Date: 2021-03-03T22:27:22+00:00

Actual source code: pipecg.c
petsc-3.14.5 2021-03-03
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      2: #include <petsc/private/kspimpl.h>

      4: /*
      5:      KSPSetUp_PIPECG - Sets up the workspace needed by the PIPECG method.

      7:       This is called once, usually automatically by KSPSolve() or KSPSetUp()
      8:      but can be called directly by KSPSetUp()
      9: */
     10: static PetscErrorCode KSPSetUp_PIPECG(KSP ksp)
     11: {

     15:   /* get work vectors needed by PIPECG */
     16:   KSPSetWorkVecs(ksp,9);
     17:   return(0);
     18: }

     20: /*
     21:  KSPSolve_PIPECG - This routine actually applies the pipelined conjugate gradient method
     22: */
     23: static PetscErrorCode  KSPSolve_PIPECG(KSP ksp)
     24: {
     26:   PetscInt       i;
     27:   PetscScalar    alpha = 0.0,beta = 0.0,gamma = 0.0,gammaold = 0.0,delta = 0.0;
     28:   PetscReal      dp    = 0.0;
     29:   Vec            X,B,Z,P,W,Q,U,M,N,R,S;
     30:   Mat            Amat,Pmat;
     31:   PetscBool      diagonalscale;

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

     37:   X = ksp->vec_sol;
     38:   B = ksp->vec_rhs;
     39:   R = ksp->work[0];
     40:   Z = ksp->work[1];
     41:   P = ksp->work[2];
     42:   N = ksp->work[3];
     43:   W = ksp->work[4];
     44:   Q = ksp->work[5];
     45:   U = ksp->work[6];
     46:   M = ksp->work[7];
     47:   S = ksp->work[8];

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

     51:   ksp->its = 0;
     52:   if (!ksp->guess_zero) {
     53:     KSP_MatMult(ksp,Amat,X,R);            /*     r <- b - Ax     */
     54:     VecAYPX(R,-1.0,B);
     55:   } else {
     56:     VecCopy(B,R);                         /*     r <- b (x is 0) */
     57:   }

     59:   KSP_PCApply(ksp,R,U);                   /*     u <- Br   */

     61:   switch (ksp->normtype) {
     62:   case KSP_NORM_PRECONDITIONED:
     63:     VecNormBegin(U,NORM_2,&dp);                /*     dp <- u'*u = e'*A'*B'*B*A'*e'     */
     64:     PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)U));
     65:     KSP_MatMult(ksp,Amat,U,W);              /*     w <- Au   */
     66:     VecNormEnd(U,NORM_2,&dp);
     67:     break;
     68:   case KSP_NORM_UNPRECONDITIONED:
     69:     VecNormBegin(R,NORM_2,&dp);                /*     dp <- r'*r = e'*A'*A*e            */
     70:     PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)R));
     71:     KSP_MatMult(ksp,Amat,U,W);              /*     w <- Au   */
     72:     VecNormEnd(R,NORM_2,&dp);
     73:     break;
     74:   case KSP_NORM_NATURAL:
     75:     VecDotBegin(R,U,&gamma);                  /*     gamma <- u'*r       */
     76:     PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)R));
     77:     KSP_MatMult(ksp,Amat,U,W);              /*     w <- Au   */
     78:     VecDotEnd(R,U,&gamma);
     79:     KSPCheckDot(ksp,gamma);
     80:     dp = PetscSqrtReal(PetscAbsScalar(gamma));                  /*     dp <- r'*u = r'*B*r = e'*A'*B*A*e */
     81:     break;
     82:   case KSP_NORM_NONE:
     83:     KSP_MatMult(ksp,Amat,U,W);
     84:     dp   = 0.0;
     85:     break;
     86:   default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
     87:   }
     88:   KSPLogResidualHistory(ksp,dp);
     89:   KSPMonitor(ksp,0,dp);
     90:   ksp->rnorm = dp;
     91:   (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP); /* test for convergence */
     92:   if (ksp->reason) return(0);

     94:   i = 0;
     95:   do {
     96:     if (i > 0 && ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
     97:       VecNormBegin(R,NORM_2,&dp);
     98:     } else if (i > 0 && ksp->normtype == KSP_NORM_PRECONDITIONED) {
     99:       VecNormBegin(U,NORM_2,&dp);
    100:     }
    101:     if (!(i == 0 && ksp->normtype == KSP_NORM_NATURAL)) {
    102:       VecDotBegin(R,U,&gamma);
    103:     }
    104:     VecDotBegin(W,U,&delta);
    105:     PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)R));

