Actual source code: cg.c

      1: #define PETSCKSP_DLL

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

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

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

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

     31:     Reference: Hestenes and Steifel, 1952.

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

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

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

     64:   /*
     65:        This implementation of CG only handles left preconditioning
     66:      so generate an error otherwise.
     67:   */
     68:   if (ksp->pc_side == PC_RIGHT) {
     69:     SETERRQ(PETSC_ERR_SUP,"No right preconditioning for KSPCG");
     70:   } else if (ksp->pc_side == PC_SYMMETRIC) {
     71:     SETERRQ(PETSC_ERR_SUP,"No symmetric preconditioning for KSPCG");
     72:   }

     74:   /* get work vectors needed by CG */
     75:   KSPDefaultGetWork(ksp,3);

     77:   /*
     78:      If user requested computations of eigenvalues then allocate work
     79:      work space needed
     80:   */
     81:   if (ksp->calc_sings) {
     82:     /* get space to store tridiagonal matrix for Lanczos */
     83:     PetscMalloc(2*(maxit+1)*sizeof(PetscScalar),&cgP->e);
     84:     PetscLogObjectMemory(ksp,2*(maxit+1)*sizeof(PetscScalar));
     85:     cgP->d                         = cgP->e + maxit + 1;
     86:     PetscMalloc(2*(maxit+1)*sizeof(PetscReal),&cgP->ee);
     87:     PetscLogObjectMemory(ksp,2*(maxit+1)*sizeof(PetscScalar));
     88:     cgP->dd                        = cgP->ee + maxit + 1;
     89:     ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_CG;
     90:     ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_CG;
     91:   }
     92:   return(0);
     93: }

     95: /*
     96:        KSPSolve_CG - This routine actually applies the conjugate gradient
     97:     method

     99:    Input Parameter:
    100: .     ksp - the Krylov space object that was set to use conjugate gradient, by, for
    101:             example, KSPCreate(MPI_Comm,KSP *ksp); KSPSetType(ksp,KSPCG);
    102: */
    105: PetscErrorCode  KSPSolve_CG(KSP ksp)
    106: {
    108:   PetscInt       i,stored_max_it,eigs;
    109:   PetscScalar    dpi,a = 1.0,beta,betaold = 1.0,b = 0,*e = 0,*d = 0,mone = -1.0,ma;
    110:   PetscReal      dp = 0.0;
    111:   Vec            X,B,Z,R,P;
    112:   KSP_CG         *cg;
    113:   Mat            Amat,Pmat;
    114:   MatStructure   pflag;
    115:   PetscTruth     diagonalscale;

    118:   PCDiagonalScale(ksp->pc,&diagonalscale);
    119:   if (diagonalscale) SETERRQ1(PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",ksp->type_name);

    121:   cg            = (KSP_CG*)ksp->data;
    122:   eigs          = ksp->calc_sings;
    123:   stored_max_it = ksp->max_it;
    124:   X             = ksp->vec_sol;
    125:   B             = ksp->vec_rhs;
    126:   R             = ksp->work[0];
    127:   Z             = ksp->work[1];
    128:   P             = ksp->work[2];

    130: #if !defined(PETSC_USE_COMPLEX)
    131: #define VecXDot(x,y,a) VecDot(x,y,a)
    132: #else
    133: #define VecXDot(x,y,a) (((cg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x,y,a) : VecTDot(x,y,a))
    134: #endif

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

    139:   ksp->its = 0;
    140:   if (!ksp->guess_zero) {
    141:     KSP_MatMult(ksp,Amat,X,R);             /*   r <- b - Ax       */
    142:     VecAYPX(R,mone,B);
    143:   } else {
    144:     VecCopy(B,R);                         /*     r <- b (x is 0) */
    145:   }
    146:   KSP_PCApply(ksp,R,Z);                   /*     z <- Br         */
    147:   VecXDot(Z,R,&beta);
    148:   if (ksp->normtype == KSP_PRECONDITIONED_NORM) {
    149:     VecNorm(Z,NORM_2,&dp);                /*    dp <- z'*z = e'*A'*B'*B*A'*e'   */
    150:   } else if (ksp->normtype == KSP_UNPRECONDITIONED_NORM) {
    151:     VecNorm(R,NORM_2,&dp);                /*    dp <- r'*r = e'*A'*A*e         */
    152:   } else if (ksp->normtype == KSP_NATURAL_NORM) {
    153:     dp = sqrt(PetscAbsScalar(beta));                           /*    dp <- r'*z = r'*B*r = e'*A'*B*A*e */
    154:   } else dp = 0.0;
    155:   KSPLogResidualHistory(ksp,dp);
    156:   KSPMonitor(ksp,0,dp);                              /* call any registered monitor routines */
    157:   ksp->rnorm = dp;

