Actual source code: cg.c

      2: /*
      3:     This file implements the conjugate gradient method in PETSc as part of
      4:     KSP. You can use this as a starting point for implementing your own
      5:     Krylov method that is not provided with PETSc.

      7:     The following basic routines are required for each Krylov method.
      8:         KSPCreate_XXX()          - Creates the Krylov context
      9:         KSPSetFromOptions_XXX()  - Sets runtime options
     10:         KSPSolve_XXX()           - Runs the Krylov method
     11:         KSPDestroy_XXX()         - Destroys the Krylov context, freeing all
     12:                                    memory it needed
     13:     Here the "_XXX" denotes a particular implementation, in this case
     14:     we use _CG (e.g. KSPCreate_CG, KSPDestroy_CG). These routines
     15:     are actually called via the common user interface routines
     16:     KSPSetType(), KSPSetFromOptions(), KSPSolve(), and KSPDestroy() so the
     17:     application code interface remains identical for all preconditioners.

     19:     Other basic routines for the KSP objects include
     20:         KSPSetUp_XXX()
     21:         KSPView_XXX()            - Prints details of solver being used.

     23:     Detailed Notes:
     24:     By default, this code implements the CG (Conjugate Gradient) method,
     25:     which is valid for real symmetric (and complex Hermitian) positive
     26:     definite matrices. Note that for the complex Hermitian case, the
     27:     VecDot() arguments within the code MUST remain in the order given
     28:     for correct computation of inner products.

     30:     Reference: Hestenes and Steifel, 1952.

     32:     By switching to the indefinite vector inner product, VecTDot(), the
     33:     same code is used for the complex symmetric case as well.  The user
     34:     must call KSPCGSetType(ksp,KSP_CG_SYMMETRIC) or use the option
     35:     -ksp_cg_type symmetric to invoke this variant for the complex case.
     36:     Note, however, that the complex symmetric code is NOT valid for
     37:     all such matrices ... and thus we don't recommend using this method.
     38: */
     39: /*
     40:     cgimpl.h defines the simple data structured used to store information
     41:     related to the type of matrix (e.g. complex symmetric) being solved and
     42:     data used during the optional Lanczo process used to compute eigenvalues
     43: */
     44: #include <../src/ksp/ksp/impls/cg/cgimpl.h>
     45: extern PetscErrorCode KSPComputeExtremeSingularValues_CG(KSP,PetscReal*,PetscReal*);
     46: extern PetscErrorCode KSPComputeEigenvalues_CG(KSP,PetscInt,PetscReal*,PetscReal*,PetscInt*);

     48: /*
     49:      KSPSetUp_CG - Sets up the workspace needed by the CG method.

     51:       This is called once, usually automatically by KSPSolve() or KSPSetUp()
     52:      but can be called directly by KSPSetUp()
     53: */
     54: static PetscErrorCode KSPSetUp_CG(KSP ksp)
     55: {
     56:   KSP_CG         *cgP = (KSP_CG*)ksp->data;
     58:   PetscInt       maxit = ksp->max_it,nwork = 3;

     61:   /* get work vectors needed by CG */
     62:   if (cgP->singlereduction) nwork += 2;
     63:   KSPSetWorkVecs(ksp,nwork);

     65:   /*
     66:      If user requested computations of eigenvalues then allocate
     67:      work space needed
     68:   */
     69:   if (ksp->calc_sings) {
     70:     PetscFree4(cgP->e,cgP->d,cgP->ee,cgP->dd);
     71:     PetscMalloc4(maxit+1,&cgP->e,maxit+1,&cgP->d,maxit+1,&cgP->ee,maxit+1,&cgP->dd);
     72:     PetscLogObjectMemory((PetscObject)ksp,2*(maxit+1)*(sizeof(PetscScalar)+sizeof(PetscReal)));

     74:     ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_CG;
     75:     ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_CG;
     76:   }
     77:   return(0);
     78: }

     80: /*
     81:      A macro used in the following KSPSolve_CG and KSPSolve_CG_SingleReduction routines
     82: */
     83: #define VecXDot(x,y,a) (((cg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x,y,a) : VecTDot(x,y,a))

     85: /*
     86:      KSPSolve_CG - This routine actually applies the conjugate gradient method

     88:      Note : this routine can be replaced with another one (see below) which implements
     89:             another variant of CG.

