Date: 2013-07-02T14:48:00+00:00

Actual source code: cg.c
petsc-3.4.2 2013-07-02

      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 vai 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,PetscScalar,&cgP->e,maxit+1,PetscScalar,&cgP->d,maxit+1,PetscReal,&cgP->ee,maxit+1,PetscReal,&cgP->dd);
     74:     PetscLogObjectMemory(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:        KSPSolve_CG - This routine actually applies the conjugate gradient  method

     85:    This routine is MUCH too messy. I has too many options (norm type and single reduction) embedded making the code confusing and likely to be buggy.

     87:    Input Parameter:
     88: .     ksp - the Krylov space object that was set to use conjugate gradient, by, for
     89:             example, KSPCreate(MPI_Comm,KSP *ksp); KSPSetType(ksp,KSPCG);
     90: */
     93: PetscErrorCode  KSPSolve_CG(KSP ksp)
     94: {
     96:   PetscInt       i,stored_max_it,eigs;
     97:   PetscScalar    dpi = 0.0,a = 1.0,beta,betaold = 1.0,b = 0,*e = 0,*d = 0,delta,dpiold;
     98:   PetscReal      dp  = 0.0;
     99:   Vec            X,B,Z,R,P,S,W;
    100:   KSP_CG         *cg;
    101:   Mat            Amat,Pmat;
    102:   MatStructure   pflag;
    103:   PetscBool      diagonalscale;

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

    109:   cg            = (KSP_CG*)ksp->data;
    110:   eigs          = ksp->calc_sings;
    111:   stored_max_it = ksp->max_it;
    112:   X             = ksp->vec_sol;
    113:   B             = ksp->vec_rhs;
    114:   R             = ksp->work[0];
    115:   Z             = ksp->work[1];
    116:   P             = ksp->work[2];
    117:   if (cg->singlereduction) {
    118:     S = ksp->work[3];
    119:     W = ksp->work[4];
    120:   } else {
    121:     S = 0;                      /* unused */
    122:     W = Z;
    123:   }

    125: #define VecXDot(x,y,a) (((cg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x,y,a) : VecTDot(x,y,a))

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

    130:   ksp->its = 0;
    131:   if (!ksp->guess_zero) {
    132:     KSP_MatMult(ksp,Amat,X,R);            /*     r <- b - Ax     */
    133:     VecAYPX(R,-1.0,B);
    134:   } else {
    135:     VecCopy(B,R);                         /*     r <- b (x is 0) */
    136:   }

    138:   switch (ksp->normtype) {
    139:   case KSP_NORM_PRECONDITIONED:
    140:     KSP_PCApply(ksp,R,Z);                   /*     z <- Br         */
    141:     VecNorm(Z,NORM_2,&dp);                /*    dp <- z'*z = e'*A'*B'*B*A'*e'     */
    142:     break;
    143:   case KSP_NORM_UNPRECONDITIONED:
    144:     VecNorm(R,NORM_2,&dp);                /*    dp <- r'*r = e'*A'*A*e            */
    145:     break;
    146:   case KSP_NORM_NATURAL:
    147:     KSP_PCApply(ksp,R,Z);                   /*     z <- Br         */
    148:     if (cg->singlereduction) {
    149:       KSP_MatMult(ksp,Amat,Z,S);
    150:       VecXDot(Z,S,&delta);
    151:     }
    152:     VecXDot(Z,R,&beta);                     /*  beta <- z'*r       */
    153:     if (PetscIsInfOrNanScalar(beta)) {
    154:       if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to Nan or Inf inner product");
    155:       else {
    156:         ksp->reason = KSP_DIVERGED_NANORINF;
    157:         return(0);
    158:       }
    159:     }
    160:     dp = PetscSqrtReal(PetscAbsScalar(beta));                           /*    dp <- r'*z = r'*B*r = e'*A'*B*A*e */
    161:     break;
    162:   case KSP_NORM_NONE:
    163:     dp = 0.0;
    164:     break;
    165:   default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
    166:   }
    167:   KSPLogResidualHistory(ksp,dp);
    168:   KSPMonitor(ksp,0,dp);
    169:   ksp->rnorm = dp;

