Date: 2016-07-24T17:06:15+00:00

Actual source code: cg.c
petsc-3.7.3 2016-07-24
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      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 are
     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>       /*I "petscksp.h" I*/
     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: */
     56: PetscErrorCode KSPSetUp_CG(KSP ksp)
     57: {
     58:   KSP_CG         *cgP = (KSP_CG*)ksp->data;
     60:   PetscInt       maxit = ksp->max_it,nwork = 3;

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

     67:   /*
     68:      If user requested computations of eigenvalues then allocate work
     69:      work space needed
     70:   */
     71:   if (ksp->calc_sings) {
     72:     /* get space to store tridiagonal matrix for Lanczos */
     73:     PetscMalloc4(maxit+1,&cgP->e,maxit+1,&cgP->d,maxit+1,&cgP->ee,maxit+1,&cgP->dd);
     74:     PetscLogObjectMemory((PetscObject)ksp,2*(maxit+1)*(sizeof(PetscScalar)+sizeof(PetscReal)));

     76:     ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_CG;
     77:     ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_CG;
     78:   }
     79:   return(0);
     80: }

     82: /*
     83:      A macro used in the following KSPSolve_CG and KSPSolve_CG_SingleReduction routines
     84: */
     85: #define VecXDot(x,y,a) (((cg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x,y,a) : VecTDot(x,y,a))

     87: /*
     88:      KSPSolve_CG - This routine actually applies the conjugate gradient method

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

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

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

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

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

    127:   ksp->its = 0;
    128:   if (!ksp->guess_zero) {
    129:     KSP_MatMult(ksp,Amat,X,R);            /*    r <- b - Ax                       */
    130:     VecAYPX(R,-1.0,B);
    131:   } else {
    132:     VecCopy(B,R);                         /*    r <- b (x is 0)                   */
    133:   }

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

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

    161:   if (ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) {
    162:     KSP_PCApply(ksp,R,Z);                /*     z <- Br                           */
    163:   }
    164:   if (ksp->normtype != KSP_NORM_NATURAL) {
    165:     VecXDot(Z,R,&beta);                  /*     beta <- z'*r                      */
    166:     KSPCheckDot(ksp,beta);
    167:   }

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

    200:     if ((dpi == 0.0) || ((i > 0) && (PetscRealPart(dpi*dpiold) <= 0.0))) {
    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:     } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED && ksp->chknorm < i+2) {
    213:       VecNorm(R,NORM_2,&dp);              /*     dp <- r'*r                       */
    214:     } else if (ksp->normtype == KSP_NORM_NATURAL) {
    215:       KSP_PCApply(ksp,R,Z);               /*     z <- Br                          */
    216:       VecXDot(Z,R,&beta);                 /*     beta <- r'*z                     */
    217:       KSPCheckDot(ksp,beta);
    218:       dp = PetscSqrtReal(PetscAbsScalar(beta));
    219:     } else {
    220:       dp = 0.0;
    221:     }
    222:     ksp->rnorm = dp;
    223:     KSPLogResidualHistory(ksp,dp);
    224:     if (eigs) cg->ned = ksp->its;
    225:     KSPMonitor(ksp,i+1,dp);
    226:     (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
    227:     if (ksp->reason) break;

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

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

    243: /*
    244:        KSPSolve_CG_SingleReduction

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

    250:        See KSPCGUseSingleReduction_CG()

    252: */
    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 = 0,*d = 0,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:       break;
    297:     case KSP_NORM_UNPRECONDITIONED:
    298:       VecNorm(R,NORM_2,&dp);              /*    dp <- r'*r = e'*A'*A*e            */
    299:       break;
    300:     case KSP_NORM_NATURAL:
    301:       KSP_PCApply(ksp,R,Z);               /*    z <- Br                           */
    302:       KSP_MatMult(ksp,Amat,Z,S);
    303:       VecXDot(Z,S,&delta);                /*    delta <- z'*A*z = r'*B*A*B*r      */
    304:       VecXDot(Z,R,&beta);                 /*    beta <- z'*r                      */
    305:       KSPCheckDot(ksp,beta);
    306:       dp = PetscSqrtReal(PetscAbsScalar(beta));                /*    dp <- r'*z = r'*B*r = e'*A'*B*A*e */
    307:       break;
    308:     case KSP_NORM_NONE:
    309:       dp = 0.0;
    310:       break;
    311:     default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
    312:   }
    313:   KSPLogResidualHistory(ksp,dp);
    314:   KSPMonitor(ksp,0,dp);
    315:   ksp->rnorm = dp;

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

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

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

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

    399:     if ((ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) || (ksp->chknorm >= i+2)) {
    400:       KSP_PCApply(ksp,R,Z);               /*    z <- Br                           */
    401:       KSP_MatMult(ksp,Amat,Z,S);
    402:     }
    403:     if ((ksp->normtype != KSP_NORM_NATURAL) || (ksp->chknorm >= i+2)) {
    404:       tmpvecs[0] = S; tmpvecs[1] = R;
    405:       VecMDot(Z,2,tmpvecs,tmp);
    406:       delta = tmp[0]; beta = tmp[1];                           /*    delta <- z'*A*z = r'*B'*A*B*r     */
    407:       KSPCheckDot(ksp,beta);                                   /*    beta <- z'*r                      */
    408:     }

