Actual source code: cg.c
petsc-3.10.5 2019-03-28
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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>
     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 work
     67:      work space needed
     68:   */
     69:   if (ksp->calc_sings) {
     70:     /* get space to store tridiagonal matrix for Lanczos */
     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 = 0,*d = 0,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:       break;
    136:     case KSP_NORM_UNPRECONDITIONED:
    137:       VecNorm(R,NORM_2,&dp);              /*    dp <- r'*r = e'*A'*A*e            */
    138:       break;
    139:     case KSP_NORM_NATURAL:
    140:       KSP_PCApply(ksp,R,Z);               /*    z <- Br                           */
    141:       VecXDot(Z,R,&beta);                 /*    beta <- z'*r                      */
    142:       KSPCheckDot(ksp,beta);
    143:       dp = PetscSqrtReal(PetscAbsScalar(beta));                /*    dp <- r'*z = r'*B*r = e'*A'*B*A*e */
    144:       break;
    145:     case KSP_NORM_NONE:
    146:       dp = 0.0;
    147:       break;
    148:     default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
    149:   }
    150:   KSPLogResidualHistory(ksp,dp);
    151:   KSPMonitor(ksp,0,dp);
    152:   ksp->rnorm = dp;

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

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

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

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

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

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

    241: /*
    242:        KSPSolve_CG_SingleReduction

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

    248:        See KSPCGUseSingleReduction_CG()

    250: */
    251: static PetscErrorCode KSPSolve_CG_SingleReduction(KSP ksp)
    252: {
    254:   PetscInt       i,stored_max_it,eigs;
    255:   PetscScalar    dpi = 0.0,a = 1.0,beta,betaold = 1.0,b = 0,*e = 0,*d = 0,delta,dpiold,tmp[2];
    256:   PetscReal      dp  = 0.0;
    257:   Vec            X,B,Z,R,P,S,W,tmpvecs[2];
    258:   KSP_CG         *cg;
    259:   Mat            Amat,Pmat;
    260:   PetscBool      diagonalscale;

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

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

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

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

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

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

    316:   if (ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) {
    317:     KSP_PCApply(ksp,R,Z);                 /*    z <- Br                           */
    318:   }
    319:   if (ksp->normtype != KSP_NORM_NATURAL) {
    320:     KSP_MatMult(ksp,Amat,Z,S);
    321:     VecXDot(Z,S,&delta);                  /*    delta <- z'*A*z = r'*B*A*B*r      */
    322:     VecXDot(Z,R,&beta);                   /*    beta <- z'*r                      */
    323:     KSPCheckDot(ksp,beta);
    324:   }

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

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

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

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

    414: /*
    415:      KSPDestroy_CG - Frees resources allocated in KSPSetup_CG and clears function
    416:                      compositions from KSPCreate_CG. If adding your own KSP implementation,
    417:                      you must be sure to free all allocated resources here to prevent
    418:                      leaks.
    419: */
    420: PetscErrorCode KSPDestroy_CG(KSP ksp)
    421: {
    422:   KSP_CG         *cg = (KSP_CG*)ksp->data;

    426:   /* free space used for singular value calculations */
    427:   if (ksp->calc_sings) {
    428:     PetscFree4(cg->e,cg->d,cg->ee,cg->dd);
    429:   }
    430:   KSPDestroyDefault(ksp);
    431:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",NULL);
    432:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGUseSingleReduction_C",NULL);
    433:   return(0);
    434: }

    436: /*
    437:      KSPView_CG - Prints information about the current Krylov method being used.
    438:                   If your Krylov method has special options or flags that information
    439:                   should be printed here.
    440: */
    441: PetscErrorCode KSPView_CG(KSP ksp,PetscViewer viewer)
    442: {
    443:   KSP_CG         *cg = (KSP_CG*)ksp->data;
    445:   PetscBool      iascii;

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

    460: /*
    461:     KSPSetFromOptions_CG - Checks the options database for options related to the
    462:                            conjugate gradient method.
    463: */
    464: PetscErrorCode KSPSetFromOptions_CG(PetscOptionItems *PetscOptionsObject,KSP ksp)
    465: {
    467:   KSP_CG         *cg = (KSP_CG*)ksp->data;