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

    174:   if (ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) {
    175:     KSP_PCApply(ksp,R,Z);                   /*     z <- Br         */
    176:   }
    177:   if (ksp->normtype != KSP_NORM_NATURAL) {
    178:     if (cg->singlereduction) {
    179:       KSP_MatMult(ksp,Amat,Z,S);
    180:       VecXDot(Z,S,&delta);
    181:     }
    182:     VecXDot(Z,R,&beta);         /*  beta <- z'*r       */
    183:     if (PetscIsInfOrNanScalar(beta)) {
    184:       if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to Nan or Inf inner product");
    185:       else {
    186:         ksp->reason = KSP_DIVERGED_NANORINF;
    187:         return(0);
    188:       }
    189:     }
    190:   }

    192:   i = 0;
    193:   do {
    194:     ksp->its = i+1;
    195:     if (beta == 0.0) {
    196:       ksp->reason = KSP_CONVERGED_ATOL;
    197:       PetscInfo(ksp,"converged due to beta = 0\n");
    198:       break;
    199: #if !defined(PETSC_USE_COMPLEX)
    200:     } else if ((i > 0) && (beta*betaold < 0.0)) {
    201:       ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
    202:       PetscInfo(ksp,"diverging due to indefinite preconditioner\n");
    203:       break;
    204: #endif
    205:     }
    206:     if (!i) {
    207:       VecCopy(Z,P);         /*     p <- z          */
    208:       b    = 0.0;
    209:     } else {
    210:       b = beta/betaold;
    211:       if (eigs) {
    212:         if (ksp->max_it != stored_max_it) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Can not change maxit AND calculate eigenvalues");
    213:         e[i] = PetscSqrtReal(PetscAbsScalar(b))/a;
    214:       }
    215:       VecAYPX(P,b,Z);    /*     p <- z + b* p   */
    216:     }
    217:     dpiold = dpi;
    218:     if (!cg->singlereduction || !i) {
    219:       KSP_MatMult(ksp,Amat,P,W);          /*     w <- Ap         */
    220:       VecXDot(P,W,&dpi);                  /*     dpi <- p'w     */
    221:     } else {
    222:       VecAYPX(W,beta/betaold,S);                  /*     w <- Ap         */
    223:       dpi  = delta - beta*beta*dpiold/(betaold*betaold);             /*     dpi <- p'w     */
    224:     }
    225:     betaold = beta;
    226:     if (PetscIsInfOrNanScalar(dpi)) {
    227:       if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to Nan or Inf inner product");
    228:       else {
    229:         ksp->reason = KSP_DIVERGED_NANORINF;
    230:         return(0);
    231:       }
    232:     }

    234:     if ((dpi == 0.0) || ((i > 0) && (PetscRealPart(dpi*dpiold) <= 0.0))) {
    235:       ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
    236:       PetscInfo(ksp,"diverging due to indefinite or negative definite matrix\n");
    237:       break;
    238:     }
    239:     a = beta/dpi;                                 /*     a = beta/p'w   */
    240:     if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b))*e[i] + 1.0/a;
    241:     VecAXPY(X,a,P);          /*     x <- x + ap     */
    242:     VecAXPY(R,-a,W);                      /*     r <- r - aw    */
    243:     if (ksp->normtype == KSP_NORM_PRECONDITIONED && ksp->chknorm < i+2) {
    244:       KSP_PCApply(ksp,R,Z);               /*     z <- Br         */
    245:       if (cg->singlereduction) {
    246:         KSP_MatMult(ksp,Amat,Z,S);
    247:       }
    248:       VecNorm(Z,NORM_2,&dp);              /*    dp <- z'*z       */
    249:     } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED && ksp->chknorm < i+2) {
    250:       VecNorm(R,NORM_2,&dp);              /*    dp <- r'*r       */
    251:     } else if (ksp->normtype == KSP_NORM_NATURAL) {
    252:       KSP_PCApply(ksp,R,Z);               /*     z <- Br         */
    253:       if (cg->singlereduction) {
    254:         PetscScalar tmp[2];
    255:         Vec         vecs[2];
    256:         vecs[0] = S; vecs[1] = R;
    257:         KSP_MatMult(ksp,Amat,Z,S);
    258:         VecMDot(Z,2,vecs,tmp);
    259:         delta = tmp[0]; beta = tmp[1];
    260:       } else {
    261:         VecXDot(Z,R,&beta);     /*  beta <- r'*z       */
    262:       }
    263:       if (PetscIsInfOrNanScalar(beta)) {
    264:         if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to Nan or Inf inner product");
    265:         else {
    266:           ksp->reason = KSP_DIVERGED_NANORINF;
    267:           return(0);
    268:         }
    269:       }
    270:       dp = PetscSqrtReal(PetscAbsScalar(beta));
    271:     } else {
    272:       dp = 0.0;
    273:     }
    274:     ksp->rnorm = dp;
    275:     KSPLogResidualHistory(ksp,dp);
    276:     KSPMonitor(ksp,i+1,dp);
    277:     (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
    278:     if (ksp->reason) break;