     91:    Input Parameter:
     92: .     ksp - the Krylov space object that was set to use conjugate gradient, by, for
     93:             example, KSPCreate(MPI_Comm,KSP *ksp); KSPSetType(ksp,KSPCG);
     94: */
     95: static PetscErrorCode KSPSolve_CG(KSP ksp)
     96: {
     98:   PetscInt       i,stored_max_it,eigs;
     99:   PetscScalar    dpi = 0.0,a = 1.0,beta,betaold = 1.0,b = 0,*e = NULL,*d = NULL,dpiold;
    100:   PetscReal      dp  = 0.0;
    101:   Vec            X,B,Z,R,P,W;
    102:   KSP_CG         *cg;
    103:   Mat            Amat,Pmat;
    104:   PetscBool      diagonalscale;

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

    110:   cg            = (KSP_CG*)ksp->data;
    111:   eigs          = ksp->calc_sings;
    112:   stored_max_it = ksp->max_it;
    113:   X             = ksp->vec_sol;
    114:   B             = ksp->vec_rhs;
    115:   R             = ksp->work[0];
    116:   Z             = ksp->work[1];
    117:   P             = ksp->work[2];
    118:   W             = Z;

    120:   if (eigs) {e = cg->e; d = cg->d; e[0] = 0.0; }
    121:   PCGetOperators(ksp->pc,&Amat,&Pmat);

    123:   ksp->its = 0;
    124:   if (!ksp->guess_zero) {
    125:     KSP_MatMult(ksp,Amat,X,R);            /*    r <- b - Ax                       */
    126:     VecAYPX(R,-1.0,B);
    127:   } else {
    128:     VecCopy(B,R);                         /*    r <- b (x is 0)                   */
    129:   }

    131:   switch (ksp->normtype) {
    132:     case KSP_NORM_PRECONDITIONED:
    133:       KSP_PCApply(ksp,R,Z);               /*    z <- Br                           */
    134:       VecNorm(Z,NORM_2,&dp);              /*    dp <- z'*z = e'*A'*B'*B*A*e       */
    135:       KSPCheckNorm(ksp,dp);
    136:       break;
    137:     case KSP_NORM_UNPRECONDITIONED:
    138:       VecNorm(R,NORM_2,&dp);              /*    dp <- r'*r = e'*A'*A*e            */
    139:       KSPCheckNorm(ksp,dp);
    140:       break;
    141:     case KSP_NORM_NATURAL:
    142:       KSP_PCApply(ksp,R,Z);               /*    z <- Br                           */
    143:       VecXDot(Z,R,&beta);                 /*    beta <- z'*r                      */
    144:       KSPCheckDot(ksp,beta);
    145:       dp = PetscSqrtReal(PetscAbsScalar(beta));                /*    dp <- r'*z = r'*B*r = e'*A'*B*A*e */
    146:       break;
    147:     case KSP_NORM_NONE:
    148:       dp = 0.0;
    149:       break;
    150:     default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
    151:   }
    152:   KSPLogResidualHistory(ksp,dp);
    153:   KSPMonitor(ksp,0,dp);
    154:   ksp->rnorm = dp;

    156:   (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP);     /* test for convergence */
    157:   if (ksp->reason) return(0);

    159:   if (ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) {
    160:     KSP_PCApply(ksp,R,Z);                /*     z <- Br                           */
    161:   }
    162:   if (ksp->normtype != KSP_NORM_NATURAL) {
    163:     VecXDot(Z,R,&beta);                  /*     beta <- z'*r                      */
    164:     KSPCheckDot(ksp,beta);
    165:   }

