Actual source code: cr.c

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

      4: static PetscErrorCode KSPSetUp_CR(KSP ksp)
      5: {

      9:   if (ksp->pc_side == PC_RIGHT) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"no right preconditioning for KSPCR");
     10:   else if (ksp->pc_side == PC_SYMMETRIC) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"no symmetric preconditioning for KSPCR");
     11:   KSPSetWorkVecs(ksp,6);
     12:   return(0);
     13: }

     15: static PetscErrorCode  KSPSolve_CR(KSP ksp)
     16: {
     18:   PetscInt       i = 0;
     19:   PetscReal      dp;
     20:   PetscScalar    ai, bi;
     21:   PetscScalar    apq,btop, bbot;
     22:   Vec            X,B,R,RT,P,AP,ART,Q;
     23:   Mat            Amat, Pmat;

     26:   X   = ksp->vec_sol;
     27:   B   = ksp->vec_rhs;
     28:   R   = ksp->work[0];
     29:   RT  = ksp->work[1];
     30:   P   = ksp->work[2];
     31:   AP  = ksp->work[3];
     32:   ART = ksp->work[4];
     33:   Q   = ksp->work[5];

     35:   /* R is the true residual norm, RT is the preconditioned residual norm */
     36:   PCGetOperators(ksp->pc,&Amat,&Pmat);
     37:   if (!ksp->guess_zero) {
     38:     KSP_MatMult(ksp,Amat,X,R);     /*   R <- A*X           */
     39:     VecAYPX(R,-1.0,B);            /*   R <- B-R == B-A*X  */
     40:   } else {
     41:     VecCopy(B,R);                  /*   R <- B (X is 0)    */
     42:   }
     43:   KSP_PCApply(ksp,R,P);     /*   P   <- B*R         */
     44:   KSP_MatMult(ksp,Amat,P,AP);      /*   AP  <- A*P         */
     45:   VecCopy(P,RT);                   /*   RT  <- P           */
     46:   VecCopy(AP,ART);                 /*   ART <- AP          */
     47:   VecDotBegin(RT,ART,&btop);          /*   (RT,ART)           */

     49:   if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
     50:     VecNormBegin(RT,NORM_2,&dp);        /*   dp <- RT'*RT       */
     51:     VecDotEnd   (RT,ART,&btop);           /*   (RT,ART)           */
     52:     VecNormEnd  (RT,NORM_2,&dp);        /*   dp <- RT'*RT       */
     53:     KSPCheckNorm(ksp,dp);
     54:   } else if (ksp->normtype == KSP_NORM_NONE) {
     55:     dp   = 0.0; /* meaningless value that is passed to monitor and convergence test */
     56:     VecDotEnd   (RT,ART,&btop);           /*   (RT,ART)           */
     57:   } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
     58:     VecNormBegin(R,NORM_2,&dp);         /*   dp <- R'*R         */
     59:     VecDotEnd   (RT,ART,&btop);          /*   (RT,ART)           */
     60:     VecNormEnd  (R,NORM_2,&dp);        /*   dp <- RT'*RT       */
     61:     KSPCheckNorm(ksp,dp);
     62:   } else if (ksp->normtype == KSP_NORM_NATURAL) {
     63:     VecDotEnd   (RT,ART,&btop);           /*   (RT,ART)           */
     64:     dp   = PetscSqrtReal(PetscAbsScalar(btop));                  /* dp = sqrt(R,AR)      */
     65:   } else SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"KSPNormType of %d not supported",(int)ksp->normtype);
     66:   if (PetscAbsScalar(btop) < 0.0) {
     67:     ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
     68:     PetscInfo(ksp,"diverging due to indefinite or negative definite matrix\n");
     69:     return(0);
     70:   }

     72:   ksp->its   = 0;
     73:   KSPMonitor(ksp,0,dp);
     74:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
     75:   ksp->rnorm = dp;
     76:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
     77:   KSPLogResidualHistory(ksp,dp);
     78:   (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP);
     79:   if (ksp->reason) return(0);

     81:   i = 0;
     82:   do {
     83:     KSP_PCApply(ksp,AP,Q);  /*   Q <- B* AP          */

