Date: 2026-07-30T21:14:10+00:00

Actual source code: denseqn.c

      1: #include <../src/ksp/ksp/utils/lmvm/dense/denseqn.h>
      2: #include <../src/ksp/ksp/utils/lmvm/blas_cyclic/blas_cyclic.h>
      3: #include <petscblaslapack.h>
      4: #include <petscmat.h>
      5: #include <petscsys.h>
      6: #include <petscsystypes.h>
      7: #include <petscis.h>
      8: #include <petscoptions.h>
      9: #include <petscdevice.h>
     10: #include <petsc/private/deviceimpl.h>

     12: static PetscErrorCode MatMult_LMVMDQN(Mat, Vec, Vec);
     13: static PetscErrorCode MatMult_LMVMDBFGS(Mat, Vec, Vec);
     14: static PetscErrorCode MatMult_LMVMDDFP(Mat, Vec, Vec);
     15: static PetscErrorCode MatSolve_LMVMDQN(Mat, Vec, Vec);
     16: static PetscErrorCode MatSolve_LMVMDBFGS(Mat, Vec, Vec);
     17: static PetscErrorCode MatSolve_LMVMDDFP(Mat, Vec, Vec);

     19: static inline PetscInt recycle_index(PetscInt m, PetscInt idx)
     20: {
     21:   return idx % m;
     22: }

     24: static inline PetscInt history_index(PetscInt m, PetscInt num_updates, PetscInt idx)
     25: {
     26:   return (idx - num_updates) + PetscMin(m, num_updates);
     27: }

     29: static inline PetscInt oldest_update(PetscInt m, PetscInt idx)
     30: {
     31:   return PetscMax(0, idx - m);
     32: }

     34: static PetscErrorCode MatView_LMVMDQN(Mat B, PetscViewer pv)
     35: {
     36:   Mat_LMVM *lmvm = (Mat_LMVM *)B->data;
     37:   Mat_DQN  *lqn  = (Mat_DQN *)lmvm->ctx;

     39:   PetscBool isascii;

     41:   PetscFunctionBegin;
     42:   PetscCall(PetscObjectTypeCompare((PetscObject)pv, PETSCVIEWERASCII, &isascii));
     43:   PetscCall(MatView_LMVM(B, pv));
     44:   PetscCall(SymBroydenRescaleView(lqn->rescale, pv));
     45:   if (isascii) PetscCall(PetscViewerASCIIPrintf(pv, "Counts: S x : %" PetscInt_FMT ", S^T x : %" PetscInt_FMT ", Y x : %" PetscInt_FMT ",  Y^T x: %" PetscInt_FMT "\n", lqn->S_count, lqn->St_count, lqn->Y_count, lqn->Yt_count));
     46:   PetscFunctionReturn(PETSC_SUCCESS);
     47: }

     49: static PetscErrorCode MatLMVMDQNResetDestructive(Mat B)
     50: {
     51:   Mat_LMVM *lmvm = (Mat_LMVM *)B->data;
     52:   Mat_DQN  *lqn  = (Mat_DQN *)lmvm->ctx;

     54:   PetscFunctionBegin;
     55:   PetscCall(MatDestroy(&lqn->HY));
     56:   PetscCall(MatDestroy(&lqn->BS));
     57:   PetscCall(MatDestroy(&lqn->StY_triu));
     58:   PetscCall(MatDestroy(&lqn->YtS_triu));
     59:   PetscCall(VecDestroy(&lqn->StFprev));
     60:   PetscCall(VecDestroy(&lqn->Fprev_ref));
     61:   lqn->Fprev_state = 0;
     62:   PetscCall(MatDestroy(&lqn->YtS_triu_strict));
     63:   PetscCall(MatDestroy(&lqn->StY_triu_strict));
     64:   PetscCall(MatDestroy(&lqn->StBS));
     65:   PetscCall(MatDestroy(&lqn->YtHY));
     66:   PetscCall(MatDestroy(&lqn->J));
     67:   PetscCall(MatDestroy(&lqn->temp_mat));
     68:   PetscCall(VecDestroy(&lqn->diag_vec));
     69:   PetscCall(VecDestroy(&lqn->diag_vec_recycle_order));
     70:   PetscCall(VecDestroy(&lqn->inv_diag_vec));
     71:   PetscCall(VecDestroy(&lqn->column_work));
     72:   PetscCall(VecDestroy(&lqn->column_work2));
     73:   PetscCall(VecDestroy(&lqn->rwork1));
     74:   PetscCall(VecDestroy(&lqn->rwork2));
     75:   PetscCall(VecDestroy(&lqn->rwork3));
     76:   PetscCall(VecDestroy(&lqn->rwork2_local));
     77:   PetscCall(VecDestroy(&lqn->rwork3_local));
     78:   PetscCall(VecDestroy(&lqn->cyclic_work_vec));
     79:   PetscCall(VecDestroyVecs(lmvm->m, &lqn->PQ));
     80:   PetscCall(PetscFree(lqn->stp));
     81:   PetscCall(PetscFree(lqn->yts));
     82:   PetscCall(PetscFree(lqn->ytq));
     83:   lqn->allocated = PETSC_FALSE;
     84:   PetscFunctionReturn(PETSC_SUCCESS);
     85: }

     87: static PetscErrorCode MatReset_LMVMDQN_Internal(Mat B, MatLMVMResetMode mode)
     88: {
     89:   Mat_LMVM *lmvm = (Mat_LMVM *)B->data;
     90:   Mat_DQN  *lqn  = (Mat_DQN *)lmvm->ctx;

     92:   PetscFunctionBegin;
     93:   lqn->watchdog         = 0;
     94:   lqn->needPQ           = PETSC_TRUE;
     95:   lqn->num_updates      = 0;
     96:   lqn->num_mult_updates = 0;
     97:   if (MatLMVMResetClearsBases(mode)) PetscCall(MatLMVMDQNResetDestructive(B));
     98:   else {
     99:     if (lqn->BS) PetscCall(MatZeroEntries(lqn->BS));
    100:     if (lqn->HY) PetscCall(MatZeroEntries(lqn->HY));
    101:     if (lqn->StY_triu) { /* Set to identity by default so it is invertible */
    102:       PetscCall(MatZeroEntries(lqn->StY_triu));
    103:       PetscCall(MatShift(lqn->StY_triu, 1.0));
    104:     }
    105:     if (lqn->YtS_triu) {
    106:       PetscCall(MatZeroEntries(lqn->YtS_triu));
    107:       PetscCall(MatShift(lqn->YtS_triu, 1.0));
    108:     }
    109:     if (lqn->YtS_triu_strict) PetscCall(MatZeroEntries(lqn->YtS_triu_strict));
    110:     if (lqn->StY_triu_strict) PetscCall(MatZeroEntries(lqn->StY_triu_strict));
    111:     if (lqn->StBS) {
    112:       PetscCall(MatZeroEntries(lqn->StBS));
    113:       PetscCall(MatShift(lqn->StBS, 1.0));
    114:     }
    115:     if (lqn->YtHY) {
    116:       PetscCall(MatZeroEntries(lqn->YtHY));
    117:       PetscCall(MatShift(lqn->YtHY, 1.0));
    118:     }
    119:     PetscCall(VecDestroy(&lqn->Fprev_ref));
    120:     lqn->Fprev_state = 0;
    121:     if (lqn->StFprev) PetscCall(VecZeroEntries(lqn->StFprev));
    122:   }
    123:   PetscFunctionReturn(PETSC_SUCCESS);
    124: }

    126: static PetscErrorCode MatReset_LMVMDQN(Mat B, MatLMVMResetMode mode)
    127: {
    128:   Mat_LMVM *lmvm = (Mat_LMVM *)B->data;
    129:   Mat_DQN  *lqn  = (Mat_DQN *)lmvm->ctx;

    131:   PetscFunctionBegin;
    132:   PetscCall(SymBroydenRescaleReset(B, lqn->rescale, mode));
    133:   PetscCall(MatReset_LMVMDQN_Internal(B, mode));
    134:   PetscFunctionReturn(PETSC_SUCCESS);
    135: }

    137: static PetscErrorCode MatAllocate_LMVMDQN_Internal(Mat B)
    138: {
    139:   Mat_LMVM *lmvm = (Mat_LMVM *)B->data;
    140:   Mat_DQN  *lqn  = (Mat_DQN *)lmvm->ctx;

    142:   PetscFunctionBegin;
    143:   if (!lqn->allocated) {
    144:     if (lmvm->m > 0) {
    145:       PetscMPIInt rank;
    146:       PetscInt    n, N, m, M;
    147:       PetscBool   is_dbfgs, is_ddfp, is_dqn;
    148:       VecType     vec_type;
    149:       MPI_Comm    comm  = PetscObjectComm((PetscObject)B);
    150:       Mat         Sfull = lmvm->basis[LMBASIS_S]->vecs;

    152:       PetscCall(PetscObjectTypeCompare((PetscObject)B, MATLMVMDBFGS, &is_dbfgs));
    153:       PetscCall(PetscObjectTypeCompare((PetscObject)B, MATLMVMDDFP, &is_ddfp));
    154:       PetscCall(PetscObjectTypeCompare((PetscObject)B, MATLMVMDQN, &is_dqn));

    156:       PetscCallMPI(MPI_Comm_rank(comm, &rank));
    157:       PetscCall(MatGetSize(B, &N, NULL));
    158:       PetscCall(MatGetLocalSize(B, &n, NULL));
    159:       M = lmvm->m;
    160:       m = (rank == 0) ? M : 0;

    162:       /* For DBFGS: Create data needed for MatSolve() eagerly; data needed for MatMult() will be created on demand
    163:        * For DDFP : Create data needed for MatMult() eagerly; data needed for MatSolve() will be created on demand
    164:        * For DQN  : Create all data eagerly */
    165:       PetscCall(VecGetType(lmvm->Xprev, &vec_type));
    166:       if (is_dqn) {
    167:         PetscCall(MatCreateDenseFromVecType(comm, vec_type, m, m, M, M, -1, NULL, &lqn->StY_triu));
    168:         PetscCall(MatCreateDenseFromVecType(comm, vec_type, m, m, M, M, -1, NULL, &lqn->YtS_triu));
    169:         PetscCall(MatCreateVecs(lqn->StY_triu, &lqn->diag_vec, &lqn->rwork1));
    170:         PetscCall(MatCreateVecs(lqn->StY_triu, &lqn->rwork2, &lqn->rwork3));
    171:       } else if (is_ddfp) {
    172:         PetscCall(MatCreateDenseFromVecType(comm, vec_type, m, m, M, M, -1, NULL, &lqn->YtS_triu));
    173:         PetscCall(MatDuplicate(Sfull, MAT_SHARE_NONZERO_PATTERN, &lqn->HY));
    174:         PetscCall(MatCreateVecs(lqn->YtS_triu, &lqn->diag_vec, &lqn->rwork1));
    175:         PetscCall(MatCreateVecs(lqn->YtS_triu, &lqn->rwork2, &lqn->rwork3));
    176:       } else if (is_dbfgs) {
    177:         PetscCall(MatCreateDenseFromVecType(comm, vec_type, m, m, M, M, -1, NULL, &lqn->StY_triu));
    178:         PetscCall(MatDuplicate(Sfull, MAT_SHARE_NONZERO_PATTERN, &lqn->BS));
    179:         PetscCall(MatCreateVecs(lqn->StY_triu, &lqn->diag_vec, &lqn->rwork1));
    180:         PetscCall(MatCreateVecs(lqn->StY_triu, &lqn->rwork2, &lqn->rwork3));
    181:       } else {
    182:         SETERRQ(PetscObjectComm((PetscObject)B), PETSC_ERR_ARG_INCOMP, "MatAllocate_LMVMDQN is only available for dense derived types. (DBFGS, DDFP, DQN");
    183:       }
    184:       /* initialize StY_triu and YtS_triu to identity, if they exist, so it is invertible */
    185:       if (lqn->StY_triu) {
    186:         PetscCall(MatZeroEntries(lqn->StY_triu));
    187:         PetscCall(MatShift(lqn->StY_triu, 1.0));
    188:       }
    189:       if (lqn->YtS_triu) {
    190:         PetscCall(MatZeroEntries(lqn->YtS_triu));
    191:         PetscCall(MatShift(lqn->YtS_triu, 1.0));
    192:       }
    193:       if (lqn->use_recursive && (is_dbfgs || is_ddfp)) {
    194:         PetscCall(VecDuplicateVecs(lmvm->Xprev, lmvm->m, &lqn->PQ));
    195:         PetscCall(VecDuplicate(lmvm->Xprev, &lqn->column_work2));
    196:         PetscCall(PetscMalloc1(lmvm->m, &lqn->yts));
    197:         if (is_dbfgs) PetscCall(PetscMalloc1(lmvm->m, &lqn->stp));
    198:         else if (is_ddfp) PetscCall(PetscMalloc1(lmvm->m, &lqn->ytq));
    199:       }
    200:       PetscCall(VecDuplicate(lqn->rwork2, &lqn->cyclic_work_vec));
    201:       PetscCall(VecZeroEntries(lqn->rwork1));
    202:       PetscCall(VecZeroEntries(lqn->rwork2));
    203:       PetscCall(VecZeroEntries(lqn->rwork3));
    204:       PetscCall(VecZeroEntries(lqn->diag_vec));
    205:     }
    206:     PetscCall(VecDuplicate(lmvm->Xprev, &lqn->column_work));
    207:     lqn->allocated = PETSC_TRUE;
    208:   }
    209:   PetscFunctionReturn(PETSC_SUCCESS);
    210: }

