Actual source code: pounders.c
petsc-3.10.5 2019-03-28
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      1:  #include <../src/tao/leastsquares/impls/pounders/pounders.h>

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    137:     VecCopy(mfqP->subx,mfqP->subpdel);
    138:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);
    139:     VecMax(mfqP->subpdel,NULL,&maxval);
    140:     if (maxval > 1e-5) {
    141:       PetscInfo(tao,"subproblem solution > upper bound\n");
    142:       tao->reason = TAO_DIVERGED_TR_REDUCTION;
    143:     }
    144:   } else {
    145:     gqt(mfqP->n,mfqP->Hres,mfqP->n,mfqP->Gres,1.0,mfqP->gqt_rtol,atol,mfqP->gqt_maxits,gnorm,qmin,mfqP->Xsubproblem,&info,&its,mfqP->work,mfqP->work2, mfqP->work3);
    146:   }
    147:   *qmin *= -1;
    148:   return(0);
    149: }

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

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

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

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

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

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

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

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

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

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

    244: PetscErrorCode phi2eval(PetscReal *x, PetscInt n, PetscReal *phi)
    245: {
    246: /* Phi = .5*[x(1)^2  sqrt(2)*x(1)*x(2) ... sqrt(2)*x(1)*x(n) ... x(2)^2 sqrt(2)*x(2)*x(3) .. x(n)^2] */
    247:   PetscInt  i,j,k;
    248:   PetscReal sqrt2 = PetscSqrtReal(2.0);

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

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

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

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

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

    292:   if (np == mfqP->n+1) {
    293:     for (i=0;i<mfqP->npmax-mfqP->n-1;i++) {
    294:       mfqP->omega[i]=0.0;
    295:     }
    296:     for (i=0;i<mfqP->n*(mfqP->n+1)/2;i++) {
    297:       mfqP->beta[i]=0.0;
    298:     }
    299:   } else {
    300:     /* Let Ltmp = (L'*L) */
    301:     PetscStackCallBLAS("BLASgemm",BLASgemm_("T","N",&blasint2,&blasint2,&blasint,&one,&mfqP->L[(mfqP->n+1)*blasint],&blasint,&mfqP->L[(mfqP->n+1)*blasint],&blasint,&zero,mfqP->L_tmp,&blasint));

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    438:     /* Get svd for L_tmp(:,n+2:np+1) (L_tmp is modified in process) */
    439:     blasint = mfqP->nmodelpoints - mfqP->n;
    440:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    441:     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","N",&blasint2,&blasint,&mfqP->L_tmp[(mfqP->n+1)*blasint2],&blasint2,mfqP->beta,mfqP->work,&blasn,mfqP->work,&blasn,mfqP->npmaxwork,&blasnmax,&info));
    442:     PetscFPTrapPop();
    443:     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine gesvd returned with value %d\n",info);

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    625:   return(0);
    626: }

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

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

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

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

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

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

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

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

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

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

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

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

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

    722:   /* Begin serial code */

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

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

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

    744:       VecGetArray(mfqP->Fhist[i],&f);
    745:       for (j=0;j<mfqP->m;j++) {
    746:         mfqP->Fdiff[ii+mfqP->n*j] = f[j] - fmin[j];
    747:       }
    748:       VecRestoreArray(mfqP->Fhist[i],&f);

    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:     tao->niter++;
    826:     /* Solve the subproblem min{Q(s): ||s|| <= 1.0} */
    827:     gqtwrap(tao,&gnm,&mdec);
    828:     /* Evaluate the function at the new point */

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

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

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

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

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

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

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

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

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

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

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

    1004: static PetscErrorCode TaoSetUp_POUNDERS(Tao tao)
    1005: {
    1006:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
    1007:   PetscInt       i,j;
    1008:   IS             isfloc,isfglob,isxloc,isxglob;

