Date: 2022-08-02T03:15:12+00:00

Actual source code: pdipm.c

      1: #include <../src/tao/constrained/impls/ipm/pdipm.h>

      3: /*
      4:    TaoPDIPMEvaluateFunctionsAndJacobians - Evaluate the objective function f, gradient fx, constraints, and all the Jacobians at current vector

      6:    Collective on tao

      8:    Input Parameter:
      9: +  tao - solver context
     10: -  x - vector at which all objects to be evaluated

     12:    Level: beginner

     14: .seealso: TaoPDIPMUpdateConstraints(), TaoPDIPMSetUpBounds()
     15: */
     16: static PetscErrorCode TaoPDIPMEvaluateFunctionsAndJacobians(Tao tao,Vec x)
     17: {
     18:   TAO_PDIPM      *pdipm=(TAO_PDIPM*)tao->data;

     20:   /* Compute user objective function and gradient */
     21:   TaoComputeObjectiveAndGradient(tao,x,&pdipm->obj,tao->gradient);

     23:   /* Equality constraints and Jacobian */
     24:   if (pdipm->Ng) {
     25:     TaoComputeEqualityConstraints(tao,x,tao->constraints_equality);
     26:     TaoComputeJacobianEquality(tao,x,tao->jacobian_equality,tao->jacobian_equality_pre);
     27:   }

     29:   /* Inequality constraints and Jacobian */
     30:   if (pdipm->Nh) {
     31:     TaoComputeInequalityConstraints(tao,x,tao->constraints_inequality);
     32:     TaoComputeJacobianInequality(tao,x,tao->jacobian_inequality,tao->jacobian_inequality_pre);
     33:   }
     34:   return 0;
     35: }

     37: /*
     38:   TaoPDIPMUpdateConstraints - Update the vectors ce and ci at x

     40:   Collective

     42:   Input Parameter:
     43: + tao - Tao context
     44: - x - vector at which constraints to be evaluated

     46:    Level: beginner

     48: .seealso: TaoPDIPMEvaluateFunctionsAndJacobians()
     49: */
     50: static PetscErrorCode TaoPDIPMUpdateConstraints(Tao tao,Vec x)
     51: {
     52:   TAO_PDIPM         *pdipm=(TAO_PDIPM*)tao->data;
     53:   PetscInt          i,offset,offset1,k,xstart;
     54:   PetscScalar       *carr;
     55:   const PetscInt    *ubptr,*lbptr,*bxptr,*fxptr;
     56:   const PetscScalar *xarr,*xuarr,*xlarr,*garr,*harr;

     58:   VecGetOwnershipRange(x,&xstart,NULL);

     60:   VecGetArrayRead(x,&xarr);
     61:   VecGetArrayRead(tao->XU,&xuarr);
     62:   VecGetArrayRead(tao->XL,&xlarr);

     64:   /* (1) Update ce vector */
     65:   VecGetArrayWrite(pdipm->ce,&carr);

     67:   if (pdipm->Ng) {
     68:     /* (1.a) Inserting updated g(x) */
     69:     VecGetArrayRead(tao->constraints_equality,&garr);
     70:     PetscMemcpy(carr,garr,pdipm->ng*sizeof(PetscScalar));
     71:     VecRestoreArrayRead(tao->constraints_equality,&garr);
     72:   }

     74:   /* (1.b) Update xfixed */
     75:   if (pdipm->Nxfixed) {
     76:     offset = pdipm->ng;
     77:     ISGetIndices(pdipm->isxfixed,&fxptr); /* global indices in x */
     78:     for (k=0;k < pdipm->nxfixed;k++) {
     79:       i = fxptr[k]-xstart;
     80:       carr[offset + k] = xarr[i] - xuarr[i];
     81:     }
     82:   }
     83:   VecRestoreArrayWrite(pdipm->ce,&carr);

     85:   /* (2) Update ci vector */
     86:   VecGetArrayWrite(pdipm->ci,&carr);

     88:   if (pdipm->Nh) {
     89:     /* (2.a) Inserting updated h(x) */
     90:     VecGetArrayRead(tao->constraints_inequality,&harr);
     91:     PetscMemcpy(carr,harr,pdipm->nh*sizeof(PetscScalar));
     92:     VecRestoreArrayRead(tao->constraints_inequality,&harr);
     93:   }

     95:   /* (2.b) Update xub */
     96:   offset = pdipm->nh;
     97:   if (pdipm->Nxub) {
     98:     ISGetIndices(pdipm->isxub,&ubptr);
     99:     for (k=0; k<pdipm->nxub; k++) {
    100:       i = ubptr[k]-xstart;
    101:       carr[offset + k] = xuarr[i] - xarr[i];
    102:     }
    103:   }

    105:   if (pdipm->Nxlb) {
    106:     /* (2.c) Update xlb */
    107:     offset += pdipm->nxub;
    108:     ISGetIndices(pdipm->isxlb,&lbptr); /* global indices in x */
    109:     for (k=0; k<pdipm->nxlb; k++) {
    110:       i = lbptr[k]-xstart;
    111:       carr[offset + k] = xarr[i] - xlarr[i];
    112:     }
    113:   }

    115:   if (pdipm->Nxbox) {
    116:     /* (2.d) Update xbox */
    117:     offset += pdipm->nxlb;
    118:     offset1 = offset + pdipm->nxbox;
    119:     ISGetIndices(pdipm->isxbox,&bxptr); /* global indices in x */
    120:     for (k=0; k<pdipm->nxbox; k++) {
    121:       i = bxptr[k]-xstart; /* local indices in x */
    122:       carr[offset+k]  = xuarr[i] - xarr[i];
    123:       carr[offset1+k] = xarr[i]  - xlarr[i];
    124:     }
    125:   }
    126:   VecRestoreArrayWrite(pdipm->ci,&carr);

    128:   /* Restoring Vectors */
    129:   VecRestoreArrayRead(x,&xarr);
    130:   VecRestoreArrayRead(tao->XU,&xuarr);
    131:   VecRestoreArrayRead(tao->XL,&xlarr);
    132:   return 0;
    133: }

    135: /*
    136:    TaoPDIPMSetUpBounds - Create upper and lower bound vectors of x

    138:    Collective

    140:    Input Parameter:
    141: .  tao - holds pdipm and XL & XU

    143:    Level: beginner

    145: .seealso: TaoPDIPMUpdateConstraints
    146: */
    147: static PetscErrorCode TaoPDIPMSetUpBounds(Tao tao)
    148: {
    149:   TAO_PDIPM         *pdipm=(TAO_PDIPM*)tao->data;
    150:   const PetscScalar *xl,*xu;
    151:   PetscInt          n,*ixlb,*ixub,*ixfixed,*ixfree,*ixbox,i,low,high,idx;
    152:   MPI_Comm          comm;
    153:   PetscInt          sendbuf[5],recvbuf[5];

    155:   /* Creates upper and lower bounds vectors on x, if not created already */
    156:   TaoComputeVariableBounds(tao);

    158:   VecGetLocalSize(tao->XL,&n);
    159:   PetscMalloc5(n,&ixlb,n,&ixub,n,&ixfree,n,&ixfixed,n,&ixbox);

    161:   VecGetOwnershipRange(tao->XL,&low,&high);
    162:   VecGetArrayRead(tao->XL,&xl);
    163:   VecGetArrayRead(tao->XU,&xu);
    164:   for (i=0; i<n; i++) {
    165:     idx = low + i;
    166:     if ((PetscRealPart(xl[i]) > PETSC_NINFINITY) && (PetscRealPart(xu[i]) < PETSC_INFINITY)) {
    167:       if (PetscRealPart(xl[i]) == PetscRealPart(xu[i])) {
    168:         ixfixed[pdipm->nxfixed++]  = idx;
    169:       } else ixbox[pdipm->nxbox++] = idx;
    170:     } else {
    171:       if ((PetscRealPart(xl[i]) > PETSC_NINFINITY) && (PetscRealPart(xu[i]) >= PETSC_INFINITY)) {
    172:         ixlb[pdipm->nxlb++] = idx;
    173:       } else if ((PetscRealPart(xl[i]) <= PETSC_NINFINITY) && (PetscRealPart(xu[i]) < PETSC_INFINITY)) {
    174:         ixub[pdipm->nxlb++] = idx;
    175:       } else  ixfree[pdipm->nxfree++] = idx;
    176:     }
    177:   }
    178:   VecRestoreArrayRead(tao->XL,&xl);
    179:   VecRestoreArrayRead(tao->XU,&xu);

    181:   PetscObjectGetComm((PetscObject)tao,&comm);
    182:   sendbuf[0] = pdipm->nxlb;
    183:   sendbuf[1] = pdipm->nxub;
    184:   sendbuf[2] = pdipm->nxfixed;
    185:   sendbuf[3] = pdipm->nxbox;
    186:   sendbuf[4] = pdipm->nxfree;

    188:   MPI_Allreduce(sendbuf,recvbuf,5,MPIU_INT,MPI_SUM,comm);
    189:   pdipm->Nxlb    = recvbuf[0];
    190:   pdipm->Nxub    = recvbuf[1];
    191:   pdipm->Nxfixed = recvbuf[2];
    192:   pdipm->Nxbox   = recvbuf[3];
    193:   pdipm->Nxfree  = recvbuf[4];

    195:   if (pdipm->Nxlb) {
    196:     ISCreateGeneral(comm,pdipm->nxlb,ixlb,PETSC_COPY_VALUES,&pdipm->isxlb);
    197:   }
    198:   if (pdipm->Nxub) {
    199:     ISCreateGeneral(comm,pdipm->nxub,ixub,PETSC_COPY_VALUES,&pdipm->isxub);
    200:   }
    201:   if (pdipm->Nxfixed) {
    202:     ISCreateGeneral(comm,pdipm->nxfixed,ixfixed,PETSC_COPY_VALUES,&pdipm->isxfixed);
    203:   }
    204:   if (pdipm->Nxbox) {
    205:     ISCreateGeneral(comm,pdipm->nxbox,ixbox,PETSC_COPY_VALUES,&pdipm->isxbox);
    206:   }
    207:   if (pdipm->Nxfree) {
    208:     ISCreateGeneral(comm,pdipm->nxfree,ixfree,PETSC_COPY_VALUES,&pdipm->isxfree);
    209:   }
    210:   PetscFree5(ixlb,ixub,ixfixed,ixbox,ixfree);
    211:   return 0;
    212: }

