Date: 2016-07-24T17:16:18+00:00

Actual source code: pounders.c
petsc-3.7.3 2016-07-24
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      1: #include <../src/tao/leastsquares/impls/pounders/pounders.h>

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

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

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

     27:   /* now  g = g + b */
     28:   VecAXPY(g, 1.0, mfqP->subb);
     29:   return(0);
     30: }
     33: static PetscErrorCode pounders_feval(Tao tao, Vec x, Vec F, PetscReal *fsum)
     34: {
     36:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
     37:   PetscInt i,row,col;
     38:   PetscReal fr,fc;
     40:   TaoComputeSeparableObjective(tao,x,F);
     41:   if (tao->sep_weights_v) {
     42:     VecPointwiseMult(mfqP->workfvec,tao->sep_weights_v,F);
     43:     VecNorm(mfqP->workfvec,NORM_2,fsum);
     44:     *fsum*=(*fsum);
     45:   } else if (tao->sep_weights_w) {
     46:     *fsum=0;
     47:     for (i=0;i<tao->sep_weights_n;i++) {
     48:       row=tao->sep_weights_rows[i];
     49:       col=tao->sep_weights_cols[i];
     50:       VecGetValues(F,1,&row,&fr);
     51:       VecGetValues(F,1,&col,&fc);
     52:       *fsum += tao->sep_weights_w[i]*fc*fr;
     53:     }
     54:   } else {
     55:     VecNorm(F,NORM_2,fsum);
     56:     *fsum*=(*fsum);
     57:   }
     58:   if (PetscIsInfOrNanReal(*fsum)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
     59:   return(0);
     60: }

     64: PetscErrorCode gqtwrap(Tao tao,PetscReal *gnorm, PetscReal *qmin)
     65: {
     67: #if defined(PETSC_USE_REAL_SINGLE)
     68:   PetscReal      atol=1.0e-5;
     69: #else
     70:   PetscReal      atol=1.0e-10;
     71: #endif
     72:   PetscInt       info,its;
     73:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;

     76:   if (! mfqP->usegqt) {
     77:     PetscReal maxval;
     78:     PetscInt  i,j;

     80:     VecSetValues(mfqP->subb,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);
     81:     VecAssemblyBegin(mfqP->subb);
     82:     VecAssemblyEnd(mfqP->subb);

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

     86:     VecSet(mfqP->subndel,-mfqP->delta);
     87:     VecSet(mfqP->subpdel,mfqP->delta);

     89:     for (i=0;i<mfqP->n;i++) {
     90:       for (j=i;j<mfqP->n;j++) {
     91:         mfqP->Hres[j+mfqP->n*i] = mfqP->Hres[mfqP->n*j+i];
     92:       }
     93:     }
     94:     MatSetValues(mfqP->subH,mfqP->n,mfqP->indices,mfqP->n,mfqP->indices,mfqP->Hres,INSERT_VALUES);
     95:     MatAssemblyBegin(mfqP->subH,MAT_FINAL_ASSEMBLY);
     96:     MatAssemblyEnd(mfqP->subH,MAT_FINAL_ASSEMBLY);

     98:     TaoResetStatistics(mfqP->subtao);
     99:     TaoSetTolerances(mfqP->subtao,*gnorm,*gnorm,PETSC_DEFAULT);
    100:     /* enforce bound constraints -- experimental */
    101:     if (tao->XU && tao->XL) {
    102:       VecCopy(tao->XU,mfqP->subxu);
    103:       VecAXPY(mfqP->subxu,-1.0,tao->solution);
    104:       VecScale(mfqP->subxu,1.0/mfqP->delta);
    105:       VecCopy(tao->XL,mfqP->subxl);
    106:       VecAXPY(mfqP->subxl,-1.0,tao->solution);
    107:       VecScale(mfqP->subxl,1.0/mfqP->delta);

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

    126:     VecCopy(mfqP->subx,mfqP->subpdel);
    127:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);
    128:     VecMax(mfqP->subpdel,NULL,&maxval);
    129:     if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"initial guess > upper bound in subproblem");

    131:     TaoSolve(mfqP->subtao);
    132:     TaoGetSolutionStatus(mfqP->subtao,NULL,qmin,NULL,NULL,NULL,NULL);

    134:     /* test bounds post-solution*/
    135:     VecCopy(mfqP->subxl,mfqP->subpdel);
    136:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subx);
    137:     VecMax(mfqP->subpdel,NULL,&maxval);
    138:     if (maxval > 1e-5) {
    139:       PetscInfo(tao,"subproblem solution < lower bound\n");
    140:       tao->reason = TAO_DIVERGED_TR_REDUCTION;
    141:     }

    143:     VecCopy(mfqP->subx,mfqP->subpdel);
    144:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);
    145:     VecMax(mfqP->subpdel,NULL,&maxval);
    146:     if (maxval > 1e-5) {
    147:       PetscInfo(tao,"subproblem solution > upper bound\n");
    148:       tao->reason = TAO_DIVERGED_TR_REDUCTION;
    149:     }
    150:   } else {
    151:     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);
    152:   }
    153:   *qmin *= -1;
    154:   return(0);
    155: }

    159: static PetscErrorCode pounders_update_res(Tao tao)
    160: {
    161:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
    162:   PetscInt i,row,col;
    163:   PetscBLASInt blasn=mfqP->n,blasn2=blasn*blasn,blasm=mfqP->m,ione=1;
    164:   PetscReal zero=0.0,one=1.0,wii,factor;

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

    175:   /* Compute Gres= sum_ij[wij * (cjgi + cigj)] */
    176:   if (tao->sep_weights_v) {
    177:     /* Vector(diagonal) weights: gres = sum_i(wii*ci*gi) */
    178:     for (i=0;i<mfqP->m;i++) {
    179:       VecGetValues(tao->sep_weights_v,1,&i,&factor);
    180:       factor=factor*mfqP->C[i];
    181:       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn,&factor,&mfqP->Fdiff[blasn*i],&ione,mfqP->Gres,&ione));
    182:     }
    183:   } else if (tao->sep_weights_n) {
    184:     /* general case: .5 * Gres= sum_ij[wij * (cjgi + cigj)] */
    185:     for (i=0;i<tao->sep_weights_n;i++) {
    186:       row=tao->sep_weights_rows[i];
    187:       col=tao->sep_weights_cols[i];

    189:       factor = tao->sep_weights_w[i]*mfqP->C[col]/2.0;
    190:       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn,&factor,&mfqP->Fdiff[blasn*row],&ione,mfqP->Gres,&ione));
    191:       factor = tao->sep_weights_w[i]*mfqP->C[row]/2.0;
    192:       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn,&factor,&mfqP->Fdiff[blasn*col],&ione,mfqP->Gres,&ione));
    193:     }
    194:   } else {
    195:     /* default: Gres= sum_i[cigi] = G*c' */
    196:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasm,&one,mfqP->Fdiff,&blasn,mfqP->C,&ione,&zero,mfqP->Gres,&ione));
    197:   }

