Date: 2016-07-24T17:16:12+00:00

Actual source code: lmvmmat.c
petsc-3.7.3 2016-07-24
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      1: #include <../src/tao/matrix/lmvmmat.h>   /*I "lmvmmat.h" */
      2: #include <petsctao.h>  /*I "petsctao.h" */
      3: #include <petscksp.h>

      5: /* This is a vile hack */
      6: #if defined(PETSC_USE_COMPLEX)
      7: #define VecDot VecDotRealPart
      8: #endif

     10: #define TaoMid(a,b,c)    (((a) < (b)) ?                    \
     11:                            (((b) < (c)) ? (b) :            \
     12:                              (((a) < (c)) ? (c) : (a))) :  \
     13:                            (((a) < (c)) ? (a) :            \
     14:                              (((b) < (c)) ? (c) : (b))))

     16: /* These lists are used for setting options */
     17: static const char *Scale_Table[64] = {"none","scalar","broyden"};

     19: static const char *Rescale_Table[64] = {"none","scalar","gl"};

     21: static const char *Limit_Table[64] = {"none","average","relative","absolute"};

     25: /*@C
     26:   MatCreateLMVM - Creates a limited memory matrix for lmvm algorithms.

     28:   Collective on A

     30:   Input Parameters:
     31: + comm - MPI Communicator
     32: . n - local size of vectors
     33: - N - global size of vectors

     35:   Output Parameters:
     36: . A - New LMVM matrix

     38:   Level: developer

     40: @*/
     41: extern PetscErrorCode MatCreateLMVM(MPI_Comm comm, PetscInt n, PetscInt N, Mat *A)
     42: {
     43:   MatLMVMCtx     *ctx;
     45:   PetscInt       nhistory;

     48:   /*  create data structure and populate with default values */
     49:   PetscNew(&ctx);
     50:   ctx->lm=5;
     51:   ctx->eps=0.0;
     52:   ctx->limitType=MatLMVM_Limit_None;
     53:   ctx->scaleType=MatLMVM_Scale_Broyden;
     54:   ctx->rScaleType = MatLMVM_Rescale_Scalar;
     55:   ctx->s_alpha = 1.0;
     56:   ctx->r_alpha = 1.0;
     57:   ctx->r_beta = 0.5;
     58:   ctx->mu = 1.0;
     59:   ctx->nu = 100.0;
     60:
     61:   ctx->phi = 0.125;
     62:
     63:   ctx->scalar_history = 1;
     64:   ctx->rescale_history = 1;
     65:
     66:   ctx->delta_min = 1e-7;
     67:   ctx->delta_max = 100.0;

     69:   /*  Begin configuration */
     70:   PetscOptionsBegin(comm,NULL,NULL,NULL);
     71:   PetscOptionsInt("-tao_lmm_vectors", "vectors to use for approximation", "", ctx->lm, &ctx->lm,NULL);
     72:   PetscOptionsReal("-tao_lmm_limit_mu", "mu limiting factor", "", ctx->mu, &ctx->mu,NULL);
     73:   PetscOptionsReal("-tao_lmm_limit_nu", "nu limiting factor", "", ctx->nu, &ctx->nu,NULL);
     74:   PetscOptionsReal("-tao_lmm_broyden_phi", "phi factor for Broyden scaling", "", ctx->phi, &ctx->phi,NULL);
     75:   PetscOptionsReal("-tao_lmm_scalar_alpha", "alpha factor for scalar scaling", "",ctx->s_alpha, &ctx->s_alpha,NULL);
     76:   PetscOptionsReal("-tao_lmm_rescale_alpha", "alpha factor for rescaling diagonal", "", ctx->r_alpha, &ctx->r_alpha,NULL);
     77:   PetscOptionsReal("-tao_lmm_rescale_beta", "beta factor for rescaling diagonal", "", ctx->r_beta, &ctx->r_beta,NULL);
     78:   PetscOptionsInt("-tao_lmm_scalar_history", "amount of history for scalar scaling", "", ctx->scalar_history, &ctx->scalar_history,NULL);
     79:   PetscOptionsInt("-tao_lmm_rescale_history", "amount of history for rescaling diagonal", "", ctx->rescale_history, &ctx->rescale_history,NULL);
     80:   PetscOptionsReal("-tao_lmm_eps", "rejection tolerance", "", ctx->eps, &ctx->eps,NULL);
     81:   PetscOptionsEList("-tao_lmm_scale_type", "scale type", "", Scale_Table, MatLMVM_Scale_Types, Scale_Table[ctx->scaleType], &ctx->scaleType,NULL);
     82:   PetscOptionsEList("-tao_lmm_rescale_type", "rescale type", "", Rescale_Table, MatLMVM_Rescale_Types, Rescale_Table[ctx->rScaleType], &ctx->rScaleType,NULL);
     83:   PetscOptionsEList("-tao_lmm_limit_type", "limit type", "", Limit_Table, MatLMVM_Limit_Types, Limit_Table[ctx->limitType], &ctx->limitType,NULL);
     84:   PetscOptionsReal("-tao_lmm_delta_min", "minimum delta value", "", ctx->delta_min, &ctx->delta_min,NULL);
     85:   PetscOptionsReal("-tao_lmm_delta_max", "maximum delta value", "", ctx->delta_max, &ctx->delta_max,NULL);
     86:   PetscOptionsEnd();

