Date: 2016-07-24T17:09:18+00:00

Actual source code: qn.c
petsc-3.7.3 2016-07-24
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      1: #include <petsc/private/snesimpl.h> /*I "petscsnes.h" I*/
      2: #include <petscdm.h>

      4: #define H(i,j)  qn->dXdFmat[i*qn->m + j]

      6: const char *const SNESQNScaleTypes[] =        {"DEFAULT","NONE","SHANNO","LINESEARCH","JACOBIAN","SNESQNScaleType","SNES_QN_SCALING_",0};
      7: const char *const SNESQNRestartTypes[] =      {"DEFAULT","NONE","POWELL","PERIODIC","SNESQNRestartType","SNES_QN_RESTART_",0};
      8: const char *const SNESQNTypes[] =             {"LBFGS","BROYDEN","BADBROYDEN","SNESQNType","SNES_QN_",0};

     10: typedef struct {
     11:   Vec               *U;                   /* Stored past states (vary from method to method) */
     12:   Vec               *V;                   /* Stored past states (vary from method to method) */
     13:   PetscInt          m;                    /* The number of kept previous steps */
     14:   PetscReal         *lambda;              /* The line search history of the method */
     15:   PetscReal         *norm;                /* norms of the steps */
     16:   PetscScalar       *alpha, *beta;
     17:   PetscScalar       *dXtdF, *dFtdX, *YtdX;
     18:   PetscBool         singlereduction;      /* Aggregated reduction implementation */
     19:   PetscScalar       *dXdFmat;             /* A matrix of values for dX_i dot dF_j */
     20:   PetscViewer       monitor;
     21:   PetscReal         powell_gamma;         /* Powell angle restart condition */
     22:   PetscReal         scaling;              /* scaling of H0 */
     23:   SNESQNType        type;                 /* the type of quasi-newton method used */
     24:   SNESQNScaleType   scale_type;           /* the type of scaling used */
     25:   SNESQNRestartType restart_type;         /* determine the frequency and type of restart conditions */
     26: } SNES_QN;

     30: PetscErrorCode SNESQNApply_Broyden(SNES snes,PetscInt it,Vec Y,Vec X,Vec Xold,Vec D)
     31: {
     32:   PetscErrorCode     ierr;
     33:   SNES_QN            *qn = (SNES_QN*)snes->data;
     34:   Vec                W   = snes->work[3];
     35:   Vec                *U  = qn->U;
     36:   PetscInt           m = qn->m;
     37:   PetscInt           k,i,j,lits,l = m;
     38:   PetscReal          unorm,a,b;
     39:   PetscReal          *lambda=qn->lambda;
     40:   PetscScalar        gdot;
     41:   PetscReal          udot;

     44:   if (it < m) l = it;
     45:   if (it > 0) {
     46:     k = (it-1)%l;
     47:     SNESLineSearchGetLambda(snes->linesearch,&lambda[k]);
     48:     VecCopy(Xold,U[k]);
     49:     VecAXPY(U[k],-1.0,X);
     50:     if (qn->monitor) {
     51:       PetscViewerASCIIAddTab(qn->monitor,((PetscObject)snes)->tablevel+2);
     52:       PetscViewerASCIIPrintf(qn->monitor, "scaling vector %D of %D by lambda: %14.12e \n",k,l,(double)lambda[k]);
     53:       PetscViewerASCIISubtractTab(qn->monitor,((PetscObject)snes)->tablevel+2);
     54:     }
     55:   }
     56:   if (qn->scale_type == SNES_QN_SCALE_JACOBIAN) {
     57:     KSPSolve(snes->ksp,D,W);
     58:     SNESCheckKSPSolve(snes);
     59:     KSPGetIterationNumber(snes->ksp,&lits);
     60:     snes->linear_its += lits;
     61:     VecCopy(W,Y);
     62:   } else {
     63:     VecCopy(D,Y);
     64:     VecScale(Y,qn->scaling);
     65:   }

     67:   /* inward recursion starting at the first update and working forward */
     68:   for (i = 0; i < l-1; i++) {
     69:     j = (it+i-l)%l;
     70:     k = (it+i-l+1)%l;
     71:     VecNorm(U[j],NORM_2,&unorm);
     72:     VecDot(U[j],Y,&gdot);
     73:     unorm *= unorm;
     74:     udot = PetscRealPart(gdot);
     75:     a = (lambda[j]/lambda[k]);
     76:     b = -(1.-lambda[j]);
     77:     a *= udot/unorm;
     78:     b *= udot/unorm;
     79:     VecAXPBYPCZ(Y,a,b,1.,U[k],U[j]);