    199:   /* compute Hres = sum_ij [wij * (*ci*Hj + cj*Hi + gi gj' + gj gi') ] */
    200:   if (tao->sep_weights_v) {
    201:     /* vector(diagonal weights) Hres = sum_i(wii*(ci*Hi + gi * gi' )*/
    202:     for (i=0;i<mfqP->m;i++) {
    203:       VecGetValues(tao->sep_weights_v,1,&i,&wii);
    204:       if (tao->niter>1) {
    205:         factor=wii*mfqP->C[i];
    206:         /* add wii * ci * Hi */
    207:         PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn2,&factor,&mfqP->H[i],&blasn2,mfqP->Hres,&ione));
    208:       }
    209:       /* add wii * gi * gi' */
    210:       PetscStackCallBLAS("BLASgemm_",BLASgemm_("N","T",&blasn,&blasn,&ione,&wii,&mfqP->Fdiff[blasn*i],&blasn,&mfqP->Fdiff[blasn*i],&blasn,&one,mfqP->Hres,&blasn));
    211:     }
    212:   } else if (tao->sep_weights_w) {
    213:     /* .5 * sum_ij [wij * (*ci*Hj + cj*Hi + gi gj' + gj gi') ] */
    214:     for (i=0;i<tao->sep_weights_n;i++) {
    215:       row=tao->sep_weights_rows[i];
    216:       col=tao->sep_weights_cols[i];
    217:       factor=tao->sep_weights_w[i]/2.0;
    218:       /* add wij * gi gj' + wij * gj gi' */
    219:       PetscStackCallBLAS("BLASgemm_",BLASgemm_("N","T",&blasn,&blasn,&ione,&factor,&mfqP->Fdiff[blasn*row],&blasn,&mfqP->Fdiff[blasn*col],&blasn,&one,mfqP->Hres,&blasn));
    220:       PetscStackCallBLAS("BLASgemm_",BLASgemm_("N","T",&blasn,&blasn,&ione,&factor,&mfqP->Fdiff[blasn*col],&blasn,&mfqP->Fdiff[blasn*row],&blasn,&one,mfqP->Hres,&blasn));
    221:     }
    222:     if (tao->niter > 1) {
    223:       for (i=0;i<tao->sep_weights_n;i++) {
    224:         row=tao->sep_weights_rows[i];
    225:         col=tao->sep_weights_cols[i];

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

    231:         /* add wij*ci*Hj */
    232:         factor = tao->sep_weights_w[i]*mfqP->C[row]/2.0;
    233:         PetscStackCallBLAS("BLASaxpy_",BLASaxpy_(&blasn2,&factor,&mfqP->H[col],&blasn2,mfqP->Hres,&ione));
    234:       }
    235:     }
    236:   } else {
    237:     /*  Hres = G*G' + 0.5 sum {F(xkin,i)*H(:,:,i)}  */
    238:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","T",&blasn,&blasn,&blasm,&one,mfqP->Fdiff, &blasn,mfqP->Fdiff, &blasn,&zero,mfqP->Hres,&blasn));

    240:     /* sum(F(xkin,i)*H(:,:,i)) */
    241:     if (tao->niter>1) {
    242:       for (i=0;i<mfqP->m;i++) {
    243:         factor = mfqP->C[i];
    244:         PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn2,&factor,&mfqP->H[i],&blasn2,mfqP->Hres,&ione));
    245:       }
    246:     }
    247:   }

    249:   return(0);
    250: }
    253: PetscErrorCode phi2eval(PetscReal *x, PetscInt n, PetscReal *phi)
    254: {
    255: /* 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] */
    256:   PetscInt  i,j,k;
    257:   PetscReal sqrt2 = PetscSqrtReal(2.0);

    260:   j=0;
    261:   for (i=0;i<n;i++) {
    262:     phi[j] = 0.5 * x[i]*x[i];
    263:     j++;
    264:     for (k=i+1;k<n;k++) {
    265:       phi[j]  = x[i]*x[k]/sqrt2;
    266:       j++;
    267:     }
    268:   }
    269:   return(0);
    270: }

    274: PetscErrorCode getquadpounders(TAO_POUNDERS *mfqP)
    275: {
    276: /* Computes the parameters of the quadratic Q(x) = c + g'*x + 0.5*x*G*x'
    277:    that satisfies the interpolation conditions Q(X[:,j]) = f(j)
    278:    for j=1,...,m and with a Hessian matrix of least Frobenius norm */

    280:     /* NB --we are ignoring c */
    281:   PetscInt     i,j,k,num,np = mfqP->nmodelpoints;
    282:   PetscReal    one = 1.0,zero=0.0,negone=-1.0;
    283:   PetscBLASInt blasnpmax = mfqP->npmax;
    284:   PetscBLASInt blasnplus1 = mfqP->n+1;
    285:   PetscBLASInt blasnp = np;
    286:   PetscBLASInt blasint = mfqP->n*(mfqP->n+1) / 2;
    287:   PetscBLASInt blasint2 = np - mfqP->n-1;
    288:   PetscBLASInt info,ione=1;
    289:   PetscReal    sqrt2 = PetscSqrtReal(2.0);

    292:   for (i=0;i<mfqP->n*mfqP->m;i++) {
    293:     mfqP->Gdel[i] = 0;
    294:   }
    295:   for (i=0;i<mfqP->n*mfqP->n*mfqP->m;i++) {
    296:     mfqP->Hdel[i] = 0;
    297:   }

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

    303:   if (np == mfqP->n+1) {
    304:     for (i=0;i<mfqP->npmax-mfqP->n-1;i++) {
    305:       mfqP->omega[i]=0.0;
    306:     }
    307:     for (i=0;i<mfqP->n*(mfqP->n+1)/2;i++) {
    308:       mfqP->beta[i]=0.0;
    309:     }
    310:   } else {
    311:     /* Let Ltmp = (L'*L) */
    312:     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));

    314:     /* factor Ltmp */
    315:     PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&blasint2,mfqP->L_tmp,&blasint,&info));
    316:     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine potrf returned with value %d\n",info);
    317:   }

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

    326:       /* Beta = L*Omega */
    327:       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasint,&blasint2,&one,&mfqP->L[(mfqP->n+1)*blasint],&blasint,mfqP->omega,&ione,&zero,mfqP->beta,&ione));
    328:     }

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

    335:     /* Gdel(:,k) = Alpha(2:n+1) */
    336:     for (i=0;i<mfqP->n;i++) {
    337:       mfqP->Gdel[i + mfqP->n*k] = mfqP->RES[mfqP->npmax*k + i+1];
    338:     }

    340:     /* Set Hdels */
    341:     num=0;
    342:     for (i=0;i<mfqP->n;i++) {
    343:       /* H[i,i,k] = Beta(num) */
    344:       mfqP->Hdel[(i*mfqP->n + i)*mfqP->m + k] = mfqP->beta[num];
    345:       num++;
    346:       for (j=i+1;j<mfqP->n;j++) {
    347:         /* H[i,j,k] = H[j,i,k] = Beta(num)/sqrt(2) */
    348:         mfqP->Hdel[(j*mfqP->n + i)*mfqP->m + k] = mfqP->beta[num]/sqrt2;
    349:         mfqP->Hdel[(i*mfqP->n + j)*mfqP->m + k] = mfqP->beta[num]/sqrt2;
    350:         num++;
    351:       }
    352:     }
    353:   }
    354:   return(0);
    355: }