    214: /*
    215:    TaoPDIPMInitializeSolution - Initialize PDIPM solution X = [x; lambdae; lambdai; z].
    216:    X consists of four subvectors in the order [x; lambdae; lambdai; z]. These
    217:      four subvectors need to be initialized and its values copied over to X. Instead
    218:      of copying, we use VecPlace/ResetArray functions to share the memory locations for
    219:      X and the subvectors

    221:    Collective

    223:    Input Parameter:
    224: .  tao - Tao context

    226:    Level: beginner
    227: */
    228: static PetscErrorCode TaoPDIPMInitializeSolution(Tao tao)
    229: {
    230:   TAO_PDIPM         *pdipm = (TAO_PDIPM*)tao->data;
    231:   PetscScalar       *Xarr,*z,*lambdai;
    232:   PetscInt          i;
    233:   const PetscScalar *xarr,*h;

    235:   VecGetArrayWrite(pdipm->X,&Xarr);

    237:   /* Set Initialize X.x = tao->solution */
    238:   VecGetArrayRead(tao->solution,&xarr);
    239:   PetscMemcpy(Xarr,xarr,pdipm->nx*sizeof(PetscScalar));
    240:   VecRestoreArrayRead(tao->solution,&xarr);

    242:   /* Initialize X.lambdae = 0.0 */
    243:   if (pdipm->lambdae) {
    244:     VecSet(pdipm->lambdae,0.0);
    245:   }

    247:   /* Initialize X.lambdai = push_init_lambdai, X.z = push_init_slack */
    248:   if (pdipm->Nci) {
    249:     VecSet(pdipm->lambdai,pdipm->push_init_lambdai);
    250:     VecSet(pdipm->z,pdipm->push_init_slack);

    252:     /* Additional modification for X.lambdai and X.z */
    253:     VecGetArrayWrite(pdipm->lambdai,&lambdai);
    254:     VecGetArrayWrite(pdipm->z,&z);
    255:     if (pdipm->Nh) {
    256:       VecGetArrayRead(tao->constraints_inequality,&h);
    257:       for (i=0; i < pdipm->nh; i++) {
    258:         if (h[i] < -pdipm->push_init_slack) z[i] = -h[i];
    259:         if (pdipm->mu/z[i] > pdipm->push_init_lambdai) lambdai[i] = pdipm->mu/z[i];
    260:       }
    261:       VecRestoreArrayRead(tao->constraints_inequality,&h);
    262:     }
    263:     VecRestoreArrayWrite(pdipm->lambdai,&lambdai);
    264:     VecRestoreArrayWrite(pdipm->z,&z);
    265:   }

    267:   VecRestoreArrayWrite(pdipm->X,&Xarr);
    268:   return 0;
    269: }

    271: /*
    272:    TaoSNESJacobian_PDIPM - Evaluate the Hessian matrix at X

    274:    Input Parameter:
    275:    snes - SNES context
    276:    X - KKT Vector
    277:    *ctx - pdipm context

    279:    Output Parameter:
    280:    J - Hessian matrix
    281:    Jpre - Preconditioner
    282: */
    283: static PetscErrorCode TaoSNESJacobian_PDIPM(SNES snes,Vec X, Mat J, Mat Jpre, void *ctx)
    284: {
    285:   Tao               tao=(Tao)ctx;
    286:   TAO_PDIPM         *pdipm = (TAO_PDIPM*)tao->data;
    287:   PetscInt          i,row,cols[2],Jrstart,rjstart,nc,j;
    288:   const PetscInt    *aj,*ranges,*Jranges,*rranges,*cranges;
    289:   const PetscScalar *Xarr,*aa;
    290:   PetscScalar       vals[2];
    291:   PetscInt          proc,nx_all,*nce_all=pdipm->nce_all;
    292:   MPI_Comm          comm;
    293:   PetscMPIInt       rank,size;
    294:   Mat               jac_equality_trans=pdipm->jac_equality_trans,jac_inequality_trans=pdipm->jac_inequality_trans;

    296:   PetscObjectGetComm((PetscObject)snes,&comm);
    297:   MPI_Comm_rank(comm,&rank);
    298:   MPI_Comm_rank(comm,&size);

    300:   MatGetOwnershipRanges(Jpre,&Jranges);
    301:   MatGetOwnershipRange(Jpre,&Jrstart,NULL);
    302:   MatGetOwnershipRangesColumn(tao->hessian,&rranges);
    303:   MatGetOwnershipRangesColumn(tao->hessian,&cranges);

    305:   VecGetArrayRead(X,&Xarr);

    307:   /* (1) insert Z and Ci to the 4th block of Jpre -- overwrite existing values */
    308:   if (pdipm->solve_symmetric_kkt) { /* 1 for eq 17 revised pdipm doc 0 for eq 18 (symmetric KKT) */
    309:     vals[0] = 1.0;
    310:     for (i=0; i < pdipm->nci; i++) {
    311:         row     = Jrstart + pdipm->off_z + i;
    312:         cols[0] = Jrstart + pdipm->off_lambdai + i;
    313:         cols[1] = row;
    314:         vals[1] = Xarr[pdipm->off_lambdai + i]/Xarr[pdipm->off_z + i];
    315:         MatSetValues(Jpre,1,&row,2,cols,vals,INSERT_VALUES);
    316:     }
    317:   } else {
    318:     for (i=0; i < pdipm->nci; i++) {
    319:       row     = Jrstart + pdipm->off_z + i;
    320:       cols[0] = Jrstart + pdipm->off_lambdai + i;
    321:       cols[1] = row;
    322:       vals[0] = Xarr[pdipm->off_z + i];
    323:       vals[1] = Xarr[pdipm->off_lambdai + i];
    324:       MatSetValues(Jpre,1,&row,2,cols,vals,INSERT_VALUES);
    325:     }
    326:   }

    328:   /* (2) insert 2nd row block of Jpre: [ grad g, 0, 0, 0] */
    329:   if (pdipm->Ng) {
    330:     MatGetOwnershipRange(tao->jacobian_equality,&rjstart,NULL);
    331:     for (i=0; i<pdipm->ng; i++) {
    332:       row = Jrstart + pdipm->off_lambdae + i;

    334:       MatGetRow(tao->jacobian_equality,i+rjstart,&nc,&aj,&aa);
    335:       proc = 0;
    336:       for (j=0; j < nc; j++) {
    337:         while (aj[j] >= cranges[proc+1]) proc++;
    338:         cols[0] = aj[j] - cranges[proc] + Jranges[proc];
    339:         MatSetValue(Jpre,row,cols[0],aa[j],INSERT_VALUES);
    340:       }
    341:       MatRestoreRow(tao->jacobian_equality,i+rjstart,&nc,&aj,&aa);
    342:       if (pdipm->kkt_pd) {
    343:         /* add shift \delta_c */
    344:         MatSetValue(Jpre,row,row,-pdipm->deltac,INSERT_VALUES);
    345:       }
    346:     }
    347:   }

    349:   /* (3) insert 3rd row block of Jpre: [ -grad h, 0, deltac, I] */
    350:   if (pdipm->Nh) {
    351:     MatGetOwnershipRange(tao->jacobian_inequality,&rjstart,NULL);
    352:     for (i=0; i < pdipm->nh; i++) {
    353:       row = Jrstart + pdipm->off_lambdai + i;
    354:       MatGetRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,&aa);
    355:       proc = 0;
    356:       for (j=0; j < nc; j++) {
    357:         while (aj[j] >= cranges[proc+1]) proc++;
    358:         cols[0] = aj[j] - cranges[proc] + Jranges[proc];
    359:         MatSetValue(Jpre,row,cols[0],-aa[j],INSERT_VALUES);
    360:       }
    361:       MatRestoreRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,&aa);
    362:       if (pdipm->kkt_pd) {
    363:         /* add shift \delta_c */
    364:         MatSetValue(Jpre,row,row,-pdipm->deltac,INSERT_VALUES);
    365:       }
    366:     }
    367:   }

    369:   /* (4) insert 1st row block of Jpre: [Wxx, grad g', -grad h', 0] */
    370:   if (pdipm->Ng) { /* grad g' */
    371:     MatTranspose(tao->jacobian_equality,MAT_REUSE_MATRIX,&jac_equality_trans);
    372:   }
    373:   if (pdipm->Nh) { /* grad h' */
    374:     MatTranspose(tao->jacobian_inequality,MAT_REUSE_MATRIX,&jac_inequality_trans);
    375:   }

    377:   VecPlaceArray(pdipm->x,Xarr);
    378:   TaoComputeHessian(tao,pdipm->x,tao->hessian,tao->hessian_pre);
    379:   VecResetArray(pdipm->x);

    381:   MatGetOwnershipRange(tao->hessian,&rjstart,NULL);
    382:   for (i=0; i<pdipm->nx; i++) {
    383:     row = Jrstart + i;

    385:     /* insert Wxx = fxx + ... -- provided by user */
    386:     MatGetRow(tao->hessian,i+rjstart,&nc,&aj,&aa);
    387:     proc = 0;
    388:     for (j=0; j < nc; j++) {
    389:       while (aj[j] >= cranges[proc+1]) proc++;
    390:       cols[0] = aj[j] - cranges[proc] + Jranges[proc];
    391:       if (row == cols[0] && pdipm->kkt_pd) {
    392:         /* add shift deltaw to Wxx component */
    393:         MatSetValue(Jpre,row,cols[0],aa[j]+pdipm->deltaw,INSERT_VALUES);
    394:       } else {
    395:         MatSetValue(Jpre,row,cols[0],aa[j],INSERT_VALUES);
    396:       }
    397:     }
    398:     MatRestoreRow(tao->hessian,i+rjstart,&nc,&aj,&aa);

    400:     /* insert grad g' */
    401:     if (pdipm->ng) {
    402:       MatGetRow(jac_equality_trans,i+rjstart,&nc,&aj,&aa);
    403:       MatGetOwnershipRanges(tao->jacobian_equality,&ranges);
    404:       proc = 0;
    405:       for (j=0; j < nc; j++) {
    406:         /* find row ownership of */
    407:         while (aj[j] >= ranges[proc+1]) proc++;
    408:         nx_all = rranges[proc+1] - rranges[proc];
    409:         cols[0] = aj[j] - ranges[proc] + Jranges[proc] + nx_all;
    410:         MatSetValue(Jpre,row,cols[0],aa[j],INSERT_VALUES);
    411:       }
    412:       MatRestoreRow(jac_equality_trans,i+rjstart,&nc,&aj,&aa);
    413:     }