    1012:   if (!tao->gradient) {VecDuplicate(tao->solution,&tao->gradient);  }
    1013:   if (!tao->stepdirection) {VecDuplicate(tao->solution,&tao->stepdirection);  }
    1014:   VecGetSize(tao->solution,&mfqP->n);
    1015:   VecGetSize(tao->sep_objective,&mfqP->m);
    1016:   mfqP->c1 = PetscSqrtReal((PetscReal)mfqP->n);
    1017:   if (mfqP->npmax == PETSC_DEFAULT) {
    1018:     mfqP->npmax = 2*mfqP->n + 1;
    1019:   }
    1020:   mfqP->npmax = PetscMin((mfqP->n+1)*(mfqP->n+2)/2,mfqP->npmax);
    1021:   mfqP->npmax = PetscMax(mfqP->npmax, mfqP->n+2);

    1023:   PetscMalloc1(tao->max_funcs+100,&mfqP->Xhist);
    1024:   PetscMalloc1(tao->max_funcs+100,&mfqP->Fhist);
    1025:   for (i=0;i<mfqP->n+1;i++) {
    1026:     VecDuplicate(tao->solution,&mfqP->Xhist[i]);
    1027:     VecDuplicate(tao->sep_objective,&mfqP->Fhist[i]);
    1028:   }
    1029:   VecDuplicate(tao->solution,&mfqP->workxvec);
    1030:   VecDuplicate(tao->sep_objective,&mfqP->workfvec);
    1031:   mfqP->nHist = 0;

    1033:   PetscMalloc1(tao->max_funcs+100,&mfqP->Fres);
    1034:   PetscMalloc1(mfqP->npmax*mfqP->m,&mfqP->RES);
    1035:   PetscMalloc1(mfqP->n,&mfqP->work);
    1036:   PetscMalloc1(mfqP->n,&mfqP->work2);
    1037:   PetscMalloc1(mfqP->n,&mfqP->work3);
    1038:   PetscMalloc1(PetscMax(mfqP->m,mfqP->n+1),&mfqP->mwork);
    1039:   PetscMalloc1(mfqP->npmax - mfqP->n - 1,&mfqP->omega);
    1040:   PetscMalloc1(mfqP->n * (mfqP->n+1) / 2,&mfqP->beta);
    1041:   PetscMalloc1(mfqP->n + 1 ,&mfqP->alpha);

    1043:   PetscMalloc1(mfqP->n*mfqP->n*mfqP->m,&mfqP->H);
    1044:   PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q);
    1045:   PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q_tmp);
    1046:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L);
    1047:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_tmp);
    1048:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_save);
    1049:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->N);
    1050:   PetscMalloc1(mfqP->npmax * (mfqP->n+1) ,&mfqP->M);
    1051:   PetscMalloc1(mfqP->npmax * (mfqP->npmax - mfqP->n - 1) , &mfqP->Z);
    1052:   PetscMalloc1(mfqP->npmax,&mfqP->tau);
    1053:   PetscMalloc1(mfqP->npmax,&mfqP->tau_tmp);
    1054:   mfqP->nmax = PetscMax(5*mfqP->npmax,mfqP->n*(mfqP->n+1)/2);
    1055:   PetscMalloc1(mfqP->nmax,&mfqP->npmaxwork);
    1056:   PetscMalloc1(mfqP->nmax,&mfqP->npmaxiwork);
    1057:   PetscMalloc1(mfqP->n,&mfqP->xmin);
    1058:   PetscMalloc1(mfqP->m,&mfqP->C);
    1059:   PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Fdiff);
    1060:   PetscMalloc1(mfqP->npmax*mfqP->n,&mfqP->Disp);
    1061:   PetscMalloc1(mfqP->n,&mfqP->Gres);
    1062:   PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Hres);
    1063:   PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Gpoints);
    1064:   PetscMalloc1(mfqP->npmax,&mfqP->model_indices);
    1065:   PetscMalloc1(mfqP->npmax,&mfqP->last_model_indices);
    1066:   PetscMalloc1(mfqP->n,&mfqP->Xsubproblem);
    1067:   PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Gdel);
    1068:   PetscMalloc1(mfqP->n*mfqP->n*mfqP->m, &mfqP->Hdel);
    1069:   PetscMalloc1(PetscMax(mfqP->m,mfqP->n),&mfqP->indices);
    1070:   PetscMalloc1(mfqP->n,&mfqP->iwork);
    1071:   PetscMalloc1(mfqP->m*mfqP->m,&mfqP->w);
    1072:   for (i=0;i<mfqP->m;i++) {
    1073:     for (j=0;j<mfqP->m;j++) {
    1074:       if (i==j) {
    1075:         mfqP->w[i+mfqP->m*j]=1.0;
    1076:       } else {
    1077:         mfqP->w[i+mfqP->m*j]=0.0;
    1078:       }
    1079:     }
    1080:   }
    1081:   for (i=0;i<PetscMax(mfqP->m,mfqP->n);i++) {
    1082:     mfqP->indices[i] = i;
    1083:   }
    1084:   MPI_Comm_size(((PetscObject)tao)->comm,&mfqP->size);
    1085:   if (mfqP->size > 1) {
    1086:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localx);
    1087:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localxmin);
    1088:     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localf);
    1089:     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localfmin);
    1090:     ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxloc);
    1091:     ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxglob);
    1092:     ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfloc);
    1093:     ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfglob);

