Date: 2015-10-02T22:20:52+00:00

Actual source code: cg.c
petsc-3.6.2 2015-10-02
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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 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,&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:        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:   PetscBool      diagonalscale;

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

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

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

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

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

    137:   switch (ksp->normtype) {
    138:   case KSP_NORM_PRECONDITIONED:
    139:     KSP_PCApply(ksp,R,Z);                   /*     z <- Br         */
    140:     VecNorm(Z,NORM_2,&dp);                /*    dp <- z'*z = e'*A'*B'*B*A'*e'     */
    141:     break;
    142:   case KSP_NORM_UNPRECONDITIONED:
    143:     VecNorm(R,NORM_2,&dp);                /*    dp <- r'*r = e'*A'*A*e            */
    144:     break;
    145:   case KSP_NORM_NATURAL:
    146:     KSP_PCApply(ksp,R,Z);                   /*     z <- Br         */
    147:     if (cg->singlereduction) {
    148:       KSP_MatMult(ksp,Amat,Z,S);
    149:       VecXDot(Z,S,&delta);
    150:     }
    151:     VecXDot(Z,R,&beta);                     /*  beta <- z'*r       */
    152:     KSPCheckDot(ksp,beta);
    153:     dp = PetscSqrtReal(PetscAbsScalar(beta));                           /*    dp <- r'*z = r'*B*r = e'*A'*B*A*e */
    154:     break;
    155:   case KSP_NORM_NONE:
    156:     dp = 0.0;
    157:     break;
    158:   default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
    159:   }
    160:   KSPLogResidualHistory(ksp,dp);
    161:   KSPMonitor(ksp,0,dp);
    162:   ksp->rnorm = dp;

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

    167:   if (ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) {
    168:     KSP_PCApply(ksp,R,Z);                   /*     z <- Br         */
    169:   }
    170:   if (ksp->normtype != KSP_NORM_NATURAL) {
    171:     if (cg->singlereduction) {
    172:       KSP_MatMult(ksp,Amat,Z,S);
    173:       VecXDot(Z,S,&delta);
    174:     }
    175:     VecXDot(Z,R,&beta);         /*  beta <- z'*r       */
    176:     KSPCheckDot(ksp,beta);
    177:   }

    179:   i = 0;
    180:   do {
    181:     ksp->its = i+1;
    182:     if (beta == 0.0) {
    183:       ksp->reason = KSP_CONVERGED_ATOL;
    184:       PetscInfo(ksp,"converged due to beta = 0\n");
    185:       break;
    186: #if !defined(PETSC_USE_COMPLEX)
    187:     } else if ((i > 0) && (beta*betaold < 0.0)) {
    188:       ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
    189:       PetscInfo(ksp,"diverging due to indefinite preconditioner\n");
    190:       break;
    191: #endif
    192:     }
    193:     if (!i) {
    194:       VecCopy(Z,P);         /*     p <- z          */
    195:       b    = 0.0;
    196:     } else {
    197:       b = beta/betaold;
    198:       if (eigs) {
    199:         if (ksp->max_it != stored_max_it) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Can not change maxit AND calculate eigenvalues");
    200:         e[i] = PetscSqrtReal(PetscAbsScalar(b))/a;
    201:       }
    202:       VecAYPX(P,b,Z);    /*     p <- z + b* p   */
    203:     }
    204:     dpiold = dpi;
    205:     if (!cg->singlereduction || !i) {
    206:       KSP_MatMult(ksp,Amat,P,W);          /*     w <- Ap         */
    207:       VecXDot(P,W,&dpi);                  /*     dpi <- p'w     */
    208:     } else {
    209:       VecAYPX(W,beta/betaold,S);                  /*     w <- Ap         */
    210:       dpi  = delta - beta*beta*dpiold/(betaold*betaold);             /*     dpi <- p'w     */
    211:     }
    212:     betaold = beta;
    213:     KSPCheckDot(ksp,beta);