    415:     /* insert -grad h' */
    416:     if (pdipm->nh) {
    417:       MatGetRow(jac_inequality_trans,i+rjstart,&nc,&aj,&aa);
    418:       MatGetOwnershipRanges(tao->jacobian_inequality,&ranges);
    419:       proc = 0;
    420:       for (j=0; j < nc; j++) {
    421:         /* find row ownership of */
    422:         while (aj[j] >= ranges[proc+1]) proc++;
    423:         nx_all = rranges[proc+1] - rranges[proc];
    424:         cols[0] = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc];
    425:         MatSetValue(Jpre,row,cols[0],-aa[j],INSERT_VALUES);
    426:       }
    427:       MatRestoreRow(jac_inequality_trans,i+rjstart,&nc,&aj,&aa);
    428:     }
    429:   }
    430:   VecRestoreArrayRead(X,&Xarr);

    432:   /* (6) assemble Jpre and J */
    433:   MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);
    434:   MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);

    436:   if (J != Jpre) {
    437:     MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
    438:     MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
    439:   }
    440:   return 0;
    441: }

    443: /*
    444:    TaoSnesFunction_PDIPM - Evaluate KKT function at X

    446:    Input Parameter:
    447:    snes - SNES context
    448:    X - KKT Vector
    449:    *ctx - pdipm

    451:    Output Parameter:
    452:    F - Updated Lagrangian vector
    453: */
    454: static PetscErrorCode TaoSNESFunction_PDIPM(SNES snes,Vec X,Vec F,void *ctx)
    455: {
    456:   Tao               tao=(Tao)ctx;
    457:   TAO_PDIPM         *pdipm = (TAO_PDIPM*)tao->data;
    458:   PetscScalar       *Farr;
    459:   Vec               x,L1;
    460:   PetscInt          i;
    461:   const PetscScalar *Xarr,*carr,*zarr,*larr;

    463:   VecSet(F,0.0);

    465:   VecGetArrayRead(X,&Xarr);
    466:   VecGetArrayWrite(F,&Farr);

    468:   /* (0) Evaluate f, fx, gradG, gradH at X.x Note: pdipm->x is not changed below */
    469:   x = pdipm->x;
    470:   VecPlaceArray(x,Xarr);
    471:   TaoPDIPMEvaluateFunctionsAndJacobians(tao,x);

    473:   /* Update ce, ci, and Jci at X.x */
    474:   TaoPDIPMUpdateConstraints(tao,x);
    475:   VecResetArray(x);

    477:   /* (1) L1 = fx + (gradG'*DE + Jce_xfixed'*lambdae_xfixed) - (gradH'*DI + Jci_xb'*lambdai_xb) */
    478:   L1 = pdipm->x;
    479:   VecPlaceArray(L1,Farr); /* L1 = 0.0 */
    480:   if (pdipm->Nci) {
    481:     if (pdipm->Nh) {
    482:       /* L1 += gradH'*DI. Note: tao->DI is not changed below */
    483:       VecPlaceArray(tao->DI,Xarr+pdipm->off_lambdai);
    484:       MatMultTransposeAdd(tao->jacobian_inequality,tao->DI,L1,L1);
    485:       VecResetArray(tao->DI);
    486:     }

    488:     /* L1 += Jci_xb'*lambdai_xb */
    489:     VecPlaceArray(pdipm->lambdai_xb,Xarr+pdipm->off_lambdai+pdipm->nh);
    490:     MatMultTransposeAdd(pdipm->Jci_xb,pdipm->lambdai_xb,L1,L1);
    491:     VecResetArray(pdipm->lambdai_xb);

    493:     /* L1 = - (gradH'*DI + Jci_xb'*lambdai_xb) */
    494:     VecScale(L1,-1.0);
    495:   }

    497:   /* L1 += fx */
    498:   VecAXPY(L1,1.0,tao->gradient);

    500:   if (pdipm->Nce) {
    501:     if (pdipm->Ng) {
    502:       /* L1 += gradG'*DE. Note: tao->DE is not changed below */
    503:       VecPlaceArray(tao->DE,Xarr+pdipm->off_lambdae);
    504:       MatMultTransposeAdd(tao->jacobian_equality,tao->DE,L1,L1);
    505:       VecResetArray(tao->DE);
    506:     }
    507:     if (pdipm->Nxfixed) {
    508:       /* L1 += Jce_xfixed'*lambdae_xfixed */
    509:       VecPlaceArray(pdipm->lambdae_xfixed,Xarr+pdipm->off_lambdae+pdipm->ng);
    510:       MatMultTransposeAdd(pdipm->Jce_xfixed,pdipm->lambdae_xfixed,L1,L1);
    511:       VecResetArray(pdipm->lambdae_xfixed);
    512:     }
    513:   }
    514:   VecResetArray(L1);

    516:   /* (2) L2 = ce(x) */
    517:   if (pdipm->Nce) {
    518:     VecGetArrayRead(pdipm->ce,&carr);
    519:     for (i=0; i<pdipm->nce; i++) Farr[pdipm->off_lambdae + i] = carr[i];
    520:     VecRestoreArrayRead(pdipm->ce,&carr);
    521:   }

    523:   if (pdipm->Nci) {
    524:     if (pdipm->solve_symmetric_kkt) {
    525:       /* (3) L3 = z - ci(x);
    526:          (4) L4 = Lambdai * e - mu/z *e  */
    527:       VecGetArrayRead(pdipm->ci,&carr);
    528:       larr = Xarr+pdipm->off_lambdai;
    529:       zarr = Xarr+pdipm->off_z;
    530:       for (i=0; i<pdipm->nci; i++) {
    531:         Farr[pdipm->off_lambdai + i] = zarr[i] - carr[i];
    532:         Farr[pdipm->off_z       + i] = larr[i] - pdipm->mu/zarr[i];
    533:       }
    534:       VecRestoreArrayRead(pdipm->ci,&carr);
    535:     } else {
    536:       /* (3) L3 = z - ci(x);
    537:          (4) L4 = Z * Lambdai * e - mu * e  */
    538:       VecGetArrayRead(pdipm->ci,&carr);
    539:       larr = Xarr+pdipm->off_lambdai;
    540:       zarr = Xarr+pdipm->off_z;
    541:       for (i=0; i<pdipm->nci; i++) {
    542:         Farr[pdipm->off_lambdai + i] = zarr[i] - carr[i];
    543:         Farr[pdipm->off_z       + i] = zarr[i]*larr[i] - pdipm->mu;
    544:       }
    545:       VecRestoreArrayRead(pdipm->ci,&carr);
    546:     }
    547:   }

    549:   VecRestoreArrayRead(X,&Xarr);
    550:   VecRestoreArrayWrite(F,&Farr);
    551:   return 0;
    552: }

    554: /*
    555:   Evaluate F(X); then update update tao->gnorm0, tao->step = mu,
    556:   tao->residual = norm2(F_x,F_z) and tao->cnorm = norm2(F_ce,F_ci).
    557: */
    558: static PetscErrorCode TaoSNESFunction_PDIPM_residual(SNES snes,Vec X,Vec F,void *ctx)
    559: {
    560:   Tao               tao=(Tao)ctx;
    561:   TAO_PDIPM         *pdipm = (TAO_PDIPM*)tao->data;
    562:   PetscScalar       *Farr,*tmparr;
    563:   Vec               L1;
    564:   PetscInt          i;
    565:   PetscReal         res[2],cnorm[2];
    566:   const PetscScalar *Xarr=NULL;

    568:   TaoSNESFunction_PDIPM(snes,X,F,(void*)tao);
    569:   VecGetArrayWrite(F,&Farr);
    570:   VecGetArrayRead(X,&Xarr);

    572:   /* compute res[0] = norm2(F_x) */
    573:   L1 = pdipm->x;
    574:   VecPlaceArray(L1,Farr);
    575:   VecNorm(L1,NORM_2,&res[0]);
    576:   VecResetArray(L1);

    578:   /* compute res[1] = norm2(F_z), cnorm[1] = norm2(F_ci) */
    579:   if (pdipm->z) {
    580:     if (pdipm->solve_symmetric_kkt) {
    581:       VecPlaceArray(pdipm->z,Farr+pdipm->off_z);
    582:       if (pdipm->Nci) {
    583:         VecGetArrayWrite(pdipm->z,&tmparr);
    584:         for (i=0; i<pdipm->nci; i++) tmparr[i] *= Xarr[pdipm->off_z + i];
    585:         VecRestoreArrayWrite(pdipm->z,&tmparr);
    586:       }

    588:       VecNorm(pdipm->z,NORM_2,&res[1]);

    590:       if (pdipm->Nci) {
    591:         VecGetArrayWrite(pdipm->z,&tmparr);
    592:         for (i=0; i<pdipm->nci; i++) {
    593:           tmparr[i] /= Xarr[pdipm->off_z + i];
    594:         }
    595:         VecRestoreArrayWrite(pdipm->z,&tmparr);
    596:       }
    597:       VecResetArray(pdipm->z);
    598:     } else { /* !solve_symmetric_kkt */
    599:       VecPlaceArray(pdipm->z,Farr+pdipm->off_z);
    600:       VecNorm(pdipm->z,NORM_2,&res[1]);
    601:       VecResetArray(pdipm->z);
    602:     }

    604:     VecPlaceArray(pdipm->ci,Farr+pdipm->off_lambdai);
    605:     VecNorm(pdipm->ci,NORM_2,&cnorm[1]);
    606:     VecResetArray(pdipm->ci);
    607:   } else {
    608:     res[1] = 0.0; cnorm[1] = 0.0;
    609:   }

    611:   /* compute cnorm[0] = norm2(F_ce) */
    612:   if (pdipm->Nce) {
    613:     VecPlaceArray(pdipm->ce,Farr+pdipm->off_lambdae);
    614:     VecNorm(pdipm->ce,NORM_2,&cnorm[0]);
    615:     VecResetArray(pdipm->ce);
    616:   } else cnorm[0] = 0.0;

    618:   VecRestoreArrayWrite(F,&Farr);
    619:   VecRestoreArrayRead(X,&Xarr);

