Date: 2022-08-02T03:14:51+00:00

Actual source code: symbrdn.c

      1: #include <../src/ksp/ksp/utils/lmvm/symbrdn/symbrdn.h>
      2: #include <../src/ksp/ksp/utils/lmvm/diagbrdn/diagbrdn.h>

      4: const char *const MatLMVMSymBroydenScaleTypes[] = {"NONE","SCALAR","DIAGONAL","USER","MatLMVMSymBrdnScaleType","MAT_LMVM_SYMBROYDEN_SCALING_",NULL};

      6: /*------------------------------------------------------------*/

      8: /*
      9:   The solution method below is the matrix-free implementation of
     10:   Equation 8.6a in Dennis and More "Quasi-Newton Methods, Motivation
     11:   and Theory" (https://epubs.siam.org/doi/abs/10.1137/1019005).

     13:   Q[i] = (B_i)^{-1}*S[i] terms are computed ahead of time whenever
     14:   the matrix is updated with a new (S[i], Y[i]) pair. This allows
     15:   repeated calls of MatSolve without incurring redundant computation.

     17:   dX <- J0^{-1} * F

     19:   for i=0,1,2,...,k
     20:     # Q[i] = (B_i)^T{-1} Y[i]

     22:     rho = 1.0 / (Y[i]^T S[i])
     23:     alpha = rho * (S[i]^T F)
     24:     zeta = 1.0 / (Y[i]^T Q[i])
     25:     gamma = zeta * (Y[i]^T dX)

     27:     dX <- dX - (gamma * Q[i]) + (alpha * Y[i])
     28:     W <- (rho * S[i]) - (zeta * Q[i])
     29:     dX <- dX + (psi[i] * (Y[i]^T Q[i]) * (W^T F) * W)
     30:   end
     31: */
     32: static PetscErrorCode MatSolve_LMVMSymBrdn(Mat B, Vec F, Vec dX)
     33: {
     34:   Mat_LMVM          *lmvm = (Mat_LMVM*)B->data;
     35:   Mat_SymBrdn       *lsb = (Mat_SymBrdn*)lmvm->ctx;
     36:   PetscInt          i, j;
     37:   PetscReal         numer;
     38:   PetscScalar       sjtpi, yjtsi, wtsi, yjtqi, sjtyi, wtyi, ytx, stf, wtf, stp, ytq;

     40:   /* Efficient shortcuts for pure BFGS and pure DFP configurations */
     41:   if (lsb->phi == 0.0) {
     42:     MatSolve_LMVMBFGS(B, F, dX);
     43:     return 0;
     44:   }
     45:   if (lsb->phi == 1.0) {
     46:     MatSolve_LMVMDFP(B, F, dX);
     47:     return 0;
     48:   }

     50:   VecCheckSameSize(F, 2, dX, 3);
     51:   VecCheckMatCompatible(B, dX, 3, F, 2);

     53:   if (lsb->needP) {
     54:     /* Start the loop for (P[k] = (B_k) * S[k]) */
     55:     for (i = 0; i <= lmvm->k; ++i) {
     56:       MatSymBrdnApplyJ0Fwd(B, lmvm->S[i], lsb->P[i]);
     57:       for (j = 0; j <= i-1; ++j) {
     58:         /* Compute the necessary dot products */
     59:         VecDotBegin(lmvm->S[j], lsb->P[i], &sjtpi);
     60:         VecDotBegin(lmvm->Y[j], lmvm->S[i], &yjtsi);
     61:         VecDotEnd(lmvm->S[j], lsb->P[i], &sjtpi);
     62:         VecDotEnd(lmvm->Y[j], lmvm->S[i], &yjtsi);
     63:         /* Compute the pure BFGS component of the forward product */
     64:         VecAXPBYPCZ(lsb->P[i], -PetscRealPart(sjtpi)/lsb->stp[j], PetscRealPart(yjtsi)/lsb->yts[j], 1.0, lsb->P[j], lmvm->Y[j]);
     65:         /* Tack on the convexly scaled extras to the forward product */
     66:         if (lsb->phi > 0.0) {
     67:           VecAXPBYPCZ(lsb->work, 1.0/lsb->yts[j], -1.0/lsb->stp[j], 0.0, lmvm->Y[j], lsb->P[j]);
     68:           VecDot(lsb->work, lmvm->S[i], &wtsi);
     69:           VecAXPY(lsb->P[i], lsb->phi*lsb->stp[j]*PetscRealPart(wtsi), lsb->work);
     70:         }
     71:       }
     72:       VecDot(lmvm->S[i], lsb->P[i], &stp);
     73:       lsb->stp[i] = PetscRealPart(stp);
     74:     }
     75:     lsb->needP = PETSC_FALSE;
     76:   }
     77:   if (lsb->needQ) {
     78:     /* Start the loop for (Q[k] = (B_k)^{-1} * Y[k]) */
     79:     for (i = 0; i <= lmvm->k; ++i) {
     80:       MatSymBrdnApplyJ0Inv(B, lmvm->Y[i], lsb->Q[i]);
     81:       for (j = 0; j <= i-1; ++j) {
     82:         /* Compute the necessary dot products */
     83:         VecDotBegin(lmvm->Y[j], lsb->Q[i], &yjtqi);
     84:         VecDotBegin(lmvm->S[j], lmvm->Y[i], &sjtyi);
     85:         VecDotEnd(lmvm->Y[j], lsb->Q[i], &yjtqi);
     86:         VecDotEnd(lmvm->S[j], lmvm->Y[i], &sjtyi);
     87:         /* Compute the pure DFP component of the inverse application*/
     88:         VecAXPBYPCZ(lsb->Q[i], -PetscRealPart(yjtqi)/lsb->ytq[j], PetscRealPart(sjtyi)/lsb->yts[j], 1.0, lsb->Q[j], lmvm->S[j]);
     89:         /* Tack on the convexly scaled extras to the inverse application*/
     90:         if (lsb->psi[j] > 0.0) {
     91:           VecAXPBYPCZ(lsb->work, 1.0/lsb->yts[j], -1.0/lsb->ytq[j], 0.0, lmvm->S[j], lsb->Q[j]);
     92:           VecDot(lsb->work, lmvm->Y[i], &wtyi);
     93:           VecAXPY(lsb->Q[i], lsb->psi[j]*lsb->ytq[j]*PetscRealPart(wtyi), lsb->work);
     94:         }
     95:       }
     96:       VecDot(lmvm->Y[i], lsb->Q[i], &ytq);
     97:       lsb->ytq[i] = PetscRealPart(ytq);
     98:       if (lsb->phi == 1.0) {
     99:         lsb->psi[i] = 0.0;
    100:       } else if (lsb->phi == 0.0) {
    101:         lsb->psi[i] = 1.0;
    102:       } else {
    103:         numer = (1.0 - lsb->phi)*lsb->yts[i]*lsb->yts[i];
    104:         lsb->psi[i] = numer / (numer + (lsb->phi*lsb->ytq[i]*lsb->stp[i]));
    105:       }
    106:     }
    107:     lsb->needQ = PETSC_FALSE;
    108:   }