    167:   i = 0;
    168:   do {
    169:     ksp->its = i+1;
    170:     if (beta == 0.0) {
    171:       ksp->reason = KSP_CONVERGED_ATOL;
    172:       PetscInfo(ksp,"converged due to beta = 0\n");
    173:       break;
    174: #if !defined(PETSC_USE_COMPLEX)
    175:     } else if ((i > 0) && (beta*betaold < 0.0)) {
    176:       if (ksp->errorifnotconverged) SETERRQ2(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"Diverged due to indefinite preconditioner, beta %g, betaold %g",(double)beta,(double)betaold);
    177:       ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
    178:       PetscInfo(ksp,"diverging due to indefinite preconditioner\n");
    179:       break;
    180: #endif
    181:     }
    182:     if (!i) {
    183:       VecCopy(Z,P);                       /*     p <- z                           */
    184:       b    = 0.0;
    185:     } else {
    186:       b = beta/betaold;
    187:       if (eigs) {
    188:         if (ksp->max_it != stored_max_it) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Can not change maxit AND calculate eigenvalues");
    189:         e[i] = PetscSqrtReal(PetscAbsScalar(b))/a;
    190:       }
    191:       VecAYPX(P,b,Z);                     /*     p <- z + b* p                    */
    192:     }
    193:     dpiold = dpi;
    194:     KSP_MatMult(ksp,Amat,P,W);            /*     w <- Ap                          */
    195:     VecXDot(P,W,&dpi);                    /*     dpi <- p'w                       */
    196:     KSPCheckDot(ksp,dpi);
    197:     betaold = beta;

    199:     if ((dpi == 0.0) || ((i > 0) && ((PetscSign(PetscRealPart(dpi))*PetscSign(PetscRealPart(dpiold))) < 0.0))) {
    200:       if (ksp->errorifnotconverged) SETERRQ2(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"Diverged due to indefinite matrix, dpi %g, dpiold %g",(double)PetscRealPart(dpi),(double)PetscRealPart(dpiold));
    201:       ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
    202:       PetscInfo(ksp,"diverging due to indefinite or negative definite matrix\n");
    203:       break;
    204:     }
    205:     a = beta/dpi;                                              /*     a = beta/p'w                     */
    206:     if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b))*e[i] + 1.0/a;
    207:     VecAXPY(X,a,P);                       /*     x <- x + ap                      */
    208:     VecAXPY(R,-a,W);                      /*     r <- r - aw                      */
    209:     if (ksp->normtype == KSP_NORM_PRECONDITIONED && ksp->chknorm < i+2) {
    210:       KSP_PCApply(ksp,R,Z);               /*     z <- Br                          */
    211:       VecNorm(Z,NORM_2,&dp);              /*     dp <- z'*z                       */
    212:       KSPCheckNorm(ksp,dp);
    213:     } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED && ksp->chknorm < i+2) {
    214:       VecNorm(R,NORM_2,&dp);              /*     dp <- r'*r                       */
    215:       KSPCheckNorm(ksp,dp);
    216:     } else if (ksp->normtype == KSP_NORM_NATURAL) {
    217:       KSP_PCApply(ksp,R,Z);               /*     z <- Br                          */
    218:       VecXDot(Z,R,&beta);                 /*     beta <- r'*z                     */
    219:       KSPCheckDot(ksp,beta);
    220:       dp = PetscSqrtReal(PetscAbsScalar(beta));
    221:     } else {
    222:       dp = 0.0;
    223:     }
    224:     ksp->rnorm = dp;
    225:     KSPLogResidualHistory(ksp,dp);
    226:     if (eigs) cg->ned = ksp->its;
    227:     KSPMonitor(ksp,i+1,dp);
    228:     (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
    229:     if (ksp->reason) break;

    231:     if ((ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) || (ksp->chknorm >= i+2)) {
    232:       KSP_PCApply(ksp,R,Z);               /*     z <- Br                          */
    233:     }
    234:     if ((ksp->normtype != KSP_NORM_NATURAL) || (ksp->chknorm >= i+2)) {
    235:       VecXDot(Z,R,&beta);                 /*     beta <- z'*r                     */
    236:       KSPCheckDot(ksp,beta);
    237:     }

    239:     i++;
    240:   } while (i<ksp->max_it);
    241:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
    242:   return(0);
    243: }

    245: /*
    246:        KSPSolve_CG_SingleReduction

    248:        This variant of CG is identical in exact arithmetic to the standard algorithm,
    249:        but is rearranged to use only a single reduction stage per iteration, using additional
    250:        intermediate vectors.