    1096:     VecScatterCreate(tao->solution,isxglob,mfqP->localx,isxloc,&mfqP->scatterx);
    1097:     VecScatterCreate(tao->sep_objective,isfglob,mfqP->localf,isfloc,&mfqP->scatterf);

    1099:     ISDestroy(&isxloc);
    1100:     ISDestroy(&isxglob);
    1101:     ISDestroy(&isfloc);
    1102:     ISDestroy(&isfglob);
    1103:   }

    1105:   if (!mfqP->usegqt) {
    1106:     KSP       ksp;
    1107:     PC        pc;
    1108:     VecCreateSeqWithArray(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Xsubproblem,&mfqP->subx);
    1109:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->subxl);
    1110:     VecDuplicate(mfqP->subxl,&mfqP->subb);
    1111:     VecDuplicate(mfqP->subxl,&mfqP->subxu);
    1112:     VecDuplicate(mfqP->subxl,&mfqP->subpdel);
    1113:     VecDuplicate(mfqP->subxl,&mfqP->subndel);
    1114:     TaoCreate(PETSC_COMM_SELF,&mfqP->subtao);
    1115:     PetscObjectIncrementTabLevel((PetscObject)mfqP->subtao, (PetscObject)tao, 1);
    1116:     TaoSetType(mfqP->subtao,TAOBNTR);
    1117:     TaoSetOptionsPrefix(mfqP->subtao,"pounders_subsolver_");
    1118:     TaoSetInitialVector(mfqP->subtao,mfqP->subx);
    1119:     TaoSetObjectiveAndGradientRoutine(mfqP->subtao,pounders_fg,(void*)mfqP);
    1120:     TaoSetMaximumIterations(mfqP->subtao,mfqP->gqt_maxits);
    1121:     TaoSetFromOptions(mfqP->subtao);
    1122:     TaoGetKSP(mfqP->subtao,&ksp);
    1123:     if (ksp) {
    1124:       KSPGetPC(ksp,&pc);
    1125:       PCSetType(pc,PCNONE);
    1126:     }
    1127:     TaoSetVariableBounds(mfqP->subtao,mfqP->subxl,mfqP->subxu);
    1128:     MatCreateSeqDense(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Hres,&mfqP->subH);
    1129:     TaoSetHessianRoutine(mfqP->subtao,mfqP->subH,mfqP->subH,pounders_h,(void*)mfqP);
    1130:   }
    1131:   return(0);
    1132: }

    1134: static PetscErrorCode TaoDestroy_POUNDERS(Tao tao)
    1135: {
    1136:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
    1137:   PetscInt       i;

