Date: 2022-03-04T17:39:02+00:00

Actual source code: groppcg.c

      1: #include <petsc/private/kspimpl.h>

      3: /*
      4:  KSPSetUp_GROPPCG - Sets up the workspace needed by the GROPPCG method.

      6:  This is called once, usually automatically by KSPSolve() or KSPSetUp()
      7:  but can be called directly by KSPSetUp()
      8: */
      9: static PetscErrorCode KSPSetUp_GROPPCG(KSP ksp)
     10: {

     14:   KSPSetWorkVecs(ksp,6);
     15:   return(0);
     16: }

     18: /*
     19:  KSPSolve_GROPPCG

     21:  Input Parameter:
     22:  .     ksp - the Krylov space object that was set to use conjugate gradient, by, for
     23:              example, KSPCreate(MPI_Comm,KSP *ksp); KSPSetType(ksp,KSPCG);
     24: */
     25: static PetscErrorCode  KSPSolve_GROPPCG(KSP ksp)
     26: {
     28:   PetscInt       i;
     29:   PetscScalar    alpha,beta = 0.0,gamma,gammaNew,t;
     30:   PetscReal      dp = 0.0;
     31:   Vec            x,b,r,p,s,S,z,Z;
     32:   Mat            Amat,Pmat;
     33:   PetscBool      diagonalscale;

     36:   PCGetDiagonalScale(ksp->pc,&diagonalscale);
     37:   if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);

     39:   x = ksp->vec_sol;
     40:   b = ksp->vec_rhs;
     41:   r = ksp->work[0];
     42:   p = ksp->work[1];
     43:   s = ksp->work[2];
     44:   S = ksp->work[3];
     45:   z = ksp->work[4];
     46:   Z = ksp->work[5];

     48:   PCGetOperators(ksp->pc,&Amat,&Pmat);

     50:   ksp->its = 0;
     51:   if (!ksp->guess_zero) {
     52:     KSP_MatMult(ksp,Amat,x,r);            /*     r <- b - Ax     */
     53:     VecAYPX(r,-1.0,b);
     54:   } else {
     55:     VecCopy(b,r);                         /*     r <- b (x is 0) */
     56:   }

     58:   KSP_PCApply(ksp,r,z);                   /*     z <- Br   */
     59:   VecCopy(z,p);                           /*     p <- z    */
     60:   VecDotBegin(r,z,&gamma);                  /*     gamma <- z'*r       */
     61:   PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)r));
     62:   KSP_MatMult(ksp,Amat,p,s);              /*     s <- Ap   */
     63:   VecDotEnd(r,z,&gamma);                  /*     gamma <- z'*r       */

     65:   switch (ksp->normtype) {
     66:   case KSP_NORM_PRECONDITIONED:
     67:     /* This could be merged with the computation of gamma above */
     68:     VecNorm(z,NORM_2,&dp);                /*     dp <- z'*z = e'*A'*B'*B*A'*e'     */
     69:     break;
     70:   case KSP_NORM_UNPRECONDITIONED:
     71:     /* This could be merged with the computation of gamma above */
     72:     VecNorm(r,NORM_2,&dp);                /*     dp <- r'*r = e'*A'*A*e            */
     73:     break;
     74:   case KSP_NORM_NATURAL:
     75:     KSPCheckDot(ksp,gamma);
     76:     dp = PetscSqrtReal(PetscAbsScalar(gamma));                  /*     dp <- r'*z = r'*B*r = e'*A'*B*A*e */
     77:     break;
     78:   case KSP_NORM_NONE:
     79:     dp = 0.0;
     80:     break;
     81:   default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
     82:   }
     83:   KSPLogResidualHistory(ksp,dp);
     84:   KSPMonitor(ksp,0,dp);
     85:   ksp->rnorm = dp;
     86:   (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP); /* test for convergence */
     87:   if (ksp->reason) return(0);

     89:   i = 0;
     90:   do {
     91:     ksp->its = i+1;
     92:     i++;

     94:     VecDotBegin(p,s,&t);
     95:     PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)p));