     81:     if (qn->monitor) {
     82:       PetscViewerASCIIAddTab(qn->monitor,((PetscObject)snes)->tablevel+2);
     83:       PetscViewerASCIIPrintf(qn->monitor, "using vector %D and %D, gdot: %14.12e\n",k,j,(double)PetscRealPart(gdot));
     84:       PetscViewerASCIISubtractTab(qn->monitor,((PetscObject)snes)->tablevel+2);
     85:     }
     86:   }
     87:   if (l > 0) {
     88:     k = (it-1)%l;
     89:     VecDot(U[k],Y,&gdot);
     90:     VecNorm(U[k],NORM_2,&unorm);
     91:     unorm *= unorm;
     92:     udot = PetscRealPart(gdot);
     93:     a = unorm/(unorm-lambda[k]*udot);
     94:     b = -(1.-lambda[k])*udot/(unorm-lambda[k]*udot);
     95:     if (qn->monitor) {
     96:       PetscViewerASCIIAddTab(qn->monitor,((PetscObject)snes)->tablevel+2);
     97:       PetscViewerASCIIPrintf(qn->monitor, "using vector %D: a: %14.12e b: %14.12e \n",k,(double)a,(double)b);
     98:       PetscViewerASCIISubtractTab(qn->monitor,((PetscObject)snes)->tablevel+2);
     99:     }
    100:     VecAXPBY(Y,b,a,U[k]);
    101:   }
    102:   l = m;
    103:   if (it+1<m)l=it+1;
    104:   k = it%l;
    105:   if (qn->monitor) {
    106:     PetscViewerASCIIAddTab(qn->monitor,((PetscObject)snes)->tablevel+2);
    107:     PetscViewerASCIIPrintf(qn->monitor, "setting vector %D of %D\n",k,l);
    108:     PetscViewerASCIISubtractTab(qn->monitor,((PetscObject)snes)->tablevel+2);
    109:   }
    110:   return(0);
    111: }

    115: PetscErrorCode SNESQNApply_BadBroyden(SNES snes,PetscInt it,Vec Y,Vec X,Vec Xold,Vec D,Vec Dold)
    116: {
    118:   SNES_QN        *qn = (SNES_QN*)snes->data;
    119:   Vec            W   = snes->work[3];
    120:   Vec            *U  = qn->U;
    121:   Vec            *T  = qn->V;

    123:   /* ksp thing for Jacobian scaling */
    124:   PetscInt           h,k,j,i,lits;
    125:   PetscInt           m = qn->m;
    126:   PetscScalar        gdot,udot;
    127:   PetscInt           l = m;

    130:   if (it < m) l = it;
    131:   VecCopy(D,Y);
    132:   if (l > 0) {
    133:     k    = (it-1)%l;
    134:     SNESLineSearchGetLambda(snes->linesearch,&qn->lambda[k]);
    135:     VecCopy(Dold,U[k]);
    136:     VecAXPY(U[k],-1.0,D);
    137:     VecCopy(Xold,T[k]);
    138:     VecAXPY(T[k],-1.0,X);
    139:   }

    141:   if (qn->scale_type == SNES_QN_SCALE_JACOBIAN) {
    142:     KSPSolve(snes->ksp,Y,W);
    143:     SNESCheckKSPSolve(snes);
    144:     KSPGetIterationNumber(snes->ksp,&lits);
    145:     snes->linear_its += lits;
    146:     VecCopy(W,Y);
    147:   } else {
    148:     VecScale(Y,qn->scaling);
    149:   }

    151:   /* inward recursion starting at the first update and working forward */
    152:   if (l > 0) {
    153:     for (i = 0; i < l-1; i++) {
    154:       j    = (it+i-l)%l;
    155:       k    = (it+i-l+1)%l;
    156:       h    = (it-1)%l;
    157:       VecDotBegin(U[j],U[h],&gdot);
    158:       VecDotBegin(U[j],U[j],&udot);
    159:       VecDotEnd(U[j],U[h],&gdot);
    160:       VecDotEnd(U[j],U[j],&udot);
    161:       VecAXPY(Y,PetscRealPart(gdot)/PetscRealPart(udot),T[k]);
    162:       VecAXPY(Y,-(1.-qn->lambda[k])*PetscRealPart(gdot)/PetscRealPart(udot),T[j]);
    163:       if (qn->monitor) {
    164:         PetscViewerASCIIAddTab(qn->monitor,((PetscObject)snes)->tablevel+2);
    165:         PetscViewerASCIIPrintf(qn->monitor, "it: %D k: %D gdot: %14.12e\n", it, k, (double)PetscRealPart(gdot));
    166:         PetscViewerASCIISubtractTab(qn->monitor,((PetscObject)snes)->tablevel+2);
    167:       }
    168:     }
    169:   }
    170:   return(0);
    171: }

    175: PetscErrorCode SNESQNApply_LBFGS(SNES snes,PetscInt it,Vec Y,Vec X,Vec Xold,Vec D,Vec Dold)
    176: {
    178:   SNES_QN        *qn    = (SNES_QN*)snes->data;
    179:   Vec            W      = snes->work[3];
    180:   Vec            *dX    = qn->U;
    181:   Vec            *dF    = qn->V;
    182:   PetscScalar    *alpha = qn->alpha;
    183:   PetscScalar    *beta  = qn->beta;
    184:   PetscScalar    *dXtdF = qn->dXtdF;
    185:   PetscScalar    *dFtdX = qn->dFtdX;
    186:   PetscScalar    *YtdX  = qn->YtdX;

    188:   /* ksp thing for Jacobian scaling */
    189:   PetscInt           k,i,j,g,lits;
    190:   PetscInt           m = qn->m;
    191:   PetscScalar        t;
    192:   PetscInt           l = m;