    212: static PetscErrorCode MatSetUp_LMVMDQN(Mat B)
    213: {
    214:   Mat_LMVM *lmvm = (Mat_LMVM *)B->data;
    215:   Mat_DQN  *lqn  = (Mat_DQN *)lmvm->ctx;

    217:   PetscFunctionBegin;
    218:   PetscCall(MatSetUp_LMVM(B));
    219:   PetscCall(SymBroydenRescaleInitializeJ0(B, lqn->rescale));
    220:   PetscCall(MatAllocate_LMVMDQN_Internal(B));
    221:   PetscFunctionReturn(PETSC_SUCCESS);
    222: }

    224: static PetscErrorCode MatSetFromOptions_LMVMDQN(Mat B, PetscOptionItems PetscOptionsObject)
    225: {
    226:   Mat_LMVM *lmvm = (Mat_LMVM *)B->data;
    227:   Mat_DQN  *lqn  = (Mat_DQN *)lmvm->ctx;
    228:   PetscBool is_dbfgs, is_ddfp, is_dqn;

    230:   PetscFunctionBegin;
    231:   PetscCall(PetscObjectTypeCompare((PetscObject)B, MATLMVMDBFGS, &is_dbfgs));
    232:   PetscCall(PetscObjectTypeCompare((PetscObject)B, MATLMVMDDFP, &is_ddfp));
    233:   PetscCall(PetscObjectTypeCompare((PetscObject)B, MATLMVMDQN, &is_dqn));
    234:   PetscCall(MatSetFromOptions_LMVM(B, PetscOptionsObject));
    235:   PetscOptionsHeadBegin(PetscOptionsObject, "Dense symmetric Broyden method for approximating SPD Jacobian actions");
    236:   if (is_dqn) {
    237:     PetscCall(PetscOptionsEnum("-mat_lqn_type", "Implementation options for L-QN", "MatLMVMDenseType", MatLMVMDenseTypes, (PetscEnum)lqn->strategy, (PetscEnum *)&lqn->strategy, NULL));
    238:   } else if (is_dbfgs) {
    239:     PetscCall(PetscOptionsBool("-mat_lbfgs_recursive", "Use recursive formulation for MatMult_LMVMDBFGS, instead of Cholesky", "", lqn->use_recursive, &lqn->use_recursive, NULL));
    240:     PetscCall(PetscOptionsEnum("-mat_lbfgs_type", "Implementation options for L-BFGS", "MatLMVMDenseType", MatLMVMDenseTypes, (PetscEnum)lqn->strategy, (PetscEnum *)&lqn->strategy, NULL));
    241:   } else if (is_ddfp) {
    242:     PetscCall(PetscOptionsBool("-mat_ldfp_recursive", "Use recursive formulation for MatSolve_LMVMDDFP, instead of Cholesky", "", lqn->use_recursive, &lqn->use_recursive, NULL));
    243:     PetscCall(PetscOptionsEnum("-mat_ldfp_type", "Implementation options for L-DFP", "MatLMVMDenseType", MatLMVMDenseTypes, (PetscEnum)lqn->strategy, (PetscEnum *)&lqn->strategy, NULL));
    244:   } else {
    245:     SETERRQ(PetscObjectComm((PetscObject)B), PETSC_ERR_ARG_INCOMP, "MatSetFromOptions_LMVMDQN is only available for dense derived types. (DBFGS, DDFP, DQN");
    246:   }
    247:   PetscCall(SymBroydenRescaleSetFromOptions(B, lqn->rescale, PetscOptionsObject));
    248:   PetscOptionsHeadEnd();
    249:   PetscFunctionReturn(PETSC_SUCCESS);
    250: }

    252: static PetscErrorCode MatDestroy_LMVMDQN(Mat B)
    253: {
    254:   Mat_LMVM *lmvm = (Mat_LMVM *)B->data;
    255:   Mat_DQN  *lqn  = (Mat_DQN *)lmvm->ctx;

    257:   PetscFunctionBegin;
    258:   PetscCall(SymBroydenRescaleDestroy(&lqn->rescale));
    259:   PetscCall(MatReset_LMVMDQN_Internal(B, MAT_LMVM_RESET_ALL));
    260:   PetscCall(PetscFree(lqn->workscalar));
    261:   PetscCall(PetscFree(lmvm->ctx));
    262:   PetscCall(MatDestroy_LMVM(B));
    263:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatLMVMSymBroydenSetDelta_C", NULL));
    264:   PetscFunctionReturn(PETSC_SUCCESS);
    265: }

    267: static PetscErrorCode MatUpdate_LMVMDQN(Mat B, Vec X, Vec F)
    268: {
    269:   Mat_LMVM *lmvm  = (Mat_LMVM *)B->data;
    270:   Mat_DQN  *lqn   = (Mat_DQN *)lmvm->ctx;
    271:   Mat       Sfull = lmvm->basis[LMBASIS_S]->vecs;
    272:   Mat       Yfull = lmvm->basis[LMBASIS_Y]->vecs;

    274:   PetscBool          is_ddfp, is_dbfgs, is_dqn;
    275:   PetscDeviceContext dctx;

    277:   PetscFunctionBegin;
    278:   if (!lmvm->m) PetscFunctionReturn(PETSC_SUCCESS);
    279:   PetscCall(PetscObjectTypeCompare((PetscObject)B, MATLMVMDBFGS, &is_dbfgs));
    280:   PetscCall(PetscObjectTypeCompare((PetscObject)B, MATLMVMDDFP, &is_ddfp));
    281:   PetscCall(PetscObjectTypeCompare((PetscObject)B, MATLMVMDQN, &is_dqn));
    282:   PetscCall(PetscDeviceContextGetCurrentContext(&dctx));
    283:   if (lmvm->prev_set) {
    284:     Vec         FX[2];
    285:     PetscScalar dotFX[2];
    286:     PetscScalar stFprev;
    287:     PetscScalar curvature, yTy;
    288:     PetscReal   curvtol;

    290:     /* Compute the new (S = X - Xprev) and (Y = F - Fprev) vectors */
    291:     PetscCall(VecAYPX(lmvm->Xprev, -1.0, X));
    292:     /* Test if the updates can be accepted */
    293:     FX[0] = lmvm->Fprev; /* dotFX[0] = s^T Fprev */
    294:     FX[1] = F;           /* dotFX[1] = s^T F     */
    295:     PetscCall(VecMDot(lmvm->Xprev, 2, FX, dotFX));
    296:     PetscCall(VecAYPX(lmvm->Fprev, -1.0, F));
    297:     PetscCall(VecDot(lmvm->Fprev, lmvm->Fprev, &yTy));
    298:     stFprev   = PetscConj(dotFX[0]);
    299:     curvature = PetscConj(dotFX[1] - dotFX[0]); /* s^T y */
    300:     if (PetscRealPart(yTy) < lmvm->eps) {
    301:       curvtol = 0.0;
    302:     } else {
    303:       curvtol = lmvm->eps * PetscRealPart(yTy);
    304:     }
    305:     if (PetscRealPart(curvature) > curvtol) {
    306:       PetscInt m     = lmvm->m;
    307:       PetscInt k     = lmvm->k;
    308:       PetscInt h_old = k - oldest_update(m, k);
    309:       PetscInt h_new = k + 1 - oldest_update(m, k + 1);
    310:       PetscInt idx   = recycle_index(m, k);

    312:       /* Update is good, accept it */
    313:       PetscCall(MatUpdateKernel_LMVM(B, lmvm->Xprev, lmvm->Fprev));
    314:       lqn->num_updates++;
    315:       lqn->watchdog = 0;
    316:       lqn->needPQ   = PETSC_TRUE;

    318:       if (h_old == m && lqn->strategy == MAT_LMVM_DENSE_REORDER) {
    319:         if (is_dqn) {
    320:           PetscCall(MatMove_LR3(B, lqn->StY_triu, m - 1));
    321:           PetscCall(MatMove_LR3(B, lqn->YtS_triu, m - 1));
    322:         } else if (is_dbfgs) {
    323:           PetscCall(MatMove_LR3(B, lqn->StY_triu, m - 1));
    324:         } else if (is_ddfp) {
    325:           PetscCall(MatMove_LR3(B, lqn->YtS_triu, m - 1));
    326:         } else {
    327:           SETERRQ(PetscObjectComm((PetscObject)B), PETSC_ERR_ARG_INCOMP, "MatUpdate_LMVMDQN is only available for dense derived types. (DBFGS, DDFP, DQN");
    328:         }
    329:       }

    331:       if (lqn->use_recursive && (is_dbfgs || is_ddfp)) lqn->yts[idx] = PetscRealPart(curvature);

    333:       if (is_dqn || is_dbfgs) { /* implement the scheme of Byrd, Nocedal, and Schnabel to save a MatMultTranspose call in the common case the       *
    334:          * H_k is immediately applied to F after begin updated.   The S^T y computation can be split up as S^T (F - F_prev) */
    335:         PetscInt     local_n;
    336:         PetscScalar *StFprev;
    337:         PetscMemType memtype;
    338:         PetscInt     StYidx;

    340:         StYidx = (lqn->strategy == MAT_LMVM_DENSE_REORDER) ? history_index(m, lqn->num_updates, k) : idx;
    341:         if (!lqn->StFprev) PetscCall(VecDuplicate(lqn->rwork1, &lqn->StFprev));
    342:         PetscCall(VecGetLocalSize(lqn->StFprev, &local_n));
    343:         PetscCall(VecGetArrayAndMemType(lqn->StFprev, &StFprev, &memtype));
    344:         if (local_n) {
    345:           if (PetscMemTypeHost(memtype)) {
    346:             StFprev[idx] = stFprev;
    347:           } else {
    348:             PetscCall(PetscDeviceRegisterMemory(&stFprev, PETSC_MEMTYPE_HOST, 1 * sizeof(stFprev)));
    349:             PetscCall(PetscDeviceRegisterMemory(StFprev, memtype, local_n * sizeof(*StFprev)));
    350:             PetscCall(PetscDeviceArrayCopy(dctx, &StFprev[idx], &stFprev, 1));
    351:           }
    352:         }
    353:         PetscCall(VecRestoreArrayAndMemType(lqn->StFprev, &StFprev));

    355:         {
    356:           Vec this_sy_col;
    357:           /* Now StFprev is updated for the new S vector.  Write -StFprev into the appropriate row */
    358:           PetscCall(MatDenseGetColumnVecWrite(lqn->StY_triu, StYidx, &this_sy_col));
    359:           PetscCall(VecAXPBY(this_sy_col, -1.0, 0.0, lqn->StFprev));

    361:           /* Now compute the new StFprev */
    362:           PetscCall(MatMultHermitianTransposeColumnRange(Sfull, F, lqn->StFprev, 0, h_new));
    363:           lqn->St_count++;

    365:           /* Now add StFprev: this_sy_col == S^T (F - Fprev) == S^T y */
    366:           PetscCall(VecAXPY(this_sy_col, 1.0, lqn->StFprev));

    368:           if (lqn->strategy == MAT_LMVM_DENSE_REORDER) PetscCall(VecRecycleOrderToHistoryOrder(B, this_sy_col, lqn->num_updates, lqn->cyclic_work_vec));
    369:           PetscCall(MatDenseRestoreColumnVecWrite(lqn->StY_triu, StYidx, &this_sy_col));
    370:         }
    371:       }

    373:       if (is_ddfp || is_dqn) {
    374:         PetscInt YtSidx;

    376:         YtSidx = (lqn->strategy == MAT_LMVM_DENSE_REORDER) ? history_index(m, lqn->num_updates, k) : idx;

    378:         {
    379:           Vec this_ys_col;