    621:   tao->gnorm0   = tao->residual;
    622:   tao->residual = PetscSqrtReal(res[0]*res[0] + res[1]*res[1]);
    623:   tao->cnorm    = PetscSqrtReal(cnorm[0]*cnorm[0] + cnorm[1]*cnorm[1]);
    624:   tao->step     = pdipm->mu;
    625:   return 0;
    626: }

    628: /*
    629:   KKTAddShifts - Check the inertia of Cholesky factor of KKT matrix.
    630:   If it does not match the numbers of prime and dual variables, add shifts to the KKT matrix.
    631: */
    632: static PetscErrorCode KKTAddShifts(Tao tao,SNES snes,Vec X)
    633: {
    634:   TAO_PDIPM      *pdipm = (TAO_PDIPM*)tao->data;
    635:   KSP            ksp;
    636:   PC             pc;
    637:   Mat            Factor;
    638:   PetscBool      isCHOL;
    639:   PetscInt       nneg,nzero,npos;

    641:   /* Get the inertia of Cholesky factor */
    642:   SNESGetKSP(snes,&ksp);
    643:   KSPGetPC(ksp,&pc);
    644:   PetscObjectTypeCompare((PetscObject)pc,PCCHOLESKY,&isCHOL);
    645:   if (!isCHOL) return 0;

    647:   PCFactorGetMatrix(pc,&Factor);
    648:   MatGetInertia(Factor,&nneg,&nzero,&npos);

    650:   if (npos < pdipm->Nx+pdipm->Nci) {
    651:     pdipm->deltaw = PetscMax(pdipm->lastdeltaw/3, 1.e-4*PETSC_MACHINE_EPSILON);
    652:     PetscInfo(tao,"Test reduced deltaw=%g; previous MatInertia: nneg %D, nzero %D, npos %D(<%D)\n",(double)pdipm->deltaw,nneg,nzero,npos,pdipm->Nx+pdipm->Nci);
    653:     TaoSNESJacobian_PDIPM(snes,X, pdipm->K, pdipm->K, tao);
    654:     PCSetUp(pc);
    655:     MatGetInertia(Factor,&nneg,&nzero,&npos);

    657:     if (npos < pdipm->Nx+pdipm->Nci) {
    658:       pdipm->deltaw = pdipm->lastdeltaw; /* in case reduction update does not help, this prevents that step from impacting increasing update */
    659:       while (npos < pdipm->Nx+pdipm->Nci && pdipm->deltaw <= 1./PETSC_SMALL) { /* increase deltaw */
    660:         PetscInfo(tao,"  deltaw=%g fails, MatInertia: nneg %D, nzero %D, npos %D(<%D)\n",(double)pdipm->deltaw,nneg,nzero,npos,pdipm->Nx+pdipm->Nci);
    661:         pdipm->deltaw = PetscMin(8*pdipm->deltaw,PetscPowReal(10,20));
    662:         TaoSNESJacobian_PDIPM(snes,X, pdipm->K, pdipm->K, tao);
    663:         PCSetUp(pc);
    664:         MatGetInertia(Factor,&nneg,&nzero,&npos);
    665:       }

    669:       PetscInfo(tao,"Updated deltaw %g\n",(double)pdipm->deltaw);
    670:       pdipm->lastdeltaw = pdipm->deltaw;
    671:       pdipm->deltaw     = 0.0;
    672:     }
    673:   }

    675:   if (nzero) { /* Jacobian is singular */
    676:     if (pdipm->deltac == 0.0) {
    677:       pdipm->deltac = PETSC_SQRT_MACHINE_EPSILON;
    678:     } else {
    679:       pdipm->deltac = pdipm->deltac*PetscPowReal(pdipm->mu,.25);
    680:     }
    681:     PetscInfo(tao,"Updated deltac=%g, MatInertia: nneg %D, nzero %D(!=0), npos %D\n",(double)pdipm->deltac,nneg,nzero,npos);
    682:     TaoSNESJacobian_PDIPM(snes,X, pdipm->K, pdipm->K, tao);
    683:     PCSetUp(pc);
    684:     MatGetInertia(Factor,&nneg,&nzero,&npos);
    685:   }
    686:   return 0;
    687: }

    689: /*
    690:   PCPreSolve_PDIPM -- called betwee MatFactorNumeric() and MatSolve()
    691: */
    692: PetscErrorCode PCPreSolve_PDIPM(PC pc,KSP ksp)
    693: {
    694:   Tao            tao;
    695:   TAO_PDIPM      *pdipm;

    697:   KSPGetApplicationContext(ksp,&tao);
    698:   pdipm = (TAO_PDIPM*)tao->data;
    699:   KKTAddShifts(tao,pdipm->snes,pdipm->X);
    700:   return 0;
    701: }

    703: /*
    704:    SNESLineSearch_PDIPM - Custom line search used with PDIPM.

    706:    Collective on TAO

    708:    Notes:
    709:    This routine employs a simple backtracking line-search to keep
    710:    the slack variables (z) and inequality constraints Lagrange multipliers
    711:    (lambdai) positive, i.e., z,lambdai >=0. It does this by calculating scalars
    712:    alpha_p and alpha_d to keep z,lambdai non-negative. The decision (x), and the
    713:    slack variables are updated as X = X - alpha_d*dx. The constraint multipliers
    714:    are updated as Lambdai = Lambdai + alpha_p*dLambdai. The barrier parameter mu
    715:    is also updated as mu = mu + z'lambdai/Nci
    716: */
    717: static PetscErrorCode SNESLineSearch_PDIPM(SNESLineSearch linesearch,void *ctx)
    718: {
    719:   Tao               tao=(Tao)ctx;
    720:   TAO_PDIPM         *pdipm = (TAO_PDIPM*)tao->data;
    721:   SNES              snes;
    722:   Vec               X,F,Y;
    723:   PetscInt          i,iter;
    724:   PetscReal         alpha_p=1.0,alpha_d=1.0,alpha[4];
    725:   PetscScalar       *Xarr,*z,*lambdai,dot,*taosolarr;
    726:   const PetscScalar *dXarr,*dz,*dlambdai;

    728:   SNESLineSearchGetSNES(linesearch,&snes);
    729:   SNESGetIterationNumber(snes,&iter);

    731:   SNESLineSearchSetReason(linesearch,SNES_LINESEARCH_SUCCEEDED);
    732:   SNESLineSearchGetVecs(linesearch,&X,&F,&Y,NULL,NULL);

    734:   VecGetArrayWrite(X,&Xarr);
    735:   VecGetArrayRead(Y,&dXarr);
    736:   z  = Xarr + pdipm->off_z;
    737:   dz = dXarr + pdipm->off_z;
    738:   for (i=0; i < pdipm->nci; i++) {
    739:     if (z[i] - dz[i] < 0.0) alpha_p = PetscMin(alpha_p, 0.9999*z[i]/dz[i]);
    740:   }

    742:   lambdai  = Xarr + pdipm->off_lambdai;
    743:   dlambdai = dXarr + pdipm->off_lambdai;

    745:   for (i=0; i<pdipm->nci; i++) {
    746:     if (lambdai[i] - dlambdai[i] < 0.0) alpha_d = PetscMin(0.9999*lambdai[i]/dlambdai[i], alpha_d);
    747:   }

    749:   alpha[0] = alpha_p;
    750:   alpha[1] = alpha_d;
    751:   VecRestoreArrayRead(Y,&dXarr);
    752:   VecRestoreArrayWrite(X,&Xarr);

    754:   /* alpha = min(alpha) over all processes */
    755:   MPI_Allreduce(alpha,alpha+2,2,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)tao));

    757:   alpha_p = alpha[2];
    758:   alpha_d = alpha[3];

    760:   /* X = X - alpha * Y */
    761:   VecGetArrayWrite(X,&Xarr);
    762:   VecGetArrayRead(Y,&dXarr);
    763:   for (i=0; i<pdipm->nx; i++) Xarr[i] -= alpha_p * dXarr[i];
    764:   for (i=0; i<pdipm->nce; i++) Xarr[i+pdipm->off_lambdae] -= alpha_d * dXarr[i+pdipm->off_lambdae];

    766:   for (i=0; i<pdipm->nci; i++) {
    767:     Xarr[i+pdipm->off_lambdai] -= alpha_d * dXarr[i+pdipm->off_lambdai];
    768:     Xarr[i+pdipm->off_z]       -= alpha_p * dXarr[i+pdipm->off_z];
    769:   }
    770:   VecGetArrayWrite(tao->solution,&taosolarr);
    771:   PetscMemcpy(taosolarr,Xarr,pdipm->nx*sizeof(PetscScalar));
    772:   VecRestoreArrayWrite(tao->solution,&taosolarr);

    774:   VecRestoreArrayWrite(X,&Xarr);
    775:   VecRestoreArrayRead(Y,&dXarr);

    777:   /* Update mu = mu_update_factor * dot(z,lambdai)/pdipm->nci at updated X */
    778:   if (pdipm->z) {
    779:     VecDot(pdipm->z,pdipm->lambdai,&dot);
    780:   } else dot = 0.0;

    782:   /* if (PetscAbsReal(pdipm->gradL) < 0.9*pdipm->mu)  */
    783:   pdipm->mu = pdipm->mu_update_factor * dot/pdipm->Nci;

    785:   /* Update F; get tao->residual and tao->cnorm */
    786:   TaoSNESFunction_PDIPM_residual(snes,X,F,(void*)tao);

    788:   tao->niter++;
    789:   TaoLogConvergenceHistory(tao,pdipm->obj,tao->residual,tao->cnorm,tao->niter);
    790:   TaoMonitor(tao,tao->niter,pdipm->obj,tao->residual,tao->cnorm,pdipm->mu);

    792:   (*tao->ops->convergencetest)(tao,tao->cnvP);
    793:   if (tao->reason) {
    794:     SNESSetConvergedReason(snes,SNES_CONVERGED_FNORM_ABS);
    795:   }
    796:   return 0;
    797: }

    799: /*
    800:    TaoSolve_PDIPM

    802:    Input Parameter:
    803:    tao - TAO context

    805:    Output Parameter:
    806:    tao - TAO context
    807: */
    808: PetscErrorCode TaoSolve_PDIPM(Tao tao)
    809: {
    810:   TAO_PDIPM          *pdipm = (TAO_PDIPM*)tao->data;
    811:   SNESLineSearch     linesearch; /* SNESLineSearch context */
    812:   Vec                dummy;