    195:   if (it < m) l = it;
    196:   VecCopy(D,Y);
    197:   if (it > 0) {
    198:     k    = (it - 1) % l;
    199:     VecCopy(D,dF[k]);
    200:     VecAXPY(dF[k], -1.0, Dold);
    201:     VecCopy(X, dX[k]);
    202:     VecAXPY(dX[k], -1.0, Xold);
    203:     if (qn->singlereduction) {
    204:       VecMDotBegin(dF[k],l,dX,dXtdF);
    205:       VecMDotBegin(dX[k],l,dF,dFtdX);
    206:       VecMDotBegin(Y,l,dX,YtdX);
    207:       VecMDotEnd(dF[k],l,dX,dXtdF);
    208:       VecMDotEnd(dX[k],l,dF,dFtdX);
    209:       VecMDotEnd(Y,l,dX,YtdX);
    210:       for (j = 0; j < l; j++) {
    211:         H(k, j) = dFtdX[j];
    212:         H(j, k) = dXtdF[j];
    213:       }
    214:       /* copy back over to make the computation of alpha and beta easier */
    215:       for (j = 0; j < l; j++) dXtdF[j] = H(j, j);
    216:     } else {
    217:       VecDot(dX[k], dF[k], &dXtdF[k]);
    218:     }
    219:     if (qn->scale_type == SNES_QN_SCALE_LINESEARCH) {
    220:       SNESLineSearchGetLambda(snes->linesearch,&qn->scaling);
    221:     }
    222:   }

    224:   /* outward recursion starting at iteration k's update and working back */
    225:   for (i=0; i<l; i++) {
    226:     k = (it-i-1)%l;
    227:     if (qn->singlereduction) {
    228:       /* construct t = dX[k] dot Y as Y_0 dot dX[k] + sum(-alpha[j]dX[k]dF[j]) */
    229:       t = YtdX[k];
    230:       for (j=0; j<i; j++) {
    231:         g  = (it-j-1)%l;
    232:         t -= alpha[g]*H(k, g);
    233:       }
    234:       alpha[k] = t/H(k,k);
    235:     } else {
    236:       VecDot(dX[k],Y,&t);
    237:       alpha[k] = t/dXtdF[k];
    238:     }
    239:     if (qn->monitor) {
    240:       PetscViewerASCIIAddTab(qn->monitor,((PetscObject)snes)->tablevel+2);
    241:       PetscViewerASCIIPrintf(qn->monitor, "it: %D k: %D alpha:        %14.12e\n", it, k, (double)PetscRealPart(alpha[k]));
    242:       PetscViewerASCIISubtractTab(qn->monitor,((PetscObject)snes)->tablevel+2);
    243:     }
    244:     VecAXPY(Y,-alpha[k],dF[k]);
    245:   }

    247:   if (qn->scale_type == SNES_QN_SCALE_JACOBIAN) {
    248:     KSPSolve(snes->ksp,Y,W);
    249:     SNESCheckKSPSolve(snes);
    250:     KSPGetIterationNumber(snes->ksp,&lits);
    251:     snes->linear_its += lits;
    252:     VecCopy(W, Y);
    253:   } else {
    254:     VecScale(Y, qn->scaling);
    255:   }
    256:   if (qn->singlereduction) {
    257:     VecMDot(Y,l,dF,YtdX);
    258:   }
    259:   /* inward recursion starting at the first update and working forward */
    260:   for (i = 0; i < l; i++) {
    261:     k = (it + i - l) % l;
    262:     if (qn->singlereduction) {
    263:       t = YtdX[k];
    264:       for (j = 0; j < i; j++) {
    265:         g  = (it + j - l) % l;
    266:         t += (alpha[g] - beta[g])*H(g, k);
    267:       }
    268:       beta[k] = t / H(k, k);
    269:     } else {
    270:       VecDot(dF[k], Y, &t);
    271:       beta[k] = t / dXtdF[k];
    272:     }
    273:     VecAXPY(Y, (alpha[k] - beta[k]), dX[k]);
    274:     if (qn->monitor) {
    275:       PetscViewerASCIIAddTab(qn->monitor,((PetscObject)snes)->tablevel+2);
    276:       PetscViewerASCIIPrintf(qn->monitor, "it: %D k: %D alpha - beta: %14.12e\n", it, k, (double)PetscRealPart(alpha[k] - beta[k]));
    277:       PetscViewerASCIISubtractTab(qn->monitor,((PetscObject)snes)->tablevel+2);
    278:     }
    279:   }
    280:   return(0);
    281: }

    285: static PetscErrorCode SNESSolve_QN(SNES snes)
    286: {
    287:   PetscErrorCode       ierr;
    288:   SNES_QN              *qn = (SNES_QN*) snes->data;
    289:   Vec                  X,Xold;
    290:   Vec                  F,W;
    291:   Vec                  Y,D,Dold;
    292:   PetscInt             i, i_r;
    293:   PetscReal            fnorm,xnorm,ynorm,gnorm;
    294:   SNESLineSearchReason lssucceed;
    295:   PetscBool            powell,periodic;
    296:   PetscScalar          DolddotD,DolddotDold;
    297:   SNESConvergedReason  reason;

    299:   /* basically just a regular newton's method except for the application of the Jacobian */

    302:   if (snes->xl || snes->xu || snes->ops->computevariablebounds) SETERRQ1(PetscObjectComm((PetscObject)snes),PETSC_ERR_ARG_WRONGSTATE, "SNES solver %s does not support bounds", ((PetscObject)snes)->type_name);