    381:           PetscCall(MatDenseGetColumnVecWrite(lqn->YtS_triu, YtSidx, &this_ys_col));
    382:           PetscCall(MatMultHermitianTransposeColumnRange(Yfull, lmvm->Xprev, this_ys_col, 0, h_new));
    383:           lqn->Yt_count++;

    385:           if (lqn->strategy == MAT_LMVM_DENSE_REORDER) PetscCall(VecRecycleOrderToHistoryOrder(B, this_ys_col, lqn->num_updates, lqn->cyclic_work_vec));
    386:           PetscCall(MatDenseRestoreColumnVecWrite(lqn->YtS_triu, YtSidx, &this_ys_col));
    387:         }
    388:       }

    390:       if (is_dbfgs || is_dqn) {
    391:         PetscCall(MatGetDiagonal(lqn->StY_triu, lqn->diag_vec));
    392:       } else if (is_ddfp) {
    393:         PetscCall(MatGetDiagonal(lqn->YtS_triu, lqn->diag_vec));
    394:       } else {
    395:         SETERRQ(PetscObjectComm((PetscObject)B), PETSC_ERR_ARG_INCOMP, "MatUpdate_LMVMDQN is only available for dense derived types. (DBFGS, DDFP, DQN");
    396:       }

    398:       if (lqn->strategy == MAT_LMVM_DENSE_REORDER) {
    399:         if (!lqn->diag_vec_recycle_order) PetscCall(VecDuplicate(lqn->diag_vec, &lqn->diag_vec_recycle_order));
    400:         PetscCall(VecCopy(lqn->diag_vec, lqn->diag_vec_recycle_order));
    401:         PetscCall(VecHistoryOrderToRecycleOrder(B, lqn->diag_vec_recycle_order, lqn->num_updates, lqn->cyclic_work_vec));
    402:       } else {
    403:         if (!lqn->diag_vec_recycle_order) {
    404:           PetscCall(PetscObjectReference((PetscObject)lqn->diag_vec));
    405:           lqn->diag_vec_recycle_order = lqn->diag_vec;
    406:         }
    407:       }

    409:       PetscCall(SymBroydenRescaleUpdate(B, lqn->rescale));
    410:     } else {
    411:       /* Update is bad, skip it */
    412:       ++lmvm->nrejects;
    413:       ++lqn->watchdog;
    414:       PetscInt m = lmvm->m;
    415:       PetscInt k = lmvm->k;
    416:       PetscInt h = k - oldest_update(m, k);

    418:       /* we still have to maintain StFprev */
    419:       if (!lqn->StFprev) PetscCall(VecDuplicate(lqn->rwork1, &lqn->StFprev));
    420:       PetscCall(MatMultHermitianTransposeColumnRange(Sfull, F, lqn->StFprev, 0, h));
    421:       lqn->St_count++;
    422:     }
    423:   }

    425:   if (lqn->watchdog > lqn->max_seq_rejects) PetscCall(MatLMVMReset(B, PETSC_FALSE));

    427:   /* Save the solution and function to be used in the next update */
    428:   PetscCall(VecCopy(X, lmvm->Xprev));
    429:   PetscCall(VecCopy(F, lmvm->Fprev));
    430:   PetscCall(PetscObjectReference((PetscObject)F));
    431:   PetscCall(VecDestroy(&lqn->Fprev_ref));
    432:   lqn->Fprev_ref = F;
    433:   PetscCall(PetscObjectStateGet((PetscObject)F, &lqn->Fprev_state));
    434:   lmvm->prev_set = PETSC_TRUE;
    435:   PetscFunctionReturn(PETSC_SUCCESS);
    436: }

    438: static PetscErrorCode MatDestroyThenCopy(Mat src, Mat *dst)
    439: {
    440:   PetscFunctionBegin;
    441:   PetscCall(MatDestroy(dst));
    442:   if (src) PetscCall(MatDuplicate(src, MAT_COPY_VALUES, dst));
    443:   PetscFunctionReturn(PETSC_SUCCESS);
    444: }

    446: static PetscErrorCode VecDestroyThenCopy(Vec src, Vec *dst)
    447: {
    448:   PetscFunctionBegin;
    449:   PetscCall(VecDestroy(dst));
    450:   if (src) {
    451:     PetscCall(VecDuplicate(src, dst));
    452:     PetscCall(VecCopy(src, *dst));
    453:   }
    454:   PetscFunctionReturn(PETSC_SUCCESS);
    455: }

    457: static PetscErrorCode MatCopy_LMVMDQN(Mat B, Mat M, MatStructure str)
    458: {
    459:   Mat_LMVM *bdata = (Mat_LMVM *)B->data;
    460:   Mat_DQN  *blqn  = (Mat_DQN *)bdata->ctx;
    461:   Mat_LMVM *mdata = (Mat_LMVM *)M->data;
    462:   Mat_DQN  *mlqn  = (Mat_DQN *)mdata->ctx;
    463:   PetscInt  i;
    464:   PetscBool is_dbfgs, is_ddfp, is_dqn;

    466:   PetscFunctionBegin;
    467:   PetscCall(SymBroydenRescaleCopy(blqn->rescale, mlqn->rescale));
    468:   mlqn->num_updates      = blqn->num_updates;
    469:   mlqn->num_mult_updates = blqn->num_mult_updates;
    470:   mlqn->dense_type       = blqn->dense_type;
    471:   mlqn->strategy         = blqn->strategy;
    472:   mlqn->S_count          = 0;
    473:   mlqn->St_count         = 0;
    474:   mlqn->Y_count          = 0;
    475:   mlqn->Yt_count         = 0;
    476:   mlqn->watchdog         = blqn->watchdog;
    477:   mlqn->max_seq_rejects  = blqn->max_seq_rejects;
    478:   mlqn->use_recursive    = blqn->use_recursive;
    479:   mlqn->needPQ           = blqn->needPQ;
    480:   if (blqn->allocated) {
    481:     PetscCall(MatAllocate_LMVMDQN_Internal(M));
    482:     PetscCall(PetscObjectTypeCompare((PetscObject)B, MATLMVMDBFGS, &is_dbfgs));
    483:     PetscCall(PetscObjectTypeCompare((PetscObject)B, MATLMVMDDFP, &is_ddfp));
    484:     PetscCall(PetscObjectTypeCompare((PetscObject)B, MATLMVMDQN, &is_dqn));
    485:     PetscCall(MatDestroyThenCopy(blqn->HY, &mlqn->BS));
    486:     PetscCall(VecDestroyThenCopy(blqn->StFprev, &mlqn->StFprev));
    487:     PetscCall(MatDestroyThenCopy(blqn->StY_triu, &mlqn->StY_triu));
    488:     PetscCall(MatDestroyThenCopy(blqn->StY_triu_strict, &mlqn->StY_triu_strict));
    489:     PetscCall(MatDestroyThenCopy(blqn->YtS_triu, &mlqn->YtS_triu));
    490:     PetscCall(MatDestroyThenCopy(blqn->YtS_triu_strict, &mlqn->YtS_triu_strict));
    491:     PetscCall(MatDestroyThenCopy(blqn->YtHY, &mlqn->YtHY));
    492:     PetscCall(MatDestroyThenCopy(blqn->StBS, &mlqn->StBS));
    493:     PetscCall(MatDestroyThenCopy(blqn->J, &mlqn->J));
    494:     PetscCall(VecDestroyThenCopy(blqn->diag_vec, &mlqn->diag_vec));
    495:     PetscCall(VecDestroyThenCopy(blqn->diag_vec_recycle_order, &mlqn->diag_vec_recycle_order));
    496:     PetscCall(VecDestroyThenCopy(blqn->inv_diag_vec, &mlqn->inv_diag_vec));
    497:     if (blqn->use_recursive && (is_dbfgs || is_ddfp)) {
    498:       for (i = 0; i < bdata->m; i++) {
    499:         PetscCall(VecDestroyThenCopy(blqn->PQ[i], &mlqn->PQ[i]));
    500:         mlqn->yts[i] = blqn->yts[i];
    501:         if (is_dbfgs) {
    502:           mlqn->stp[i] = blqn->stp[i];
    503:         } else if (is_ddfp) {
    504:           mlqn->ytq[i] = blqn->ytq[i];
    505:         }
    506:       }
    507:     }
    508:   }
    509:   PetscCall(PetscObjectReference((PetscObject)blqn->Fprev_ref));
    510:   PetscCall(VecDestroy(&mlqn->Fprev_ref));
    511:   mlqn->Fprev_ref   = blqn->Fprev_ref;
    512:   mlqn->Fprev_state = blqn->Fprev_state;
    513:   PetscFunctionReturn(PETSC_SUCCESS);
    514: }

    516: static PetscErrorCode MatMult_LMVMDQN(Mat B, Vec X, Vec Z)
    517: {
    518:   PetscFunctionBegin;
    519:   PetscCall(MatMult_LMVMDDFP(B, X, Z));
    520:   PetscFunctionReturn(PETSC_SUCCESS);
    521: }

    523: static PetscErrorCode MatSolve_LMVMDQN(Mat H, Vec F, Vec dX)
    524: {
    525:   PetscFunctionBegin;
    526:   PetscCall(MatSolve_LMVMDBFGS(H, F, dX));
    527:   PetscFunctionReturn(PETSC_SUCCESS);
    528: }

    530: static PetscErrorCode MatLMVMSymBroydenSetDelta_LMVMDQN(Mat B, PetscScalar delta)
    531: {
    532:   Mat_LMVM *lmvm = (Mat_LMVM *)B->data;
    533:   Mat_DQN  *lqn  = (Mat_DQN *)lmvm->ctx;

    535:   PetscFunctionBegin;
    536:   PetscCall(SymBroydenRescaleSetDelta(B, lqn->rescale, PetscAbsReal(PetscRealPart(delta))));
    537:   PetscFunctionReturn(PETSC_SUCCESS);
    538: }

    540: /*
    541:   This dense representation uses Davidon-Fletcher-Powell (DFP) for MatMult,
    542:   and Broyden-Fletcher-Goldfarb-Shanno (BFGS) for MatSolve. This implementation
    543:   results in avoiding costly Cholesky factorization, at the cost of duality cap.
    544:   Please refer to MatLMVMDDFP and MatLMVMDBFGS for more information.
    545: */
    546: PetscErrorCode MatCreate_LMVMDQN(Mat B)
    547: {
    548:   Mat_LMVM *lmvm;
    549:   Mat_DQN  *lqn;

    551:   PetscFunctionBegin;
    552:   PetscCall(MatCreate_LMVM(B));
    553:   PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATLMVMDQN));
    554:   PetscCall(MatSetOption(B, MAT_HERMITIAN, PETSC_TRUE));
    555:   PetscCall(MatSetOption(B, MAT_SPD, PETSC_TRUE));
    556:   PetscCall(MatSetOption(B, MAT_SPD_ETERNAL, PETSC_TRUE));
    557:   B->ops->view           = MatView_LMVMDQN;
    558:   B->ops->setup          = MatSetUp_LMVMDQN;
    559:   B->ops->setfromoptions = MatSetFromOptions_LMVMDQN;
    560:   B->ops->destroy        = MatDestroy_LMVMDQN;

    562:   lmvm              = (Mat_LMVM *)B->data;
    563:   lmvm->ops->reset  = MatReset_LMVMDQN;
    564:   lmvm->ops->update = MatUpdate_LMVMDQN;
    565:   lmvm->ops->mult   = MatMult_LMVMDQN;
    566:   lmvm->ops->solve  = MatSolve_LMVMDQN;
    567:   lmvm->ops->copy   = MatCopy_LMVMDQN;

    569:   lmvm->ops->multht  = lmvm->ops->mult;
    570:   lmvm->ops->solveht = lmvm->ops->solve;

    572:   PetscCall(PetscNew(&lqn));
    573:   lmvm->ctx            = (void *)lqn;
    574:   lqn->allocated       = PETSC_FALSE;
    575:   lqn->use_recursive   = PETSC_FALSE;
    576:   lqn->needPQ          = PETSC_FALSE;
    577:   lqn->watchdog        = 0;
    578:   lqn->max_seq_rejects = lmvm->m / 2;
    579:   lqn->strategy        = MAT_LMVM_DENSE_INPLACE;

    581:   PetscCall(SymBroydenRescaleCreate(&lqn->rescale));
    582:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatLMVMSymBroydenSetDelta_C", MatLMVMSymBroydenSetDelta_LMVMDQN));
    583:   PetscFunctionReturn(PETSC_SUCCESS);
    584: }

    586: /*@
    587:   MatCreateLMVMDQN - Creates a dense representation of the limited-memory
    588:   Quasi-Newton approximation to a Hessian.