    110:   /* Start the outer iterations for ((B^{-1}) * dX) */
    111:   MatSymBrdnApplyJ0Inv(B, F, dX);
    112:   for (i = 0; i <= lmvm->k; ++i) {
    113:     /* Compute the necessary dot products -- store yTs and yTp for inner iterations later */
    114:     VecDotBegin(lmvm->Y[i], dX, &ytx);
    115:     VecDotBegin(lmvm->S[i], F, &stf);
    116:     VecDotEnd(lmvm->Y[i], dX, &ytx);
    117:     VecDotEnd(lmvm->S[i], F, &stf);
    118:     /* Compute the pure DFP component */
    119:     VecAXPBYPCZ(dX, -PetscRealPart(ytx)/lsb->ytq[i], PetscRealPart(stf)/lsb->yts[i], 1.0, lsb->Q[i], lmvm->S[i]);
    120:     /* Tack on the convexly scaled extras */
    121:     VecAXPBYPCZ(lsb->work, 1.0/lsb->yts[i], -1.0/lsb->ytq[i], 0.0, lmvm->S[i], lsb->Q[i]);
    122:     VecDot(lsb->work, F, &wtf);
    123:     VecAXPY(dX, lsb->psi[i]*lsb->ytq[i]*PetscRealPart(wtf), lsb->work);
    124:   }

    126:   return 0;
    127: }

    129: /*------------------------------------------------------------*/

    131: /*
    132:   The forward-product below is the matrix-free implementation of
    133:   Equation 16 in Dennis and Wolkowicz "Sizing and Least Change Secant
    134:   Methods" (http://www.caam.rice.edu/caam/trs/90/TR90-05.pdf).

    136:   P[i] = (B_i)*S[i] terms are computed ahead of time whenever
    137:   the matrix is updated with a new (S[i], Y[i]) pair. This allows
    138:   repeated calls of MatMult inside KSP solvers without unnecessarily
    139:   recomputing P[i] terms in expensive nested-loops.

    141:   Z <- J0 * X

    143:   for i=0,1,2,...,k
    144:     # P[i] = (B_k) * S[i]

    146:     rho = 1.0 / (Y[i]^T S[i])
    147:     alpha = rho * (Y[i]^T F)
    148:     zeta = 1.0 / (S[i]^T P[i])
    149:     gamma = zeta * (S[i]^T dX)

    151:     dX <- dX - (gamma * P[i]) + (alpha * S[i])
    152:     W <- (rho * Y[i]) - (zeta * P[i])
    153:     dX <- dX + (phi * (S[i]^T P[i]) * (W^T F) * W)
    154:   end
    155: */
    156: static PetscErrorCode MatMult_LMVMSymBrdn(Mat B, Vec X, Vec Z)
    157: {
    158:   Mat_LMVM          *lmvm = (Mat_LMVM*)B->data;
    159:   Mat_SymBrdn       *lsb = (Mat_SymBrdn*)lmvm->ctx;
    160:   PetscInt          i, j;
    161:   PetscScalar         sjtpi, yjtsi, wtsi, stz, ytx, wtx, stp;

    163:   /* Efficient shortcuts for pure BFGS and pure DFP configurations */
    164:   if (lsb->phi == 0.0) {
    165:     MatMult_LMVMBFGS(B, X, Z);
    166:     return 0;
    167:   }
    168:   if (lsb->phi == 1.0) {
    169:     MatMult_LMVMDFP(B, X, Z);
    170:     return 0;
    171:   }

    173:   VecCheckSameSize(X, 2, Z, 3);
    174:   VecCheckMatCompatible(B, X, 2, Z, 3);