    816:   /* Initialize all variables */
    817:   TaoPDIPMInitializeSolution(tao);

    819:   /* Set linesearch */
    820:   SNESGetLineSearch(pdipm->snes,&linesearch);
    821:   SNESLineSearchSetType(linesearch,SNESLINESEARCHSHELL);
    822:   SNESLineSearchShellSetUserFunc(linesearch,SNESLineSearch_PDIPM,tao);
    823:   SNESLineSearchSetFromOptions(linesearch);

    825:   tao->reason = TAO_CONTINUE_ITERATING;

    827:   /* -tao_monitor for iteration 0 and check convergence */
    828:   VecDuplicate(pdipm->X,&dummy);
    829:   TaoSNESFunction_PDIPM_residual(pdipm->snes,pdipm->X,dummy,(void*)tao);

    831:   TaoLogConvergenceHistory(tao,pdipm->obj,tao->residual,tao->cnorm,tao->niter);
    832:   TaoMonitor(tao,tao->niter,pdipm->obj,tao->residual,tao->cnorm,pdipm->mu);
    833:   VecDestroy(&dummy);
    834:   (*tao->ops->convergencetest)(tao,tao->cnvP);
    835:   if (tao->reason) {
    836:     SNESSetConvergedReason(pdipm->snes,SNES_CONVERGED_FNORM_ABS);
    837:   }

    839:   while (tao->reason == TAO_CONTINUE_ITERATING) {
    840:     SNESConvergedReason reason;
    841:     SNESSolve(pdipm->snes,NULL,pdipm->X);

    843:     /* Check SNES convergence */
    844:     SNESGetConvergedReason(pdipm->snes,&reason);
    845:     if (reason < 0) {
    846:       PetscPrintf(PetscObjectComm((PetscObject)pdipm->snes),"SNES solve did not converged due to reason %D\n",reason);
    847:     }

    849:     /* Check TAO convergence */
    851:   }
    852:   return 0;
    853: }

    855: /*
    856:   TaoView_PDIPM - View PDIPM

    858:    Input Parameter:
    859:     tao - TAO object
    860:     viewer - PetscViewer

    862:    Output:
    863: */
    864: PetscErrorCode TaoView_PDIPM(Tao tao,PetscViewer viewer)
    865: {
    866:   TAO_PDIPM      *pdipm = (TAO_PDIPM *)tao->data;

    868:   tao->constrained = PETSC_TRUE;
    869:   PetscViewerASCIIPushTab(viewer);
    870:   PetscViewerASCIIPrintf(viewer,"Number of prime=%D, Number of dual=%D\n",pdipm->Nx+pdipm->Nci,pdipm->Nce + pdipm->Nci);
    871:   if (pdipm->kkt_pd) {
    872:     PetscViewerASCIIPrintf(viewer,"KKT shifts deltaw=%g, deltac=%g\n",(double)pdipm->deltaw,(double)pdipm->deltac);
    873:   }
    874:   PetscViewerASCIIPopTab(viewer);
    875:   return 0;
    876: }

    878: /*
    879:    TaoSetup_PDIPM - Sets up tao and pdipm

    881:    Input Parameter:
    882:    tao - TAO object

    884:    Output:   pdipm - initialized object
    885: */
    886: PetscErrorCode TaoSetup_PDIPM(Tao tao)
    887: {
    888:   TAO_PDIPM         *pdipm = (TAO_PDIPM*)tao->data;
    889:   PetscErrorCode    ierr;
    890:   MPI_Comm          comm;
    891:   PetscMPIInt       size;
    892:   PetscInt          row,col,Jcrstart,Jcrend,k,tmp,nc,proc,*nh_all,*ng_all;
    893:   PetscInt          offset,*xa,*xb,i,j,rstart,rend;
    894:   PetscScalar       one=1.0,neg_one=-1.0;
    895:   const PetscInt    *cols,*rranges,*cranges,*aj,*ranges;
    896:   const PetscScalar *aa,*Xarr;
    897:   Mat               J,jac_equality_trans,jac_inequality_trans;
    898:   Mat               Jce_xfixed_trans,Jci_xb_trans;
    899:   PetscInt          *dnz,*onz,rjstart,nx_all,*nce_all,*Jranges,cols1[2];

    901:   PetscObjectGetComm((PetscObject)tao,&comm);
    902:   MPI_Comm_size(comm,&size);

    904:   /* (1) Setup Bounds and create Tao vectors */
    905:   TaoPDIPMSetUpBounds(tao);

    907:   if (!tao->gradient) {
    908:     VecDuplicate(tao->solution,&tao->gradient);
    909:     VecDuplicate(tao->solution,&tao->stepdirection);
    910:   }

    912:   /* (2) Get sizes */
    913:   /* Size of vector x - This is set by TaoSetSolution */
    914:   VecGetSize(tao->solution,&pdipm->Nx);
    915:   VecGetLocalSize(tao->solution,&pdipm->nx);

    917:   /* Size of equality constraints and vectors */
    918:   if (tao->constraints_equality) {
    919:     VecGetSize(tao->constraints_equality,&pdipm->Ng);
    920:     VecGetLocalSize(tao->constraints_equality,&pdipm->ng);
    921:   } else {
    922:     pdipm->ng = pdipm->Ng = 0;
    923:   }

    925:   pdipm->nce = pdipm->ng + pdipm->nxfixed;
    926:   pdipm->Nce = pdipm->Ng + pdipm->Nxfixed;

    928:   /* Size of inequality constraints and vectors */
    929:   if (tao->constraints_inequality) {
    930:     VecGetSize(tao->constraints_inequality,&pdipm->Nh);
    931:     VecGetLocalSize(tao->constraints_inequality,&pdipm->nh);
    932:   } else {
    933:     pdipm->nh = pdipm->Nh = 0;
    934:   }

    936:   pdipm->nci = pdipm->nh + pdipm->nxlb + pdipm->nxub + 2*pdipm->nxbox;
    937:   pdipm->Nci = pdipm->Nh + pdipm->Nxlb + pdipm->Nxub + 2*pdipm->Nxbox;

    939:   /* Full size of the KKT system to be solved */
    940:   pdipm->n = pdipm->nx + pdipm->nce + 2*pdipm->nci;
    941:   pdipm->N = pdipm->Nx + pdipm->Nce + 2*pdipm->Nci;

    943:   /* (3) Offsets for subvectors */
    944:   pdipm->off_lambdae = pdipm->nx;
    945:   pdipm->off_lambdai = pdipm->off_lambdae + pdipm->nce;
    946:   pdipm->off_z       = pdipm->off_lambdai + pdipm->nci;

    948:   /* (4) Create vectors and subvectors */
    949:   /* Ce and Ci vectors */
    950:   VecCreate(comm,&pdipm->ce);
    951:   VecSetSizes(pdipm->ce,pdipm->nce,pdipm->Nce);
    952:   VecSetFromOptions(pdipm->ce);

    954:   VecCreate(comm,&pdipm->ci);
    955:   VecSetSizes(pdipm->ci,pdipm->nci,pdipm->Nci);
    956:   VecSetFromOptions(pdipm->ci);

    958:   /* X=[x; lambdae; lambdai; z] for the big KKT system */
    959:   VecCreate(comm,&pdipm->X);
    960:   VecSetSizes(pdipm->X,pdipm->n,pdipm->N);
    961:   VecSetFromOptions(pdipm->X);

    963:   /* Subvectors; they share local arrays with X */
    964:   VecGetArrayRead(pdipm->X,&Xarr);
    965:   /* x shares local array with X.x */
    966:   if (pdipm->Nx) {
    967:     VecCreateMPIWithArray(comm,1,pdipm->nx,pdipm->Nx,Xarr,&pdipm->x);
    968:   }

    970:   /* lambdae shares local array with X.lambdae */
    971:   if (pdipm->Nce) {
    972:     VecCreateMPIWithArray(comm,1,pdipm->nce,pdipm->Nce,Xarr+pdipm->off_lambdae,&pdipm->lambdae);
    973:   }

    975:   /* tao->DE shares local array with X.lambdae_g */
    976:   if (pdipm->Ng) {
    977:     VecCreateMPIWithArray(comm,1,pdipm->ng,pdipm->Ng,Xarr+pdipm->off_lambdae,&tao->DE);

    979:     VecCreate(comm,&pdipm->lambdae_xfixed);
    980:     VecSetSizes(pdipm->lambdae_xfixed,pdipm->nxfixed,PETSC_DECIDE);
    981:     VecSetFromOptions(pdipm->lambdae_xfixed);
    982:   }

    984:   if (pdipm->Nci) {
    985:     /* lambdai shares local array with X.lambdai */
    986:     VecCreateMPIWithArray(comm,1,pdipm->nci,pdipm->Nci,Xarr+pdipm->off_lambdai,&pdipm->lambdai);

    988:     /* z for slack variables; it shares local array with X.z */
    989:     VecCreateMPIWithArray(comm,1,pdipm->nci,pdipm->Nci,Xarr+pdipm->off_z,&pdipm->z);
    990:   }

    992:   /* tao->DI which shares local array with X.lambdai_h */
    993:   if (pdipm->Nh) {
    994:     VecCreateMPIWithArray(comm,1,pdipm->nh,pdipm->Nh,Xarr+pdipm->off_lambdai,&tao->DI);
    995:   }
    996:   VecCreate(comm,&pdipm->lambdai_xb);
    997:   VecSetSizes(pdipm->lambdai_xb,(pdipm->nci - pdipm->nh),PETSC_DECIDE);
    998:   VecSetFromOptions(pdipm->lambdai_xb);

    1000:   VecRestoreArrayRead(pdipm->X,&Xarr);

    1002:   /* (5) Create Jacobians Jce_xfixed and Jci */
    1003:   /* (5.1) PDIPM Jacobian of equality bounds cebound(x) = J_nxfixed */
    1004:   if (pdipm->Nxfixed) {
    1005:     /* Create Jce_xfixed */
    1006:     MatCreate(comm,&pdipm->Jce_xfixed);
    1007:     MatSetSizes(pdipm->Jce_xfixed,pdipm->nxfixed,pdipm->nx,PETSC_DECIDE,pdipm->Nx);
    1008:     MatSetFromOptions(pdipm->Jce_xfixed);
    1009:     MatSeqAIJSetPreallocation(pdipm->Jce_xfixed,1,NULL);
    1010:     MatMPIAIJSetPreallocation(pdipm->Jce_xfixed,1,NULL,1,NULL);