    304:   PetscCitationsRegister(SNESCitation,&SNEScite);
    305:   F    = snes->vec_func;                /* residual vector */
    306:   Y    = snes->vec_sol_update;          /* search direction generated by J^-1D*/
    307:   W    = snes->work[3];
    308:   X    = snes->vec_sol;                 /* solution vector */
    309:   Xold = snes->work[0];

    311:   /* directions generated by the preconditioned problem with F_pre = F or x - M(x, b) */
    312:   D    = snes->work[1];
    313:   Dold = snes->work[2];

    315:   snes->reason = SNES_CONVERGED_ITERATING;

    317:   PetscObjectSAWsTakeAccess((PetscObject)snes);
    318:   snes->iter = 0;
    319:   snes->norm = 0.;
    320:   PetscObjectSAWsGrantAccess((PetscObject)snes);

    322:   if (snes->pc && snes->pcside == PC_LEFT && snes->functype == SNES_FUNCTION_PRECONDITIONED) {
    323:     SNESApplyNPC(snes,X,NULL,F);
    324:     SNESGetConvergedReason(snes->pc,&reason);
    325:     if (reason < 0  && reason != SNES_DIVERGED_MAX_IT) {
    326:       snes->reason = SNES_DIVERGED_INNER;
    327:       return(0);
    328:     }
    329:     VecNorm(F,NORM_2,&fnorm);
    330:   } else {
    331:     if (!snes->vec_func_init_set) {
    332:       SNESComputeFunction(snes,X,F);
    333:     } else snes->vec_func_init_set = PETSC_FALSE;

    335:     VecNorm(F,NORM_2,&fnorm);
    336:     SNESCheckFunctionNorm(snes,fnorm);
    337:   }
    338:   if (snes->pc && snes->pcside == PC_LEFT && snes->functype == SNES_FUNCTION_UNPRECONDITIONED) {
    339:       SNESApplyNPC(snes,X,F,D);
    340:       SNESGetConvergedReason(snes->pc,&reason);
    341:       if (reason < 0  && reason != SNES_DIVERGED_MAX_IT) {
    342:         snes->reason = SNES_DIVERGED_INNER;
    343:         return(0);
    344:       }
    345:   } else {
    346:     VecCopy(F,D);
    347:   }

    349:   PetscObjectSAWsTakeAccess((PetscObject)snes);
    350:   snes->norm = fnorm;
    351:   PetscObjectSAWsGrantAccess((PetscObject)snes);
    352:   SNESLogConvergenceHistory(snes,fnorm,0);
    353:   SNESMonitor(snes,0,fnorm);

    355:   /* test convergence */
    356:   (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);
    357:   if (snes->reason) return(0);

    359:   if (snes->pc && snes->pcside == PC_RIGHT) {
    360:     PetscLogEventBegin(SNES_NPCSolve,snes->pc,X,0,0);
    361:     SNESSolve(snes->pc,snes->vec_rhs,X);
    362:     PetscLogEventEnd(SNES_NPCSolve,snes->pc,X,0,0);
    363:     SNESGetConvergedReason(snes->pc,&reason);
    364:     if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
    365:       snes->reason = SNES_DIVERGED_INNER;
    366:       return(0);
    367:     }
    368:     SNESGetNPCFunction(snes,F,&fnorm);
    369:     VecCopy(F,D);
    370:   }

    372:   /* scale the initial update */
    373:   if (qn->scale_type == SNES_QN_SCALE_JACOBIAN) {
    374:     SNESComputeJacobian(snes,X,snes->jacobian,snes->jacobian_pre);
    375:     KSPSetOperators(snes->ksp,snes->jacobian,snes->jacobian_pre);
    376:   }

    378:   for (i = 0, i_r = 0; i < snes->max_its; i++, i_r++) {
    379:     if (qn->scale_type == SNES_QN_SCALE_SHANNO && i_r > 0) {
    380:       PetscScalar ff,xf;
    381:       VecCopy(Dold,Y);
    382:       VecCopy(Xold,W);
    383:       VecAXPY(Y,-1.0,D);
    384:       VecAXPY(W,-1.0,X);
    385:       VecDotBegin(Y,Y,&ff);
    386:       VecDotBegin(W,Y,&xf);
    387:       VecDotEnd(Y,Y,&ff);
    388:       VecDotEnd(W,Y,&xf);
    389:       qn->scaling = PetscRealPart(xf)/PetscRealPart(ff);
    390:       if (qn->monitor) {
    391:         PetscViewerASCIIAddTab(qn->monitor,((PetscObject)snes)->tablevel+2);
    392:         PetscViewerASCIIPrintf(qn->monitor, "Shanno scaling %D %g\n", i,(double)qn->scaling);
    393:         PetscViewerASCIISubtractTab(qn->monitor,((PetscObject)snes)->tablevel+2);
    394:       }
    395:     }
    396:     switch (qn->type) {
    397:     case SNES_QN_BADBROYDEN:
    398:       SNESQNApply_BadBroyden(snes,i_r,Y,X,Xold,D,Dold);
    399:       break;
    400:     case SNES_QN_BROYDEN:
    401:       SNESQNApply_Broyden(snes,i_r,Y,X,Xold,D);
    402:       break;
    403:     case SNES_QN_LBFGS:
    404:       SNESQNApply_LBFGS(snes,i_r,Y,X,Xold,D,Dold);
    405:       break;
    406:     }
    407:     /* line search for lambda */
    408:     ynorm = 1; gnorm = fnorm;
    409:     VecCopy(D, Dold);
    410:     VecCopy(X, Xold);
    411:     SNESLineSearchApply(snes->linesearch, X, F, &fnorm, Y);
    412:     if (snes->reason == SNES_DIVERGED_FUNCTION_COUNT) break;
    413:     SNESLineSearchGetReason(snes->linesearch, &lssucceed);
    414:     SNESLineSearchGetNorms(snes->linesearch, &xnorm, &fnorm, &ynorm);
    415:     if (lssucceed) {
    416:       if (++snes->numFailures >= snes->maxFailures) {
    417:         snes->reason = SNES_DIVERGED_LINE_SEARCH;
    418:         break;
    419:       }
    420:     }
    421:     if (qn->scale_type == SNES_QN_SCALE_LINESEARCH) {
    422:       SNESLineSearchGetLambda(snes->linesearch, &qn->scaling);
    423:     }