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

    162:   i = 0;
    163:   do {
    164:      ksp->its = i+1;
    165:      VecXDot(Z,R,&beta);     /*     beta <- r'z     */
    166:      if (beta == 0.0) {
    167:        ksp->reason = KSP_CONVERGED_ATOL;
    168:        PetscLogInfo((ksp,"KSPSolve_CG:converged due to beta = 0\n"));
    169:        break;
    170: #if !defined(PETSC_USE_COMPLEX)
    171:      } else if (beta < 0.0) {
    172:        ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
    173:        PetscLogInfo((ksp,"KSPSolve_CG:diverging due to indefinite preconditioner\n"));
    174:        break;
    175: #endif
    176:      }
    177:      if (!i) {
    178:        VecCopy(Z,P);         /*     p <- z          */
    179:      } else {
    180:          b = beta/betaold;
    181:          if (eigs) {
    182:            if (ksp->max_it != stored_max_it) {
    183:              SETERRQ(PETSC_ERR_SUP,"Can not change maxit AND calculate eigenvalues");
    184:            }
    185:            e[i] = sqrt(PetscAbsScalar(b))/a;
    186:          }
    187:          VecAYPX(P,b,Z);    /*     p <- z + b* p   */
    188:      }
    189:      betaold = beta;
    190:      KSP_MatMult(ksp,Amat,P,Z);      /*     z <- Kp         */
    191:      VecXDot(P,Z,&dpi);      /*     dpi <- z'p      */
    192:      if (PetscAbsScalar(dpi) <= 0.0) {
    193:        ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
    194:        PetscLogInfo((ksp,"KSPSolve_CG:diverging due to indefinite or negative definite matrix\n"));
    195:        break;
    196:      }
    197:      a = beta/dpi;                                 /*     a = beta/p'z    */
    198:      if (eigs) {
    199:        d[i] = sqrt(PetscAbsScalar(b))*e[i] + 1.0/a;
    200:      }
    201:      VecAXPY(X,a,P);          /*     x <- x + ap     */
    202:      ma = -a; VecAXPY(R,ma,Z);                      /*     r <- r - az     */
    203:      if (ksp->normtype == KSP_PRECONDITIONED_NORM) {
    204:        KSP_PCApply(ksp,R,Z);        /*     z <- Br         */
    205:        VecNorm(Z,NORM_2,&dp);              /*    dp <- z'*z       */
    206:      } else if (ksp->normtype == KSP_UNPRECONDITIONED_NORM) {
    207:        VecNorm(R,NORM_2,&dp);              /*    dp <- r'*r       */
    208:      } else if (ksp->normtype == KSP_NATURAL_NORM) {
    209:        dp = sqrt(PetscAbsScalar(beta));
    210:      } else {
    211:        dp = 0.0;
    212:      }
    213:      ksp->rnorm = dp;
    214:      KSPLogResidualHistory(ksp,dp);
    215:      KSPMonitor(ksp,i+1,dp);
    216:      (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
    217:      if (ksp->reason) break;
    218:      if (ksp->normtype != KSP_PRECONDITIONED_NORM) {
    219:        KSP_PCApply(ksp,R,Z); /* z <- Br  */
    220:      }
    221:      i++;
    222:   } while (i<ksp->max_it);
    223:   if (i >= ksp->max_it) {
    224:     ksp->reason = KSP_DIVERGED_ITS;
    225:   }
    226:   return(0);
    227: }
    228: /*
    229:        KSPDestroy_CG - Frees all memory space used by the Krylov method

    231: */
    234: PetscErrorCode KSPDestroy_CG(KSP ksp)
    235: {
    236:   KSP_CG         *cg = (KSP_CG*)ksp->data;

    240:   /* free space used for singular value calculations */
    241:   if (ksp->calc_sings) {
    242:     PetscFree(cg->e);
    243:     PetscFree(cg->ee);
    244:   }

    246:   KSPDefaultFreeWork(ksp);
    247:
    248:   /* free the context variable */
    249:   PetscFree(cg);
    250:   return(0);
    251: }

    253: /*
    254:      KSPView_CG - Prints information about the current Krylov method being used