     88:   /*  Complete configuration */
     89:   ctx->rescale_history = PetscMin(ctx->rescale_history, ctx->lm);
     90:   PetscMalloc1(ctx->lm+1,&ctx->rho);
     91:   PetscMalloc1(ctx->lm+1,&ctx->beta);

     93:   nhistory = PetscMax(ctx->scalar_history,1);
     94:   PetscMalloc1(nhistory,&ctx->yy_history);
     95:   PetscMalloc1(nhistory,&ctx->ys_history);
     96:   PetscMalloc1(nhistory,&ctx->ss_history);

     98:   nhistory = PetscMax(ctx->rescale_history,1);
     99:   PetscMalloc1(nhistory,&ctx->yy_rhistory);
    100:   PetscMalloc1(nhistory,&ctx->ys_rhistory);
    101:   PetscMalloc1(nhistory,&ctx->ss_rhistory);

    103:   /*  Finish initializations */
    104:   ctx->lmnow = 0;
    105:   ctx->iter = 0;
    106:   ctx->nupdates = 0;
    107:   ctx->nrejects = 0;
    108:   ctx->delta = 1.0;

    110:   ctx->Gprev = 0;
    111:   ctx->Xprev = 0;

    113:   ctx->scale = 0;
    114:   ctx->useScale = PETSC_FALSE;

    116:   ctx->H0_mat = 0;
    117:   ctx->H0_ksp = 0;
    118:   ctx->H0_norm = 0;
    119:   ctx->useDefaultH0 = PETSC_TRUE;

    121:   MatCreateShell(comm, n, n, N, N, ctx, A);
    122:   MatShellSetOperation(*A,MATOP_DESTROY,(void(*)(void))MatDestroy_LMVM);
    123:   MatShellSetOperation(*A,MATOP_VIEW,(void(*)(void))MatView_LMVM);
    124:   return(0);
    125: }

    129: extern PetscErrorCode MatLMVMSolve(Mat A, Vec b, Vec x)
    130: {
    131:   PetscReal      sq, yq, dd;
    132:   PetscInt       ll;
    133:   PetscBool      scaled;
    134:   MatLMVMCtx     *shell;

    141:   MatShellGetContext(A,(void**)&shell);
    142:   if (shell->lmnow < 1) {
    143:     shell->rho[0] = 1.0;
    144:     shell->theta = 1.0;
    145:   }

    147:   VecCopy(b,x);
    148:   for (ll = 0; ll < shell->lmnow; ++ll) {
    149:     VecDot(x,shell->S[ll],&sq);
    150:     shell->beta[ll] = sq * shell->rho[ll];
    151:     VecAXPY(x,-shell->beta[ll],shell->Y[ll]);
    152:   }

    154:   scaled = PETSC_FALSE;
    155:   if (!scaled && !shell->useDefaultH0 && shell->H0_mat) {
    156:     KSPSolve(shell->H0_ksp,x,shell->U);
    157:     VecScale(shell->U, shell->theta);
    158:     VecDot(x,shell->U,&dd);
    159:     if ((dd > 0.0) && !PetscIsInfOrNanReal(dd)) {
    160:       /*  Accept Hessian solve */
    161:       VecCopy(shell->U,x);
    162:       scaled = PETSC_TRUE;
    163:     }
    164:   }

    166:   if (!scaled && shell->useScale) {
    167:     VecPointwiseMult(shell->U,x,shell->scale);
    168:     VecDot(x,shell->U,&dd);
    169:     if ((dd > 0.0) && !PetscIsInfOrNanReal(dd)) {
    170:       /*  Accept scaling */
    171:       VecCopy(shell->U,x);
    172:       scaled = PETSC_TRUE;
    173:     }
    174:   }

    176:   if (!scaled) {
    177:     switch(shell->scaleType) {
    178:     case MatLMVM_Scale_None:
    179:       break;

    181:     case MatLMVM_Scale_Scalar:
    182:       VecScale(x,shell->sigma);
    183:       break;

    185:     case MatLMVM_Scale_Broyden:
    186:       VecPointwiseMult(x,x,shell->D);
    187:       break;
    188:     }
    189:   }
    190:   for (ll = shell->lmnow-1; ll >= 0; --ll) {
    191:     VecDot(x,shell->Y[ll],&yq);
    192:     VecAXPY(x,shell->beta[ll]-yq*shell->rho[ll],shell->S[ll]);
    193:   }
    194:   return(0);
    195: }

    199: extern PetscErrorCode MatView_LMVM(Mat A, PetscViewer pv)
    200: {
    201:   PetscBool      isascii;
    203:   MatLMVMCtx     *lmP;