    1012:     MatGetOwnershipRange(pdipm->Jce_xfixed,&Jcrstart,&Jcrend);
    1013:     ISGetIndices(pdipm->isxfixed,&cols);
    1014:     k = 0;
    1015:     for (row = Jcrstart; row < Jcrend; row++) {
    1016:       MatSetValues(pdipm->Jce_xfixed,1,&row,1,cols+k,&one,INSERT_VALUES);
    1017:       k++;
    1018:     }
    1019:     ISRestoreIndices(pdipm->isxfixed, &cols);
    1020:     MatAssemblyBegin(pdipm->Jce_xfixed,MAT_FINAL_ASSEMBLY);
    1021:     MatAssemblyEnd(pdipm->Jce_xfixed,MAT_FINAL_ASSEMBLY);
    1022:   }

    1024:   /* (5.2) PDIPM inequality Jacobian Jci = [tao->jacobian_inequality; ...] */
    1025:   MatCreate(comm,&pdipm->Jci_xb);
    1026:   MatSetSizes(pdipm->Jci_xb,pdipm->nci-pdipm->nh,pdipm->nx,PETSC_DECIDE,pdipm->Nx);
    1027:   MatSetFromOptions(pdipm->Jci_xb);
    1028:   MatSeqAIJSetPreallocation(pdipm->Jci_xb,1,NULL);
    1029:   MatMPIAIJSetPreallocation(pdipm->Jci_xb,1,NULL,1,NULL);

    1031:   MatGetOwnershipRange(pdipm->Jci_xb,&Jcrstart,&Jcrend);
    1032:   offset = Jcrstart;
    1033:   if (pdipm->Nxub) {
    1034:     /* Add xub to Jci_xb */
    1035:     ISGetIndices(pdipm->isxub,&cols);
    1036:     k = 0;
    1037:     for (row = offset; row < offset + pdipm->nxub; row++) {
    1038:       MatSetValues(pdipm->Jci_xb,1,&row,1,cols+k,&neg_one,INSERT_VALUES);
    1039:       k++;
    1040:     }
    1041:     ISRestoreIndices(pdipm->isxub, &cols);
    1042:   }

    1044:   if (pdipm->Nxlb) {
    1045:     /* Add xlb to Jci_xb */
    1046:     ISGetIndices(pdipm->isxlb,&cols);
    1047:     k = 0;
    1048:     offset += pdipm->nxub;
    1049:     for (row = offset; row < offset + pdipm->nxlb; row++) {
    1050:       MatSetValues(pdipm->Jci_xb,1,&row,1,cols+k,&one,INSERT_VALUES);
    1051:       k++;
    1052:     }
    1053:     ISRestoreIndices(pdipm->isxlb, &cols);
    1054:   }

    1056:   /* Add xbox to Jci_xb */
    1057:   if (pdipm->Nxbox) {
    1058:     ISGetIndices(pdipm->isxbox,&cols);
    1059:     k = 0;
    1060:     offset += pdipm->nxlb;
    1061:     for (row = offset; row < offset + pdipm->nxbox; row++) {
    1062:       MatSetValues(pdipm->Jci_xb,1,&row,1,cols+k,&neg_one,INSERT_VALUES);
    1063:       tmp = row + pdipm->nxbox;
    1064:       MatSetValues(pdipm->Jci_xb,1,&tmp,1,cols+k,&one,INSERT_VALUES);
    1065:       k++;
    1066:     }
    1067:     ISRestoreIndices(pdipm->isxbox, &cols);
    1068:   }

    1070:   MatAssemblyBegin(pdipm->Jci_xb,MAT_FINAL_ASSEMBLY);
    1071:   MatAssemblyEnd(pdipm->Jci_xb,MAT_FINAL_ASSEMBLY);
    1072:   /* MatView(pdipm->Jci_xb,PETSC_VIEWER_STDOUT_WORLD); */

    1074:   /* (6) Set up ISs for PC Fieldsplit */
    1075:   if (pdipm->solve_reduced_kkt) {
    1076:     PetscMalloc2(pdipm->nx+pdipm->nce,&xa,2*pdipm->nci,&xb);
    1077:     for (i=0; i < pdipm->nx + pdipm->nce; i++) xa[i] = i;
    1078:     for (i=0; i < 2*pdipm->nci; i++) xb[i] = pdipm->off_lambdai + i;

    1080:     ISCreateGeneral(comm,pdipm->nx+pdipm->nce,xa,PETSC_OWN_POINTER,&pdipm->is1);
    1081:     ISCreateGeneral(comm,2*pdipm->nci,xb,PETSC_OWN_POINTER,&pdipm->is2);
    1082:   }

    1084:   /* (7) Gather offsets from all processes */
    1085:   PetscMalloc1(size,&pdipm->nce_all);

    1087:   /* Get rstart of KKT matrix */
    1088:   MPI_Scan(&pdipm->n,&rstart,1,MPIU_INT,MPI_SUM,comm);
    1089:   rstart -= pdipm->n;

    1091:   MPI_Allgather(&pdipm->nce,1,MPIU_INT,pdipm->nce_all,1,MPIU_INT,comm);

    1093:   PetscMalloc3(size,&ng_all,size,&nh_all,size,&Jranges);
    1094:   MPI_Allgather(&rstart,1,MPIU_INT,Jranges,1,MPIU_INT,comm);
    1095:   MPI_Allgather(&pdipm->nh,1,MPIU_INT,nh_all,1,MPIU_INT,comm);
    1096:   MPI_Allgather(&pdipm->ng,1,MPIU_INT,ng_all,1,MPIU_INT,comm);

    1098:   MatGetOwnershipRanges(tao->hessian,&rranges);
    1099:   MatGetOwnershipRangesColumn(tao->hessian,&cranges);

    1101:   if (pdipm->Ng) {
    1102:     TaoComputeJacobianEquality(tao,tao->solution,tao->jacobian_equality,tao->jacobian_equality_pre);
    1103:     MatTranspose(tao->jacobian_equality,MAT_INITIAL_MATRIX,&pdipm->jac_equality_trans);
    1104:   }
    1105:   if (pdipm->Nh) {
    1106:     TaoComputeJacobianInequality(tao,tao->solution,tao->jacobian_inequality,tao->jacobian_inequality_pre);
    1107:     MatTranspose(tao->jacobian_inequality,MAT_INITIAL_MATRIX,&pdipm->jac_inequality_trans);
    1108:   }

    1110:   /* Count dnz,onz for preallocation of KKT matrix */
    1111:   jac_equality_trans   = pdipm->jac_equality_trans;
    1112:   jac_inequality_trans = pdipm->jac_inequality_trans;
    1113:   nce_all = pdipm->nce_all;

    1115:   if (pdipm->Nxfixed) {
    1116:     MatTranspose(pdipm->Jce_xfixed,MAT_INITIAL_MATRIX,&Jce_xfixed_trans);
    1117:   }
    1118:   MatTranspose(pdipm->Jci_xb,MAT_INITIAL_MATRIX,&Jci_xb_trans);

    1120:   MatPreallocateInitialize(comm,pdipm->n,pdipm->n,dnz,onz);

    1122:   /* 1st row block of KKT matrix: [Wxx; gradCe'; -gradCi'; 0] */
    1123:   TaoPDIPMEvaluateFunctionsAndJacobians(tao,pdipm->x);
    1124:   TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);

    1126:   /* Insert tao->hessian */
    1127:   MatGetOwnershipRange(tao->hessian,&rjstart,NULL);
    1128:   for (i=0; i<pdipm->nx; i++) {
    1129:     row = rstart + i;

    1131:     MatGetRow(tao->hessian,i+rjstart,&nc,&aj,NULL);
    1132:     proc = 0;
    1133:     for (j=0; j < nc; j++) {
    1134:       while (aj[j] >= cranges[proc+1]) proc++;
    1135:       col = aj[j] - cranges[proc] + Jranges[proc];
    1136:       MatPreallocateSet(row,1,&col,dnz,onz);
    1137:     }
    1138:     MatRestoreRow(tao->hessian,i+rjstart,&nc,&aj,NULL);

    1140:     if (pdipm->ng) {
    1141:       /* Insert grad g' */
    1142:       MatGetRow(jac_equality_trans,i+rjstart,&nc,&aj,NULL);
    1143:       MatGetOwnershipRanges(tao->jacobian_equality,&ranges);
    1144:       proc = 0;
    1145:       for (j=0; j < nc; j++) {
    1146:         /* find row ownership of */
    1147:         while (aj[j] >= ranges[proc+1]) proc++;
    1148:         nx_all = rranges[proc+1] - rranges[proc];
    1149:         col = aj[j] - ranges[proc] + Jranges[proc] + nx_all;
    1150:         MatPreallocateSet(row,1,&col,dnz,onz);
    1151:       }
    1152:       MatRestoreRow(jac_equality_trans,i+rjstart,&nc,&aj,NULL);
    1153:     }

    1155:     /* Insert Jce_xfixed^T' */
    1156:     if (pdipm->nxfixed) {
    1157:       MatGetRow(Jce_xfixed_trans,i+rjstart,&nc,&aj,NULL);
    1158:       MatGetOwnershipRanges(pdipm->Jce_xfixed,&ranges);
    1159:       proc = 0;
    1160:       for (j=0; j < nc; j++) {
    1161:         /* find row ownership of */
    1162:         while (aj[j] >= ranges[proc+1]) proc++;
    1163:         nx_all = rranges[proc+1] - rranges[proc];
    1164:         col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + ng_all[proc];
    1165:         MatPreallocateSet(row,1,&col,dnz,onz);
    1166:       }
    1167:       MatRestoreRow(Jce_xfixed_trans,i+rjstart,&nc,&aj,NULL);
    1168:     }

    1170:     if (pdipm->nh) {
    1171:       /* Insert -grad h' */
    1172:       MatGetRow(jac_inequality_trans,i+rjstart,&nc,&aj,NULL);
    1173:       MatGetOwnershipRanges(tao->jacobian_inequality,&ranges);
    1174:       proc = 0;
    1175:       for (j=0; j < nc; j++) {
    1176:         /* find row ownership of */
    1177:         while (aj[j] >= ranges[proc+1]) proc++;
    1178:         nx_all = rranges[proc+1] - rranges[proc];
    1179:         col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc];
    1180:         MatPreallocateSet(row,1,&col,dnz,onz);
    1181:       }
    1182:       MatRestoreRow(jac_inequality_trans,i+rjstart,&nc,&aj,NULL);
    1183:     }