    252:        See KSPCGUseSingleReduction_CG()

    254: */
    255: static PetscErrorCode KSPSolve_CG_SingleReduction(KSP ksp)
    256: {
    258:   PetscInt       i,stored_max_it,eigs;
    259:   PetscScalar    dpi = 0.0,a = 1.0,beta,betaold = 1.0,b = 0,*e = NULL,*d = NULL,delta,dpiold,tmp[2];
    260:   PetscReal      dp  = 0.0;
    261:   Vec            X,B,Z,R,P,S,W,tmpvecs[2];
    262:   KSP_CG         *cg;
    263:   Mat            Amat,Pmat;
    264:   PetscBool      diagonalscale;

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

    270:   cg            = (KSP_CG*)ksp->data;
    271:   eigs          = ksp->calc_sings;
    272:   stored_max_it = ksp->max_it;
    273:   X             = ksp->vec_sol;
    274:   B             = ksp->vec_rhs;
    275:   R             = ksp->work[0];
    276:   Z             = ksp->work[1];
    277:   P             = ksp->work[2];
    278:   S             = ksp->work[3];
    279:   W             = ksp->work[4];

    281:   if (eigs) {e = cg->e; d = cg->d; e[0] = 0.0; }
    282:   PCGetOperators(ksp->pc,&Amat,&Pmat);

    284:   ksp->its = 0;
    285:   if (!ksp->guess_zero) {
    286:     KSP_MatMult(ksp,Amat,X,R);            /*    r <- b - Ax                       */
    287:     VecAYPX(R,-1.0,B);
    288:   } else {
    289:     VecCopy(B,R);                         /*    r <- b (x is 0)                   */
    290:   }

    292:   switch (ksp->normtype) {
    293:     case KSP_NORM_PRECONDITIONED:
    294:       KSP_PCApply(ksp,R,Z);               /*    z <- Br                           */
    295:       VecNorm(Z,NORM_2,&dp);              /*    dp <- z'*z = e'*A'*B'*B*A'*e'     */
    296:       KSPCheckNorm(ksp,dp);
    297:       break;
    298:     case KSP_NORM_UNPRECONDITIONED:
    299:       VecNorm(R,NORM_2,&dp);              /*    dp <- r'*r = e'*A'*A*e            */
    300:       KSPCheckNorm(ksp,dp);
    301:       break;
    302:     case KSP_NORM_NATURAL:
    303:       KSP_PCApply(ksp,R,Z);               /*    z <- Br                           */
    304:       KSP_MatMult(ksp,Amat,Z,S);
    305:       VecXDot(Z,S,&delta);                /*    delta <- z'*A*z = r'*B*A*B*r      */
    306:       VecXDot(Z,R,&beta);                 /*    beta <- z'*r                      */
    307:       KSPCheckDot(ksp,beta);
    308:       dp = PetscSqrtReal(PetscAbsScalar(beta));                /*    dp <- r'*z = r'*B*r = e'*A'*B*A*e */
    309:       break;
    310:     case KSP_NORM_NONE:
    311:       dp = 0.0;
    312:       break;
    313:     default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
    314:   }
    315:   KSPLogResidualHistory(ksp,dp);
    316:   KSPMonitor(ksp,0,dp);
    317:   ksp->rnorm = dp;

    319:   (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP);     /* test for convergence */
    320:   if (ksp->reason) return(0);

    322:   if (ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) {
    323:     KSP_PCApply(ksp,R,Z);                 /*    z <- Br                           */
    324:   }
    325:   if (ksp->normtype != KSP_NORM_NATURAL) {
    326:     KSP_MatMult(ksp,Amat,Z,S);
    327:     VecXDot(Z,S,&delta);                  /*    delta <- z'*A*z = r'*B*A*B*r      */
    328:     VecXDot(Z,R,&beta);                   /*    beta <- z'*r                      */
    329:     KSPCheckDot(ksp,beta);
    330:   }