     85:     VecDot(AP,Q,&apq);
     86:     KSPCheckDot(ksp,apq);
     87:     if (PetscRealPart(apq) <= 0.0) {
     88:       ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
     89:       PetscInfo(ksp,"KSPSolve_CR:diverging due to indefinite or negative definite PC\n");
     90:       break;
     91:     }
     92:     ai = btop/apq;                                      /* ai = (RT,ART)/(AP,Q)  */

     94:     VecAXPY(X,ai,P);              /*   X   <- X + ai*P     */
     95:     VecAXPY(RT,-ai,Q);             /*   RT  <- RT - ai*Q    */
     96:     KSP_MatMult(ksp,Amat,RT,ART);  /*   ART <-   A*RT       */
     97:     bbot = btop;
     98:     VecDotBegin(RT,ART,&btop);

    100:     if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
    101:       VecNormBegin(RT,NORM_2,&dp);      /*   dp <- || RT ||      */
    102:       VecDotEnd   (RT,ART,&btop);
    103:       VecNormEnd  (RT,NORM_2,&dp);      /*   dp <- || RT ||      */
    104:       KSPCheckNorm(ksp,dp);
    105:     } else if (ksp->normtype == KSP_NORM_NATURAL) {
    106:       VecDotEnd(RT,ART,&btop);
    107:       dp   = PetscSqrtReal(PetscAbsScalar(btop));                /* dp = sqrt(R,AR)       */
    108:     } else if (ksp->normtype == KSP_NORM_NONE) {
    109:       VecDotEnd(RT,ART,&btop);
    110:       dp   = 0.0; /* meaningless value that is passed to monitor and convergence test */
    111:     } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
    112:       VecAXPY(R,ai,AP);           /*   R   <- R - ai*AP    */
    113:       VecNormBegin(R,NORM_2,&dp);       /*   dp <- R'*R          */
    114:       VecDotEnd   (RT,ART,&btop);
    115:       VecNormEnd  (R,NORM_2,&dp);       /*   dp <- R'*R          */
    116:       KSPCheckNorm(ksp,dp);
    117:     } else SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"KSPNormType of %d not supported",(int)ksp->normtype);
    118:     if (PetscAbsScalar(btop) < 0.0) {
    119:       ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
    120:       PetscInfo(ksp,"diverging due to indefinite or negative definite PC\n");
    121:       break;
    122:     }

    124:     PetscObjectSAWsTakeAccess((PetscObject)ksp);
    125:     ksp->its++;
    126:     ksp->rnorm = dp;
    127:     PetscObjectSAWsGrantAccess((PetscObject)ksp);

    129:     KSPLogResidualHistory(ksp,dp);
    130:     KSPMonitor(ksp,i+1,dp);
    131:     (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
    132:     if (ksp->reason) break;

    134:     bi   = btop/bbot;
    135:     VecAYPX(P,bi,RT);              /*   P <- RT + Bi P     */
    136:     VecAYPX(AP,bi,ART);            /*   AP <- ART + Bi AP  */
    137:     i++;
    138:   } while (i<ksp->max_it);
    139:   if (i >= ksp->max_it) ksp->reason =  KSP_DIVERGED_ITS;
    140:   return(0);
    141: }

    144: /*MC
    145:      KSPCR - This code implements the (preconditioned) conjugate residuals method

    147:    Options Database Keys:
    148: .   see KSPSolve()

    150:    Level: beginner

    152:    Notes:
    153:     The operator and the preconditioner must be symmetric for this method. The
    154:           preconditioner must be POSITIVE-DEFINITE and the operator POSITIVE-SEMIDEFINITE.
    155:           Support only for left preconditioning.

    157:    References:
    158: .   1. - Magnus R. Hestenes and Eduard Stiefel, Methods of Conjugate Gradients for Solving Linear Systems,
    159:    Journal of Research of the National Bureau of Standards Vol. 49, No. 6, December 1952 Research Paper 2379

    161: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPCG
    162: M*/
    163: PETSC_EXTERN PetscErrorCode KSPCreate_CR(KSP ksp)
    164: {

    168:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    169:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,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_CR;
    174:   ksp->ops->solve          = KSPSolve_CR;
    175:   ksp->ops->destroy        = KSPDestroyDefault;
    176:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    177:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
    178:   ksp->ops->setfromoptions = NULL;
    179:   ksp->ops->view           = NULL;
    180:   return(0);
    181: }