    425:     /* convergence monitoring */
    426:     PetscInfo4(snes,"fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lssucceed=%d\n",(double)fnorm,(double)gnorm,(double)ynorm,(int)lssucceed);

    428:     if (snes->pc && snes->pcside == PC_RIGHT) {
    429:       PetscLogEventBegin(SNES_NPCSolve,snes->pc,X,0,0);
    430:       SNESSolve(snes->pc,snes->vec_rhs,X);
    431:       PetscLogEventEnd(SNES_NPCSolve,snes->pc,X,0,0);
    432:       SNESGetConvergedReason(snes->pc,&reason);
    433:       if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
    434:         snes->reason = SNES_DIVERGED_INNER;
    435:         return(0);
    436:       }
    437:       SNESGetNPCFunction(snes,F,&fnorm);
    438:     }

    440:     SNESSetIterationNumber(snes, i+1);
    441:     snes->norm = fnorm;

    443:     SNESLogConvergenceHistory(snes,snes->norm,snes->iter);
    444:     SNESMonitor(snes,snes->iter,snes->norm);
    445:     /* set parameter for default relative tolerance convergence test */
    446:     (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);
    447:     if (snes->reason) return(0);
    448:     if (snes->pc && snes->pcside == PC_LEFT && snes->functype == SNES_FUNCTION_UNPRECONDITIONED) {
    449:       SNESApplyNPC(snes,X,F,D);
    450:       SNESGetConvergedReason(snes->pc,&reason);
    451:       if (reason < 0  && reason != SNES_DIVERGED_MAX_IT) {
    452:         snes->reason = SNES_DIVERGED_INNER;
    453:         return(0);
    454:       }
    455:     } else {
    456:       VecCopy(F, D);
    457:     }
    458:     powell = PETSC_FALSE;
    459:     if (qn->restart_type == SNES_QN_RESTART_POWELL && i_r > 1) {
    460:       /* check restart by Powell's Criterion: |F^T H_0 Fold| > powell_gamma * |Fold^T H_0 Fold| */
    461:       if (qn->scale_type == SNES_QN_SCALE_JACOBIAN) {
    462:         MatMult(snes->jacobian_pre,Dold,W);
    463:       } else {
    464:         VecCopy(Dold,W);
    465:       }
    466:       VecDotBegin(W, Dold, &DolddotDold);
    467:       VecDotBegin(W, D, &DolddotD);
    468:       VecDotEnd(W, Dold, &DolddotDold);
    469:       VecDotEnd(W, D, &DolddotD);
    470:       if (PetscAbs(PetscRealPart(DolddotD)) > qn->powell_gamma*PetscAbs(PetscRealPart(DolddotDold))) powell = PETSC_TRUE;
    471:     }
    472:     periodic = PETSC_FALSE;
    473:     if (qn->restart_type == SNES_QN_RESTART_PERIODIC) {
    474:       if (i_r>qn->m-1) periodic = PETSC_TRUE;
    475:     }
    476:     /* restart if either powell or periodic restart is satisfied. */
    477:     if (powell || periodic) {
    478:       if (qn->monitor) {
    479:         PetscViewerASCIIAddTab(qn->monitor,((PetscObject)snes)->tablevel+2);
    480:         if (powell) {
    481:           PetscViewerASCIIPrintf(qn->monitor, "Powell restart! |%14.12e| > %6.4f*|%14.12e| i_r = %D\n", (double)PetscRealPart(DolddotD), (double)qn->powell_gamma, (double)PetscRealPart(DolddotDold),i_r);
    482:         } else {
    483:           PetscViewerASCIIPrintf(qn->monitor, "Periodic restart! i_r = %D\n", i_r);
    484:         }
    485:         PetscViewerASCIISubtractTab(qn->monitor,((PetscObject)snes)->tablevel+2);
    486:       }
    487:       i_r = -1;
    488:       /* general purpose update */
    489:       if (snes->ops->update) {
    490:         (*snes->ops->update)(snes, snes->iter);
    491:       }
    492:       if (qn->scale_type == SNES_QN_SCALE_JACOBIAN) {
    493:         SNESComputeJacobian(snes,X,snes->jacobian,snes->jacobian_pre);
    494:       }
    495:     }
    496:     /* general purpose update */
    497:     if (snes->ops->update) {
    498:       (*snes->ops->update)(snes, snes->iter);
    499:     }
    500:   }
    501:   if (i == snes->max_its) {
    502:     PetscInfo1(snes, "Maximum number of iterations has been reached: %D\n", snes->max_its);
    503:     if (!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
    504:   }
    505:   return(0);
    506: }