    332:   i = 0;
    333:   do {
    334:     ksp->its = i+1;
    335:     if (beta == 0.0) {
    336:       ksp->reason = KSP_CONVERGED_ATOL;
    337:       PetscInfo(ksp,"converged due to beta = 0\n");
    338:       break;
    339: #if !defined(PETSC_USE_COMPLEX)
    340:     } else if ((i > 0) && (beta*betaold < 0.0)) {
    341:       if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"Diverged due to indefinite preconditioner");
    342:       ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
    343:       PetscInfo(ksp,"diverging due to indefinite preconditioner\n");
    344:       break;
    345: #endif
    346:     }
    347:     if (!i) {
    348:       VecCopy(Z,P);                       /*    p <- z                           */
    349:       b    = 0.0;
    350:     } else {
    351:       b = beta/betaold;
    352:       if (eigs) {
    353:         if (ksp->max_it != stored_max_it) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Can not change maxit AND calculate eigenvalues");
    354:         e[i] = PetscSqrtReal(PetscAbsScalar(b))/a;
    355:       }
    356:       VecAYPX(P,b,Z);                     /*    p <- z + b* p                     */
    357:     }
    358:     dpiold = dpi;
    359:     if (!i) {
    360:       KSP_MatMult(ksp,Amat,P,W);          /*    w <- Ap                           */
    361:       VecXDot(P,W,&dpi);                  /*    dpi <- p'w                        */
    362:     } else {
    363:       VecAYPX(W,beta/betaold,S);          /*    w <- Ap                           */
    364:       dpi  = delta - beta*beta*dpiold/(betaold*betaold);       /*    dpi <- p'w                        */
    365:     }
    366:     betaold = beta;
    367:     KSPCheckDot(ksp,beta);

    369:     if ((dpi == 0.0) || ((i > 0) && (PetscRealPart(dpi*dpiold) <= 0.0))) {
    370:       if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"Diverged due to indefinite matrix");
    371:       ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
    372:       PetscInfo(ksp,"diverging due to indefinite or negative definite matrix\n");
    373:       break;
    374:     }
    375:     a = beta/dpi;                                              /*    a = beta/p'w                      */
    376:     if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b))*e[i] + 1.0/a;
    377:     VecAXPY(X,a,P);                       /*    x <- x + ap                       */
    378:     VecAXPY(R,-a,W);                      /*    r <- r - aw                       */
    379:     if (ksp->normtype == KSP_NORM_PRECONDITIONED && ksp->chknorm < i+2) {
    380:       KSP_PCApply(ksp,R,Z);               /*    z <- Br                           */
    381:       KSP_MatMult(ksp,Amat,Z,S);
    382:       VecNorm(Z,NORM_2,&dp);              /*    dp <- z'*z                        */
    383:       KSPCheckNorm(ksp,dp);
    384:     } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED && ksp->chknorm < i+2) {
    385:       VecNorm(R,NORM_2,&dp);              /*    dp <- r'*r                        */
    386:       KSPCheckNorm(ksp,dp);
    387:     } else if (ksp->normtype == KSP_NORM_NATURAL) {
    388:       KSP_PCApply(ksp,R,Z);               /*    z <- Br                           */
    389:       tmpvecs[0] = S; tmpvecs[1] = R;
    390:       KSP_MatMult(ksp,Amat,Z,S);
    391:       VecMDot(Z,2,tmpvecs,tmp);          /*    delta <- z'*A*z = r'*B*A*B*r      */
    392:       delta = tmp[0]; beta = tmp[1];                           /*    beta <- z'*r                      */
    393:       KSPCheckDot(ksp,beta);
    394:       dp = PetscSqrtReal(PetscAbsScalar(beta));                /*    dp <- r'*z = r'*B*r = e'*A'*B*A*e */
    395:     } else {
    396:       dp = 0.0;
    397:     }
    398:     ksp->rnorm = dp;
    399:     KSPLogResidualHistory(ksp,dp);
    400:     if (eigs) cg->ned = ksp->its;
    401:     KSPMonitor(ksp,i+1,dp);
    402:     (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
    403:     if (ksp->reason) break;

    405:     if ((ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) || (ksp->chknorm >= i+2)) {
    406:       KSP_PCApply(ksp,R,Z);               /*    z <- Br                           */
    407:       KSP_MatMult(ksp,Amat,Z,S);
    408:     }
    409:     if ((ksp->normtype != KSP_NORM_NATURAL) || (ksp->chknorm >= i+2)) {
    410:       tmpvecs[0] = S; tmpvecs[1] = R;
    411:       VecMDot(Z,2,tmpvecs,tmp);
    412:       delta = tmp[0]; beta = tmp[1];                           /*    delta <- z'*A*z = r'*B'*A*B*r     */
    413:       KSPCheckDot(ksp,beta);                                   /*    beta <- z'*r                      */
    414:     }

    416:     i++;
    417:   } while (i<ksp->max_it);
    418:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
    419:   return(0);
    420: }