    215:     if ((dpi == 0.0) || ((i > 0) && (PetscRealPart(dpi*dpiold) <= 0.0))) {
    216:       ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
    217:       PetscInfo(ksp,"diverging due to indefinite or negative definite matrix\n");
    218:       break;
    219:     }
    220:     a = beta/dpi;                                 /*     a = beta/p'w   */
    221:     if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b))*e[i] + 1.0/a;
    222:     VecAXPY(X,a,P);          /*     x <- x + ap     */
    223:     VecAXPY(R,-a,W);                      /*     r <- r - aw    */
    224:     if (ksp->normtype == KSP_NORM_PRECONDITIONED && ksp->chknorm < i+2) {
    225:       KSP_PCApply(ksp,R,Z);               /*     z <- Br         */
    226:       if (cg->singlereduction) {
    227:         KSP_MatMult(ksp,Amat,Z,S);
    228:       }
    229:       VecNorm(Z,NORM_2,&dp);              /*    dp <- z'*z       */
    230:     } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED && ksp->chknorm < i+2) {
    231:       VecNorm(R,NORM_2,&dp);              /*    dp <- r'*r       */
    232:     } else if (ksp->normtype == KSP_NORM_NATURAL) {
    233:       KSP_PCApply(ksp,R,Z);               /*     z <- Br         */
    234:       if (cg->singlereduction) {
    235:         PetscScalar tmp[2];
    236:         Vec         vecs[2];
    237:         vecs[0] = S; vecs[1] = R;
    238:         KSP_MatMult(ksp,Amat,Z,S);
    239:         VecMDot(Z,2,vecs,tmp);
    240:         delta = tmp[0]; beta = tmp[1];
    241:       } else {
    242:         VecXDot(Z,R,&beta);     /*  beta <- r'*z       */
    243:       }
    244:       KSPCheckDot(ksp,beta);
    245:       dp = PetscSqrtReal(PetscAbsScalar(beta));
    246:     } else {
    247:       dp = 0.0;
    248:     }
    249:     ksp->rnorm = dp;
    250:     KSPLogResidualHistory(ksp,dp);
    251:     KSPMonitor(ksp,i+1,dp);
    252:     (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
    253:     if (ksp->reason) break;

    255:     if ((ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) || (ksp->chknorm >= i+2)) {
    256:       KSP_PCApply(ksp,R,Z);                   /*     z <- Br         */
    257:       if (cg->singlereduction) {
    258:         KSP_MatMult(ksp,Amat,Z,S);
    259:       }
    260:     }
    261:     if ((ksp->normtype != KSP_NORM_NATURAL) || (ksp->chknorm >= i+2)) {
    262:       if (cg->singlereduction) {
    263:         PetscScalar tmp[2];
    264:         Vec         vecs[2];
    265:         vecs[0] = S; vecs[1] = R;
    266:         VecMDot(Z,2,vecs,tmp);
    267:         delta = tmp[0]; beta = tmp[1];
    268:       } else {
    269:         VecXDot(Z,R,&beta);        /*  beta <- z'*r       */
    270:       }
    271:       KSPCheckDot(ksp,beta);
    272:     }

    274:     i++;
    275:   } while (i<ksp->max_it);
    276:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
    277:   if (eigs) cg->ned = ksp->its;
    278:   return(0);
    279: }

    283: PetscErrorCode KSPDestroy_CG(KSP ksp)
    284: {
    285:   KSP_CG         *cg = (KSP_CG*)ksp->data;

    289:   /* free space used for singular value calculations */
    290:   if (ksp->calc_sings) {
    291:     PetscFree4(cg->e,cg->d,cg->ee,cg->dd);
    292:   }
    293:   KSPDestroyDefault(ksp);
    294:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",NULL);
    295:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGUseSingleReduction_C",NULL);
    296:   return(0);
    297: }

    299: /*
    300:      KSPView_CG - Prints information about the current Krylov method being used

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

    306: */
    309: PetscErrorCode KSPView_CG(KSP ksp,PetscViewer viewer)
    310: {
    311: #if defined(PETSC_USE_COMPLEX)
    312:   KSP_CG         *cg = (KSP_CG*)ksp->data;
    314:   PetscBool      iascii;