    206:   MatShellGetContext(A,(void**)&lmP);
    207:   PetscObjectTypeCompare((PetscObject)pv,PETSCVIEWERASCII,&isascii);
    208:   if (isascii) {
    209:     PetscViewerASCIIPrintf(pv,"LMVM Matrix\n");
    210:     PetscViewerASCIIPrintf(pv," Number of vectors: %D\n",lmP->lm);
    211:     PetscViewerASCIIPrintf(pv," scale type: %s\n",Scale_Table[lmP->scaleType]);
    212:     PetscViewerASCIIPrintf(pv," rescale type: %s\n",Rescale_Table[lmP->rScaleType]);
    213:     PetscViewerASCIIPrintf(pv," limit type: %s\n",Limit_Table[lmP->limitType]);
    214:     PetscViewerASCIIPrintf(pv," updates: %D\n",lmP->nupdates);
    215:     PetscViewerASCIIPrintf(pv," rejects: %D\n",lmP->nrejects);
    216:   }
    217:   return(0);
    218: }

    222: extern PetscErrorCode MatDestroy_LMVM(Mat M)
    223: {
    224:   MatLMVMCtx     *ctx;

    228:   MatShellGetContext(M,(void**)&ctx);
    229:   if (ctx->allocated) {
    230:     if (ctx->Xprev) {
    231:       PetscObjectDereference((PetscObject)ctx->Xprev);
    232:     }
    233:     if (ctx->Gprev) {
    234:       PetscObjectDereference((PetscObject)ctx->Gprev);
    235:     }

    237:     VecDestroyVecs(ctx->lm+1,&ctx->S);
    238:     VecDestroyVecs(ctx->lm+1,&ctx->Y);
    239:     VecDestroy(&ctx->D);
    240:     VecDestroy(&ctx->U);
    241:     VecDestroy(&ctx->V);
    242:     VecDestroy(&ctx->W);
    243:     VecDestroy(&ctx->P);
    244:     VecDestroy(&ctx->Q);
    245:     VecDestroy(&ctx->H0_norm);
    246:     if (ctx->scale) {
    247:       VecDestroy(&ctx->scale);
    248:     }
    249:   }
    250:   if (ctx->H0_mat) {
    251:     PetscObjectDereference((PetscObject)ctx->H0_mat);
    252:     KSPDestroy(&ctx->H0_ksp);
    253:   }
    254:   PetscFree(ctx->rho);
    255:   PetscFree(ctx->beta);
    256:   PetscFree(ctx->yy_history);
    257:   PetscFree(ctx->ys_history);
    258:   PetscFree(ctx->ss_history);
    259:   PetscFree(ctx->yy_rhistory);
    260:   PetscFree(ctx->ys_rhistory);
    261:   PetscFree(ctx->ss_rhistory);
    262:   PetscFree(ctx);
    263:   return(0);
    264: }

    268: extern PetscErrorCode MatLMVMReset(Mat M)
    269: {
    271:   MatLMVMCtx     *ctx;
    272:   PetscInt       i;

    275:   MatShellGetContext(M,(void**)&ctx);
    276:   if (ctx->Gprev) {
    277:     PetscObjectDereference((PetscObject)ctx->Gprev);
    278:   }
    279:   if (ctx->Xprev) {
    280:     PetscObjectDereference((PetscObject)ctx->Xprev);
    281:   }
    282:   ctx->Gprev = ctx->Y[ctx->lm];
    283:   ctx->Xprev = ctx->S[ctx->lm];
    284:   PetscObjectReference((PetscObject)ctx->Gprev);
    285:   PetscObjectReference((PetscObject)ctx->Xprev);
    286:   for (i=0; i<ctx->lm; ++i) {
    287:     ctx->rho[i] = 0.0;
    288:   }
    289:   ctx->rho[0] = 1.0;

    291:   /*  Set the scaling and diagonal scaling matrix */
    292:   switch(ctx->scaleType) {
    293:   case MatLMVM_Scale_None:
    294:     ctx->sigma = 1.0;
    295:     break;
    296:   case MatLMVM_Scale_Scalar:
    297:     ctx->sigma = ctx->delta;
    298:     break;
    299:   case MatLMVM_Scale_Broyden:
    300:     VecSet(ctx->D,ctx->delta);
    301:     break;
    302:   }

    304:   ctx->iter=0;
    305:   ctx->nupdates=0;
    306:   ctx->lmnow=0;
    307:   return(0);
    308: }

    312: extern PetscErrorCode MatLMVMUpdate(Mat M, Vec x, Vec g)
    313: {
    314:   MatLMVMCtx     *ctx;
    315:   PetscReal      rhotemp, rhotol;
    316:   PetscReal      y0temp, s0temp;
    317:   PetscReal      yDy, yDs, sDs;
    318:   PetscReal      sigmanew, denom;
    320:   PetscInt       i;
    321:   PetscBool      same;
    322:   PetscReal      yy_sum=0.0, ys_sum=0.0, ss_sum=0.0;