    176:   if (lsb->needP) {
    177:     /* Start the loop for (P[k] = (B_k) * S[k]) */
    178:     for (i = 0; i <= lmvm->k; ++i) {
    179:       MatSymBrdnApplyJ0Fwd(B, lmvm->S[i], lsb->P[i]);
    180:       for (j = 0; j <= i-1; ++j) {
    181:         /* Compute the necessary dot products */
    182:         VecDotBegin(lmvm->S[j], lsb->P[i], &sjtpi);
    183:         VecDotBegin(lmvm->Y[j], lmvm->S[i], &yjtsi);
    184:         VecDotEnd(lmvm->S[j], lsb->P[i], &sjtpi);
    185:         VecDotEnd(lmvm->Y[j], lmvm->S[i], &yjtsi);
    186:         /* Compute the pure BFGS component of the forward product */
    187:         VecAXPBYPCZ(lsb->P[i], -PetscRealPart(sjtpi)/lsb->stp[j], PetscRealPart(yjtsi)/lsb->yts[j], 1.0, lsb->P[j], lmvm->Y[j]);
    188:         /* Tack on the convexly scaled extras to the forward product */
    189:         if (lsb->phi > 0.0) {
    190:           VecAXPBYPCZ(lsb->work, 1.0/lsb->yts[j], -1.0/lsb->stp[j], 0.0, lmvm->Y[j], lsb->P[j]);
    191:           VecDot(lsb->work, lmvm->S[i], &wtsi);
    192:           VecAXPY(lsb->P[i], lsb->phi*lsb->stp[j]*PetscRealPart(wtsi), lsb->work);
    193:         }
    194:       }
    195:       VecDot(lmvm->S[i], lsb->P[i], &stp);
    196:       lsb->stp[i] = PetscRealPart(stp);
    197:     }
    198:     lsb->needP = PETSC_FALSE;
    199:   }

    201:   /* Start the outer iterations for (B * X) */
    202:   MatSymBrdnApplyJ0Fwd(B, X, Z);
    203:   for (i = 0; i <= lmvm->k; ++i) {
    204:     /* Compute the necessary dot products */
    205:     VecDotBegin(lmvm->S[i], Z, &stz);
    206:     VecDotBegin(lmvm->Y[i], X, &ytx);
    207:     VecDotEnd(lmvm->S[i], Z, &stz);
    208:     VecDotEnd(lmvm->Y[i], X, &ytx);
    209:     /* Compute the pure BFGS component */
    210:     VecAXPBYPCZ(Z, -PetscRealPart(stz)/lsb->stp[i], PetscRealPart(ytx)/lsb->yts[i], 1.0, lsb->P[i], lmvm->Y[i]);
    211:     /* Tack on the convexly scaled extras */
    212:     VecAXPBYPCZ(lsb->work, 1.0/lsb->yts[i], -1.0/lsb->stp[i], 0.0, lmvm->Y[i], lsb->P[i]);
    213:     VecDot(lsb->work, X, &wtx);
    214:     VecAXPY(Z, lsb->phi*lsb->stp[i]*PetscRealPart(wtx), lsb->work);
    215:   }
    216:   return 0;
    217: }

    219: /*------------------------------------------------------------*/

    221: static PetscErrorCode MatUpdate_LMVMSymBrdn(Mat B, Vec X, Vec F)
    222: {
    223:   Mat_LMVM          *lmvm = (Mat_LMVM*)B->data;
    224:   Mat_SymBrdn       *lsb = (Mat_SymBrdn*)lmvm->ctx;
    225:   Mat_LMVM          *dbase;
    226:   Mat_DiagBrdn      *dctx;
    227:   PetscInt          old_k, i;
    228:   PetscReal         curvtol;
    229:   PetscScalar       curvature, ytytmp, ststmp;

    231:   if (!lmvm->m) return 0;
    232:   if (lmvm->prev_set) {
    233:     /* Compute the new (S = X - Xprev) and (Y = F - Fprev) vectors */
    234:     VecAYPX(lmvm->Xprev, -1.0, X);
    235:     VecAYPX(lmvm->Fprev, -1.0, F);
    236:     /* Test if the updates can be accepted */
    237:     VecDotBegin(lmvm->Xprev, lmvm->Fprev, &curvature);
    238:     VecDotBegin(lmvm->Xprev, lmvm->Xprev, &ststmp);
    239:     VecDotEnd(lmvm->Xprev, lmvm->Fprev, &curvature);
    240:     VecDotEnd(lmvm->Xprev, lmvm->Xprev, &ststmp);
    241:     if (PetscRealPart(ststmp) < lmvm->eps) {
    242:       curvtol = 0.0;
    243:     } else {
    244:       curvtol = lmvm->eps * PetscRealPart(ststmp);
    245:     }
    246:     if (PetscRealPart(curvature) > curvtol) {
    247:       /* Update is good, accept it */
    248:       lsb->watchdog = 0;
    249:       lsb->needP = lsb->needQ = PETSC_TRUE;
    250:       old_k = lmvm->k;
    251:       MatUpdateKernel_LMVM(B, lmvm->Xprev, lmvm->Fprev);
    252:       /* If we hit the memory limit, shift the yts, yty and sts arrays */
    253:       if (old_k == lmvm->k) {
    254:         for (i = 0; i <= lmvm->k-1; ++i) {
    255:           lsb->yts[i] = lsb->yts[i+1];
    256:           lsb->yty[i] = lsb->yty[i+1];
    257:           lsb->sts[i] = lsb->sts[i+1];
    258:         }
    259:       }
    260:       /* Update history of useful scalars */
    261:       VecDot(lmvm->Y[lmvm->k], lmvm->Y[lmvm->k], &ytytmp);
    262:       lsb->yts[lmvm->k] = PetscRealPart(curvature);
    263:       lsb->yty[lmvm->k] = PetscRealPart(ytytmp);
    264:       lsb->sts[lmvm->k] = PetscRealPart(ststmp);
    265:       /* Compute the scalar scale if necessary */
    266:       if (lsb->scale_type == MAT_LMVM_SYMBROYDEN_SCALE_SCALAR) {
    267:         MatSymBrdnComputeJ0Scalar(B);
    268:       }
    269:     } else {
    270:       /* Update is bad, skip it */
    271:       ++lmvm->nrejects;
    272:       ++lsb->watchdog;
    273:     }
    274:   } else {
    275:     switch (lsb->scale_type) {
    276:     case MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL:
    277:       dbase = (Mat_LMVM*)lsb->D->data;
    278:       dctx = (Mat_DiagBrdn*)dbase->ctx;
    279:       VecSet(dctx->invD, lsb->delta);
    280:       break;
    281:     case MAT_LMVM_SYMBROYDEN_SCALE_SCALAR:
    282:       lsb->sigma = lsb->delta;
    283:       break;
    284:     case MAT_LMVM_SYMBROYDEN_SCALE_NONE:
    285:       lsb->sigma = 1.0;
    286:       break;
    287:     default:
    288:       break;
    289:     }
    290:   }

