Date: 2015-10-02T22:31:22+00:00

Actual source code: pounders.c
petsc-3.6.2 2015-10-02
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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: }

     34: PetscErrorCode gqtwrap(Tao tao,PetscReal *gnorm, PetscReal *qmin)
     35: {
     37: #if defined(PETSC_USE_REAL_SINGLE)
     38:   PetscReal      atol=1.0e-5;
     39: #else
     40:   PetscReal      atol=1.0e-10;
     41: #endif
     42:   PetscInt       info,its;
     43:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;

     46:   if (! mfqP->usegqt) {
     47:     PetscReal maxval;
     48:     PetscInt  i,j;

     50:     VecSetValues(mfqP->subb,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);
     51:     VecAssemblyBegin(mfqP->subb);
     52:     VecAssemblyEnd(mfqP->subb);

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

     56:     VecSet(mfqP->subndel,-mfqP->delta);
     57:     VecSet(mfqP->subpdel,mfqP->delta);

     59:     for (i=0;i<mfqP->n;i++) {
     60:       for (j=i;j<mfqP->n;j++) {
     61:         mfqP->Hres[j+mfqP->n*i] = mfqP->Hres[mfqP->n*j+i];
     62:       }
     63:     }
     64:     MatSetValues(mfqP->subH,mfqP->n,mfqP->indices,mfqP->n,mfqP->indices,mfqP->Hres,INSERT_VALUES);
     65:     MatAssemblyBegin(mfqP->subH,MAT_FINAL_ASSEMBLY);
     66:     MatAssemblyEnd(mfqP->subH,MAT_FINAL_ASSEMBLY);

     68:     TaoResetStatistics(mfqP->subtao);
     69:     TaoSetTolerances(mfqP->subtao,PETSC_DEFAULT,PETSC_DEFAULT,*gnorm,*gnorm,PETSC_DEFAULT);
     70:     /* enforce bound constraints -- experimental */
     71:     if (tao->XU && tao->XL) {
     72:       VecCopy(tao->XU,mfqP->subxu);
     73:       VecAXPY(mfqP->subxu,-1.0,tao->solution);
     74:       VecScale(mfqP->subxu,1.0/mfqP->delta);
     75:       VecCopy(tao->XL,mfqP->subxl);
     76:       VecAXPY(mfqP->subxl,-1.0,tao->solution);
     77:       VecScale(mfqP->subxl,1.0/mfqP->delta);

     79:       VecPointwiseMin(mfqP->subxu,mfqP->subxu,mfqP->subpdel);
     80:       VecPointwiseMax(mfqP->subxl,mfqP->subxl,mfqP->subndel);
     81:     } else {
     82:       VecCopy(mfqP->subpdel,mfqP->subxu);
     83:       VecCopy(mfqP->subndel,mfqP->subxl);
     84:     }
     85:     /* Make sure xu > xl */
     86:     VecCopy(mfqP->subxl,mfqP->subpdel);
     87:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);
     88:     VecMax(mfqP->subpdel,NULL,&maxval);
     89:     if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"upper bound < lower bound in subproblem");
     90:     /* Make sure xu > tao->solution > xl */
     91:     VecCopy(mfqP->subxl,mfqP->subpdel);
     92:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subx);
     93:     VecMax(mfqP->subpdel,NULL,&maxval);
     94:     if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"initial guess < lower bound in subproblem");

     96:     VecCopy(mfqP->subx,mfqP->subpdel);
     97:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);
     98:     VecMax(mfqP->subpdel,NULL,&maxval);
     99:     if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"initial guess > upper bound in subproblem");

    101:     TaoSolve(mfqP->subtao);
    102:     TaoGetSolutionStatus(mfqP->subtao,NULL,qmin,NULL,NULL,NULL,NULL);

    104:     /* test bounds post-solution*/
    105:     VecCopy(mfqP->subxl,mfqP->subpdel);
    106:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subx);
    107:     VecMax(mfqP->subpdel,NULL,&maxval);
    108:     if (maxval > 1e-5) {
    109:       PetscInfo(tao,"subproblem solution < lower bound\n");
    110:       tao->reason = TAO_DIVERGED_TR_REDUCTION;
    111:     }

    113:     VecCopy(mfqP->subx,mfqP->subpdel);
    114:     VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);
    115:     VecMax(mfqP->subpdel,NULL,&maxval);
    116:     if (maxval > 1e-5) {
    117:       PetscInfo(tao,"subproblem solution > upper bound\n");
    118:       tao->reason = TAO_DIVERGED_TR_REDUCTION;
    119:     }
    120:   } else {
    121:     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);
    122:   }
    123:   *qmin *= -1;
    124:   return(0);
    125: }

    129: PetscErrorCode phi2eval(PetscReal *x, PetscInt n, PetscReal *phi)
    130: {
    131: /* 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] */
    132:   PetscInt  i,j,k;
    133:   PetscReal sqrt2 = PetscSqrtReal(2.0);

    136:   j=0;
    137:   for (i=0;i<n;i++) {
    138:     phi[j] = 0.5 * x[i]*x[i];
    139:     j++;
    140:     for (k=i+1;k<n;k++) {
    141:       phi[j]  = x[i]*x[k]/sqrt2;
    142:       j++;
    143:     }
    144:   }
    145:   return(0);
    146: }

    150: PetscErrorCode getquadpounders(TAO_POUNDERS *mfqP)
    151: {
    152: /* Computes the parameters of the quadratic Q(x) = c + g'*x + 0.5*x*G*x'
    153:    that satisfies the interpolation conditions Q(X[:,j]) = f(j)
    154:    for j=1,...,m and with a Hessian matrix of least Frobenius norm */

    156:     /* NB --we are ignoring c */
    157:   PetscInt     i,j,k,num,np = mfqP->nmodelpoints;
    158:   PetscReal    one = 1.0,zero=0.0,negone=-1.0;
    159:   PetscBLASInt blasnpmax = mfqP->npmax;
    160:   PetscBLASInt blasnplus1 = mfqP->n+1;
    161:   PetscBLASInt blasnp = np;
    162:   PetscBLASInt blasint = mfqP->n*(mfqP->n+1) / 2;
    163:   PetscBLASInt blasint2 = np - mfqP->n-1;
    164:   PetscBLASInt info,ione=1;
    165:   PetscReal    sqrt2 = PetscSqrtReal(2.0);

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

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

    179:   if (np == mfqP->n+1) {
    180:     for (i=0;i<mfqP->npmax-mfqP->n-1;i++) {
    181:       mfqP->omega[i]=0.0;
    182:     }
    183:     for (i=0;i<mfqP->n*(mfqP->n+1)/2;i++) {
    184:       mfqP->beta[i]=0.0;
    185:     }
    186:   } else {
    187:     /* Let Ltmp = (L'*L) */
    188:     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));

    190:     /* factor Ltmp */
    191:     PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&blasint2,mfqP->L_tmp,&blasint,&info));
    192:     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine potrf returned with value %d\n",info);
    193:   }

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

    202:       /* Beta = L*Omega */
    203:       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasint,&blasint2,&one,&mfqP->L[(mfqP->n+1)*blasint],&blasint,mfqP->omega,&ione,&zero,mfqP->beta,&ione));
    204:     }

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

    211:     /* Gdel(:,k) = Alpha(2:n+1) */
    212:     for (i=0;i<mfqP->n;i++) {
    213:       mfqP->Gdel[i + mfqP->n*k] = mfqP->RES[mfqP->npmax*k + i+1];
    214:     }