    317:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    318:   if (iascii) {
    319:     PetscViewerASCIIPrintf(viewer,"  CG or CGNE: variant %s\n",KSPCGTypes[cg->type]);
    320:   }
    321: #endif
    322:   return(0);
    323: }

    325: /*
    326:     KSPSetFromOptions_CG - Checks the options database for options related to the
    327:                            conjugate gradient method.
    328: */
    331: PetscErrorCode KSPSetFromOptions_CG(PetscOptions *PetscOptionsObject,KSP ksp)
    332: {
    334:   KSP_CG         *cg = (KSP_CG*)ksp->data;

    337:   PetscOptionsHead(PetscOptionsObject,"KSP CG and CGNE options");
    338: #if defined(PETSC_USE_COMPLEX)
    339:   PetscOptionsEnum("-ksp_cg_type","Matrix is Hermitian or complex symmetric","KSPCGSetType",KSPCGTypes,(PetscEnum)cg->type,
    340:                           (PetscEnum*)&cg->type,NULL);
    341: #endif
    342:   PetscOptionsBool("-ksp_cg_single_reduction","Merge inner products into single MPI_Allreduce()","KSPCGUseSingleReduction",cg->singlereduction,&cg->singlereduction,NULL);
    343:   PetscOptionsTail();
    344:   return(0);
    345: }

    347: /*
    348:     KSPCGSetType_CG - This is an option that is SPECIFIC to this particular Krylov method.
    349:                       This routine is registered below in KSPCreate_CG() and called from the
    350:                       routine KSPCGSetType() (see the file cgtype.c).
    351: */
    354: static PetscErrorCode  KSPCGSetType_CG(KSP ksp,KSPCGType type)
    355: {
    356:   KSP_CG *cg = (KSP_CG*)ksp->data;

    359:   cg->type = type;
    360:   return(0);
    361: }

    365: static PetscErrorCode  KSPCGUseSingleReduction_CG(KSP ksp,PetscBool flg)
    366: {
    367:   KSP_CG *cg = (KSP_CG*)ksp->data;

    370:   cg->singlereduction = flg;
    371:   return(0);
    372: }

    374: /*
    375:     KSPCreate_CG - Creates the data structure for the Krylov method CG and sets the
    376:        function pointers for all the routines it needs to call (KSPSolve_CG() etc)

    378:     It must be labeled as PETSC_EXTERN to be dynamically linkable in C++
    379: */
    380: /*MC
    381:      KSPCG - The preconditioned conjugate gradient (PCG) iterative method

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

    388:    Level: beginner

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

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

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

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

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

    407: M*/
    410: PETSC_EXTERN PetscErrorCode KSPCreate_CG(KSP ksp)
    411: {
    413:   KSP_CG         *cg;

    416:   PetscNewLog(ksp,&cg);
    417: #if !defined(PETSC_USE_COMPLEX)
    418:   cg->type = KSP_CG_SYMMETRIC;
    419: #else
    420:   cg->type = KSP_CG_HERMITIAN;
    421: #endif
    422:   ksp->data = (void*)cg;

    424:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    425:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,2);
    426:   KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,2);
    427:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,2);

    429:   /*
    430:        Sets the functions that are associated with this data structure
    431:        (in C++ this is the same as defining virtual functions)
    432:   */
    433:   ksp->ops->setup          = KSPSetUp_CG;
    434:   ksp->ops->solve          = KSPSolve_CG;
    435:   ksp->ops->destroy        = KSPDestroy_CG;
    436:   ksp->ops->view           = KSPView_CG;
    437:   ksp->ops->setfromoptions = KSPSetFromOptions_CG;
    438:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    439:   ksp->ops->buildresidual  = KSPBuildResidualDefault;

    441:   /*
    442:       Attach the function KSPCGSetType_CG() to this object. The routine
    443:       KSPCGSetType() checks for this attached function and calls it if it finds
    444:       it. (Sort of like a dynamic member function that can be added at run time
    445:   */
    446:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",KSPCGSetType_CG);
    447:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGUseSingleReduction_C",KSPCGUseSingleReduction_CG);
    448:   return(0);
    449: }