     97:     KSP_PCApply(ksp,s,S);         /*   S <- Bs       */

     99:     VecDotEnd(p,s,&t);

    101:     alpha = gamma / t;
    102:     VecAXPY(x, alpha,p);   /*     x <- x + alpha * p   */
    103:     VecAXPY(r,-alpha,s);   /*     r <- r - alpha * s   */
    104:     VecAXPY(z,-alpha,S);   /*     z <- z - alpha * S   */

    106:     if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
    107:       VecNormBegin(r,NORM_2,&dp);
    108:     } else if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
    109:       VecNormBegin(z,NORM_2,&dp);
    110:     }
    111:     VecDotBegin(r,z,&gammaNew);
    112:     PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)r));

    114:     KSP_MatMult(ksp,Amat,z,Z);      /*   Z <- Az       */

    116:     if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
    117:       VecNormEnd(r,NORM_2,&dp);
    118:     } else if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
    119:       VecNormEnd(z,NORM_2,&dp);
    120:     }
    121:     VecDotEnd(r,z,&gammaNew);

    123:     if (ksp->normtype == KSP_NORM_NATURAL) {
    124:       KSPCheckDot(ksp,gammaNew);
    125:       dp = PetscSqrtReal(PetscAbsScalar(gammaNew));                  /*     dp <- r'*z = r'*B*r = e'*A'*B*A*e */
    126:     } else if (ksp->normtype == KSP_NORM_NONE) {
    127:       dp = 0.0;
    128:     }
    129:     ksp->rnorm = dp;
    130:     KSPLogResidualHistory(ksp,dp);
    131:     KSPMonitor(ksp,i,dp);
    132:     (*ksp->converged)(ksp,i,dp,&ksp->reason,ksp->cnvP);
    133:     if (ksp->reason) return(0);

    135:     beta  = gammaNew / gamma;
    136:     gamma = gammaNew;
    137:     VecAYPX(p,beta,z);   /*     p <- z + beta * p   */
    138:     VecAYPX(s,beta,Z);   /*     s <- Z + beta * s   */

    140:   } while (i<ksp->max_it);

    142:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
    143:   return(0);
    144: }

    146: PETSC_INTERN PetscErrorCode KSPBuildResidual_CG(KSP,Vec,Vec,Vec*);

    148: /*MC
    149:    KSPGROPPCG - A pipelined conjugate gradient method from Bill Gropp

    151:    This method has two reductions, one of which is overlapped with the matrix-vector product and one of which is
    152:    overlapped with the preconditioner.

    154:    See also KSPPIPECG, which has only a single reduction that overlaps both the matrix-vector product and the preconditioner.

    156:    Level: intermediate

    158:    Notes:
    159:    MPI configuration may be necessary for reductions to make asynchronous progress, which is important for performance of pipelined methods.
    160:    See the FAQ on the PETSc website for details.

    162:    Contributed by:
    163:    Pieter Ghysels, Universiteit Antwerpen, Intel Exascience lab Flanders

    165:    Reference:
    166:    http://www.cs.uiuc.edu/~wgropp/bib/talks/tdata/2012/icerm.pdf

    168: .seealso: KSPCreate(), KSPSetType(), KSPPIPECG, KSPPIPECR, KSPPGMRES, KSPCG, KSPCGUseSingleReduction()
    169: M*/

    171: PETSC_EXTERN PetscErrorCode KSPCreate_GROPPCG(KSP ksp)
    172: {

    176:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,2);
    177:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,2);
    178:   KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,2);
    179:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);

    181:   ksp->ops->setup          = KSPSetUp_GROPPCG;
    182:   ksp->ops->solve          = KSPSolve_GROPPCG;
    183:   ksp->ops->destroy        = KSPDestroyDefault;
    184:   ksp->ops->view           = NULL;
    185:   ksp->ops->setfromoptions = NULL;
    186:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    187:   ksp->ops->buildresidual  = KSPBuildResidual_CG;
    188:   return(0);
    189: }