    292:   /* Update the scaling */
    293:   if (lsb->scale_type == MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL) {
    294:     MatLMVMUpdate(lsb->D, X, F);
    295:   }

    297:   if (lsb->watchdog > lsb->max_seq_rejects) {
    298:     MatLMVMReset(B, PETSC_FALSE);
    299:     if (lsb->scale_type == MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL) {
    300:       MatLMVMReset(lsb->D, PETSC_FALSE);
    301:     }
    302:   }

    304:   /* Save the solution and function to be used in the next update */
    305:   VecCopy(X, lmvm->Xprev);
    306:   VecCopy(F, lmvm->Fprev);
    307:   lmvm->prev_set = PETSC_TRUE;
    308:   return 0;
    309: }

    311: /*------------------------------------------------------------*/

    313: static PetscErrorCode MatCopy_LMVMSymBrdn(Mat B, Mat M, MatStructure str)
    314: {
    315:   Mat_LMVM          *bdata = (Mat_LMVM*)B->data;
    316:   Mat_SymBrdn       *blsb = (Mat_SymBrdn*)bdata->ctx;
    317:   Mat_LMVM          *mdata = (Mat_LMVM*)M->data;
    318:   Mat_SymBrdn       *mlsb = (Mat_SymBrdn*)mdata->ctx;
    319:   PetscInt          i;

    321:   mlsb->phi = blsb->phi;
    322:   mlsb->needP = blsb->needP;
    323:   mlsb->needQ = blsb->needQ;
    324:   for (i=0; i<=bdata->k; ++i) {
    325:     mlsb->stp[i] = blsb->stp[i];
    326:     mlsb->ytq[i] = blsb->ytq[i];
    327:     mlsb->yts[i] = blsb->yts[i];
    328:     mlsb->psi[i] = blsb->psi[i];
    329:     VecCopy(blsb->P[i], mlsb->P[i]);
    330:     VecCopy(blsb->Q[i], mlsb->Q[i]);
    331:   }
    332:   mlsb->scale_type      = blsb->scale_type;
    333:   mlsb->alpha           = blsb->alpha;
    334:   mlsb->beta            = blsb->beta;
    335:   mlsb->rho             = blsb->rho;
    336:   mlsb->delta           = blsb->delta;
    337:   mlsb->sigma_hist      = blsb->sigma_hist;
    338:   mlsb->watchdog        = blsb->watchdog;
    339:   mlsb->max_seq_rejects = blsb->max_seq_rejects;
    340:   switch (blsb->scale_type) {
    341:   case MAT_LMVM_SYMBROYDEN_SCALE_SCALAR:
    342:     mlsb->sigma = blsb->sigma;
    343:     break;
    344:   case MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL:
    345:     MatCopy(blsb->D, mlsb->D, SAME_NONZERO_PATTERN);
    346:     break;
    347:   case MAT_LMVM_SYMBROYDEN_SCALE_NONE:
    348:     mlsb->sigma = 1.0;
    349:     break;
    350:   default:
    351:     break;
    352:   }
    353:   return 0;
    354: }

    356: /*------------------------------------------------------------*/

    358: static PetscErrorCode MatReset_LMVMSymBrdn(Mat B, PetscBool destructive)
    359: {
    360:   Mat_LMVM          *lmvm = (Mat_LMVM*)B->data;
    361:   Mat_SymBrdn       *lsb = (Mat_SymBrdn*)lmvm->ctx;
    362:   Mat_LMVM          *dbase;
    363:   Mat_DiagBrdn      *dctx;

    365:   lsb->watchdog = 0;
    366:   lsb->needP = lsb->needQ = PETSC_TRUE;
    367:   if (lsb->allocated) {
    368:     if (destructive) {
    369:       VecDestroy(&lsb->work);
    370:       PetscFree5(lsb->stp, lsb->ytq, lsb->yts, lsb->yty, lsb->sts);
    371:       PetscFree(lsb->psi);
    372:       VecDestroyVecs(lmvm->m, &lsb->P);
    373:       VecDestroyVecs(lmvm->m, &lsb->Q);
    374:       switch (lsb->scale_type) {
    375:       case MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL:
    376:         MatLMVMReset(lsb->D, PETSC_TRUE);
    377:         break;
    378:       default:
    379:         break;
    380:       }
    381:       lsb->allocated = PETSC_FALSE;
    382:     } else {
    383:       PetscMemzero(lsb->psi, lmvm->m);
    384:       switch (lsb->scale_type) {
    385:       case MAT_LMVM_SYMBROYDEN_SCALE_SCALAR:
    386:         lsb->sigma = lsb->delta;
    387:         break;
    388:       case MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL:
    389:         MatLMVMReset(lsb->D, PETSC_FALSE);
    390:         dbase = (Mat_LMVM*)lsb->D->data;
    391:         dctx = (Mat_DiagBrdn*)dbase->ctx;
    392:         VecSet(dctx->invD, lsb->delta);
    393:         break;
    394:       case MAT_LMVM_SYMBROYDEN_SCALE_NONE:
    395:         lsb->sigma = 1.0;
    396:         break;
    397:       default:
    398:         break;
    399:       }
    400:     }
    401:   }
    402:   MatReset_LMVM(B, destructive);
    403:   return 0;
    404: }