    422: /*
    423:      KSPDestroy_CG - Frees resources allocated in KSPSetup_CG and clears function
    424:                      compositions from KSPCreate_CG. If adding your own KSP implementation,
    425:                      you must be sure to free all allocated resources here to prevent
    426:                      leaks.
    427: */
    428: PetscErrorCode KSPDestroy_CG(KSP ksp)
    429: {
    430:   KSP_CG         *cg = (KSP_CG*)ksp->data;

    434:   PetscFree4(cg->e,cg->d,cg->ee,cg->dd);
    435:   KSPDestroyDefault(ksp);
    436:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",NULL);
    437:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGUseSingleReduction_C",NULL);
    438:   return(0);
    439: }

    441: /*
    442:      KSPView_CG - Prints information about the current Krylov method being used.
    443:                   If your Krylov method has special options or flags that information
    444:                   should be printed here.
    445: */
    446: PetscErrorCode KSPView_CG(KSP ksp,PetscViewer viewer)
    447: {
    448:   KSP_CG         *cg = (KSP_CG*)ksp->data;
    450:   PetscBool      iascii;

    453:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    454:   if (iascii) {
    455: #if defined(PETSC_USE_COMPLEX)
    456:     PetscViewerASCIIPrintf(viewer,"  variant %s\n",KSPCGTypes[cg->type]);
    457: #endif
    458:     if (cg->singlereduction) {
    459:       PetscViewerASCIIPrintf(viewer,"  using single-reduction variant\n");
    460:     }
    461:   }
    462:   return(0);
    463: }

    465: /*
    466:     KSPSetFromOptions_CG - Checks the options database for options related to the
    467:                            conjugate gradient method.
    468: */
    469: PetscErrorCode KSPSetFromOptions_CG(PetscOptionItems *PetscOptionsObject,KSP ksp)
    470: {
    472:   KSP_CG         *cg = (KSP_CG*)ksp->data;
    473:   PetscBool      flg;

    476:   PetscOptionsHead(PetscOptionsObject,"KSP CG and CGNE options");
    477: #if defined(PETSC_USE_COMPLEX)
    478:   PetscOptionsEnum("-ksp_cg_type","Matrix is Hermitian or complex symmetric","KSPCGSetType",KSPCGTypes,(PetscEnum)cg->type,
    479:                           (PetscEnum*)&cg->type,NULL);
    480: #endif
    481:   PetscOptionsBool("-ksp_cg_single_reduction","Merge inner products into single MPIU_Allreduce()","KSPCGUseSingleReduction",cg->singlereduction,&cg->singlereduction,&flg);
    482:   if (flg) {
    483:     KSPCGUseSingleReduction(ksp,cg->singlereduction);
    484:   }
    485:   PetscOptionsTail();
    486:   return(0);
    487: }

    489: /*
    490:     KSPCGSetType_CG - This is an option that is SPECIFIC to this particular Krylov method.
    491:                       This routine is registered below in KSPCreate_CG() and called from the
    492:                       routine KSPCGSetType() (see the file cgtype.c).
    493: */
    494: PetscErrorCode  KSPCGSetType_CG(KSP ksp,KSPCGType type)
    495: {
    496:   KSP_CG *cg = (KSP_CG*)ksp->data;

    499:   cg->type = type;
    500:   return(0);
    501: }

    503: /*
    504:     KSPCGUseSingleReduction_CG

    506:     This routine sets a flag to use a variant of CG. Note that (in somewhat
    507:     atypical fashion) it also swaps out the routine called when KSPSolve()
    508:     is invoked.
    509: */
    510: static PetscErrorCode  KSPCGUseSingleReduction_CG(KSP ksp,PetscBool flg)
    511: {
    512:   KSP_CG *cg = (KSP_CG*)ksp->data;

    515:   cg->singlereduction = flg;
    516:   if (cg->singlereduction) {
    517:     ksp->ops->solve = KSPSolve_CG_SingleReduction;
    518:   } else {
    519:     ksp->ops->solve = KSPSolve_CG;
    520:   }
    521:   return(0);
    522: }

    524: PETSC_INTERN PetscErrorCode KSPBuildResidual_CG(KSP ksp,Vec t,Vec v,Vec *V)
    525: {