    590:   Collective

    592:   Input Parameters:
    593: + comm - MPI communicator
    594: . n    - number of local rows for storage vectors
    595: - N    - global size of the storage vectors

    597:   Output Parameter:
    598: . B - the matrix

    600:   Level: advanced

    602:   Note:
    603:   It is recommended that one use the `MatCreate()`, `MatSetType()` and/or `MatSetFromOptions()`
    604:   paradigm instead of this routine directly.

    606: .seealso: `MatCreate()`, `MATLMVM`, `MATLMVMDBFGS`, `MATLMVMDDFP`, `MatCreateLMVMDDFP()`, `MatCreateLMVMDBFGS()`
    607: @*/
    608: PetscErrorCode MatCreateLMVMDQN(MPI_Comm comm, PetscInt n, PetscInt N, Mat *B)
    609: {
    610:   PetscFunctionBegin;
    611:   PetscCall(KSPInitializePackage());
    612:   PetscCall(MatCreate(comm, B));
    613:   PetscCall(MatSetSizes(*B, n, n, N, N));
    614:   PetscCall(MatSetType(*B, MATLMVMDQN));
    615:   PetscCall(MatSetUp(*B));
    616:   PetscFunctionReturn(PETSC_SUCCESS);
    617: }

    619: static PetscErrorCode MatDQNApplyJ0Fwd(Mat B, Vec X, Vec Z)
    620: {
    621:   PetscFunctionBegin;
    622:   PetscCall(MatLMVMApplyJ0Fwd(B, X, Z));
    623:   PetscFunctionReturn(PETSC_SUCCESS);
    624: }

    626: static PetscErrorCode MatDQNApplyJ0Inv(Mat B, Vec F, Vec dX)
    627: {
    628:   PetscFunctionBegin;
    629:   PetscCall(MatLMVMApplyJ0Inv(B, F, dX));
    630:   PetscFunctionReturn(PETSC_SUCCESS);
    631: }

    633: /* This is not Bunch-Kaufman LDLT: here L is strictly lower triangular part of STY */
    634: static PetscErrorCode MatGetLDLT(Mat B, Mat result)
    635: {
    636:   Mat_LMVM *lmvm  = (Mat_LMVM *)B->data;
    637:   Mat_DQN  *lbfgs = (Mat_DQN *)lmvm->ctx;
    638:   PetscInt  m_local;

    640:   PetscFunctionBegin;
    641:   if (!lbfgs->temp_mat) PetscCall(MatDuplicate(lbfgs->YtS_triu_strict, MAT_SHARE_NONZERO_PATTERN, &lbfgs->temp_mat));
    642:   PetscCall(MatCopy(lbfgs->YtS_triu_strict, lbfgs->temp_mat, SAME_NONZERO_PATTERN));
    643:   PetscCall(MatDiagonalScale(lbfgs->temp_mat, lbfgs->inv_diag_vec, NULL));
    644:   PetscCall(MatGetLocalSize(result, &m_local, NULL));
    645:   // need to conjugate and conjugate again because we have MatTransposeMatMult but not MatHermitianTransposeMatMult()
    646:   PetscCall(MatConjugate(lbfgs->temp_mat));
    647:   if (m_local) {
    648:     Mat temp_local, YtS_local, result_local;
    649:     PetscCall(MatDenseGetLocalMatrix(lbfgs->YtS_triu_strict, &YtS_local));
    650:     PetscCall(MatDenseGetLocalMatrix(lbfgs->temp_mat, &temp_local));
    651:     PetscCall(MatDenseGetLocalMatrix(result, &result_local));
    652:     PetscCall(MatTransposeMatMult(YtS_local, temp_local, MAT_REUSE_MATRIX, PETSC_DETERMINE, &result_local));
    653:   }
    654:   PetscCall(MatConjugate(result));
    655:   PetscFunctionReturn(PETSC_SUCCESS);
    656: }

    658: static PetscErrorCode MatLMVMDBFGSUpdateMultData(Mat B)
    659: {
    660:   Mat_LMVM *lmvm  = (Mat_LMVM *)B->data;
    661:   Mat_DQN  *lbfgs = (Mat_DQN *)lmvm->ctx;
    662:   PetscInt  m     = lmvm->m, m_local;
    663:   PetscInt  k     = lmvm->k;
    664:   PetscInt  h     = k - oldest_update(m, k);
    665:   PetscInt  j_0;
    666:   PetscInt  prev_oldest;
    667:   Mat       J_local;
    668:   Mat       Sfull = lmvm->basis[LMBASIS_S]->vecs;
    669:   Mat       Yfull = lmvm->basis[LMBASIS_Y]->vecs;

    671:   PetscFunctionBegin;
    672:   if (!lbfgs->YtS_triu_strict) {
    673:     PetscCall(MatDuplicate(lbfgs->StY_triu, MAT_SHARE_NONZERO_PATTERN, &lbfgs->YtS_triu_strict));
    674:     PetscCall(MatDestroy(&lbfgs->StBS));
    675:     PetscCall(MatDuplicate(lbfgs->StY_triu, MAT_SHARE_NONZERO_PATTERN, &lbfgs->StBS));
    676:     PetscCall(MatDestroy(&lbfgs->J));
    677:     PetscCall(MatDuplicate(lbfgs->StY_triu, MAT_SHARE_NONZERO_PATTERN, &lbfgs->J));
    678:     PetscCall(MatDestroy(&lbfgs->BS));
    679:     PetscCall(MatDuplicate(Yfull, MAT_SHARE_NONZERO_PATTERN, &lbfgs->BS));
    680:     PetscCall(MatShift(lbfgs->StBS, 1.0));
    681:     lbfgs->num_mult_updates = oldest_update(m, k);
    682:   }
    683:   if (lbfgs->num_mult_updates == k) PetscFunctionReturn(PETSC_SUCCESS);

    685:   /* B_0 may have been updated, we must recompute B_0 S and S^T B_0 S */
    686:   for (PetscInt j = oldest_update(m, k); j < k; j++) {
    687:     Vec      s_j;
    688:     Vec      Bs_j;
    689:     Vec      StBs_j;
    690:     PetscInt S_idx    = recycle_index(m, j);
    691:     PetscInt StBS_idx = lbfgs->strategy == MAT_LMVM_DENSE_INPLACE ? S_idx : history_index(m, k, j);

    693:     PetscCall(MatDenseGetColumnVecWrite(lbfgs->BS, S_idx, &Bs_j));
    694:     PetscCall(MatDenseGetColumnVecRead(Sfull, S_idx, &s_j));
    695:     PetscCall(MatDQNApplyJ0Fwd(B, s_j, Bs_j));
    696:     PetscCall(MatDenseRestoreColumnVecRead(Sfull, S_idx, &s_j));
    697:     PetscCall(MatDenseGetColumnVecWrite(lbfgs->StBS, StBS_idx, &StBs_j));
    698:     PetscCall(MatMultHermitianTransposeColumnRange(Sfull, Bs_j, StBs_j, 0, h));
    699:     lbfgs->St_count++;
    700:     if (lbfgs->strategy == MAT_LMVM_DENSE_REORDER) PetscCall(VecRecycleOrderToHistoryOrder(B, StBs_j, lbfgs->num_updates, lbfgs->cyclic_work_vec));
    701:     PetscCall(MatDenseRestoreColumnVecWrite(lbfgs->StBS, StBS_idx, &StBs_j));
    702:     PetscCall(MatDenseRestoreColumnVecWrite(lbfgs->BS, S_idx, &Bs_j));
    703:   }
    704:   prev_oldest = oldest_update(m, lbfgs->num_mult_updates);
    705:   if (lbfgs->strategy == MAT_LMVM_DENSE_REORDER && prev_oldest < oldest_update(m, k)) {
    706:     /* move the YtS entries that have been computed and need to be kept back up */
    707:     PetscInt m_keep = m - (oldest_update(m, k) - prev_oldest);

    709:     PetscCall(MatMove_LR3(B, lbfgs->YtS_triu_strict, m_keep));
    710:   }
    711:   PetscCall(MatGetLocalSize(lbfgs->YtS_triu_strict, &m_local, NULL));
    712:   j_0 = PetscMax(lbfgs->num_mult_updates, oldest_update(m, k));
    713:   for (PetscInt j = j_0; j < k; j++) {
    714:     PetscInt S_idx   = recycle_index(m, j);
    715:     PetscInt YtS_idx = lbfgs->strategy == MAT_LMVM_DENSE_INPLACE ? S_idx : history_index(m, k, j);
    716:     Vec      s_j, Yts_j;

    718:     PetscCall(MatDenseGetColumnVecRead(Sfull, S_idx, &s_j));
    719:     PetscCall(MatDenseGetColumnVecWrite(lbfgs->YtS_triu_strict, YtS_idx, &Yts_j));
    720:     PetscCall(MatMultHermitianTransposeColumnRange(Yfull, s_j, Yts_j, 0, h));
    721:     lbfgs->Yt_count++;
    722:     if (lbfgs->strategy == MAT_LMVM_DENSE_REORDER) PetscCall(VecRecycleOrderToHistoryOrder(B, Yts_j, lbfgs->num_updates, lbfgs->cyclic_work_vec));
    723:     PetscCall(MatDenseRestoreColumnVecWrite(lbfgs->YtS_triu_strict, YtS_idx, &Yts_j));
    724:     PetscCall(MatDenseRestoreColumnVecRead(Sfull, S_idx, &s_j));
    725:     /* zero the corresponding row */
    726:     if (m_local > 0) {
    727:       Mat YtS_local, YtS_row;

    729:       PetscCall(MatDenseGetLocalMatrix(lbfgs->YtS_triu_strict, &YtS_local));
    730:       PetscCall(MatDenseGetSubMatrix(YtS_local, YtS_idx, YtS_idx + 1, PETSC_DECIDE, PETSC_DECIDE, &YtS_row));
    731:       PetscCall(MatZeroEntries(YtS_row));
    732:       PetscCall(MatDenseRestoreSubMatrix(YtS_local, &YtS_row));
    733:     }
    734:   }
    735:   if (!lbfgs->inv_diag_vec) PetscCall(VecDuplicate(lbfgs->diag_vec, &lbfgs->inv_diag_vec));
    736:   PetscCall(VecCopy(lbfgs->diag_vec, lbfgs->inv_diag_vec));
    737:   PetscCall(VecReciprocal(lbfgs->inv_diag_vec));
    738:   PetscCall(MatDenseGetLocalMatrix(lbfgs->J, &J_local));
    739:   PetscCall(MatSetFactorType(J_local, MAT_FACTOR_NONE));
    740:   PetscCall(MatGetLDLT(B, lbfgs->J));
    741:   PetscCall(MatAXPY(lbfgs->J, 1.0, lbfgs->StBS, SAME_NONZERO_PATTERN));
    742:   if (m_local) {
    743:     PetscCall(MatSetOption(J_local, MAT_SPD, PETSC_TRUE));
    744:     PetscCall(MatCholeskyFactor(J_local, NULL, NULL));
    745:   }
    746:   lbfgs->num_mult_updates = lbfgs->num_updates;
    747:   PetscFunctionReturn(PETSC_SUCCESS);
    748: }

    750: /* Solves for
    751:  * [ I | -S R^{-T} ] [  I  | 0 ] [ H_0 | 0 ] [ I | Y ] [      I      ]
    752:  *                   [-----+---] [-----+---] [---+---] [-------------]
    753:  *                   [ Y^T | I ] [  0  | D ] [ 0 | I ] [ -R^{-1} S^T ]  */

    755: static PetscErrorCode MatSolve_LMVMDBFGS(Mat H, Vec F, Vec dX)
    756: {
    757:   Mat_LMVM        *lmvm   = (Mat_LMVM *)H->data;
    758:   Mat_DQN         *lbfgs  = (Mat_DQN *)lmvm->ctx;
    759:   Vec              rwork1 = lbfgs->rwork1;
    760:   PetscInt         m      = lmvm->m;
    761:   PetscInt         k      = lmvm->k;
    762:   PetscInt         h      = k - oldest_update(m, k);
    763:   Mat              Sfull  = lmvm->basis[LMBASIS_S]->vecs;
    764:   Mat              Yfull  = lmvm->basis[LMBASIS_Y]->vecs;
    765:   PetscObjectState Fstate;

    767:   PetscFunctionBegin;
    768:   VecCheckSameSize(F, 2, dX, 3);
    769:   VecCheckMatCompatible(H, dX, 3, F, 2);

    771:   /* Block Version */
    772:   if (!lbfgs->num_updates) {
    773:     PetscCall(MatDQNApplyJ0Inv(H, F, dX));
    774:     PetscFunctionReturn(PETSC_SUCCESS); /* No updates stored yet */
    775:   }