    510: static PetscErrorCode SNESSetUp_QN(SNES snes)
    511: {
    512:   SNES_QN        *qn = (SNES_QN*)snes->data;
    514:   DM             dm;

    518:   if (!snes->vec_sol) {
    519:     SNESGetDM(snes,&dm);
    520:     DMCreateGlobalVector(dm,&snes->vec_sol);
    521:   }

    523:   VecDuplicateVecs(snes->vec_sol, qn->m, &qn->U);
    524:   if (qn->type != SNES_QN_BROYDEN) VecDuplicateVecs(snes->vec_sol, qn->m, &qn->V);
    525:   PetscMalloc4(qn->m,&qn->alpha,qn->m,&qn->beta,qn->m,&qn->dXtdF,qn->m,&qn->lambda);

    527:   if (qn->singlereduction) {
    528:     PetscMalloc3(qn->m*qn->m,&qn->dXdFmat,qn->m,&qn->dFtdX,qn->m,&qn->YtdX);
    529:   }
    530:   SNESSetWorkVecs(snes,4);
    531:   /* set method defaults */
    532:   if (qn->scale_type == SNES_QN_SCALE_DEFAULT) {
    533:     if (qn->type == SNES_QN_BADBROYDEN) {
    534:       qn->scale_type = SNES_QN_SCALE_NONE;
    535:     } else {
    536:       qn->scale_type = SNES_QN_SCALE_SHANNO;
    537:     }
    538:   }
    539:   if (qn->restart_type == SNES_QN_RESTART_DEFAULT) {
    540:     if (qn->type == SNES_QN_LBFGS) {
    541:       qn->restart_type = SNES_QN_RESTART_POWELL;
    542:     } else {
    543:       qn->restart_type = SNES_QN_RESTART_PERIODIC;
    544:     }
    545:   }

    547:   if (qn->scale_type == SNES_QN_SCALE_JACOBIAN) {
    548:     SNESSetUpMatrices(snes);
    549:   }
    550:   if (snes->pcside == PC_LEFT && snes->functype == SNES_FUNCTION_DEFAULT) {snes->functype = SNES_FUNCTION_UNPRECONDITIONED;}
    551:   return(0);
    552: }

    556: static PetscErrorCode SNESReset_QN(SNES snes)
    557: {
    559:   SNES_QN        *qn;

    562:   if (snes->data) {
    563:     qn = (SNES_QN*)snes->data;
    564:     if (qn->U) {
    565:       VecDestroyVecs(qn->m, &qn->U);
    566:     }
    567:     if (qn->V) {
    568:       VecDestroyVecs(qn->m, &qn->V);
    569:     }
    570:     if (qn->singlereduction) {
    571:       PetscFree3(qn->dXdFmat, qn->dFtdX, qn->YtdX);
    572:     }
    573:     PetscFree4(qn->alpha,qn->beta,qn->dXtdF,qn->lambda);
    574:   }
    575:   return(0);
    576: }

    580: static PetscErrorCode SNESDestroy_QN(SNES snes)
    581: {

    585:   SNESReset_QN(snes);
    586:   PetscFree(snes->data);
    587:   PetscObjectComposeFunction((PetscObject)snes,"",NULL);
    588:   return(0);
    589: }

    593: static PetscErrorCode SNESSetFromOptions_QN(PetscOptionItems *PetscOptionsObject,SNES snes)
    594: {

    596:   PetscErrorCode    ierr;
    597:   SNES_QN           *qn    = (SNES_QN*)snes->data;
    598:   PetscBool         monflg = PETSC_FALSE,flg;
    599:   SNESLineSearch    linesearch;
    600:   SNESQNRestartType rtype = qn->restart_type;
    601:   SNESQNScaleType   stype = qn->scale_type;
    602:   SNESQNType        qtype = qn->type;

    605:   PetscOptionsHead(PetscOptionsObject,"SNES QN options");
    606:   PetscOptionsInt("-snes_qn_m","Number of past states saved for L-BFGS methods","SNESQN",qn->m,&qn->m,NULL);
    607:   PetscOptionsReal("-snes_qn_powell_gamma","Powell angle tolerance",          "SNESQN", qn->powell_gamma, &qn->powell_gamma, NULL);
    608:   PetscOptionsBool("-snes_qn_monitor",         "Monitor for the QN methods",      "SNESQN", monflg, &monflg, NULL);
    609:   PetscOptionsBool("-snes_qn_single_reduction", "Aggregate reductions",           "SNESQN", qn->singlereduction, &qn->singlereduction, NULL);
    610:   PetscOptionsEnum("-snes_qn_scale_type","Scaling type","SNESQNSetScaleType",SNESQNScaleTypes,(PetscEnum)stype,(PetscEnum*)&stype,&flg);
    611:   if (flg) SNESQNSetScaleType(snes,stype);

    613:   PetscOptionsEnum("-snes_qn_restart_type","Restart type","SNESQNSetRestartType",SNESQNRestartTypes,(PetscEnum)rtype,(PetscEnum*)&rtype,&flg);
    614:   if (flg) SNESQNSetRestartType(snes,rtype);

