Actual source code: qcg.c
petsc-3.10.5 2019-03-28
Report Typos and Errors

      2:  #include <../src/ksp/ksp/impls/qcg/qcgimpl.h>

      4: static PetscErrorCode KSPQCGQuadraticRoots(Vec,Vec,PetscReal,PetscReal*,PetscReal*);

      6: /*@
      7:     KSPQCGSetTrustRegionRadius - Sets the radius of the trust region.

      9:     Logically Collective on KSP

     11:     Input Parameters:
     12: +   ksp   - the iterative context
     13: -   delta - the trust region radius (Infinity is the default)

     15:     Options Database Key:
     16: .   -ksp_qcg_trustregionradius <delta>

     18:     Level: advanced

     20: .keywords: KSP, QCG, set, trust region radius
     21: @*/
     22: PetscErrorCode  KSPQCGSetTrustRegionRadius(KSP ksp,PetscReal delta)
     23: {

     28:   if (delta < 0.0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Tolerance must be non-negative");
     29:   PetscTryMethod(ksp,"KSPQCGSetTrustRegionRadius_C",(KSP,PetscReal),(ksp,delta));
     30:   return(0);
     31: }

     33: /*@
     34:     KSPQCGGetTrialStepNorm - Gets the norm of a trial step vector.  The WCG step may be
     35:     constrained, so this is not necessarily the length of the ultimate step taken in QCG.

     37:     Not Collective

     39:     Input Parameter:
     40: .   ksp - the iterative context

     42:     Output Parameter:
     43: .   tsnorm - the norm

     45:     Level: advanced
     46: @*/
     47: PetscErrorCode  KSPQCGGetTrialStepNorm(KSP ksp,PetscReal *tsnorm)
     48: {

     53:   PetscUseMethod(ksp,"KSPQCGGetTrialStepNorm_C",(KSP,PetscReal*),(ksp,tsnorm));
     54:   return(0);
     55: }

     57: /*@
     58:     KSPQCGGetQuadratic - Gets the value of the quadratic function, evaluated at the new iterate:

     60:        q(s) = g^T * s + 0.5 * s^T * H * s

     62:     which satisfies the Euclidian Norm trust region constraint

     64:        || D * s || <= delta,

     66:     where

     68:      delta is the trust region radius,
     69:      g is the gradient vector, and
     70:      H is Hessian matrix,
     71:      D is a scaling matrix.

     73:     Collective on KSP

     75:     Input Parameter:
     76: .   ksp - the iterative context

     78:     Output Parameter:
     79: .   quadratic - the quadratic function evaluated at the new iterate

     81:     Level: advanced
     82: @*/
     83: PetscErrorCode  KSPQCGGetQuadratic(KSP ksp,PetscReal *quadratic)
     84: {

     89:   PetscUseMethod(ksp,"KSPQCGGetQuadratic_C",(KSP,PetscReal*),(ksp,quadratic));
     90:   return(0);
     91: }

     94: PetscErrorCode KSPSolve_QCG(KSP ksp)
     95: {
     96: /*
     97:    Correpondence with documentation above:
     98:       B = g = gradient,
     99:       X = s = step
    100:    Note:  This is not coded correctly for complex arithmetic!
    101:  */

    103:   KSP_QCG        *pcgP = (KSP_QCG*)ksp->data;
    104:   Mat            Amat,Pmat;
    105:   Vec            W,WA,WA2,R,P,ASP,BS,X,B;
    106:   PetscScalar    scal,beta,rntrn,step;
    107:   PetscReal      q1,q2,xnorm,step1,step2,rnrm,btx,xtax;
    108:   PetscReal      ptasp,rtr,wtasp,bstp;
    109:   PetscReal      dzero = 0.0,bsnrm;
    111:   PetscInt       i,maxit;
    112:   PC             pc = ksp->pc;
    113:   PCSide         side;
    114:   PetscBool      diagonalscale;

    117:   PCGetDiagonalScale(ksp->pc,&diagonalscale);
    118:   if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);
    119:   if (ksp->transpose_solve) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Currently does not support transpose solve");

    121:   ksp->its = 0;
    122:   maxit    = ksp->max_it;
    123:   WA       = ksp->work[0];
    124:   R        = ksp->work[1];
    125:   P        = ksp->work[2];
    126:   ASP      = ksp->work[3];
    127:   BS       = ksp->work[4];
    128:   W        = ksp->work[5];
    129:   WA2      = ksp->work[6];
    130:   X        = ksp->vec_sol;
    131:   B        = ksp->vec_rhs;

    133:   if (pcgP->delta <= dzero) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Input error: delta <= 0");
    134:   KSPGetPCSide(ksp,&side);
    135:   if (side != PC_SYMMETRIC) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Requires symmetric preconditioner!");