    216:     /* Set Hdels */
    217:     num=0;
    218:     for (i=0;i<mfqP->n;i++) {
    219:       /* H[i,i,k] = Beta(num) */
    220:       mfqP->Hdel[(i*mfqP->n + i)*mfqP->m + k] = mfqP->beta[num];
    221:       num++;
    222:       for (j=i+1;j<mfqP->n;j++) {
    223:         /* H[i,j,k] = H[j,i,k] = Beta(num)/sqrt(2) */
    224:         mfqP->Hdel[(j*mfqP->n + i)*mfqP->m + k] = mfqP->beta[num]/sqrt2;
    225:         mfqP->Hdel[(i*mfqP->n + j)*mfqP->m + k] = mfqP->beta[num]/sqrt2;
    226:         num++;
    227:       }
    228:     }
    229:   }
    230:   return(0);
    231: }

    235: PetscErrorCode morepoints(TAO_POUNDERS *mfqP)
    236: {
    237:   /* Assumes mfqP->model_indices[0]  is minimum index
    238:    Finishes adding points to mfqP->model_indices (up to npmax)
    239:    Computes L,Z,M,N
    240:    np is actual number of points in model (should equal npmax?) */
    241:   PetscInt        point,i,j,offset;
    242:   PetscInt        reject;
    243:   PetscBLASInt    blasn=mfqP->n,blasnpmax=mfqP->npmax,blasnplus1=mfqP->n+1,info,blasnmax=mfqP->nmax,blasint,blasint2,blasnp,blasmaxmn;
    244:   const PetscReal *x;
    245:   PetscReal       normd;
    246:   PetscErrorCode  ierr;

    249:   /* Initialize M,N */
    250:   for (i=0;i<mfqP->n+1;i++) {
    251:     VecGetArrayRead(mfqP->Xhist[mfqP->model_indices[i]],&x);
    252:     mfqP->M[(mfqP->n+1)*i] = 1.0;
    253:     for (j=0;j<mfqP->n;j++) {
    254:       mfqP->M[j+1+((mfqP->n+1)*i)] = (x[j]  - mfqP->xmin[j]) / mfqP->delta;
    255:     }
    256:     VecRestoreArrayRead(mfqP->Xhist[mfqP->model_indices[i]],&x);
    257:     phi2eval(&mfqP->M[1+((mfqP->n+1)*i)],mfqP->n,&mfqP->N[mfqP->n*(mfqP->n+1)/2 * i]);
    258:   }

    260:   /* Now we add points until we have npmax starting with the most recent ones */
    261:   point = mfqP->nHist-1;
    262:   mfqP->nmodelpoints = mfqP->n+1;
    263:   while (mfqP->nmodelpoints < mfqP->npmax && point>=0) {
    264:     /* Reject any points already in the model */
    265:     reject = 0;
    266:     for (j=0;j<mfqP->n+1;j++) {
    267:       if (point == mfqP->model_indices[j]) {
    268:         reject = 1;
    269:         break;
    270:       }
    271:     }

    273:     /* Reject if norm(d) >c2 */
    274:     if (!reject) {
    275:       VecCopy(mfqP->Xhist[point],mfqP->workxvec);
    276:       VecAXPY(mfqP->workxvec,-1.0,mfqP->Xhist[mfqP->minindex]);
    277:       VecNorm(mfqP->workxvec,NORM_2,&normd);
    278:       normd /= mfqP->delta;
    279:       if (normd > mfqP->c2) {
    280:         reject =1;
    281:       }
    282:     }
    283:     if (reject){
    284:       point--;
    285:       continue;
    286:     }

    288:     VecGetArrayRead(mfqP->Xhist[point],&x);
    289:     mfqP->M[(mfqP->n+1)*mfqP->nmodelpoints] = 1.0;
    290:     for (j=0;j<mfqP->n;j++) {
    291:       mfqP->M[j+1+((mfqP->n+1)*mfqP->nmodelpoints)] = (x[j]  - mfqP->xmin[j]) / mfqP->delta;
    292:     }
    293:     VecRestoreArrayRead(mfqP->Xhist[point],&x);
    294:     phi2eval(&mfqP->M[1+(mfqP->n+1)*mfqP->nmodelpoints],mfqP->n,&mfqP->N[mfqP->n*(mfqP->n+1)/2 * (mfqP->nmodelpoints)]);

    296:     /* Update QR factorization */
    297:     /* Copy M' to Q_tmp */
    298:     for (i=0;i<mfqP->n+1;i++) {
    299:       for (j=0;j<mfqP->npmax;j++) {
    300:         mfqP->Q_tmp[j+mfqP->npmax*i] = mfqP->M[i+(mfqP->n+1)*j];
    301:       }
    302:     }
    303:     blasnp = mfqP->nmodelpoints+1;
    304:     /* Q_tmp,R = qr(M') */
    305:     blasmaxmn=PetscMax(mfqP->m,mfqP->n+1);
    306:     PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&blasnp,&blasnplus1,mfqP->Q_tmp,&blasnpmax,mfqP->tau_tmp,mfqP->mwork,&blasmaxmn,&info));
    307:     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine geqrf returned with value %d\n",info);

    309:     /* Reject if min(svd(N*Q(:,n+2:np+1)) <= theta2 */
    310:     /* L = N*Qtmp */
    311:     blasint2 = mfqP->n * (mfqP->n+1) / 2;
    312:     /* Copy N to L_tmp */
    313:     for (i=0;i<mfqP->n*(mfqP->n+1)/2 * mfqP->npmax;i++) {
    314:       mfqP->L_tmp[i]= mfqP->N[i];
    315:     }
    316:     /* Copy L_save to L_tmp */

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

    322:     /* Copy L_tmp to L_save */
    323:     for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
    324:       mfqP->L_save[i] = mfqP->L_tmp[i];
    325:     }

    327:     /* Get svd for L_tmp(:,n+2:np+1) (L_tmp is modified in process) */
    328:     blasint = mfqP->nmodelpoints - mfqP->n;
    329:     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));
    330:     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine gesvd returned with value %d\n",info);

    332:     if (mfqP->beta[PetscMin(blasint,blasint2)-1] > mfqP->theta2) {
    333:       /* accept point */
    334:       mfqP->model_indices[mfqP->nmodelpoints] = point;
    335:       /* Copy Q_tmp to Q */
    336:       for (i=0;i<mfqP->npmax* mfqP->npmax;i++) {
    337:         mfqP->Q[i] = mfqP->Q_tmp[i];
    338:       }
    339:       for (i=0;i<mfqP->npmax;i++){
    340:         mfqP->tau[i] = mfqP->tau_tmp[i];
    341:       }
    342:       mfqP->nmodelpoints++;
    343:       blasnp = mfqP->nmodelpoints;

    345:       /* Copy L_save to L */
    346:       for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
    347:         mfqP->L[i] = mfqP->L_save[i];
    348:       }
    349:     }
    350:     point--;
    351:   }

    353:   blasnp = mfqP->nmodelpoints;
    354:   /* Copy Q(:,n+2:np) to Z */
    355:   /* First set Q_tmp to I */
    356:   for (i=0;i<mfqP->npmax*mfqP->npmax;i++) {
    357:     mfqP->Q_tmp[i] = 0.0;
    358:   }
    359:   for (i=0;i<mfqP->npmax;i++) {
    360:     mfqP->Q_tmp[i + mfqP->npmax*i] = 1.0;
    361:   }