    529:   VecCopy(ksp->work[0],v);
    530:   *V   = v;
    531:   return(0);
    532: }

    534: /*
    535:     KSPCreate_CG - Creates the data structure for the Krylov method CG and sets the
    536:        function pointers for all the routines it needs to call (KSPSolve_CG() etc)

    538:     It must be labeled as PETSC_EXTERN to be dynamically linkable in C++
    539: */
    540: /*MC
    541:      KSPCG - The Preconditioned Conjugate Gradient (PCG) iterative method

    543:    Options Database Keys:
    544: +   -ksp_cg_type Hermitian - (for complex matrices only) indicates the matrix is Hermitian, see KSPCGSetType()
    545: .   -ksp_cg_type symmetric - (for complex matrices only) indicates the matrix is symmetric
    546: -   -ksp_cg_single_reduction - performs both inner products needed in the algorithm with a single MPIU_Allreduce() call, see KSPCGUseSingleReduction()

    548:    Level: beginner

    550:    Notes:
    551:     The PCG method requires both the matrix and preconditioner to be symmetric positive (or negative) (semi) definite.

    553:    Only left preconditioning is supported; there are several ways to motivate preconditioned CG, but they all produce the same algorithm.
    554:    One can interpret preconditioning A with B to mean any of the following\:
    555: .n  (1) Solve a left-preconditioned system BAx = Bb, using inv(B) to define an inner product in the algorithm.
    556: .n  (2) Solve a right-preconditioned system ABy = b, x = By, using B to define an inner product in the algorithm.
    557: .n  (3) Solve a symmetrically-preconditioned system, E^TAEy = E^Tb, x = Ey, where B = EE^T.
    558: .n  (4) Solve Ax=b with CG, but use the inner product defined by B to define the method [2].
    559: .n  In all cases, the resulting algorithm only requires application of B to vectors.

    561:    For complex numbers there are two different CG methods, one for Hermitian symmetric matrices and one for non-Hermitian symmetric matrices. Use
    562:    KSPCGSetType() to indicate which type you are using.

    564:    Developer Notes:
    565:     KSPSolve_CG() should actually query the matrix to determine if it is Hermitian symmetric or not and NOT require the user to
    566:    indicate it to the KSP object.

    568:    References:
    569: +   1. - Magnus R. Hestenes and Eduard Stiefel, Methods of Conjugate Gradients for Solving Linear Systems,
    570:    Journal of Research of the National Bureau of Standards Vol. 49, No. 6, December 1952 Research Paper 2379
    571: -   2. - Josef Malek and Zdenek Strakos, Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs,
    572:     SIAM, 2014.

    574: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP,
    575:            KSPCGSetType(), KSPCGUseSingleReduction(), KSPPIPECG, KSPGROPPCG

    577: M*/
    578: PETSC_EXTERN PetscErrorCode KSPCreate_CG(KSP ksp)
    579: {
    581:   KSP_CG         *cg;

    584:   PetscNewLog(ksp,&cg);
    585: #if !defined(PETSC_USE_COMPLEX)
    586:   cg->type = KSP_CG_SYMMETRIC;
    587: #else
    588:   cg->type = KSP_CG_HERMITIAN;
    589: #endif
    590:   ksp->data = (void*)cg;

    592:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    593:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,2);
    594:   KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,2);
    595:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);

    597:   /*
    598:        Sets the functions that are associated with this data structure
    599:        (in C++ this is the same as defining virtual functions)
    600:   */
    601:   ksp->ops->setup          = KSPSetUp_CG;
    602:   ksp->ops->solve          = KSPSolve_CG;
    603:   ksp->ops->destroy        = KSPDestroy_CG;
    604:   ksp->ops->view           = KSPView_CG;
    605:   ksp->ops->setfromoptions = KSPSetFromOptions_CG;
    606:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    607:   ksp->ops->buildresidual  = KSPBuildResidual_CG;

    609:   /*
    610:       Attach the function KSPCGSetType_CG() to this object. The routine
    611:       KSPCGSetType() checks for this attached function and calls it if it finds
    612:       it. (Sort of like a dynamic member function that can be added at run time
    613:   */
    614:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",KSPCGSetType_CG);
    615:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGUseSingleReduction_C",KSPCGUseSingleReduction_CG);
    616:   return(0);
    617: }