
1093:     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localfmin);
1094:     ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxloc);
1095:     ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxglob);
1096:     ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfloc);
1097:     ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfglob);


1100:     VecScatterCreate(tao->solution,isxglob,mfqP->localx,isxloc,&mfqP->scatterx);
1101:     VecScatterCreate(tao->ls_res,isfglob,mfqP->localf,isfloc,&mfqP->scatterf);

1103:     ISDestroy(&isxloc);
1104:     ISDestroy(&isxglob);
1105:     ISDestroy(&isfloc);
1106:     ISDestroy(&isfglob);
1107:   }

1109:   if (!mfqP->usegqt) {
1110:     KSP       ksp;
1111:     PC        pc;
1112:     VecCreateSeqWithArray(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Xsubproblem,&mfqP->subx);
1113:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->subxl);
1114:     VecDuplicate(mfqP->subxl,&mfqP->subb);
1115:     VecDuplicate(mfqP->subxl,&mfqP->subxu);
1116:     VecDuplicate(mfqP->subxl,&mfqP->subpdel);
1117:     VecDuplicate(mfqP->subxl,&mfqP->subndel);
1118:     TaoCreate(PETSC_COMM_SELF,&mfqP->subtao);
1119:     PetscObjectIncrementTabLevel((PetscObject)mfqP->subtao, (PetscObject)tao, 1);
1120:     TaoSetType(mfqP->subtao,TAOBNTR);
1121:     TaoSetOptionsPrefix(mfqP->subtao,"pounders_subsolver_");
1122:     TaoSetInitialVector(mfqP->subtao,mfqP->subx);
1123:     TaoSetObjectiveAndGradientRoutine(mfqP->subtao,pounders_fg,(void*)mfqP);
1124:     TaoSetMaximumIterations(mfqP->subtao,mfqP->gqt_maxits);
1125:     TaoSetFromOptions(mfqP->subtao);
1126:     TaoGetKSP(mfqP->subtao,&ksp);
1127:     if (ksp) {
1128:       KSPGetPC(ksp,&pc);
1129:       PCSetType(pc,PCNONE);
1130:     }
1131:     TaoSetVariableBounds(mfqP->subtao,mfqP->subxl,mfqP->subxu);
1132:     MatCreateSeqDense(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Hres,&mfqP->subH);
1133:     TaoSetHessianRoutine(mfqP->subtao,mfqP->subH,mfqP->subH,pounders_h,(void*)mfqP);
1134:   }
1135:   return(0);
1136: }

1138: static PetscErrorCode TaoDestroy_POUNDERS(Tao tao)
1139: {
1140:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
1141:   PetscInt       i;

1145:   if (!mfqP->usegqt) {
1146:     TaoDestroy(&mfqP->subtao);
1147:     VecDestroy(&mfqP->subx);
1148:     VecDestroy(&mfqP->subxl);
1149:     VecDestroy(&mfqP->subxu);
1150:     VecDestroy(&mfqP->subb);
1151:     VecDestroy(&mfqP->subpdel);
1152:     VecDestroy(&mfqP->subndel);
1153:     MatDestroy(&mfqP->subH);
1154:   }
1155:   PetscFree(mfqP->Fres);
1156:   PetscFree(mfqP->RES);
1157:   PetscFree(mfqP->work);
1158:   PetscFree(mfqP->work2);
1159:   PetscFree(mfqP->work3);
1160:   PetscFree(mfqP->mwork);
1161:   PetscFree(mfqP->omega);
1162:   PetscFree(mfqP->beta);
1163:   PetscFree(mfqP->alpha);
1164:   PetscFree(mfqP->H);
1165:   PetscFree(mfqP->Q);
1166:   PetscFree(mfqP->Q_tmp);
1167:   PetscFree(mfqP->L);
1168:   PetscFree(mfqP->L_tmp);
1169:   PetscFree(mfqP->L_save);
1170:   PetscFree(mfqP->N);
1171:   PetscFree(mfqP->M);
1172:   PetscFree(mfqP->Z);
1173:   PetscFree(mfqP->tau);
1174:   PetscFree(mfqP->tau_tmp);
1175:   PetscFree(mfqP->npmaxwork);
1176:   PetscFree(mfqP->npmaxiwork);
1177:   PetscFree(mfqP->xmin);
1178:   PetscFree(mfqP->C);
1179:   PetscFree(mfqP->Fdiff);
1180:   PetscFree(mfqP->Disp);
1181:   PetscFree(mfqP->Gres);
1182:   PetscFree(mfqP->Hres);
1183:   PetscFree(mfqP->Gpoints);
1184:   PetscFree(mfqP->model_indices);
1185:   PetscFree(mfqP->last_model_indices);
1186:   PetscFree(mfqP->Xsubproblem);
1187:   PetscFree(mfqP->Gdel);
1188:   PetscFree(mfqP->Hdel);
1189:   PetscFree(mfqP->indices);
1190:   PetscFree(mfqP->iwork);
1191:   PetscFree(mfqP->w);
1192:   for (i=0;i<mfqP->nHist;i++) {
1193:     VecDestroy(&mfqP->Xhist[i]);
1194:     VecDestroy(&mfqP->Fhist[i]);
1195:   }
1196:   VecDestroy(&mfqP->workxvec);
1197:   VecDestroy(&mfqP->workfvec);
1198:   PetscFree(mfqP->Xhist);
1199:   PetscFree(mfqP->Fhist);

