Date: 2015-10-02T22:20:55+00:00

Actual source code: cgne.c
petsc-3.6.2 2015-10-02
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      2: /*
      3:        cgimpl.h defines the simple data structured used to store information
      4:     related to the type of matrix (e.g. complex symmetric) being solved and
      5:     data used during the optional Lanczo process used to compute eigenvalues
      6: */
      7: #include <../src/ksp/ksp/impls/cg/cgimpl.h>       /*I "petscksp.h" I*/
      8: extern PetscErrorCode KSPComputeExtremeSingularValues_CG(KSP,PetscReal*,PetscReal*);
      9: extern PetscErrorCode KSPComputeEigenvalues_CG(KSP,PetscInt,PetscReal*,PetscReal*,PetscInt*);

     13: static PetscErrorCode  KSPCGSetType_CGNE(KSP ksp,KSPCGType type)
     14: {
     15:   KSP_CG *cg = (KSP_CG*)ksp->data;

     18:   cg->type = type;
     19:   return(0);
     20: }

     23: /*
     24:      KSPSetUp_CGNE - Sets up the workspace needed by the CGNE method.

     26:      IDENTICAL TO THE CG ONE EXCEPT for one extra work vector!
     27: */
     30: PetscErrorCode KSPSetUp_CGNE(KSP ksp)
     31: {
     32:   KSP_CG         *cgP = (KSP_CG*)ksp->data;
     34:   PetscInt       maxit = ksp->max_it;

     37:   /* get work vectors needed by CGNE */
     38:   KSPSetWorkVecs(ksp,4);

     40:   /*
     41:      If user requested computations of eigenvalues then allocate work
     42:      work space needed
     43:   */
     44:   if (ksp->calc_sings) {
     45:     /* get space to store tridiagonal matrix for Lanczos */
     46:     PetscMalloc4(maxit+1,&cgP->e,maxit+1,&cgP->d,maxit+1,&cgP->ee,maxit+1,&cgP->dd);
     47:     PetscLogObjectMemory((PetscObject)ksp,2*(maxit+1)*(sizeof(PetscScalar)+sizeof(PetscReal)));
     48:   }
     49:   return(0);
     50: }

     52: /*
     53:        KSPSolve_CGNE - This routine actually applies the conjugate gradient
     54:     method

     56:    Input Parameter:
     57: .     ksp - the Krylov space object that was set to use conjugate gradient, by, for
     58:             example, KSPCreate(MPI_Comm,KSP *ksp); KSPSetType(ksp,KSPCG);

     61:     Virtually identical to the KSPSolve_CG, it should definitely reuse the same code.

     63: */
     66: PetscErrorCode  KSPSolve_CGNE(KSP ksp)
     67: {
     69:   PetscInt       i,stored_max_it,eigs;
     70:   PetscScalar    dpi,a = 1.0,beta,betaold = 1.0,b = 0,*e = 0,*d = 0;
     71:   PetscReal      dp = 0.0;
     72:   Vec            X,B,Z,R,P,T;
     73:   KSP_CG         *cg;
     74:   Mat            Amat,Pmat;
     75:   PetscBool      diagonalscale,transpose_pc;

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

     82:   cg            = (KSP_CG*)ksp->data;
     83:   eigs          = ksp->calc_sings;
     84:   stored_max_it = ksp->max_it;
     85:   X             = ksp->vec_sol;
     86:   B             = ksp->vec_rhs;
     87:   R             = ksp->work[0];
     88:   Z             = ksp->work[1];
     89:   P             = ksp->work[2];
     90:   T             = ksp->work[3];