    327:   PetscObjectTypeCompare((PetscObject)M,MATSHELL,&same);
    328:   if (!same) SETERRQ(PETSC_COMM_SELF,1,"Matrix M is not type MatLMVM");
    329:   MatShellGetContext(M,(void**)&ctx);
    330:   if (!ctx->allocated) {
    331:     MatLMVMAllocateVectors(M, x);
    332:   }

    334:   if (0 == ctx->iter) {
    335:     MatLMVMReset(M);
    336:   }  else {
    337:     VecAYPX(ctx->Gprev,-1.0,g);
    338:     VecAYPX(ctx->Xprev,-1.0,x);

    340:     VecDot(ctx->Gprev,ctx->Xprev,&rhotemp);
    341:     VecDot(ctx->Gprev,ctx->Gprev,&y0temp);

    343:     rhotol = ctx->eps * y0temp;
    344:     if (rhotemp > rhotol) {
    345:       ++ctx->nupdates;

    347:       ctx->lmnow = PetscMin(ctx->lmnow+1, ctx->lm);
    348:       ierr=PetscObjectDereference((PetscObject)ctx->S[ctx->lm]);
    349:       ierr=PetscObjectDereference((PetscObject)ctx->Y[ctx->lm]);
    350:       for (i = ctx->lm-1; i >= 0; --i) {
    351:         ctx->S[i+1] = ctx->S[i];
    352:         ctx->Y[i+1] = ctx->Y[i];
    353:         ctx->rho[i+1] = ctx->rho[i];
    354:       }
    355:       ctx->S[0] = ctx->Xprev;
    356:       ctx->Y[0] = ctx->Gprev;
    357:       PetscObjectReference((PetscObject)ctx->S[0]);
    358:       PetscObjectReference((PetscObject)ctx->Y[0]);
    359:       ctx->rho[0] = 1.0 / rhotemp;

    361:       /*  Compute the scaling */
    362:       switch(ctx->scaleType) {
    363:       case MatLMVM_Scale_None:
    364:         break;

    366:       case MatLMVM_Scale_Scalar:
    367:         /*  Compute s^T s  */
    368:           VecDot(ctx->Xprev,ctx->Xprev,&s0temp);

    370:         /*  Scalar is positive; safeguards are not required. */

    372:         /*  Save information for scalar scaling */
    373:         ctx->yy_history[(ctx->nupdates - 1) % ctx->scalar_history] = y0temp;
    374:         ctx->ys_history[(ctx->nupdates - 1) % ctx->scalar_history] = rhotemp;
    375:         ctx->ss_history[(ctx->nupdates - 1) % ctx->scalar_history] = s0temp;

    377:         /*  Compute summations for scalar scaling */
    378:         yy_sum = 0;     /*  No safeguard required; y^T y > 0 */
    379:         ys_sum = 0;     /*  No safeguard required; y^T s > 0 */
    380:         ss_sum = 0;     /*  No safeguard required; s^T s > 0 */
    381:         for (i = 0; i < PetscMin(ctx->nupdates, ctx->scalar_history); ++i) {
    382:           yy_sum += ctx->yy_history[i];
    383:           ys_sum += ctx->ys_history[i];
    384:           ss_sum += ctx->ss_history[i];
    385:         }

    387:         if (0.0 == ctx->s_alpha) {
    388:           /*  Safeguard ys_sum  */
    389:           if (0.0 == ys_sum) {
    390:             ys_sum = TAO_ZERO_SAFEGUARD;
    391:           }

    393:           sigmanew = ss_sum / ys_sum;
    394:         } else if (1.0 == ctx->s_alpha) {
    395:           /*  Safeguard yy_sum  */
    396:           if (0.0 == yy_sum) {
    397:             yy_sum = TAO_ZERO_SAFEGUARD;
    398:           }

    400:           sigmanew = ys_sum / yy_sum;
    401:         } else {
    402:           denom = 2*ctx->s_alpha*yy_sum;

    404:           /*  Safeguard denom */
    405:           if (0.0 == denom) {
    406:             denom = TAO_ZERO_SAFEGUARD;
    407:           }

    409:           sigmanew = ((2*ctx->s_alpha-1)*ys_sum +  PetscSqrtReal((2*ctx->s_alpha-1)*(2*ctx->s_alpha-1)*ys_sum*ys_sum - 4*(ctx->s_alpha)*(ctx->s_alpha-1)*yy_sum*ss_sum)) / denom;
    410:         }

    412:         switch(ctx->limitType) {
    413:         case MatLMVM_Limit_Average:
    414:           if (1.0 == ctx->mu) {
    415:             ctx->sigma = sigmanew;
    416:           } else if (ctx->mu) {
    417:             ctx->sigma = ctx->mu * sigmanew + (1.0 - ctx->mu) * ctx->sigma;
    418:           }
    419:           break;

    421:         case MatLMVM_Limit_Relative:
    422:           if (ctx->mu) {
    423:             ctx->sigma = TaoMid((1.0 - ctx->mu) * ctx->sigma, sigmanew, (1.0 + ctx->mu) * ctx->sigma);
    424:           }
    425:           break;