    359: PetscErrorCode morepoints(TAO_POUNDERS *mfqP)
    360: {
    361:   /* Assumes mfqP->model_indices[0]  is minimum index
    362:    Finishes adding points to mfqP->model_indices (up to npmax)
    363:    Computes L,Z,M,N
    364:    np is actual number of points in model (should equal npmax?) */
    365:   PetscInt        point,i,j,offset;
    366:   PetscInt        reject;
    367:   PetscBLASInt    blasn=mfqP->n,blasnpmax=mfqP->npmax,blasnplus1=mfqP->n+1,info,blasnmax=mfqP->nmax,blasint,blasint2,blasnp,blasmaxmn;
    368:   const PetscReal *x;
    369:   PetscReal       normd;
    370:   PetscErrorCode  ierr;

    373:   /* Initialize M,N */
    374:   for (i=0;i<mfqP->n+1;i++) {
    375:     VecGetArrayRead(mfqP->Xhist[mfqP->model_indices[i]],&x);
    376:     mfqP->M[(mfqP->n+1)*i] = 1.0;
    377:     for (j=0;j<mfqP->n;j++) {
    378:       mfqP->M[j+1+((mfqP->n+1)*i)] = (x[j]  - mfqP->xmin[j]) / mfqP->delta;
    379:     }
    380:     VecRestoreArrayRead(mfqP->Xhist[mfqP->model_indices[i]],&x);
    381:     phi2eval(&mfqP->M[1+((mfqP->n+1)*i)],mfqP->n,&mfqP->N[mfqP->n*(mfqP->n+1)/2 * i]);
    382:   }

    384:   /* Now we add points until we have npmax starting with the most recent ones */
    385:   point = mfqP->nHist-1;
    386:   mfqP->nmodelpoints = mfqP->n+1;
    387:   while (mfqP->nmodelpoints < mfqP->npmax && point>=0) {
    388:     /* Reject any points already in the model */
    389:     reject = 0;
    390:     for (j=0;j<mfqP->n+1;j++) {
    391:       if (point == mfqP->model_indices[j]) {
    392:         reject = 1;
    393:         break;
    394:       }
    395:     }

    397:     /* Reject if norm(d) >c2 */
    398:     if (!reject) {
    399:       VecCopy(mfqP->Xhist[point],mfqP->workxvec);
    400:       VecAXPY(mfqP->workxvec,-1.0,mfqP->Xhist[mfqP->minindex]);
    401:       VecNorm(mfqP->workxvec,NORM_2,&normd);
    402:       normd /= mfqP->delta;
    403:       if (normd > mfqP->c2) {
    404:         reject =1;
    405:       }
    406:     }
    407:     if (reject){
    408:       point--;
    409:       continue;
    410:     }

    412:     VecGetArrayRead(mfqP->Xhist[point],&x);
    413:     mfqP->M[(mfqP->n+1)*mfqP->nmodelpoints] = 1.0;
    414:     for (j=0;j<mfqP->n;j++) {
    415:       mfqP->M[j+1+((mfqP->n+1)*mfqP->nmodelpoints)] = (x[j]  - mfqP->xmin[j]) / mfqP->delta;
    416:     }
    417:     VecRestoreArrayRead(mfqP->Xhist[point],&x);
    418:     phi2eval(&mfqP->M[1+(mfqP->n+1)*mfqP->nmodelpoints],mfqP->n,&mfqP->N[mfqP->n*(mfqP->n+1)/2 * (mfqP->nmodelpoints)]);

    420:     /* Update QR factorization */
    421:     /* Copy M' to Q_tmp */
    422:     for (i=0;i<mfqP->n+1;i++) {
    423:       for (j=0;j<mfqP->npmax;j++) {
    424:         mfqP->Q_tmp[j+mfqP->npmax*i] = mfqP->M[i+(mfqP->n+1)*j];
    425:       }
    426:     }
    427:     blasnp = mfqP->nmodelpoints+1;
    428:     /* Q_tmp,R = qr(M') */
    429:     blasmaxmn=PetscMax(mfqP->m,mfqP->n+1);
    430:     PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&blasnp,&blasnplus1,mfqP->Q_tmp,&blasnpmax,mfqP->tau_tmp,mfqP->mwork,&blasmaxmn,&info));
    431:     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine geqrf returned with value %d\n",info);

    433:     /* Reject if min(svd(N*Q(:,n+2:np+1)) <= theta2 */
    434:     /* L = N*Qtmp */
    435:     blasint2 = mfqP->n * (mfqP->n+1) / 2;
    436:     /* Copy N to L_tmp */
    437:     for (i=0;i<mfqP->n*(mfqP->n+1)/2 * mfqP->npmax;i++) {
    438:       mfqP->L_tmp[i]= mfqP->N[i];
    439:     }
    440:     /* Copy L_save to L_tmp */

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

    446:     /* Copy L_tmp to L_save */
    447:     for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
    448:       mfqP->L_save[i] = mfqP->L_tmp[i];
    449:     }

    451:     /* Get svd for L_tmp(:,n+2:np+1) (L_tmp is modified in process) */
    452:     blasint = mfqP->nmodelpoints - mfqP->n;
    453:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    454:     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));
    455:     PetscFPTrapPop();
    456:     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine gesvd returned with value %d\n",info);

    458:     if (mfqP->beta[PetscMin(blasint,blasint2)-1] > mfqP->theta2) {
    459:       /* accept point */
    460:       mfqP->model_indices[mfqP->nmodelpoints] = point;
    461:       /* Copy Q_tmp to Q */
    462:       for (i=0;i<mfqP->npmax* mfqP->npmax;i++) {
    463:         mfqP->Q[i] = mfqP->Q_tmp[i];
    464:       }
    465:       for (i=0;i<mfqP->npmax;i++){
    466:         mfqP->tau[i] = mfqP->tau_tmp[i];
    467:       }
    468:       mfqP->nmodelpoints++;
    469:       blasnp = mfqP->nmodelpoints;

    471:       /* Copy L_save to L */
    472:       for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
    473:         mfqP->L[i] = mfqP->L_save[i];
    474:       }
    475:     }
    476:     point--;
    477:   }

    479:   blasnp = mfqP->nmodelpoints;
    480:   /* Copy Q(:,n+2:np) to Z */
    481:   /* First set Q_tmp to I */
    482:   for (i=0;i<mfqP->npmax*mfqP->npmax;i++) {
    483:     mfqP->Q_tmp[i] = 0.0;
    484:   }
    485:   for (i=0;i<mfqP->npmax;i++) {
    486:     mfqP->Q_tmp[i + mfqP->npmax*i] = 1.0;
    487:   }