    616:   PetscOptionsEnum("-snes_qn_type","Quasi-Newton update type","",SNESQNTypes,(PetscEnum)qtype,(PetscEnum*)&qtype,&flg);
    617:   if (flg) {SNESQNSetType(snes,qtype);}
    618:   PetscOptionsTail();
    619:   if (!snes->linesearch) {
    620:     SNESGetLineSearch(snes, &linesearch);
    621:     if (qn->type == SNES_QN_LBFGS) {
    622:       SNESLineSearchSetType(linesearch, SNESLINESEARCHCP);
    623:     } else if (qn->type == SNES_QN_BROYDEN) {
    624:       SNESLineSearchSetType(linesearch, SNESLINESEARCHBASIC);
    625:     } else {
    626:       SNESLineSearchSetType(linesearch, SNESLINESEARCHL2);
    627:     }
    628:   }
    629:   if (monflg) {
    630:     qn->monitor = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)snes));
    631:   }
    632:   return(0);
    633: }

    637: static PetscErrorCode SNESView_QN(SNES snes, PetscViewer viewer)
    638: {
    639:   SNES_QN        *qn    = (SNES_QN*)snes->data;
    640:   PetscBool      iascii;

    644:   PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);
    645:   if (iascii) {
    646:     PetscViewerASCIIPrintf(viewer,"  QN type is %s, restart type is %s, scale type is %s\n",SNESQNTypes[qn->type],SNESQNRestartTypes[qn->restart_type],SNESQNScaleTypes[qn->scale_type]);
    647:     PetscViewerASCIIPrintf(viewer,"  Stored subspace size: %D\n", qn->m);
    648:     if (qn->singlereduction) {
    649:       PetscViewerASCIIPrintf(viewer,"  Using the single reduction variant.\n");
    650:     }
    651:   }
    652:   return(0);
    653: }

    657: /*@
    658:     SNESQNSetRestartType - Sets the restart type for SNESQN.

    660:     Logically Collective on SNES

    662:     Input Parameters:
    663: +   snes - the iterative context
    664: -   rtype - restart type

    666:     Options Database:
    667: +   -snes_qn_restart_type <powell,periodic,none> - set the restart type
    668: -   -snes_qn_m <m> - sets the number of stored updates and the restart period for periodic

    670:     Level: intermediate

    672:     SNESQNRestartTypes:
    673: +   SNES_QN_RESTART_NONE - never restart
    674: .   SNES_QN_RESTART_POWELL - restart based upon descent criteria
    675: -   SNES_QN_RESTART_PERIODIC - restart after a fixed number of iterations

    677: .keywords: SNES, SNESQN, restart, type, set SNESLineSearch, SNESQNRestartType
    678: @*/
    679: PetscErrorCode SNESQNSetRestartType(SNES snes, SNESQNRestartType rtype)
    680: {

    685:   PetscTryMethod(snes,"SNESQNSetRestartType_C",(SNES,SNESQNRestartType),(snes,rtype));
    686:   return(0);
    687: }

    691: /*@
    692:     SNESQNSetScaleType - Sets the scaling type for the inner inverse Jacobian in SNESQN.

    694:     Logically Collective on SNES

    696:     Input Parameters:
    697: +   snes - the iterative context
    698: -   stype - scale type

    700:     Options Database:
    701: .   -snes_qn_scale_type <shanno,none,linesearch,jacobian>

    703:     Level: intermediate

    705:     SNESQNScaleTypes:
    706: +   SNES_QN_SCALE_NONE - don't scale the problem
    707: .   SNES_QN_SCALE_SHANNO - use shanno scaling
    708: .   SNES_QN_SCALE_LINESEARCH - scale based upon line search lambda
    709: -   SNES_QN_SCALE_JACOBIAN - scale by solving a linear system coming from the Jacobian you provided with SNESSetJacobian() computed at the first iteration
    710:                              of QN and at ever restart.

    712: .keywords: scaling type

    714: .seealso: SNES, SNESQN, SNESLineSearch, SNESQNScaleType, SNESetJacobian()
    715: @*/

    717: PetscErrorCode SNESQNSetScaleType(SNES snes, SNESQNScaleType stype)
    718: {

    723:   PetscTryMethod(snes,"SNESQNSetScaleType_C",(SNES,SNESQNScaleType),(snes,stype));
    724:   return(0);
    725: }

    729: PetscErrorCode SNESQNSetScaleType_QN(SNES snes, SNESQNScaleType stype)
    730: {
    731:   SNES_QN *qn = (SNES_QN*)snes->data;

    734:   qn->scale_type = stype;
    735:   return(0);
    736: }

    740: PetscErrorCode SNESQNSetRestartType_QN(SNES snes, SNESQNRestartType rtype)
    741: {
    742:   SNES_QN *qn = (SNES_QN*)snes->data;

    745:   qn->restart_type = rtype;
    746:   return(0);
    747: }

    751: /*@
    752:     SNESQNSetType - Sets the quasi-Newton variant to be used in SNESQN.

