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

  3: /*
  4:      KSPSetUp_PIPECR - Sets up the workspace needed by the PIPECR method.

  6:       This is called once, usually automatically by KSPSolve() or KSPSetUp()
  7:      but can be called directly by KSPSetUp()
  8: */
 11: PetscErrorCode KSPSetUp_PIPECR(KSP ksp)
 12: {

 16:   /* get work vectors needed by PIPECR */
 17:   KSPSetWorkVecs(ksp,7);
 18:   return(0);
 19: }

 21: /*
 22:  KSPSolve_PIPECR - This routine actually applies the pipelined conjugate residual method

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

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

 57:   ksp->its = 0;
 58:   /* we don't have an R vector, so put the (unpreconditioned) residual in w for now */
 59:   if (!ksp->guess_zero) {
 60:     KSP_MatMult(ksp,Amat,X,W);            /*     w <- b - Ax     */
 61:     VecAYPX(W,-1.0,B);
 62:   } else {
 63:     VecCopy(B,W);                         /*     w <- b (x is 0) */
 64:   }
 65:   KSP_PCApply(ksp,W,U);                   /*     u <- Bw   */

 67:   switch (ksp->normtype) {
 68:   case KSP_NORM_PRECONDITIONED:
 69:     VecNormBegin(U,NORM_2,&dp);           /*     dp <- u'*u = e'*A'*B'*B*A'*e'     */
 70:     PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)U));
 71:     KSP_MatMult(ksp,Amat,U,W);            /*     w <- Au   */
 72:     VecNormEnd(U,NORM_2,&dp);
 73:     break;
 74:   case KSP_NORM_NONE:
 75:     KSP_MatMult(ksp,Amat,U,W);
 76:     dp   = 0.0;
 77:     break;
 78:   default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
 79:   }
 80:   KSPLogResidualHistory(ksp,dp);
 81:   KSPMonitor(ksp,0,dp);
 82:   ksp->rnorm = dp;
 83:   (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP); /* test for convergence */
 84:   if (ksp->reason) return(0);

 86:   i = 0;
 87:   do {
 88:     KSP_PCApply(ksp,W,M);            /*   m <- Bw       */

 90:     if (i > 0 && ksp->normtype == KSP_NORM_PRECONDITIONED) {
 91:       VecNormBegin(U,NORM_2,&dp);
 92:     }
 93:     VecDotBegin(W,U,&gamma);
 94:     VecDotBegin(M,W,&delta);
 95:     PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)U));

 97:     KSP_MatMult(ksp,Amat,M,N);       /*   n <- Am       */

 99:     if (i > 0 && ksp->normtype == KSP_NORM_PRECONDITIONED) {
100:       VecNormEnd(U,NORM_2,&dp);
101:     }
102:     VecDotEnd(W,U,&gamma);
103:     VecDotEnd(M,W,&delta);

105:     if (i > 0) {
106:       if (ksp->normtype == KSP_NORM_NONE) dp = 0.0;
107:       ksp->rnorm = dp;
108:       KSPLogResidualHistory(ksp,dp);
109:       KSPMonitor(ksp,i,dp);
110:       (*ksp->converged)(ksp,i,dp,&ksp->reason,ksp->cnvP);
111:       if (ksp->reason) break;
112:     }

114:     if (i == 0) {
115:       alpha = gamma / delta;
116:       VecCopy(N,Z);        /*     z <- n          */
117:       VecCopy(M,Q);        /*     q <- m          */
118:       VecCopy(U,P);        /*     p <- u          */
119:     } else {
120:       beta  = gamma / gammaold;
121:       alpha = gamma / (delta - beta / alpha * gamma);
122:       VecAYPX(Z,beta,N);   /*     z <- n + beta * z   */
123:       VecAYPX(Q,beta,M);   /*     q <- m + beta * q   */
124:       VecAYPX(P,beta,U);   /*     p <- u + beta * p   */
125:     }
126:     VecAXPY(X, alpha,P); /*     x <- x + alpha * p   */
127:     VecAXPY(U,-alpha,Q); /*     u <- u - alpha * q   */
128:     VecAXPY(W,-alpha,Z); /*     w <- w - alpha * z   */
129:     gammaold = gamma;
130:     i++;
131:     ksp->its = i;

133:     /* if (i%50 == 0) { */
134:     /*   KSP_MatMult(ksp,Amat,X,W);            /\*     w <- b - Ax     *\/ */
135:     /*   VecAYPX(W,-1.0,B); */
136:     /*   KSP_PCApply(ksp,W,U); */
137:     /*   KSP_MatMult(ksp,Amat,U,W); */
138:     /* } */

140:   } while (i<ksp->max_it);
141:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
142:   return(0);
143: }

145: /*MC
146:    KSPPIPECR - Pipelined conjugate residual method

148:    There method has only a single non-blocking reduction per iteration, compared to 2 blocking for standard CR.  The
149:    non-blocking reduction is overlapped by the matrix-vector product, but not preconditioner application.

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

153:    Level:
154:    beginner

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

160:    Contributed by:
161:    Pieter Ghysels, Universiteit Antwerpen, Intel Exascience lab Flanders

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

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

172: PETSC_EXTERN PetscErrorCode KSPCreate_PIPECR(KSP ksp)
173: {

177:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,1);
178:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);

180:   ksp->ops->setup          = KSPSetUp_PIPECR;
181:   ksp->ops->solve          = KSPSolve_PIPECR;
182:   ksp->ops->destroy        = KSPDestroyDefault;
183:   ksp->ops->view           = 0;
184:   ksp->ops->setfromoptions = 0;
185:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
186:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
187:   return(0);
188: }