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

    367:   /* Copy Q_tmp(:,n+2:np) to Z) */
    368:   offset = mfqP->npmax * (mfqP->n+1);
    369:   for (i=offset;i<mfqP->npmax*mfqP->npmax;i++) {
    370:     mfqP->Z[i-offset] = mfqP->Q_tmp[i];
    371:   }

    373:   if (mfqP->nmodelpoints == mfqP->n + 1) {
    374:     /* Set L to I_{n+1} */
    375:     for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
    376:       mfqP->L[i] = 0.0;
    377:     }
    378:     for (i=0;i<mfqP->n;i++) {
    379:       mfqP->L[(mfqP->n*(mfqP->n+1)/2)*i + i] = 1.0;
    380:     }
    381:   }
    382:   return(0);
    383: }

    387: /* Only call from modelimprove, addpoint() needs ->Q_tmp and ->work to be set */
    388: PetscErrorCode addpoint(Tao tao, TAO_POUNDERS *mfqP, PetscInt index)
    389: {

    393:   /* Create new vector in history: X[newidx] = X[mfqP->index] + delta*X[index]*/
    394:   VecDuplicate(mfqP->Xhist[0],&mfqP->Xhist[mfqP->nHist]);
    395:   VecSetValues(mfqP->Xhist[mfqP->nHist],mfqP->n,mfqP->indices,&mfqP->Q_tmp[index*mfqP->npmax],INSERT_VALUES);
    396:   VecAssemblyBegin(mfqP->Xhist[mfqP->nHist]);
    397:   VecAssemblyEnd(mfqP->Xhist[mfqP->nHist]);
    398:   VecAYPX(mfqP->Xhist[mfqP->nHist],mfqP->delta,mfqP->Xhist[mfqP->minindex]);

    400:   /* Project into feasible region */
    401:   if (tao->XU && tao->XL) {
    402:     VecMedian(mfqP->Xhist[mfqP->nHist], tao->XL, tao->XU, mfqP->Xhist[mfqP->nHist]);
    403:   }

    405:   /* Compute value of new vector */
    406:   VecDuplicate(mfqP->Fhist[0],&mfqP->Fhist[mfqP->nHist]);
    407:   CHKMEMQ;
    408:   TaoComputeSeparableObjective(tao,mfqP->Xhist[mfqP->nHist],mfqP->Fhist[mfqP->nHist]);
    409:   VecNorm(mfqP->Fhist[mfqP->nHist],NORM_2,&mfqP->Fres[mfqP->nHist]);
    410:   if (PetscIsInfOrNanReal(mfqP->Fres[mfqP->nHist])) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
    411:   mfqP->Fres[mfqP->nHist]*=mfqP->Fres[mfqP->nHist];

    413:   /* Add new vector to model */
    414:   mfqP->model_indices[mfqP->nmodelpoints] = mfqP->nHist;
    415:   mfqP->nmodelpoints++;
    416:   mfqP->nHist++;
    417:   return(0);
    418: }

    422: PetscErrorCode modelimprove(Tao tao, TAO_POUNDERS *mfqP, PetscInt addallpoints)
    423: {
    424:   /* modeld = Q(:,np+1:n)' */
    426:   PetscInt       i,j,minindex=0;
    427:   PetscReal      dp,half=0.5,one=1.0,minvalue=PETSC_INFINITY;
    428:   PetscBLASInt   blasn=mfqP->n,  blasnpmax = mfqP->npmax, blask,info;
    429:   PetscBLASInt   blas1=1,blasnmax = mfqP->nmax;

    431:   blask = mfqP->nmodelpoints;
    432:   /* Qtmp = I(n x n) */
    433:   for (i=0;i<mfqP->n;i++) {
    434:     for (j=0;j<mfqP->n;j++) {
    435:       mfqP->Q_tmp[i + mfqP->npmax*j] = 0.0;
    436:     }
    437:   }
    438:   for (j=0;j<mfqP->n;j++) {
    439:     mfqP->Q_tmp[j + mfqP->npmax*j] = 1.0;
    440:   }

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

    445:   for (i=mfqP->nmodelpoints;i<mfqP->n;i++) {
    446:     dp = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->Gres,&blas1);
    447:     if (dp>0.0) { /* Model says use the other direction! */
    448:       for (j=0;j<mfqP->n;j++) {
    449:         mfqP->Q_tmp[i*mfqP->npmax+j] *= -1;
    450:       }
    451:     }
    452:     /* mfqP->work[i] = Cres+Modeld(i,:)*(Gres+.5*Hres*Modeld(i,:)') */
    453:     for (j=0;j<mfqP->n;j++) {
    454:       mfqP->work2[j] = mfqP->Gres[j];
    455:     }
    456:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&half,mfqP->Hres,&blasn,&mfqP->Q_tmp[i*mfqP->npmax], &blas1, &one, mfqP->work2,&blas1));
    457:     mfqP->work[i] = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->work2,&blas1);
    458:     if (i==mfqP->nmodelpoints || mfqP->work[i] < minvalue) {
    459:       minindex=i;
    460:       minvalue = mfqP->work[i];
    461:     }
    462:     if (addallpoints != 0) {
    463:       addpoint(tao,mfqP,i);
    464:     }
    465:   }
    466:   if (!addallpoints) {
    467:     addpoint(tao,mfqP,minindex);
    468:   }
    469:   return(0);
    470: }

    475: PetscErrorCode affpoints(TAO_POUNDERS *mfqP, PetscReal *xmin,PetscReal c)
    476: {
    477:   PetscInt        i,j;
    478:   PetscBLASInt    blasm=mfqP->m,blasj,blask,blasn=mfqP->n,ione=1,info;
    479:   PetscBLASInt    blasnpmax = mfqP->npmax,blasmaxmn;
    480:   PetscReal       proj,normd;
    481:   const PetscReal *x;
    482:   PetscErrorCode  ierr;

    485:   for (i=mfqP->nHist-1;i>=0;i--) {
    486:     VecGetArrayRead(mfqP->Xhist[i],&x);
    487:     for (j=0;j<mfqP->n;j++) {
    488:       mfqP->work[j] = (x[j] - xmin[j])/mfqP->delta;
    489:     }
    490:     VecRestoreArrayRead(mfqP->Xhist[i],&x);
    491:     PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,mfqP->work,&ione,mfqP->work2,&ione));
    492:     normd = BLASnrm2_(&blasn,mfqP->work,&ione);
    493:     if (normd <= c*c) {
    494:       blasj=PetscMax((mfqP->n - mfqP->nmodelpoints),0);
    495:       if (!mfqP->q_is_I) {
    496:         /* project D onto null */
    497:         blask=(mfqP->nmodelpoints);
    498:         PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&ione,&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->work2,&ione,mfqP->mwork,&blasm,&info));
    499:         if (info < 0) SETERRQ1(PETSC_COMM_SELF,1,"ormqr returned value %d\n",info);
    500:       }
    501:       proj = BLASnrm2_(&blasj,&mfqP->work2[mfqP->nmodelpoints],&ione);