    777:   PetscCall(PetscObjectStateGet((PetscObject)F, &Fstate));
    778:   if (F == lbfgs->Fprev_ref && Fstate == lbfgs->Fprev_state) {
    779:     PetscCall(VecCopy(lbfgs->StFprev, rwork1));
    780:   } else {
    781:     PetscCall(MatMultHermitianTransposeColumnRange(Sfull, F, rwork1, 0, h));
    782:     lbfgs->St_count++;
    783:   }

    785:   /* Reordering rwork1, as STY is in history order, while S is in recycled order */
    786:   if (lbfgs->strategy == MAT_LMVM_DENSE_REORDER) PetscCall(VecRecycleOrderToHistoryOrder(H, rwork1, lbfgs->num_updates, lbfgs->cyclic_work_vec));
    787:   PetscCall(MatUpperTriangularSolveInPlace(H, lbfgs->StY_triu, rwork1, PETSC_FALSE, lbfgs->num_updates, lbfgs->strategy));
    788:   PetscCall(VecScale(rwork1, -1.0));
    789:   if (lbfgs->strategy == MAT_LMVM_DENSE_REORDER) PetscCall(VecHistoryOrderToRecycleOrder(H, rwork1, lbfgs->num_updates, lbfgs->cyclic_work_vec));

    791:   PetscCall(VecCopy(F, lbfgs->column_work));
    792:   PetscCall(MatMultAddColumnRange(Yfull, rwork1, lbfgs->column_work, lbfgs->column_work, 0, h));
    793:   lbfgs->Y_count++;

    795:   PetscCall(VecPointwiseMult(rwork1, lbfgs->diag_vec_recycle_order, rwork1));
    796:   PetscCall(MatDQNApplyJ0Inv(H, lbfgs->column_work, dX));

    798:   PetscCall(MatMultHermitianTransposeAddColumnRange(Yfull, dX, rwork1, rwork1, 0, h));
    799:   lbfgs->Yt_count++;

    801:   if (lbfgs->strategy == MAT_LMVM_DENSE_REORDER) PetscCall(VecRecycleOrderToHistoryOrder(H, rwork1, lbfgs->num_updates, lbfgs->cyclic_work_vec));
    802:   PetscCall(MatUpperTriangularSolveInPlace(H, lbfgs->StY_triu, rwork1, PETSC_TRUE, lbfgs->num_updates, lbfgs->strategy));
    803:   PetscCall(VecScale(rwork1, -1.0));
    804:   if (lbfgs->strategy == MAT_LMVM_DENSE_REORDER) PetscCall(VecHistoryOrderToRecycleOrder(H, rwork1, lbfgs->num_updates, lbfgs->cyclic_work_vec));

    806:   PetscCall(MatMultAddColumnRange(Sfull, rwork1, dX, dX, 0, h));
    807:   lbfgs->S_count++;
    808:   PetscFunctionReturn(PETSC_SUCCESS);
    809: }

    811: /* Solves for
    812:    B_0 - [ Y | B_0 S] [ -D  |    L^T    ]^-1 [   Y^T   ]
    813:                       [-----+-----------]    [---------]
    814:                       [  L  | S^T B_0 S ]    [ S^T B_0 ]

    816:    Above is equivalent to

    818:    B_0 - [ Y | B_0 S] [[     I     | 0 ][ -D  | 0 ][ I | -D^{-1} L^T ]]^-1 [   Y^T   ]
    819:                       [[-----------+---][-----+---][---+-------------]]    [---------]
    820:                       [[ -L D^{-1} | I ][  0  | J ][ 0 |       I     ]]    [ S^T B_0 ]

    822:    where J = S^T B_0 S + L D^{-1} L^T

    824:    becomes

    826:    B_0 - [ Y | B_0 S] [ I | D^{-1} L^T ][ -D^{-1}  |   0    ][    I     | 0 ] [   Y^T   ]
    827:                       [---+------------][----------+--------][----------+---] [---------]
    828:                       [ 0 |     I      ][     0    | J^{-1} ][ L D^{-1} | I ] [ S^T B_0 ]

    830:                       =

    832:    B_0 + [ Y | B_0 S] [ D^{-1} | 0 ][ I | L^T ][ I |    0    ][     I    | 0 ] [   Y^T   ]
    833:                       [--------+---][---+-----][---+---------][----------+---] [---------]
    834:                       [ 0      | I ][ 0 |  I  ][ 0 | -J^{-1} ][ L D^{-1} | I ] [ S^T B_0 ]

    836:                       (Note that YtS_triu_strict is L^T)
    837:    Byrd, Nocedal, Schnabel 1994

    839:    Alternative approach: considering the fact that DFP is dual to BFGS, use MatMult of DPF:
    840:    (See ddfp.c's MatMult_LMVMDDFP)

    842: */
    843: static PetscErrorCode MatMult_LMVMDBFGS(Mat B, Vec X, Vec Z)
    844: {
    845:   Mat_LMVM *lmvm  = (Mat_LMVM *)B->data;
    846:   Mat_DQN  *lbfgs = (Mat_DQN *)lmvm->ctx;
    847:   Mat       J_local;
    848:   PetscInt  idx, i, j, m_local, local_n;
    849:   PetscInt  m     = lmvm->m;
    850:   PetscInt  k     = lmvm->k;
    851:   PetscInt  h     = k - oldest_update(m, k);
    852:   Mat       Sfull = lmvm->basis[LMBASIS_S]->vecs;
    853:   Mat       Yfull = lmvm->basis[LMBASIS_Y]->vecs;

    855:   PetscFunctionBegin;
    856:   VecCheckSameSize(X, 2, Z, 3);
    857:   VecCheckMatCompatible(B, X, 2, Z, 3);

    859:   /* Cholesky Version */
    860:   /* Start with the B0 term */
    861:   PetscCall(MatDQNApplyJ0Fwd(B, X, Z));
    862:   if (!lbfgs->num_updates) PetscFunctionReturn(PETSC_SUCCESS); /* No updates stored yet */

    864:   if (lbfgs->use_recursive) {
    865:     PetscDeviceContext dctx;
    866:     PetscMemType       memtype;
    867:     PetscScalar        stz, ytx, stp, sjtpi, yjtsi, *workscalar;
    868:     PetscInt           oldest = oldest_update(m, k);

    870:     PetscCall(PetscDeviceContextGetCurrentContext(&dctx));
    871:     /* Recursive formulation to avoid Cholesky. Not a dense formulation */
    872:     PetscCall(MatMultHermitianTransposeColumnRange(Yfull, X, lbfgs->rwork1, 0, h));
    873:     lbfgs->Yt_count++;

    875:     PetscCall(VecGetLocalSize(lbfgs->rwork1, &local_n));

    877:     if (lbfgs->needPQ) {
    878:       PetscInt oldest = oldest_update(m, k);
    879:       for (i = oldest; i < k; ++i) {
    880:         idx = recycle_index(m, i);
    881:         /* column_work = S[idx] */
    882:         PetscCall(MatGetColumnVector(Sfull, lbfgs->column_work, idx));
    883:         PetscCall(MatDQNApplyJ0Fwd(B, lbfgs->column_work, lbfgs->PQ[idx]));
    884:         PetscCall(MatMultHermitianTransposeColumnRange(Yfull, lbfgs->column_work, lbfgs->rwork3, 0, h));
    885:         PetscCall(VecGetArrayAndMemType(lbfgs->rwork3, &workscalar, &memtype));
    886:         for (j = oldest; j < i; ++j) {
    887:           PetscInt idx_j = recycle_index(m, j);
    888:           /* Copy yjtsi in device-aware manner */
    889:           if (local_n) {
    890:             if (PetscMemTypeHost(memtype)) {
    891:               yjtsi = workscalar[idx_j];
    892:             } else {
    893:               PetscCall(PetscDeviceRegisterMemory(&yjtsi, PETSC_MEMTYPE_HOST, sizeof(yjtsi)));
    894:               PetscCall(PetscDeviceRegisterMemory(workscalar, memtype, local_n * sizeof(*workscalar)));
    895:               PetscCall(PetscDeviceArrayCopy(dctx, &yjtsi, &workscalar[idx_j], 1));
    896:             }
    897:           }
    898:           PetscCallMPI(MPI_Bcast(&yjtsi, 1, MPIU_SCALAR, 0, PetscObjectComm((PetscObject)B)));
    899:           /* column_work2 = S[j] */
    900:           PetscCall(MatGetColumnVector(Sfull, lbfgs->column_work2, idx_j));
    901:           PetscCall(VecDot(lbfgs->PQ[idx], lbfgs->column_work2, &sjtpi));
    902:           /* column_work2 = Y[j] */
    903:           PetscCall(MatGetColumnVector(Yfull, lbfgs->column_work2, idx_j));
    904:           /* Compute the pure BFGS component of the forward product */
    905:           PetscCall(VecAXPBYPCZ(lbfgs->PQ[idx], -sjtpi / lbfgs->stp[idx_j], yjtsi / lbfgs->yts[idx_j], 1.0, lbfgs->PQ[idx_j], lbfgs->column_work2));
    906:         }
    907:         PetscCall(VecDot(lbfgs->PQ[idx], lbfgs->column_work, &stp));
    908:         lbfgs->stp[idx] = PetscRealPart(stp);
    909:       }
    910:       lbfgs->needPQ = PETSC_FALSE;
    911:     }

    913:     PetscCall(VecGetArrayAndMemType(lbfgs->rwork1, &workscalar, &memtype));
    914:     for (i = oldest; i < k; ++i) {
    915:       idx = recycle_index(m, i);
    916:       /* Copy stz[i], ytx[i] in device-aware manner */
    917:       if (local_n) {
    918:         if (PetscMemTypeHost(memtype)) {
    919:           ytx = workscalar[idx];
    920:         } else {
    921:           PetscCall(PetscDeviceRegisterMemory(&ytx, PETSC_MEMTYPE_HOST, 1 * sizeof(ytx)));
    922:           PetscCall(PetscDeviceRegisterMemory(workscalar, memtype, local_n * sizeof(*workscalar)));
    923:           PetscCall(PetscDeviceArrayCopy(dctx, &ytx, &workscalar[idx], 1));
    924:         }
    925:       }
    926:       PetscCallMPI(MPI_Bcast(&ytx, 1, MPIU_SCALAR, 0, PetscObjectComm((PetscObject)B)));
    927:       /* column_work : S[i], column_work2 : Y[i] */
    928:       PetscCall(MatGetColumnVector(Sfull, lbfgs->column_work, idx));
    929:       PetscCall(MatGetColumnVector(Yfull, lbfgs->column_work2, idx));
    930:       PetscCall(VecDot(Z, lbfgs->column_work, &stz));
    931:       PetscCall(VecAXPBYPCZ(Z, -stz / lbfgs->stp[idx], ytx / lbfgs->yts[idx], 1.0, lbfgs->PQ[idx], lbfgs->column_work2));
    932:     }
    933:     PetscCall(VecRestoreArrayAndMemType(lbfgs->rwork1, &workscalar));
    934:   } else {
    935:     PetscCall(MatLMVMDBFGSUpdateMultData(B));
    936:     PetscCall(MatMultHermitianTransposeColumnRange(Yfull, X, lbfgs->rwork1, 0, h));
    937:     lbfgs->Yt_count++;
    938:     PetscCall(MatMultHermitianTransposeColumnRange(Sfull, Z, lbfgs->rwork2, 0, h));
    939:     lbfgs->St_count++;
    940:     if (lbfgs->strategy == MAT_LMVM_DENSE_REORDER) {
    941:       PetscCall(VecRecycleOrderToHistoryOrder(B, lbfgs->rwork1, lbfgs->num_updates, lbfgs->cyclic_work_vec));
    942:       PetscCall(VecRecycleOrderToHistoryOrder(B, lbfgs->rwork2, lbfgs->num_updates, lbfgs->cyclic_work_vec));
    943:     }

    945:     PetscCall(VecPointwiseMult(lbfgs->rwork1, lbfgs->rwork1, lbfgs->inv_diag_vec));
    946:     if (PetscDefined(USE_COMPLEX)) PetscCall(MatConjugate(lbfgs->YtS_triu_strict));
    947:     PetscCall(MatMultTransposeAdd(lbfgs->YtS_triu_strict, lbfgs->rwork1, lbfgs->rwork2, lbfgs->rwork2));
    948:     if (PetscDefined(USE_COMPLEX)) PetscCall(MatConjugate(lbfgs->YtS_triu_strict));