    470:   PetscOptionsHead(PetscOptionsObject,"KSP CG and CGNE options");
    471: #if defined(PETSC_USE_COMPLEX)
    472:   PetscOptionsEnum("-ksp_cg_type","Matrix is Hermitian or complex symmetric","KSPCGSetType",KSPCGTypes,(PetscEnum)cg->type,
    473:                           (PetscEnum*)&cg->type,NULL);
    474: #endif
    475:   PetscOptionsBool("-ksp_cg_single_reduction","Merge inner products into single MPIU_Allreduce()","KSPCGUseSingleReduction",cg->singlereduction,&cg->singlereduction,NULL);
    476:   PetscOptionsTail();
    477:   return(0);
    478: }

    480: /*
    481:     KSPCGSetType_CG - This is an option that is SPECIFIC to this particular Krylov method.
    482:                       This routine is registered below in KSPCreate_CG() and called from the
    483:                       routine KSPCGSetType() (see the file cgtype.c).
    484: */
    485: PetscErrorCode  KSPCGSetType_CG(KSP ksp,KSPCGType type)
    486: {
    487:   KSP_CG *cg = (KSP_CG*)ksp->data;

    490:   cg->type = type;
    491:   return(0);
    492: }

    494: /*
    495:     KSPCGUseSingleReduction_CG

    497:     This routine sets a flag to use a variant of CG. Note that (in somewhat
    498:     atypical fashion) it also swaps out the routine called when KSPSolve()
    499:     is invoked.
    500: */
    501: static PetscErrorCode  KSPCGUseSingleReduction_CG(KSP ksp,PetscBool flg)
    502: {
    503:   KSP_CG *cg = (KSP_CG*)ksp->data;

    506:   cg->singlereduction = flg;
    507:   if (cg->singlereduction) {
    508:     ksp->ops->solve = KSPSolve_CG_SingleReduction;
    509:   } else {
    510:     ksp->ops->solve = KSPSolve_CG;
    511:   }
    512:   return(0);
    513: }

    515: /*
    516:     KSPCreate_CG - Creates the data structure for the Krylov method CG and sets the
    517:        function pointers for all the routines it needs to call (KSPSolve_CG() etc)

    519:     It must be labeled as PETSC_EXTERN to be dynamically linkable in C++
    520: */
    521: /*MC
    522:      KSPCG - The Preconditioned Conjugate Gradient (PCG) iterative method

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

    529:    Level: beginner

    531:    Notes:
    532:     The PCG method requires both the matrix and preconditioner to be symmetric positive (or negative) (semi) definite.
    533:
    534:    Only left preconditioning is supported; there are several ways to motivate preconditioned CG, but they all produce the same algorithm.
    535:    One can interpret preconditioning A with B to mean any of the following\:
    536: .n  (1) Solve a left-preconditioned system BAx = Bb, using inv(B) to define an inner product in the algorithm.
    537: .n  (2) Solve a right-preconditioned system ABy = b, x = By, using B to define an inner product in the algorithm.
    538: .n  (3) Solve a symmetrically-preconditioned system, E^TAEy = E^Tb, x = Ey, where B = EE^T.
    539: .n  (4) Solve Ax=b with CG, but use the inner product defined by B to define the method [2].
    540: .n  In all cases, the resulting algorithm only requires application of B to vectors.

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

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

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

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

    558: M*/
    559: PETSC_EXTERN PetscErrorCode KSPCreate_CG(KSP ksp)
    560: {
    562:   KSP_CG         *cg;

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

    573:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    574:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,2);
    575:   KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,2);
    576:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);

    578:   /*
    579:        Sets the functions that are associated with this data structure
    580:        (in C++ this is the same as defining virtual functions)
    581:   */
    582:   ksp->ops->setup          = KSPSetUp_CG;
    583:   ksp->ops->solve          = KSPSolve_CG;
    584:   ksp->ops->destroy        = KSPDestroy_CG;
    585:   ksp->ops->view           = KSPView_CG;
    586:   ksp->ops->setfromoptions = KSPSetFromOptions_CG;
    587:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    588:   ksp->ops->buildresidual  = KSPBuildResidualDefault;

    590:   /*
    591:       Attach the function KSPCGSetType_CG() to this object. The routine
    592:       KSPCGSetType() checks for this attached function and calls it if it finds
    593:       it. (Sort of like a dynamic member function that can be added at run time
    594:   */
    595:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",KSPCGSetType_CG);
    596:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGUseSingleReduction_C",KSPCGUseSingleReduction_CG);
    597:   return(0);
    598: }