    503:       if (proj >= mfqP->theta1) { /* add this index to model */
    504:         mfqP->model_indices[mfqP->nmodelpoints]=i;
    505:         mfqP->nmodelpoints++;
    506:         PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,mfqP->work,&ione,&mfqP->Q_tmp[mfqP->npmax*(mfqP->nmodelpoints-1)],&ione));
    507:         blask=mfqP->npmax*(mfqP->nmodelpoints);
    508:         PetscStackCallBLAS("BLAScopy",BLAScopy_(&blask,mfqP->Q_tmp,&ione,mfqP->Q,&ione));
    509:         blask = mfqP->nmodelpoints;
    510:         blasmaxmn = PetscMax(mfqP->m,mfqP->n);
    511:         PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->mwork,&blasmaxmn,&info));
    512:         if (info < 0) SETERRQ1(PETSC_COMM_SELF,1,"geqrf returned value %d\n",info);
    513:         mfqP->q_is_I = 0;
    514:       }
    515:       if (mfqP->nmodelpoints == mfqP->n)  {
    516:         break;
    517:       }
    518:     }
    519:   }

    521:   return(0);
    522: }

    526: static PetscErrorCode TaoSolve_POUNDERS(Tao tao)
    527: {
    528:   TAO_POUNDERS       *mfqP = (TAO_POUNDERS *)tao->data;
    529:   PetscInt           i,ii,j,k,l;
    530:   PetscReal          step=1.0;
    531:   TaoConvergedReason reason = TAO_CONTINUE_ITERATING;
    532:   PetscInt           low,high;
    533:   PetscReal          minnorm;
    534:   PetscReal          *x,*f;
    535:   const PetscReal    *xmint,*fmin;
    536:   PetscReal          cres,deltaold;
    537:   PetscReal          gnorm;
    538:   PetscBLASInt       info,ione=1,iblas;
    539:   PetscBool          valid,same;
    540:   PetscReal          mdec, rho, normxsp;
    541:   PetscReal          one=1.0,zero=0.0,ratio;
    542:   PetscBLASInt       blasm,blasn,blasnpmax,blasn2;
    543:   PetscErrorCode     ierr;
    544:   static PetscBool   set = PETSC_FALSE;

    546:   /* n = # of parameters
    547:      m = dimension (components) of function  */
    549:   PetscCitationsRegister("@article{UNEDF0,\n"
    550:                                 "title = {Nuclear energy density optimization},\n"
    551:                                 "author = {Kortelainen, M.  and Lesinski, T.  and Mor\'e, J.  and Nazarewicz, W.\n"
    552:                                 "          and Sarich, J.  and Schunck, N.  and Stoitsov, M. V. and Wild, S. },\n"
    553:                                 "journal = {Phys. Rev. C},\n"
    554:                                 "volume = {82},\n"
    555:                                 "number = {2},\n"
    556:                                 "pages = {024313},\n"
    557:                                 "numpages = {18},\n"
    558:                                 "year = {2010},\n"
    559:                                 "month = {Aug},\n"
    560:                                 "doi = {10.1103/PhysRevC.82.024313}\n}\n",&set);
    561:   tao->niter=0;
    562:   if (tao->XL && tao->XU) {
    563:     /* Check x0 <= XU */
    564:     PetscReal val;
    565:     VecCopy(tao->solution,mfqP->Xhist[0]);
    566:     VecAXPY(mfqP->Xhist[0],-1.0,tao->XU);
    567:     VecMax(mfqP->Xhist[0],NULL,&val);
    568:     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 > upper bound");

    570:     /* Check x0 >= xl */
    571:     VecCopy(tao->XL,mfqP->Xhist[0]);
    572:     VecAXPY(mfqP->Xhist[0],-1.0,tao->solution);
    573:     VecMax(mfqP->Xhist[0],NULL,&val);
    574:     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 < lower bound");

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

    578:     VecSet(mfqP->Xhist[0],mfqP->delta);
    579:     VecAXPY(mfqP->Xhist[0],1.0,tao->solution);
    580:     VecAXPY(mfqP->Xhist[0],-1.0,tao->XU);
    581:     VecMax(mfqP->Xhist[0],NULL,&val);
    582:     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 + delta > upper bound");
    583:   }

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

    589:   VecCopy(tao->solution,mfqP->Xhist[0]);
    590:   CHKMEMQ;
    591:   TaoComputeSeparableObjective(tao,tao->solution,mfqP->Fhist[0]);

    593:   VecNorm(mfqP->Fhist[0],NORM_2,&mfqP->Fres[0]);
    594:   if (PetscIsInfOrNanReal(mfqP->Fres[0])) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
    595:   mfqP->Fres[0]*=mfqP->Fres[0];
    596:   mfqP->minindex = 0;
    597:   minnorm = mfqP->Fres[0];
    598:   TaoMonitor(tao, tao->niter, minnorm, PETSC_INFINITY, 0.0, step, &reason);
    599:   tao->niter++;

    601:   VecGetOwnershipRange(mfqP->Xhist[0],&low,&high);
    602:   for (i=1;i<mfqP->n+1;i++) {
    603:     VecCopy(tao->solution,mfqP->Xhist[i]);
    604:     if (i-1 >= low && i-1 < high) {
    605:       VecGetArray(mfqP->Xhist[i],&x);
    606:       x[i-1-low] += mfqP->delta;
    607:       VecRestoreArray(mfqP->Xhist[i],&x);
    608:     }
    609:     CHKMEMQ;
    610:     TaoComputeSeparableObjective(tao,mfqP->Xhist[i],mfqP->Fhist[i]);
    611:     VecNorm(mfqP->Fhist[i],NORM_2,&mfqP->Fres[i]);
    612:     if (PetscIsInfOrNanReal(mfqP->Fres[i])) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
    613:     mfqP->Fres[i]*=mfqP->Fres[i];
    614:     if (mfqP->Fres[i] < minnorm) {
    615:       mfqP->minindex = i;
    616:       minnorm = mfqP->Fres[i];
    617:     }
    618:   }
    619:   VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);
    620:   VecCopy(mfqP->Fhist[mfqP->minindex],tao->sep_objective);
    621:   /* Gather mpi vecs to one big local vec */

    623:   /* Begin serial code */

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

    630:   if (mfqP->size == 1) {
    631:     VecGetArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
    632:     for (i=0;i<mfqP->n;i++) mfqP->xmin[i] = xmint[i];
    633:     VecRestoreArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
    634:     VecGetArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);
    635:     for (i=0;i<mfqP->n+1;i++) {
    636:       if (i == mfqP->minindex) continue;

    638:       VecGetArray(mfqP->Xhist[i],&x);
    639:       for (j=0;j<mfqP->n;j++) {
    640:         mfqP->Disp[ii+mfqP->npmax*j] = (x[j] - mfqP->xmin[j])/mfqP->delta;
    641:       }
    642:       VecRestoreArray(mfqP->Xhist[i],&x);

    644:       VecGetArray(mfqP->Fhist[i],&f);
    645:       for (j=0;j<mfqP->m;j++) {
    646:         mfqP->Fdiff[ii+mfqP->n*j] = f[j] - fmin[j];
    647:       }
    648:       VecRestoreArray(mfqP->Fhist[i],&f);
    649:       mfqP->model_indices[ii++] = i;

    651:     }
    652:     for (j=0;j<mfqP->m;j++) {
    653:       mfqP->C[j] = fmin[j];
    654:     }
    655:     VecRestoreArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);
    656:   } else {
    657:     VecScatterBegin(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);
    658:     VecScatterEnd(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);
    659:     VecGetArrayRead(mfqP->localxmin,&xmint);
    660:     for (i=0;i<mfqP->n;i++) mfqP->xmin[i] = xmint[i];
    661:     VecRestoreArrayRead(mfqP->localxmin,&xmint);