    280:     if ((ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) || (ksp->chknorm >= i+2)) {
    281:       KSP_PCApply(ksp,R,Z);                   /*     z <- Br         */
    282:       if (cg->singlereduction) {
    283:         KSP_MatMult(ksp,Amat,Z,S);
    284:       }
    285:     }
    286:     if ((ksp->normtype != KSP_NORM_NATURAL) || (ksp->chknorm >= i+2)) {
    287:       if (cg->singlereduction) {
    288:         PetscScalar tmp[2];
    289:         Vec         vecs[2];
    290:         vecs[0] = S; vecs[1] = R;
    291:         VecMDot(Z,2,vecs,tmp);
    292:         delta = tmp[0]; beta = tmp[1];
    293:       } else {
    294:         VecXDot(Z,R,&beta);        /*  beta <- z'*r       */
    295:       }
    296:       if (PetscIsInfOrNanScalar(beta)) {
    297:         if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to Nan or Inf inner product");
    298:         else {
    299:           ksp->reason = KSP_DIVERGED_NANORINF;
    300:           return(0);
    301:         }
    302:       }
    303:     }

    305:     i++;
    306:   } while (i<ksp->max_it);
    307:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
    308:   return(0);
    309: }

    313: PetscErrorCode KSPDestroy_CG(KSP ksp)
    314: {
    315:   KSP_CG         *cg = (KSP_CG*)ksp->data;

    319:   /* free space used for singular value calculations */
    320:   if (ksp->calc_sings) {
    321:     PetscFree4(cg->e,cg->d,cg->ee,cg->dd);
    322:   }
    323:   KSPDestroyDefault(ksp);
    324:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",NULL);
    325:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGUseSingleReduction_C",NULL);
    326:   return(0);
    327: }

    329: /*
    330:      KSPView_CG - Prints information about the current Krylov method being used

    332:       Currently this only prints information to a file (or stdout) about the
    333:       symmetry of the problem. If your Krylov method has special options or
    334:       flags that information should be printed here.

    336: */
    339: PetscErrorCode KSPView_CG(KSP ksp,PetscViewer viewer)
    340: {
    341: #if defined(PETSC_USE_COMPLEX)
    342:   KSP_CG         *cg = (KSP_CG*)ksp->data;
    344:   PetscBool      iascii;

    347:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    348:   if (iascii) {
    349:     PetscViewerASCIIPrintf(viewer,"  CG or CGNE: variant %s\n",KSPCGTypes[cg->type]);
    350:   }
    351: #endif
    352:   return(0);
    353: }

    355: /*
    356:     KSPSetFromOptions_CG - Checks the options database for options related to the
    357:                            conjugate gradient method.
    358: */
    361: PetscErrorCode KSPSetFromOptions_CG(KSP ksp)
    362: {
    364:   KSP_CG         *cg = (KSP_CG*)ksp->data;

