Date: 2015-10-02T22:21:32+00:00

Actual source code: qcg.c
petsc-3.6.2 2015-10-02
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      2: #include <petsc/private/kspimpl.h>             /*I "petscksp.h" I*/
      3: #include <../src/ksp/ksp/impls/qcg/qcgimpl.h>

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

      9: /*@
     10:     KSPQCGSetTrustRegionRadius - Sets the radius of the trust region.

     12:     Logically Collective on KSP

     14:     Input Parameters:
     15: +   ksp   - the iterative context
     16: -   delta - the trust region radius (Infinity is the default)

     18:     Options Database Key:
     19: .   -ksp_qcg_trustregionradius <delta>

     21:     Level: advanced

     23: .keywords: KSP, QCG, set, trust region radius
     24: @*/
     25: PetscErrorCode  KSPQCGSetTrustRegionRadius(KSP ksp,PetscReal delta)
     26: {

     31:   if (delta < 0.0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Tolerance must be non-negative");
     32:   PetscTryMethod(ksp,"KSPQCGSetTrustRegionRadius_C",(KSP,PetscReal),(ksp,delta));
     33:   return(0);
     34: }

     38: /*@
     39:     KSPQCGGetTrialStepNorm - Gets the norm of a trial step vector.  The WCG step may be
     40:     constrained, so this is not necessarily the length of the ultimate step taken in QCG.

     42:     Not Collective

     44:     Input Parameter:
     45: .   ksp - the iterative context

     47:     Output Parameter:
     48: .   tsnorm - the norm

     50:     Level: advanced
     51: @*/
     52: PetscErrorCode  KSPQCGGetTrialStepNorm(KSP ksp,PetscReal *tsnorm)
     53: {

     58:   PetscUseMethod(ksp,"KSPQCGGetTrialStepNorm_C",(KSP,PetscReal*),(ksp,tsnorm));
     59:   return(0);
     60: }

     64: /*@
     65:     KSPQCGGetQuadratic - Gets the value of the quadratic function, evaluated at the new iterate:

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

     69:     which satisfies the Euclidian Norm trust region constraint

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

     73:     where

     75:      delta is the trust region radius,
     76:      g is the gradient vector, and
     77:      H is Hessian matrix,
     78:      D is a scaling matrix.

     80:     Collective on KSP

     82:     Input Parameter:
     83: .   ksp - the iterative context

     85:     Output Parameter:
     86: .   quadratic - the quadratic function evaluated at the new iterate

     88:     Level: advanced
     89: @*/
     90: PetscErrorCode  KSPQCGGetQuadratic(KSP ksp,PetscReal *quadratic)
     91: {

     96:   PetscUseMethod(ksp,"KSPQCGGetQuadratic_C",(KSP,PetscReal*),(ksp,quadratic));
     97:   return(0);
     98: }

    103: PetscErrorCode KSPSolve_QCG(KSP ksp)
    104: {
    105: /*
    106:    Correpondence with documentation above:
    107:       B = g = gradient,
    108:       X = s = step
    109:    Note:  This is not coded correctly for complex arithmetic!
    110:  */

    112:   KSP_QCG        *pcgP = (KSP_QCG*)ksp->data;
    113:   Mat            Amat,Pmat;
    114:   Vec            W,WA,WA2,R,P,ASP,BS,X,B;
    115:   PetscScalar    scal,beta,rntrn,step;
    116:   PetscReal      q1,q2,xnorm,step1,step2,rnrm,btx,xtax;
    117:   PetscReal      ptasp,rtr,wtasp,bstp;
    118:   PetscReal      dzero = 0.0,bsnrm;
    120:   PetscInt       i,maxit;
    121:   PC             pc = ksp->pc;
    122:   PCSide         side;
    123:   PetscBool      diagonalscale;

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

    130:   ksp->its = 0;
    131:   maxit    = ksp->max_it;
    132:   WA       = ksp->work[0];
    133:   R        = ksp->work[1];
    134:   P        = ksp->work[2];
    135:   ASP      = ksp->work[3];
    136:   BS       = ksp->work[4];
    137:   W        = ksp->work[5];
    138:   WA2      = ksp->work[6];
    139:   X        = ksp->vec_sol;
    140:   B        = ksp->vec_rhs;

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

    146:   /* Initialize variables */
    147:   VecSet(W,0.0);  /* W = 0 */
    148:   VecSet(X,0.0);  /* X = 0 */
    149:   PCGetOperators(pc,&Amat,&Pmat);