    950:     if (!lbfgs->rwork2_local) PetscCall(VecCreateLocalVector(lbfgs->rwork2, &lbfgs->rwork2_local));
    951:     if (!lbfgs->rwork3_local) PetscCall(VecCreateLocalVector(lbfgs->rwork3, &lbfgs->rwork3_local));
    952:     PetscCall(VecGetLocalVectorRead(lbfgs->rwork2, lbfgs->rwork2_local));
    953:     PetscCall(VecGetLocalVector(lbfgs->rwork3, lbfgs->rwork3_local));
    954:     PetscCall(MatDenseGetLocalMatrix(lbfgs->J, &J_local));
    955:     PetscCall(VecGetSize(lbfgs->rwork2_local, &m_local));
    956:     if (m_local) {
    957:       PetscCall(MatDenseGetLocalMatrix(lbfgs->J, &J_local));
    958:       PetscCall(MatSolve(J_local, lbfgs->rwork2_local, lbfgs->rwork3_local));
    959:     }
    960:     PetscCall(VecRestoreLocalVector(lbfgs->rwork3, lbfgs->rwork3_local));
    961:     PetscCall(VecRestoreLocalVectorRead(lbfgs->rwork2, lbfgs->rwork2_local));
    962:     PetscCall(VecScale(lbfgs->rwork3, -1.0));

    964:     PetscCall(MatMult(lbfgs->YtS_triu_strict, lbfgs->rwork3, lbfgs->rwork2));
    965:     PetscCall(VecPointwiseMult(lbfgs->rwork2, lbfgs->rwork2, lbfgs->inv_diag_vec));
    966:     PetscCall(VecAXPY(lbfgs->rwork1, 1.0, lbfgs->rwork2));

    968:     if (lbfgs->strategy == MAT_LMVM_DENSE_REORDER) {
    969:       PetscCall(VecHistoryOrderToRecycleOrder(B, lbfgs->rwork1, lbfgs->num_updates, lbfgs->cyclic_work_vec));
    970:       PetscCall(VecHistoryOrderToRecycleOrder(B, lbfgs->rwork3, lbfgs->num_updates, lbfgs->cyclic_work_vec));
    971:     }

    973:     PetscCall(MatMultAddColumnRange(Yfull, lbfgs->rwork1, Z, Z, 0, h));
    974:     lbfgs->Y_count++;
    975:     PetscCall(MatMultAddColumnRange(lbfgs->BS, lbfgs->rwork3, Z, Z, 0, h));
    976:     lbfgs->S_count++;
    977:   }
    978:   PetscFunctionReturn(PETSC_SUCCESS);
    979: }

    981: /*
    982:   This dense representation reduces the L-BFGS update to a series of
    983:   matrix-vector products with dense matrices in lieu of the conventional matrix-free
    984:   two-loop algorithm.
    985: */
    986: PetscErrorCode MatCreate_LMVMDBFGS(Mat B)
    987: {
    988:   Mat_LMVM *lmvm;
    989:   Mat_DQN  *lbfgs;

    991:   PetscFunctionBegin;
    992:   PetscCall(MatCreate_LMVM(B));
    993:   PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATLMVMDBFGS));
    994:   PetscCall(MatSetOption(B, MAT_HERMITIAN, PETSC_TRUE));
    995:   PetscCall(MatSetOption(B, MAT_SPD, PETSC_TRUE));
    996:   PetscCall(MatSetOption(B, MAT_SPD_ETERNAL, PETSC_TRUE));
    997:   B->ops->view           = MatView_LMVMDQN;
    998:   B->ops->setup          = MatSetUp_LMVMDQN;
    999:   B->ops->setfromoptions = MatSetFromOptions_LMVMDQN;
    1000:   B->ops->destroy        = MatDestroy_LMVMDQN;

    1002:   lmvm              = (Mat_LMVM *)B->data;
    1003:   lmvm->ops->reset  = MatReset_LMVMDQN;
    1004:   lmvm->ops->update = MatUpdate_LMVMDQN;
    1005:   lmvm->ops->mult   = MatMult_LMVMDBFGS;
    1006:   lmvm->ops->solve  = MatSolve_LMVMDBFGS;
    1007:   lmvm->ops->copy   = MatCopy_LMVMDQN;

    1009:   lmvm->ops->multht  = lmvm->ops->mult;
    1010:   lmvm->ops->solveht = lmvm->ops->solve;

    1012:   PetscCall(PetscNew(&lbfgs));
    1013:   lmvm->ctx              = (void *)lbfgs;
    1014:   lbfgs->allocated       = PETSC_FALSE;
    1015:   lbfgs->use_recursive   = PETSC_TRUE;
    1016:   lbfgs->needPQ          = PETSC_TRUE;
    1017:   lbfgs->watchdog        = 0;
    1018:   lbfgs->max_seq_rejects = lmvm->m / 2;
    1019:   lbfgs->strategy        = MAT_LMVM_DENSE_INPLACE;

    1021:   PetscCall(SymBroydenRescaleCreate(&lbfgs->rescale));
    1022:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatLMVMSymBroydenSetDelta_C", MatLMVMSymBroydenSetDelta_LMVMDQN));
    1023:   PetscFunctionReturn(PETSC_SUCCESS);
    1024: }

    1026: /*@
    1027:   MatCreateLMVMDBFGS - Creates a dense representation of the limited-memory
    1028:   Broyden-Fletcher-Goldfarb-Shanno (BFGS) approximation to a Hessian.

    1030:   Collective

    1032:   Input Parameters:
    1033: + comm - MPI communicator
    1034: . n    - number of local rows for storage vectors
    1035: - N    - global size of the storage vectors

    1037:   Output Parameter:
    1038: . B - the matrix

    1040:   Level: advanced

    1042:   Note:
    1043:   It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions()
    1044:   paradigm instead of this routine directly.

    1046: .seealso: `MatCreate()`, `MATLMVM`, `MATLMVMDBFGS`, `MatCreateLMVMBFGS()`
    1047: @*/
    1048: PetscErrorCode MatCreateLMVMDBFGS(MPI_Comm comm, PetscInt n, PetscInt N, Mat *B)
    1049: {
    1050:   PetscFunctionBegin;
    1051:   PetscCall(KSPInitializePackage());
    1052:   PetscCall(MatCreate(comm, B));
    1053:   PetscCall(MatSetSizes(*B, n, n, N, N));
    1054:   PetscCall(MatSetType(*B, MATLMVMDBFGS));
    1055:   PetscCall(MatSetUp(*B));
    1056:   PetscFunctionReturn(PETSC_SUCCESS);
    1057: }

    1059: /* here R is strictly upper triangular part of STY */
    1060: static PetscErrorCode MatGetRTDR(Mat B, Mat result)
    1061: {
    1062:   Mat_LMVM *lmvm = (Mat_LMVM *)B->data;
    1063:   Mat_DQN  *ldfp = (Mat_DQN *)lmvm->ctx;
    1064:   PetscInt  m_local;

    1066:   PetscFunctionBegin;
    1067:   if (!ldfp->temp_mat) PetscCall(MatDuplicate(ldfp->StY_triu_strict, MAT_SHARE_NONZERO_PATTERN, &ldfp->temp_mat));
    1068:   PetscCall(MatCopy(ldfp->StY_triu_strict, ldfp->temp_mat, SAME_NONZERO_PATTERN));
    1069:   PetscCall(MatDiagonalScale(ldfp->temp_mat, ldfp->inv_diag_vec, NULL));
    1070:   PetscCall(MatGetLocalSize(result, &m_local, NULL));
    1071:   // need to conjugate and conjugate again because we have MatTransposeMatMult but not MatHermitianTransposeMatMult()
    1072:   PetscCall(MatConjugate(ldfp->temp_mat));
    1073:   if (m_local) {
    1074:     Mat temp_local, StY_local, result_local;
    1075:     PetscCall(MatDenseGetLocalMatrix(ldfp->StY_triu_strict, &StY_local));
    1076:     PetscCall(MatDenseGetLocalMatrix(ldfp->temp_mat, &temp_local));
    1077:     PetscCall(MatDenseGetLocalMatrix(result, &result_local));
    1078:     PetscCall(MatTransposeMatMult(StY_local, temp_local, MAT_REUSE_MATRIX, PETSC_DETERMINE, &result_local));
    1079:   }
    1080:   PetscCall(MatConjugate(result));
    1081:   PetscFunctionReturn(PETSC_SUCCESS);
    1082: }

    1084: static PetscErrorCode MatLMVMDDFPUpdateSolveData(Mat B)
    1085: {
    1086:   Mat_LMVM *lmvm = (Mat_LMVM *)B->data;
    1087:   Mat_DQN  *ldfp = (Mat_DQN *)lmvm->ctx;
    1088:   PetscInt  m    = lmvm->m, m_local;
    1089:   PetscInt  k    = lmvm->k;
    1090:   PetscInt  h    = k - oldest_update(m, k);
    1091:   PetscInt  j_0;
    1092:   PetscInt  prev_oldest;
    1093:   Mat       Sfull = lmvm->basis[LMBASIS_S]->vecs;
    1094:   Mat       Yfull = lmvm->basis[LMBASIS_Y]->vecs;
    1095:   Mat       J_local;

    1097:   PetscFunctionBegin;
    1098:   if (!ldfp->StY_triu_strict) {
    1099:     PetscCall(MatDuplicate(ldfp->YtS_triu, MAT_SHARE_NONZERO_PATTERN, &ldfp->StY_triu_strict));
    1100:     PetscCall(MatDestroy(&ldfp->YtHY));
    1101:     PetscCall(MatDuplicate(ldfp->YtS_triu, MAT_SHARE_NONZERO_PATTERN, &ldfp->YtHY));
    1102:     PetscCall(MatDestroy(&ldfp->J));
    1103:     PetscCall(MatDuplicate(ldfp->YtS_triu, MAT_SHARE_NONZERO_PATTERN, &ldfp->J));
    1104:     PetscCall(MatDestroy(&ldfp->HY));
    1105:     PetscCall(MatDuplicate(Yfull, MAT_SHARE_NONZERO_PATTERN, &ldfp->HY));
    1106:     PetscCall(MatShift(ldfp->YtHY, 1.0));
    1107:     ldfp->num_mult_updates = oldest_update(m, k);
    1108:   }
    1109:   if (ldfp->num_mult_updates == k) PetscFunctionReturn(PETSC_SUCCESS);

    1111:   /* H_0 may have been updated, we must recompute H_0 Y and Y^T H_0 Y */
    1112:   for (PetscInt j = oldest_update(m, k); j < k; j++) {
    1113:     Vec      y_j;
    1114:     Vec      Hy_j;
    1115:     Vec      YtHy_j;
    1116:     PetscInt Y_idx    = recycle_index(m, j);
    1117:     PetscInt YtHY_idx = ldfp->strategy == MAT_LMVM_DENSE_INPLACE ? Y_idx : history_index(m, k, j);

    1119:     PetscCall(MatDenseGetColumnVecWrite(ldfp->HY, Y_idx, &Hy_j));
    1120:     PetscCall(MatDenseGetColumnVecRead(Yfull, Y_idx, &y_j));
    1121:     PetscCall(MatDQNApplyJ0Inv(B, y_j, Hy_j));
    1122:     PetscCall(MatDenseRestoreColumnVecRead(Yfull, Y_idx, &y_j));
    1123:     PetscCall(MatDenseGetColumnVecWrite(ldfp->YtHY, YtHY_idx, &YtHy_j));
    1124:     PetscCall(MatMultHermitianTransposeColumnRange(Yfull, Hy_j, YtHy_j, 0, h));
    1125:     ldfp->Yt_count++;
    1126:     if (ldfp->strategy == MAT_LMVM_DENSE_REORDER) PetscCall(VecRecycleOrderToHistoryOrder(B, YtHy_j, ldfp->num_updates, ldfp->cyclic_work_vec));
    1127:     PetscCall(MatDenseRestoreColumnVecWrite(ldfp->YtHY, YtHY_idx, &YtHy_j));
    1128:     PetscCall(MatDenseRestoreColumnVecWrite(ldfp->HY, Y_idx, &Hy_j));
    1129:   }
    1130:   prev_oldest = oldest_update(m, ldfp->num_mult_updates);
    1131:   if (ldfp->strategy == MAT_LMVM_DENSE_REORDER && prev_oldest < oldest_update(m, k)) {
    1132:     /* move the YtS entries that have been computed and need to be kept back up */
    1133:     PetscInt m_keep = m - (oldest_update(m, k) - prev_oldest);

    1135:     PetscCall(MatMove_LR3(B, ldfp->StY_triu_strict, m_keep));
    1136:   }
    1137:   PetscCall(MatGetLocalSize(ldfp->StY_triu_strict, &m_local, NULL));
    1138:   j_0 = PetscMax(ldfp->num_mult_updates, oldest_update(m, k));
    1139:   for (PetscInt j = j_0; j < k; j++) {
    1140:     PetscInt Y_idx   = recycle_index(m, j);
    1141:     PetscInt StY_idx = ldfp->strategy == MAT_LMVM_DENSE_INPLACE ? Y_idx : history_index(m, k, j);
    1142:     Vec      y_j, Sty_j;