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

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

     97:   ksp->its = 0;
     98:   KSP_MatMultTranspose(ksp,Amat,B,T);
     99:   if (!ksp->guess_zero) {
    100:     KSP_MatMult(ksp,Amat,X,P);
    101:     KSP_MatMultTranspose(ksp,Amat,P,R);
    102:     VecAYPX(R,-1.0,T);
    103:   } else {
    104:     VecCopy(T,R);              /*     r <- b (x is 0) */
    105:   }
    106:   KSP_PCApply(ksp,R,T);
    107:   if (transpose_pc) {
    108:     KSP_PCApplyTranspose(ksp,T,Z);
    109:   } else {
    110:     KSP_PCApply(ksp,T,Z);
    111:   }

    113:   if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
    114:     VecNorm(Z,NORM_2,&dp); /*    dp <- z'*z       */
    115:   } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
    116:     VecNorm(R,NORM_2,&dp); /*    dp <- r'*r       */
    117:   } else if (ksp->normtype == KSP_NORM_NATURAL) {
    118:     VecXDot(Z,R,&beta);
    119:     dp   = PetscSqrtReal(PetscAbsScalar(beta));
    120:   } else dp = 0.0;
    121:   KSPLogResidualHistory(ksp,dp);
    122:   KSPMonitor(ksp,0,dp);
    123:   ksp->rnorm = dp;
    124:   (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP); /* test for convergence */
    125:   if (ksp->reason) return(0);

    127:   i = 0;
    128:   do {
    129:     ksp->its = i+1;
    130:     VecXDot(Z,R,&beta); /*     beta <- r'z     */
    131:     if (beta == 0.0) {
    132:       ksp->reason = KSP_CONVERGED_ATOL;
    133:       PetscInfo(ksp,"converged due to beta = 0\n");
    134:       break;
    135: #if !defined(PETSC_USE_COMPLEX)
    136:     } else if (beta < 0.0) {
    137:       ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
    138:       PetscInfo(ksp,"diverging due to indefinite preconditioner\n");
    139:       break;
    140: #endif
    141:     }
    142:     if (!i) {
    143:       VecCopy(Z,P);          /*     p <- z          */
    144:       b    = 0.0;
    145:     } else {
    146:       b = beta/betaold;
    147:       if (eigs) {
    148:         if (ksp->max_it != stored_max_it) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Can not change maxit AND calculate eigenvalues");
    149:         e[i] = PetscSqrtReal(PetscAbsScalar(b))/a;
    150:       }
    151:       VecAYPX(P,b,Z);     /*     p <- z + b* p   */
    152:     }
    153:     betaold = beta;
    154:     KSP_MatMult(ksp,Amat,P,T);
    155:     KSP_MatMultTranspose(ksp,Amat,T,Z);
    156:     VecXDot(P,Z,&dpi);    /*     dpi <- z'p      */
    157:     a       = beta/dpi;                            /*     a = beta/p'z    */
    158:     if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b))*e[i] + 1.0/a;
    159:     VecAXPY(X,a,P);           /*     x <- x + ap     */
    160:     VecAXPY(R,-a,Z);                       /*     r <- r - az     */
    161:     if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
    162:       KSP_PCApply(ksp,R,T);
    163:       if (transpose_pc) {
    164:         KSP_PCApplyTranspose(ksp,T,Z);
    165:       } else {
    166:         KSP_PCApply(ksp,T,Z);
    167:       }
    168:       VecNorm(Z,NORM_2,&dp);              /*    dp <- z'*z       */
    169:     } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
    170:       VecNorm(R,NORM_2,&dp);
    171:     } else if (ksp->normtype == KSP_NORM_NATURAL) {
    172:       dp = PetscSqrtReal(PetscAbsScalar(beta));
    173:     } else {
    174:       dp = 0.0;
    175:     }
    176:     ksp->rnorm = dp;
    177:     KSPLogResidualHistory(ksp,dp);
    178:     KSPMonitor(ksp,i+1,dp);
    179:     (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
    180:     if (ksp->reason) break;
    181:     if (ksp->normtype != KSP_NORM_PRECONDITIONED) {
    182:       if (transpose_pc) {
    183:         KSP_PCApplyTranspose(ksp,T,Z);
    184:       } else {
    185:         KSP_PCApply(ksp,T,Z);
    186:       }
    187:     }
    188:     i++;
    189:   } while (i<ksp->max_it);
    190:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
    191:   if (eigs) cg->ned = ksp->its;
    192:   return(0);
    193: }