    410:     i++;
    411:   } while (i<ksp->max_it);
    412:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
    413:   return(0);
    414: }

    416: /*
    417:      KSPDestroy_CG - Frees resources allocated in KSPSetup_CG and clears function
    418:                      compositions from KSPCreate_CG. If adding your own KSP implementation,
    419:                      you must be sure to free all allocated resources here to prevent
    420:                      leaks.
    421: */
    424: PetscErrorCode KSPDestroy_CG(KSP ksp)
    425: {
    426:   KSP_CG         *cg = (KSP_CG*)ksp->data;

    430:   /* free space used for singular value calculations */
    431:   if (ksp->calc_sings) {
    432:     PetscFree4(cg->e,cg->d,cg->ee,cg->dd);
    433:   }
    434:   KSPDestroyDefault(ksp);
    435:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",NULL);
    436:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGUseSingleReduction_C",NULL);
    437:   return(0);
    438: }

    440: /*
    441:      KSPView_CG - Prints information about the current Krylov method being used.
    442:                   If your Krylov method has special options or flags that information
    443:                   should be printed here.
    444: */
    447: PetscErrorCode KSPView_CG(KSP ksp,PetscViewer viewer)
    448: {
    449:   KSP_CG         *cg = (KSP_CG*)ksp->data;
    451:   PetscBool      iascii;

    454:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    455:   if (iascii) {
    456: #if defined(PETSC_USE_COMPLEX)
    457:     PetscViewerASCIIPrintf(viewer,"  CG or CGNE: variant %s\n",KSPCGTypes[cg->type]);
    458: #endif
    459:     if (cg->singlereduction) {
    460:       PetscViewerASCIIPrintf(viewer,"  CG: using single-reduction variant\n");
    461:     }
    462:   }
    463:   return(0);
    464: }

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

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

    488: /*
    489:     KSPCGSetType_CG - This is an option that is SPECIFIC to this particular Krylov method.
    490:                       This routine is registered below in KSPCreate_CG() and called from the
    491:                       routine KSPCGSetType() (see the file cgtype.c).
    492: */
    495: static PetscErrorCode  KSPCGSetType_CG(KSP ksp,KSPCGType type)
    496: {
    497:   KSP_CG *cg = (KSP_CG*)ksp->data;

    500:   cg->type = type;
    501:   return(0);
    502: }

    504: /*
    505:     KSPCGUseSingleReduction_CG

    507:     This routine sets a flag to use a variant of CG. Note that (in somewhat
    508:     atypical fashion) it also swaps out the routine called when KSPSolve()
    509:     is invoked.
    510: */
    513: static PetscErrorCode  KSPCGUseSingleReduction_CG(KSP ksp,PetscBool flg)
    514: {
    515:   KSP_CG *cg = (KSP_CG*)ksp->data;

    518:   cg->singlereduction = flg;
    519:   if (cg->singlereduction) {
    520:     ksp->ops->solve = KSPSolve_CG_SingleReduction;
    521:   } else {
    522:     ksp->ops->solve = KSPSolve_CG;
    523:   }
    524:   return(0);
    525: }

    527: /*
    528:     KSPCreate_CG - Creates the data structure for the Krylov method CG and sets the
    529:        function pointers for all the routines it needs to call (KSPSolve_CG() etc)

    531:     It must be labeled as PETSC_EXTERN to be dynamically linkable in C++
    532: */
    533: /*MC
    534:      KSPCG - The preconditioned conjugate gradient (PCG) iterative method

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

    541:    Level: beginner

    543:    Notes: The PCG method requires both the matrix and preconditioner to be symmetric positive (or negative) (semi) definite
    544:           Only left preconditioning is supported.

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

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

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

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

    559: M*/
    562: PETSC_EXTERN PetscErrorCode KSPCreate_CG(KSP ksp)
    563: {
    565:   KSP_CG         *cg;

    568:   PetscNewLog(ksp,&cg);
    569: #if !defined(PETSC_USE_COMPLEX)
    570:   cg->type = KSP_CG_SYMMETRIC;
    571: #else
    572:   cg->type = KSP_CG_HERMITIAN;
    573: #endif
    574:   ksp->data = (void*)cg;

    576:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    577:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,2);
    578:   KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,2);

    580:   /*
    581:        Sets the functions that are associated with this data structure
    582:        (in C++ this is the same as defining virtual functions)
    583:   */
    584:   ksp->ops->setup          = KSPSetUp_CG;
    585:   ksp->ops->solve          = KSPSolve_CG;
    586:   ksp->ops->destroy        = KSPDestroy_CG;
    587:   ksp->ops->view           = KSPView_CG;
    588:   ksp->ops->setfromoptions = KSPSetFromOptions_CG;
    589:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    590:   ksp->ops->buildresidual  = KSPBuildResidualDefault;

    592:   /*
    593:       Attach the function KSPCGSetType_CG() to this object. The routine
    594:       KSPCGSetType() checks for this attached function and calls it if it finds
    595:       it. (Sort of like a dynamic member function that can be added at run time
    596:   */
    597:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",KSPCGSetType_CG);
    598:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGUseSingleReduction_C",KSPCGUseSingleReduction_CG);
    599:   return(0);
    600: }