    1144:     PetscCall(MatDenseGetColumnVecRead(Yfull, Y_idx, &y_j));
    1145:     PetscCall(MatDenseGetColumnVecWrite(ldfp->StY_triu_strict, StY_idx, &Sty_j));
    1146:     PetscCall(MatMultHermitianTransposeColumnRange(Sfull, y_j, Sty_j, 0, h));
    1147:     ldfp->St_count++;
    1148:     if (ldfp->strategy == MAT_LMVM_DENSE_REORDER) PetscCall(VecRecycleOrderToHistoryOrder(B, Sty_j, ldfp->num_updates, ldfp->cyclic_work_vec));
    1149:     PetscCall(MatDenseRestoreColumnVecWrite(ldfp->StY_triu_strict, StY_idx, &Sty_j));
    1150:     PetscCall(MatDenseRestoreColumnVecRead(Yfull, Y_idx, &y_j));
    1151:     /* zero the corresponding row */
    1152:     if (m_local > 0) {
    1153:       Mat StY_local, StY_row;

    1155:       PetscCall(MatDenseGetLocalMatrix(ldfp->StY_triu_strict, &StY_local));
    1156:       PetscCall(MatDenseGetSubMatrix(StY_local, StY_idx, StY_idx + 1, PETSC_DECIDE, PETSC_DECIDE, &StY_row));
    1157:       PetscCall(MatZeroEntries(StY_row));
    1158:       PetscCall(MatDenseRestoreSubMatrix(StY_local, &StY_row));
    1159:     }
    1160:   }
    1161:   if (!ldfp->inv_diag_vec) PetscCall(VecDuplicate(ldfp->diag_vec, &ldfp->inv_diag_vec));
    1162:   PetscCall(VecCopy(ldfp->diag_vec, ldfp->inv_diag_vec));
    1163:   PetscCall(VecReciprocal(ldfp->inv_diag_vec));
    1164:   PetscCall(MatDenseGetLocalMatrix(ldfp->J, &J_local));
    1165:   PetscCall(MatSetFactorType(J_local, MAT_FACTOR_NONE));
    1166:   PetscCall(MatGetRTDR(B, ldfp->J));
    1167:   PetscCall(MatAXPY(ldfp->J, 1.0, ldfp->YtHY, SAME_NONZERO_PATTERN));
    1168:   if (m_local) {
    1169:     PetscCall(MatSetOption(J_local, MAT_SPD, PETSC_TRUE));
    1170:     PetscCall(MatCholeskyFactor(J_local, NULL, NULL));
    1171:   }
    1172:   ldfp->num_mult_updates = ldfp->num_updates;
    1173:   PetscFunctionReturn(PETSC_SUCCESS);
    1174: }

    1176: /* Solves for

    1178:    H_0 - [ S | H_0 Y] [ -D  |    R.T    ]^-1 [   S^T   ]
    1179:                       [-----+-----------]    [---------]
    1180:                       [  R  | Y^T H_0 Y ]    [ Y^T H_0 ]

    1182:    Above is equivalent to

    1184:    H_0 - [ S | H_0 Y] [[     I     | 0 ][ -D | 0 ][ I | -D^{-1} R^T ]]^-1 [   S^T   ]
    1185:                       [[-----------+---][----+---][---+-------------]]    [---------]
    1186:                       [[ -R D^{-1} | I ][  0 | J ][ 0 |      I      ]]    [ Y^T H_0 ]

    1188:    where J = Y^T H_0 Y + R D^{-1} R.T

    1190:    becomes

    1192:    H_0 - [ S | H_0 Y] [ I | D^{-1} R^T ][ -D^{-1}  |   0    ][     I    | 0 ] [   S^T   ]
    1193:                       [---+------------][----------+--------][----------+---] [---------]
    1194:                       [ 0 |      I     ][     0    | J^{-1} ][ R D^{-1} | I ] [ Y^T H_0 ]

    1196:                       =

    1198:    H_0 + [ S | H_0 Y] [ D^{-1} | 0 ][ I | R^T ][ I |    0    ][     I    | 0 ] [   S^T   ]
    1199:                       [--------+---][---+-----][---+---------][----------+---] [---------]
    1200:                       [ 0      | I ][ 0 |  I  ][ 0 | -J^{-1} ][ R D^{-1} | I ] [ Y^T H_0 ]

    1202:                       (Note that StY_triu_strict is R)
    1203:    Byrd, Nocedal, Schnabel 1994

    1205: */
    1206: static PetscErrorCode MatSolve_LMVMDDFP(Mat H, Vec F, Vec dX)
    1207: {
    1208:   Mat_LMVM *lmvm = (Mat_LMVM *)H->data;
    1209:   Mat_DQN  *ldfp = (Mat_DQN *)lmvm->ctx;
    1210:   PetscInt  m    = lmvm->m;
    1211:   PetscInt  k    = lmvm->k;
    1212:   PetscInt  h    = k - oldest_update(m, k);
    1213:   PetscInt  idx, i, j, local_n;
    1214:   PetscInt  m_local;
    1215:   Mat       J_local;
    1216:   Mat       Sfull = lmvm->basis[LMBASIS_S]->vecs;
    1217:   Mat       Yfull = lmvm->basis[LMBASIS_Y]->vecs;

    1219:   PetscFunctionBegin;
    1220:   VecCheckSameSize(F, 2, dX, 3);
    1221:   VecCheckMatCompatible(H, dX, 3, F, 2);

    1223:   /* Cholesky Version */
    1224:   /* Start with the B0 term */
    1225:   PetscCall(MatDQNApplyJ0Inv(H, F, dX));
    1226:   if (!ldfp->num_updates) PetscFunctionReturn(PETSC_SUCCESS); /* No updates stored yet */

    1228:   if (ldfp->use_recursive) {
    1229:     PetscDeviceContext dctx;
    1230:     PetscMemType       memtype;
    1231:     PetscScalar        stf, ytx, ytq, yjtqi, sjtyi, *workscalar;

    1233:     PetscCall(PetscDeviceContextGetCurrentContext(&dctx));
    1234:     /* Recursive formulation to avoid Cholesky. Not a dense formulation */
    1235:     PetscCall(MatMultHermitianTransposeColumnRange(Sfull, F, ldfp->rwork1, 0, h));
    1236:     ldfp->Yt_count++;

    1238:     PetscCall(VecGetLocalSize(ldfp->rwork1, &local_n));

    1240:     PetscInt oldest = oldest_update(m, k);

    1242:     if (ldfp->needPQ) {
    1243:       PetscInt oldest = oldest_update(m, k);
    1244:       for (i = oldest; i < k; ++i) {
    1245:         idx = recycle_index(m, i);
    1246:         /* column_work = S[idx] */
    1247:         PetscCall(MatGetColumnVector(Yfull, ldfp->column_work, idx));
    1248:         PetscCall(MatDQNApplyJ0Inv(H, ldfp->column_work, ldfp->PQ[idx]));
    1249:         PetscCall(MatMultHermitianTransposeColumnRange(Sfull, ldfp->column_work, ldfp->rwork3, 0, h));
    1250:         PetscCall(VecGetArrayAndMemType(ldfp->rwork3, &workscalar, &memtype));
    1251:         for (j = oldest; j < i; ++j) {
    1252:           PetscInt idx_j = recycle_index(m, j);
    1253:           /* Copy sjtyi in device-aware manner */
    1254:           if (local_n) {
    1255:             if (PetscMemTypeHost(memtype)) {
    1256:               sjtyi = workscalar[idx_j];
    1257:             } else {
    1258:               PetscCall(PetscDeviceRegisterMemory(&sjtyi, PETSC_MEMTYPE_HOST, 1 * sizeof(sjtyi)));
    1259:               PetscCall(PetscDeviceRegisterMemory(workscalar, memtype, local_n * sizeof(*workscalar)));
    1260:               PetscCall(PetscDeviceArrayCopy(dctx, &sjtyi, &workscalar[idx_j], 1));
    1261:             }
    1262:           }
    1263:           PetscCallMPI(MPI_Bcast(&sjtyi, 1, MPIU_SCALAR, 0, PetscObjectComm((PetscObject)H)));
    1264:           /* column_work2 = Y[j] */
    1265:           PetscCall(MatGetColumnVector(Yfull, ldfp->column_work2, idx_j));
    1266:           PetscCall(VecDot(ldfp->PQ[idx], ldfp->column_work2, &yjtqi));
    1267:           /* column_work2 = Y[j] */
    1268:           PetscCall(MatGetColumnVector(Sfull, ldfp->column_work2, idx_j));
    1269:           /* Compute the pure BFGS component of the forward product */
    1270:           PetscCall(VecAXPBYPCZ(ldfp->PQ[idx], -yjtqi / ldfp->ytq[idx_j], sjtyi / ldfp->yts[idx_j], 1.0, ldfp->PQ[idx_j], ldfp->column_work2));
    1271:         }
    1272:         PetscCall(VecDot(ldfp->PQ[idx], ldfp->column_work, &ytq));
    1273:         ldfp->ytq[idx] = PetscRealPart(ytq);
    1274:       }
    1275:       ldfp->needPQ = PETSC_FALSE;
    1276:     }

    1278:     PetscCall(VecGetArrayAndMemType(ldfp->rwork1, &workscalar, &memtype));
    1279:     for (i = oldest; i < k; ++i) {
    1280:       idx = recycle_index(m, i);
    1281:       /* Copy stz[i], ytx[i] in device-aware manner */
    1282:       if (local_n) {
    1283:         if (PetscMemTypeHost(memtype)) {
    1284:           stf = workscalar[idx];
    1285:         } else {
    1286:           PetscCall(PetscDeviceRegisterMemory(&stf, PETSC_MEMTYPE_HOST, sizeof(stf)));
    1287:           PetscCall(PetscDeviceRegisterMemory(workscalar, memtype, local_n * sizeof(*workscalar)));
    1288:           PetscCall(PetscDeviceArrayCopy(dctx, &stf, &workscalar[idx], 1));
    1289:         }
    1290:       }
    1291:       PetscCallMPI(MPI_Bcast(&stf, 1, MPIU_SCALAR, 0, PetscObjectComm((PetscObject)H)));
    1292:       /* column_work : S[i], column_work2 : Y[i] */
    1293:       PetscCall(MatGetColumnVector(Sfull, ldfp->column_work, idx));
    1294:       PetscCall(MatGetColumnVector(Yfull, ldfp->column_work2, idx));
    1295:       PetscCall(VecDot(dX, ldfp->column_work2, &ytx));
    1296:       PetscCall(VecAXPBYPCZ(dX, -ytx / ldfp->ytq[idx], stf / ldfp->yts[idx], 1.0, ldfp->PQ[idx], ldfp->column_work));
    1297:     }
    1298:     PetscCall(VecRestoreArrayAndMemType(ldfp->rwork1, &workscalar));
    1299:   } else {
    1300:     PetscCall(MatLMVMDDFPUpdateSolveData(H));
    1301:     PetscCall(MatMultHermitianTransposeColumnRange(Sfull, F, ldfp->rwork1, 0, h));
    1302:     ldfp->St_count++;
    1303:     PetscCall(MatMultHermitianTransposeColumnRange(Yfull, dX, ldfp->rwork2, 0, h));
    1304:     ldfp->Yt_count++;
    1305:     if (ldfp->strategy == MAT_LMVM_DENSE_REORDER) {
    1306:       PetscCall(VecRecycleOrderToHistoryOrder(H, ldfp->rwork1, ldfp->num_updates, ldfp->cyclic_work_vec));
    1307:       PetscCall(VecRecycleOrderToHistoryOrder(H, ldfp->rwork2, ldfp->num_updates, ldfp->cyclic_work_vec));
    1308:     }

    1310:     PetscCall(VecPointwiseMult(ldfp->rwork3, ldfp->rwork1, ldfp->inv_diag_vec));
    1311:     if (PetscDefined(USE_COMPLEX)) PetscCall(MatConjugate(ldfp->StY_triu_strict));
    1312:     PetscCall(MatMultTransposeAdd(ldfp->StY_triu_strict, ldfp->rwork3, ldfp->rwork2, ldfp->rwork2));
    1313:     if (PetscDefined(USE_COMPLEX)) PetscCall(MatConjugate(ldfp->StY_triu_strict));