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

    493:   /* Copy Q_tmp(:,n+2:np) to Z) */
    494:   offset = mfqP->npmax * (mfqP->n+1);
    495:   for (i=offset;i<mfqP->npmax*mfqP->npmax;i++) {
    496:     mfqP->Z[i-offset] = mfqP->Q_tmp[i];
    497:   }

    499:   if (mfqP->nmodelpoints == mfqP->n + 1) {
    500:     /* Set L to I_{n+1} */
    501:     for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
    502:       mfqP->L[i] = 0.0;
    503:     }
    504:     for (i=0;i<mfqP->n;i++) {
    505:       mfqP->L[(mfqP->n*(mfqP->n+1)/2)*i + i] = 1.0;
    506:     }
    507:   }
    508:   return(0);
    509: }

    513: /* Only call from modelimprove, addpoint() needs ->Q_tmp and ->work to be set */
    514: PetscErrorCode addpoint(Tao tao, TAO_POUNDERS *mfqP, PetscInt index)
    515: {

    519:   /* Create new vector in history: X[newidx] = X[mfqP->index] + delta*X[index]*/
    520:   VecDuplicate(mfqP->Xhist[0],&mfqP->Xhist[mfqP->nHist]);
    521:   VecSetValues(mfqP->Xhist[mfqP->nHist],mfqP->n,mfqP->indices,&mfqP->Q_tmp[index*mfqP->npmax],INSERT_VALUES);
    522:   VecAssemblyBegin(mfqP->Xhist[mfqP->nHist]);
    523:   VecAssemblyEnd(mfqP->Xhist[mfqP->nHist]);
    524:   VecAYPX(mfqP->Xhist[mfqP->nHist],mfqP->delta,mfqP->Xhist[mfqP->minindex]);

    526:   /* Project into feasible region */
    527:   if (tao->XU && tao->XL) {
    528:     VecMedian(mfqP->Xhist[mfqP->nHist], tao->XL, tao->XU, mfqP->Xhist[mfqP->nHist]);
    529:   }

    531:   /* Compute value of new vector */
    532:   VecDuplicate(mfqP->Fhist[0],&mfqP->Fhist[mfqP->nHist]);
    533:   CHKMEMQ;
    534:   pounders_feval(tao,mfqP->Xhist[mfqP->nHist],mfqP->Fhist[mfqP->nHist],&mfqP->Fres[mfqP->nHist]);

    536:   /* Add new vector to model */
    537:   mfqP->model_indices[mfqP->nmodelpoints] = mfqP->nHist;
    538:   mfqP->nmodelpoints++;
    539:   mfqP->nHist++;
    540:   return(0);
    541: }

    545: PetscErrorCode modelimprove(Tao tao, TAO_POUNDERS *mfqP, PetscInt addallpoints)
    546: {
    547:   /* modeld = Q(:,np+1:n)' */
    549:   PetscInt       i,j,minindex=0;
    550:   PetscReal      dp,half=0.5,one=1.0,minvalue=PETSC_INFINITY;
    551:   PetscBLASInt   blasn=mfqP->n,  blasnpmax = mfqP->npmax, blask,info;
    552:   PetscBLASInt   blas1=1,blasnmax = mfqP->nmax;

    554:   blask = mfqP->nmodelpoints;
    555:   /* Qtmp = I(n x n) */
    556:   for (i=0;i<mfqP->n;i++) {
    557:     for (j=0;j<mfqP->n;j++) {
    558:       mfqP->Q_tmp[i + mfqP->npmax*j] = 0.0;
    559:     }
    560:   }
    561:   for (j=0;j<mfqP->n;j++) {
    562:     mfqP->Q_tmp[j + mfqP->npmax*j] = 1.0;
    563:   }

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

    568:   for (i=mfqP->nmodelpoints;i<mfqP->n;i++) {
    569:     dp = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->Gres,&blas1);
    570:     if (dp>0.0) { /* Model says use the other direction! */
    571:       for (j=0;j<mfqP->n;j++) {
    572:         mfqP->Q_tmp[i*mfqP->npmax+j] *= -1;
    573:       }
    574:     }
    575:     /* mfqP->work[i] = Cres+Modeld(i,:)*(Gres+.5*Hres*Modeld(i,:)') */
    576:     for (j=0;j<mfqP->n;j++) {
    577:       mfqP->work2[j] = mfqP->Gres[j];
    578:     }
    579:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&half,mfqP->Hres,&blasn,&mfqP->Q_tmp[i*mfqP->npmax], &blas1, &one, mfqP->work2,&blas1));
    580:     mfqP->work[i] = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->work2,&blas1);
    581:     if (i==mfqP->nmodelpoints || mfqP->work[i] < minvalue) {
    582:       minindex=i;
    583:       minvalue = mfqP->work[i];
    584:     }
    585:     if (addallpoints != 0) {
    586:       addpoint(tao,mfqP,i);
    587:     }
    588:   }
    589:   if (!addallpoints) {
    590:     addpoint(tao,mfqP,minindex);
    591:   }
    592:   return(0);
    593: }

    598: PetscErrorCode affpoints(TAO_POUNDERS *mfqP, PetscReal *xmin,PetscReal c)
    599: {
    600:   PetscInt        i,j;
    601:   PetscBLASInt    blasm=mfqP->m,blasj,blask,blasn=mfqP->n,ione=1,info;
    602:   PetscBLASInt    blasnpmax = mfqP->npmax,blasmaxmn;
    603:   PetscReal       proj,normd;
    604:   const PetscReal *x;
    605:   PetscErrorCode  ierr;

    608:   for (i=mfqP->nHist-1;i>=0;i--) {
    609:     VecGetArrayRead(mfqP->Xhist[i],&x);
    610:     for (j=0;j<mfqP->n;j++) {
    611:       mfqP->work[j] = (x[j] - xmin[j])/mfqP->delta;
    612:     }
    613:     VecRestoreArrayRead(mfqP->Xhist[i],&x);
    614:     PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,mfqP->work,&ione,mfqP->work2,&ione));
    615:     normd = BLASnrm2_(&blasn,mfqP->work,&ione);
    616:     if (normd <= c*c) {
    617:       blasj=PetscMax((mfqP->n - mfqP->nmodelpoints),0);
    618:       if (!mfqP->q_is_I) {
    619:         /* project D onto null */
    620:         blask=(mfqP->nmodelpoints);
    621:         PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&ione,&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->work2,&ione,mfqP->mwork,&blasm,&info));
    622:         if (info < 0) SETERRQ1(PETSC_COMM_SELF,1,"ormqr returned value %d\n",info);
    623:       }
    624:       proj = BLASnrm2_(&blasj,&mfqP->work2[mfqP->nmodelpoints],&ione);