    427:         case MatLMVM_Limit_Absolute:
    428:           if (ctx->nu) {
    429:             ctx->sigma = TaoMid(ctx->sigma - ctx->nu, sigmanew, ctx->sigma + ctx->nu);
    430:           }
    431:           break;

    433:         default:
    434:           ctx->sigma = sigmanew;
    435:           break;
    436:         }
    437:         break;

    439:       case MatLMVM_Scale_Broyden:
    440:         /*  Original version */
    441:         /*  Combine DFP and BFGS */

    443:         /*  This code appears to be numerically unstable.  We use the */
    444:         /*  original version because this was used to generate all of */
    445:         /*  the data and because it may be the least unstable of the */
    446:         /*  bunch. */

    448:         /*  P = Q = inv(D); */
    449:         VecCopy(ctx->D,ctx->P);
    450:         VecReciprocal(ctx->P);
    451:         VecCopy(ctx->P,ctx->Q);

    453:         /*  V = y*y */
    454:         VecPointwiseMult(ctx->V,ctx->Gprev,ctx->Gprev);

    456:         /*  W = inv(D)*s */
    457:         VecPointwiseMult(ctx->W,ctx->Xprev,ctx->P);
    458:         VecDot(ctx->W,ctx->Xprev,&sDs);

    460:         /*  Safeguard rhotemp and sDs */
    461:         if (0.0 == rhotemp) {
    462:           rhotemp = TAO_ZERO_SAFEGUARD;
    463:         }

    465:         if (0.0 == sDs) {
    466:           sDs = TAO_ZERO_SAFEGUARD;
    467:         }

    469:         if (1.0 != ctx->phi) {
    470:           /*  BFGS portion of the update */
    471:           /*  U = (inv(D)*s)*(inv(D)*s) */
    472:           VecPointwiseMult(ctx->U,ctx->W,ctx->W);

    474:           /*  Assemble */
    475:           VecAXPY(ctx->P,1.0/rhotemp,ctx->V);
    476:           VecAXPY(ctx->P,-1.0/sDs,ctx->U);
    477:         }

    479:         if (0.0 != ctx->phi) {
    480:           /*  DFP portion of the update */
    481:           /*  U = inv(D)*s*y */
    482:           VecPointwiseMult(ctx->U, ctx->W, ctx->Gprev);

    484:           /*  Assemble */
    485:           VecAXPY(ctx->Q,1.0/rhotemp + sDs/(rhotemp*rhotemp), ctx->V);
    486:           VecAXPY(ctx->Q,-2.0/rhotemp,ctx->U);
    487:         }

    489:         if (0.0 == ctx->phi) {
    490:             VecCopy(ctx->P,ctx->U);
    491:         } else if (1.0 == ctx->phi) {
    492:             VecCopy(ctx->Q,ctx->U);
    493:         } else {
    494:           /*  Broyden update U=(1-phi)*P + phi*Q */
    495:             VecCopy(ctx->Q,ctx->U);
    496:             VecAXPBY(ctx->U,1.0-ctx->phi, ctx->phi, ctx->P);
    497:         }

    499:         /*  Obtain inverse and ensure positive definite */
    500:         VecReciprocal(ctx->U);
    501:         VecAbs(ctx->U);

    503:         switch(ctx->rScaleType) {
    504:         case MatLMVM_Rescale_None:
    505:             break;

    507:         case MatLMVM_Rescale_Scalar:
    508:         case MatLMVM_Rescale_GL:
    509:           if (ctx->rScaleType == MatLMVM_Rescale_GL) {
    510:             /*  Gilbert and Lemarachal use the old diagonal */
    511:             VecCopy(ctx->D,ctx->P);
    512:           } else {
    513:             /*  The default version uses the current diagonal */
    514:               VecCopy(ctx->U,ctx->P);
    515:           }

    517:           /*  Compute s^T s  */
    518:           VecDot(ctx->Xprev,ctx->Xprev,&s0temp);

    520:           /*  Save information for special cases of scalar rescaling */
    521:           ctx->yy_rhistory[(ctx->nupdates - 1) % ctx->rescale_history] = y0temp;
    522:           ctx->ys_rhistory[(ctx->nupdates - 1) % ctx->rescale_history] = rhotemp;
    523:           ctx->ss_rhistory[(ctx->nupdates - 1) % ctx->rescale_history] = s0temp;

    525:           if (0.5 == ctx->r_beta) {
    526:             if (1 == PetscMin(ctx->nupdates, ctx->rescale_history)) {
    527:               VecPointwiseMult(ctx->V,ctx->Y[0],ctx->P);
    528:               VecDot(ctx->V,ctx->Y[0],&yy_sum);

    530:               VecPointwiseDivide(ctx->W,ctx->S[0],ctx->P);
    531:               VecDot(ctx->W,ctx->S[0],&ss_sum);

    533:               ys_sum = ctx->ys_rhistory[0];
    534:             } else {
    535:               VecCopy(ctx->P,ctx->Q);
    536:               VecReciprocal(ctx->Q);

