Date: 2022-03-31T04:48:08+00:00

Actual source code: cgne.c

      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>
      8: extern PetscErrorCode KSPComputeExtremeSingularValues_CG(KSP,PetscReal*,PetscReal*);
      9: extern PetscErrorCode KSPComputeEigenvalues_CG(KSP,PetscInt,PetscReal*,PetscReal*,PetscInt*);

     11: static PetscErrorCode  KSPCGSetType_CGNE(KSP ksp,KSPCGType type)
     12: {
     13:   KSP_CG *cg = (KSP_CG*)ksp->data;

     15:   cg->type = type;
     16:   return 0;
     17: }

     19: /*
     20:      KSPSetUp_CGNE - Sets up the workspace needed by the CGNE method.

     22:      IDENTICAL TO THE CG ONE EXCEPT for one extra work vector!
     23: */
     24: static PetscErrorCode KSPSetUp_CGNE(KSP ksp)
     25: {
     26:   KSP_CG         *cgP = (KSP_CG*)ksp->data;
     27:   PetscInt       maxit = ksp->max_it;

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

     32:   /*
     33:      If user requested computations of eigenvalues then allocate work
     34:      work space needed
     35:   */
     36:   if (ksp->calc_sings) {
     37:     /* get space to store tridiagonal matrix for Lanczos */
     38:     PetscMalloc4(maxit,&cgP->e,maxit,&cgP->d,maxit,&cgP->ee,maxit,&cgP->dd);
     39:     PetscLogObjectMemory((PetscObject)ksp,2*maxit*(sizeof(PetscScalar)+sizeof(PetscReal)));

     41:     ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_CG;
     42:     ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_CG;
     43:   }
     44:   return 0;
     45: }

     47: /*
     48:        KSPSolve_CGNE - This routine actually applies the conjugate gradient
     49:     method

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

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

     57: */
     58: static PetscErrorCode  KSPSolve_CGNE(KSP ksp)
     59: {
     60:   PetscInt       i,stored_max_it,eigs;
     61:   PetscScalar    dpi,a = 1.0,beta,betaold = 1.0,b = 0,*e = NULL,*d = NULL;
     62:   PetscReal      dp = 0.0;
     63:   Vec            X,B,Z,R,P,T;
     64:   KSP_CG         *cg;
     65:   Mat            Amat,Pmat;
     66:   PetscBool      diagonalscale,transpose_pc;

     68:   PCGetDiagonalScale(ksp->pc,&diagonalscale);
     70:   PCApplyTransposeExists(ksp->pc,&transpose_pc);

     72:   cg            = (KSP_CG*)ksp->data;
     73:   eigs          = ksp->calc_sings;
     74:   stored_max_it = ksp->max_it;
     75:   X             = ksp->vec_sol;
     76:   B             = ksp->vec_rhs;
     77:   R             = ksp->work[0];
     78:   Z             = ksp->work[1];
     79:   P             = ksp->work[2];
     80:   T             = ksp->work[3];

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

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

     87:   ksp->its = 0;
     88:   KSP_MatMultTranspose(ksp,Amat,B,T);
     89:   if (!ksp->guess_zero) {
     90:     KSP_MatMult(ksp,Amat,X,P);
     91:     KSP_MatMultTranspose(ksp,Amat,P,R);
     92:     VecAYPX(R,-1.0,T);
     93:   } else {
     94:     VecCopy(T,R);              /*     r <- b (x is 0) */
     95:   }
     96:   if (transpose_pc) {
     97:     KSP_PCApplyTranspose(ksp,R,T);
     98:   } else {
     99:     KSP_PCApply(ksp,R,T);
    100:   }
    101:   KSP_PCApply(ksp,T,Z);

    103:   if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
    104:     VecNorm(Z,NORM_2,&dp); /*    dp <- z'*z       */
    105:   } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
    106:     VecNorm(R,NORM_2,&dp); /*    dp <- r'*r       */
    107:   } else if (ksp->normtype == KSP_NORM_NATURAL) {
    108:     VecXDot(Z,R,&beta);
    109:     KSPCheckDot(ksp,beta);
    110:     dp   = PetscSqrtReal(PetscAbsScalar(beta));
    111:   } else dp = 0.0;
    112:   KSPLogResidualHistory(ksp,dp);
    113:   KSPMonitor(ksp,0,dp);
    114:   ksp->rnorm = dp;
    115:   (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP); /* test for convergence */
    116:   if (ksp->reason) return 0;

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

    186: /*
    187:     KSPCreate_CGNE - Creates the data structure for the Krylov method CGNE and sets the
    188:        function pointers for all the routines it needs to call (KSPSolve_CGNE() etc)

    190:     It must be labeled as PETSC_EXTERN to be dynamically linkable in C++
    191: */

    193: /*MC
    194:      KSPCGNE - Applies the preconditioned conjugate gradient method to the normal equations
    195:           without explicitly forming A^t*A

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

    200:    Level: beginner

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

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

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

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

    218:    This only supports left preconditioning.

    220:    This object is subclassed off of KSPCG

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

    225: M*/

    227: PETSC_EXTERN PetscErrorCode KSPCreate_CGNE(KSP ksp)
    228: {
    229:   KSP_CG         *cg;

    231:   PetscNewLog(ksp,&cg);
    232: #if !defined(PETSC_USE_COMPLEX)
    233:   cg->type = KSP_CG_SYMMETRIC;
    234: #else
    235:   cg->type = KSP_CG_HERMITIAN;
    236: #endif
    237:   ksp->data = (void*)cg;
    238:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    239:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,2);
    240:   KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,2);
    241:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);

    243:   /*
    244:        Sets the functions that are associated with this data structure
    245:        (in C++ this is the same as defining virtual functions)
    246:   */
    247:   ksp->ops->setup          = KSPSetUp_CGNE;
    248:   ksp->ops->solve          = KSPSolve_CGNE;
    249:   ksp->ops->destroy        = KSPDestroy_CG;
    250:   ksp->ops->view           = KSPView_CG;
    251:   ksp->ops->setfromoptions = KSPSetFromOptions_CG;
    252:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    253:   ksp->ops->buildresidual  = KSPBuildResidualDefault;

    255:   /*
    256:       Attach the function KSPCGSetType_CGNE() to this object. The routine
    257:       KSPCGSetType() checks for this attached function and calls it if it finds
    258:       it. (Sort of like a dynamic member function that can be added at run time
    259:   */
    260:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",KSPCGSetType_CGNE);
    261:   return 0;
    262: }