    626:       if (proj >= mfqP->theta1) { /* add this index to model */
    627:         mfqP->model_indices[mfqP->nmodelpoints]=i;
    628:         mfqP->nmodelpoints++;
    629:         PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,mfqP->work,&ione,&mfqP->Q_tmp[mfqP->npmax*(mfqP->nmodelpoints-1)],&ione));
    630:         blask=mfqP->npmax*(mfqP->nmodelpoints);
    631:         PetscStackCallBLAS("BLAScopy",BLAScopy_(&blask,mfqP->Q_tmp,&ione,mfqP->Q,&ione));
    632:         blask = mfqP->nmodelpoints;
    633:         blasmaxmn = PetscMax(mfqP->m,mfqP->n);
    634:         PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->mwork,&blasmaxmn,&info));
    635:         if (info < 0) SETERRQ1(PETSC_COMM_SELF,1,"geqrf returned value %d\n",info);
    636:         mfqP->q_is_I = 0;
    637:       }
    638:       if (mfqP->nmodelpoints == mfqP->n)  {
    639:         break;
    640:       }
    641:     }
    642:   }

    644:   return(0);
    645: }

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

    669:   /* n = # of parameters
    670:      m = dimension (components) of function  */
    672:   PetscCitationsRegister("@article{UNEDF0,\n"
    673:                                 "title = {Nuclear energy density optimization},\n"
    674:                                 "author = {Kortelainen, M.  and Lesinski, T.  and Mor\'e, J.  and Nazarewicz, W.\n"
    675:                                 "          and Sarich, J.  and Schunck, N.  and Stoitsov, M. V. and Wild, S. },\n"
    676:                                 "journal = {Phys. Rev. C},\n"
    677:                                 "volume = {82},\n"
    678:                                 "number = {2},\n"
    679:                                 "pages = {024313},\n"
    680:                                 "numpages = {18},\n"
    681:                                 "year = {2010},\n"
    682:                                 "month = {Aug},\n"
    683:                                 "doi = {10.1103/PhysRevC.82.024313}\n}\n",&set);
    684:   tao->niter=0;
    685:   if (tao->XL && tao->XU) {
    686:     /* Check x0 <= XU */
    687:     PetscReal val;
    688:     VecCopy(tao->solution,mfqP->Xhist[0]);
    689:     VecAXPY(mfqP->Xhist[0],-1.0,tao->XU);
    690:     VecMax(mfqP->Xhist[0],NULL,&val);
    691:     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 > upper bound");

    693:     /* Check x0 >= xl */
    694:     VecCopy(tao->XL,mfqP->Xhist[0]);
    695:     VecAXPY(mfqP->Xhist[0],-1.0,tao->solution);
    696:     VecMax(mfqP->Xhist[0],NULL,&val);
    697:     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 < lower bound");

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

    701:     VecSet(mfqP->Xhist[0],mfqP->delta);
    702:     VecAXPY(mfqP->Xhist[0],1.0,tao->solution);
    703:     VecAXPY(mfqP->Xhist[0],-1.0,tao->XU);
    704:     VecMax(mfqP->Xhist[0],NULL,&val);
    705:     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 + delta > upper bound");
    706:   }

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

    712:   VecCopy(tao->solution,mfqP->Xhist[0]);
    713:   CHKMEMQ;
    714:   pounders_feval(tao,tao->solution,mfqP->Fhist[0],&mfqP->Fres[0]);
    715:   mfqP->minindex = 0;
    716:   minnorm = mfqP->Fres[0];
    717:   TaoMonitor(tao, tao->niter, minnorm, PETSC_INFINITY, 0.0, step, &reason);
    718:   tao->niter++;

    720:   VecGetOwnershipRange(mfqP->Xhist[0],&low,&high);
    721:   for (i=1;i<mfqP->n+1;i++) {
    722:     VecCopy(tao->solution,mfqP->Xhist[i]);
    723:     if (i-1 >= low && i-1 < high) {
    724:       VecGetArray(mfqP->Xhist[i],&x);
    725:       x[i-1-low] += mfqP->delta;
    726:       VecRestoreArray(mfqP->Xhist[i],&x);
    727:     }
    728:     CHKMEMQ;
    729:     pounders_feval(tao,mfqP->Xhist[i],mfqP->Fhist[i],&mfqP->Fres[i]);
    730:     if (mfqP->Fres[i] < minnorm) {
    731:       mfqP->minindex = i;
    732:       minnorm = mfqP->Fres[i];
    733:     }
    734:   }
    735:   VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);
    736:   VecCopy(mfqP->Fhist[mfqP->minindex],tao->sep_objective);
    737:   /* Gather mpi vecs to one big local vec */

    739:   /* Begin serial code */

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

    746:   if (mfqP->size == 1) {
    747:     VecGetArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
    748:     for (i=0;i<mfqP->n;i++) mfqP->xmin[i] = xmint[i];
    749:     VecRestoreArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
    750:     VecGetArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);
    751:     for (i=0;i<mfqP->n+1;i++) {
    752:       if (i == mfqP->minindex) continue;

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

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

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

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

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

    794:       VecScatterBegin(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);
    795:       VecScatterEnd(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);
    796:       VecGetArray(mfqP->localf,&f);
    797:       for (j=0;j<mfqP->m;j++) {
    798:         mfqP->Fdiff[i*mfqP->n+j] = f[j] - fmin[j];
    799:       }
    800:       VecRestoreArray(mfqP->localf,&f);
    801:     }
    802:     for (j=0;j<mfqP->m;j++) {
    803:       mfqP->C[j] = fmin[j];
    804:     }
    805:     VecRestoreArrayRead(mfqP->localfmin,&fmin);
    806:   }

    808:   /* Determine the initial quadratic models */
    809:   /* G = D(ModelIn,:) \ (F(ModelIn,1:m)-repmat(F(xkin,1:m),n,1)); */
    810:   /* D (nxn) Fdiff (nxm)  => G (nxm) */
    811:   blasncopy = blasn;
    812:   PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&blasn,&blasm,mfqP->Disp,&blasnpmax,mfqP->iwork,mfqP->Fdiff,&blasncopy,&info));
    813:   PetscInfo1(tao,"gesv returned %d\n",info);

    815:   cres = minnorm;
    816:   pounders_update_res(tao);

    818:   valid = PETSC_TRUE;

    820:   VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);
    821:   VecAssemblyBegin(tao->gradient);
    822:   VecAssemblyEnd(tao->gradient);
    823:   VecNorm(tao->gradient,NORM_2,&gnorm);
    824:   gnorm *= mfqP->delta;
    825:   VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);
    826:   TaoMonitor(tao, tao->niter, minnorm, gnorm, 0.0, step, &reason);
    827:   mfqP->nHist = mfqP->n+1;
    828:   mfqP->nmodelpoints = mfqP->n+1;

    830:   while (reason == TAO_CONTINUE_ITERATING) {
    831:     PetscReal gnm = 1e-4;
    832:     tao->niter++;
    833:     /* Solve the subproblem min{Q(s): ||s|| <= delta} */
    834:     gqtwrap(tao,&gnm,&mdec);
    835:     /* Evaluate the function at the new point */