    538:               /*  Compute summations for scalar scaling */
    539:               yy_sum = 0;       /*  No safeguard required */
    540:               ys_sum = 0;       /*  No safeguard required */
    541:               ss_sum = 0;       /*  No safeguard required */
    542:               for (i = 0; i < PetscMin(ctx->nupdates, ctx->rescale_history); ++i) {
    543:                 VecPointwiseMult(ctx->V,ctx->Y[i],ctx->P);
    544:                 VecDot(ctx->V,ctx->Y[i],&yDy);
    545:                 yy_sum += yDy;

    547:                 VecPointwiseMult(ctx->W,ctx->S[i],ctx->Q);
    548:                 VecDot(ctx->W,ctx->S[i],&sDs);
    549:                 ss_sum += sDs;
    550:                 ys_sum += ctx->ys_rhistory[i];
    551:               }
    552:             }
    553:           } else if (0.0 == ctx->r_beta) {
    554:             if (1 == PetscMin(ctx->nupdates, ctx->rescale_history)) {
    555:               /*  Compute summations for scalar scaling */
    556:               VecPointwiseDivide(ctx->W,ctx->S[0],ctx->P);

    558:               VecDot(ctx->W, ctx->Y[0], &ys_sum);
    559:               VecDot(ctx->W, ctx->W, &ss_sum);
    560:               yy_sum += ctx->yy_rhistory[0];
    561:             } else {
    562:               VecCopy(ctx->Q, ctx->P);
    563:               VecReciprocal(ctx->Q);

    565:               /*  Compute summations for scalar scaling */
    566:               yy_sum = 0;       /*  No safeguard required */
    567:               ys_sum = 0;       /*  No safeguard required */
    568:               ss_sum = 0;       /*  No safeguard required */
    569:               for (i = 0; i < PetscMin(ctx->nupdates, ctx->rescale_history); ++i) {
    570:                 VecPointwiseMult(ctx->W, ctx->S[i], ctx->Q);
    571:                 VecDot(ctx->W, ctx->Y[i], &yDs);
    572:                 ys_sum += yDs;

    574:                 VecDot(ctx->W, ctx->W, &sDs);
    575:                 ss_sum += sDs;

    577:                 yy_sum += ctx->yy_rhistory[i];
    578:               }
    579:             }
    580:           } else if (1.0 == ctx->r_beta) {
    581:             /*  Compute summations for scalar scaling */
    582:             yy_sum = 0; /*  No safeguard required */
    583:             ys_sum = 0; /*  No safeguard required */
    584:             ss_sum = 0; /*  No safeguard required */
    585:             for (i = 0; i < PetscMin(ctx->nupdates, ctx->rescale_history); ++i) {
    586:               VecPointwiseMult(ctx->V, ctx->Y[i], ctx->P);
    587:               VecDot(ctx->V, ctx->S[i], &yDs);
    588:               ys_sum += yDs;

    590:               VecDot(ctx->V, ctx->V, &yDy);
    591:               yy_sum += yDy;

    593:               ss_sum += ctx->ss_rhistory[i];
    594:             }
    595:           } else {
    596:             VecCopy(ctx->Q, ctx->P);

    598:             VecPow(ctx->P, ctx->r_beta);
    599:             VecPointwiseDivide(ctx->Q, ctx->P, ctx->Q);

    601:             /*  Compute summations for scalar scaling */
    602:             yy_sum = 0; /*  No safeguard required */
    603:             ys_sum = 0; /*  No safeguard required */
    604:             ss_sum = 0; /*  No safeguard required */
    605:             for (i = 0; i < PetscMin(ctx->nupdates, ctx->rescale_history); ++i) {
    606:               VecPointwiseMult(ctx->V, ctx->P, ctx->Y[i]);
    607:               VecPointwiseMult(ctx->W, ctx->Q, ctx->S[i]);

    609:               VecDot(ctx->V, ctx->V, &yDy);
    610:               VecDot(ctx->V, ctx->W, &yDs);
    611:               VecDot(ctx->W, ctx->W, &sDs);

    613:               yy_sum += yDy;
    614:               ys_sum += yDs;
    615:               ss_sum += sDs;
    616:             }
    617:           }

    619:           if (0.0 == ctx->r_alpha) {
    620:             /*  Safeguard ys_sum  */
    621:             if (0.0 == ys_sum) {
    622:               ys_sum = TAO_ZERO_SAFEGUARD;
    623:             }

    625:             sigmanew = ss_sum / ys_sum;
    626:           } else if (1.0 == ctx->r_alpha) {
    627:             /*  Safeguard yy_sum  */
    628:             if (0.0 == yy_sum) {
    629:               ys_sum = TAO_ZERO_SAFEGUARD;
    630:             }

    632:             sigmanew = ys_sum / yy_sum;
    633:           } else {
    634:             denom = 2*ctx->r_alpha*yy_sum;

    636:             /*  Safeguard denom */
    637:             if (0.0 == denom) {
    638:               denom = TAO_ZERO_SAFEGUARD;
    639:             }