    137:   /* Initialize variables */
    138:   VecSet(W,0.0);  /* W = 0 */
    139:   VecSet(X,0.0);  /* X = 0 */
    140:   PCGetOperators(pc,&Amat,&Pmat);

    142:   /* Compute:  BS = D^{-1} B */
    143:   PCApplySymmetricLeft(pc,B,BS);

    145:   VecNorm(BS,NORM_2,&bsnrm);
    146:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
    147:   ksp->its   = 0;
    148:   ksp->rnorm = bsnrm;
    149:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
    150:   KSPLogResidualHistory(ksp,bsnrm);
    151:   KSPMonitor(ksp,0,bsnrm);
    152:   (*ksp->converged)(ksp,0,bsnrm,&ksp->reason,ksp->cnvP);
    153:   if (ksp->reason) return(0);

    155:   /* Compute the initial scaled direction and scaled residual */
    156:   VecCopy(BS,R);
    157:   VecScale(R,-1.0);
    158:   VecCopy(R,P);
    159:   VecDotRealPart(R,R,&rtr);

    161:   for (i=0; i<=maxit; i++) {
    162:     PetscObjectSAWsTakeAccess((PetscObject)ksp);
    163:     ksp->its++;
    164:     PetscObjectSAWsGrantAccess((PetscObject)ksp);

    166:     /* Compute:  asp = D^{-T}*A*D^{-1}*p  */
    167:     PCApplySymmetricRight(pc,P,WA);
    168:     KSP_MatMult(ksp,Amat,WA,WA2);
    169:     PCApplySymmetricLeft(pc,WA2,ASP);

    171:     /* Check for negative curvature */
    172:     VecDotRealPart(P,ASP,&ptasp);
    173:     if (ptasp <= dzero) {

    175:       /* Scaled negative curvature direction:  Compute a step so that
    176:         ||w + step*p|| = delta and QS(w + step*p) is least */

    178:       if (!i) {
    179:         VecCopy(P,X);
    180:         VecNorm(X,NORM_2,&xnorm);
    181:         scal = pcgP->delta / xnorm;
    182:         VecScale(X,scal);
    183:       } else {
    184:         /* Compute roots of quadratic */
    185:         KSPQCGQuadraticRoots(W,P,pcgP->delta,&step1,&step2);
    186:         VecDotRealPart(W,ASP,&wtasp);
    187:         VecDotRealPart(BS,P,&bstp);
    188:         VecCopy(W,X);
    189:         q1   = step1*(bstp + wtasp + .5*step1*ptasp);
    190:         q2   = step2*(bstp + wtasp + .5*step2*ptasp);
    191:         if (q1 <= q2) {
    192:           VecAXPY(X,step1,P);
    193:         } else {
    194:           VecAXPY(X,step2,P);
    195:         }
    196:       }
    197:       pcgP->ltsnrm = pcgP->delta;                       /* convergence in direction of */
    198:       ksp->reason  = KSP_CONVERGED_CG_NEG_CURVE;  /* negative curvature */
    199:       if (!i) {
    200:         PetscInfo1(ksp,"negative curvature: delta=%g\n",(double)pcgP->delta);
    201:       } else {
    202:         PetscInfo3(ksp,"negative curvature: step1=%g, step2=%g, delta=%g\n",(double)step1,(double)step2,(double)pcgP->delta);
    203:       }

    205:     } else {
    206:       /* Compute step along p */
    207:       step = rtr/ptasp;
    208:       VecCopy(W,X);        /*  x = w  */
    209:       VecAXPY(X,step,P);   /*  x <- step*p + x  */
    210:       VecNorm(X,NORM_2,&pcgP->ltsnrm);

    212:       if (pcgP->ltsnrm > pcgP->delta) {
    213:         /* Since the trial iterate is outside the trust region,
    214:             evaluate a constrained step along p so that
    215:                     ||w + step*p|| = delta
    216:           The positive step is always better in this case. */
    217:         if (!i) {
    218:           scal = pcgP->delta / pcgP->ltsnrm;
    219:           VecScale(X,scal);
    220:         } else {
    221:           /* Compute roots of quadratic */
    222:           KSPQCGQuadraticRoots(W,P,pcgP->delta,&step1,&step2);
    223:           VecCopy(W,X);
    224:           VecAXPY(X,step1,P);  /*  x <- step1*p + x  */
    225:         }
    226:         pcgP->ltsnrm = pcgP->delta;
    227:         ksp->reason  = KSP_CONVERGED_CG_CONSTRAINED; /* convergence along constrained step */
    228:         if (!i) {
    229:           PetscInfo1(ksp,"constrained step: delta=%g\n",(double)pcgP->delta);
    230:         } else {
    231:           PetscInfo3(ksp,"constrained step: step1=%g, step2=%g, delta=%g\n",(double)step1,(double)step2,(double)pcgP->delta);
    232:         }