1201:   if (mfqP->size > 1) {
1202:     VecDestroy(&mfqP->localx);
1203:     VecDestroy(&mfqP->localxmin);
1204:     VecDestroy(&mfqP->localf);
1205:     VecDestroy(&mfqP->localfmin);
1206:   }
1207:   PetscFree(tao->data);
1208:   return(0);
1209: }

1211: static PetscErrorCode TaoSetFromOptions_POUNDERS(PetscOptionItems *PetscOptionsObject,Tao tao)
1212: {
1213:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;

1217:   PetscOptionsHead(PetscOptionsObject,"POUNDERS method for least-squares optimization");
1218:   PetscOptionsReal("-tao_pounders_delta","initial delta","",mfqP->delta,&mfqP->delta0,NULL);
1219:   mfqP->delta = mfqP->delta0;
1220:   PetscOptionsInt("-tao_pounders_npmax","max number of points in model","",mfqP->npmax,&mfqP->npmax,NULL);
1221:   PetscOptionsBool("-tao_pounders_gqt","use gqt algorithm for subproblem","",mfqP->usegqt,&mfqP->usegqt,NULL);
1222:   PetscOptionsTail();
1223:   return(0);
1224: }

1226: static PetscErrorCode TaoView_POUNDERS(Tao tao, PetscViewer viewer)
1227: {
1228:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS *)tao->data;
1229:   PetscBool      isascii;

1233:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
1234:   if (isascii) {
1235:     PetscViewerASCIIPrintf(viewer, "initial delta: %g\n",(double)mfqP->delta0);
1236:     PetscViewerASCIIPrintf(viewer, "final delta: %g\n",(double)mfqP->delta);
1237:     PetscViewerASCIIPrintf(viewer, "model points: %D\n",mfqP->nmodelpoints);
1238:     if (mfqP->usegqt) {
1239:       PetscViewerASCIIPrintf(viewer, "subproblem solver: gqt\n");
1240:     } else {
1241:       TaoView(mfqP->subtao, viewer);
1242:     }
1243:   }
1244:   return(0);
1245: }
1246: /*MC
1247:   TAOPOUNDERS - POUNDERS derivate-free model-based algorithm for nonlinear least squares

1249:   Options Database Keys:
1250: + -tao_pounders_delta - initial step length
1251: . -tao_pounders_npmax - maximum number of points in model
1252: - -tao_pounders_gqt - use gqt algorithm for subproblem instead of TRON

1254:   Level: beginner

1256: M*/

1258: PETSC_EXTERN PetscErrorCode TaoCreate_POUNDERS(Tao tao)
1259: {
1260:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;

1264:   tao->ops->setup = TaoSetUp_POUNDERS;
1265:   tao->ops->solve = TaoSolve_POUNDERS;
1266:   tao->ops->view = TaoView_POUNDERS;
1267:   tao->ops->setfromoptions = TaoSetFromOptions_POUNDERS;
1268:   tao->ops->destroy = TaoDestroy_POUNDERS;

1270:   PetscNewLog(tao,&mfqP);
1271:   tao->data = (void*)mfqP;
1272:   /* Override default settings (unless already changed) */
1273:   if (!tao->max_it_changed) tao->max_it = 2000;
1274:   if (!tao->max_funcs_changed) tao->max_funcs = 4000;
1275:   mfqP->npmax = PETSC_DEFAULT;
1276:   mfqP->delta0 = 0.1;
1277:   mfqP->delta = 0.1;
1278:   mfqP->deltamax=1e3;
1279:   mfqP->deltamin=1e-6;
1280:   mfqP->c2 = 10.0;
1281:   mfqP->theta1=1e-5;
1282:   mfqP->theta2=1e-4;
1283:   mfqP->gamma0=0.5;
1284:   mfqP->gamma1=2.0;
1285:   mfqP->eta0 = 0.0;
1286:   mfqP->eta1 = 0.1;
1287:   mfqP->usegqt = PETSC_FALSE;
1288:   mfqP->gqt_rtol = 0.001;
1289:   mfqP->gqt_maxits = 50;
1290:   mfqP->workxvec = 0;
1291:   return(0);
1292: }