Date: 2022-08-02T03:14:40+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: {
     11:   KSPSetWorkVecs(ksp,6);
     12:   return 0;
     13: }

     15: /*
     16:  KSPSolve_GROPPCG

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

     31:   PCGetDiagonalScale(ksp->pc,&diagonalscale);

     34:   x = ksp->vec_sol;
     35:   b = ksp->vec_rhs;
     36:   r = ksp->work[0];
     37:   p = ksp->work[1];
     38:   s = ksp->work[2];
     39:   S = ksp->work[3];
     40:   z = ksp->work[4];
     41:   Z = ksp->work[5];

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

     45:   ksp->its = 0;
     46:   if (!ksp->guess_zero) {
     47:     KSP_MatMult(ksp,Amat,x,r);            /*     r <- b - Ax     */
     48:     VecAYPX(r,-1.0,b);
     49:   } else {
     50:     VecCopy(b,r);                         /*     r <- b (x is 0) */
     51:   }

     53:   KSP_PCApply(ksp,r,z);                   /*     z <- Br   */
     54:   VecCopy(z,p);                           /*     p <- z    */
     55:   VecDotBegin(r,z,&gamma);                  /*     gamma <- z'*r       */
     56:   PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)r));
     57:   KSP_MatMult(ksp,Amat,p,s);              /*     s <- Ap   */
     58:   VecDotEnd(r,z,&gamma);                  /*     gamma <- z'*r       */

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

     84:   i = 0;
     85:   do {
     86:     ksp->its = i+1;
     87:     i++;

     89:     VecDotBegin(p,s,&t);
     90:     PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)p));

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

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

     96:     alpha = gamma / t;
     97:     VecAXPY(x, alpha,p);   /*     x <- x + alpha * p   */
     98:     VecAXPY(r,-alpha,s);   /*     r <- r - alpha * s   */
     99:     VecAXPY(z,-alpha,S);   /*     z <- z - alpha * S   */

    101:     if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
    102:       VecNormBegin(r,NORM_2,&dp);
    103:     } else if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
    104:       VecNormBegin(z,NORM_2,&dp);
    105:     }
    106:     VecDotBegin(r,z,&gammaNew);
    107:     PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)r));

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

    111:     if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
    112:       VecNormEnd(r,NORM_2,&dp);
    113:     } else if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
    114:       VecNormEnd(z,NORM_2,&dp);
    115:     }
    116:     VecDotEnd(r,z,&gammaNew);

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

    130:     beta  = gammaNew / gamma;
    131:     gamma = gammaNew;
    132:     VecAYPX(p,beta,z);   /*     p <- z + beta * p   */
    133:     VecAYPX(s,beta,Z);   /*     s <- Z + beta * s   */

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

    137:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
    138:   return 0;
    139: }

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

    143: /*MC
    144:    KSPGROPPCG - A pipelined conjugate gradient method from Bill Gropp

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

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

    151:    Level: intermediate

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

    157:    Contributed by:
    158:    Pieter Ghysels, Universiteit Antwerpen, Intel Exascience lab Flanders

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

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

    166: PETSC_EXTERN PetscErrorCode KSPCreate_GROPPCG(KSP ksp)
    167: {
    168:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,2);
    169:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,2);
    170:   KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,2);
    171:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);

    173:   ksp->ops->setup          = KSPSetUp_GROPPCG;
    174:   ksp->ops->solve          = KSPSolve_GROPPCG;
    175:   ksp->ops->destroy        = KSPDestroyDefault;
    176:   ksp->ops->view           = NULL;
    177:   ksp->ops->setfromoptions = NULL;
    178:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    179:   ksp->ops->buildresidual  = KSPBuildResidual_CG;
    180:   return 0;
    181: }