    663:     VecScatterBegin(mfqP->scatterf,mfqP->Fhist[mfqP->minindex],mfqP->localfmin,INSERT_VALUES,SCATTER_FORWARD);
    664:     VecScatterEnd(mfqP->scatterf,mfqP->Fhist[mfqP->minindex],mfqP->localfmin,INSERT_VALUES,SCATTER_FORWARD);
    665:     VecGetArrayRead(mfqP->localfmin,&fmin);
    666:     for (i=0;i<mfqP->n+1;i++) {
    667:       if (i == mfqP->minindex) continue;

    669:       mfqP->model_indices[ii++] = i;
    670:       VecScatterBegin(mfqP->scatterx,mfqP->Xhist[ii],mfqP->localx,INSERT_VALUES, SCATTER_FORWARD);
    671:       VecScatterEnd(mfqP->scatterx,mfqP->Xhist[ii],mfqP->localx,INSERT_VALUES, SCATTER_FORWARD);
    672:       VecGetArray(mfqP->localx,&x);
    673:       for (j=0;j<mfqP->n;j++) {
    674:         mfqP->Disp[i+mfqP->npmax*j] = (x[j] - mfqP->xmin[j])/mfqP->delta;
    675:       }
    676:       VecRestoreArray(mfqP->localx,&x);

    678:       VecScatterBegin(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);
    679:       VecScatterEnd(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);
    680:       VecGetArray(mfqP->localf,&f);
    681:       for (j=0;j<mfqP->m;j++) {
    682:         mfqP->Fdiff[i*mfqP->n+j] = f[j] - fmin[j];
    683:       }
    684:       VecRestoreArray(mfqP->localf,&f);
    685:     }
    686:     for (j=0;j<mfqP->m;j++) {
    687:       mfqP->C[j] = fmin[j];
    688:     }
    689:     VecRestoreArrayRead(mfqP->localfmin,&fmin);
    690:   }

    692:   /* Determine the initial quadratic models */
    693:   /* G = D(ModelIn,:) \ (F(ModelIn,1:m)-repmat(F(xkin,1:m),n,1)); */
    694:   /* D (nxn) Fdiff (nxm)  => G (nxm) */
    695:   blasn2 = blasn;
    696:   PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&blasn,&blasm,mfqP->Disp,&blasnpmax,mfqP->iwork,mfqP->Fdiff,&blasn2,&info));
    697:   PetscInfo1(tao,"gesv returned %d\n",info);

    699:   cres = minnorm;
    700:   /* Gres = G*F(xkin,1:m)'  G (nxm)   Fk (m)   */
    701:   PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasm,&one,mfqP->Fdiff,&blasn,mfqP->C,&ione,&zero,mfqP->Gres,&ione));

    703:   /*  Hres = G*G'  */
    704:   PetscStackCallBLAS("BLASgemm",BLASgemm_("N","T",&blasn,&blasn,&blasm,&one,mfqP->Fdiff, &blasn,mfqP->Fdiff,&blasn,&zero,mfqP->Hres,&blasn));

    706:   valid = PETSC_TRUE;

    708:   VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);
    709:   VecAssemblyBegin(tao->gradient);
    710:   VecAssemblyEnd(tao->gradient);
    711:   VecNorm(tao->gradient,NORM_2,&gnorm);
    712:   gnorm *= mfqP->delta;
    713:   VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);
    714:   TaoMonitor(tao, tao->niter, minnorm, gnorm, 0.0, step, &reason);
    715:   mfqP->nHist = mfqP->n+1;
    716:   mfqP->nmodelpoints = mfqP->n+1;

    718:   while (reason == TAO_CONTINUE_ITERATING) {
    719:     PetscReal gnm = 1e-4;
    720:     tao->niter++;
    721:     /* Solve the subproblem min{Q(s): ||s|| <= delta} */
    722:     gqtwrap(tao,&gnm,&mdec);
    723:     /* Evaluate the function at the new point */

    725:     for (i=0;i<mfqP->n;i++) {
    726:         mfqP->work[i] = mfqP->Xsubproblem[i]*mfqP->delta + mfqP->xmin[i];
    727:     }
    728:     VecDuplicate(tao->solution,&mfqP->Xhist[mfqP->nHist]);
    729:     VecDuplicate(tao->sep_objective,&mfqP->Fhist[mfqP->nHist]);
    730:     VecSetValues(mfqP->Xhist[mfqP->nHist],mfqP->n,mfqP->indices,mfqP->work,INSERT_VALUES);
    731:     VecAssemblyBegin(mfqP->Xhist[mfqP->nHist]);
    732:     VecAssemblyEnd(mfqP->Xhist[mfqP->nHist]);

    734:     TaoComputeSeparableObjective(tao,mfqP->Xhist[mfqP->nHist],mfqP->Fhist[mfqP->nHist]);
    735:     VecNorm(mfqP->Fhist[mfqP->nHist],NORM_2,&mfqP->Fres[mfqP->nHist]);
    736:     if (PetscIsInfOrNanReal(mfqP->Fres[mfqP->nHist])) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
    737:     mfqP->Fres[mfqP->nHist]*=mfqP->Fres[mfqP->nHist];
    738:     rho = (mfqP->Fres[mfqP->minindex] - mfqP->Fres[mfqP->nHist]) / mdec;
    739:     mfqP->nHist++;

    741:     /* Update the center */
    742:     if ((rho >= mfqP->eta1) || (rho > mfqP->eta0 && valid==PETSC_TRUE)) {
    743:       /* Update model to reflect new base point */
    744:       for (i=0;i<mfqP->n;i++) {
    745:         mfqP->work[i] = (mfqP->work[i] - mfqP->xmin[i])/mfqP->delta;
    746:       }
    747:       for (j=0;j<mfqP->m;j++) {
    748:         /* C(j) = C(j) + work*G(:,j) + .5*work*H(:,:,j)*work';
    749:          G(:,j) = G(:,j) + H(:,:,j)*work' */
    750:         for (k=0;k<mfqP->n;k++) {
    751:           mfqP->work2[k]=0.0;
    752:           for (l=0;l<mfqP->n;l++) {
    753:             mfqP->work2[k]+=mfqP->H[j + mfqP->m*(k + l*mfqP->n)]*mfqP->work[l];
    754:           }
    755:         }
    756:         for (i=0;i<mfqP->n;i++) {
    757:           mfqP->C[j]+=mfqP->work[i]*(mfqP->Fdiff[i + mfqP->n* j] + 0.5*mfqP->work2[i]);
    758:           mfqP->Fdiff[i+mfqP->n*j] +=mfqP-> work2[i];
    759:         }
    760:       }
    761:       /* Cres += work*Gres + .5*work*Hres*work';
    762:        Gres += Hres*work'; */

    764:       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&one,mfqP->Hres,&blasn,mfqP->work,&ione,&zero,mfqP->work2,&ione));
    765:       for (i=0;i<mfqP->n;i++) {
    766:         cres += mfqP->work[i]*(mfqP->Gres[i]  + 0.5*mfqP->work2[i]);
    767:         mfqP->Gres[i] += mfqP->work2[i];
    768:       }
    769:       mfqP->minindex = mfqP->nHist-1;
    770:       minnorm = mfqP->Fres[mfqP->minindex];
    771:       VecCopy(mfqP->Fhist[mfqP->minindex],tao->sep_objective);
    772:       /* Change current center */
    773:       VecGetArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
    774:       for (i=0;i<mfqP->n;i++) {
    775:         mfqP->xmin[i] = xmint[i];
    776:       }
    777:       VecRestoreArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
    778:     }