    1185:     /* Insert Jci_xb^T' */
    1186:     MatGetRow(Jci_xb_trans,i+rjstart,&nc,&aj,NULL);
    1187:     MatGetOwnershipRanges(pdipm->Jci_xb,&ranges);
    1188:     proc = 0;
    1189:     for (j=0; j < nc; j++) {
    1190:       /* find row ownership of */
    1191:       while (aj[j] >= ranges[proc+1]) proc++;
    1192:       nx_all = rranges[proc+1] - rranges[proc];
    1193:       col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc] + nh_all[proc];
    1194:       MatPreallocateSet(row,1,&col,dnz,onz);
    1195:     }
    1196:     MatRestoreRow(Jci_xb_trans,i+rjstart,&nc,&aj,NULL);
    1197:   }

    1199:   /* 2nd Row block of KKT matrix: [grad Ce, deltac*I, 0, 0] */
    1200:   if (pdipm->Ng) {
    1201:     MatGetOwnershipRange(tao->jacobian_equality,&rjstart,NULL);
    1202:     for (i=0; i < pdipm->ng; i++) {
    1203:       row = rstart + pdipm->off_lambdae + i;

    1205:       MatGetRow(tao->jacobian_equality,i+rjstart,&nc,&aj,NULL);
    1206:       proc = 0;
    1207:       for (j=0; j < nc; j++) {
    1208:         while (aj[j] >= cranges[proc+1]) proc++;
    1209:         col = aj[j] - cranges[proc] + Jranges[proc];
    1210:         MatPreallocateSet(row,1,&col,dnz,onz); /* grad g */
    1211:       }
    1212:       MatRestoreRow(tao->jacobian_equality,i+rjstart,&nc,&aj,NULL);
    1213:     }
    1214:   }
    1215:   /* Jce_xfixed */
    1216:   if (pdipm->Nxfixed) {
    1217:     MatGetOwnershipRange(pdipm->Jce_xfixed,&Jcrstart,NULL);
    1218:     for (i=0; i < (pdipm->nce - pdipm->ng); i++) {
    1219:       row = rstart + pdipm->off_lambdae + pdipm->ng + i;

    1221:       MatGetRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,NULL);

    1224:       proc = 0;
    1225:       j    = 0;
    1226:       while (cols[j] >= cranges[proc+1]) proc++;
    1227:       col = cols[j] - cranges[proc] + Jranges[proc];
    1228:       MatPreallocateSet(row,1,&col,dnz,onz);
    1229:       MatRestoreRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,NULL);
    1230:     }
    1231:   }

    1233:   /* 3rd Row block of KKT matrix: [ gradCi, 0, deltac*I, -I] */
    1234:   if (pdipm->Nh) {
    1235:     MatGetOwnershipRange(tao->jacobian_inequality,&rjstart,NULL);
    1236:     for (i=0; i < pdipm->nh; i++) {
    1237:       row = rstart + pdipm->off_lambdai + i;

    1239:       MatGetRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,NULL);
    1240:       proc = 0;
    1241:       for (j=0; j < nc; j++) {
    1242:         while (aj[j] >= cranges[proc+1]) proc++;
    1243:         col = aj[j] - cranges[proc] + Jranges[proc];
    1244:         MatPreallocateSet(row,1,&col,dnz,onz); /* grad h */
    1245:       }
    1246:       MatRestoreRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,NULL);
    1247:     }
    1248:     /* I */
    1249:     for (i=0; i < pdipm->nh; i++) {
    1250:       row = rstart + pdipm->off_lambdai + i;
    1251:       col = rstart + pdipm->off_z + i;
    1252:       MatPreallocateSet(row,1,&col,dnz,onz);
    1253:     }
    1254:   }

    1256:   /* Jci_xb */
    1257:   MatGetOwnershipRange(pdipm->Jci_xb,&Jcrstart,NULL);
    1258:   for (i=0; i < (pdipm->nci - pdipm->nh); i++) {
    1259:     row = rstart + pdipm->off_lambdai + pdipm->nh + i;

    1261:     MatGetRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,NULL);
    1263:     proc = 0;
    1264:     for (j=0; j < nc; j++) {
    1265:       while (cols[j] >= cranges[proc+1]) proc++;
    1266:       col = cols[j] - cranges[proc] + Jranges[proc];
    1267:       MatPreallocateSet(row,1,&col,dnz,onz);
    1268:     }
    1269:     MatRestoreRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,NULL);
    1270:     /* I */
    1271:     col = rstart + pdipm->off_z + pdipm->nh + i;
    1272:     MatPreallocateSet(row,1,&col,dnz,onz);
    1273:   }

    1275:   /* 4-th Row block of KKT matrix: Z and Ci */
    1276:   for (i=0; i < pdipm->nci; i++) {
    1277:     row     = rstart + pdipm->off_z + i;
    1278:     cols1[0] = rstart + pdipm->off_lambdai + i;
    1279:     cols1[1] = row;
    1280:     MatPreallocateSet(row,2,cols1,dnz,onz);
    1281:   }

    1283:   /* diagonal entry */
    1284:   for (i=0; i<pdipm->n; i++) dnz[i]++; /* diagonal entry */

    1286:   /* Create KKT matrix */
    1287:   MatCreate(comm,&J);
    1288:   MatSetSizes(J,pdipm->n,pdipm->n,PETSC_DECIDE,PETSC_DECIDE);
    1289:   MatSetFromOptions(J);
    1290:   MatSeqAIJSetPreallocation(J,0,dnz);
    1291:   MatMPIAIJSetPreallocation(J,0,dnz,0,onz);
    1292:   MatPreallocateFinalize(dnz,onz);
    1293:   pdipm->K = J;

    1295:   /* (8) Insert constant entries to  K */
    1296:   /* Set 0.0 to diagonal of K, so that the solver does not complain *about missing diagonal value */
    1297:   MatGetOwnershipRange(J,&rstart,&rend);
    1298:   for (i=rstart; i<rend; i++) {
    1299:     MatSetValue(J,i,i,0.0,INSERT_VALUES);
    1300:   }
    1301:   /* In case Wxx has no diagonal entries preset set diagonal to deltaw given */
    1302:   if (pdipm->kkt_pd) {
    1303:       for (i=0; i<pdipm->nh; i++) {
    1304:         row  = rstart + i;
    1305:         MatSetValue(J,row,row,pdipm->deltaw,INSERT_VALUES);
    1306:       }
    1307:   }

    1309:   /* Row block of K: [ grad Ce, 0, 0, 0] */
    1310:   if (pdipm->Nxfixed) {
    1311:     MatGetOwnershipRange(pdipm->Jce_xfixed,&Jcrstart,NULL);
    1312:     for (i=0; i < (pdipm->nce - pdipm->ng); i++) {
    1313:       row = rstart + pdipm->off_lambdae + pdipm->ng + i;

    1315:       MatGetRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,&aa);
    1316:       proc = 0;
    1317:       for (j=0; j < nc; j++) {
    1318:         while (cols[j] >= cranges[proc+1]) proc++;
    1319:         col = cols[j] - cranges[proc] + Jranges[proc];
    1320:         MatSetValue(J,row,col,aa[j],INSERT_VALUES); /* grad Ce */
    1321:         MatSetValue(J,col,row,aa[j],INSERT_VALUES); /* grad Ce' */
    1322:       }
    1323:       MatRestoreRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,&aa);
    1324:     }
    1325:   }

    1327:   /* Row block of K: [ -grad Ci, 0, 0, I] */
    1328:   MatGetOwnershipRange(pdipm->Jci_xb,&Jcrstart,NULL);
    1329:   for (i=0; i < pdipm->nci - pdipm->nh; i++) {
    1330:     row = rstart + pdipm->off_lambdai + pdipm->nh + i;

    1332:     MatGetRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,&aa);
    1333:     proc = 0;
    1334:     for (j=0; j < nc; j++) {
    1335:       while (cols[j] >= cranges[proc+1]) proc++;
    1336:       col = cols[j] - cranges[proc] + Jranges[proc];
    1337:       MatSetValue(J,col,row,-aa[j],INSERT_VALUES);
    1338:       MatSetValue(J,row,col,-aa[j],INSERT_VALUES);
    1339:     }
    1340:     MatRestoreRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,&aa);

    1342:     col = rstart + pdipm->off_z + pdipm->nh + i;
    1343:     MatSetValue(J,row,col,1,INSERT_VALUES);
    1344:   }

    1346:   for (i=0; i < pdipm->nh; i++) {
    1347:     row = rstart + pdipm->off_lambdai + i;
    1348:     col = rstart + pdipm->off_z + i;
    1349:     MatSetValue(J,row,col,1,INSERT_VALUES);
    1350:   }

    1352:   /* Row block of K: [ 0, 0, I, ...] */
    1353:   for (i=0; i < pdipm->nci; i++) {
    1354:     row = rstart + pdipm->off_z + i;
    1355:     col = rstart + pdipm->off_lambdai + i;
    1356:     MatSetValue(J,row,col,1,INSERT_VALUES);
    1357:   }

    1359:   if (pdipm->Nxfixed) {
    1360:     MatDestroy(&Jce_xfixed_trans);
    1361:   }
    1362:   MatDestroy(&Jci_xb_trans);
    1363:   PetscFree3(ng_all,nh_all,Jranges);

    1365:   /* (9) Set up nonlinear solver SNES */
    1366:   SNESSetFunction(pdipm->snes,NULL,TaoSNESFunction_PDIPM,(void*)tao);
    1367:   SNESSetJacobian(pdipm->snes,J,J,TaoSNESJacobian_PDIPM,(void*)tao);

    1369:   if (pdipm->solve_reduced_kkt) {
    1370:     PC pc;
    1371:     KSPGetPC(tao->ksp,&pc);
    1372:     PCSetType(pc,PCFIELDSPLIT);
    1373:     PCFieldSplitSetType(pc,PC_COMPOSITE_SCHUR);
    1374:     PCFieldSplitSetIS(pc,"2",pdipm->is2);
    1375:     PCFieldSplitSetIS(pc,"1",pdipm->is1);
    1376:   }
    1377:   SNESSetFromOptions(pdipm->snes);