    1315:     if (!ldfp->rwork2_local) PetscCall(VecCreateLocalVector(ldfp->rwork2, &ldfp->rwork2_local));
    1316:     if (!ldfp->rwork3_local) PetscCall(VecCreateLocalVector(ldfp->rwork3, &ldfp->rwork3_local));
    1317:     PetscCall(VecGetLocalVectorRead(ldfp->rwork2, ldfp->rwork2_local));
    1318:     PetscCall(VecGetLocalVector(ldfp->rwork3, ldfp->rwork3_local));
    1319:     PetscCall(MatDenseGetLocalMatrix(ldfp->J, &J_local));
    1320:     PetscCall(VecGetSize(ldfp->rwork2_local, &m_local));
    1321:     if (m_local) {
    1322:       Mat J_local;

    1324:       PetscCall(MatDenseGetLocalMatrix(ldfp->J, &J_local));
    1325:       PetscCall(MatSolve(J_local, ldfp->rwork2_local, ldfp->rwork3_local));
    1326:     }
    1327:     PetscCall(VecRestoreLocalVector(ldfp->rwork3, ldfp->rwork3_local));
    1328:     PetscCall(VecRestoreLocalVectorRead(ldfp->rwork2, ldfp->rwork2_local));
    1329:     PetscCall(VecScale(ldfp->rwork3, -1.0));

    1331:     PetscCall(MatMultAdd(ldfp->StY_triu_strict, ldfp->rwork3, ldfp->rwork1, ldfp->rwork1));
    1332:     PetscCall(VecPointwiseMult(ldfp->rwork1, ldfp->rwork1, ldfp->inv_diag_vec));

    1334:     if (ldfp->strategy == MAT_LMVM_DENSE_REORDER) {
    1335:       PetscCall(VecHistoryOrderToRecycleOrder(H, ldfp->rwork1, ldfp->num_updates, ldfp->cyclic_work_vec));
    1336:       PetscCall(VecHistoryOrderToRecycleOrder(H, ldfp->rwork3, ldfp->num_updates, ldfp->cyclic_work_vec));
    1337:     }

    1339:     PetscCall(MatMultAddColumnRange(Sfull, ldfp->rwork1, dX, dX, 0, h));
    1340:     ldfp->S_count++;
    1341:     PetscCall(MatMultAddColumnRange(ldfp->HY, ldfp->rwork3, dX, dX, 0, h));
    1342:     ldfp->Y_count++;
    1343:   }
    1344:   PetscFunctionReturn(PETSC_SUCCESS);
    1345: }

    1347: /* Solves for
    1348:    (Theorem 1, Erway, Jain, and Marcia, 2013)

    1350:    B_0 - [ Y | B_0 S] [ -R^{-T} (D + S^T B_0 S) R^{-1} | R^{-T} ] [   Y^T   ]
    1351:                       ---------------------------------+--------] [---------]
    1352:                       [             R^{-1}             |   0    ] [ S^T B_0 ]

    1354:    (Note: R above is right triangular part of YTS)
    1355:    which becomes,

    1357:    [ I | -Y L^{-T} ] [  I  | 0 ] [ B_0 | 0 ] [ I | S ] [      I      ]
    1358:                      [-----+---] [-----+---] [---+---] [-------------]
    1359:                      [ S^T | I ] [  0  | D ] [ 0 | I ] [ -L^{-1} Y^T ]

    1361:    (Note: L above is right triangular part of STY)

    1363: */
    1364: static PetscErrorCode MatMult_LMVMDDFP(Mat B, Vec X, Vec Z)
    1365: {
    1366:   Mat_LMVM        *lmvm   = (Mat_LMVM *)B->data;
    1367:   Mat_DQN         *ldfp   = (Mat_DQN *)lmvm->ctx;
    1368:   Vec              rwork1 = ldfp->rwork1;
    1369:   PetscInt         m      = lmvm->m;
    1370:   PetscInt         k      = lmvm->k;
    1371:   PetscInt         h      = k - oldest_update(m, k);
    1372:   Mat              Sfull  = lmvm->basis[LMBASIS_S]->vecs;
    1373:   Mat              Yfull  = lmvm->basis[LMBASIS_Y]->vecs;
    1374:   PetscObjectState Xstate;

    1376:   PetscFunctionBegin;
    1377:   VecCheckSameSize(X, 2, Z, 3);
    1378:   VecCheckMatCompatible(B, X, 2, Z, 3);

    1380:   /* DFP Version. Erway, Jain, Marcia, 2013, Theorem 1 */
    1381:   /* Block Version */
    1382:   if (!ldfp->num_updates) {
    1383:     PetscCall(MatDQNApplyJ0Fwd(B, X, Z));
    1384:     PetscFunctionReturn(PETSC_SUCCESS); /* No updates stored yet */
    1385:   }

    1387:   PetscCall(PetscObjectStateGet((PetscObject)X, &Xstate));
    1388:   PetscCall(MatMultHermitianTransposeColumnRange(Yfull, X, rwork1, 0, h));

    1390:   /* Reordering rwork1, as STY is in history order, while Y is in recycled order */
    1391:   if (ldfp->strategy == MAT_LMVM_DENSE_REORDER) PetscCall(VecRecycleOrderToHistoryOrder(B, rwork1, ldfp->num_updates, ldfp->cyclic_work_vec));
    1392:   PetscCall(MatUpperTriangularSolveInPlace(B, ldfp->YtS_triu, rwork1, PETSC_FALSE, ldfp->num_updates, ldfp->strategy));
    1393:   PetscCall(VecScale(rwork1, -1.0));
    1394:   if (ldfp->strategy == MAT_LMVM_DENSE_REORDER) PetscCall(VecHistoryOrderToRecycleOrder(B, rwork1, ldfp->num_updates, ldfp->cyclic_work_vec));

    1396:   PetscCall(VecCopy(X, ldfp->column_work));
    1397:   PetscCall(MatMultAddColumnRange(Sfull, rwork1, ldfp->column_work, ldfp->column_work, 0, h));
    1398:   ldfp->S_count++;

    1400:   PetscCall(VecPointwiseMult(rwork1, ldfp->diag_vec_recycle_order, rwork1));
    1401:   PetscCall(MatDQNApplyJ0Fwd(B, ldfp->column_work, Z));

    1403:   PetscCall(MatMultHermitianTransposeAddColumnRange(Sfull, Z, rwork1, rwork1, 0, h));
    1404:   ldfp->St_count++;

    1406:   if (ldfp->strategy == MAT_LMVM_DENSE_REORDER) PetscCall(VecRecycleOrderToHistoryOrder(B, rwork1, ldfp->num_updates, ldfp->cyclic_work_vec));
    1407:   PetscCall(MatUpperTriangularSolveInPlace(B, ldfp->YtS_triu, rwork1, PETSC_TRUE, ldfp->num_updates, ldfp->strategy));
    1408:   PetscCall(VecScale(rwork1, -1.0));
    1409:   if (ldfp->strategy == MAT_LMVM_DENSE_REORDER) PetscCall(VecHistoryOrderToRecycleOrder(B, rwork1, ldfp->num_updates, ldfp->cyclic_work_vec));

    1411:   PetscCall(MatMultAddColumnRange(Yfull, rwork1, Z, Z, 0, h));
    1412:   ldfp->Y_count++;
    1413:   PetscFunctionReturn(PETSC_SUCCESS);
    1414: }

    1416: /*
    1417:    This dense representation reduces the L-DFP update to a series of
    1418:    matrix-vector products with dense matrices in lieu of the conventional
    1419:    matrix-free two-loop algorithm.
    1420: */
    1421: PetscErrorCode MatCreate_LMVMDDFP(Mat B)
    1422: {
    1423:   Mat_LMVM *lmvm;
    1424:   Mat_DQN  *ldfp;

    1426:   PetscFunctionBegin;
    1427:   PetscCall(MatCreate_LMVM(B));
    1428:   PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATLMVMDDFP));
    1429:   PetscCall(MatSetOption(B, MAT_HERMITIAN, PETSC_TRUE));
    1430:   PetscCall(MatSetOption(B, MAT_SPD, PETSC_TRUE));
    1431:   PetscCall(MatSetOption(B, MAT_SPD_ETERNAL, PETSC_TRUE));
    1432:   B->ops->view           = MatView_LMVMDQN;
    1433:   B->ops->setup          = MatSetUp_LMVMDQN;
    1434:   B->ops->setfromoptions = MatSetFromOptions_LMVMDQN;
    1435:   B->ops->destroy        = MatDestroy_LMVMDQN;

    1437:   lmvm              = (Mat_LMVM *)B->data;
    1438:   lmvm->ops->reset  = MatReset_LMVMDQN;
    1439:   lmvm->ops->update = MatUpdate_LMVMDQN;
    1440:   lmvm->ops->mult   = MatMult_LMVMDDFP;
    1441:   lmvm->ops->solve  = MatSolve_LMVMDDFP;
    1442:   lmvm->ops->copy   = MatCopy_LMVMDQN;

    1444:   lmvm->ops->multht  = lmvm->ops->mult;
    1445:   lmvm->ops->solveht = lmvm->ops->solve;

    1447:   PetscCall(PetscNew(&ldfp));
    1448:   lmvm->ctx             = (void *)ldfp;
    1449:   ldfp->allocated       = PETSC_FALSE;
    1450:   ldfp->watchdog        = 0;
    1451:   ldfp->max_seq_rejects = lmvm->m / 2;
    1452:   ldfp->strategy        = MAT_LMVM_DENSE_INPLACE;
    1453:   ldfp->use_recursive   = PETSC_TRUE;
    1454:   ldfp->needPQ          = PETSC_TRUE;

    1456:   PetscCall(SymBroydenRescaleCreate(&ldfp->rescale));
    1457:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatLMVMSymBroydenSetDelta_C", MatLMVMSymBroydenSetDelta_LMVMDQN));
    1458:   PetscFunctionReturn(PETSC_SUCCESS);
    1459: }

    1461: /*@
    1462:   MatCreateLMVMDDFP - Creates a dense representation of the limited-memory
    1463:   Davidon-Fletcher-Powell (DFP) approximation to a Hessian.

    1465:   Collective

    1467:   Input Parameters:
    1468: + comm - MPI communicator
    1469: . n    - number of local rows for storage vectors
    1470: - N    - global size of the storage vectors

    1472:   Output Parameter:
    1473: . B - the matrix

    1475:   Level: advanced

    1477:   Note:
    1478:   It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions()
    1479:   paradigm instead of this routine directly.

    1481: .seealso: `MatCreate()`, `MATLMVM`, `MATLMVMDDFP`, `MatCreateLMVMDFP()`
    1482: @*/
    1483: PetscErrorCode MatCreateLMVMDDFP(MPI_Comm comm, PetscInt n, PetscInt N, Mat *B)
    1484: {
    1485:   PetscFunctionBegin;
    1486:   PetscCall(KSPInitializePackage());
    1487:   PetscCall(MatCreate(comm, B));
    1488:   PetscCall(MatSetSizes(*B, n, n, N, N));
    1489:   PetscCall(MatSetType(*B, MATLMVMDDFP));
    1490:   PetscCall(MatSetUp(*B));
    1491:   PetscFunctionReturn(PETSC_SUCCESS);
    1492: }

    1494: /*@
    1495:   MatLMVMDenseSetType - Sets the memory storage type for dense `MATLMVM`

    1497:   Input Parameters:
    1498: + B    - the `MATLMVM` matrix
    1499: - type - scale type, see `MatLMVMDenseSetType`

    1501:   Options Database Keys:
    1502: + -mat_lqn_type   (reorder|inplace) - set the strategy
    1503: . -mat_lbfgs_type (reorder|inplace) - set the strategy
    1504: - -mat_ldfp_type  (reorder|inplace) - set the strategy

    1506:   Level: intermediate

    1508:   MatLMVMDenseTypes\:
    1509: +   `MAT_LMVM_DENSE_REORDER` - reorders memory to minimize kernel launch
    1510: -   `MAT_LMVM_DENSE_INPLACE` - launches kernel inplace to minimize memory movement

    1512: .seealso: [](ch_ksp), `MATLMVMDQN`, `MATLMVMDBFGS`, `MATLMVMDDFP`, `MatLMVMDenseType`
    1513: @*/
    1514: PetscErrorCode MatLMVMDenseSetType(Mat B, MatLMVMDenseType type)
    1515: {
    1516:   Mat_LMVM *lmvm = (Mat_LMVM *)B->data;
    1517:   Mat_DQN  *lqn  = (Mat_DQN *)lmvm->ctx;

    1519:   PetscFunctionBegin;
    1521:   lqn->strategy = type;
    1522:   PetscFunctionReturn(PETSC_SUCCESS);
    1523: }