    780:     /* Evaluate at a model-improving point if necessary */
    781:     if (valid == PETSC_FALSE) {
    782:       mfqP->q_is_I = 1;
    783:       mfqP->nmodelpoints = 0;
    784:       affpoints(mfqP,mfqP->xmin,mfqP->c1);
    785:       if (mfqP->nmodelpoints < mfqP->n) {
    786:         PetscInfo(tao,"Model not valid -- model-improving\n");
    787:         modelimprove(tao,mfqP,1);
    788:       }
    789:     }

    791:     /* Update the trust region radius */
    792:     deltaold = mfqP->delta;
    793:     normxsp = 0;
    794:     for (i=0;i<mfqP->n;i++) {
    795:       normxsp += mfqP->Xsubproblem[i]*mfqP->Xsubproblem[i];
    796:     }
    797:     normxsp = PetscSqrtReal(normxsp);
    798:     if (rho >= mfqP->eta1 && normxsp > 0.5*mfqP->delta) {
    799:       mfqP->delta = PetscMin(mfqP->delta*mfqP->gamma1,mfqP->deltamax);
    800:     } else if (valid == PETSC_TRUE) {
    801:       mfqP->delta = PetscMax(mfqP->delta*mfqP->gamma0,mfqP->deltamin);
    802:     }

    804:     /* Compute the next interpolation set */
    805:     mfqP->q_is_I = 1;
    806:     mfqP->nmodelpoints=0;
    807:     affpoints(mfqP,mfqP->xmin,mfqP->c1);
    808:     if (mfqP->nmodelpoints == mfqP->n) {
    809:       valid = PETSC_TRUE;
    810:     } else {
    811:       valid = PETSC_FALSE;
    812:       affpoints(mfqP,mfqP->xmin,mfqP->c2);
    813:       if (mfqP->n > mfqP->nmodelpoints) {
    814:         PetscInfo(tao,"Model not valid -- adding geometry points\n");
    815:         modelimprove(tao,mfqP,mfqP->n - mfqP->nmodelpoints);
    816:       }
    817:     }
    818:     for (i=mfqP->nmodelpoints;i>0;i--) {
    819:       mfqP->model_indices[i] = mfqP->model_indices[i-1];
    820:     }
    821:     mfqP->nmodelpoints++;
    822:     mfqP->model_indices[0] = mfqP->minindex;
    823:     morepoints(mfqP);
    824:     for (i=0;i<mfqP->nmodelpoints;i++) {
    825:       VecGetArray(mfqP->Xhist[mfqP->model_indices[i]],&x);
    826:       for (j=0;j<mfqP->n;j++) {
    827:         mfqP->Disp[i + mfqP->npmax*j] = (x[j]  - mfqP->xmin[j]) / deltaold;
    828:       }
    829:       VecRestoreArray(mfqP->Xhist[mfqP->model_indices[i]],&x);
    830:       VecGetArray(mfqP->Fhist[mfqP->model_indices[i]],&f);
    831:       for (j=0;j<mfqP->m;j++) {
    832:         for (k=0;k<mfqP->n;k++)  {
    833:           mfqP->work[k]=0.0;
    834:           for (l=0;l<mfqP->n;l++) {
    835:             mfqP->work[k] += mfqP->H[j + mfqP->m*(k + mfqP->n*l)] * mfqP->Disp[i + mfqP->npmax*l];
    836:           }
    837:         }
    838:         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];
    839:       }
    840:       VecRestoreArray(mfqP->Fhist[mfqP->model_indices[i]],&f);
    841:     }

    843:     /* Update the quadratic model */
    844:     getquadpounders(mfqP);
    845:     VecGetArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);
    846:     PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasm,fmin,&ione,mfqP->C,&ione));
    847:     /* G = G*(delta/deltaold) + Gdel */
    848:     ratio = mfqP->delta/deltaold;
    849:     iblas = blasm*blasn;
    850:     PetscStackCallBLAS("BLASscal",BLASscal_(&iblas,&ratio,mfqP->Fdiff,&ione));
    851:     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&one,mfqP->Gdel,&ione,mfqP->Fdiff,&ione));
    852:     /* H = H*(delta/deltaold) + Hdel */
    853:     iblas = blasm*blasn*blasn;
    854:     ratio *= ratio;
    855:     PetscStackCallBLAS("BLASscal",BLASscal_(&iblas,&ratio,mfqP->H,&ione));
    856:     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&one,mfqP->Hdel,&ione,mfqP->H,&ione));

    858:     /* Get residuals */
    859:     cres = mfqP->Fres[mfqP->minindex];
    860:     /* Gres = G*F(xkin,1:m)' */
    861:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasm,&one,mfqP->Fdiff,&blasn,mfqP->C,&ione,&zero,mfqP->Gres,&ione));
    862:     /* Hres = sum i=1..m {F(xkin,i)*H(:,:,i)}   + G*G' */
    863:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","T",&blasn,&blasn,&blasm,&one,mfqP->Fdiff,&blasn,mfqP->Fdiff,&blasn,&zero,mfqP->Hres,&blasn));

    865:     iblas = mfqP->n*mfqP->n;

    867:     for (j=0;j<mfqP->m;j++) {
    868:       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&fmin[j],&mfqP->H[j],&blasm,mfqP->Hres,&ione));
    869:     }

    871:     /* Export solution and gradient residual to TAO */
    872:     VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);
    873:     VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);
    874:     VecAssemblyBegin(tao->gradient);
    875:     VecAssemblyEnd(tao->gradient);
    876:     VecNorm(tao->gradient,NORM_2,&gnorm);
    877:     gnorm *= mfqP->delta;
    878:     /*  final criticality test */
    879:     TaoMonitor(tao, tao->niter, minnorm, gnorm, 0.0, step, &reason);
    880:     /* test for repeated model */
    881:     if (mfqP->nmodelpoints==mfqP->last_nmodelpoints) {
    882:       same = PETSC_TRUE;
    883:     } else {
    884:       same = PETSC_FALSE;
    885:     }
    886:     for (i=0;i<mfqP->nmodelpoints;i++) {
    887:       if (same) {
    888:         if (mfqP->model_indices[i] == mfqP->last_model_indices[i]) {
    889:           same = PETSC_TRUE;
    890:         } else {
    891:           same = PETSC_FALSE;
    892:         }
    893:       }
    894:       mfqP->last_model_indices[i] = mfqP->model_indices[i];
    895:     }
    896:     mfqP->last_nmodelpoints = mfqP->nmodelpoints;
    897:     if (same && mfqP->delta == deltaold) {
    898:       PetscInfo(tao,"Identical model used in successive iterations\n");
    899:       reason = TAO_CONVERGED_STEPTOL;
    900:       tao->reason = TAO_CONVERGED_STEPTOL;
    901:     }
    902:   }
    903:   return(0);
    904: }

    908: static PetscErrorCode TaoSetUp_POUNDERS(Tao tao)
    909: {
    910:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
    911:   PetscInt       i;
    912:   IS             isfloc,isfglob,isxloc,isxglob;