    107:     KSP_PCApply(ksp,W,M);           /*   m <- Bw       */
    108:     KSP_MatMult(ksp,Amat,M,N);      /*   n <- Am       */

    110:     if (i > 0 && ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
    111:       VecNormEnd(R,NORM_2,&dp);
    112:     } else if (i > 0 && ksp->normtype == KSP_NORM_PRECONDITIONED) {
    113:       VecNormEnd(U,NORM_2,&dp);
    114:     }
    115:     if (!(i == 0 && ksp->normtype == KSP_NORM_NATURAL)) {
    116:       VecDotEnd(R,U,&gamma);
    117:     }
    118:     VecDotEnd(W,U,&delta);

    120:     if (i > 0) {
    121:       if (ksp->normtype == KSP_NORM_NATURAL) dp = PetscSqrtReal(PetscAbsScalar(gamma));
    122:       else if (ksp->normtype == KSP_NORM_NONE) dp = 0.0;

    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);
    129:     }

    131:     if (i == 0) {
    132:       alpha = gamma / delta;
    133:       VecCopy(N,Z);        /*     z <- n          */
    134:       VecCopy(M,Q);        /*     q <- m          */
    135:       VecCopy(U,P);        /*     p <- u          */
    136:       VecCopy(W,S);        /*     s <- w          */
    137:     } else {
    138:       beta  = gamma / gammaold;
    139:       alpha = gamma / (delta - beta / alpha * gamma);
    140:       VecAYPX(Z,beta,N);   /*     z <- n + beta * z   */
    141:       VecAYPX(Q,beta,M);   /*     q <- m + beta * q   */
    142:       VecAYPX(P,beta,U);   /*     p <- u + beta * p   */
    143:       VecAYPX(S,beta,W);   /*     s <- w + beta * s   */
    144:     }
    145:     VecAXPY(X, alpha,P); /*     x <- x + alpha * p   */
    146:     VecAXPY(U,-alpha,Q); /*     u <- u - alpha * q   */
    147:     VecAXPY(W,-alpha,Z); /*     w <- w - alpha * z   */
    148:     VecAXPY(R,-alpha,S); /*     r <- r - alpha * s   */
    149:     gammaold = gamma;
    150:     i++;
    151:     ksp->its = i;

    153:     /* if (i%50 == 0) { */
    154:     /*   KSP_MatMult(ksp,Amat,X,R);            /\*     w <- b - Ax     *\/ */
    155:     /*   VecAYPX(R,-1.0,B); */
    156:     /*   KSP_PCApply(ksp,R,U); */
    157:     /*   KSP_MatMult(ksp,Amat,U,W); */
    158:     /* } */

    160:   } while (i<=ksp->max_it);
    161:   if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
    162:   return(0);
    163: }

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

    167: /*MC
    168:    KSPPIPECG - Pipelined conjugate gradient method.

    170:    This method has only a single non-blocking reduction per iteration, compared to 2 blocking for standard CG.  The
    171:    non-blocking reduction is overlapped by the matrix-vector product and preconditioner application.

    173:    See also KSPPIPECR, where the reduction is only overlapped with the matrix-vector product.

    175:    Level: intermediate

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

    181:    Contributed by:
    182:    Pieter Ghysels, Universiteit Antwerpen, Intel Exascience lab Flanders

    184:    Reference:
    185:    P. Ghysels and W. Vanroose, "Hiding global synchronization latency in the preconditioned Conjugate Gradient algorithm",
    186:    Submitted to Parallel Computing, 2012.

    188: .seealso: KSPCreate(), KSPSetType(), KSPPIPECR, KSPGROPPCG, KSPPGMRES, KSPCG, KSPCGUseSingleReduction()
    189: M*/
    190: PETSC_EXTERN PetscErrorCode KSPCreate_PIPECG(KSP ksp)
    191: {

    195:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,2);
    196:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,2);
    197:   KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,2);
    198:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);

    200:   ksp->ops->setup          = KSPSetUp_PIPECG;
    201:   ksp->ops->solve          = KSPSolve_PIPECG;
    202:   ksp->ops->destroy        = KSPDestroyDefault;
    203:   ksp->ops->view           = NULL;
    204:   ksp->ops->setfromoptions = NULL;
    205:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    206:   ksp->ops->buildresidual  = KSPBuildResidual_CG;
    207:   return(0);
    208: }