    234:       } else {
    235:         /* Evaluate the current step */
    236:         VecCopy(X,W);  /* update interior iterate */
    237:         VecAXPY(R,-step,ASP); /* r <- -step*asp + r */
    238:         VecNorm(R,NORM_2,&rnrm);

    240:         PetscObjectSAWsTakeAccess((PetscObject)ksp);
    241:         ksp->rnorm = rnrm;
    242:         PetscObjectSAWsGrantAccess((PetscObject)ksp);
    243:         KSPLogResidualHistory(ksp,rnrm);
    244:         KSPMonitor(ksp,i+1,rnrm);
    245:         (*ksp->converged)(ksp,i+1,rnrm,&ksp->reason,ksp->cnvP);
    246:         if (ksp->reason) {                 /* convergence for */
    247:           PetscInfo3(ksp,"truncated step: step=%g, rnrm=%g, delta=%g\n",(double)PetscRealPart(step),(double)rnrm,(double)pcgP->delta);
    248:         }
    249:       }
    250:     }
    251:     if (ksp->reason) break;  /* Convergence has been attained */
    252:     else {                   /* Compute a new AS-orthogonal direction */
    253:       VecDot(R,R,&rntrn);
    254:       beta = rntrn/rtr;
    255:       VecAYPX(P,beta,R);  /*  p <- r + beta*p  */
    256:       rtr  = PetscRealPart(rntrn);
    257:     }
    258:   }
    259:   if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;

    261:   /* Unscale x */
    262:   VecCopy(X,WA2);
    263:   PCApplySymmetricRight(pc,WA2,X);

    265:   KSP_MatMult(ksp,Amat,X,WA);
    266:   VecDotRealPart(B,X,&btx);
    267:   VecDotRealPart(X,WA,&xtax);

    269:   pcgP->quadratic = btx + .5*xtax;
    270:   return(0);
    271: }

    273: PetscErrorCode KSPSetUp_QCG(KSP ksp)
    274: {

    278:   /* Get work vectors from user code */
    279:   KSPSetWorkVecs(ksp,7);
    280:   return(0);
    281: }

    283: PetscErrorCode KSPDestroy_QCG(KSP ksp)
    284: {

    288:   PetscObjectComposeFunction((PetscObject)ksp,"KSPQCGGetQuadratic_C",NULL);
    289:   PetscObjectComposeFunction((PetscObject)ksp,"KSPQCGGetTrialStepNorm_C",NULL);
    290:   PetscObjectComposeFunction((PetscObject)ksp,"KSPQCGSetTrustRegionRadius_C",NULL);
    291:   KSPDestroyDefault(ksp);
    292:   return(0);
    293: }

    295: static PetscErrorCode  KSPQCGSetTrustRegionRadius_QCG(KSP ksp,PetscReal delta)
    296: {
    297:   KSP_QCG *cgP = (KSP_QCG*)ksp->data;

    300:   cgP->delta = delta;
    301:   return(0);
    302: }

    304: static PetscErrorCode  KSPQCGGetTrialStepNorm_QCG(KSP ksp,PetscReal *ltsnrm)
    305: {
    306:   KSP_QCG *cgP = (KSP_QCG*)ksp->data;

    309:   *ltsnrm = cgP->ltsnrm;
    310:   return(0);
    311: }

    313: static PetscErrorCode  KSPQCGGetQuadratic_QCG(KSP ksp,PetscReal *quadratic)
    314: {
    315:   KSP_QCG *cgP = (KSP_QCG*)ksp->data;

    318:   *quadratic = cgP->quadratic;
    319:   return(0);
    320: }

    322: PetscErrorCode KSPSetFromOptions_QCG(PetscOptionItems *PetscOptionsObject,KSP ksp)
    323: {
    325:   PetscReal      delta;
    326:   KSP_QCG        *cgP = (KSP_QCG*)ksp->data;
    327:   PetscBool      flg;

    330:   PetscOptionsHead(PetscOptionsObject,"KSP QCG Options");
    331:   PetscOptionsReal("-ksp_qcg_trustregionradius","Trust Region Radius","KSPQCGSetTrustRegionRadius",cgP->delta,&delta,&flg);
    332:   if (flg) { KSPQCGSetTrustRegionRadius(ksp,delta); }
    333:   PetscOptionsTail();
    334:   return(0);
    335: }

    337: /*MC
    338:      KSPQCG -   Code to run conjugate gradient method subject to a constraint
    339:          on the solution norm. This is used in Trust Region methods for nonlinear equations, SNESNEWTONTR

    341:    Options Database Keys:
    342: .      -ksp_qcg_trustregionradius <r> - Trust Region Radius

    344:    Notes:
    345:     This is rarely used directly

    347:    Level: developer

    349:   Notes:
    350:     Use preconditioned conjugate gradient to compute
    351:       an approximate minimizer of the quadratic function

    353:             q(s) = g^T * s + .5 * s^T * H * s

    355:    subject to the Euclidean norm trust region constraint

    357:             || D * s || <= delta,

    359:    where

    361:      delta is the trust region radius,
    362:      g is the gradient vector, and
    363:      H is Hessian matrix,
    364:      D is a scaling matrix.

