Date: 2015-10-02T22:21:06+00:00

Actual source code: pipecg.c
petsc-3.6.2 2015-10-02
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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: */
     12: PetscErrorCode KSPSetUp_PIPECG(KSP ksp)
     13: {

     17:   /* get work vectors needed by PIPECG */
     18:   KSPSetWorkVecs(ksp,9);
     19:   return(0);
     20: }

     22: /*
     23:  KSPSolve_PIPECG - This routine actually applies the pipelined conjugate gradient method

     25:  Input Parameter:
     26:  .     ksp - the Krylov space object that was set to use conjugate gradient, by, for
     27:              example, KSPCreate(MPI_Comm,KSP *ksp); KSPSetType(ksp,KSPCG);
     28: */
     31: PetscErrorCode  KSPSolve_PIPECG(KSP ksp)
     32: {
     34:   PetscInt       i;
     35:   PetscScalar    alpha = 0.0,beta = 0.0,gamma = 0.0,gammaold = 0.0,delta = 0.0;
     36:   PetscReal      dp    = 0.0;
     37:   Vec            X,B,Z,P,W,Q,U,M,N,R,S;
     38:   Mat            Amat,Pmat;
     39:   PetscBool      diagonalscale;

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

     45:   X = ksp->vec_sol;
     46:   B = ksp->vec_rhs;
     47:   M = ksp->work[0];
     48:   Z = ksp->work[1];
     49:   P = ksp->work[2];
     50:   N = ksp->work[3];
     51:   W = ksp->work[4];
     52:   Q = ksp->work[5];
     53:   U = ksp->work[6];
     54:   R = ksp->work[7];
     55:   S = ksp->work[8];

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

     59:   ksp->its = 0;
     60:   if (!ksp->guess_zero) {
     61:     KSP_MatMult(ksp,Amat,X,R);            /*     r <- b - Ax     */
     62:     VecAYPX(R,-1.0,B);
     63:   } else {
     64:     VecCopy(B,R);                         /*     r <- b (x is 0) */
     65:   }

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

     69:   switch (ksp->normtype) {
     70:   case KSP_NORM_PRECONDITIONED:
     71:     VecNormBegin(U,NORM_2,&dp);                /*     dp <- u'*u = e'*A'*B'*B*A'*e'     */
     72:     PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)U));
     73:     KSP_MatMult(ksp,Amat,U,W);              /*     w <- Au   */
     74:     VecNormEnd(U,NORM_2,&dp);
     75:     break;
     76:   case KSP_NORM_UNPRECONDITIONED:
     77:     VecNormBegin(R,NORM_2,&dp);                /*     dp <- r'*r = e'*A'*A*e            */
     78:     PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)R));
     79:     KSP_MatMult(ksp,Amat,U,W);              /*     w <- Au   */
     80:     VecNormEnd(R,NORM_2,&dp);
     81:     break;
     82:   case KSP_NORM_NATURAL:
     83:     VecDotBegin(R,U,&gamma);                  /*     gamma <- u'*r       */
     84:     PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)R));
     85:     KSP_MatMult(ksp,Amat,U,W);              /*     w <- Au   */
     86:     VecDotEnd(R,U,&gamma);
     87:     KSPCheckDot(ksp,gamma);
     88:     dp = PetscSqrtReal(PetscAbsScalar(gamma));                  /*     dp <- r'*u = r'*B*r = e'*A'*B*A*e */
     89:     break;
     90:   case KSP_NORM_NONE:
     91:     KSP_MatMult(ksp,Amat,U,W);
     92:     dp   = 0.0;
     93:     break;
     94:   default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
     95:   }
     96:   KSPLogResidualHistory(ksp,dp);
     97:   KSPMonitor(ksp,0,dp);
     98:   ksp->rnorm = dp;
     99:   (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP); /* test for convergence */
    100:   if (ksp->reason) return(0);

    102:   i = 0;
    103:   do {
    104:     if (i > 0 && ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
    105:       VecNormBegin(R,NORM_2,&dp);
    106:     } else if (i > 0 && ksp->normtype == KSP_NORM_PRECONDITIONED) {
    107:       VecNormBegin(U,NORM_2,&dp);
    108:     }
    109:     if (!(i == 0 && ksp->normtype == KSP_NORM_NATURAL)) {
    110:       VecDotBegin(R,U,&gamma);
    111:     }
    112:     VecDotBegin(W,U,&delta);
    113:     PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)R));