    406: /*------------------------------------------------------------*/

    408: static PetscErrorCode MatAllocate_LMVMSymBrdn(Mat B, Vec X, Vec F)
    409: {
    410:   Mat_LMVM          *lmvm = (Mat_LMVM*)B->data;
    411:   Mat_SymBrdn       *lsb = (Mat_SymBrdn*)lmvm->ctx;

    413:   MatAllocate_LMVM(B, X, F);
    414:   if (!lsb->allocated) {
    415:     VecDuplicate(X, &lsb->work);
    416:     if (lmvm->m > 0) {
    417:       PetscMalloc5(lmvm->m,&lsb->stp,lmvm->m,&lsb->ytq,lmvm->m,&lsb->yts,lmvm->m,&lsb->yty,lmvm->m,&lsb->sts);
    418:       PetscCalloc1(lmvm->m,&lsb->psi);
    419:       VecDuplicateVecs(X, lmvm->m, &lsb->P);
    420:       VecDuplicateVecs(X, lmvm->m, &lsb->Q);
    421:     }
    422:     switch (lsb->scale_type) {
    423:     case MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL:
    424:       MatLMVMAllocate(lsb->D, X, F);
    425:       break;
    426:     default:
    427:       break;
    428:     }
    429:     lsb->allocated = PETSC_TRUE;
    430:   }
    431:   return 0;
    432: }

    434: /*------------------------------------------------------------*/

    436: static PetscErrorCode MatDestroy_LMVMSymBrdn(Mat B)
    437: {
    438:   Mat_LMVM          *lmvm = (Mat_LMVM*)B->data;
    439:   Mat_SymBrdn       *lsb = (Mat_SymBrdn*)lmvm->ctx;

    441:   if (lsb->allocated) {
    442:     VecDestroy(&lsb->work);
    443:     PetscFree5(lsb->stp, lsb->ytq, lsb->yts, lsb->yty, lsb->sts);
    444:     PetscFree(lsb->psi);
    445:     VecDestroyVecs(lmvm->m, &lsb->P);
    446:     VecDestroyVecs(lmvm->m, &lsb->Q);
    447:     lsb->allocated = PETSC_FALSE;
    448:   }
    449:   MatDestroy(&lsb->D);
    450:   PetscFree(lmvm->ctx);
    451:   MatDestroy_LMVM(B);
    452:   return 0;
    453: }

    455: /*------------------------------------------------------------*/

    457: static PetscErrorCode MatSetUp_LMVMSymBrdn(Mat B)
    458: {
    459:   Mat_LMVM          *lmvm = (Mat_LMVM*)B->data;
    460:   Mat_SymBrdn       *lsb = (Mat_SymBrdn*)lmvm->ctx;
    461:   PetscInt          n, N;

    463:   MatSetUp_LMVM(B);
    464:   if (!lsb->allocated) {
    465:     VecDuplicate(lmvm->Xprev, &lsb->work);
    466:     if (lmvm->m > 0) {
    467:       PetscMalloc5(lmvm->m,&lsb->stp,lmvm->m,&lsb->ytq,lmvm->m,&lsb->yts,lmvm->m,&lsb->yty,lmvm->m,&lsb->sts);
    468:       PetscCalloc1(lmvm->m,&lsb->psi);
    469:       VecDuplicateVecs(lmvm->Xprev, lmvm->m, &lsb->P);
    470:       VecDuplicateVecs(lmvm->Xprev, lmvm->m, &lsb->Q);
    471:     }
    472:     switch (lsb->scale_type) {
    473:     case MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL:
    474:       MatGetLocalSize(B, &n, &n);
    475:       MatGetSize(B, &N, &N);
    476:       MatSetSizes(lsb->D, n, n, N, N);
    477:       MatSetUp(lsb->D);
    478:       break;
    479:     default:
    480:       break;
    481:     }
    482:     lsb->allocated = PETSC_TRUE;
    483:   }
    484:   return 0;
    485: }

    487: /*------------------------------------------------------------*/

    489: PetscErrorCode MatView_LMVMSymBrdn(Mat B, PetscViewer pv)
    490: {
    491:   Mat_LMVM          *lmvm = (Mat_LMVM*)B->data;
    492:   Mat_SymBrdn       *lsb = (Mat_SymBrdn*)lmvm->ctx;
    493:   PetscBool         isascii;

    495:   PetscObjectTypeCompare((PetscObject)pv,PETSCVIEWERASCII,&isascii);
    496:   if (isascii) {
    497:     PetscViewerASCIIPrintf(pv,"Scale type: %s\n",MatLMVMSymBroydenScaleTypes[lsb->scale_type]);
    498:     PetscViewerASCIIPrintf(pv,"Scale history: %d\n",lsb->sigma_hist);
    499:     PetscViewerASCIIPrintf(pv,"Scale params: alpha=%g, beta=%g, rho=%g\n",(double)lsb->alpha, (double)lsb->beta, (double)lsb->rho);
    500:     PetscViewerASCIIPrintf(pv,"Convex factors: phi=%g, theta=%g\n",(double)lsb->phi, (double)lsb->theta);
    501:   }
    502:   MatView_LMVM(B, pv);
    503:   if (lsb->scale_type == MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL) {
    504:     MatView(lsb->D, pv);
    505:   }
    506:   return 0;
    507: }