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

    154:   VecNorm(BS,NORM_2,&bsnrm);
    155:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
    156:   ksp->its   = 0;
    157:   ksp->rnorm = bsnrm;
    158:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
    159:   KSPLogResidualHistory(ksp,bsnrm);
    160:   KSPMonitor(ksp,0,bsnrm);
    161:   (*ksp->converged)(ksp,0,bsnrm,&ksp->reason,ksp->cnvP);
    162:   if (ksp->reason) return(0);

    164:   /* Compute the initial scaled direction and scaled residual */
    165:   VecCopy(BS,R);
    166:   VecScale(R,-1.0);
    167:   VecCopy(R,P);
    168:   VecDotRealPart(R,R,&rtr);

    170:   for (i=0; i<=maxit; i++) {
    171:     PetscObjectSAWsTakeAccess((PetscObject)ksp);
    172:     ksp->its++;
    173:     PetscObjectSAWsGrantAccess((PetscObject)ksp);

    175:     /* Compute:  asp = D^{-T}*A*D^{-1}*p  */
    176:     PCApplySymmetricRight(pc,P,WA);
    177:     KSP_MatMult(ksp,Amat,WA,WA2);
    178:     PCApplySymmetricLeft(pc,WA2,ASP);

    180:     /* Check for negative curvature */
    181:     VecDotRealPart(P,ASP,&ptasp);
    182:     if (ptasp <= dzero) {

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

    187:       if (!i) {
    188:         VecCopy(P,X);
    189:         VecNorm(X,NORM_2,&xnorm);
    190:         scal = pcgP->delta / xnorm;
    191:         VecScale(X,scal);
    192:       } else {
    193:         /* Compute roots of quadratic */
    194:         KSPQCGQuadraticRoots(W,P,pcgP->delta,&step1,&step2);
    195:         VecDotRealPart(W,ASP,&wtasp);
    196:         VecDotRealPart(BS,P,&bstp);
    197:         VecCopy(W,X);
    198:         q1   = step1*(bstp + wtasp + .5*step1*ptasp);
    199:         q2   = step2*(bstp + wtasp + .5*step2*ptasp);
    200:         if (q1 <= q2) {
    201:           VecAXPY(X,step1,P);
    202:         } else {
    203:           VecAXPY(X,step2,P);
    204:         }
    205:       }
    206:       pcgP->ltsnrm = pcgP->delta;                       /* convergence in direction of */
    207:       ksp->reason  = KSP_CONVERGED_CG_NEG_CURVE;  /* negative curvature */
    208:       if (!i) {
    209:         PetscInfo1(ksp,"negative curvature: delta=%g\n",(double)pcgP->delta);
    210:       } else {
    211:         PetscInfo3(ksp,"negative curvature: step1=%g, step2=%g, delta=%g\n",(double)step1,(double)step2,(double)pcgP->delta);
    212:       }

    214:     } else {
    215:       /* Compute step along p */
    216:       step = rtr/ptasp;
    217:       VecCopy(W,X);        /*  x = w  */
    218:       VecAXPY(X,step,P);   /*  x <- step*p + x  */
    219:       VecNorm(X,NORM_2,&pcgP->ltsnrm);

    221:       if (pcgP->ltsnrm > pcgP->delta) {
    222:         /* Since the trial iterate is outside the trust region,
    223:             evaluate a constrained step along p so that
    224:                     ||w + step*p|| = delta
    225:           The positive step is always better in this case. */
    226:         if (!i) {
    227:           scal = pcgP->delta / pcgP->ltsnrm;
    228:           VecScale(X,scal);
    229:         } else {
    230:           /* Compute roots of quadratic */
    231:           KSPQCGQuadraticRoots(W,P,pcgP->delta,&step1,&step2);
    232:           VecCopy(W,X);
    233:           VecAXPY(X,step1,P);  /*  x <- step1*p + x  */
    234:         }
    235:         pcgP->ltsnrm = pcgP->delta;
    236:         ksp->reason  = KSP_CONVERGED_CG_CONSTRAINED; /* convergence along constrained step */
    237:         if (!i) {
    238:           PetscInfo1(ksp,"constrained step: delta=%g\n",(double)pcgP->delta);
    239:         } else {
    240:           PetscInfo3(ksp,"constrained step: step1=%g, step2=%g, delta=%g\n",(double)step1,(double)step2,(double)pcgP->delta);
    241:         }