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

    118:     if (i > 0 && ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
    119:       VecNormEnd(R,NORM_2,&dp);
    120:     } else if (i > 0 && ksp->normtype == KSP_NORM_PRECONDITIONED) {
    121:       VecNormEnd(U,NORM_2,&dp);
    122:     }
    123:     if (!(i == 0 && ksp->normtype == KSP_NORM_NATURAL)) {
    124:       VecDotEnd(R,U,&gamma);
    125:     }
    126:     VecDotEnd(W,U,&delta);

    128:     if (i > 0) {
    129:       if (ksp->normtype == KSP_NORM_NATURAL) dp = PetscSqrtReal(PetscAbsScalar(gamma));
    130:       else if (ksp->normtype == KSP_NORM_NONE) dp = 0.0;

    132:       ksp->rnorm = dp;
    133:       KSPLogResidualHistory(ksp,dp);
    134:       KSPMonitor(ksp,i,dp);
    135:       (*ksp->converged)(ksp,i,dp,&ksp->reason,ksp->cnvP);
    136:       if (ksp->reason) break;
    137:     }

    139:     if (i == 0) {
    140:       alpha = gamma / delta;
    141:       VecCopy(N,Z);        /*     z <- n          */
    142:       VecCopy(M,Q);        /*     q <- m          */
    143:       VecCopy(U,P);        /*     p <- u          */
    144:       VecCopy(W,S);        /*     s <- w          */
    145:     } else {
    146:       beta  = gamma / gammaold;
    147:       alpha = gamma / (delta - beta / alpha * gamma);
    148:       VecAYPX(Z,beta,N);   /*     z <- n + beta * z   */
    149:       VecAYPX(Q,beta,M);   /*     q <- m + beta * q   */
    150:       VecAYPX(P,beta,U);   /*     p <- u + beta * p   */
    151:       VecAYPX(S,beta,W);   /*     s <- w + beta * s   */
    152:     }
    153:     VecAXPY(X, alpha,P); /*     x <- x + alpha * p   */
    154:     VecAXPY(U,-alpha,Q); /*     u <- u - alpha * q   */
    155:     VecAXPY(W,-alpha,Z); /*     w <- w - alpha * z   */
    156:     VecAXPY(R,-alpha,S); /*     r <- r - alpha * s   */
    157:     gammaold = gamma;
    158:     i++;
    159:     ksp->its = i;

    161:     /* if (i%50 == 0) { */
    162:     /*   KSP_MatMult(ksp,Amat,X,R);            /\*     w <- b - Ax     *\/ */
    163:     /*   VecAYPX(R,-1.0,B); */
    164:     /*   KSP_PCApply(ksp,R,U); */
    165:     /*   KSP_MatMult(ksp,Amat,U,W); */
    166:     /* } */

    168:   } while (i<ksp->max_it);
    169:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
    170:   return(0);
    171: }

    174: /*MC
    175:    KSPPIPECG - Pipelined conjugate gradient method.

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

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

    182:    Level: intermediate

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

    188:    Contributed by:
    189:    Pieter Ghysels, Universiteit Antwerpen, Intel Exascience lab Flanders

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

    195: .seealso: KSPCreate(), KSPSetType(), KSPPIPECR, KSPGROPPCG, KSPPGMRES, KSPCG, KSPCGUseSingleReduction()
    196: M*/
    199: PETSC_EXTERN PetscErrorCode KSPCreate_PIPECG(KSP ksp)
    200: {

    204:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,2);
    205:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,2);
    206:   KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,2);
    207:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,2);

    209:   ksp->ops->setup          = KSPSetUp_PIPECG;
    210:   ksp->ops->solve          = KSPSolve_PIPECG;
    211:   ksp->ops->destroy        = KSPDestroyDefault;
    212:   ksp->ops->view           = 0;
    213:   ksp->ops->setfromoptions = 0;
    214:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    215:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
    216:   return(0);
    217: }