    641:             sigmanew = ((2*ctx->r_alpha-1)*ys_sum + PetscSqrtReal((2*ctx->r_alpha-1)*(2*ctx->r_alpha-1)*ys_sum*ys_sum - 4*ctx->r_alpha*(ctx->r_alpha-1)*yy_sum*ss_sum)) / denom;
    642:           }

    644:           /*  If Q has small values, then Q^(r_beta - 1) */
    645:           /*  can have very large values.  Hence, ys_sum */
    646:           /*  and ss_sum can be infinity.  In this case, */
    647:           /*  sigmanew can either be not-a-number or infinity. */

    649:           if (PetscIsInfOrNanReal(sigmanew)) {
    650:             /*  sigmanew is not-a-number; skip rescaling */
    651:           } else if (!sigmanew) {
    652:             /*  sigmanew is zero; this is a bad case; skip rescaling */
    653:           } else {
    654:             /*  sigmanew is positive */
    655:             VecScale(ctx->U, sigmanew);
    656:           }
    657:           break;
    658:         }

    660:         /*  Modify for previous information */
    661:         switch(ctx->limitType) {
    662:         case MatLMVM_Limit_Average:
    663:           if (1.0 == ctx->mu) {
    664:             VecCopy(ctx->D, ctx->U);
    665:           } else if (ctx->mu) {
    666:             VecAXPBY(ctx->D,ctx->mu, 1.0-ctx->mu,ctx->U);
    667:           }
    668:           break;

    670:         case MatLMVM_Limit_Relative:
    671:           if (ctx->mu) {
    672:             /*  P = (1-mu) * D */
    673:             VecAXPBY(ctx->P, 1.0-ctx->mu, 0.0, ctx->D);
    674:             /*  Q = (1+mu) * D */
    675:             VecAXPBY(ctx->Q, 1.0+ctx->mu, 0.0, ctx->D);
    676:             VecMedian(ctx->P, ctx->U, ctx->Q, ctx->D);
    677:           }
    678:           break;

    680:         case MatLMVM_Limit_Absolute:
    681:           if (ctx->nu) {
    682:             VecCopy(ctx->P, ctx->D);
    683:             VecShift(ctx->P, -ctx->nu);
    684:             VecCopy(ctx->D, ctx->Q);
    685:             VecShift(ctx->Q, ctx->nu);
    686:             VecMedian(ctx->P, ctx->U, ctx->Q, ctx->P);
    687:           }
    688:           break;

    690:         default:
    691:             VecCopy(ctx->U, ctx->D);
    692:           break;
    693:         }
    694:         break;
    695:       }
    696:       PetscObjectDereference((PetscObject)ctx->Xprev);
    697:       PetscObjectDereference((PetscObject)ctx->Gprev);
    698:       ctx->Xprev = ctx->S[ctx->lm];
    699:       ctx->Gprev = ctx->Y[ctx->lm];
    700:       PetscObjectReference((PetscObject)ctx->S[ctx->lm]);
    701:       PetscObjectReference((PetscObject)ctx->Y[ctx->lm]);

    703:     } else {
    704:       ++ctx->nrejects;
    705:     }
    706:   }

    708:   ++ctx->iter;
    709:   VecCopy(x, ctx->Xprev);
    710:   VecCopy(g, ctx->Gprev);
    711:   return(0);
    712: }

    716: extern PetscErrorCode MatLMVMSetDelta(Mat m, PetscReal d)
    717: {
    718:   MatLMVMCtx     *ctx;
    720:   PetscBool      same;

    724:   PetscObjectTypeCompare((PetscObject)m,MATSHELL,&same);
    725:   if (!same) SETERRQ(PETSC_COMM_SELF,1,"Matrix m is not type MatLMVM");
    726:   MatShellGetContext(m,(void**)&ctx);
    727:   ctx->delta = PetscAbsReal(d);
    728:   ctx->delta = PetscMax(ctx->delta_min, ctx->delta);
    729:   ctx->delta = PetscMin(ctx->delta_max, ctx->delta);
    730:   return(0);
    731: }

    735: extern PetscErrorCode MatLMVMSetScale(Mat m, Vec s)
    736: {
    737:   MatLMVMCtx     *ctx;
    739:   PetscBool      same;

    743:   PetscObjectTypeCompare((PetscObject)m,MATSHELL,&same);
    744:   if (!same) SETERRQ(PETSC_COMM_SELF,1,"Matrix m is not type MatLMVM");
    745:   MatShellGetContext(m,(void**)&ctx);

    747:   VecDestroy(&ctx->scale);
    748:   if (s) {
    749:     VecDuplicate(s,&ctx->scale);
    750:   }
    751:   return(0);
    752: }

    756: extern PetscErrorCode MatLMVMGetRejects(Mat m, PetscInt *nrejects)
    757: {
    758:   MatLMVMCtx     *ctx;
    760:   PetscBool      same;