    754:     Logically Collective on SNES

    756:     Input Parameters:
    757: +   snes - the iterative context
    758: -   qtype - variant type

    760:     Options Database:
    761: .   -snes_qn_type <lbfgs,broyden,badbroyden>

    763:     Level: beginner

    765:     SNESQNTypes:
    766: +   SNES_QN_LBFGS - LBFGS variant
    767: .   SNES_QN_BROYDEN - Broyden variant
    768: -   SNES_QN_BADBROYDEN - Bad Broyden variant

    770: .keywords: SNES, SNESQN, type, set, SNESQNType
    771: @*/

    773: PetscErrorCode SNESQNSetType(SNES snes, SNESQNType qtype)
    774: {

    779:   PetscTryMethod(snes,"SNESQNSetType_C",(SNES,SNESQNType),(snes,qtype));
    780:   return(0);
    781: }

    785: PetscErrorCode SNESQNSetType_QN(SNES snes, SNESQNType qtype)
    786: {
    787:   SNES_QN *qn = (SNES_QN*)snes->data;

    790:   qn->type = qtype;
    791:   return(0);
    792: }

    794: /* -------------------------------------------------------------------------- */
    795: /*MC
    796:       SNESQN - Limited-Memory Quasi-Newton methods for the solution of nonlinear systems.

    798:       Options Database:

    800: +     -snes_qn_m <m> - Number of past states saved for the L-Broyden methods.
    801: +     -snes_qn_restart_type <powell,periodic,none> - set the restart type
    802: .     -snes_qn_powell_gamma - Angle condition for restart.
    803: .     -snes_qn_powell_descent - Descent condition for restart.
    804: .     -snes_qn_type <lbfgs,broyden,badbroyden> - QN type
    805: .     -snes_qn_scale_type <shanno,none,linesearch,jacobian> - scaling performed on inner Jacobian
    806: .     -snes_linesearch_type <cp, l2, basic> - Type of line search.
    807: -     -snes_qn_monitor - Monitors the quasi-newton Jacobian.

    809:       Notes: This implements the L-BFGS, Broyden, and "Bad" Broyden algorithms for the solution of F(x) = b using
    810:       previous change in F(x) and x to form the approximate inverse Jacobian using a series of multiplicative rank-one
    811:       updates.

    813:       When using a nonlinear preconditioner, one has two options as to how the preconditioner is applied.  The first of
    814:       these options, sequential, uses the preconditioner to generate a new solution and function and uses those at this
    815:       iteration as the current iteration's values when constructing the approximate Jacobian.  The second, composed,
    816:       perturbs the problem the Jacobian represents to be P(x, b) - x = 0, where P(x, b) is the preconditioner.

    818:       References:
    819: +   1. -   Kelley, C.T., Iterative Methods for Linear and Nonlinear Equations, Chapter 8, SIAM, 1995.
    820: .   2. -   R. Byrd, J. Nocedal, R. Schnabel, Representations of Quasi Newton Matrices and their use in Limited Memory Methods,
    821:       Technical Report, Northwestern University, June 1992.
    822: .   3. -   Peter N. Brown, Alan C. Hindmarsh, Homer F. Walker, Experiments with Quasi-Newton Methods in Solving Stiff ODE
    823:       Systems, SIAM J. Sci. Stat. Comput. Vol 6(2), April 1985.
    824: -   4. -   Peter R. Brune, Matthew G. Knepley, Barry F. Smith, and Xuemin Tu, "Composing Scalable Nonlinear Algebraic Solvers",
    825:        SIAM Review, 57(4), 2015

    827:       Level: beginner

    829: .seealso:  SNESCreate(), SNES, SNESSetType(), SNESNEWTONLS, SNESNEWTONTR

    831: M*/
    834: PETSC_EXTERN PetscErrorCode SNESCreate_QN(SNES snes)
    835: {
    837:   SNES_QN        *qn;

    840:   snes->ops->setup          = SNESSetUp_QN;
    841:   snes->ops->solve          = SNESSolve_QN;
    842:   snes->ops->destroy        = SNESDestroy_QN;
    843:   snes->ops->setfromoptions = SNESSetFromOptions_QN;
    844:   snes->ops->view           = SNESView_QN;
    845:   snes->ops->reset          = SNESReset_QN;

    847:   snes->pcside = PC_LEFT;

    849:   snes->usespc  = PETSC_TRUE;
    850:   snes->usesksp = PETSC_FALSE;

    852:   if (!snes->tolerancesset) {
    853:     snes->max_funcs = 30000;
    854:     snes->max_its   = 10000;
    855:   }

    857:   PetscNewLog(snes,&qn);
    858:   snes->data          = (void*) qn;
    859:   qn->m               = 10;
    860:   qn->scaling         = 1.0;
    861:   qn->U               = NULL;
    862:   qn->V               = NULL;
    863:   qn->dXtdF           = NULL;
    864:   qn->dFtdX           = NULL;
    865:   qn->dXdFmat         = NULL;
    866:   qn->monitor         = NULL;
    867:   qn->singlereduction = PETSC_TRUE;
    868:   qn->powell_gamma    = 0.9999;
    869:   qn->scale_type      = SNES_QN_SCALE_DEFAULT;
    870:   qn->restart_type    = SNES_QN_RESTART_DEFAULT;
    871:   qn->type            = SNES_QN_LBFGS;

    873:   PetscObjectComposeFunction((PetscObject)snes,"SNESQNSetScaleType_C",SNESQNSetScaleType_QN);
    874:   PetscObjectComposeFunction((PetscObject)snes,"SNESQNSetRestartType_C",SNESQNSetRestartType_QN);
    875:   PetscObjectComposeFunction((PetscObject)snes,"SNESQNSetType_C",SNESQNSetType_QN);
    876:   return(0);
    877: }