    916:   if (!tao->gradient) {VecDuplicate(tao->solution,&tao->gradient);  }
    917:   if (!tao->stepdirection) {VecDuplicate(tao->solution,&tao->stepdirection);  }
    918:   VecGetSize(tao->solution,&mfqP->n);
    919:   VecGetSize(tao->sep_objective,&mfqP->m);
    920:   mfqP->c1 = PetscSqrtReal((PetscReal)mfqP->n);
    921:   if (mfqP->npmax == PETSC_DEFAULT) {
    922:     mfqP->npmax = 2*mfqP->n + 1;
    923:   }
    924:   mfqP->npmax = PetscMin((mfqP->n+1)*(mfqP->n+2)/2,mfqP->npmax);
    925:   mfqP->npmax = PetscMax(mfqP->npmax, mfqP->n+2);

    927:   PetscMalloc1(tao->max_funcs+10,&mfqP->Xhist);
    928:   PetscMalloc1(tao->max_funcs+10,&mfqP->Fhist);
    929:   for (i=0;i<mfqP->n +1;i++) {
    930:     VecDuplicate(tao->solution,&mfqP->Xhist[i]);
    931:     VecDuplicate(tao->sep_objective,&mfqP->Fhist[i]);
    932:   }
    933:   VecDuplicate(tao->solution,&mfqP->workxvec);
    934:   mfqP->nHist = 0;

    936:   PetscMalloc1(tao->max_funcs+10,&mfqP->Fres);
    937:   PetscMalloc1(mfqP->npmax*mfqP->m,&mfqP->RES);
    938:   PetscMalloc1(mfqP->n,&mfqP->work);
    939:   PetscMalloc1(mfqP->n,&mfqP->work2);
    940:   PetscMalloc1(mfqP->n,&mfqP->work3);
    941:   PetscMalloc1(PetscMax(mfqP->m,mfqP->n+1),&mfqP->mwork);
    942:   PetscMalloc1(mfqP->npmax - mfqP->n - 1,&mfqP->omega);
    943:   PetscMalloc1(mfqP->n * (mfqP->n+1) / 2,&mfqP->beta);
    944:   PetscMalloc1(mfqP->n + 1 ,&mfqP->alpha);

    946:   PetscMalloc1(mfqP->n*mfqP->n*mfqP->m,&mfqP->H);
    947:   PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q);
    948:   PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q_tmp);
    949:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L);
    950:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_tmp);
    951:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_save);
    952:   PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->N);
    953:   PetscMalloc1(mfqP->npmax * (mfqP->n+1) ,&mfqP->M);
    954:   PetscMalloc1(mfqP->npmax * (mfqP->npmax - mfqP->n - 1) , &mfqP->Z);
    955:   PetscMalloc1(mfqP->npmax,&mfqP->tau);
    956:   PetscMalloc1(mfqP->npmax,&mfqP->tau_tmp);
    957:   mfqP->nmax = PetscMax(5*mfqP->npmax,mfqP->n*(mfqP->n+1)/2);
    958:   PetscMalloc1(mfqP->nmax,&mfqP->npmaxwork);
    959:   PetscMalloc1(mfqP->nmax,&mfqP->npmaxiwork);
    960:   PetscMalloc1(mfqP->n,&mfqP->xmin);
    961:   PetscMalloc1(mfqP->m,&mfqP->C);
    962:   PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Fdiff);
    963:   PetscMalloc1(mfqP->npmax*mfqP->n,&mfqP->Disp);
    964:   PetscMalloc1(mfqP->n,&mfqP->Gres);
    965:   PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Hres);
    966:   PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Gpoints);
    967:   PetscMalloc1(mfqP->npmax,&mfqP->model_indices);
    968:   PetscMalloc1(mfqP->npmax,&mfqP->last_model_indices);
    969:   PetscMalloc1(mfqP->n,&mfqP->Xsubproblem);
    970:   PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Gdel);
    971:   PetscMalloc1(mfqP->n*mfqP->n*mfqP->m, &mfqP->Hdel);
    972:   PetscMalloc1(PetscMax(mfqP->m,mfqP->n),&mfqP->indices);
    973:   PetscMalloc1(mfqP->n,&mfqP->iwork);
    974:   for (i=0;i<PetscMax(mfqP->m,mfqP->n);i++) {
    975:     mfqP->indices[i] = i;
    976:   }
    977:   MPI_Comm_size(((PetscObject)tao)->comm,&mfqP->size);
    978:   if (mfqP->size > 1) {
    979:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localx);
    980:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localxmin);
    981:     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localf);
    982:     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localfmin);
    983:     ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxloc);
    984:     ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxglob);
    985:     ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfloc);
    986:     ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfglob);

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

    992:     ISDestroy(&isxloc);
    993:     ISDestroy(&isxglob);
    994:     ISDestroy(&isfloc);
    995:     ISDestroy(&isfglob);
    996:   }

    998:   if (!mfqP->usegqt) {
    999:     KSP       ksp;
    1000:     PC        pc;
    1001:     VecCreateSeqWithArray(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Xsubproblem,&mfqP->subx);
    1002:     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->subxl);
    1003:     VecDuplicate(mfqP->subxl,&mfqP->subb);
    1004:     VecDuplicate(mfqP->subxl,&mfqP->subxu);
    1005:     VecDuplicate(mfqP->subxl,&mfqP->subpdel);
    1006:     VecDuplicate(mfqP->subxl,&mfqP->subndel);
    1007:     TaoCreate(PETSC_COMM_SELF,&mfqP->subtao);
    1008:     TaoSetType(mfqP->subtao,TAOTRON);
    1009:     TaoSetOptionsPrefix(mfqP->subtao,"pounders_subsolver_");
    1010:     TaoSetInitialVector(mfqP->subtao,mfqP->subx);
    1011:     TaoSetObjectiveAndGradientRoutine(mfqP->subtao,pounders_fg,(void*)mfqP);
    1012:     TaoSetMaximumIterations(mfqP->subtao,mfqP->gqt_maxits);
    1013:     TaoSetFromOptions(mfqP->subtao);
    1014:     TaoGetKSP(mfqP->subtao,&ksp);
    1015:     if (ksp) {
    1016:       KSPGetPC(ksp,&pc);
    1017:       PCSetType(pc,PCNONE);
    1018:     }
    1019:     TaoSetVariableBounds(mfqP->subtao,mfqP->subxl,mfqP->subxu);
    1020:     MatCreateSeqDense(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Hres,&mfqP->subH);
    1021:     TaoSetHessianRoutine(mfqP->subtao,mfqP->subH,mfqP->subH,pounders_h,(void*)mfqP);
    1022:   }
    1023:   return(0);
    1024: }

    1028: static PetscErrorCode TaoDestroy_POUNDERS(Tao tao)
    1029: {
    1030:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
    1031:   PetscInt       i;