    243:       } else {
    244:         /* Evaluate the current step */
    245:         VecCopy(X,W);  /* update interior iterate */
    246:         VecAXPY(R,-step,ASP); /* r <- -step*asp + r */
    247:         VecNorm(R,NORM_2,&rnrm);

    249:         PetscObjectSAWsTakeAccess((PetscObject)ksp);
    250:         ksp->rnorm = rnrm;
    251:         PetscObjectSAWsGrantAccess((PetscObject)ksp);
    252:         KSPLogResidualHistory(ksp,rnrm);
    253:         KSPMonitor(ksp,i+1,rnrm);
    254:         (*ksp->converged)(ksp,i+1,rnrm,&ksp->reason,ksp->cnvP);
    255:         if (ksp->reason) {                 /* convergence for */
    256:           PetscInfo3(ksp,"truncated step: step=%g, rnrm=%g, delta=%g\n",(double)PetscRealPart(step),(double)rnrm,(double)pcgP->delta);
    257:         }
    258:       }
    259:     }
    260:     if (ksp->reason) break;  /* Convergence has been attained */
    261:     else {                   /* Compute a new AS-orthogonal direction */
    262:       VecDot(R,R,&rntrn);
    263:       beta = rntrn/rtr;
    264:       VecAYPX(P,beta,R);  /*  p <- r + beta*p  */
    265:       rtr  = PetscRealPart(rntrn);
    266:     }
    267:   }
    268:   if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;

    270:   /* Unscale x */
    271:   VecCopy(X,WA2);
    272:   PCApplySymmetricRight(pc,WA2,X);

    274:   KSP_MatMult(ksp,Amat,X,WA);
    275:   VecDotRealPart(B,X,&btx);
    276:   VecDotRealPart(X,WA,&xtax);

    278:   pcgP->quadratic = btx + .5*xtax;
    279:   return(0);
    280: }

    284: PetscErrorCode KSPSetUp_QCG(KSP ksp)
    285: {

    289:   /* Get work vectors from user code */
    290:   KSPSetWorkVecs(ksp,7);
    291:   return(0);
    292: }

    296: PetscErrorCode KSPDestroy_QCG(KSP ksp)
    297: {

    301:   PetscObjectComposeFunction((PetscObject)ksp,"KSPQCGGetQuadratic_C",NULL);
    302:   PetscObjectComposeFunction((PetscObject)ksp,"KSPQCGGetTrialStepNorm_C",NULL);
    303:   PetscObjectComposeFunction((PetscObject)ksp,"KSPQCGSetTrustRegionRadius_C",NULL);
    304:   KSPDestroyDefault(ksp);
    305:   return(0);
    306: }

    310: static PetscErrorCode  KSPQCGSetTrustRegionRadius_QCG(KSP ksp,PetscReal delta)
    311: {
    312:   KSP_QCG *cgP = (KSP_QCG*)ksp->data;

    315:   cgP->delta = delta;
    316:   return(0);
    317: }

    321: static PetscErrorCode  KSPQCGGetTrialStepNorm_QCG(KSP ksp,PetscReal *ltsnrm)
    322: {
    323:   KSP_QCG *cgP = (KSP_QCG*)ksp->data;

    326:   *ltsnrm = cgP->ltsnrm;
    327:   return(0);
    328: }

    332: static PetscErrorCode  KSPQCGGetQuadratic_QCG(KSP ksp,PetscReal *quadratic)
    333: {
    334:   KSP_QCG *cgP = (KSP_QCG*)ksp->data;

    337:   *quadratic = cgP->quadratic;
    338:   return(0);
    339: }

    343: PetscErrorCode KSPSetFromOptions_QCG(PetscOptions *PetscOptionsObject,KSP ksp)
    344: {
    346:   PetscReal      delta;
    347:   KSP_QCG        *cgP = (KSP_QCG*)ksp->data;
    348:   PetscBool      flg;

    351:   PetscOptionsHead(PetscOptionsObject,"KSP QCG Options");
    352:   PetscOptionsReal("-ksp_qcg_trustregionradius","Trust Region Radius","KSPQCGSetTrustRegionRadius",cgP->delta,&delta,&flg);
    353:   if (flg) { KSPQCGSetTrustRegionRadius(ksp,delta); }
    354:   PetscOptionsTail();
    355:   return(0);
    356: }

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

    362:    Options Database Keys:
    363: .      -ksp_qcg_trustregionradius <r> - Trust Region Radius

    365:    Notes: This is rarely used directly

    367:    Level: developer

    369:   Notes:  Use preconditioned conjugate gradient to compute
    370:       an approximate minimizer of the quadratic function

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

    374:    subject to the Euclidean norm trust region constraint

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

    378:    where

    380:      delta is the trust region radius,
    381:      g is the gradient vector, and
    382:      H is Hessian matrix,
    383:      D is a scaling matrix.