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

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

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

    851:     /* Update the center */
    852:     if ((rho >= mfqP->eta1) || (rho > mfqP->eta0 && valid==PETSC_TRUE)) {
    853:       /* Update model to reflect new base point */
    854:       for (i=0;i<mfqP->n;i++) {
    855:         mfqP->work[i] = (mfqP->work[i] - mfqP->xmin[i])/mfqP->delta;
    856:       }
    857:       for (j=0;j<mfqP->m;j++) {
    858:         /* C(j) = C(j) + work*G(:,j) + .5*work*H(:,:,j)*work';
    859:          G(:,j) = G(:,j) + H(:,:,j)*work' */
    860:         for (k=0;k<mfqP->n;k++) {
    861:           mfqP->work2[k]=0.0;
    862:           for (l=0;l<mfqP->n;l++) {
    863:             mfqP->work2[k]+=mfqP->H[j + mfqP->m*(k + l*mfqP->n)]*mfqP->work[l];
    864:           }
    865:         }
    866:         for (i=0;i<mfqP->n;i++) {
    867:           mfqP->C[j]+=mfqP->work[i]*(mfqP->Fdiff[i + mfqP->n* j] + 0.5*mfqP->work2[i]);
    868:           mfqP->Fdiff[i+mfqP->n*j] +=mfqP-> work2[i];
    869:         }
    870:       }
    871:       /* Cres += work*Gres + .5*work*Hres*work';
    872:        Gres += Hres*work'; */

    874:       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&one,mfqP->Hres,&blasn,mfqP->work,&ione,&zero,mfqP->work2,&ione));
    875:       for (i=0;i<mfqP->n;i++) {
    876:         cres += mfqP->work[i]*(mfqP->Gres[i]  + 0.5*mfqP->work2[i]);
    877:         mfqP->Gres[i] += mfqP->work2[i];
    878:       }
    879:       mfqP->minindex = mfqP->nHist-1;
    880:       minnorm = mfqP->Fres[mfqP->minindex];
    881:       VecCopy(mfqP->Fhist[mfqP->minindex],tao->sep_objective);
    882:       /* Change current center */
    883:       VecGetArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
    884:       for (i=0;i<mfqP->n;i++) {
    885:         mfqP->xmin[i] = xmint[i];
    886:       }
    887:       VecRestoreArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
    888:     }

    890:     /* Evaluate at a model-improving point if necessary */
    891:     if (valid == PETSC_FALSE) {
    892:       mfqP->q_is_I = 1;
    893:       mfqP->nmodelpoints = 0;
    894:       affpoints(mfqP,mfqP->xmin,mfqP->c1);
    895:       if (mfqP->nmodelpoints < mfqP->n) {
    896:         PetscInfo(tao,"Model not valid -- model-improving\n");
    897:         modelimprove(tao,mfqP,1);
    898:       }
    899:     }

    901:     /* Update the trust region radius */
    902:     deltaold = mfqP->delta;
    903:     normxsp = 0;
    904:     for (i=0;i<mfqP->n;i++) {
    905:       normxsp += mfqP->Xsubproblem[i]*mfqP->Xsubproblem[i];
    906:     }
    907:     normxsp = PetscSqrtReal(normxsp);
    908:     if (rho >= mfqP->eta1 && normxsp > 0.5*mfqP->delta) {
    909:       mfqP->delta = PetscMin(mfqP->delta*mfqP->gamma1,mfqP->deltamax);
    910:     } else if (valid == PETSC_TRUE) {
    911:       mfqP->delta = PetscMax(mfqP->delta*mfqP->gamma0,mfqP->deltamin);
    912:     }

    914:     /* Compute the next interpolation set */
    915:     mfqP->q_is_I = 1;
    916:     mfqP->nmodelpoints=0;
    917:     affpoints(mfqP,mfqP->xmin,mfqP->c1);
    918:     if (mfqP->nmodelpoints == mfqP->n) {
    919:       valid = PETSC_TRUE;
    920:     } else {
    921:       valid = PETSC_FALSE;
    922:       affpoints(mfqP,mfqP->xmin,mfqP->c2);
    923:       if (mfqP->n > mfqP->nmodelpoints) {
    924:         PetscInfo(tao,"Model not valid -- adding geometry points\n");
    925:         modelimprove(tao,mfqP,mfqP->n - mfqP->nmodelpoints);
    926:       }
    927:     }
    928:     for (i=mfqP->nmodelpoints;i>0;i--) {
    929:       mfqP->model_indices[i] = mfqP->model_indices[i-1];
    930:     }
    931:     mfqP->nmodelpoints++;
    932:     mfqP->model_indices[0] = mfqP->minindex;
    933:     morepoints(mfqP);
    934:     for (i=0;i<mfqP->nmodelpoints;i++) {
    935:       VecGetArray(mfqP->Xhist[mfqP->model_indices[i]],&x);
    936:       for (j=0;j<mfqP->n;j++) {
    937:         mfqP->Disp[i + mfqP->npmax*j] = (x[j]  - mfqP->xmin[j]) / deltaold;
    938:       }
    939:       VecRestoreArray(mfqP->Xhist[mfqP->model_indices[i]],&x);
    940:       VecGetArray(mfqP->Fhist[mfqP->model_indices[i]],&f);
    941:       for (j=0;j<mfqP->m;j++) {
    942:         for (k=0;k<mfqP->n;k++)  {
    943:           mfqP->work[k]=0.0;
    944:           for (l=0;l<mfqP->n;l++) {
    945:             mfqP->work[k] += mfqP->H[j + mfqP->m*(k + mfqP->n*l)] * mfqP->Disp[i + mfqP->npmax*l];
    946:           }
    947:         }
    948:         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];
    949:       }
    950:       VecRestoreArray(mfqP->Fhist[mfqP->model_indices[i]],&f);
    951:     }

    953:     /* Update the quadratic model */
    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:     TaoMonitor(tao, tao->niter, minnorm, gnorm, 0.0, step, &reason);
    981:     /* test for repeated model */
    982:     if (mfqP->nmodelpoints==mfqP->last_nmodelpoints) {
    983:       same = PETSC_TRUE;
    984:     } else {
    985:       same = PETSC_FALSE;
    986:     }
    987:     for (i=0;i<mfqP->nmodelpoints;i++) {
    988:       if (same) {
    989:         if (mfqP->model_indices[i] == mfqP->last_model_indices[i]) {
    990:           same = PETSC_TRUE;
    991:         } else {
    992:           same = PETSC_FALSE;
    993:         }
    994:       }
    995:       mfqP->last_model_indices[i] = mfqP->model_indices[i];
    996:     }
    997:     mfqP->last_nmodelpoints = mfqP->nmodelpoints;
    998:     if (same && mfqP->delta == deltaold) {
    999:       PetscInfo(tao,"Identical model used in successive iterations\n");
    1000:       reason = TAO_CONVERGED_STEPTOL;
    1001:       tao->reason = TAO_CONVERGED_STEPTOL;
    1002:     }
    1003:   }
    1004:   return(0);
    1005: }

    1009: static PetscErrorCode TaoSetUp_POUNDERS(Tao tao)
    1010: {
    1011:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
    1012:   PetscInt       i,j;
    1013:   IS             isfloc,isfglob,isxloc,isxglob;