    1035:   if (!mfqP->usegqt) {
    1036:     TaoDestroy(&mfqP->subtao);
    1037:     VecDestroy(&mfqP->subx);
    1038:     VecDestroy(&mfqP->subxl);
    1039:     VecDestroy(&mfqP->subxu);
    1040:     VecDestroy(&mfqP->subb);
    1041:     VecDestroy(&mfqP->subpdel);
    1042:     VecDestroy(&mfqP->subndel);
    1043:     MatDestroy(&mfqP->subH);
    1044:   }
    1045:   PetscFree(mfqP->Fres);
    1046:   PetscFree(mfqP->RES);
    1047:   PetscFree(mfqP->work);
    1048:   PetscFree(mfqP->work2);
    1049:   PetscFree(mfqP->work3);
    1050:   PetscFree(mfqP->mwork);
    1051:   PetscFree(mfqP->omega);
    1052:   PetscFree(mfqP->beta);
    1053:   PetscFree(mfqP->alpha);
    1054:   PetscFree(mfqP->H);
    1055:   PetscFree(mfqP->Q);
    1056:   PetscFree(mfqP->Q_tmp);
    1057:   PetscFree(mfqP->L);
    1058:   PetscFree(mfqP->L_tmp);
    1059:   PetscFree(mfqP->L_save);
    1060:   PetscFree(mfqP->N);
    1061:   PetscFree(mfqP->M);
    1062:   PetscFree(mfqP->Z);
    1063:   PetscFree(mfqP->tau);
    1064:   PetscFree(mfqP->tau_tmp);
    1065:   PetscFree(mfqP->npmaxwork);
    1066:   PetscFree(mfqP->npmaxiwork);
    1067:   PetscFree(mfqP->xmin);
    1068:   PetscFree(mfqP->C);
    1069:   PetscFree(mfqP->Fdiff);
    1070:   PetscFree(mfqP->Disp);
    1071:   PetscFree(mfqP->Gres);
    1072:   PetscFree(mfqP->Hres);
    1073:   PetscFree(mfqP->Gpoints);
    1074:   PetscFree(mfqP->model_indices);
    1075:   PetscFree(mfqP->last_model_indices);
    1076:   PetscFree(mfqP->Xsubproblem);
    1077:   PetscFree(mfqP->Gdel);
    1078:   PetscFree(mfqP->Hdel);
    1079:   PetscFree(mfqP->indices);
    1080:   PetscFree(mfqP->iwork);

    1082:   for (i=0;i<mfqP->nHist;i++) {
    1083:     VecDestroy(&mfqP->Xhist[i]);
    1084:     VecDestroy(&mfqP->Fhist[i]);
    1085:   }
    1086:   if (mfqP->workxvec) {
    1087:     VecDestroy(&mfqP->workxvec);
    1088:   }
    1089:   PetscFree(mfqP->Xhist);
    1090:   PetscFree(mfqP->Fhist);

    1092:   if (mfqP->size > 1) {
    1093:     VecDestroy(&mfqP->localx);
    1094:     VecDestroy(&mfqP->localxmin);
    1095:     VecDestroy(&mfqP->localf);
    1096:     VecDestroy(&mfqP->localfmin);
    1097:   }
    1098:   PetscFree(tao->data);
    1099:   return(0);
    1100: }

    1104: static PetscErrorCode TaoSetFromOptions_POUNDERS(PetscOptions *PetscOptionsObject,Tao tao)
    1105: {
    1106:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;

    1110:   PetscOptionsHead(PetscOptionsObject,"POUNDERS method for least-squares optimization");
    1111:   PetscOptionsReal("-tao_pounders_delta","initial delta","",mfqP->delta,&mfqP->delta0,NULL);
    1112:   mfqP->delta = mfqP->delta0;
    1113:   mfqP->npmax = PETSC_DEFAULT;
    1114:   PetscOptionsInt("-tao_pounders_npmax","max number of points in model","",mfqP->npmax,&mfqP->npmax,NULL);
    1115:   mfqP->usegqt = PETSC_FALSE;
    1116:   PetscOptionsBool("-tao_pounders_gqt","use gqt algorithm for subproblem","",mfqP->usegqt,&mfqP->usegqt,NULL);
    1117:   PetscOptionsTail();
    1118:   return(0);
    1119: }

    1123: static PetscErrorCode TaoView_POUNDERS(Tao tao, PetscViewer viewer)
    1124: {
    1125:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS *)tao->data;
    1126:   PetscBool      isascii;
    1127:   PetscInt       nits;

    1131:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    1132:   if (isascii) {
    1133:     PetscViewerASCIIPushTab(viewer);
    1134:     PetscViewerASCIIPrintf(viewer, "initial delta: %g\n",(double)mfqP->delta0);
    1135:     PetscViewerASCIIPrintf(viewer, "final delta: %g\n",(double)mfqP->delta);
    1136:     PetscViewerASCIIPrintf(viewer, "model points: %D\n",mfqP->nmodelpoints);
    1137:     if (mfqP->usegqt) {
    1138:       PetscViewerASCIIPrintf(viewer, "subproblem solver: gqt\n");
    1139:     } else {
    1140:       PetscViewerASCIIPrintf(viewer, "subproblem solver: %s\n",((PetscObject)mfqP->subtao)->type_name);
    1141:       TaoGetTotalIterationNumber(mfqP->subtao,&nits);
    1142:       PetscViewerASCIIPrintf(viewer, "total subproblem iterations: %D\n",nits);
    1143:     }
    1144:     PetscViewerASCIIPopTab(viewer);
    1145:   }
    1146:   return(0);
    1147: }
    1148: /*MC
    1149:   TAOPOUNDERS - POUNDERS derivate-free model-based algorithm for nonlinear least squares

    1151:   Options Database Keys:
    1152: + -tao_pounders_delta - initial step length
    1153: . -tao_pounders_npmax - maximum number of points in model
    1154: - -tao_pounders_gqt - use gqt algorithm for subproblem instead of TRON

    1156:   Level: beginner
    1157:
    1158: M*/

    1162: PETSC_EXTERN PetscErrorCode TaoCreate_POUNDERS(Tao tao)
    1163: {
    1164:   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;

    1168:   tao->ops->setup = TaoSetUp_POUNDERS;
    1169:   tao->ops->solve = TaoSolve_POUNDERS;
    1170:   tao->ops->view = TaoView_POUNDERS;
    1171:   tao->ops->setfromoptions = TaoSetFromOptions_POUNDERS;
    1172:   tao->ops->destroy = TaoDestroy_POUNDERS;

    1174:   PetscNewLog(tao,&mfqP);
    1175:   tao->data = (void*)mfqP;
    1176:   /* Override default settings (unless already changed) */
    1177:   if (!tao->max_it_changed) tao->max_it = 2000;
    1178:   if (!tao->max_funcs_changed) tao->max_funcs = 4000;
    1179: #if defined(PETSC_USE_REAL_SINGLE)
    1180:   if (!tao->fatol_changed) tao->fatol = 1.0e-4;
    1181:   if (!tao->frtol_changed) tao->frtol = 1.0e-4;
    1182:   mfqP->deltamin=1e-3;
    1183: #else
    1184:   if (!tao->fatol_changed) tao->fatol = 1.0e-8;
    1185:   if (!tao->frtol_changed) tao->frtol = 1.0e-8;
    1186:   mfqP->deltamin=1e-6;
    1187: #endif
    1188:   mfqP->delta0 = 0.1;
    1189:   mfqP->delta = 0.1;
    1190:   mfqP->deltamax=1e3;
    1191:   mfqP->c2 = 100.0;
    1192:   mfqP->theta1=1e-5;
    1193:   mfqP->theta2=1e-4;
    1194:   mfqP->gamma0=0.5;
    1195:   mfqP->gamma1=2.0;
    1196:   mfqP->eta0 = 0.0;
    1197:   mfqP->eta1 = 0.1;
    1198:   mfqP->gqt_rtol = 0.001;
    1199:   mfqP->gqt_maxits = 50;
    1200:   mfqP->workxvec = 0;
    1201:   return(0);
    1202: }