    366:    KSPConvergedReason may be
    367: $  KSP_CONVERGED_CG_NEG_CURVE if convergence is reached along a negative curvature direction,
    368: $  KSP_CONVERGED_CG_CONSTRAINED if convergence is reached along a constrained step,
    369: $  other KSP converged/diverged reasons

    372:   Notes:
    373:   Currently we allow symmetric preconditioning with the following scaling matrices:
    374:       PCNONE:   D = Identity matrix
    375:       PCJACOBI: D = diag [d_1, d_2, ...., d_n], where d_i = sqrt(H[i,i])
    376:       PCICC:    D = L^T, implemented with forward and backward solves.
    377:                 Here L is an incomplete Cholesky factor of H.

    379:   References:
    380: .  1. - Trond Steihaug, The Conjugate Gradient Method and Trust Regions in Large Scale Optimization,
    381:    SIAM Journal on Numerical Analysis, Vol. 20, No. 3 (Jun., 1983).

    383: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPQCGSetTrustRegionRadius()
    384:            KSPQCGGetTrialStepNorm(), KSPQCGGetQuadratic()
    385: M*/

    387: PETSC_EXTERN PetscErrorCode KSPCreate_QCG(KSP ksp)
    388: {
    390:   KSP_QCG        *cgP;

    393:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_SYMMETRIC,3);
    394:   PetscNewLog(ksp,&cgP);

    396:   ksp->data                = (void*)cgP;
    397:   ksp->ops->setup          = KSPSetUp_QCG;
    398:   ksp->ops->setfromoptions = KSPSetFromOptions_QCG;
    399:   ksp->ops->solve          = KSPSolve_QCG;
    400:   ksp->ops->destroy        = KSPDestroy_QCG;
    401:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    402:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
    403:   ksp->ops->setfromoptions = 0;
    404:   ksp->ops->view           = 0;

    406:   PetscObjectComposeFunction((PetscObject)ksp,"KSPQCGGetQuadratic_C",KSPQCGGetQuadratic_QCG);
    407:   PetscObjectComposeFunction((PetscObject)ksp,"KSPQCGGetTrialStepNorm_C",KSPQCGGetTrialStepNorm_QCG);
    408:   PetscObjectComposeFunction((PetscObject)ksp,"KSPQCGSetTrustRegionRadius_C",KSPQCGSetTrustRegionRadius_QCG);
    409:   cgP->delta = PETSC_MAX_REAL; /* default trust region radius is infinite */
    410:   return(0);
    411: }

    413: /* ---------------------------------------------------------- */
    414: /*
    415:   KSPQCGQuadraticRoots - Computes the roots of the quadratic,
    416:          ||s + step*p|| - delta = 0
    417:    such that step1 >= 0 >= step2.
    418:    where
    419:       delta:
    420:         On entry delta must contain scalar delta.
    421:         On exit delta is unchanged.
    422:       step1:
    423:         On entry step1 need not be specified.
    424:         On exit step1 contains the non-negative root.
    425:       step2:
    426:         On entry step2 need not be specified.
    427:         On exit step2 contains the non-positive root.
    428:    C code is translated from the Fortran version of the MINPACK-2 Project,
    429:    Argonne National Laboratory, Brett M. Averick and Richard G. Carter.
    430: */
    431: static PetscErrorCode KSPQCGQuadraticRoots(Vec s,Vec p,PetscReal delta,PetscReal *step1,PetscReal *step2)
    432: {
    433:   PetscReal      dsq,ptp,pts,rad,sts;

    437:   VecDotRealPart(p,s,&pts);
    438:   VecDotRealPart(p,p,&ptp);
    439:   VecDotRealPart(s,s,&sts);
    440:   dsq  = delta*delta;
    441:   rad  = PetscSqrtReal((pts*pts) - ptp*(sts - dsq));
    442:   if (pts > 0.0) {
    443:     *step2 = -(pts + rad)/ptp;
    444:     *step1 = (sts - dsq)/(ptp * *step2);
    445:   } else {
    446:     *step1 = -(pts - rad)/ptp;
    447:     *step2 = (sts - dsq)/(ptp * *step1);
    448:   }
    449:   return(0);
    450: }