    195: /*
    196:     KSPCreate_CGNE - Creates the data structure for the Krylov method CGNE and sets the
    197:        function pointers for all the routines it needs to call (KSPSolve_CGNE() etc)

    199:     It must be labeled as PETSC_EXTERN to be dynamically linkable in C++
    200: */

    202: /*MC
    203:      KSPCGNE - Applies the preconditioned conjugate gradient method to the normal equations
    204:           without explicitly forming A^t*A

    206:    Options Database Keys:
    207: .   -ksp_cg_type <Hermitian or symmetric - (for complex matrices only) indicates the matrix is Hermitian or symmetric

    210:    Level: beginner

    212:    Notes: eigenvalue computation routines will return information about the
    213:           spectrum of A^t*A, rather than A.

    216:    CGNE is a general-purpose non-symmetric method. It works well when the singular values are much better behaved than
    217:    eigenvalues. A unitary matrix is a classic example where CGNE converges in one iteration, but GMRES and CGS need N
    218:    iterations (see Nachtigal, Reddy, and Trefethen, "How fast are nonsymmetric matrix iterations", 1992). If you intend
    219:    to solve least squares problems, use KSPLSQR.

    221:    This is NOT a different algorithm then used with KSPCG, it merely uses that algorithm with the
    222:    matrix defined by A^t*A and preconditioner defined by B^t*B where B is the preconditioner for A.

    224:    This method requires that one be able to apply the transpose of the preconditioner and operator
    225:    as well as the operator and preconditioner. If the transpose of the preconditioner is not available then
    226:    the preconditioner is used in its place so one ends up preconditioning A'A with B B. Seems odd?

    228:    This only supports left preconditioning.

    230:    This object is subclassed off of KSPCG

    232: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP,
    233:            KSPCGSetType(), KSPBICG

    235: M*/

    237: extern PetscErrorCode KSPDestroy_CG(KSP);
    238: extern PetscErrorCode KSPReset_CG(KSP);
    239: extern PetscErrorCode KSPView_CG(KSP,PetscViewer);
    240: extern PetscErrorCode KSPSetFromOptions_CG(PetscOptions *PetscOptionsObject,KSP);
    241: PETSC_EXTERN PetscErrorCode KSPCGSetType_CG(KSP,KSPCGType);

    245: PETSC_EXTERN PetscErrorCode KSPCreate_CGNE(KSP ksp)
    246: {
    248:   KSP_CG         *cg;

    251:   PetscNewLog(ksp,&cg);
    252: #if !defined(PETSC_USE_COMPLEX)
    253:   cg->type = KSP_CG_SYMMETRIC;
    254: #else
    255:   cg->type = KSP_CG_HERMITIAN;
    256: #endif
    257:   ksp->data = (void*)cg;
    258:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    259:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,2);
    260:   KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,2);

    262:   /*
    263:        Sets the functions that are associated with this data structure
    264:        (in C++ this is the same as defining virtual functions)
    265:   */
    266:   ksp->ops->setup          = KSPSetUp_CGNE;
    267:   ksp->ops->solve          = KSPSolve_CGNE;
    268:   ksp->ops->destroy        = KSPDestroy_CG;
    269:   ksp->ops->view           = KSPView_CG;
    270:   ksp->ops->setfromoptions = KSPSetFromOptions_CG;
    271:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    272:   ksp->ops->buildresidual  = KSPBuildResidualDefault;

    274:   /*
    275:       Attach the function KSPCGSetType_CGNE() to this object. The routine
    276:       KSPCGSetType() checks for this attached function and calls it if it finds
    277:       it. (Sort of like a dynamic member function that can be added at run time
    278:   */
    279:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",KSPCGSetType_CGNE);
    280:   return(0);
    281: }