    764:   PetscObjectTypeCompare((PetscObject)m,MATSHELL,&same);
    765:   if (!same) SETERRQ(PETSC_COMM_SELF,1,"Matrix m is not type MatLMVM");
    766:   MatShellGetContext(m,(void**)&ctx);
    767:   *nrejects = ctx->nrejects;
    768:   return(0);
    769: }

    773: extern PetscErrorCode MatLMVMSetH0(Mat m, Mat H0)
    774: {
    775:   MatLMVMCtx     *ctx;
    777:   PetscBool      same;

    781:   PetscObjectTypeCompare((PetscObject)m,MATSHELL,&same);
    782:   if (!same) SETERRQ(PETSC_COMM_SELF,1,"Matrix m is not type MatLMVM");
    783:   MatShellGetContext(m,(void**)&ctx);

    785:   ctx->H0_mat = H0;
    786:   PetscObjectReference((PetscObject)ctx->H0_mat);

    788:   ctx->useDefaultH0 = PETSC_FALSE;

    790:   KSPCreate(PetscObjectComm((PetscObject)H0), &ctx->H0_ksp);
    791:   KSPSetOperators(ctx->H0_ksp, H0, H0);
    792:   /* its options prefix and setup is handled in TaoSolve_LMVM/TaoSolve_BLMVM */
    793:   return(0);
    794: }

    798: extern PetscErrorCode MatLMVMGetH0(Mat m, Mat *H0)
    799: {
    800:   MatLMVMCtx     *ctx;
    802:   PetscBool      same;

    806:   PetscObjectTypeCompare((PetscObject)m,MATSHELL,&same);
    807:   if (!same) SETERRQ(PETSC_COMM_SELF,1,"Matrix m is not type MatLMVM");

    809:   MatShellGetContext(m,(void**)&ctx);
    810:   *H0  = ctx->H0_mat;
    811:   return(0);
    812: }

    816: extern PetscErrorCode MatLMVMGetH0KSP(Mat m, KSP *H0ksp)
    817: {
    818:   MatLMVMCtx     *ctx;
    820:   PetscBool      same;

    824:   PetscObjectTypeCompare((PetscObject)m,MATSHELL,&same);
    825:   if (!same) SETERRQ(PETSC_COMM_SELF,1,"Matrix m is not type MatLMVM");

    827:   MatShellGetContext(m,(void**)&ctx);
    828:   *H0ksp  = ctx->H0_ksp;
    829:   return(0);
    830: }

    834: extern PetscErrorCode MatLMVMGetX0(Mat m, Vec x)
    835: {
    837:     return(0);
    838: }

    842: extern PetscErrorCode MatLMVMSetPrev(Mat M, Vec x, Vec g)
    843: {
    844:   MatLMVMCtx     *ctx;
    846:   PetscBool      same;

    851:   PetscObjectTypeCompare((PetscObject)M,MATSHELL,&same);
    852:   if (!same) SETERRQ(PETSC_COMM_SELF,1,"Matrix M is not type MatLMVM");
    853:   MatShellGetContext(M,(void**)&ctx);
    854:   if (ctx->nupdates == 0) {
    855:     MatLMVMUpdate(M,x,g);
    856:   } else {
    857:     VecCopy(x,ctx->Xprev);
    858:     VecCopy(g,ctx->Gprev);
    859:     /*  TODO scaling specific terms */
    860:   }
    861:   return(0);
    862: }

    866: extern PetscErrorCode MatLMVMRefine(Mat coarse, Mat op, Vec fineX, Vec fineG)
    867: {
    869:   PetscBool      same;

    876:   PetscObjectTypeCompare((PetscObject)coarse,MATSHELL,&same);
    877:   if (!same) SETERRQ(PETSC_COMM_SELF,1,"Matrix m is not type MatLMVM");
    878:   PetscObjectTypeCompare((PetscObject)op,MATSHELL,&same);
    879:   if (!same) SETERRQ(PETSC_COMM_SELF,1,"Matrix m is not type MatLMVM");
    880:   return(0);
    881: }

    885: extern PetscErrorCode MatLMVMAllocateVectors(Mat m, Vec v)
    886: {
    888:   MatLMVMCtx     *ctx;
    889:   PetscBool      same;

    894:   PetscObjectTypeCompare((PetscObject)m,MATSHELL,&same);
    895:   if (!same) SETERRQ(PETSC_COMM_SELF,1,"Matrix m is not type MatLMVM");
    896:   MatShellGetContext(m,(void**)&ctx);

    898:   /*  Perform allocations */
    899:   VecDuplicateVecs(v,ctx->lm+1,&ctx->S);
    900:   VecDuplicateVecs(v,ctx->lm+1,&ctx->Y);
    901:   VecDuplicate(v,&ctx->D);
    902:   VecDuplicate(v,&ctx->U);
    903:   VecDuplicate(v,&ctx->V);
    904:   VecDuplicate(v,&ctx->W);
    905:   VecDuplicate(v,&ctx->P);
    906:   VecDuplicate(v,&ctx->Q);
    907:   VecDuplicate(v,&ctx->H0_norm);
    908:   ctx->allocated = PETSC_TRUE;
    909:   return(0);
    910: }