    1141:   if (!mfqP->usegqt) {
    1142:     TaoDestroy(&mfqP->subtao);
    1143:     VecDestroy(&mfqP->subx);
    1144:     VecDestroy(&mfqP->subxl);
    1145:     VecDestroy(&mfqP->subxu);
    1146:     VecDestroy(&mfqP->subb);
    1147:     VecDestroy(&mfqP->subpdel);
    1148:     VecDestroy(&mfqP->subndel);
    1149:     MatDestroy(&mfqP->subH);
    1150:   }
    1151:   PetscFree(mfqP->Fres);
    1152:   PetscFree(mfqP->RES);
    1153:   PetscFree(mfqP->work);
    1154:   PetscFree(mfqP->work2);
    1155:   PetscFree(mfqP->work3);
    1156:   PetscFree(mfqP->mwork);
    1157:   PetscFree(mfqP->omega);
    1158:   PetscFree(mfqP->beta);
    1159:   PetscFree(mfqP->alpha);
    1160:   PetscFree(mfqP->H);
    1161:   PetscFree(mfqP->Q);
    1162:   PetscFree(mfqP->Q_tmp);
    1163:   PetscFree(mfqP->L);
    1164:   PetscFree(mfqP->L_tmp);
    1165:   PetscFree(mfqP->L_save);
    1166:   PetscFree(mfqP->N);
    1167:   PetscFree(mfqP->M);
    1168:   PetscFree(mfqP->Z);
    1169:   PetscFree(mfqP->tau);
    1170:   PetscFree(mfqP->tau_tmp);
    1171:   PetscFree(mfqP->npmaxwork);
    1172:   PetscFree(mfqP->npmaxiwork);
    1173:   PetscFree(mfqP->xmin);
    1174:   PetscFree(mfqP->C);
    1175:   PetscFree(mfqP->Fdiff);
    1176:   PetscFree(mfqP->Disp);
    1177:   PetscFree(mfqP->Gres);
    1178:   PetscFree(mfqP->Hres);
    1179:   PetscFree(mfqP->Gpoints);
    1180:   PetscFree(mfqP->model_indices);
    1181:   PetscFree(mfqP->last_model_indices);
    1182:   PetscFree(mfqP->Xsubproblem);
    1183:   PetscFree(mfqP->Gdel);
    1184:   PetscFree(mfqP->Hdel);
    1185:   PetscFree(mfqP->indices);
    1186:   PetscFree(mfqP->iwork);
    1187:   PetscFree(mfqP->w);
    1188:   for (i=0;i<mfqP->nHist;i++) {
    1189:     VecDestroy(&mfqP->Xhist[i]);
    1190:     VecDestroy(&mfqP->Fhist[i]);
    1191:   }
    1192:   VecDestroy(&mfqP->workxvec);
    1193:   VecDestroy(&mfqP->workfvec);
    1194:   PetscFree(mfqP->Xhist);
    1195:   PetscFree(mfqP->Fhist);

    1197:   if (mfqP->size > 1) {
    1198:     VecDestroy(&mfqP->localx);
    1199:     VecDestroy(&mfqP->localxmin);
    1200:     VecDestroy(&mfqP->localf);
    1201:     VecDestroy(&mfqP->localfmin);
    1202:   }
    1203:   PetscFree(tao->data);
    1204:   return(0);
    1205: }

    1207: static PetscErrorCode TaoSetFromOptions_POUNDERS(PetscOptionItems *PetscOptionsObject,Tao tao)
    1208: {
    1209:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;

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

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

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

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

    1250:   Level: beginner

    1252: M*/

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

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

    1266:   PetscNewLog(tao,&mfqP);
    1267:   tao->data = (void*)mfqP;
    1268:   /* Override default settings (unless already changed) */
    1269:   if (!tao->max_it_changed) tao->max_it = 2000;
    1270:   if (!tao->max_funcs_changed) tao->max_funcs = 4000;
    1271:   mfqP->npmax = PETSC_DEFAULT;
    1272:   mfqP->delta0 = 0.1;
    1273:   mfqP->delta = 0.1;
    1274:   mfqP->deltamax=1e3;
    1275:   mfqP->deltamin=1e-6;
    1276:   mfqP->c2 = 10.0;
    1277:   mfqP->theta1=1e-5;
    1278:   mfqP->theta2=1e-4;
    1279:   mfqP->gamma0=0.5;
    1280:   mfqP->gamma1=2.0;
    1281:   mfqP->eta0 = 0.0;
    1282:   mfqP->eta1 = 0.1;
    1283:   mfqP->usegqt = PETSC_FALSE;
    1284:   mfqP->gqt_rtol = 0.001;
    1285:   mfqP->gqt_maxits = 50;
    1286:   mfqP->workxvec = 0;
    1287:   return(0);
    1288: }