    509: /*------------------------------------------------------------*/

    511: PetscErrorCode MatSetFromOptions_LMVMSymBrdn(PetscOptionItems *PetscOptionsObject, Mat B)
    512: {
    513:   Mat_LMVM                     *lmvm = (Mat_LMVM*)B->data;
    514:   Mat_SymBrdn                  *lsb = (Mat_SymBrdn*)lmvm->ctx;

    516:   MatSetFromOptions_LMVM(PetscOptionsObject, B);
    517:   PetscOptionsHead(PetscOptionsObject,"Restricted/Symmetric Broyden method for approximating SPD Jacobian actions (MATLMVMSYMBRDN)");
    518:   PetscOptionsReal("-mat_lmvm_phi","(developer) convex ratio between BFGS and DFP components of the update","",lsb->phi,&lsb->phi,NULL);
    520:   MatSetFromOptions_LMVMSymBrdn_Private(PetscOptionsObject, B);
    521:   PetscOptionsTail();
    522:   return 0;
    523: }

    525: PetscErrorCode MatSetFromOptions_LMVMSymBrdn_Private(PetscOptionItems *PetscOptionsObject, Mat B)
    526: {
    527:   Mat_LMVM                     *lmvm = (Mat_LMVM*)B->data;
    528:   Mat_SymBrdn                  *lsb = (Mat_SymBrdn*)lmvm->ctx;
    529:   Mat_LMVM                     *dbase;
    530:   Mat_DiagBrdn                 *dctx;
    531:   MatLMVMSymBroydenScaleType   stype = lsb->scale_type;
    532:   PetscBool                    flg;

    534:   PetscOptionsReal("-mat_lmvm_beta","(developer) exponential factor in the diagonal J0 scaling","",lsb->beta,&lsb->beta,NULL);
    535:   PetscOptionsReal("-mat_lmvm_theta","(developer) convex ratio between BFGS and DFP components of the diagonal J0 scaling","",lsb->theta,&lsb->theta,NULL);
    537:   PetscOptionsReal("-mat_lmvm_rho","(developer) update limiter in the J0 scaling","",lsb->rho,&lsb->rho,NULL);
    539:   PetscOptionsReal("-mat_lmvm_alpha","(developer) convex ratio in the J0 scaling","",lsb->alpha,&lsb->alpha,NULL);
    541:   PetscOptionsBoundedInt("-mat_lmvm_sigma_hist","(developer) number of past updates to use in the default J0 scalar","",lsb->sigma_hist,&lsb->sigma_hist,NULL,1);
    542:   PetscOptionsEnum("-mat_lmvm_scale_type", "(developer) scaling type applied to J0","MatLMVMSymBrdnScaleType",MatLMVMSymBroydenScaleTypes,(PetscEnum)stype,(PetscEnum*)&stype,&flg);
    543:   if (flg) MatLMVMSymBroydenSetScaleType(B, stype);
    544:   if (lsb->scale_type == MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL) {
    545:     MatSetFromOptions(lsb->D);
    546:     dbase = (Mat_LMVM*)lsb->D->data;
    547:     dctx = (Mat_DiagBrdn*)dbase->ctx;
    548:     dctx->delta_min  = lsb->delta_min;
    549:     dctx->delta_max  = lsb->delta_max;
    550:     dctx->theta      = lsb->theta;
    551:     dctx->rho        = lsb->rho;
    552:     dctx->alpha      = lsb->alpha;
    553:     dctx->beta       = lsb->beta;
    554:     dctx->sigma_hist = lsb->sigma_hist;
    555:   }
    556:   return 0;
    557: }

    559: /*------------------------------------------------------------*/

    561: PetscErrorCode MatCreate_LMVMSymBrdn(Mat B)
    562: {
    563:   Mat_LMVM          *lmvm;
    564:   Mat_SymBrdn       *lsb;

    566:   MatCreate_LMVM(B);
    567:   PetscObjectChangeTypeName((PetscObject)B, MATLMVMSYMBROYDEN);
    568:   MatSetOption(B, MAT_SPD, PETSC_TRUE);
    569:   B->ops->view = MatView_LMVMSymBrdn;
    570:   B->ops->setfromoptions = MatSetFromOptions_LMVMSymBrdn;
    571:   B->ops->setup = MatSetUp_LMVMSymBrdn;
    572:   B->ops->destroy = MatDestroy_LMVMSymBrdn;
    573:   B->ops->solve = MatSolve_LMVMSymBrdn;

    575:   lmvm = (Mat_LMVM*)B->data;
    576:   lmvm->square = PETSC_TRUE;
    577:   lmvm->ops->allocate = MatAllocate_LMVMSymBrdn;
    578:   lmvm->ops->reset = MatReset_LMVMSymBrdn;
    579:   lmvm->ops->update = MatUpdate_LMVMSymBrdn;
    580:   lmvm->ops->mult = MatMult_LMVMSymBrdn;
    581:   lmvm->ops->copy = MatCopy_LMVMSymBrdn;

    583:   PetscNewLog(B, &lsb);
    584:   lmvm->ctx = (void*)lsb;
    585:   lsb->allocated       = PETSC_FALSE;
    586:   lsb->needP           = lsb->needQ = PETSC_TRUE;
    587:   lsb->phi             = 0.125;
    588:   lsb->theta           = 0.125;
    589:   lsb->alpha           = 1.0;
    590:   lsb->rho             = 1.0;
    591:   lsb->beta            = 0.5;
    592:   lsb->sigma           = 1.0;
    593:   lsb->delta           = 1.0;
    594:   lsb->delta_min       = 1e-7;
    595:   lsb->delta_max       = 100.0;
    596:   lsb->sigma_hist      = 1;
    597:   lsb->scale_type      = MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL;
    598:   lsb->watchdog        = 0;
    599:   lsb->max_seq_rejects = lmvm->m/2;

    601:   MatCreate(PetscObjectComm((PetscObject)B), &lsb->D);
    602:   MatSetType(lsb->D, MATLMVMDIAGBROYDEN);
    603:   MatSetOptionsPrefix(lsb->D, "J0_");
    604:   return 0;
    605: }

    607: /*------------------------------------------------------------*/

    609: /*@
    610:    MatLMVMSymBroydenSetDelta - Sets the starting value for the diagonal scaling vector computed
    611:    in the SymBrdn approximations (also works for BFGS and DFP).