    1017:   if (!tao->gradient) {VecDuplicate(tao->solution,&tao->gradient);  }
    1018:   if (!tao->stepdirection) {VecDuplicate(tao->solution,&tao->stepdirection);  }
    1019:   VecGetSize(tao->solution,&mfqP->n);
    1020:   VecGetSize(tao->sep_objective,&mfqP->m);
    1021:   mfqP->c1 = PetscSqrtReal((PetscReal)mfqP->n);
    1022:   if (mfqP->npmax == PETSC_DEFAULT) {
    1023:     mfqP->npmax = 2*mfqP->n + 1;
    1024:   }
    1025:   mfqP->npmax = PetscMin((mfqP->n+1)*(mfqP->n+2)/2,mfqP->npmax);
    1026:   mfqP->npmax = PetscMax(mfqP->npmax, mfqP->n+2);

    1028:   PetscMalloc1(tao->max_funcs+10,&mfqP->Xhist);
    1029:   PetscMalloc1(tao->max_funcs+10,&mfqP->Fhist);
    1030:   for (i=0;i<mfqP->n +1;i++) {
    1031:     VecDuplicate(tao->solution,&mfqP->Xhist[i]);
    1032:     VecDuplicate(tao->sep_objective,&mfqP->Fhist[i]);
    1033:   }
    1034:   VecDuplicate(tao->solution,&mfqP->workxvec);
    1035:   VecDuplicate(tao->sep_objective,&mfqP->workfvec);
    1036:   mfqP->nHist = 0;

    1038:   PetscMalloc1(tao->max_funcs+10,&mfqP->Fres);
    1039:   PetscMalloc1(mfqP->npmax*mfqP->m,&mfqP->RES);
    1040:   PetscMalloc1(mfqP->n,&mfqP->work);
    1041:   PetscMalloc1(mfqP->n,&mfqP->work2);
    1042:   PetscMalloc1(mfqP->n,&mfqP->work3);
    1043:   PetscMalloc1(PetscMax(mfqP->m,mfqP->n+1),&mfqP->mwork);
    1044:   PetscMalloc1(mfqP->npmax - mfqP->n - 1,&mfqP->omega);
    1045:   PetscMalloc1(mfqP->n * (mfqP->n+1) / 2,&mfqP->beta);
    1046:   PetscMalloc1(mfqP->n + 1 ,&mfqP->alpha);

    1048:   PetscMalloc1(mfqP->n*mfqP->n*mfqP->m,&mfqP->H);
    1049:   PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q);
    1050:   PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q_tmp);
    1051:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L);
    1052:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_tmp);
    1053:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_save);
    1054:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->N);
    1055:   PetscMalloc1(mfqP->npmax * (mfqP->n+1) ,&mfqP->M);
    1056:   PetscMalloc1(mfqP->npmax * (mfqP->npmax - mfqP->n - 1) , &mfqP->Z);
    1057:   PetscMalloc1(mfqP->npmax,&mfqP->tau);
    1058:   PetscMalloc1(mfqP->npmax,&mfqP->tau_tmp);
    1059:   mfqP->nmax = PetscMax(5*mfqP->npmax,mfqP->n*(mfqP->n+1)/2);
    1060:   PetscMalloc1(mfqP->nmax,&mfqP->npmaxwork);
    1061:   PetscMalloc1(mfqP->nmax,&mfqP->npmaxiwork);
    1062:   PetscMalloc1(mfqP->n,&mfqP->xmin);
    1063:   PetscMalloc1(mfqP->m,&mfqP->C);
    1064:   PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Fdiff);
    1065:   PetscMalloc1(mfqP->npmax*mfqP->n,&mfqP->Disp);
    1066:   PetscMalloc1(mfqP->n,&mfqP->Gres);
    1067:   PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Hres);
    1068:   PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Gpoints);
    1069:   PetscMalloc1(mfqP->npmax,&mfqP->model_indices);
    1070:   PetscMalloc1(mfqP->npmax,&mfqP->last_model_indices);
    1071:   PetscMalloc1(mfqP->n,&mfqP->Xsubproblem);
    1072:   PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Gdel);
    1073:   PetscMalloc1(mfqP->n*mfqP->n*mfqP->m, &mfqP->Hdel);
    1074:   PetscMalloc1(PetscMax(mfqP->m,mfqP->n),&mfqP->indices);
    1075:   PetscMalloc1(mfqP->n,&mfqP->iwork);
    1076:   PetscMalloc1(mfqP->m*mfqP->m,&mfqP->w);
    1077:   for (i=0;i<mfqP->m;i++) {
    1078:     for (j=0;j<mfqP->m;j++) {
    1079:       if (i==j) {
    1080:         mfqP->w[i+mfqP->m*j]=1.0;
    1081:       } else {
    1082:         mfqP->w[i+mfqP->m*j]=0.0;
    1083:       }
    1084:     }
    1085:   }
    1086:   for (i=0;i<PetscMax(mfqP->m,mfqP->n);i++) {
    1087:     mfqP->indices[i] = i;
    1088:   }
    1089:   MPI_Comm_size(((PetscObject)tao)->comm,&mfqP->size);
    1090:   if (mfqP->size > 1) {
    1091:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localx);
    1092:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localxmin);
    1093:     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localf);
    1094:     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localfmin);
    1095:     ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxloc);
    1096:     ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxglob);
    1097:     ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfloc);
    1098:     ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfglob);

    1101:     VecScatterCreate(tao->solution,isxglob,mfqP->localx,isxloc,&mfqP->scatterx);
    1102:     VecScatterCreate(tao->sep_objective,isfglob,mfqP->localf,isfloc,&mfqP->scatterf);

    1104:     ISDestroy(&isxloc);
    1105:     ISDestroy(&isxglob);
    1106:     ISDestroy(&isfloc);
    1107:     ISDestroy(&isfglob);
    1108:   }

    1110:   if (!mfqP->usegqt) {
    1111:     KSP       ksp;
    1112:     PC        pc;
    1113:     VecCreateSeqWithArray(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Xsubproblem,&mfqP->subx);
    1114:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->subxl);
    1115:     VecDuplicate(mfqP->subxl,&mfqP->subb);
    1116:     VecDuplicate(mfqP->subxl,&mfqP->subxu);
    1117:     VecDuplicate(mfqP->subxl,&mfqP->subpdel);
    1118:     VecDuplicate(mfqP->subxl,&mfqP->subndel);
    1119:     TaoCreate(PETSC_COMM_SELF,&mfqP->subtao);
    1120:     TaoSetType(mfqP->subtao,TAOTRON);
    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: }

    1140: static PetscErrorCode TaoDestroy_POUNDERS(Tao tao)
    1141: {
    1142:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
    1143:   PetscInt       i;