    385:    KSPConvergedReason may be
    386: $  KSP_CONVERGED_CG_NEG_CURVE if convergence is reached along a negative curvature direction,
    387: $  KSP_CONVERGED_CG_CONSTRAINED if convergence is reached along a constrained step,
    388: $  other KSP converged/diverged reasons

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

    398:   References:
    399:    The Conjugate Gradient Method and Trust Regions in Large Scale Optimization, Trond Steihaug
    400:    SIAM Journal on Numerical Analysis, Vol. 20, No. 3 (Jun., 1983), pp. 626-637

    402: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPQCGSetTrustRegionRadius()
    403:            KSPQCGGetTrialStepNorm(), KSPQCGGetQuadratic()
    404: M*/

    408: PETSC_EXTERN PetscErrorCode KSPCreate_QCG(KSP ksp)
    409: {
    411:   KSP_QCG        *cgP;

    414:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_SYMMETRIC,3);
    415:   PetscNewLog(ksp,&cgP);

    417:   ksp->data                = (void*)cgP;
    418:   ksp->ops->setup          = KSPSetUp_QCG;
    419:   ksp->ops->setfromoptions = KSPSetFromOptions_QCG;
    420:   ksp->ops->solve          = KSPSolve_QCG;
    421:   ksp->ops->destroy        = KSPDestroy_QCG;
    422:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    423:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
    424:   ksp->ops->setfromoptions = 0;
    425:   ksp->ops->view           = 0;

    427:   PetscObjectComposeFunction((PetscObject)ksp,"KSPQCGGetQuadratic_C",KSPQCGGetQuadratic_QCG);
    428:   PetscObjectComposeFunction((PetscObject)ksp,"KSPQCGGetTrialStepNorm_C",KSPQCGGetTrialStepNorm_QCG);
    429:   PetscObjectComposeFunction((PetscObject)ksp,"KSPQCGSetTrustRegionRadius_C",KSPQCGSetTrustRegionRadius_QCG);
    430:   cgP->delta = PETSC_MAX_REAL; /* default trust region radius is infinite */
    431:   return(0);
    432: }

    434: /* ---------------------------------------------------------- */
    437: /*
    438:   KSPQCGQuadraticRoots - Computes the roots of the quadratic,
    439:          ||s + step*p|| - delta = 0
    440:    such that step1 >= 0 >= step2.
    441:    where
    442:       delta:
    443:         On entry delta must contain scalar delta.
    444:         On exit delta is unchanged.
    445:       step1:
    446:         On entry step1 need not be specified.
    447:         On exit step1 contains the non-negative root.
    448:       step2:
    449:         On entry step2 need not be specified.
    450:         On exit step2 contains the non-positive root.
    451:    C code is translated from the Fortran version of the MINPACK-2 Project,
    452:    Argonne National Laboratory, Brett M. Averick and Richard G. Carter.
    453: */
    454: static PetscErrorCode KSPQCGQuadraticRoots(Vec s,Vec p,PetscReal delta,PetscReal *step1,PetscReal *step2)
    455: {
    456:   PetscReal      dsq,ptp,pts,rad,sts;

    460:   VecDotRealPart(p,s,&pts);
    461:   VecDotRealPart(p,p,&ptp);
    462:   VecDotRealPart(s,s,&sts);
    463:   dsq  = delta*delta;
    464:   rad  = PetscSqrtReal((pts*pts) - ptp*(sts - dsq));
    465:   if (pts > 0.0) {
    466:     *step2 = -(pts + rad)/ptp;
    467:     *step1 = (sts - dsq)/(ptp * *step2);
    468:   } else {
    469:     *step1 = -(pts - rad)/ptp;
    470:     *step2 = (sts - dsq)/(ptp * *step1);
    471:   }
    472:   return(0);
    473: }