    613:    Input Parameters:
    614: +  B - LMVM matrix
    615: -  delta - initial value for diagonal scaling

    617:    Level: intermediate
    618: @*/

    620: PetscErrorCode MatLMVMSymBroydenSetDelta(Mat B, PetscScalar delta)
    621: {
    622:   Mat_LMVM          *lmvm = (Mat_LMVM*)B->data;
    623:   Mat_SymBrdn       *lsb = (Mat_SymBrdn*)lmvm->ctx;
    624:   PetscBool         is_bfgs, is_dfp, is_symbrdn, is_symbadbrdn;

    626:   PetscObjectTypeCompare((PetscObject)B, MATLMVMBFGS, &is_bfgs);
    627:   PetscObjectTypeCompare((PetscObject)B, MATLMVMDFP, &is_dfp);
    628:   PetscObjectTypeCompare((PetscObject)B, MATLMVMSYMBROYDEN, &is_symbrdn);
    629:   PetscObjectTypeCompare((PetscObject)B, MATLMVMSYMBADBROYDEN, &is_symbadbrdn);
    631:   lsb->delta = PetscAbsReal(PetscRealPart(delta));
    632:   lsb->delta = PetscMin(lsb->delta, lsb->delta_max);
    633:   lsb->delta = PetscMax(lsb->delta, lsb->delta_min);
    634:   return 0;
    635: }

    637: /*------------------------------------------------------------*/

    639: /*@
    640:     MatLMVMSymBroydenSetScaleType - Sets the scale type for symmetric Broyden-type updates.

    642:     Input Parameters:
    643: +   snes - the iterative context
    644: -   rtype - restart type

    646:     Options Database:
    647: .   -mat_lmvm_scale_type <none,scalar,diagonal> - set the scaling type

    649:     Level: intermediate

    651:     MatLMVMSymBrdnScaleTypes:
    652: +   MAT_LMVM_SYMBROYDEN_SCALE_NONE - initial Hessian is the identity matrix
    653: .   MAT_LMVM_SYMBROYDEN_SCALE_SCALAR - use the Shanno scalar as the initial Hessian
    654: -   MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL - use a diagonalized BFGS update as the initial Hessian

    656: .seealso: MATLMVMSYMBROYDEN, MatCreateLMVMSymBroyden()
    657: @*/
    658: PetscErrorCode MatLMVMSymBroydenSetScaleType(Mat B, MatLMVMSymBroydenScaleType stype)
    659: {
    660:   Mat_LMVM          *lmvm = (Mat_LMVM*)B->data;
    661:   Mat_SymBrdn       *lsb = (Mat_SymBrdn*)lmvm->ctx;

    664:   lsb->scale_type = stype;
    665:   return 0;
    666: }

    668: /*------------------------------------------------------------*/

    670: /*@
    671:    MatCreateLMVMSymBroyden - Creates a limited-memory Symmetric Broyden-type matrix used
    672:    for approximating Jacobians. L-SymBrdn is a convex combination of L-DFP and
    673:    L-BFGS such that SymBrdn = (1 - phi)*BFGS + phi*DFP. The combination factor
    674:    phi is restricted to the range [0, 1], where the L-SymBrdn matrix is guaranteed
    675:    to be symmetric positive-definite.

    677:    The provided local and global sizes must match the solution and function vectors
    678:    used with MatLMVMUpdate() and MatSolve(). The resulting L-SymBrdn matrix will have
    679:    storage vectors allocated with VecCreateSeq() in serial and VecCreateMPI() in
    680:    parallel. To use the L-SymBrdn matrix with other vector types, the matrix must be
    681:    created using MatCreate() and MatSetType(), followed by MatLMVMAllocate().
    682:    This ensures that the internal storage and work vectors are duplicated from the
    683:    correct type of vector.

    685:    Collective

    687:    Input Parameters:
    688: +  comm - MPI communicator, set to PETSC_COMM_SELF
    689: .  n - number of local rows for storage vectors
    690: -  N - global size of the storage vectors

    692:    Output Parameter:
    693: .  B - the matrix

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

    698:    Options Database Keys:
    699: +   -mat_lmvm_num_vecs - maximum number of correction vectors (i.e.: updates) stored
    700: .   -mat_lmvm_phi - (developer) convex ratio between BFGS and DFP components of the update
    701: .   -mat_lmvm_scale_type - (developer) type of scaling applied to J0 (none, scalar, diagonal)
    702: .   -mat_lmvm_theta - (developer) convex ratio between BFGS and DFP components of the diagonal J0 scaling
    703: .   -mat_lmvm_rho - (developer) update limiter for the J0 scaling
    704: .   -mat_lmvm_alpha - (developer) coefficient factor for the quadratic subproblem in J0 scaling
    705: .   -mat_lmvm_beta - (developer) exponential factor for the diagonal J0 scaling
    706: -   -mat_lmvm_sigma_hist - (developer) number of past updates to use in J0 scaling