    367:   PetscOptionsHead("KSP CG and CGNE options");
    368: #if defined(PETSC_USE_COMPLEX)
    369:   PetscOptionsEnum("-ksp_cg_type","Matrix is Hermitian or complex symmetric","KSPCGSetType",KSPCGTypes,(PetscEnum)cg->type,
    370:                           (PetscEnum*)&cg->type,NULL);
    371: #endif
    372:   PetscOptionsBool("-ksp_cg_single_reduction","Merge inner products into single MPI_Allreduce()",
    373:                           "KSPCGUseSingleReduction",cg->singlereduction,&cg->singlereduction,NULL);
    374:   PetscOptionsTail();
    375:   return(0);
    376: }

    378: /*
    379:     KSPCGSetType_CG - This is an option that is SPECIFIC to this particular Krylov method.
    380:                       This routine is registered below in KSPCreate_CG() and called from the
    381:                       routine KSPCGSetType() (see the file cgtype.c).
    382: */
    385: static PetscErrorCode  KSPCGSetType_CG(KSP ksp,KSPCGType type)
    386: {
    387:   KSP_CG *cg = (KSP_CG*)ksp->data;

    390:   cg->type = type;
    391:   return(0);
    392: }

    396: static PetscErrorCode  KSPCGUseSingleReduction_CG(KSP ksp,PetscBool flg)
    397: {
    398:   KSP_CG *cg = (KSP_CG*)ksp->data;

    401:   cg->singlereduction = flg;
    402:   return(0);
    403: }

    405: /*
    406:     KSPCreate_CG - Creates the data structure for the Krylov method CG and sets the
    407:        function pointers for all the routines it needs to call (KSPSolve_CG() etc)

    409:     It must be wrapped in EXTERN_C_BEGIN to be dynamically linkable in C++
    410: */
    411: /*MC
    412:      KSPCG - The preconditioned conjugate gradient (PCG) iterative method

    414:    Options Database Keys:
    415: +   -ksp_cg_type Hermitian - (for complex matrices only) indicates the matrix is Hermitian, see KSPCGSetType()
    416: .   -ksp_cg_type symmetric - (for complex matrices only) indicates the matrix is symmetric
    417: -   -ksp_cg_single_reduction - performs both inner products needed in the algorithm with a single MPI_Allreduce() call, see KSPCGUseSingleReduction()

    419:    Level: beginner

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

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

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

    430:    References:
    431:    Methods of Conjugate Gradients for Solving Linear Systems, Magnus R. Hestenes and Eduard Stiefel,
    432:    Journal of Research of the National Bureau of Standards Vol. 49, No. 6, December 1952 Research Paper 2379
    433:    pp. 409--436.

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

    438: M*/
    441: PETSC_EXTERN PetscErrorCode KSPCreate_CG(KSP ksp)
    442: {
    444:   KSP_CG         *cg;

    447:   PetscNewLog(ksp,KSP_CG,&cg);
    448: #if !defined(PETSC_USE_COMPLEX)
    449:   cg->type = KSP_CG_SYMMETRIC;
    450: #else
    451:   cg->type = KSP_CG_HERMITIAN;
    452: #endif
    453:   ksp->data = (void*)cg;

    455:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,2);
    456:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,1);
    457:   KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,1);
    458:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);

    460:   /*
    461:        Sets the functions that are associated with this data structure
    462:        (in C++ this is the same as defining virtual functions)
    463:   */
    464:   ksp->ops->setup          = KSPSetUp_CG;
    465:   ksp->ops->solve          = KSPSolve_CG;
    466:   ksp->ops->destroy        = KSPDestroy_CG;
    467:   ksp->ops->view           = KSPView_CG;
    468:   ksp->ops->setfromoptions = KSPSetFromOptions_CG;
    469:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    470:   ksp->ops->buildresidual  = KSPBuildResidualDefault;

    472:   /*
    473:       Attach the function KSPCGSetType_CG() to this object. The routine
    474:       KSPCGSetType() checks for this attached function and calls it if it finds
    475:       it. (Sort of like a dynamic member function that can be added at run time
    476:   */
    477:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",KSPCGSetType_CG);
    478:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGUseSingleReduction_C",KSPCGUseSingleReduction_CG);
    479:   return(0);
    480: }