    1379:   /* (10) Setup PCPreSolve() for pdipm->solve_symmetric_kkt */
    1380:   if (pdipm->solve_symmetric_kkt) {
    1381:     KSP       ksp;
    1382:     PC        pc;
    1383:     PetscBool isCHOL;
    1384:     SNESGetKSP(pdipm->snes,&ksp);
    1385:     KSPGetPC(ksp,&pc);
    1386:     PCSetPreSolve(pc,PCPreSolve_PDIPM);

    1388:     PetscObjectTypeCompare((PetscObject)pc,PCCHOLESKY,&isCHOL);
    1389:     if (isCHOL) {
    1390:       Mat        Factor;
    1391:       PetscBool  isMUMPS;
    1392:       PCFactorGetMatrix(pc,&Factor);
    1393:       PetscObjectTypeCompare((PetscObject)Factor,"mumps",&isMUMPS);
    1394:       if (isMUMPS) { /* must set mumps ICNTL(13)=1 and ICNTL(24)=1 to call MatGetInertia() */
    1395: #if defined(PETSC_HAVE_MUMPS)
    1396:         MatMumpsSetIcntl(Factor,24,1); /* detection of null pivot rows */
    1397:         if (size > 1) {
    1398:           MatMumpsSetIcntl(Factor,13,1); /* parallelism of the root node (enable ScaLAPACK) and its splitting */
    1399:         }
    1400: #else
    1401:         SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_SUP,"Requires external package MUMPS");
    1402: #endif
    1403:       }
    1404:     }
    1405:   }
    1406:   return 0;
    1407: }

    1409: /*
    1410:    TaoDestroy_PDIPM - Destroys the pdipm object

    1412:    Input:
    1413:    full pdipm

    1415:    Output:
    1416:    Destroyed pdipm
    1417: */
    1418: PetscErrorCode TaoDestroy_PDIPM(Tao tao)
    1419: {
    1420:   TAO_PDIPM      *pdipm = (TAO_PDIPM*)tao->data;

    1422:   /* Freeing Vectors assocaiated with KKT (X) */
    1423:   VecDestroy(&pdipm->x); /* Solution x */
    1424:   VecDestroy(&pdipm->lambdae); /* Equality constraints lagrangian multiplier*/
    1425:   VecDestroy(&pdipm->lambdai); /* Inequality constraints lagrangian multiplier*/
    1426:   VecDestroy(&pdipm->z);       /* Slack variables */
    1427:   VecDestroy(&pdipm->X);       /* Big KKT system vector [x; lambdae; lambdai; z] */

    1429:   /* work vectors */
    1430:   VecDestroy(&pdipm->lambdae_xfixed);
    1431:   VecDestroy(&pdipm->lambdai_xb);

    1433:   /* Legrangian equality and inequality Vec */
    1434:   VecDestroy(&pdipm->ce); /* Vec of equality constraints */
    1435:   VecDestroy(&pdipm->ci); /* Vec of inequality constraints */

    1437:   /* Matrices */
    1438:   MatDestroy(&pdipm->Jce_xfixed);
    1439:   MatDestroy(&pdipm->Jci_xb)); /* Jacobian of inequality constraints Jci = [tao->jacobian_inequality ; J(nxub); J(nxlb; J(nxbx)] */
    1440:   MatDestroy(&pdipm->K);

    1442:   /* Index Sets */
    1443:   if (pdipm->Nxub) {
    1444:     ISDestroy(&pdipm->isxub);    /* Finite upper bound only -inf < x < ub */
    1445:   }

    1447:   if (pdipm->Nxlb) {
    1448:     ISDestroy(&pdipm->isxlb);    /* Finite lower bound only  lb <= x < inf */
    1449:   }

    1451:   if (pdipm->Nxfixed) {
    1452:     ISDestroy(&pdipm->isxfixed); /* Fixed variables         lb =  x = ub */
    1453:   }

    1455:   if (pdipm->Nxbox) {
    1456:     ISDestroy(&pdipm->isxbox);   /* Boxed variables         lb <= x <= ub */
    1457:   }

    1459:   if (pdipm->Nxfree) {
    1460:     ISDestroy(&pdipm->isxfree);  /* Free variables        -inf <= x <= inf */
    1461:   }

    1463:   if (pdipm->solve_reduced_kkt) {
    1464:     ISDestroy(&pdipm->is1);
    1465:     ISDestroy(&pdipm->is2);
    1466:   }

    1468:   /* SNES */
    1469:   SNESDestroy(&pdipm->snes); /* Nonlinear solver */
    1470:   PetscFree(pdipm->nce_all);
    1471:   MatDestroy(&pdipm->jac_equality_trans);
    1472:   MatDestroy(&pdipm->jac_inequality_trans);

    1474:   /* Destroy pdipm */
    1475:   PetscFree(tao->data); /* Holding locations of pdipm */

    1477:   /* Destroy Dual */
    1478:   VecDestroy(&tao->DE); /* equality dual */
    1479:   VecDestroy(&tao->DI); /* dinequality dual */
    1480:   return 0;
    1481: }

    1483: PetscErrorCode TaoSetFromOptions_PDIPM(PetscOptionItems *PetscOptionsObject,Tao tao)
    1484: {
    1485:   TAO_PDIPM      *pdipm = (TAO_PDIPM*)tao->data;

    1487:   PetscOptionsHead(PetscOptionsObject,"PDIPM method for constrained optimization");
    1488:   PetscOptionsReal("-tao_pdipm_push_init_slack","parameter to push initial slack variables away from bounds",NULL,pdipm->push_init_slack,&pdipm->push_init_slack,NULL);
    1489:   PetscOptionsReal("-tao_pdipm_push_init_lambdai","parameter to push initial (inequality) dual variables away from bounds",NULL,pdipm->push_init_lambdai,&pdipm->push_init_lambdai,NULL);
    1490:   PetscOptionsBool("-tao_pdipm_solve_reduced_kkt","Solve reduced KKT system using Schur-complement",NULL,pdipm->solve_reduced_kkt,&pdipm->solve_reduced_kkt,NULL);
    1491:   PetscOptionsReal("-tao_pdipm_mu_update_factor","Update scalar for barrier parameter (mu) update",NULL,pdipm->mu_update_factor,&pdipm->mu_update_factor,NULL);
    1492:   PetscOptionsBool("-tao_pdipm_symmetric_kkt","Solve non reduced symmetric KKT system",NULL,pdipm->solve_symmetric_kkt,&pdipm->solve_symmetric_kkt,NULL);
    1493:   PetscOptionsBool("-tao_pdipm_kkt_shift_pd","Add shifts to make KKT matrix positive definite",NULL,pdipm->kkt_pd,&pdipm->kkt_pd,NULL);
    1494:   PetscOptionsTail();
    1495:   return 0;
    1496: }

    1498: /*MC
    1499:   TAOPDIPM - Barrier-based primal-dual interior point algorithm for generally constrained optimization.

    1501:   Option Database Keys:
    1502: +   -tao_pdipm_push_init_lambdai - parameter to push initial dual variables away from bounds (> 0)
    1503: .   -tao_pdipm_push_init_slack - parameter to push initial slack variables away from bounds (> 0)
    1504: .   -tao_pdipm_mu_update_factor - update scalar for barrier parameter (mu) update (> 0)
    1505: .   -tao_pdipm_symmetric_kkt - Solve non-reduced symmetric KKT system
    1506: -   -tao_pdipm_kkt_shift_pd - Add shifts to make KKT matrix positive definite

    1508:   Level: beginner
    1509: M*/
    1510: PETSC_EXTERN PetscErrorCode TaoCreate_PDIPM(Tao tao)
    1511: {
    1512:   TAO_PDIPM      *pdipm;

    1514:   tao->ops->setup          = TaoSetup_PDIPM;
    1515:   tao->ops->solve          = TaoSolve_PDIPM;
    1516:   tao->ops->setfromoptions = TaoSetFromOptions_PDIPM;
    1517:   tao->ops->view           = TaoView_PDIPM;
    1518:   tao->ops->destroy        = TaoDestroy_PDIPM;

    1520:   PetscNewLog(tao,&pdipm);
    1521:   tao->data = (void*)pdipm;

    1523:   pdipm->nx      = pdipm->Nx      = 0;
    1524:   pdipm->nxfixed = pdipm->Nxfixed = 0;
    1525:   pdipm->nxlb    = pdipm->Nxlb    = 0;
    1526:   pdipm->nxub    = pdipm->Nxub    = 0;
    1527:   pdipm->nxbox   = pdipm->Nxbox   = 0;
    1528:   pdipm->nxfree  = pdipm->Nxfree  = 0;

    1530:   pdipm->ng = pdipm->Ng = pdipm->nce = pdipm->Nce = 0;
    1531:   pdipm->nh = pdipm->Nh = pdipm->nci = pdipm->Nci = 0;
    1532:   pdipm->n  = pdipm->N  = 0;
    1533:   pdipm->mu = 1.0;
    1534:   pdipm->mu_update_factor = 0.1;

    1536:   pdipm->deltaw     = 0.0;
    1537:   pdipm->lastdeltaw = 3*1.e-4;
    1538:   pdipm->deltac     = 0.0;
    1539:   pdipm->kkt_pd     = PETSC_FALSE;

    1541:   pdipm->push_init_slack     = 1.0;
    1542:   pdipm->push_init_lambdai   = 1.0;
    1543:   pdipm->solve_reduced_kkt   = PETSC_FALSE;
    1544:   pdipm->solve_symmetric_kkt = PETSC_TRUE;

    1546:   /* Override default settings (unless already changed) */
    1547:   if (!tao->max_it_changed) tao->max_it = 200;
    1548:   if (!tao->max_funcs_changed) tao->max_funcs = 500;

    1550:   SNESCreate(((PetscObject)tao)->comm,&pdipm->snes);
    1551:   SNESSetOptionsPrefix(pdipm->snes,tao->hdr.prefix);
    1552:   SNESGetKSP(pdipm->snes,&tao->ksp);
    1553:   PetscObjectReference((PetscObject)tao->ksp);
    1554:   KSPSetApplicationContext(tao->ksp,(void *)tao);
    1555:   return 0;
    1556: }