    708:    Level: intermediate

    710: .seealso: MatCreate(), MATLMVM, MATLMVMSYMBROYDEN, MatCreateLMVMDFP(), MatCreateLMVMSR1(),
    711:           MatCreateLMVMBFGS(), MatCreateLMVMBrdn(), MatCreateLMVMBadBrdn()
    712: @*/
    713: PetscErrorCode MatCreateLMVMSymBroyden(MPI_Comm comm, PetscInt n, PetscInt N, Mat *B)
    714: {
    715:   MatCreate(comm, B);
    716:   MatSetSizes(*B, n, n, N, N);
    717:   MatSetType(*B, MATLMVMSYMBROYDEN);
    718:   MatSetUp(*B);
    719:   return 0;
    720: }

    722: /*------------------------------------------------------------*/

    724: PetscErrorCode MatSymBrdnApplyJ0Fwd(Mat B, Vec X, Vec Z)
    725: {
    726:   Mat_LMVM          *lmvm = (Mat_LMVM*)B->data;
    727:   Mat_SymBrdn       *lsb = (Mat_SymBrdn*)lmvm->ctx;

    729:   if (lmvm->J0 || lmvm->user_pc || lmvm->user_ksp || lmvm->user_scale) {
    730:     lsb->scale_type = MAT_LMVM_SYMBROYDEN_SCALE_USER;
    731:     MatLMVMApplyJ0Fwd(B, X, Z);
    732:   } else {
    733:     switch (lsb->scale_type) {
    734:     case MAT_LMVM_SYMBROYDEN_SCALE_SCALAR:
    735:       VecCopy(X, Z);
    736:       VecScale(Z, 1.0/lsb->sigma);
    737:       break;
    738:     case MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL:
    739:       MatMult(lsb->D, X, Z);
    740:       break;
    741:     case MAT_LMVM_SYMBROYDEN_SCALE_NONE:
    742:     default:
    743:       VecCopy(X, Z);
    744:       break;
    745:     }
    746:   }
    747:   return 0;
    748: }

    750: /*------------------------------------------------------------*/

    752: PetscErrorCode MatSymBrdnApplyJ0Inv(Mat B, Vec F, Vec dX)
    753: {
    754:   Mat_LMVM          *lmvm = (Mat_LMVM*)B->data;
    755:   Mat_SymBrdn       *lsb = (Mat_SymBrdn*)lmvm->ctx;

    757:   if (lmvm->J0 || lmvm->user_pc || lmvm->user_ksp || lmvm->user_scale) {
    758:     lsb->scale_type = MAT_LMVM_SYMBROYDEN_SCALE_USER;
    759:     MatLMVMApplyJ0Inv(B, F, dX);
    760:   } else {
    761:     switch (lsb->scale_type) {
    762:     case MAT_LMVM_SYMBROYDEN_SCALE_SCALAR:
    763:       VecCopy(F, dX);
    764:       VecScale(dX, lsb->sigma);
    765:       break;
    766:     case MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL:
    767:       MatSolve(lsb->D, F, dX);
    768:       break;
    769:     case MAT_LMVM_SYMBROYDEN_SCALE_NONE:
    770:     default:
    771:       VecCopy(F, dX);
    772:       break;
    773:     }
    774:   }
    775:   return 0;
    776: }

    778: /*------------------------------------------------------------*/

    780: PetscErrorCode MatSymBrdnComputeJ0Scalar(Mat B)
    781: {
    782:   Mat_LMVM          *lmvm = (Mat_LMVM*)B->data;
    783:   Mat_SymBrdn       *lsb = (Mat_SymBrdn*)lmvm->ctx;
    784:   PetscInt          i, start;
    785:   PetscReal         a, b, c, sig1, sig2, signew;

    787:   if (lsb->sigma_hist == 0) {
    788:     signew = 1.0;
    789:   } else {
    790:     start = PetscMax(0, lmvm->k-lsb->sigma_hist+1);
    791:     signew = 0.0;
    792:     if (lsb->alpha == 1.0) {
    793:       for (i = start; i <= lmvm->k; ++i) {
    794:         signew += lsb->yts[i]/lsb->yty[i];
    795:       }
    796:     } else if (lsb->alpha == 0.5) {
    797:       for (i = start; i <= lmvm->k; ++i) {
    798:         signew += lsb->sts[i]/lsb->yty[i];
    799:       }
    800:       signew = PetscSqrtReal(signew);
    801:     } else if (lsb->alpha == 0.0) {
    802:       for (i = start; i <= lmvm->k; ++i) {
    803:         signew += lsb->sts[i]/lsb->yts[i];
    804:       }
    805:     } else {
    806:       /* compute coefficients of the quadratic */
    807:       a = b = c = 0.0;
    808:       for (i = start; i <= lmvm->k; ++i) {
    809:         a += lsb->yty[i];
    810:         b += lsb->yts[i];
    811:         c += lsb->sts[i];
    812:       }
    813:       a *= lsb->alpha;
    814:       b *= -(2.0*lsb->alpha - 1.0);
    815:       c *= lsb->alpha - 1.0;
    816:       /* use quadratic formula to find roots */
    817:       sig1 = (-b + PetscSqrtReal(b*b - 4.0*a*c))/(2.0*a);
    818:       sig2 = (-b - PetscSqrtReal(b*b - 4.0*a*c))/(2.0*a);
    819:       /* accept the positive root as the scalar */
    820:       if (sig1 > 0.0) {
    821:         signew = sig1;
    822:       } else if (sig2 > 0.0) {
    823:         signew = sig2;
    824:       } else {
    825:         SETERRQ(PetscObjectComm((PetscObject)B), PETSC_ERR_CONV_FAILED, "Cannot find positive scalar");
    826:       }
    827:     }
    828:   }
    829:   lsb->sigma = lsb->rho*signew + (1.0 - lsb->rho)*lsb->sigma;
    830:   return 0;
    831: }