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

    260: */
    263: PetscErrorCode KSPView_CG(KSP ksp,PetscViewer viewer)
    264: {
    265: #if defined(PETSC_USE_COMPLEX)
    266:   KSP_CG         *cg = (KSP_CG *)ksp->data;
    268:   PetscTruth     iascii;

    271:   PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);
    272:   if (iascii) {
    273:     PetscViewerASCIIPrintf(viewer,"  CG or CGNE: variant %s\n",KSPCGTypes[cg->type]);
    274:   } else {
    275:     SETERRQ1(PETSC_ERR_SUP,"Viewer type %s not supported for KSP cg",((PetscObject)viewer)->type_name);
    276:   }
    277: #endif
    278:   return(0);
    279: }

    281: /*
    282:     KSPSetFromOptions_CG - Checks the options database for options related to the
    283:                            conjugate gradient method.
    284: */
    287: PetscErrorCode KSPSetFromOptions_CG(KSP ksp)
    288: {
    289: #if defined(PETSC_USE_COMPLEX)
    291:   KSP_CG         *cg = (KSP_CG *)ksp->data;
    292: #endif

    295: #if defined(PETSC_USE_COMPLEX)
    296:   PetscOptionsHead("KSP CG and CGNE options");
    297:   PetscOptionsEnum("-ksp_cg_type","Matrix is Hermitian or complex symmetric","KSPCGSetType",KSPCGTypes,(PetscEnum)cg->type,
    298:                           (PetscEnum*)&cg->type,PETSC_NULL);
    299:   PetscOptionsTail();
    300: #endif
    301:   return(0);
    302: }

    304: /*
    305:     KSPCGSetType_CG - This is an option that is SPECIFIC to this particular Krylov method.
    306:                       This routine is registered below in KSPCreate_CG() and called from the
    307:                       routine KSPCGSetType() (see the file cgtype.c).

    310: */
    314: PetscErrorCode PETSCKSP_DLLEXPORT KSPCGSetType_CG(KSP ksp,KSPCGType type)
    315: {
    316:   KSP_CG *cg;

    319:   cg = (KSP_CG *)ksp->data;
    320:   cg->type = type;
    321:   return(0);
    322: }

    325: /*
    326:     KSPCreate_CG - Creates the data structure for the Krylov method CG and sets the
    327:        function pointers for all the routines it needs to call (KSPSolve_CG() etc)

    330: */
    331: /*MC
    332:      KSPCG - The preconditioned conjugate gradient (PCG) iterative method

    334:    Options Database Keys:
    335: +   -ksp_cg_Hermitian - (for complex matrices only) indicates the matrix is Hermitian
    336: -   -ksp_cg_symmetric - (for complex matrices only) indicates the matrix is symmetric

    338:    Level: beginner

    340:    Notes: The PCG method requires both the matrix and preconditioner to
    341:           be symmetric positive (semi) definite

    343: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP,
    344:            KSPCGSetType()

    346: M*/
    350: PetscErrorCode PETSCKSP_DLLEXPORT KSPCreate_CG(KSP ksp)
    351: {
    353:   KSP_CG         *cg;

    356:   PetscNew(KSP_CG,&cg);
    357:   PetscLogObjectMemory(ksp,sizeof(KSP_CG));
    358: #if !defined(PETSC_USE_COMPLEX)
    359:   cg->type                       = KSP_CG_SYMMETRIC;
    360: #else
    361:   cg->type                       = KSP_CG_HERMITIAN;
    362: #endif
    363:   ksp->data                      = (void*)cg;
    364:   ksp->pc_side                   = PC_LEFT;

    366:   /*
    367:        Sets the functions that are associated with this data structure
    368:        (in C++ this is the same as defining virtual functions)
    369:   */
    370:   ksp->ops->setup                = KSPSetUp_CG;
    371:   ksp->ops->solve                = KSPSolve_CG;
    372:   ksp->ops->destroy              = KSPDestroy_CG;
    373:   ksp->ops->view                 = KSPView_CG;
    374:   ksp->ops->setfromoptions       = KSPSetFromOptions_CG;
    375:   ksp->ops->buildsolution        = KSPDefaultBuildSolution;
    376:   ksp->ops->buildresidual        = KSPDefaultBuildResidual;

    378:   /*
    379:       Attach the function KSPCGSetType_CG() to this object. The routine
    380:       KSPCGSetType() checks for this attached function and calls it if it finds
    381:       it. (Sort of like a dynamic member function that can be added at run time
    382:   */
    383:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPCGSetType_C","KSPCGSetType_CG",
    384:                                      KSPCGSetType_CG);
    385:   return(0);
    386: }