    1147:   if (!mfqP->usegqt) {
    1148:     TaoDestroy(&mfqP->subtao);
    1149:     VecDestroy(&mfqP->subx);
    1150:     VecDestroy(&mfqP->subxl);
    1151:     VecDestroy(&mfqP->subxu);
    1152:     VecDestroy(&mfqP->subb);
    1153:     VecDestroy(&mfqP->subpdel);
    1154:     VecDestroy(&mfqP->subndel);
    1155:     MatDestroy(&mfqP->subH);
    1156:   }
    1157:   PetscFree(mfqP->Fres);
    1158:   PetscFree(mfqP->RES);
    1159:   PetscFree(mfqP->work);
    1160:   PetscFree(mfqP->work2);
    1161:   PetscFree(mfqP->work3);
    1162:   PetscFree(mfqP->mwork);
    1163:   PetscFree(mfqP->omega);
    1164:   PetscFree(mfqP->beta);
    1165:   PetscFree(mfqP->alpha);
    1166:   PetscFree(mfqP->H);
    1167:   PetscFree(mfqP->Q);
    1168:   PetscFree(mfqP->Q_tmp);
    1169:   PetscFree(mfqP->L);
    1170:   PetscFree(mfqP->L_tmp);
    1171:   PetscFree(mfqP->L_save);
    1172:   PetscFree(mfqP->N);
    1173:   PetscFree(mfqP->M);
    1174:   PetscFree(mfqP->Z);
    1175:   PetscFree(mfqP->tau);
    1176:   PetscFree(mfqP->tau_tmp);
    1177:   PetscFree(mfqP->npmaxwork);
    1178:   PetscFree(mfqP->npmaxiwork);
    1179:   PetscFree(mfqP->xmin);
    1180:   PetscFree(mfqP->C);
    1181:   PetscFree(mfqP->Fdiff);
    1182:   PetscFree(mfqP->Disp);
    1183:   PetscFree(mfqP->Gres);
    1184:   PetscFree(mfqP->Hres);
    1185:   PetscFree(mfqP->Gpoints);
    1186:   PetscFree(mfqP->model_indices);
    1187:   PetscFree(mfqP->last_model_indices);
    1188:   PetscFree(mfqP->Xsubproblem);
    1189:   PetscFree(mfqP->Gdel);
    1190:   PetscFree(mfqP->Hdel);
    1191:   PetscFree(mfqP->indices);
    1192:   PetscFree(mfqP->iwork);
    1193:   PetscFree(mfqP->w);
    1194:   for (i=0;i<mfqP->nHist;i++) {
    1195:     VecDestroy(&mfqP->Xhist[i]);
    1196:     VecDestroy(&mfqP->Fhist[i]);
    1197:   }
    1198:   VecDestroy(&mfqP->workxvec);
    1199:   VecDestroy(&mfqP->workfvec);
    1200:   PetscFree(mfqP->Xhist);
    1201:   PetscFree(mfqP->Fhist);

    1203:   if (mfqP->size > 1) {
    1204:     VecDestroy(&mfqP->localx);
    1205:     VecDestroy(&mfqP->localxmin);
    1206:     VecDestroy(&mfqP->localf);
    1207:     VecDestroy(&mfqP->localfmin);
    1208:   }
    1209:   PetscFree(tao->data);
    1210:   return(0);
    1211: }

    1215: static PetscErrorCode TaoSetFromOptions_POUNDERS(PetscOptionItems *PetscOptionsObject,Tao tao)
    1216: {
    1217:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;

    1221:   PetscOptionsHead(PetscOptionsObject,"POUNDERS method for least-squares optimization");
    1222:   PetscOptionsReal("-tao_pounders_delta","initial delta","",mfqP->delta,&mfqP->delta0,NULL);
    1223:   mfqP->delta = mfqP->delta0;
    1224:   mfqP->npmax = PETSC_DEFAULT;
    1225:   PetscOptionsInt("-tao_pounders_npmax","max number of points in model","",mfqP->npmax,&mfqP->npmax,NULL);
    1226:   mfqP->usegqt = PETSC_FALSE;
    1227:   PetscOptionsBool("-tao_pounders_gqt","use gqt algorithm for subproblem","",mfqP->usegqt,&mfqP->usegqt,NULL);
    1228:   PetscOptionsTail();
    1229:   return(0);
    1230: }

    1234: static PetscErrorCode TaoView_POUNDERS(Tao tao, PetscViewer viewer)
    1235: {
    1236:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS *)tao->data;
    1237:   PetscBool      isascii;
    1238:   PetscInt       nits;

    1242:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    1243:   if (isascii) {
    1244:     PetscViewerASCIIPushTab(viewer);
    1245:     PetscViewerASCIIPrintf(viewer, "initial delta: %g\n",(double)mfqP->delta0);
    1246:     PetscViewerASCIIPrintf(viewer, "final delta: %g\n",(double)mfqP->delta);
    1247:     PetscViewerASCIIPrintf(viewer, "model points: %D\n",mfqP->nmodelpoints);
    1248:     if (mfqP->usegqt) {
    1249:       PetscViewerASCIIPrintf(viewer, "subproblem solver: gqt\n");
    1250:     } else {
    1251:       PetscViewerASCIIPrintf(viewer, "subproblem solver: %s\n",((PetscObject)mfqP->subtao)->type_name);
    1252:       TaoGetTotalIterationNumber(mfqP->subtao,&nits);
    1253:       PetscViewerASCIIPrintf(viewer, "total subproblem iterations: %D\n",nits);
    1254:     }
    1255:     PetscViewerASCIIPopTab(viewer);
    1256:   }
    1257:   return(0);
    1258: }
    1259: /*MC
    1260:   TAOPOUNDERS - POUNDERS derivate-free model-based algorithm for nonlinear least squares

    1262:   Options Database Keys:
    1263: + -tao_pounders_delta - initial step length
    1264: . -tao_pounders_npmax - maximum number of points in model
    1265: - -tao_pounders_gqt - use gqt algorithm for subproblem instead of TRON

    1267:   Level: beginner
    1268:
    1269: M*/

    1273: PETSC_EXTERN PetscErrorCode TaoCreate_POUNDERS(Tao tao)
    1274: {
    1275:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;

    1279:   tao->ops->setup = TaoSetUp_POUNDERS;
    1280:   tao->ops->solve = TaoSolve_POUNDERS;
    1281:   tao->ops->view = TaoView_POUNDERS;
    1282:   tao->ops->setfromoptions = TaoSetFromOptions_POUNDERS;
    1283:   tao->ops->destroy = TaoDestroy_POUNDERS;

    1285:   PetscNewLog(tao,&mfqP);
    1286:   tao->data = (void*)mfqP;
    1287:   /* Override default settings (unless already changed) */
    1288:   if (!tao->max_it_changed) tao->max_it = 2000;
    1289:   if (!tao->max_funcs_changed) tao->max_funcs = 4000;
    1290:   mfqP->delta0 = 0.1;
    1291:   mfqP->delta = 0.1;
    1292:   mfqP->deltamax=1e3;
    1293:   mfqP->deltamin=1e-6;
    1294:   mfqP->c2 = 100.0;
    1295:   mfqP->theta1=1e-5;
    1296:   mfqP->theta2=1e-4;
    1297:   mfqP->gamma0=0.5;
    1298:   mfqP->gamma1=2.0;
    1299:   mfqP->eta0 = 0.0;
    1300:   mfqP->eta1 = 0.1;
    1301:   mfqP->gqt_rtol = 0.001;
    1302:   mfqP->gqt_maxits = 50;
    1303:   mfqP->workxvec = 0;
    1304:   return(0);
    1305: }